1st Condensed Editon, Interstellar CMBR Surfing: An Intuitive Simple Mathematical Argument Affirming The Possibility Of Highly Relativistic Traditional CMBR Sail Powered Star Ships.

I have been climbing the CMBR sailing ship gamma factor ladder today and have  determined the intellegable plausibility for obtaining relativistic gamma factors of 3 for manned star-ship style space arks powered by traditionally oriented CMBR sails made of ordinary periodic table elements.

I plan to go climb much much higher in the days and weeks ahead using assumptions of sails made or ordinary periodic table elements.

 

Now, the CMBR incident on the light sail from behind will generally require either a monolithic light sail of near nanometer thickness or perhaps a grid like sail with a cross-weave for which the lines or fibers are separated by less than 0.25 millimeters in order to reflect the vast majority of the incident CMBR for space craft traveling at mildly relativistic velocities. For grid like sails, the advantage of sail porosity enables much higher mass specific capture areas. Since the Doppler blue shifted light incident from directly in front of the sail or nearly so will be much shorter in wavelength than the backwardly incident light for high gamma factor sails, the forwardly incident light can largely pass through the sail openings providing a means for the backwardly incident light to push the sail efficiently forward for cases where the sail is transmissive from front to back to a suitable degree.

 

 

Now radiation pressure is equal to σT⁴/C and {2 [σT⁴/C]} for reflected radiation. However, for a space craft traveling through a black body radiation field, the apparent temperature of the radiation increases in proportion to γ and so the black body power impinging on the space craft from directly in front grows in proportion to T⁴ and thus  to γ⁴.

 

 

The temperature of a black body is T = {P/[(A)(σ)(e)]}^1/4 = {P/{(A)[5.670400(40) x 10^-8 W m^-2 K^-4]} ^1/4}. Therefore, the cosmic microwave background radiation pressure on a perfectly reflective flat bow  relativistic space craft is roughly equal to  {2 [σT_cmbr ⁴/C]} γ⁴ = {2 [σT_cmbr ⁴/C]} { {1/{1 – [(v/C)²]}^1/2}  ⁴} =   {2 [σT_cmbr ⁴/C]} {1/{1 – [(v/C)²]}²} where γ is constant and T_cmbr is constant. However, the light pressure incident from directly behind will be approximately equal to {2 [σT_cmbr ⁴/C]}/{1/{1 – [(v/C)²]}²}. In actuality, not all of the light is directly incident from the back and so there will be angular affects that result in loss of driving power. However, we will assume that all of the radiation is absorbed and then re-cycled and released as a perfect backwardly directed laser beam.

 

 

Assuming that the velocity of the sail starts out at (Zero) C, the optical pressure will be equal to {2 [σT_cmbr ⁴/C]}/γ⁴ = {2 [σT_cmbr ⁴/C]}/{ {1/{1 – [(v/C)²]}^1/2} ⁴} = {2{[5.670400(40) x 10^-8 W m^-2 K^-4][(2.725 K)⁴]/(300,000,000 m/s)}}/(1²) = 2.0844  x 10^-14 Newtons/m². For a 10,000 km by 10,000 km sail, the drive force will be 2.0844 Newtons.

 

 

Now, how are we going to deploy such a sail in a meaningful manner? The solution is obvious my dear Watson! Use a grid.

 

 

Consider that a monolithic one nanometer thick sail made of STP H₂O density carbonaceous materials would have a mass of  100,000 thousand metric tons, assuming that the space craft plus her sail had a mass of 208,440 metric tons, the craft would start out with an acceleration of F/M = a = 2.0844 N/208,440,000 kg = 10^-8 meter/s². After traveling 6 x 10¹⁵ seconds or about 200,000,000 years, the velocity of the space craft will be 0.20 C and the relativistic Lorentz transformation factor will be 1.0206 thus permitting the above Newtonian formula to apply.

 

 

For such a space craft that deployed a linear series of 1,000 tethered sails where each sail was separated by an efficient 10 sail widths, a space craft having a total mass of 208, 440,000 metric tons could be identically accelerated. The mass of the crew quarters would be 108,440,000 metric tons.

 

 

For such a space craft that deployed a linear series of 1,000,000 tethered sails where each sail was separated by an efficient 10 sail widths, a space craft having a total mass of 208, 440,000,000  metric tons could be identically accelerated. The mass of the crew quarters would be 108,440,000,000  metric tons. For cosmic journeys, this is not bad.

 

 

Some supermaterials already in laboratory existence such as carbon nanotubes can in theory be used to construct large space elevators that would extend from the surface of the Earth near the Equator to locations significantly father than geosynchronous orbit. Such tethers would perhaps have the equivalent of 0.1 G or 1m/s² acceleration based force pulling on it which would be commensurate with a cable roughly 100,000 km long accelerated at 1 m/s². Thus,  a cable that is 10¹³ km long or one light-year long could in theory withstand 10^-8 m/s² levels of acceleration. A linear series of tethered leading sails numbering 1,000,000 where each sail would have a width of 10,000 kilometers and be serially spaced a distance of 100,000 kilometers would have a length of 10¹¹ kilometers.  Thus, a series of 100 million tethered sails might conceivably pull a sail craft combination having a mass of 20,844,000,000,000 metric tons and a crew quarters having a mass of 10,844,000,000,000 metric tons.

 

 

Some high-end carbonaceous super-materials include:

 

 

1) carbon nano-tubes;
2) boron-nitride nanotubes;
3) buckyball-sheets;
4) layered sheet arrangements of graphene;
5) graphene-oxide paper;
6) fabrics composed of a weave or knit on carbon atom chains;
7) diamond fiber-based fabric;
8) carbon nitride fiber-based fabric;
9) combinations of two or more of the above, and the like material

 

 

Metalization would help in these regards.

 

 

The sails could have nanotech self-repair mechanisms. An ideal mechanism would entail sails constructed of metallic hydrogen where the hydrogen would be captured from interstellar space and incorporated into the sail membrane(s) in order to re-supply sail atoms knocked loose by interstellar atom and molecular species.

 

 

However, much higher sail velocities are anticipatable with much greater accelerations as will be covered in the next post in this series.

 

 

However, we can also deploy gridded sails. For example, consider a sail that is comprised on one nanometer wide fibers in a cross-weave where adjacent parallel  fibers are separated by 200 microns. Also consider situations where the fibers are one side reflective and one side transmissive. A sail comprised of such a material will have a mass specific capture area that is 1/100,000 that of a one nanometer thick monolithic sail.

 

 

Considering that such a sail that is gridded with the above  one nanometer thick sail fiber construction made of STP H₂O density carbonaceous materials would have a mass of  one metric ton for a sail area of 10⁸ square kilometers, assuming that the space craft plus her sail had a mass of 208,440 metric tons, the craft would start out with an acceleration of F/M = a = 2.0844 N/208,440,000 kg = 10^-8 meter/s². After traveling 6 x 10¹⁵ seconds or about 200,000,000 years, the velocity of the space craft will be 0.20 C and the relativistic Lorentz transformation factor will be 1.0206 thus permitting the above Newtonian formula to apply.

 

 

For such a space craft that deployed a linear series of 1,000 tethered sails where each sail was separated by an efficient 10 sail widths, a space craft having a total mass of 208, 440,000 metric tons could be identically accelerated. The mass of the crew quarters would be 208, 439,000 metric tons.

 

 

For such a space craft that deployed a linear series of 1,000,000 tethered sails where each sail was separated by an efficient 10 sail widths, a space craft having a total mass of 208, 440,000,000  metric tons could be identically accelerated. The mass of the crew quarters would be 208, 439,000,000 metric tons. For cosmic journeys, this is not bad.

 

 

A series of 100 million tethered sails might conceivably pull a sail craft combination having a mass of 20,844,000,000,000 metric tons and a crew quarters having a mass of 20,843,900,000,000 metric tons.

 

 

Consider again that such sails which  are gridded with the above  one nanometer thick sail fiber construction made of STP H₂O density carbonaceous materials would have a mass of  one metric ton each, assuming that the space craft plus her sail had a mass of 208,440 metric tons, the craft would start out with an acceleration of F/M = a = 2084.4 N/208,440,000 kg = 10^-5 meter/s² for cases where the craft would utilized 1,000 tethered driving sails. After traveling 6 x 10¹²  seconds or about 200,000 years, the velocity of the space craft will be 0.20 C.

 

 

Now consider a space craft having a mass of 208,440 metric tons driven by 10,000 such one metric tons sails. For such a space craft that deployed a linear series of 10,000 tethered sails where each sail was separated by an efficient 10 sail widths, the space craft having a total mass of 208, 440 metric tons would start out with an acceleration of F/M = a = 2084.4 N/208,440,000 kg = 10^-4  meter/s². After traveling 6 x 10¹¹ seconds or about 20,000 years, the velocity of the space craft will be 0.20 C.

 

 

We can consider more robust gridded sails such as those made from 10 nanometer diameter fibers spaced 200 microns apart. Each such sail would have a mass of 100 metric  tons. Thus, a space craft having a total mass of 208,440 metric tons that is driven by 1,000 such sails would too start out with an acceleration of F/M = a = 2084.4 N/208,440,000 kg = 10^-5 meter/s² and achieve a velocity of 0.20 C after 200,000 years.

 

 

Cnsider a sail that is comprised on 316.2  nanometer wide fibers in a cross-weave where adjacent parallel  fibers are separated by 200 microns. Also consider situations where the fibers are one side reflective and one side transmissive. A sail comprised of such a material will have a mass specific capture area that is equal to that of a one nanometer thick monolithic sail.

 

 

Consider that such a sail which is gridded with the above  316.2  nanometer thick sail fiber construction made of STP H₂O density carbonaceous materials would have a mass of  100,000 metric tons for a capture area of 10⁸ square kilometers. Assuming that the space craft plus her sail had a mass of 208,440 metric tons, the craft would start out with an acceleration of F/M = a = 2.0844 N/208,440,000 kg = 10^-8 meter/s². After traveling 6 x 10¹⁵ seconds or about 200,000,000 years, the velocity of the space craft will be 0.20 C and the relativistic Lorentz transformation factor will be 1.0206 thus permitting the above Newtonian formula to apply.

 

 

For such a space craft that deployed a linear series of 1,000 tethered sails where each sail was separated by an efficient 10 sail widths, a space craft having a total mass of 208, 440,000 metric tons could be identically accelerated. The mass of the crew quarters would be 208, 439,000 metric tons.

 

 

For such a space craft that deployed a linear series of 1,000,000 tethered sails where each sail was separated by an efficient 10 sail widths, a space craft having a total mass of 208, 440,000,000  metric tons could be identically accelerated. The mass of the crew quarters would be 208, 439,000,000 metric tons. For cosmic journeys, this is not bad.

 

 

A series of 100 million tethered sails might conceivably pull a sail craft combination having a mass of 20,844,000,000,000 metric tons and a crew quarters having a mass of 20,843,900,000,000 metric tons.

 

 

The background interstellar and intergalactic matter might not erode even many of highly relativistic sail of sub-micron thickness.

 

 

The diametrical cross-sectional area of our observable universe is close to 10 ⁴⁷  square kilometers and the mass of the total mass energy of the observable universe is only about 10 ⁵⁰ metric tons of which only 4 percent is baryonic.  Thus,  an average column spanning the diameter of the entire visible universe would have an H2O STP matter thickness of only 25 micrometers for reactive matter.

 

 

However,  this is not a concern for the following reasons.

 

 

First, the sails could be replaceable grid sails and driven by optical, IR, microwave or rf radiation. The mass of such sails can be reduced by many orders of magnitude relative to monolithic sails that are only micrometer scales in thickness.

 

 

Second, sails having a very thick cable or thread like construction are conceivable where the cables or wires would be many times if not several orders of magnitude thicker than 25 microns. The sails could be mostly empty space to almost entirely empty space to reflect long wave rF phased array beams.

 

 

As for concerns about over burdening the conductive or super-conductive wires or cables used for such sails by extremely intense rF beams, note that such reflective members could be very conductive to superconductive to thereby yield near perfect reflection. The EM energy that was not reflected would largely pass through the openings in the sail grid.

 

 

Second, a magnetic and/or electric field based scoop or anti-scoop could divert the chargons away from the sail just as an extended electrodynamic scoop for an interstellar ramjet would. Electro-dynamic-hydro-dynamic-plasma-drive features could utilize the diverted plasma in a reactive and gainful manner.

 

 

The sail might be deployed in a manner that is orthogonal to the ship’s velocity vector.  The sail might be parallel to the space craft velocity vector and driven obliquely from behind. This way, the effective thickness of the sail could be thousands of miles and the sail could include electro-dynamic-hydro-dynamic-plasma-drive features.

 

 

Fourth, the above parallel sail could conceivably be made of negative refraction index materials that would be pulled forward by incident star light and highly blue-shifted CMBR, far infrared, and non-CMBR radio sources.

 

 

Fifth, the sail can simply be a deployed mag-sail or M2P2 type of sail or any other magnetic or plasma bottle sail. It is possible that a plasma affixed to the space craft to be driven by rf radation, and even source based laser light upon attainment of extreme space craft gamma factors could be easily reflected by such sails. Plasma makes an excellent rF reflector even at very small densities.

 

 

I have done a lot of writing on parallel sails such as negative refraction index monolithic and grid sails capable of extreme gamma factors.

 

 

Sixth, some sail materials such as any future forms of super-strong very conductive to super-conductive metallic hydrogen can be used as nuclear fusion fuel for fusion rockets upon degradation to useless levels.

 

 

Seventh, it has been proposed that very thin,  metallic,  very low gas density containing balloons might be used for nuclear warhead decoys and which could survive 100 meter proximity detonation to a one kiloton neutron bomb in the vacuum of space. The rate of radiative cooling would be tens of billions of Kelvins per second due to the extreme thinness of the balloon membranes and most of the neutrons would pass right through the balloon without interacting or by only depositing a very small portion of the particles kinetic energy into the balloon and enclosed gas. Interstellar chargons are more reactive to electronic shell structures but not by that much.

 

 

The general idea for obliquely oriented beams involves the beamed energy incident on both sides of the sail. The sail could include a surface of hair like cilia or any other surface contour that would work so as to much more effectively grab ahold of the light.

 

 

In addition, the sail could be fabricated from photovoltaic materials in order to provide power for electro-dynamic-hydrodynamic-plasma-drives or chargon rockets, or perhaps even photon rockets.

 

 

For extreme gamma factors, the CMBR and starlight will be highly blue-shifted and will be relativistically abberated to what would approach a point source in front of the space craft at gamma = infinity. A sail parallel to the space craft velocity vector made of a suitable negative electromagnetic refraction index material will be pulled forward even by light incident on the sail at a very shallow angle from in front of the space craft.

 

 

To enhance the negative refraction index sails capture of EM energy, the sails may have negative index hairs or cilia distributed along its length.

 

 

Negative refraction index materials have actually been measured to be pulled on by incident light. Duke University and other academic and government labs are researching the various aspects of negative refraction index materials.

 

I have no problem with space craft being pulled forward by forward incident light. After all, the paradigm of light speed velocity limits may or may not have been shattered with any future validation or not of the CERN superluminal neutrino results. The big bang may have been the most recent free lunch. There is no reason why the big bang could not have started with miniscule quantities of mass-energy.

 

 

A good abstract for a great paper on negative super-pressure of light acting on a negative refractive index material is

 

Henri Lezec
(Center for Nanoscale Science and Technology, NIST)

 

Forty years ago, V. Veselago derived the electromagnetic properties of a hypothetical material having simultaneously-negative values of electric permittivity and magnetic permeability [1]. Such a material, denominated “left-handed”, was predicted to exhibit a negative index of refraction, as well as a number of other counter-intuitive optical properties. For example, it was hypothesized that a perfect mirror illuminated with a plane wave would experience a negative radiation pressure (pull) when immersed in a left-handed medium, as opposed to the usual positive radiation pressure experienced when facing a dielectric medium such as air or glass. Since left-handed materials are not available in nature, considerable efforts are currently under way to implement them under the form of artificial “metamaterials” — composite media with tailored bulk optical characteristics resulting from constituent structures which are smaller in both size and density than the effective wavelength in the medium. Here we show how surface-plasmon modes propagating in a stacked array of metal-insulator-metal (MIM) waveguides can be harnessed to yield a volumetric left-handed metamaterial characterized by an in-plane-isotropic negative index of refraction over a broad frequency range spanning the blue and green. By sculpting this material with a focused-ion beam we realize prisms and micro-cantilevers which we use to demonstrate, for the first time, (a) in-plane isotropic negative-refraction at optical frequencies, and (b) negative radiation pressure. We predict and experimentally verify a negative “superpressure”, the magnitude of which exceeds the photon pressure experienced by a perfect mirror by more than a factor of two. 1) V. Veselago, \textit{ Sov. Phys. Usp. }10, p.509 (1968).

 

Available at:

 

http://meetings.aps.org/Meeting/MAR09/Event/93172

 

The sail might not need to  be held by guy lines. A strong magnetic field based coupling or electrical charged based connection might work.

 

 

Another option is to fabricate the sail guy lines out of graphene, carbon nanotubes, boron nitride nanotubes, graphene oxide paper, and the like. A cable constructed from such materials could stretch for about 20 to 50 kilometers yet still handle tens to hundreds of Earth G’s. The tensile strength of graphene is close to 18 million PSI for perfect forms.

 

 

Materials such as solid quarkoniums and somehow stabilized neutroniums, and perhaps even Higgsiniums would be better yet, but such materials may only exist in nature in extreme mass quantity states as of the present cosmic era.

 

 

The collection area of the sail can be very, very, large. A large electro-dynamic scoop could extent very far out from the sail.

 

 

Regarding nanotech self-assembly mechanisms, just simply greatly increase the capture area of a electrodynamic scoop to collect enough interstellar materials and use most of the collected interstellar material as an EHPD, an MHPD, or a combination of the two and use the rest of the materials for sail repair.

 

Regarding holding M2P2 plasma affixed to the ship under high gamma factor condition, simply increase the strength of the fastening fields.

 

 

Now regarding interstellar matter density near our solar system of one particle for every 10 cm³, the density would  work out to be a layer of hydrogen or helium atoms about one atom thick for a column that is one light-year long. Not a show stopper for light sails or sails that are electro-dynamically shielded or protected.

 

 

If extreme materials are used with excellent reflectance, we could simply use a sail that has a thickness of one millimeter or more and which is monolithic, or better yet,  use a sail with grid lines that are one millimeter or perhaps much greater in thickness. This way, a sail that has an area of only one square kilometer can intercept a beam having an equivalent black body temperature of several thousand Kelvins provided it is constructed of suitably refractive materials.

 

 

We could simply use electrodynamic methods of grabbing ahold of the interstellar gas and diverting around the space craft and sail. The power to operate the electrodynamic mechanisms can be supplied by beams. The electrodynamic methods can include lasers for ionization, or rf radiation where the gamma factors are suitably large, magnetic fields, electric fields, plasma fields affixed to the space craft, and the like.

 

 

Then there is always the possibilities for sails comprised of truly exotic materials such as somehow stabilized neutroniums, quarkoniums, higgsiniums, monopoliums, and perhaps even raw space-time-mass-energy forms such as the “Yelm” of mid-20th Century big bang theory.

Since one cubic meter of neutronium would have a mass of about 10¹⁵ tons. A 1,000 kilometer long thread of the stuff that has a cross-sectional area of 1,000,000 neutrons would have a mass of only one kilogram. A 1 kilometer long thread having a cross-sectional area of 1 billion neutrons would have a mass of only 1 kilogram. Lines made of quarkoniums could have the same length and cross-section but would be 10 to 1,000 times more massive. Higgsiniums would be all the more massive.

 

 

Provided such extreme materials could be developed, they could also serve as electric current carrying magnetic sail components. Anyhow magnetic sails can be made of any ordinary conducting or superconducting period table materials.

 

 

It is also conceivable that a hybrid sail can be used where a current carrying magsail would deflect plasma away from a monolithic and grid like light sail or rf sail.

 

 

Now, regarding the subject of sail erosion by exposure to interstellar or intergalactic gas, we must realize that the kinetic energy of a gas atom traveling at a velocity of 86.7 percent of the speed of light with respect to the sail would be equal to the binding energy of roughly 10 billion atoms within a sail of micron thickness. Thus, the fact that 10 billion atoms could be dislodged should all of the energy of the gas atom be deposited within the sail. Incident gas atoms having even higher associated gamma factors with respect to the star ship sail could potentially knock loose even more atoms. Perhaps, there is no reason to worry about sail erosion in spite of this for the following reasons.

 

 

First, extremely relativistic particles would likely deposit only a small portion of its energy within the sail thereby greatly lessening the number of atoms that would be knocked loose. This fact would apply to chargons as well as neutral incident particles.

 

 

Second, for sails of near micron thickness, atoms that were knocked loose would likely simply be re-assimilated by the bulk sail materials. Perhaps the only chance for an atom to be knocked loose would include atoms located on the backward side of the sail.  Atoms for which bonds where broken within the bulk sail material would tend to simply re-bond with adjacent atoms.

 

 

Third, since the incident gas or plasma particle would deposit only a small portion of its energy within the sail, the kinetic energy per particle for particles that are knocked loose may be only slightly in excess of the binding energy of the dislodged atoms. Basically, the kinetic energy of the dislodged atoms could likely be re-absorbed and/or radiated away thereby promoting rebinding of the dislodged atoms.

 

 

Fourth, for cases where the sail would completely absorb the kinetic energy of the incident gas or plasma particles such as an alpha particle, for the case of a one micron thick sail, the sail would obviously be able to complete stop the chargon without losing it. Thus, any atoms disbonded by the incident chargon would also likely be captured and prevented from leaving the sail material.

 

Fifth, for grid like sails, the grid lines might be positively chargeable so that incident interstellar or intergalactic ions are pushed away from the grid lines and through the openings within the grid like sails. The effect would be similar to the Vander walls force that keeps neutral atoms from being squeezed together to tightly.

 

 

 

We now perform a reality check on the above formulations.

 

Consider the space craft at a stationary state. The CMBR appears equally bright from all directions within about 1 part in 30,000.

 

Now, the apparent angle, θ_s,  of CMBR pre-incident on the space craft at an angle of 90 degrees or with respect to the length of the space craft relative to the source reference frame at v = zero C will appear to be incoming at an angle, θ_o,  of 90 degrees with respect to the space craft,  ship’s reference frame.

 

If we consider the effects of relativistic aberration, the general formula for apparent shift in angle of incidence of the CMBR from the ship’s perspective is

 

Cos θ_o = {[cos θ_s] – (v/C)}/{1 – [(v/C) cos θ_s]}

 

Now say we desire to find the range of CMBR angles incident on the space craft with respect to the space craft reference frame for space craft velocities of 0.20 C.

 

Now since we are considering an angle of θ_o = π/2, cos θ_o = zero. Using the above formula, we achieve Cos θ_o = {[cos θ_s] – (v/C)}/{1 – [(v/C) cos θ_s]} = Cos π/2 = {[cos θ_s] – (0.20)}/{1 – [(0.20) cos θ_s]} = zero = {[cos θ_s] – (0.20)}/{1 – [(0.20) cos θ_s]}.

 

Thus, (zero) {1 – [(0.20) cos θ_s]} = {[cos θ_s] – (0.20)} = zero.

 

Therefore, cos θ_s = 0.20 — > θ_s  = 78.463 degrees. We will make a first order assumption that the incident CMBR from behind has a frequency of f’ = f / {γ [1 + (β cosine θ)]} = f / {1.02062 [1 + [0.2 cosine ( 0)]]} = (0.816497161) f. Thus, we will assume that θ = 0 degrees for the following 5 scenarios where we assume that the CMBR is directly incident from behind.

 

The radiated power received by the sail will be [(78.463)²/(90²)] f’ = [(78.463)²/(90²)] f / {γ [1 + (β cosine θ)]} = [(78.463)²/(90²)] f / {1.02062 [1 + [0.2 cosine ( 0)]]} = [(78.463)²/(90²)] (0.816497161) f =

 

Once again, the temperature of a black body is T = {P/[(A)(σ)(e)]}^1/4 = {P/{(A)[5.670400(40) x 10^-8 W m^-2 K^-4]} ^1/4}. The light pressure incident from directly behind will be approximately equal to [(θ_s)²/(90²)] {2 {σ {{(T_cmbr)/{γ [1 + (β cosine θ)]}}}⁴/C}} =  [(78.463)²/(90²)] {2 {[5.670400(40) x 10^-8 W m^-2 K^-4] {[(T_cmbr) (0.816497161) ]⁴}/C}} = 4.632092076  x 10^-15 Newtons/m². In actuality, not all of the light is directly incident from the back and so there will be angular affects that result in loss of driving power. However, we will assume that all of the radiation is absorbed and then re-cycled and released as a perfect backwardly directed laser beam.

 

Now  E_gain = ʃF^odx = ʃ(0,10²⁵) F^odx = ʃ(0,10²⁵)(10¹⁴) [4.632092076  x 10^-15 N] ^odx = 4.632092076 x 10²⁴ Joules.

 

Now, a 208,440 metric invariant mass space craft traveling at a starting velocity of 0.2 C has a kinetic energy of {1.02062[M C²]} – [M C²] = {1.02062[208,440,000  C²]} – [208,440,000  C²] =  1.9146 x 10²⁵ Joules – 1.87596 x 10²⁵ Joules = 3.864 x 10²³ Joules. When  4.632092076 x 10²⁴ Joules is added, the total gamma factor becomes [5.01849 x 10²⁴ Joules + 1.87596 x 10²⁵ Joules]/ [1.87596 x 10²⁵ Joules] = 1.2675. The associated space craft velocity will be equal to 0.6142 C.

 

Likewise doing iterated numerical approximations with v = 0.6142 C to obtain another higher velocity and then repeating the steps over and over again will give a first order approximation for space craft terminal velocity.

 

So we have reasonably demonstrated that CMBR sails can drive very large space arks to velocities considered fast by interstellar propulsion physicists. Typically, fast interstellar travel occurs at a better part of the speed of light.

 

However, a much finer scale is needed to produce results for many such steps where the computed velocity would not significantly diverge from the actual velocity obtained.

 

Note that here, I neglect the effects of mass based astrodynamic drag. I have come up with several mechanisms by which massive astrodynamic drag can be almost entirely eliminated and will post on this subject later this month.

 

 

 

Now consider again that radiation pressure is equal to σT⁴/C and {2 [σT⁴/C]} for reflected radiation. However, for a space craft traveling through a black body radiation field, the apparent temperature of the radiation increases in proportion to γ and so the black body power impinging on the space craft from directly in front grows in proportion to T⁴ and thus  to γ⁴.

 

 

The temperature of a black body is T = {P/[(A)(σ)(e)]}^1/4 = {P/{(A)[5.670400(40) x 10^-8 W m^-2 K^-4]} ^1/4}. Therefore, the cosmic microwave background radiation pressure on a perfectly reflective flat bow  relativistic space craft is approximately equal to  {2 [σT_cmbr ⁴/C]} γ⁴ = {2 [σT_cmbr ⁴/C]} { {1/{1 – [(v/C)²]}^1/2}  ⁴} =   {2 [σT_cmbr ⁴/C]} {1/{1 – [(v/C)²]}²} where γ is constant and T_cmbr is constant. However, the light pressure incident from directly behind will be approximately equal to {2 [σT_cmbr ⁴/C]}/{1/{1 – [(v/C)²]}²}. In actuality, not all of the light is directly incident from the back and so there will be angular affects that result in loss of driving power. However, we will assume that all of the radiation is absorbed and then re-cycled and released as a perfect backwardly directed laser beam. We will assume that CMBR light which is forwardly incident completely passes through the sail.

 

 

Assuming that the velocity of the sail starts out at (Zero) C, the optical pressure will be equal to {{2 [σT_cmbr⁴/C]}/γ⁴} = {{2 [σT_cmbr⁴/C]}/ { {1/{1 – [(v/C)²]}^1/2} ⁴} } = {{2{[5.670400(40) x 10^-8 W m^-2 K^-4][(2.725 K)⁴]/(300,000,000 m/s)}}/(1²)} = [2.0844355 x 10^-14] Newtons/m². For a 10,000 km by 10,000 km sail, the drive force will be 2.0844 Newtons. A 100,000 km by 100,000 km sail will produce a driving force of 208.44 Newtons.

 

Now assume that the sail is monolithic, made of one nanometer thick carbonaceous, STP water density materials. The sail would have a mass of 10,000,000 thousand metric tons. Assuming that the space craft plus her sail had a mass of 20,844,000 metric tons, the craft would start out with an acceleration of F/M = a = 208.44 N/20,844,000,000 kg = 10^-8 meter/s². After traveling 6 x 10¹⁵ seconds or about 200,000,000 years, the velocity of the space craft will be 0.20 C and the relativistic Lorentz transformation factor will be 1.0206 thus permitting the above Newtonian formula to apply as a reasonable approximation.

 

Assume that the background gas and dust that contacts the sail over a path length of 1 light year has an invariant  mass of (0.06667 kg)( 10¹⁴){[ 3 x 10¹⁰]^-1} = 222.2 kg. The momentum of the gas and dust with respect to the sail will be (m)(v) = (222.2 kg)(50,000,000 m/s) =1.111 x 10¹⁰  kg m s. Now Force equal dP/dt. Therefore, the force on the sail is on average equal to F_0.05C  = dP_0.2C/dt = 71.677 Newtons.. For a velocity of 0.02 C, the net propulsive force is 208.44 N – 71.67 N = 136.76 N which will still obviously permit 0.2 C velocities.

 

For such a space craft that deployed a linear series of 1,000 tethered sails where each sail was separated by an efficient 10 sail widths, a space craft having a total mass of 208, 440,000 metric tons could be identically accelerated. The mass of the crew quarters would be 108,440,000 metric tons. For such a space craft that deployed a linear series of 1,000,000 tethered sails where each sail was separated by an efficient 10 sail widths, a space craft having a total mass of 208, 440,000,000  metric tons could be identically accelerated. The mass of the crew quarters would be 108,440,000,000  metric tons. For cosmic journeys, this is not bad. A series of 100 million tethered sails might conceivably pull a sail craft combination having a mass of 20,844,000,000,000 metric tons and a crew quarters having a mass of 10,844,000,000,000 metric tons. For a velocity of 0.2 C, the each of the latter massed space craft would have the same ratio of backward driving force and massive drag force. The caveat is simply the deployment of commensurate numbers of sails simultaneously in a spatial series along the space craft velocity vector.

 

 

Now assume that the sail is a gridded fabric or net made of STP water density conducting 0.4 nanometer wide, one nanometer thick,  carbonaceous fibers that are separated by 0.0005 meters such as in a judicious cross weave spacing. A one square meter portion of the net will have a mass of 0.8 x 10^-12 kilograms. A 0.08 kilogram sail will have a plan-form area of 10⁵ square kilometers. A 8,000 kilogram sail will have a plan-form area of 10¹⁰ square kilometers and will have an acceleration of F/M = A = 208.44 Newtons/8,000 kg = 0.026055 m/s².  A space craft having a total mass of  8,000 metric tons will have an initial acceleration of 0.000026055 m/s².   In 80,000 years, the velocity of the 8,000 metric ton  system will be about 0.215388 C assuming Newtonian approximations.

 

Now, the 10¹⁰ square kilometer plan-form area gridded sail will have a massive species contact area of [10¹⁰km²]/1,250,000 = 8,000 km². So the background gas and dust that contacts the sail over a path length of 1 light year would have an invariant  mass of (0.06667 kg)( 10¹⁴){[ 3 x 10¹⁰]^-1}/(1,250,000) = 0.00017776 kg. The momentum of the gas and dust with respect to the sail will be (m)(v) = (0.00017776 kg)(50,000,000 m/s) =8,888 kg m/s. Now Force equal dP/dt. Therefore, the force on the sail is on average equal to F_0.2C  = dP_0.2C/dt = 0.000057341Newtons.. For a velocity of 0.2 C, the ratio of the driving force to massive drag force is [208.44 N/ 0.000057341 N] = 3,635,095.

 

The last result in the above paragraph is intreguing because it suggest that an ordinary CMBR sail-material configuration  could gainfully accelerate even in an environment such as local interstellar space where the baryonic mass density may be as much as one million times that of the observable universe on average.

 

Now, the apparent angle, θ_s,  of CMBR pre-incident on the space craft at an angle of 90 degrees or with respect to the length of the space craft relative to the source reference frame at v = zero C will appear to be incoming at an angle, θ_o,  of 90 degrees with respect to the space craft,  ship’s reference frame.

 

If we consider the effects of relativistic aberration, the general formula for apparent shift in angle of incidence of the CMBR from the ship’s perspective is

 

Cos θ_o = {[cos θ_s] – (v/C)}/{1 – [(v/C) cos θ_s]}. Now assume θ_s = 14.48 degrees, and a gamma factor of 3, Cos θ_o = {[cos (19.47 degrees)] – (0.942809)}/{1 – [(0.942809) cos (19.47 degrees)]}~ 0 — > θ_o = 90 degrees. Now (14.48²)/(90²) => (0.0468)/(4.5⁴) = 0.000114128. Now the grid would need to expand in area by a factor of 0.000114128^-1 = 8,762.

 

The grid line spacing can be increased by a factor of 3 thus yielding an increase in grid area by a factor of essentially 2. I obtained the areal expansion factor of 2 by inspection of hand-drawn grids although I am certain topologists and geometers have long since figured out the general relationships for various factors of line distance expansion for square gridded figures. However, we still need to increase the grid area by another factor of 4,381. Simply deploying  4,381 + 1 expanded sails = 4,382 expanded sails each having a mass of 8,000 kilograms will produce a complete sail rigging having a mass of 35,056 metric tons. Include a tether sub-rigging to link the sails in a serial distribution along with the rest of the mass of the space craft to yield a total craft mass of 200,000 metric tons and we obtain a forward oriented driving force still equal to 208.44 N. So the background gas and dust that contacts the fully deployed rigging at a gamma factor of 3 over a path length of 1 light year has an invariant  mass of {(0.06667 kg)( 10¹⁴){[ 3 x 10¹⁰]^-1}/(1,250,000)} (4,382)   = [0.00017776  kg](4,382) =  0.778944 kg.

 

 

Now,  the formula for relativistic momentum of a massive particle  is M₀ v γ = M₀ v /{{1 – [(v/C)²]}^1/2}. However, the number of interstellar or intergalactic massive particles impinging on a relativistic space craft per unit of time, ship’s frame, t,  is proportional  to (γ)v = {1/{{1 – [(v/C)²]}^1/2}v. Now, dP/dt = F which is is expressed in Newtons. Therefore, the force acting on a space craft, ship’s frame,  from the interstellar massive background is equal to d[(M₀ v γ) (γ)(v/C)ǀ]/dt = d{{M₀ v /{{1 – [(v/C)²]}^1/2}} {1/{{1 – [(v/C)²]}^1/2}}v}/dt where M₀ is the incident mass over the  the constant distance interval of (Delta x) background reference frame. The drag energy is thus equal to {d[(M₀ v γ) (γ)(v/C)]/dt} (Delta x) = {d{{M₀ v /{{1 – [(v/C)²]}^1/2}} {1/{{1 – [(v/C)²]}^1/2}}v/C}/dt} (Delta x) where t is the ship time.  The quantity γv/C = {1/{{1 – [(v/C)²]}^1/2}}v/C is considered dimensionless and is of a constant scalar form.

The momentum of the 0.778944 kg invariant mass with respect to the space craft will be M₀ v γ = M₀ v /{{1 – [(v/C)²]}^1/2} = (0.778944 kg)(282,842,700 m/s)(3) = 6.60956  x 10⁸  kg m/s. The force acting on the space craft will be d[(M₀ v γ) (γ)(v/C)ǀ]/dt = d{{M₀ v /{{1 – [(v/C)²]}^1/2}} {1/{{1 – [(v/C)²]}^1/2}}v}/dt = {[(0.778944 kg  (282,842,700 m/s)(3) (3)[( 282,842,700 m/s) /(300,000,000 m/s)]}/{(31,000,000 s)/[(3)/(0.942816)]} = 191.889 Newtons. The net driving force would be 208.44 N – 191.889 N = 16.551 N.

Thus, it is safe to say that our space craft could accelerate to a velocity of 0.942816 C or to a gamma factor of 3  and still maintain a gainfull driving force. Now KE = ʃ F∙ dx = F(cos α)(Δx) = F(cos 0)(Δx) = (F)(Δx) for parallel force and velocity vectors. Assuming a driving force of 16.551 Newtons during the entire trip to a gamma factor of 3, we will further assume that (F)(Δx) = [3 MC² – MC²] = 2MC² = (2)(200,000,000 kg)[(300,000,000 m/s)²]  =  3.6 x 10²⁵  joules. Dividing the energy by F yields x = distance travelled = [3.6 x 10²⁵J]/(16.551 N) = 2.175 x 10²⁴ meters = 217,510,000 light years.

Now,  a high end carbonaceous super-material having a cross sectional area of 1.3708 x 10^-9 square meters can support 208.44 Newtons assuming a yield strength of 10⁷ kilograms per square inch. A cable having such a cross-section and having a mass of 10,000 metric tons would plausibly have a length of (10,000)[1.3708 x 10^-9] meters or 1.3708 x 10¹³  meters or 1.3708 x 10¹⁰ kilometers. However, a cable with a cross-sectional area 1,000 times as great having the same length would have a mass of 10,000,000 metric tons and could conceivably tether 1,000 of  the previously described 20,000 kilogram gridded sails each having a plan form area of 10¹⁰ square kilometers and each producing a driving force of  208.44 Newtons.  Such a tethered sail system could propel a space craft having a total mass of 20 million metric tons, of which 10,020,000 metric tons would exist as the sail rigging. Each sail would be linearly separated by 1.3708 x 10⁷ kilometers. A cable having a cross-sectional area that is ten time greater yet could power a space craft having a total mass of 200 million metric tons of which 100,200,000 metric tons would be incorporated into the sail rigging.For the latter example, the sails would be separated by 1.3708 x 10⁶ kilomters thus preventing all but trivial shadowing of the driving CMBR at velocities of 0.2 C and only moderate shadowing at a gamma factor of 3.

The value of gamma = 3 is close to the maximum value conceivable with purely backward impinging, CMBR driven planar or plane-like sails, that are oriented orthogonally to the space craft velocity vector where the sails are made of ordinary atomic elements based materials and are of gridded forms for  the next billion years or so. This is because the baryonic mass density of the observable universe will very only slightly over this time period thus at best promoting a slight decrease in drag for the above systems at a gamma factor of 3.  Significantly higher gamma factors with self repairing grids are possible for universal ages that several or more times that of the present universe due to intergalactic massive rareification.

In order to compute a gamma factor of 3, an interpolated value for back-ward red-shift of about 4.5 was assumed as an approximately average value. Since the mass specific capture area and the associated massive drag values used are not absolute requirements, the adjustment of the latter values by a few percent can compensate for inaccuracies in the former estimated average and permit the actual maximum possible gamma factor per given intergalactic massive density to very by perhaps as much as plus or minus a few percent. The point is that because of the subject degrees of freedom in the engineering and applied physics for the above conjectural specific examples, the maximum gamma factor of 3 is a very good ball park to aim for in any future real world systems we will design.

Now, in addition of electromagnetic negative refractive index materials which have been demonstrated within research facilities, it may be possible that massive particle and perhaps even gravitational wave negative refraction index materials could be fashioned into sails that are pulled forward by the incident mass-energies. No one at present really knows if the later two types of materials are possible to construct, however, such materials are tantalizing to consider because of the implications of perpetual and increasing pull sail accelerations,  as long as the mass-energy influxes would not thermally or mechanically over burdern the negative refraction index materials.

However, we do not necessarily need even the still controversial pull sail negative electromagnetic refraction index drives. Ordinary positive index materials that are one way transmissive and which are suitably contoured can provide much higher gamma factors in the present cosmic era even in consideration of massive astrodynamic drag. I will describe such  increasing more extreme scenarios in an ongoing series of posts on the subject of plausible one way transmissive, positive refraction index, material based sails involving intelligible speculations regarding such sails made of ordinary atomic elements.

I will post further on this subject later today.

 

Regards;

 

Jim

 

Copyright James M. Essig  January 26, 2011  All Rights Reserved.

 

Interstellar CMBR Sailing: 3rd Edition.

You ever wonder whether or not physicists and theoretical engineers will at some point in time determine how to obtain a free lunch? Well, for all practical purposes, we have a free lunch. It is called the cosmic microwave background energy or CMBR and may be available in infinite quantities given that our entire universe may have an infinite volume and spatial extent, and perhaps also forward potential time extension. The CMBR will always be available provided no further phase changes or symmetric breaking events will convert the background photonic radiations to another useless form. As such, photons and electromagnetic waves are theoretically perfectly stable. As a Catholic and affectionato for the Holy Bible, I like to muse at times on the metaphor that light was the first element of creation in at least some translations. Now, the actual meaning of light is most likely a metaphor, but given that our universe in the Big Bang may have started out from pure energy where such energy was embodied in the start of the initial space-time and mass energy forms in a kind of space-time-energy unification, perhaps the Bible has a deeper meaning here that was somehow preserved from antiquity.

That space and time are intimately tied to electromagnetic radiation is obvious when one considered the ubiquitous inclusion of the speed of light in vacuu as a constant in virtually all special and general relativistic formulations. Even in classical electromagnetic theory, the velocity of light is intimately related to the properties of space time including the magnetic permeability and electric permittivity of free space by the formula C = {1/[μ₀ ɛ₀]}^1/2.

I am sure that most of the concepts expressed within this post have been contemplated by others before.

By now the reader is aware of the concept of light sail(s) driven space craft that can reach relativistic velocities. A space craft traveling at extreme gamma factors using an ordinary beam sail will experience extreme astro-dynamic drag, and the sail would likely be ionized by the drag induced friction. This is largely due to the fact that most beam sail space craft contemplate beam sails that are orthogonally spread  with respect to the craft velocity vector and thus which have a very large surface area to experience forward drag.

Suppose a relativistic rocket was powered by energy captured by an attached square or rectangular CMBR  sail that is  oriented in a perpendicular to the velocity vector of the space craft. The equation for Doppler shifting of  CMBR acting on the sail would then be:  

1 + z = {1 + [ ν (cos θ)/C]}/{[1 - [(v/C)²]]^1/2}

or,

z  = {1 + [ ν (cos θ)/C]}/{[1 - [(v/C)²]]^1/2} – 1

f’ = f / {γ [1 + (β cosine θ)]}

which reduces to F’ = f/γ for a radiation source and space craft moving in a direction perpendicular to the line connecting these reference frames with respect to a space craft observer since cos (π/2) = zero where f represents frequency. Here, θ is the angle of view with respect to the space craft velocity vector or the perceived angle of  radiation incidence on the sail with respect to the direction of space craft travel,  with respect to the space craft.

Now,  the energy of a photon is as follows:

E = [h/(2 π)] ω = hf = hC/λ 

where h is the Planck Constant and λ  is the photon wave-length.

Therefore, the energies of the individual CMBR photons impinging on the light sail oriented in a direction perpendicular to it from the space craft’s perspective from directly behind are equal to:

E + =  hf/{γ [1 + (β cos  θ)]} = hf /{γ [1 + (β cos  (0)]}

which reduces to;

hf /{γ [1 + β ]}.

Now,  the CMBR power impinging on the space craft sail per differential unit of time element (space craft reference frame), per differential unit of angle of pre-incidence (space craft reference frame), per differential element of sail area (space craft reference frame) for black body radiation is a function of γ ⁴. This is because the black body radiation frequency curve peak is proportional to black body source temperature and an incident source photon’s frequency is proportional gamma. Since black body total power emission per unit of surface area is proportional to the  fourth power of the temperature of the black body, the above differential area element of the sail will receive a total power that scales with γ ⁴. Black body emitter frequency distribution scales as a function of gamma relative to a moving observer traveling at a factor of γ with respect to the source for directly approaching observers and 1/ γ for directly receding observers.

Planck’s Law states that

I(ѵ,T)dѵ = {[2hѵ³]/C²}{1/{[e^[(hѵ)/(kT)]] -1}}dѵ

λ_max = b/T

where λ max,  is a function only of the temperature.

P_net = P_emit – P_absorbed

Applying the Stefan–Boltzmann law,

P_net = A σ e (T⁴ – T₀⁴)

where sigma =  σ = (2π⁵k_B⁴)/(15 h³ C²) = (π²k_B⁴)/(60 ђ³ C²)

or  where sigma =  σ = 5.670400(40) x 10^-8 W m^-2 K^-4

Therefore, the apparent spectral temperature of the CMBR radiation incident on the sail per unit angle of CMBR incidence for a stationary sail is:

{[P_cmbr/(A σ e)] ^1/4}

The apparent spectral temperature of the CMBR radiation incident on the sail per unit of apparent angle of incidence of the CMBR with respect to the space craft reference frame-based observer(s) for a sail traveling at a given velocity for backwardly impinging radiation is:

T_app = {∫(0, π/2){{{[P_cmbr/(e σ)]^1/4}/{γ [1 +  [(v/C) cos θ]]}}⁴}{{∫(y₁,y₂){ ∫(x₁,x₂) dx} dy}^-1} dθ}^1/4

 

= {∫(0, π/2){{{[P_cmbr/(e σ)]^1/4} /{{1/{[1 – [(v/C)² ]] ^1/2}} [1 +  [(v/C) cos θ]]}}⁴}{{∫(y₁,y₂){ ∫(x₁,x₂) dx} dy}^-1} dθ}^1/4

 

 

= {∫(0, π/2){{{[Pcmbr/(e σ)]^1/4}/{{1/{[1 – [(v/C)² ]] ^1/2}} [1 + [(v/C) cos θ]]}}⁴}[(∫d A)^-1] dθ}^1/4

where P_cmbr is the background CMBR power incident on the sail, dA is the differential element of sail area with respect to the space craft reference frame, v is the velocity of the space craft with respect to the background, and θ is the angle of radiation incidence on the sail with respect to a sail based observer. Theta ranges from π/2 radians for radiation traveling in an orthogonal direction with respect to the ship velocity vector to zero radians for radiation traveling in a parallel direction with respect to the ship velocity vector.

The total power backwardly incident upon the sail with respect to the sail’s reference frame for a given gamma factor  is  therefore:

P = ∫(y₁,y₂) {∫(x₁,x₂) {∫ (0, π/2) {{{(T_cmbr) /{γ [1 + [(v/C) cos θ]]}}⁴} σ e} dθ}dx}dy

= ∫(y₁,y₂) {∫(x₁,x₂) {∫ (0, π/2) {{{(T_cmbr) /{{1/{[1 + [(v/C)² ]] ^1/2}}  [1 + [(v/C) cos θ]]}}⁴} σ e} dθ}dx}dy

= ∫ {∫ (0, π/2) {{{(T_cmbr) /{{1/{[1 – [(v/C)² ]] ^1/2}}  [1 + [(v/C) cos θ]]}}⁴} σ e} dθ} dA

Here, T_cmbr is the background CMBR temperature.

Note that in the above calculations and the ones that follow, all of the relevant backwardly incident background energies are assumed to be initially absorbed by the sail even if the sail acquires a temperature significantly above absolute zero and thereby produces thermal electromagnetic black body emissions. I describe potential methods of the absorption of nearly all incident radiations even in cases where relativistic aberration would otherwise cause the bulk of the impinging radiation to easily reflect off the sail because of increasingly shallow angles of incidence. The forwardly incident radiation is assumed to completely pass through the sail without exchange of momentum.

We can numerically integrate the relativistic  energy growth of the ship in small time steps as follows:

∫P₁dt₁ + ∫P₂dt₂ + ∫P₃dt₃ +, …, + ∫P_ndt_n

Thus, the following expression can be used to compute relativistic energy gain by the ship in terms of t.

Egain  = Σ (0,n)    { ∫ (t_ai, t_bi) { ∫  (y₁, y₂){ ∫  (x₁,x₂){ ∫ (0,  π/2) {{{T_cmbr /{{{1/{[1 – [(v_i/C) ²]] ^1/2}}}[1 + [(v_i/C) cos θ]]}} ⁴} σ e}dθ}dx}dy} dt}      

Here,  t_ai, t_bi, and dt are the times in the background reference frame.

Note, the reason why I assume the latter three times are background reference frame times is such that for a space craft traveling at a velocity of just under 1 C, where gamma is held constant, the energy gain for the space craft will be proportional to the length of the path traveled by the space craft according to the background reference frame. The distance of space craft travel  is proportional to the time of space craft travel with respect to the background reference frame. The same is true for a space craft traveling at any velocity held constant, thus the reason for the performance of the numerical integration for each time step where the velocity is incrementally increased but held constant for each time step.

Alternatively, we can use the following series:

Egain =  Σ (1,n) { ∫ (t_ai, t_bi) {∫ {∫ (0, π/2)  {{{T_cmbr /{{1/{[1 – [(v_i/C) ²]] ^1/2}}[1 + [(v_i/C) cos θ]]}} ⁴} σ e}dθ} dA}dt}    

where t_ai and t_bi and dt are the times in the background reference frame.

Now for constant acceleration ship time, T₀ = (c/g) ln {{[[ (C²) + (V₀ ²)] ^1/2]   –   [V₀/[[1 – [(V₀/C) ²]] ^1/2 ]]} { [(C ²) + [[(g)(t)  + [V₀ /[1 – [(V₀/C) ²]] ^1/2 ] ²]] ^1/2] + [(g)(t)] +  [V₀/[[1 – [(V₀/C) ²]] ^1/2]]} / (C ²)}. We can incorporate the expression for T₀ prefaced by the notation Delta to indicate the time steps,  ship time,  of uniform duration ship frame.

For computation in terms of T₀, we obtain:

Egain = Σ (0,n)    {{ ∫  (y₁, y₂){ ∫  (x₁,x₂){ ∫ (0,  π/2) {{{T_cmbr /{{{1/{[1 – [(v_i/C) ²]] ^1/2}}}[1 + [(v_i/C) cos θ]]}} ⁴} σ e}dθ}dx}dy} {(Delta) {(c/g) ln {{[[ (C²) + (V_0i ²)] ^1/2]   –   [V_0i/[[1 – [(V_0i/C) ²]] ^1/2 ]]} { [(C ²) + [[(g_i)(t_i)  + [V_0i /[1 – [(V_0i/C) ²]] ^1/2 ] ²]] ^1/2] + [(g_i)(t_i)] +  [V₀/[[1 – [(V_0i/C) ²]] ^1/2]]} / (C ²)}}} {1/{[1 – [(v_i/C) ²]] ^1/2}}}  .     

where t_i is the time in the background reference frame and g_i is the ship acceleration in the ship’s reference frame.

Note that the above formulas provide precise calculations for many numerical iterations involving small increments for velocity increase and small time steps in the ship’s frame.

Alternatively, we can use the following series:

Egain =  Σ (1,n) { {∫ {∫ (0, π/2)  {{{T_cmbr /{{1/{[1 – [(v_i/C) ²]] ^1/2}}[1 + [(v_i/C) cos θ]]}} ⁴} σ e}dθ} dA} {(Delta) {(c/g) ln {{[[ (C²) + (V_0i ²)] ^1/2]   –   [V_0i/[[1 – [(V_0i/C) ²]] ^1/2 ]]} { [(C ²) + [[(g_i)(t_i)  + [V_0i /[1 – [(V_0i/C) ²]] ^1/2 ] ²]] ^1/2] + [(g_i)(t_i)] +  [V_0i/[[1 – [(V_0i/C) ²]] ^1/2]]} / (C ²)}}} {1/{[1 – [(v_i/C) ²]] ^1/2}}}             

Another method entails integration with respect to space craft velocity with respect to the background and integration with respect to time as follows:

E_gain = ∫ (v₁, v₂)  {{∫  (t₁, t₂) { ∫ (y₁, y₂){ ∫ (x₁,x₂){ ∫ (0,  π/2) {{{T_cmbr {1/{[1 – [(v/C) ²]] ^1/2}}[1 + [(v/C) cos θ]]} ⁴} σ e}dθ}dx}dy} dt}/v}dv

Or alternatively,

E_gain =  ∫(v₁,v₂) {∫ (t₁,t₂){∫  {∫ (0,  π/2) {{{_Tcmbr/{{{1/{[1 – [(v/C) ²]] ^1/2}}[1 + [(v/C) cos θ]]}}⁴} σ e} dθ} dA}dt}/v}dv

where t₁ and t₂ and dt are the times in the background reference frame.

Now, E_gain in practice needs to take into account the radiative temperature of the sail.

Now, given that

P_net = A σ e (T⁴ – T₀⁴)

where T is the body temperature and T₀ is the surrounding temperature, we can re-interpret T as the impinging radiation’s black body temperature and T₀ as the emitted thermal radiation black body temperature. So in other words, if the impinging temperature is 10 times higher in Kelvins then the thermal radiative temperature, the net power input into the sail is 10⁴ or 10,000 times greater than the power loss through radiative emissions.

The net power delivered to the  sail will be equal to the power intake minus the power thermally radiated as

P = {∫(y₁,y₂) {∫(x₁,x₂) {∫ (0, π/2) {{{(T_cmbr) /{γ [1 + [(v/C) cos θ]]}}⁴} σ e} dθ}dx}dy} – {∫(y₁,y₂) {∫(x₁,x₂) (T₀⁴ σ e) dx}dy}

= {∫(y₁,y₂) {∫(x₁,x₂) {∫ (0, π/2) {{{(T_cmbr) /{{1/{[1 + [(v/C)² ]] ^1/2}}  [1 + [(v/C) cos θ]]}}⁴} σ e} dθ}dx}dy}  – {∫(y₁,y₂) {∫(x₁,x₂) (T₀⁴ σ e) dx}dy}

= { ∫ {∫ (0, π/2) {{{(T_cmbr) /{{1/{[1 – [(v/C)² ]] ^1/2}}  [1 + [(v/C) cos θ]]}}⁴} σ e} dθ} dA} -

- {∫(T₀⁴ σ e) dA}

The following expression can be used to compute relativistic energy gain by the ship in consideration of the black body emissions from the sail heated by CMBR.

From computation in terms of t, we obtain:

Egain  = {Σ (0,n)   { ∫ (t_ai, t_bi) { ∫  (y₁, y₂){ ∫  (x₁,x₂){ ∫ (0,  π/2) {{{T_cmbr /{{{1/{[1 – [(v_i/C) ²]] ^1/2}}}[1 + [(v_i/C) cos θ]]}} ⁴} σ e}dθ}dx}dy} dt}}   – {Σ (0,n) {∫ (t_ai, t_bi) {∫(y₁,y₂) {∫(x₁,x₂) (T⁴_0i σ e) dx}dy}dt}}     

where t_ai and t_bi and dt are the times in the background reference frame.

Now ship time = T₀ = {(c/g_n) ln {[[ (C²) + (V₀ ²)] ^1/2]   –   [V₀/[[1 – [(V₀/C) ²]] ^1/2 ]]} { [(C ²) + [[(g_n)(t_n)  + [V₀ /[1 – [(V₀/C) ²]] ^1/2 ] ²]] ^1/2] + [(g_n)(t_n)] +  [V₀/[[1 – [(V₀/C) ²]] ^1/2]]} / (C ²)}}

Computation in terms of T₀, we obtain:

Egain  = {Σ (0,n)   {{ ∫  (y₁, y₂){ ∫  (x₁,x₂){ ∫ (0,  π/2) {{{T_cmbr /{{{1/{[1 – [(v_i/C) ²]] ^1/2}}}[1 + [(v_i/C) cos θ]]}} ⁴} σ e}dθ}dx}dy} {(Delta) {(c/g_i) ln {{[[ (C²) + (V_0i ²)] ^1/2]   –   [V_0i/[[1 – [(V_0i/C) ²]] ^1/2 ]]} { [(C ²) + [[(g_i)(t)  + [V_0i /[1 – [(V_0i/C) ²]] ^1/2 ] ²]] ^1/2] + [(g_i)(t)] +  [V_0i/[[1 – [(V_0i/C) ²]] ^1/2]]} / (C ²)}}} {1/{[1 – [(v_i/C)² ]] ^1/2}}}}    – {Σ (0,n)  {{∫(y₁,y₂) {∫(x₁,x₂) (T⁴_0i σ e) dx}dy}    {(Delta) {(c/g_i) ln {{[[ (C²) + (V_0i ²)] ^1/2]   –   [V_0i/[[1 – [(V_0i/C) ²]] ^1/2 ]]} { [(C ²) + [[(g_i)(t_i)  + [V_0i /[1 – [(V_0i/C) ²]] ^1/2 ] ²]] ^1/2] + [(g_i)(t_i)] +  [V_0i/[[1 – [(V_0i/C) ²]] ^1/2]]} / (C ²)}}} {1/{[1 – [(v_i/C)² ]] ^1/2}} }} 

where T₀ is the ship time.

Alternatively, we can use the following series calculated with  t:

Egain  =  {Σ (1,n) { ∫ (t_ai, t_bi) {∫ {∫ (0, π/2)  {{{T_cmbr /{{1/{[1 – [(v_i/C) ²]] ^1/2}}[1 + [(v_i/C) cos θ]]}} ⁴} σ e}dθ} dA}dt}}   -  {Σ (1,n) ∫ (t_ai, t_bi) {∫ (T⁴ _0i σ e) dA}dt}   

where t_ai and t_bi and dt are the times in the background reference frame.

Calculating with respect to T₀, we obtain:

Egain =  {Σ (1,n)  {∫ {∫ (0, π/2)  {{{T_cmbr /{{1/{[1 – [(v_i/C) ²]] ^1/2}}[1 + [(v_i/C) cos θ]]}} ⁴} σ e}dθ} dA}}   -  {Σ (1,n) {∫ (T⁴ _0i σ e) dA}   {(Delta) {(c/g_i) ln {{[[ (C²) + (V_0i ²)] ^1/2]   –   [V_0i/[[1 – [(V_0i/C) ²]] ^1/2 ]]} { [(C ²) + [[(g_i)(t_i)  + [V_0i /[1 – [(V_0i/C) ²]] ^1/2 ] ²]] ^1/2] + [(g_i)(t_i)] +  [V_0i/[[1 – [(V_0i/C) ²]] ^1/2]]} / (C ²)}}} {1/{[1 – [(v_i/C)² ]] ^1/2}}}.

Integrating with respect to time and velocity;

the formulas for total kinetic energy  gain are:

E_gain = {∫ (v₁, v₂)  {{∫  (t₁, t₂) { ∫ (y₁, y₂){ ∫ (x₁,x₂){ ∫ (0,  π/2) {{{T_cmbr {1/{[1 – [(v/C) ²]] ^1/2}}[1 + [(v/C) cos θ]]} ⁴} σ e}dθ}dx}dy} dt}/v}dv} -  E_{rad lost}

or alternatively,

E_gain =  {∫(v₁,v₂) {{∫ (t₁,t₂){∫  {∫ (0,  π/2) {{{_Tcmbr/{{1/{[1 – [(v/C) ²]] ^1/2}}[1 + [(v/C) cos θ]]}}⁴} σ e} dθ} dA}dt}/v}dv} -  E_{rad lost}

 

 

where t_ai and t_bi , t_i, and dt are the times in the background reference frame, g_i is the ship acceleration in the ship’s reference frame, and V_0i is the starting velocity at the beginning of each time of Delta T₀,  or ship time.

Now, the CMBR incident on the light sail from behind will generally require either a monolithic light sail of near nanometer thickness or perhaps a grid like sail with a cross-weave for which the lines or fibers are separated by less than 0.25 millimeters in order to reflect the vast majority of the incident CMBR for space craft traveling at mildly relativistic velocities. For grid like sails, the advantage of sail porosity enables much higher mass specific capture areas. Since the Doppler blue shifted light incident from directly in front of the sail or nearly so will be much shorter in wavelength than the backwardly incident light for high gamma factor sails, the forwardly incident light can largely pass through the sail openings providing a means for the backwardly incident light to push the sail efficiently forward for cases where the sail is transmissive from front to back to a suitable degree.

Now radiation pressure is equal to σT⁴/C and {2 [σT⁴/C]} for reflected radiation. However, for a space craft traveling through a black body radiation field, the apparent temperature of the radiation increases in proportion to γ and so the black body power impinging on the space craft from directly in front grows in proportion to T⁴ and thus  to γ⁴.

The temperature of a black body is T = {P/[(A)(σ)(e)]}^1/4 = {P/{(A)[5.670400(40) x 10^-8 W m^-2 K^-4]} ^1/4}. Therefore, the cosmic microwave background radiation pressure on a perfectly reflective flat bow  relativistic space craft is roughly equal to  {2 [σT_cmbr ⁴/C]} γ⁴ = {2 [σT_cmbr ⁴/C]} { {1/{1 – [(v/C)²]}^1/2}  ⁴} =   {2 [σT_cmbr ⁴/C]} {1/{1 – [(v/C)²]}²} where γ is constant and T_cmbr is constant. However, the light pressure incident from directly behind will be approximately equal to {2 [σT_cmbr ⁴/C]}/{1/{1 – [(v/C)²]}²}. In actuality, not all of the light is directly incident from the back and so there will be angular affects that result in loss of driving power. However, we will assume that all of the radiation is absorbed and then re-cycled and released as a perfect backwardly directed laser beam.

Assuming that the velocity of the sail starts out at (Zero) C, the optical pressure will be equal to {2 [σT_cmbr ⁴/C]}/γ⁴ = {2 [σT_cmbr ⁴/C]}/{ {1/{1 – [(v/C)²]}^1/2} ⁴} = {2{[5.670400(40) x 10^-8 W m^-2 K^-4][(2.725 K)⁴]/(300,000,000 m/s)}}/(1²) = 2.0844  x 10^-14 Newtons/m². For a 10,000 km by 10,000 km sail, the drive force will be 2.0844 Newtons.

Now, how are we going to deploy such a sail in a meaningful manner? The solution is obvious my dear Watson! Use a grid.

Consider that a monolithic one nanometer thick sail made of STP H₂O density carbonaceous materials would have a mass of  100,000 thousand metric tons, assuming that the space craft plus her sail had a mass of 208,440 metric tons, the craft would start out with an acceleration of F/M = a = 2.0844 N/208,440,000 kg = 10^-8 meter/s². After traveling 6 x 10¹⁵ seconds or about 200,000,000 years, the velocity of the space craft will be 0.20 C and the relativistic Lorentz transformation factor will be 1.0206 thus permitting the above Newtonian formula to apply.

For such a space craft that deployed a linear series of 1,000 tethered sails where each sail was separated by an efficient 10 sail widths, a space craft having a total mass of 208, 440,000 metric tons could be identically accelerated. The mass of the crew quarters would be 108,440,000 metric tons.

For such a space craft that deployed a linear series of 1,000,000 tethered sails where each sail was separated by an efficient 10 sail widths, a space craft having a total mass of 208, 440,000,000  metric tons could be identically accelerated. The mass of the crew quarters would be 108,440,000,000  metric tons. For cosmic journeys, this is not bad.

Some supermaterials already in laboratory existence such as carbon nanotubes can in theory be used to construct large space elevators that would extend from the surface of the Earth near the Equator to locations significantly father than geosynchronous orbit. Such tethers would perhaps have the equivalent of 0.1 G or 1m/s² acceleration based force pulling on it which would be commensurate with a cable roughly 100,000 km long accelerated at 1 m/s². Thus,  a cable that is 10¹³ km long or one light-year long could in theory withstand 10^-8 m/s² levels of acceleration. A linear series of tethered leading sails numbering 1,000,000 where each sail would have a width of 10,000 kilometers and be serially spaced a distance of 100,000 kilometers would have a length of 10¹¹ kilometers.  Thus, a series of 100 million tethered sails might conceivably pull a sail craft combination having a mass of 20,844,000,000,000 metric tons and a crew quarters having a mass of 10,844,000,000,000 metric tons.

Some high-end carbonaceous super-materials include:

1) carbon nano-tubes;
2) boron-nitride nanotubes;
3) buckyball-sheets;
4) layered sheet arrangements of graphene;
5) graphene-oxide paper;
6) fabrics composed of a weave or knit on carbon atom chains;
7) diamond fiber-based fabric;
8) carbon nitride fiber-based fabric;
9) combinations of two or more of the above, and the like material

Metalization would help in these regards.

The sails could have nanotech self-repair mechanisms. An ideal mechanism would entail sails constructed of metallic hydrogen where the hydrogen would be captured from interstellar space and incorporated into the sail membrane(s) in order to re-supply sail atoms knocked loose by interstellar atom and molecular species.

However, much higher sail velocities are anticipatable with much greater accelerations as will be covered in the next post in this series.

However, we can also deploy gridded sails. For example, consider a sail that is comprised on one nanometer wide fibers in a cross-weave where adjacent parallel  fibers are separated by 200 microns. Also consider situations where the fibers are one side reflective and one side transmissive. A sail comprised of such a material will have a mass specific capture area that is 1/100,000 that of a one nanometer thick monolithic sail.

Considering that such a sail that is gridded with the above  one nanometer thick sail fiber construction made of STP H₂O density carbonaceous materials would have a mass of  one metric ton for a sail area of 10⁸ square kilometers, assuming that the space craft plus her sail had a mass of 208,440 metric tons, the craft would start out with an acceleration of F/M = a = 2.0844 N/208,440,000 kg = 10^-8 meter/s². After traveling 6 x 10¹⁵ seconds or about 200,000,000 years, the velocity of the space craft will be 0.20 C and the relativistic Lorentz transformation factor will be 1.0206 thus permitting the above Newtonian formula to apply.

For such a space craft that deployed a linear series of 1,000 tethered sails where each sail was separated by an efficient 10 sail widths, a space craft having a total mass of 208, 440,000 metric tons could be identically accelerated. The mass of the crew quarters would be 208, 439,000 metric tons.

For such a space craft that deployed a linear series of 1,000,000 tethered sails where each sail was separated by an efficient 10 sail widths, a space craft having a total mass of 208, 440,000,000  metric tons could be identically accelerated. The mass of the crew quarters would be 208, 439,000,000 metric tons. For cosmic journeys, this is not bad.

A series of 100 million tethered sails might conceivably pull a sail craft combination having a mass of 20,844,000,000,000 metric tons and a crew quarters having a mass of 20,843,900,000,000 metric tons.

Consider again that such sails which  are gridded with the above  one nanometer thick sail fiber construction made of STP H₂O density carbonaceous materials would have a mass of  one metric ton each, assuming that the space craft plus her sail had a mass of 208,440 metric tons, the craft would start out with an acceleration of F/M = a = 2084.4 N/208,440,000 kg = 10^-5 meter/s² for cases where the craft would utilized 1,000 tethered driving sails. After traveling 6 x 10¹²  seconds or about 200,000 years, the velocity of the space craft will be 0.20 C.

Now consider a space craft having a mass of 208,440 metric tons driven by 10,000 such one metric tons sails. For such a space craft that deployed a linear series of 10,000 tethered sails where each sail was separated by an efficient 10 sail widths, the space craft having a total mass of 208, 440 metric tons would start out with an acceleration of F/M = a = 2084.4 N/208,440,000 kg = 10^-4  meter/s². After traveling 6 x 10¹¹ seconds or about 20,000 years, the velocity of the space craft will be 0.20 C.

We can consider more robust gridded sails such as those made from 10 nanometer diameter fibers spaced 200 microns apart. Each such sail would have a mass of 100 metric  tons. Thus, a space craft having a total mass of 208,440 metric tons that is driven by 1,000 such sails would too start out with an acceleration of F/M = a = 2084.4 N/208,440,000 kg = 10^-5 meter/s² and achieve a velocity of 0.20 C after 200,000 years.

Cnsider a sail that is comprised on 316.2  nanometer wide fibers in a cross-weave where adjacent parallel  fibers are separated by 200 microns. Also consider situations where the fibers are one side reflective and one side transmissive. A sail comprised of such a material will have a mass specific capture area that is equal to that of a one nanometer thick monolithic sail.

Consider that such a sail which is gridded with the above  316.2  nanometer thick sail fiber construction made of STP H₂O density carbonaceous materials would have a mass of  100,000 metric tons for a capture area of 10⁸ square kilometers. Assuming that the space craft plus her sail had a mass of 208,440 metric tons, the craft would start out with an acceleration of F/M = a = 2.0844 N/208,440,000 kg = 10^-8 meter/s². After traveling 6 x 10¹⁵ seconds or about 200,000,000 years, the velocity of the space craft will be 0.20 C and the relativistic Lorentz transformation factor will be 1.0206 thus permitting the above Newtonian formula to apply.

For such a space craft that deployed a linear series of 1,000 tethered sails where each sail was separated by an efficient 10 sail widths, a space craft having a total mass of 208, 440,000 metric tons could be identically accelerated. The mass of the crew quarters would be 208, 439,000 metric tons.

For such a space craft that deployed a linear series of 1,000,000 tethered sails where each sail was separated by an efficient 10 sail widths, a space craft having a total mass of 208, 440,000,000  metric tons could be identically accelerated. The mass of the crew quarters would be 208, 439,000,000 metric tons. For cosmic journeys, this is not bad.

A series of 100 million tethered sails might conceivably pull a sail craft combination having a mass of 20,844,000,000,000 metric tons and a crew quarters having a mass of 20,843,900,000,000 metric tons.

The background interstellar and intergalactic matter might not erode even many of highly relativistic sail of sub-micron thickness.

The diametrical cross-sectional area of our observable universe is close to 10 ⁴⁷  square kilometers and the mass of the total mass energy of the observable universe is only about 10 ⁵⁰ metric tons of which only 4 percent is baryonic.  Thus,  an average column spanning the diameter of the entire visible universe would have an H2O STP matter thickness of only 25 micrometers for reactive matter.

However,  this is not a concern for the following reasons.

First, the sails could be replaceable grid sails and driven by optical, IR, microwave or rf radiation. The mass of such sails can be reduced by many orders of magnitude relative to monolithic sails that are only micrometer scales in thickness.

Second, sails having a very thick cable or thread like construction are conceivable where the cables or wires would be many times if not several orders of magnitude thicker than 25 microns. The sails could be mostly empty space to almost entirely empty space to reflect long wave rF phased array beams.

As for concerns about over burdening the conductive or super-conductive wires or cables used for such sails by extremely intense rF beams, note that such reflective members could be very conductive to superconductive to thereby yield near perfect reflection. The EM energy that was not reflected would largely pass through the openings in the sail grid.

Second, a magnetic and/or electric field based scoop or anti-scoop could divert the chargons away from the sail just as an extended electrodynamic scoop for an interstellar ramjet would. Electro-dynamic-hydro-dynamic-plasma-drive features could utilize the diverted plasma in a reactive and gainful manner.

The sail might be deployed in a manner that is orthogonal to the ship’s velocity vector.  The sail might be parallel to the space craft velocity vector and driven obliquely from behind. This way, the effective thickness of the sail could be thousands of miles and the sail could include electro-dynamic-hydro-dynamic-plasma-drive features.

Fourth, the above parallel sail could conceivably be made of negative refraction index materials that would be pulled forward by incident star light and highly blue-shifted CMBR, far infrared, and non-CMBR radio sources.

Fifth, the sail can simply be a deployed mag-sail or M2P2 type of sail or any other magnetic or plasma bottle sail. It is possible that a plasma affixed to the space craft to be driven by rf radation, and even source based laser light upon attainment of extreme space craft gamma factors could be easily reflected by such sails. Plasma makes an excellent rF reflector even at very small densities.

I have done a lot of writing on parallel sails such as negative refraction index monolithic and grid sails capable of extreme gamma factors.

Sixth, some sail materials such as any future forms of super-strong very conductive to super-conductive metallic hydrogen can be used as nuclear fusion fuel for fusion rockets upon degradation to useless levels.

Seventh, it has been proposed that very thin,  metallic,  very low gas density containing balloons might be used for nuclear warhead decoys and which could survive 100 meter proximity detonation to a one kiloton neutron bomb in the vacuum of space. The rate of radiative cooling would be tens of billions of Kelvins per second due to the extreme thinness of the balloon membranes and most of the neutrons would pass right through the balloon without interacting or by only depositing a very small portion of the particles kinetic energy into the balloon and enclosed gas. Interstellar chargons are more reactive to electronic shell structures but not by that much.

The general idea for obliquely oriented beams involves the beamed energy incident on both sides of the sail. The sail could include a surface of hair like cilia or any other surface contour that would work so as to much more effectively grab ahold of the light.

In addition, the sail could be fabricated from photovoltaic materials in order to provide power for electro-dynamic-hydrodynamic-plasma-drives or chargon rockets, or perhaps even photon rockets.

For extreme gamma factors, the CMBR and starlight will be highly blue-shifted and will be relativistically abberated to what would approach a point source in front of the space craft at gamma = infinity. A sail parallel to the space craft velocity vector made of a suitable negative electromagnetic refraction index material will be pulled forward even by light incident on the sail at a very shallow angle from in front of the space craft.

To enhance the negative refraction index sails capture of EM energy, the sails may have negative index hairs or cilia distributed along its length.

Negative refraction index materials have actually been measured to be pulled on by incident light. Duke University and other academic and government labs are researching the various aspects of negative refraction index materials.

I have no problem with space craft being pulled forward by forward incident light. After all, the paradigm of light speed velocity limits may or may not have been shattered with any future validation or not of the CERN superluminal neutrino results. The big bang may have been the most recent free lunch. There is no reason why the big bang could not have started with miniscule quantities of mass-energy.

A good abstract for a great paper on negative super-pressure of light acting on a negative refractive index material is

Henri Lezec
(Center for Nanoscale Science and Technology, NIST)

Forty years ago, V. Veselago derived the electromagnetic properties of a hypothetical material having simultaneously-negative values of electric permittivity and magnetic permeability [1]. Such a material, denominated “left-handed”, was predicted to exhibit a negative index of refraction, as well as a number of other counter-intuitive optical properties. For example, it was hypothesized that a perfect mirror illuminated with a plane wave would experience a negative radiation pressure (pull) when immersed in a left-handed medium, as opposed to the usual positive radiation pressure experienced when facing a dielectric medium such as air or glass. Since left-handed materials are not available in nature, considerable efforts are currently under way to implement them under the form of artificial “metamaterials” — composite media with tailored bulk optical characteristics resulting from constituent structures which are smaller in both size and density than the effective wavelength in the medium. Here we show how surface-plasmon modes propagating in a stacked array of metal-insulator-metal (MIM) waveguides can be harnessed to yield a volumetric left-handed metamaterial characterized by an in-plane-isotropic negative index of refraction over a broad frequency range spanning the blue and green. By sculpting this material with a focused-ion beam we realize prisms and micro-cantilevers which we use to demonstrate, for the first time, (a) in-plane isotropic negative-refraction at optical frequencies, and (b) negative radiation pressure. We predict and experimentally verify a negative “superpressure”, the magnitude of which exceeds the photon pressure experienced by a perfect mirror by more than a factor of two. 1) V. Veselago, \textit{ Sov. Phys. Usp. }10, p.509 (1968).

Available at:

http://meetings.aps.org/Meeting/MAR09/Event/93172

The sail might not need to  be held by guy lines. A strong magnetic field based coupling or electrical charged based connection might work.

Another option is to fabricate the sail guy lines out of graphene, carbon nanotubes, boron nitride nanotubes, graphene oxide paper, and the like. A cable constructed from such materials could stretch for about 20 to 50 kilometers yet still handle tens to hundreds of Earth G’s. The tensile strength of graphene is close to 18 million PSI for perfect forms.

Materials such as solid quarkoniums and somehow stabilized neutroniums, and perhaps even Higgsiniums would be better yet, but such materials may only exist in nature in extreme mass quantity states as of the present cosmic era.

The collection area of the sail can be very, very, large. A large electro-dynamic scoop could extent very far out from the sail.

Regarding nanotech self-assembly mechanisms, just simply greatly increase the capture area of a electrodynamic scoop to collect enough interstellar materials and use most of the collected interstellar material as an EHPD, an MHPD, or a combination of the two and use the rest of the materials for sail repair.

Regarding holding M2P2 plasma affixed to the ship under high gamma factor condition, simply increase the strength of the fastening fields.

Now regarding interstellar matter density near our solar system of one particle for every 10 cm³, the density would  work out to be a layer of hydrogen or helium atoms about one atom thick for a column that is one light-year long. Not a show stopper for light sails or sails that are electro-dynamically shielded or protected.

If extreme materials are used with excellent reflectance, we could simply use a sail that has a thickness of one millimeter or more and which is monolithic, or better yet,  use a sail with grid lines that are one millimeter or perhaps much greater in thickness. This way, a sail that has an area of only one square kilometer can intercept a beam having an equivalent black body temperature of several thousand Kelvins provided it is constructed of suitably refractive materials.

We could simply use electrodynamic methods of grabbing ahold of the interstellar gas and diverting around the space craft and sail. The power to operate the electrodynamic mechanisms can be supplied by beams. The electrodynamic methods can include lasers for ionization, or rf radiation where the gamma factors are suitably large, magnetic fields, electric fields, plasma fields affixed to the space craft, and the like.

Then there is always the possibilities for sails comprised of truly exotic materials such as somehow stabilized neutroniums, quarkoniums, higgsiniums, monopoliums, and perhaps even raw space-time-mass-energy forms such as the “Yelm” of mid-20th Century big bang theory.

Since one cubic meter of neutronium would have a mass of about 10¹⁵ tons. A 1,000 kilometer long thread of the stuff that has a cross-sectional area of 1,000,000 neutrons would have a mass of only one kilogram. A 1 kilometer long thread having a cross-sectional area of 1 billion neutrons would have a mass of only 1 kilogram. Lines made of quarkoniums could have the same length and cross-section but would be 10 to 1,000 times more massive. Higgsiniums would be all the more massive.

Provided such extreme materials could be developed, they could also serve as electric current carrying magnetic sail components. Anyhow magnetic sails can be made of any ordinary conducting or superconducting period table materials.

It is also conceivable that a hybrid sail can be used where a current carrying magsail would deflect plasma away from a monolithic and grid like light sail or rf sail.

Now, regarding the subject of sail erosion by exposure to interstellar or intergalactic gas, we must realize that the kinetic energy of a gas atom traveling at a velocity of 86.7 percent of the speed of light with respect to the sail would be equal to the binding energy of roughly 10 billion atoms within a sail of micron thickness. Thus, the fact that 10 billion atoms could be dislodged should all of the energy of the gas atom be deposited within the sail. Incident gas atoms having even higher associated gamma factors with respect to the star ship sail could potentially knock loose even more atoms. Perhaps, there is no reason to worry about sail erosion in spite of this for the following reasons.

First, extremely relativistic particles would likely deposit only a small portion of its energy within the sail thereby greatly lessening the number of atoms that would be knocked loose. This fact would apply to chargons as well as neutral incident particles.

Second, for sails of near micron thickness, atoms that were knocked loose would likely simply be re-assimilated by the bulk sail materials. Perhaps the only chance for an atom to be knocked loose would include atoms located on the backward side of the sail.  Atoms for which bonds where broken within the bulk sail material would tend to simply re-bond with adjacent atoms.

Third, since the incident gas or plasma particle would deposit only a small portion of its energy within the sail, the kinetic energy per particle for particles that are knocked loose may be only slightly in excess of the binding energy of the dislodged atoms. Basically, the kinetic energy of the dislodged atoms could likely be re-absorbed and/or radiated away thereby promoting rebinding of the dislodged atoms.

Fourth, for cases where the sail would completely absorb the kinetic energy of the incident gas or plasma particles such as an alpha particle, for the case of a one micron thick sail, the sail would obviously be able to complete stop the chargon without losing it. Thus, any atoms disbonded by the incident chargon would also likely be captured and prevented from leaving the sail material.

Fifth, for grid like sails, the grid lines might be positively chargeable so that incident interstellar or intergalactic ions are pushed away from the grid lines and through the openings within the grid like sails. The effect would be similar to the Vander walls force that keeps neutral atoms from being squeezed together to tightly.

We now perform a reality check on the above formulations.

Consider the space craft at a stationary state. The CMBR appears equally bright from all directions within about 1 part in 30,000.

Now, the apparent angle, θ_s,  of CMBR pre-incident on the space craft at an angle of 90 degrees or with respect to the length of the space craft relative to the source reference frame at v = zero C will appear to be incoming at an angle, θ_o,  of 90 degrees with respect to the space craft,  ship’s reference frame.

If we consider the effects of relativistic aberration, the general formula for apparent shift in angle of incidence of the CMBR from the ship’s perspective is

Cos θ_o = {[cos θ_s] – (v/C)}/{1 – [(v/C) cos θ_s]}

Now say we desire to find the range of CMBR angles incident on the space craft with respect to the space craft reference frame for space craft velocities of 0.20 C.

Now since we are considering an angle of θ_o = π/2, cos θ_o = zero. Using the above formula, we achieve Cos θ_o = {[cos θ_s] – (v/C)}/{1 – [(v/C) cos θ_s]} = Cos π/2 = {[cos θ_s] – (0.20)}/{1 – [(0.20) cos θ_s]} = zero = {[cos θ_s] – (0.20)}/{1 – [(0.20) cos θ_s]}.

Thus, (zero) {1 – [(0.20) cos θ_s]} = {[cos θ_s] – (0.20)} = zero.

Therefore, cos θ_s = 0.20 — > θ_s  = 78.463 degrees. We will make a first order assumption that the incident CMBR from behind has a frequency of f’ = f / {γ [1 + (β cosine θ)]} = f / {1.02062 [1 + [0.2 cosine ( 0)]]} = (0.816497161) f. Thus, we will assume that θ = 0 degrees for the following 5 scenarios where we assume that the CMBR is directly incident from behind.

The radiated power received by the sail will be [(78.463)²/(90²)] f’ = [(78.463)²/(90²)] f / {γ [1 + (β cosine θ)]} = [(78.463)²/(90²)] f / {1.02062 [1 + [0.2 cosine ( 0)]]} = [(78.463)²/(90²)] (0.816497161) f =

Once again, the temperature of a black body is T = {P/[(A)(σ)(e)]}^1/4 = {P/{(A)[5.670400(40) x 10^-8 W m^-2 K^-4]} ^1/4}. The light pressure incident from directly behind will be approximately equal to [(θ_s)²/(90²)] {2 {σ {{(T_cmbr)/{γ [1 + (β cosine θ)]}}}⁴/C}} =  [(78.463)²/(90²)] {2 {[5.670400(40) x 10^-8 W m^-2 K^-4] {[(T_cmbr) (0.816497161) ]⁴}/C}} = 4.632092076  x 10^-15 Newtons/m². In actuality, not all of the light is directly incident from the back and so there will be angular affects that result in loss of driving power. However, we will assume that all of the radiation is absorbed and then re-cycled and released as a perfect backwardly directed laser beam.

Now  E_gain = ʃF^odx = ʃ(0,10²⁵) F^odx = ʃ(0,10²⁵)(10¹⁴) [4.632092076  x 10^-15 N] ^odx = 4.632092076 x 10²⁴ Joules.

Now, a 208,440 metric invariant mass space craft traveling at a starting velocity of 0.2 C has a kinetic energy of {1.02062[M C²]} – [M C²] = {1.02062[208,440,000  C²]} – [208,440,000  C²] =  1.9146 x 10²⁵ Joules – 1.87596 x 10²⁵ Joules = 3.864 x 10²³ Joules. When  4.632092076 x 10²⁴ Joules is added, the total gamma factor becomes [5.01849 x 10²⁴ Joules + 1.87596 x 10²⁵ Joules]/ [1.87596 x 10²⁵ Joules] = 1.2675. The associated space craft velocity will be equal to 0.6142 C.

Likewise doing iterated numerical approximations with v = 0.6142 C to obtain another higher velocity and then repeating the steps over and over again will give a first order approximation for space craft terminal velocity.

So we have reasonably demonstrated that CMBR sails can drive very large space arks to velocities considered fast by interstellar propulsion physicists. Typically, fast interstellar travel occurs at a better part of the speed of light.

However, a much finer scale is needed to produce results for many such steps where the computed velocity would not significantly diverge from the actual velocity obtained.

Note that here, I neglect the effects of mass based astrodynamic drag. I have come up with several mechanisms by which massive astrodynamic drag can be almost entirely eliminated and will post on this subject later this month.

 

The total kinetic energy gain for the craft will be

E _totalgain = ʃF ₁^odx₁  +  ʃF ₂^odx₂ + ʃF ₃^odx₃ + … +ʃF _n^odx_n

= {{ʃ{[(θ_s1)²/ ((90 degrees) ²)] {2 {σ {{(T_cmbr)/{γ₁ [1 + (β₁ cosine θ)]}}}⁴/C}}}^odx₁}(A)}+  {{ʃ{[(θ_s2)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{γ₂ [1 + (β₂ cosine θ)]}}}⁴/C}}} ^odx₂}(A)} + {{ʃ{[(θ_s3)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{γ₃ [1 + (β₃ cosine θ)]}}}⁴/C}}} ^odx₃}(A)} + … +{{ʃ{[(θ_sn)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{γ_n [1 + (β_n cosine θ)]}}}⁴/C}}} ^odx_n}(A)}

 

= ʃ{[(θ_s1)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{{1/{1 – [(v₁/C)²]}^1/2} [1 + (β₁ cosine θ)]}}}⁴/C}}}^odx₁  +  ʃ{[(θ_s2)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{ {1/{1 – [(v₂/C)²]}^1/2}  [1 + (β₂ cosine θ)]}}}⁴/C}}} ^odx₂ + ʃ{[(θ_s3)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{ {1/{1 – [(v₃/C)²]}^1/2}  [1 + (β₃ cosine θ)]}}}⁴/C}}} ^odx₃ + … +ʃ{[(θ_sn)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{ {1/{1 – [(v_n/C)²]}^1/2}  [1 + (β_n cosine θ)]}}}⁴/C}}} ^odx_n

 

= Σ (i = 1, i = n) ʃF _i^odx_i   = Σ (i = 1, i = n) ʃ{[(θ_si)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{γ_i [1 + (β_i cosine θ)]}}}⁴/C}}}^odx_i

=   Σ (i = 1, i = n) ʃ{[(θ_si)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{ {1/{1 – [(v_i/C)²]}^1/2}  [1 + (β_i cosine θ)]}}}⁴/C}}} ^odx_i

 

The following numerical formula offers a first order approximation of space craft gamma factor  gain;

{[E_KEtotalgain] + [M_restC²]}/[M_restC²]= {[ʃF ₁^odx₁]  +  [ʃF ₂^odx₂]  + [ʃF ₃^odx₃ ] + … + [ʃF _n^odx_n] + [M_restC²]}/[M_restC²] 

= {{{ʃ{[(θ_s1)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{γ₁ [1 + (β₁ cosine θ)]}}}⁴/C}}}^odx₁}(A)}+  {{ʃ{[(θ_s2)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{γ₂ [1 + (β₂ cosine θ)]}}}⁴/C}}} ^odx₂ }(A)}  + {{ʃ{[(θ_s3)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{γ₃ [1 + (β₃ cosine θ)]}}}⁴/C}}} ^odx₃ }(A)} + … + {{ʃ{[(θ_sn)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{γ_n [1 + (β_n cosine θ)]}}}⁴/C}}} ^odx_n}(A)}+ [M_restC²]}/[M_restC²] 

 

= {{{ʃ{[(θ_s1)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{{1/{1 – [(v₁/C)²]}^1/2} [1 + (β₁ cosine θ)]}}}⁴/C}}}^odx₁  }(A)}  +  {{ʃ{[(θ_s2)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{ {1/{1 – [(v₂/C)²]}^1/2}  [1 + (β₂ cosine θ)]}}}⁴/C}}} ^odx₂ }(A)} +   {{ʃ{[(θ_s3)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{ {1/{1 – [(v₃/C)²]}^1/2}  [1 + (β₃ cosine θ)]}}}⁴/C}}} ^odx₃ }(A)} + … +  {{ʃ{[(θ_sn)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{ {1/{1 – [(v_n/C)²]}^1/2}  [1 + (β_n cosine θ)]}}}⁴/C}}} ^odx_n}(A)}+ [M_restC²]}/[M_restC²] 

 

= {{Σ (i = 1, i = n) ʃF _i^odx_i }+ [M_restC²]}/[M_restC²]   = {{Σ (i = 1, i = n) {{ʃ{[(θ_si)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{γ_i [1 + (β_i cosine θ)]}}}⁴/C}}}^odx_i}(A)}}+ [M_restC²]}/[M_restC²] 

=   {{Σ (i = 1, i = n) ʃ{[(θ_si)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{ {1/{1 – [(v_i/C)²]}^1/2}  [1 + (β_i cosine θ)]}}}⁴/C}}} ^odx_i}+ [M_restC²]}/[M_restC²] 

Now, v = C{[-[1/γ²] + 1]^1/2} according to Special Relativity. Consequently, the following formulas can be used to compute v by numerical trial and error.

v = C{{-{1/{{[E_KEtotalgain] + [M_restC²]}/[M_restC²]}²} – 1}^1/2}  

 

=  C{{-{1/{{[ʃF ₁^odx₁]  + [ʃF ₂^odx₂]  + [ʃF ₃^odx₃ ] + ʃF _n^odx_n]} + [M_restC²]}/[M_restC²]}  ²}} + 1}^1/2}

=  C{{-{1/{{{{ʃ{[(θ_s1)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{γ₁ [1 + (β₁ cosine θ)]}}}⁴/C}}}^odx₁}(A)}+   {{ʃ{[(θ_s2)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{γ₂ [1 + (β₂ cosine θ)]}}}⁴/C}}} ^odx₂ }(A)} +  {{ʃ{[(θ_s3)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{γ₃ [1 + (β₃ cosine θ)]}}}⁴/C}}} ^odx₃ }(A)}   + … + {{ʃ{[(θ_sn)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{γ_n [1 + (β_n cosine θ)]}}}⁴/C}}} ^odx_n}(A)}+ [M_restC²]}/[M_restC²]}  ²}} + 1}^1/2}

=  C{{-{1/{{{{ʃ{[(θ_s1)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{{1/{1 – [(v₁/C)²]}^1/2} [1 + (β₁ cosine θ)]}}}⁴/C}}}^odx₁  }(A)} +  {{ʃ{[(θ_s2)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{ {1/{1 – [(v₂/C)²]}^1/2}  [1 + (β₂ cosine θ)]}}}⁴/C}}} ^odx₂ }(A)} +  {{ʃ{[(θ_s3)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{ {1/{1 – [(v₃/C)²]}^1/2}  [1 + (β₃ cosine θ)]}}}⁴/C}}} ^odx₃ }(A)} + … +  {{ʃ{[(θ_sn)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{ {1/{1 – [(v_n/C)²]}^1/2}  [1 + (β_n cosine θ)]}}}⁴/C}}} ^odx_n}(A)}+ [M_restC²]}/[M_restC²]}²}} + 1}^1/2}.   .

=  C{{-{1/{{{{Σ (i = 1, i = n) ʃF _i^odx_i }+ [M_restC²]}/[M_restC²]}   ²}} + 1}^1/2} 

=    C{{-{1/{{{{Σ (i = 1, i = n) {{ʃ{[(θ_si)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{γ_i [1 + (β_i cosine θ)]}}}⁴/C}}}^odx_i}(A)}}+ [M_restC²]}/[M_restC²]}  ²}} + 1}^1/2} 

=   C{{-{1/{{{{Σ (i = 1, i = n) {{ʃ{[(θ_si)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{ {1/{1 – [(v_i/C)²]}^1/2}  [1 + (β_i cosine θ)]}}}⁴/C}}} ^odx_i}(A)}}+ [M_restC²]}/[M_restC²]}  ²}} + 1}^1/2}

When the to two sides of the above equations are equal, we will have thus computed relativistic velocity, v.   

As you can see, for cases where there is much natural variation in acceleration with respect to the space craft frame, and for travel over very long distances, many iterations or steps need to be used in numerical algorithms to get mil spec and super-mil-spec results. Such precision is needed when traveling near light speed otherwise mission disaster could happen. In actuality, the above formulations would not be fit for mil spec computations because of the mere approximation to the actual vehicular performance.

We now consider scenarios where the photon angle of incidence from behind is considered and where drag effects are neglected for total space craft energy gains, accrued gamma factors, and accrued velocities. Here, we consider only angular values of radiation incident on the sail for which the radiation exerts forward pressure. In otherwords, we only consider values of θ₀ less than or equal to 90 degrees or π/2 radians. We also assume perfect backward sail reflectivity or trivially imperfect backward reflectivity and trivial massive astrodynamic drag.

The total kinetic energy gain for the craft will be

E _totalgain = ʃF ₁^odx₁  +  ʃF ₂^odx₂ + ʃF ₃^odx₃ + … +ʃF _n^odx_n

= {Σ(i = 1, i = n) {{{[[(θ_01i,1²) - (θ_02i,1²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,1 , θ_s2i,1)}^-1}{{[dr_bi,1/dr_ai,1]}│(r_b1i,1 , r_b2i,1)}[cos [(θ_01i,1 +  θ_02i,1)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ₁ [1 + [β₁cosine [(θ_01i,1 + θ_02i,1)/2]]]}}}⁴/C}}}^odx₁}/n}(A)}}}  

+  {Σ(i = 1, i = n) {{{[[(θ_01i,2²) - (θ_02i,2²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,2 , θ_s2i,2)}^-1}{{[dr_bi,2/dr_ai,2]}│(r_b1i,2 , r_b2i,2)}[cos [(θ_01i,2 +  θ_02i,2)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ₂ [1 + [β₂cosine [(θ_01i,2 + θ_02i,2)/2]]]}}}⁴/C}}}^odx₂}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{[[(θ_01i,3²) - (θ_02i,3²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,3 , θ_s2i,3)}^-1}{{[dr_bi,3/dr_ai,3]}│(r_b1i,3 , r_b2i,3)}[cos [(θ_01i,3 +  θ_02i,3)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ₃ [1 + [β₃cosine [(θ_01i,3 + θ_02i,3)/2]]]}}}⁴/C}}}^odx₃}/n}(A)}}} 

+ … +    {Σ(i = 1, i = n) {{{[[(θ_01i,m²) - (θ_02i,m²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,m , θ_s2i,m)}^-1}{{[dr_bi,m/dr_ai,m]}│(r_b1i,m , r_b2i,m)}[cos [(θ_01i,m +  θ_02i,m)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ_m[1 + [β₂cosine [(θ_01i,m + θ_02i,m)/2]]]}}}⁴/C}}}^odx_m}/n}(A)}}} 

= {Σ(i = 1, i = n) {{{[[(θ_01i,1²) - (θ_02i,1²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,1 , θ_s2i,1)}^-1}{{[dr_bi,1/dr_ai,1]}│(r_b1i,1 , r_b2i,1)}[cos [(θ_01i,1 +  θ_02i,1)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{{1/{1 – [(v₁/C)²]}^1/2}  [1 + [(v₁/C)cosine [(θ_01i,1 + θ_02i,1)/2]]]}}}⁴/C}}}^odx₁}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{[[(θ_01i,2²) - (θ_02i,2²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,2 , θ_s2i,2)}^-1}{{[dr_bi,2/dr_ai,2]}│(r_b1i,2 , r_b2i,2)}[cos [(θ_01i,2 +  θ_02i,2)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v₂/C)²]}^1/2}  [1 + [(v₂/C)cosine [(θ_01i,2 + θ_02i,2)/2]]]}}}⁴/C}}}^odx₂}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{[[(θ_01i,3²) - (θ_02i,3²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,3 , θ_s2i,3)}^-1}{{[dr_bi,3/dr_ai,3]}│(r_b1i,3 , r_b2i,3)}[cos [(θ_01i,3 +  θ_02i,3)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v₃/C)²]}^1/2}  [1 + [(v₃/C)cosine [(θ_01i,3 + θ_02i,3)/2]]]}}}⁴/C}}}^odx₃}/n}(A)}}} 

+ … +    {Σ(i = 1, i = n) {{{[[(θ_01i,m²) - (θ_02i,m²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,m , θ_s2i,m)}^-1}{{[dr_bi,m/dr_ai,m]}│(r_b1i,m , r_b2i,m)}[cos [(θ_01i,m +  θ_02i,m)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v_m/C)²]}^1/2} [1 + [(v_m/C)cosine [(θ_01i,m + θ_02i,m)/2]]]}}}⁴/C}}}^odx_m}/n}(A)}}} 

=  Σ(i = 1, i = m)   {Σ(i = 1, i = n) {{{[[(θ_01i,j²) - (θ_02i,j²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,j , θ_s2i,j)}^-1}{{[dr_bi,j/dr_ai,j]}│(r_b1i,j , r_b2i,j)}[cos [(θ_01i,j +  θ_02i,j)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ_j [1 + [β_jcosine [(θ_01i,j + θ_02i,j)/2]]]}}}⁴/C}}}^odx_j}/n}(A)}}} 

= Σ(i = 1, i = m)   {Σ(i = 1, i = n) {{{[[(θ_01i,j²) - (θ_02i,j²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,j , θ_s2i,j)}^-1}{{[dr_bi,j/dr_ai,j]}│(r_b1i,j , r_b2i,j)}[cos [(θ_01i,j +  θ_02i,j)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v_j/C)²]}^1/2}  [1 + [(v_j/C)cosine [(θ_01i,j + θ_02i,j)/2]]]}}}⁴/C}}}^odx_j}/n}(A)}}} 

= {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_sli,1]}}}

²} – {{cos^-1 {{[cos θ_s2i,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_s2i,1]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v₁/C)}/{1 – [(v₁/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,1 , θ_s2i,1)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v₁ /C)}/{1 – [(v₁/C) cos θ_s]}}}}│[cos  θ_s1i,1 ,  cos θ_s2i,1]}{cos {{{cos^-1 {{[cos θ_sli,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_sli,1]}}}+  {cos^-1 {{[cos θ_s2i,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_s2i,1]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ₁ {1 + {β₁cosine {{{cos^-1 {{[cos θ_sli,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_sli,1]}}}+ {cos^-1 {{[cos θ_s2i,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_s2i,1]}}}}/2}}}}}}⁴/C}}}^odx₁}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_sli,2]}}}

²} – {{cos^-1 {{[cos θ_s2i,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_s2i,2]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v₂/C)}/{1 – [(v₂/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,2 , θ_s2i,2)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v₂ /C)}/{1 – [(v₂/C) cos θ_s]}}}}│[cos  θ_s1i,2 ,  cos θ_s2i,2]}{cos {{{cos^-1 {{[cos θ_sli,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_sli,2]}}}+  {cos^-1 {{[cos θ_s2i,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_s2i,2]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ₂ {1 + {β₂cosine {{{cos^-1 {{[cos θ_sli,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_sli,2]}}}+ {cos^-1 {{[cos θ_s2i,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_s2i,2]}}}}/2}}}}}}⁴/C}}}^odx₂}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_sli,3]}}}

²} – {{cos^-1 {{[cos θ_s2i,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_s2i,3]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v₃/C)}/{1 – [(v₃/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,3 , θ_s2i,3)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v₃ /C)}/{1 – [(v₃/C) cos θ_s]}}}}│[cos  θ_s1i,3 ,  cos θ_s2i,3]}{cos {{{cos^-1 {{[cos θ_sli,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_sli,3]}}}+  {cos^-1 {{[cos θ_s2i,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_s2i,3]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ₃ {1 + {β₃cosine {{{cos^-1 {{[cos θ_sli,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_sli,3]}}}+ {cos^-1 {{[cos θ_s2i,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_s2i,3]}}}}/2}}}}}}⁴/C}}}^odx₃}/n}(A)}}} 

+ … +   {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_sli,m]}}}

²} – {{cos^-1 {{[cos θ_s2i,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_s2i,m]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v_m/C)}/{1 – [(v_m/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,m , θ_s2i,m)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v_m /C)}/{1 – [(v_m/C) cos θ_s]}}}}│[cos  θ_s1i,m ,  cos θ_s2i,m]}{cos {{{cos^-1 {{[cos θ_sli,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_sli,m]}}}+  {cos^-1 {{[cos θ_s2i,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_s2i,m]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ_m {1 + {β_mcosine {{{cos^-1 {{[cos θ_sli,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_sli,m]}}}+ {cos^-1 {{[cos θ_s2i,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_s2i,m]}}}}/2}}}}}}⁴/C}}}^odx_m}/n}(A)}}} 

= {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_sli,1]}}}

²} – {{cos^-1 {{[cos θ_s2i,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_s2i,1]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v₁/C)}/{1 – [(v₁/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,1 , θ_s2i,1)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v₁ /C)}/{1 – [(v₁/C) cos θ_s]}}}}│[cos  θ_s1i,1 ,  cos θ_s2i,1]}{cos {{{cos^-1 {{[cos θ_sli,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_sli,1]}}}+  {cos^-1 {{[cos θ_s2i,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_s2i,1]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v₁/C)²]}^1/2}   {1 + {(v₁/C)cosine {{{cos^-1 {{[cos θ_sli,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_sli,1]}}}+ {cos^-1 {{[cos θ_s2i,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_s2i,1]}}}}/2}}}}}}⁴/C}}}^odx₁}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_sli,2]}}}

²} – {{cos^-1 {{[cos θ_s2i,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_s2i,2]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v₂/C)}/{1 – [(v₂/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,2 , θ_s2i,2)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v₂ /C)}/{1 – [(v₂/C) cos θ_s]}}}}│[cos  θ_s1i,2 ,  cos θ_s2i,2]}{cos {{{cos^-1 {{[cos θ_sli,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_sli,2]}}}+  {cos^-1 {{[cos θ_s2i,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_s2i,2]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v₂/C)²]}^1/2}   {1 + {(v₂/C)cosine {{{cos^-1 {{[cos θ_sli,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_sli,2]}}}+ {cos^-1 {{[cos θ_s2i,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_s2i,2]}}}}/2}}}}}}⁴/C}}}^odx₂}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_sli,3]}}}

²} – {{cos^-1 {{[cos θ_s2i,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_s2i,3]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v₃/C)}/{1 – [(v₃/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,3 , θ_s2i,3)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v₃ /C)}/{1 – [(v₃/C) cos θ_s]}}}}│[cos  θ_s1i,3 ,  cos θ_s2i,3]}{cos {{{cos^-1 {{[cos θ_sli,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_sli,3]}}}+  {cos^-1 {{[cos θ_s2i,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_s2i,3]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v₃/C)²]}^1/2}   {1 + {(v₃/C)cosine {{{cos^-1 {{[cos θ_sli,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_sli,3]}}}+ {cos^-1 {{[cos θ_s2i,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_s2i,3]}}}}/2}}}}}}⁴/C}}}^odx₃}/n}(A)}}} 

+ … +   {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_sli,m]}}}

²} – {{cos^-1 {{[cos θ_s2i,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_s2i,m]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v_m/C)}/{1 – [(v_m/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,m , θ_s2i,m)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v_m /C)}/{1 – [(v_m/C) cos θ_s]}}}}│[cos  θ_s1i,m ,  cos θ_s2i,m]}{cos {{{cos^-1 {{[cos θ_sli,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_sli,m]}}}+  {cos^-1 {{[cos θ_s2i,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_s2i,m]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v_m/C)²]}^1/2}   {1 + {(v_m/C)cosine {{{cos^-1 {{[cos θ_sli,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_sli,m]}}}+ {cos^-1 {{[cos θ_s2i,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_s2i,m]}}}}/2}}}}}}⁴/C}}}^odx_m}/n}(A)}}} 

Σ ( j= 1, j = m) {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}

²} – {{cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v_j/C)}/{1 – [(v_j/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,j , θ_s2i,j)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v_j /C)}/{1 – [(v_j/C) cos θ_s]}}}}│[cos  θ_s1i,j ,  cos θ_s2i,j]}{cos {{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}+  {cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ_j {1 + {β_jcosine {{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}+ {cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}}/2}}}}}}⁴/C}}}^odx_j}/n}(A)}}} 

= Σ ( j= 1, j = m) {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}

²} – {{cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v_j/C)}/{1 – [(v_j/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,j , θ_s2i,j)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v_j /C)}/{1 – [(v_j/C) cos θ_s]}}}}│[cos  θ_s1i,j ,  cos θ_s2i,j]}{cos {{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}+  {cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v_j/C)²]}^1/2}   {1 + {(v_j/C)cosine {{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}+ {cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}}/2}}}}}}⁴/C}}}^odx_j}/n}(A)}}} 

 

 

The following numerical formula offers a first order approximation of space craft gamma factor  gain;

{[E_KEtotalgain] + [M_restC²]}/[M_restC²]= {[ʃF ₁^odx₁]  +  [ʃF ₂^odx₂]  + [ʃF ₃^odx₃ ] + … + [ʃF _n^odx_n] + [M_restC²]}/[M_restC²] 

 

 

= {{{Σ(i = 1, i = n) {{{[[(θ_01i,1²) - (θ_02i,1²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,1 , θ_s2i,1)}^-1}{{[dr_bi,1/dr_ai,1]}│(r_b1i,1 , r_b2i,1)}[cos [(θ_01i,1 +  θ_02i,1)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ₁ [1 + [β₁cosine [(θ_01i,1 + θ_02i,1)/2]]]}}}⁴/C}}}^odx₁}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{[[(θ_01i,2²) - (θ_02i,2²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,2 , θ_s2i,2)}^-1}{{[dr_bi,2/dr_ai,2]}│(r_b1i,2 , r_b2i,2)}[cos [(θ_01i,2 +  θ_02i,2)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ₂ [1 + [β₂cosine [(θ_01i,2 + θ_02i,2)/2]]]}}}⁴/C}}}^odx₂}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{[[(θ_01i,3²) - (θ_02i,3²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,3 , θ_s2i,3)}^-1}{{[dr_bi,3/dr_ai,3]}│(r_b1i,3 , r_b2i,3)}[cos [(θ_01i,3 +  θ_02i,3)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ₃ [1 + [β₃cosine [(θ_01i,3 + θ_02i,3)/2]]]}}}⁴/C}}}^odx₃}/n}(A)}}} 

+ … +    {Σ(i = 1, i = n) {{{[[(θ_01i,m²) - (θ_02i,m²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,m , θ_s2i,m)}^-1}{{[dr_bi,m/dr_ai,m]}│(r_b1i,m , r_b2i,m)}[cos [(θ_01i,m +  θ_02i,m)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ_m[1 + [β₂cosine [(θ_01i,m + θ_02i,m)/2]]]}}}⁴/C}}}^odx_m}/n}(A)}}}}  + [M_restC²]}/[M_restC²] 

= {{{Σ(i = 1, i = n) {{{[[(θ_01i,1²) - (θ_02i,1²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,1 , θ_s2i,1)}^-1}{{[dr_bi,1/dr_ai,1]}│(r_b1i,1 , r_b2i,1)}[cos [(θ_01i,1 +  θ_02i,1)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{{1/{1 – [(v₁/C)²]}^1/2}  [1 + [(v₁/C)cosine [(θ_01i,1 + θ_02i,1)/2]]]}}}⁴/C}}}^odx₁}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{[[(θ_01i,2²) - (θ_02i,2²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,2 , θ_s2i,2)}^-1}{{[dr_bi,2/dr_ai,2]}│(r_b1i,2 , r_b2i,2)}[cos [(θ_01i,2 +  θ_02i,2)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v₂/C)²]}^1/2}  [1 + [(v₂/C)cosine [(θ_01i,2 + θ_02i,2)/2]]]}}}⁴/C}}}^odx₂}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{[[(θ_01i,3²) - (θ_02i,3²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,3 , θ_s2i,3)}^-1}{{[dr_bi,3/dr_ai,3]}│(r_b1i,3 , r_b2i,3)}[cos [(θ_01i,3 +  θ_02i,3)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v₃/C)²]}^1/2}  [1 + [(v₃/C)cosine [(θ_01i,3 + θ_02i,3)/2]]]}}}⁴/C}}}^odx₃}/n}(A)}}} 

+ … +    {Σ(i = 1, i = n) {{{[[(θ_01i,m²) - (θ_02i,m²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,m , θ_s2i,m)}^-1}{{[dr_bi,m/dr_ai,m]}│(r_b1i,m , r_b2i,m)}[cos [(θ_01i,m +  θ_02i,m)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v_m/C)²]}^1/2} [1 + [(v_m/C)cosine [(θ_01i,m + θ_02i,m)/2]]]}}}⁴/C}}}^odx_m}/n}(A)}}}}  + [M_restC²]}/[M_restC²] 

 

 

=  {{Σ(i = 1, i = m)   {Σ(i = 1, i = n) {{{[[(θ_01i,j²) - (θ_02i,j²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,j , θ_s2i,j)}^-1}{{[dr_bi,j/dr_ai,j]}│(r_b1i,j , r_b2i,j)}[cos [(θ_01i,j +  θ_02i,j)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ_j [1 + [β_jcosine [(θ_01i,j + θ_02i,j)/2]]]}}}⁴/C}}}^odx_j}/n}(A)}}}}  + [M_restC²]}/[M_restC²] 

= {{Σ(i = 1, i = m)   {Σ(i = 1, i = n) {{{[[(θ_01i,j²) - (θ_02i,j²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,j , θ_s2i,j)}^-1}{{[dr_bi,j/dr_ai,j]}│(r_b1i,j , r_b2i,j)}[cos [(θ_01i,j +  θ_02i,j)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v_j/C)²]}^1/2}  [1 + [(v_j/C)cosine [(θ_01i,j + θ_02i,j)/2]]]}}}⁴/C}}}^odx_j}/n}(A)}}} + [M_restC²]}/[M_restC²]   

 

 

 

 

= {{{Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_sli,1]}}}

²} – {{cos^-1 {{[cos θ_s2i,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_s2i,1]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v₁/C)}/{1 – [(v₁/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,1 , θ_s2i,1)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v₁ /C)}/{1 – [(v₁/C) cos θ_s]}}}}│[cos  θ_s1i,1 ,  cos θ_s2i,1]}{cos {{{cos^-1 {{[cos θ_sli,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_sli,1]}}}+  {cos^-1 {{[cos θ_s2i,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_s2i,1]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ₁ {1 + {β₁cosine {{{cos^-1 {{[cos θ_sli,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_sli,1]}}}+ {cos^-1 {{[cos θ_s2i,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_s2i,1]}}}}/2}}}}}}⁴/C}}}^odx₁}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_sli,2]}}}

²} – {{cos^-1 {{[cos θ_s2i,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_s2i,2]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v₂/C)}/{1 – [(v₂/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,2 , θ_s2i,2)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v₂ /C)}/{1 – [(v₂/C) cos θ_s]}}}}│[cos  θ_s1i,2 ,  cos θ_s2i,2]}{cos {{{cos^-1 {{[cos θ_sli,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_sli,2]}}}+  {cos^-1 {{[cos θ_s2i,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_s2i,2]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ₂ {1 + {β₂cosine {{{cos^-1 {{[cos θ_sli,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_sli,2]}}}+ {cos^-1 {{[cos θ_s2i,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_s2i,2]}}}}/2}}}}}}⁴/C}}}^odx₂}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_sli,3]}}}

²} – {{cos^-1 {{[cos θ_s2i,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_s2i,3]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v₃/C)}/{1 – [(v₃/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,3 , θ_s2i,3)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v₃ /C)}/{1 – [(v₃/C) cos θ_s]}}}}│[cos  θ_s1i,3 ,  cos θ_s2i,3]}{cos {{{cos^-1 {{[cos θ_sli,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_sli,3]}}}+  {cos^-1 {{[cos θ_s2i,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_s2i,3]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ₃ {1 + {β₃cosine {{{cos^-1 {{[cos θ_sli,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_sli,3]}}}+ {cos^-1 {{[cos θ_s2i,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_s2i,3]}}}}/2}}}}}}⁴/C}}}^odx₃}/n}(A)}}} 

+ … +   {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_sli,m]}}}

²} – {{cos^-1 {{[cos θ_s2i,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_s2i,m]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v_m/C)}/{1 – [(v_m/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,m , θ_s2i,m)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v_m /C)}/{1 – [(v_m/C) cos θ_s]}}}}│[cos  θ_s1i,m ,  cos θ_s2i,m]}{cos {{{cos^-1 {{[cos θ_sli,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_sli,m]}}}+  {cos^-1 {{[cos θ_s2i,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_s2i,m]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ_m {1 + {β_mcosine {{{cos^-1 {{[cos θ_sli,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_sli,m]}}}+ {cos^-1 {{[cos θ_s2i,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_s2i,m]}}}}/2}}}}}}⁴/C}}}^odx_m}/n}(A)}}}} + [M_restC²]}/[M_restC²]   

= {{{Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_sli,1]}}}

²} – {{cos^-1 {{[cos θ_s2i,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_s2i,1]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v₁/C)}/{1 – [(v₁/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,1 , θ_s2i,1)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v₁ /C)}/{1 – [(v₁/C) cos θ_s]}}}}│[cos  θ_s1i,1 ,  cos θ_s2i,1]}{cos {{{cos^-1 {{[cos θ_sli,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_sli,1]}}}+  {cos^-1 {{[cos θ_s2i,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_s2i,1]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v₁/C)²]}^1/2}   {1 + {(v₁/C)cosine {{{cos^-1 {{[cos θ_sli,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_sli,1]}}}+ {cos^-1 {{[cos θ_s2i,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_s2i,1]}}}}/2}}}}}}⁴/C}}}^odx₁}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_sli,2]}}}

²} – {{cos^-1 {{[cos θ_s2i,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_s2i,2]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v₂/C)}/{1 – [(v₂/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,2 , θ_s2i,2)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v₂ /C)}/{1 – [(v₂/C) cos θ_s]}}}}│[cos  θ_s1i,2 ,  cos θ_s2i,2]}{cos {{{cos^-1 {{[cos θ_sli,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_sli,2]}}}+  {cos^-1 {{[cos θ_s2i,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_s2i,2]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v₂/C)²]}^1/2}   {1 + {(v₂/C)cosine {{{cos^-1 {{[cos θ_sli,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_sli,2]}}}+ {cos^-1 {{[cos θ_s2i,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_s2i,2]}}}}/2}}}}}}⁴/C}}}^odx₂}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_sli,3]}}}

²} – {{cos^-1 {{[cos θ_s2i,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_s2i,3]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v₃/C)}/{1 – [(v₃/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,3 , θ_s2i,3)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v₃ /C)}/{1 – [(v₃/C) cos θ_s]}}}}│[cos  θ_s1i,3 ,  cos θ_s2i,3]}{cos {{{cos^-1 {{[cos θ_sli,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_sli,3]}}}+  {cos^-1 {{[cos θ_s2i,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_s2i,3]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v₃/C)²]}^1/2}   {1 + {(v₃/C)cosine {{{cos^-1 {{[cos θ_sli,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_sli,3]}}}+ {cos^-1 {{[cos θ_s2i,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_s2i,3]}}}}/2}}}}}}⁴/C}}}^odx₃}/n}(A)}}} 

+ … +   {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_sli,m]}}}

²} – {{cos^-1 {{[cos θ_s2i,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_s2i,m]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v_m/C)}/{1 – [(v_m/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,m , θ_s2i,m)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v_m /C)}/{1 – [(v_m/C) cos θ_s]}}}}│[cos  θ_s1i,m ,  cos θ_s2i,m]}{cos {{{cos^-1 {{[cos θ_sli,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_sli,m]}}}+  {cos^-1 {{[cos θ_s2i,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_s2i,m]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v_m/C)²]}^1/2}   {1 + {(v_m/C)cosine {{{cos^-1 {{[cos θ_sli,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_sli,m]}}}+ {cos^-1 {{[cos θ_s2i,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_s2i,m]}}}}/2}}}}}}⁴/C}}}^odx_m}/n}(A)}}}}  [M_restC²]}/[M_restC²]   

 

 

 

 

{{Σ ( j= 1, j = m) {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}

²} – {{cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v_j/C)}/{1 – [(v_j/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,j , θ_s2i,j)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v_j /C)}/{1 – [(v_j/C) cos θ_s]}}}}│[cos  θ_s1i,j ,  cos θ_s2i,j]}{cos {{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}+  {cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ_j {1 + {β_jcosine {{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}+ {cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}}/2}}}}}}⁴/C}}}^odx_j}/n}(A)}}}} + [M_restC²]}/[M_restC²]     

= {{Σ ( j= 1, j = m) {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}

²} – {{cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v_j/C)}/{1 – [(v_j/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,j , θ_s2i,j)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v_j /C)}/{1 – [(v_j/C) cos θ_s]}}}}│[cos  θ_s1i,j ,  cos θ_s2i,j]}{cos {{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}+  {cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v_j/C)²]}^1/2}   {1 + {(v_j/C)cosine {{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}+ {cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}}/2}}}}}}⁴/C}}}^odx_j}/n}(A)}}}} + [M_restC²]}/[M_restC²]    

For total accrued velocity, v, we have

 

v = C{{-{1/{{{Σ(i = 1, i = m)   {Σ(i = 1, i = n) {{{[[(θ_01i,j²) - (θ_02i,j²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,j , θ_s2i,j)}^-1}{{[dr_bi,j/dr_ai,j]}│(r_b1i,j , r_b2i,j)}[cos [(θ_01i,j +  θ_02i,j)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ_j [1 + [β_jcosine [(θ_01i,j + θ_02i,j)/2]]]}}}⁴/C}}}^odx_j}/n}(A)}}}}  + [M_restC²]}/[M_restC²]}  ²}} + 1}^1/2}

= C{{-{1/{{{Σ(i = 1, i = m)   {Σ(i = 1, i = n) {{{[[(θ_01i,j²) - (θ_02i,j²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,j , θ_s2i,j)}^-1}{{[dr_bi,j/dr_ai,j]}│(r_b1i,j , r_b2i,j)}[cos [(θ_01i,j +  θ_02i,j)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v_j/C)²]}^1/2}  [1 + [(v_j/C)cosine [(θ_01i,j + θ_02i,j)/2]]]}}}⁴/C}}}^odx_j}/n}(A)}}} + [M_restC²]}/[M_restC²]} ²}} + 1}^1/2}

= C{{-{1/{{{Σ ( j= 1, j = m) {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}

²} – {{cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v_j/C)}/{1 – [(v_j/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,j , θ_s2i,j)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v_j /C)}/{1 – [(v_j/C) cos θ_s]}}}}│[cos  θ_s1i,j ,  cos θ_s2i,j]}{cos {{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}+  {cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ_j {1 + {β_jcosine {{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}+ {cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}}/2}}}}}}⁴/C}}}^odx_j}/n}(A)}}}} + [M_restC²]}/[M_restC²]}     

²}} + 1}^1/2}

= C{{-{1/{{{Σ ( j= 1, j = m) {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}

²} – {{cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v_j/C)}/{1 – [(v_j/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,j , θ_s2i,j)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v_j /C)}/{1 – [(v_j/C) cos θ_s]}}}}│[cos  θ_s1i,j ,  cos θ_s2i,j]}{cos {{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}+  {cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v_j/C)²]}^1/2}   {1 + {(v_j/C)cosine {{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}+ {cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}}/2}}}}}}⁴/C}}}^odx_j}/n}(A)}}}} + [M_restC²]}/[M_restC²]  ²}} + 1}^1/2}

As you can see, attempts at analytic solutions and even non-computational numerical solutions would pose a proverbial night-mare.

Now consider again that radiation pressure is equal to σT⁴/C and {2 [σT⁴/C]} for reflected radiation. However, for a space craft traveling through a black body radiation field, the apparent temperature of the radiation increases in proportion to γ and so the black body power impinging on the space craft from directly in front grows in proportion to T⁴ and thus  to γ⁴.

The temperature of a black body is T = {P/[(A)(σ)(e)]}^1/4 = {P/{(A)[5.670400(40) x 10^-8 W m^-2 K^-4]} ^1/4}. Therefore, the cosmic microwave background radiation pressure on a perfectly reflective flat bow  relativistic space craft is approximately equal to  {2 [σT_cmbr ⁴/C]} γ⁴ = {2 [σT_cmbr ⁴/C]} { {1/{1 – [(v/C)²]}^1/2}  ⁴} =   {2 [σT_cmbr ⁴/C]} {1/{1 – [(v/C)²]}²} where γ is constant and T_cmbr is constant. However, the light pressure incident from directly behind will be approximately equal to {2 [σT_cmbr ⁴/C]}/{1/{1 – [(v/C)²]}²}. In actuality, not all of the light is directly incident from the back and so there will be angular affects that result in loss of driving power. However, we will assume that all of the radiation is absorbed and then re-cycled and released as a perfect backwardly directed laser beam. We will assume that CMBR light which is forwardly incident completely passes through the sail.

Assuming that the velocity of the sail starts out at (Zero) C, the optical pressure will be equal to {{2 [σT_cmbr⁴/C]}/γ⁴} = {{2 [σT_cmbr⁴/C]}/ { {1/{1 – [(v/C)²]}^1/2} ⁴} } = {{2{[5.670400(40) x 10^-8 W m^-2 K^-4][(2.725 K)⁴]/(300,000,000 m/s)}}/(1²)} = [2.0844355 x 10^-14] Newtons/m². For a 10,000 km by 10,000 km sail, the drive force will be 2.0844 Newtons. A 100,000 km by 100,000 km sail will produce a driving force of 208.44 Newtons.

Now assume that the sail is monolithic, made of one nanometer thick carbonaceous, STP water density materials. The sail would have a mass of 10,000,000 thousand metric tons. Assuming that the space craft plus her sail had a mass of 20,844,000 metric tons, the craft would start out with an acceleration of F/M = a = 208.44 N/20,844,000,000 kg = 10^-8 meter/s². After traveling 6 x 10¹⁵ seconds or about 200,000,000 years, the velocity of the space craft will be 0.20 C and the relativistic Lorentz transformation factor will be 1.0206 thus permitting the above Newtonian formula to apply as a reasonable approximation.

Assume that the background gas and dust that contacts the sail over a path length of 1 light year has an invariant  mass of (0.06667 kg)( 10¹⁴){[ 3 x 10¹⁰]^-1} = 222.2 kg. The momentum of the gas and dust with respect to the sail will be (m)(v) = (222.2 kg)(50,000,000 m/s) =1.111 x 10¹⁰  kg m s. Now Force equal dP/dt. Therefore, the force on the sail is on average equal to F_0.05C  = dP_0.2C/dt = 71.677 Newtons.. For a velocity of 0.02 C, the net propulsive force is 208.44 N – 71.67 N = 136.76 N which will still obviously permit 0.2 C velocities.

For such a space craft that deployed a linear series of 1,000 tethered sails where each sail was separated by an efficient 10 sail widths, a space craft having a total mass of 208, 440,000 metric tons could be identically accelerated. The mass of the crew quarters would be 108,440,000 metric tons. For such a space craft that deployed a linear series of 1,000,000 tethered sails where each sail was separated by an efficient 10 sail widths, a space craft having a total mass of 208, 440,000,000  metric tons could be identically accelerated. The mass of the crew quarters would be 108,440,000,000  metric tons. For cosmic journeys, this is not bad. A series of 100 million tethered sails might conceivably pull a sail craft combination having a mass of 20,844,000,000,000 metric tons and a crew quarters having a mass of 10,844,000,000,000 metric tons. For a velocity of 0.2 C, the each of the latter massed space craft would have the same ratio of backward driving force and massive drag force. The caveat is simply the deployment of commensurate numbers of sails simultaneously in a spatial series along the space craft velocity vector.

Now assume that the sail is a gridded fabric or net made of STP water density conducting 0.4 nanometer wide, one nanometer thick,  carbonaceous fibers that are separated by 0.0005 meters such as in a judicious cross weave spacing. A one square meter portion of the net will have a mass of 0.8 x 10^-12 kilograms. A 0.08 kilogram sail will have a plan-form area of 10⁵ square kilometers. A 8,000 kilogram sail will have a plan-form area of 10¹⁰ square kilometers and will have an acceleration of F/M = A = 208.44 Newtons/8,000 kg = 0.026055 m/s².  A space craft having a total mass of  8,000 metric tons will have an initial acceleration of 0.000026055 m/s².   In 80,000 years, the velocity of the 8,000 metric ton  system will be about 0.215388 C assuming Newtonian approximations.

Now, the 10¹⁰ square kilometer plan-form area gridded sail will have a massive species contact area of [10¹⁰km²]/1,250,000 = 8,000 km². So the background gas and dust that contacts the sail over a path length of 1 light year would have an invariant  mass of (0.06667 kg)( 10¹⁴){[ 3 x 10¹⁰]^-1}/(1,250,000) = 0.00017776 kg. The momentum of the gas and dust with respect to the sail will be (m)(v) = (0.00017776 kg)(50,000,000 m/s) =8,888 kg m/s. Now Force equal dP/dt. Therefore, the force on the sail is on average equal to F_0.2C  = dP_0.2C/dt = 0.000057341Newtons.. For a velocity of 0.2 C, the ratio of the driving force to massive drag force is [208.44 N/ 0.000057341 N] = 3,635,095.

 

The last result in the above paragraph is intreguing because it suggest that an ordinary CMBR sail-material configuration  could gainfully accelerate even in an environment such as local interstellar space where the baryonic mass density may be as much as one million times that of the observable universe on average.

Now, the apparent angle, θ_s,  of CMBR pre-incident on the space craft at an angle of 90 degrees or with respect to the length of the space craft relative to the source reference frame at v = zero C will appear to be incoming at an angle, θ_o,  of 90 degrees with respect to the space craft,  ship’s reference frame.

If we consider the effects of relativistic aberration, the general formula for apparent shift in angle of incidence of the CMBR from the ship’s perspective is

Cos θ_o = {[cos θ_s] – (v/C)}/{1 – [(v/C) cos θ_s]}. Now assume θ_s = 14.48 degrees, and a gamma factor of 3, Cos θ_o = {[cos (19.47 degrees)] – (0.942809)}/{1 – [(0.942809) cos (19.47 degrees)]}~ 0 — > θ_o = 90 degrees. Now (14.48²)/(90²) => (0.0468)/(4.5⁴) = 0.000114128. Now the grid would need to expand in area by a factor of 0.000114128^-1 = 8,762.

The grid line spacing can be increased by a factor of 3 thus yielding an increase in grid area by a factor of essentially 2. I obtained the areal expansion factor of 2 by inspection of hand-drawn grids although I am certain topologists and geometers have long since figured out the general relationships for various factors of line distance expansion for square gridded figures. However, we still need to increase the grid area by another factor of 4,381. Simply deploying  4,381 + 1 expanded sails = 4,382 expanded sails each having a mass of 8,000 kilograms will produce a complete sail rigging having a mass of 35,056 metric tons. Include a tether sub-rigging to link the sails in a serial distribution along with the rest of the mass of the space craft to yield a total craft mass of 200,000 metric tons and we obtain a forward oriented driving force still equal to 208.44 N. So the background gas and dust that contacts the fully deployed rigging at a gamma factor of 3 over a path length of 1 light year has an invariant  mass of {(0.06667 kg)( 10¹⁴){[ 3 x 10¹⁰]^-1}/(1,250,000)} (4,382)   = [0.00017776  kg](4,382) =  0.778944 kg.

Now,  the formula for relativistic momentum of a massive particle  is M₀ v γ = M₀ v /{{1 – [(v/C)²]}^1/2}. However, the number of interstellar or intergalactic massive particles impinging on a relativistic space craft per unit of time, ship’s frame, t,  is proportional  to (γ)v = {1/{{1 – [(v/C)²]}^1/2}v. Now, dP/dt = F which is is expressed in Newtons. Therefore, the force acting on a space craft, ship’s frame,  from the interstellar massive background is equal to d[(M₀ v γ) (γ)(v/C)ǀ]/dt = d{{M₀ v /{{1 – [(v/C)²]}^1/2}} {1/{{1 – [(v/C)²]}^1/2}}v}/dt where M₀ is the incident mass over the  the constant distance interval of (Delta x) background reference frame. The drag energy is thus equal to {d[(M₀ v γ) (γ)(v/C)]/dt} (Delta x) = {d{{M₀ v /{{1 – [(v/C)²]}^1/2}} {1/{{1 – [(v/C)²]}^1/2}}v/C}/dt} (Delta x) where t is the ship time.  The quantity γv/C = {1/{{1 – [(v/C)²]}^1/2}}v/C is considered dimensionless and is of a constant scalar form.

The momentum of the 0.778944 kg invariant mass with respect to the space craft will be M₀ v γ = M₀ v /{{1 – [(v/C)²]}^1/2} = (0.778944 kg)(282,842,700 m/s)(3) = 6.60956  x 10⁸  kg m/s. The force acting on the space craft will be d[(M₀ v γ) (γ)(v/C)ǀ]/dt = d{{M₀ v /{{1 – [(v/C)²]}^1/2}} {1/{{1 – [(v/C)²]}^1/2}}v}/dt = {[(0.778944 kg  (282,842,700 m/s)(3) (3)[( 282,842,700 m/s) /(300,000,000 m/s)]}/{(31,000,000 s)/[(3)/(0.942816)]} = 191.889 Newtons. The net driving force would be 208.44 N – 191.889 N = 16.551 N.

Thus, it is safe to say that our space craft could accelerate to a velocity of 0.942816 C or to a gamma factor of 3  and still maintain a gainfull driving force. Now KE = ʃ F∙ dx = F(cos α)(Δx) = F(cos 0)(Δx) = (F)(Δx) for parallel force and velocity vectors. Assuming a driving force of 16.551 Newtons during the entire trip to a gamma factor of 3, we will further assume that (F)(Δx) = [3 MC² – MC²] = 2MC² = (2)(200,000,000 kg)[(300,000,000 m/s)²]  =  3.6 x 10²⁵  joules. Dividing the energy by F yields x = distance travelled = [3.6 x 10²⁵J]/(16.551 N) = 2.175 x 10²⁴ meters = 217,510,000 light years.

Now,  a high end carbonaceous super-material having a cross sectional area of 1.3708 x 10^-9 square meters can support 208.44 Newtons assuming a yield strength of 10⁷ kilograms per square inch. A cable having such a cross-section and having a mass of 10,000 metric tons would plausibly have a length of (10,000)[1.3708 x 10^-9] meters or 1.3708 x 10¹³  meters or 1.3708 x 10¹⁰ kilometers. However, a cable with a cross-sectional area 1,000 times as great having the same length would have a mass of 10,000,000 metric tons and could conceivably tether 1,000 of  the previously described 20,000 kilogram gridded sails each having a plan form area of 10¹⁰ square kilometers and each producing a driving force of  208.44 Newtons.  Such a tethered sail system could propel a space craft having a total mass of 20 million metric tons, of which 10,020,000 metric tons would exist as the sail rigging. Each sail would be linearly separated by 1.3708 x 10⁷ kilometers. A cable having a cross-sectional area that is ten time greater yet could power a space craft having a total mass of 200 million metric tons of which 100,200,000 metric tons would be incorporated into the sail rigging.For the latter example, the sails would be separated by 1.3708 x 10⁶ kilomters thus preventing all but trivial shadowing of the driving CMBR at velocities of 0.2 C and only moderate shadowing at a gamma factor of 3.

The value of gamma = 3 is close to the maximum value conceivable with purely backward impinging, CMBR driven planar or plane-like sails, that are oriented orthogonally to the space craft velocity vector where the sails are made of ordinary atomic elements based materials and are of gridded forms for  the next billion years or so. This is because the baryonic mass density of the observable universe will very only slightly over this time period thus at best promoting a slight decrease in drag for the above systems at a gamma factor of 3.  Significantly higher gamma factors with self repairing grids are possible for universal ages that several or more times that of the present universe due to intergalactic massive rareification.

In order to compute a gamma factor of 3, an interpolated value for back-ward red-shift of about 4.5 was assumed as an approximately average value. Since the mass specific capture area and the associated massive drag values used are not absolute requirements, the adjustment of the latter values by a few percent can compensate for inaccuracies in the former estimated average and permit the actual maximum possible gamma factor per given intergalactic massive density to very by perhaps as much as plus or minus a few percent. The point is that because of the subject degrees of freedom in the engineering and applied physics for the above conjectural specific examples, the maximum gamma factor of 3 is a very good ball park to aim for in any future real world systems we will design.

Now, in addition of electromagnetic negative refractive index materials which have been demonstrated within research facilities, it may be possible that massive particle and perhaps even gravitational wave negative refraction index materials could be fashioned into sails that are pulled forward by the incident mass-energies. No one at present really knows if the later two types of materials are possible to construct, however, such materials are tantalizing to consider because of the implications of perpetual and increasing pull sail accelerations,  as long as the mass-energy influxes would not thermally or mechanically over burdern the negative refraction index materials.

However, we do not necessarily need even the still controversial pull sail negative electromagnetic refraction index drives. Ordinary positive index materials that are one way transmissive and which are suitably contoured can provide much higher gamma factors in the present cosmic era even in consideration of massive astrodynamic drag. I will describe such  increasing more extreme scenarios in an ongoing series of posts on the subject of plausible one way transmissive, positive refraction index, material based sails involving intelligible speculations regarding such sails made of ordinary atomic elements.

I will post further on this subject later today. It is time for me to log off, turn off my computer and catch some sleep.

Regards;

Jim

Copyright James M. Essig  January 27, 2011  All Rights Reserved.

Interstellar CMBR Surfing: 2nd Edition.

You ever wonder whether or not physicists and theoretical engineers will at some point in time determine how to obtain a free lunch? Well, for all practical purposes, we have a free lunch. It is called the cosmic microwave background energy or CMBR and may be available in infinite quantities given that our entire universe may have an infinite volume and spatial extent, and perhaps also forward potential time extension. The CMBR will always be available provided no further phase changes or symmetric breaking events will convert the background photonic radiations to another useless form. As such, photons and electromagnetic waves are theoretically perfectly stable. As a Catholic and affectionato for the Holy Bible, I like to muse at times on the metaphor that light was the first element of creation in at least some translations. Now, the actual meaning of light is most likely a metaphor, but given that our universe in the Big Bang may have started out from pure energy where such energy was embodied in the start of the initial space-time and mass energy forms in a kind of space-time-energy unification, perhaps the Bible has a deeper meaning here that was somehow preserved from antiquity.

That space and time are intimately tied to electromagnetic radiation is obvious when one considered the ubiquitous inclusion of the speed of light in vacuu as a constant in virtually all special and general relativistic formulations. Even in classical electromagnetic theory, the velocity of light is intimately related to the properties of space time including the magnetic permeability and electric permittivity of free space by the formula C = {1/[μ₀ ɛ₀]}^1/2.

I am sure that most of the concepts expressed within this post have been contemplated by others before.

By now the reader is aware of the concept of light sail(s) driven space craft that can reach relativistic velocities. A space craft traveling at extreme gamma factors using an ordinary beam sail will experience extreme astro-dynamic drag, and the sail would likely be ionized by the drag induced friction. This is largely due to the fact that most beam sail space craft contemplate beam sails that are orthogonally spread  with respect to the craft velocity vector and thus which have a very large surface area to experience forward drag.

Suppose a relativistic rocket was powered by energy captured by an attached square or rectangular CMBR  sail that is  oriented in a perpendicular to the velocity vector of the space craft. The equation for Doppler shifting of  CMBR acting on the sail would then be:  

1 + z = {1 + [ ν (cos θ)/C]}/{[1 - [(v/C)²]]^1/2}

or,

z  = {1 + [ ν (cos θ)/C]}/{[1 - [(v/C)²]]^1/2} – 1

f’ = f / {γ [1 + (β cosine θ)]}

which reduces to F’ = f/γ for a radiation source and space craft moving in a direction perpendicular to the line connecting these reference frames with respect to a space craft observer since cos (π/2) = zero where f represents frequency. Here, θ is the angle of view with respect to the space craft velocity vector or the perceived angle of  radiation incidence on the sail with respect to the direction of space craft travel,  with respect to the space craft.

Now,  the energy of a photon is as follows:

E = [h/(2 π)] ω = hf = hC/λ 

where h is the Planck Constant and λ  is the photon wave-length.

Therefore, the energies of the individual CMBR photons impinging on the light sail oriented in a direction perpendicular to it from the space craft’s perspective from directly behind are equal to:

E + =  hf/{γ [1 + (β cos  θ)]} = hf /{γ [1 + (β cos  (0)]}

which reduces to;

hf /{γ [1 + β ]}.

Now,  the CMBR power impinging on the space craft sail per differential unit of time element (space craft reference frame), per differential unit of angle of pre-incidence (space craft reference frame), per differential element of sail area (space craft reference frame) for black body radiation is a function of γ ⁴. This is because the black body radiation frequency curve peak is proportional to black body source temperature and an incident source photon’s frequency is proportional gamma. Since black body total power emission per unit of surface area is proportional to the  fourth power of the temperature of the black body, the above differential area element of the sail will receive a total power that scales with γ ⁴. Black body emitter frequency distribution scales as a function of gamma relative to a moving observer traveling at a factor of γ with respect to the source for directly approaching observers and 1/ γ for directly receding observers.

Planck’s Law states that

 

I(ѵ,T)dѵ = {[2hѵ³]/C²}{1/{[e^[(hѵ)/(kT)]] -1}}dѵ

 

λ_max = b/T

 

 

 

 

where λ max,  is a function only of the temperature.

P_net = P_emit – P_absorbed

Applying the Stefan–Boltzmann law,

P_net = A σ e (T⁴ – T₀⁴)

 

 

where sigma =  σ = (2π⁵k_B⁴)/(15 h³ C²) = (π²k_B⁴)/(60 ђ³ C²)

 

 

 

 

or  where sigma =  σ = 5.670400(40) x 10^-8 W m^-2 K^-4

Therefore, the apparent spectral temperature of the CMBR radiation incident on the sail per unit angle of CMBR incidence for a stationary sail is:

{[P_cmbr/(A σ e)] ^1/4}

The apparent spectral temperature of the CMBR radiation incident on the sail per unit of apparent angle of incidence of the CMBR with respect to the space craft reference frame-based observer(s) for a sail traveling at a given velocity for backwardly impinging radiation is:

T_app = {∫(0, π/2){{{[P_cmbr/(e σ)]^1/4}/{γ [1 +  [(v/C) cos θ]]}}⁴}{{∫(y₁,y₂){ ∫(x₁,x₂) dx} dy}^-1} dθ}^1/4

 

= {∫(0, π/2){{{[P_cmbr/(e σ)]^1/4} /{{1/{[1 – [(v/C)² ]] ^1/2}} [1 +  [(v/C) cos θ]]}}⁴}{{∫(y₁,y₂){ ∫(x₁,x₂) dx} dy}^-1} dθ}^1/4

 

 

= {∫(0, π/2){{{[Pcmbr/(e σ)]^1/4}/{{1/{[1 – [(v/C)² ]] ^1/2}} [1 + [(v/C) cos θ]]}}⁴}[(∫d A)^-1] dθ}^1/4

where P_cmbr is the background CMBR power incident on the sail, dA is the differential element of sail area with respect to the space craft reference frame, v is the velocity of the space craft with respect to the background, and θ is the angle of radiation incidence on the sail with respect to a sail based observer. Theta ranges from π/2 radians for radiation traveling in an orthogonal direction with respect to the ship velocity vector to zero radians for radiation traveling in a parallel direction with respect to the ship velocity vector.

The total power backwardly incident upon the sail with respect to the sail’s reference frame for a given gamma factor  is  therefore:

P = ∫(y₁,y₂) {∫(x₁,x₂) {∫ (0, π/2) {{{(T_cmbr) /{γ [1 + [(v/C) cos θ]]}}⁴} σ e} dθ}dx}dy

= ∫(y₁,y₂) {∫(x₁,x₂) {∫ (0, π/2) {{{(T_cmbr) /{{1/{[1 + [(v/C)² ]] ^1/2}}  [1 + [(v/C) cos θ]]}}⁴} σ e} dθ}dx}dy

= ∫ {∫ (0, π/2) {{{(T_cmbr) /{{1/{[1 – [(v/C)² ]] ^1/2}}  [1 + [(v/C) cos θ]]}}⁴} σ e} dθ} dA

Here, T_cmbr is the background CMBR temperature.

Note that in the above calculations and the ones that follow, all of the relevant backwardly incident background energies are assumed to be initially absorbed by the sail even if the sail acquires a temperature significantly above absolute zero and thereby produces thermal electromagnetic black body emissions. I describe potential methods of the absorption of nearly all incident radiations even in cases where relativistic aberration would otherwise cause the bulk of the impinging radiation to easily reflect off the sail because of increasingly shallow angles of incidence. The forwardly incident radiation is assumed to completely pass through the sail without exchange of momentum.

We can numerically integrate the relativistic  energy growth of the ship in small time steps as follows:

∫P₁dt₁ + ∫P₂dt₂ + ∫P₃dt₃ +, …, + ∫P_ndt_n

Thus, the following expression can be used to compute relativistic energy gain by the ship in terms of t.

Egain  = Σ (0,n)    { ∫ (t_ai, t_bi) { ∫  (y₁, y₂){ ∫  (x₁,x₂){ ∫ (0,  π/2) {{{T_cmbr /{{{1/{[1 – [(v_i/C) ²]] ^1/2}}}[1 + [(v_i/C) cos θ]]}} ⁴} σ e}dθ}dx}dy} dt}      

Here,  t_ai, t_bi, and dt are the times in the background reference frame.

Note, the reason why I assume the latter three times are background reference frame times is such that for a space craft traveling at a velocity of just under 1 C, where gamma is held constant, the energy gain for the space craft will be proportional to the length of the path traveled by the space craft according to the background reference frame. The distance of space craft travel  is proportional to the time of space craft travel with respect to the background reference frame. The same is true for a space craft traveling at any velocity held constant, thus the reason for the performance of the numerical integration for each time step where the velocity is incrementally increased but held constant for each time step.

Alternatively, we can use the following series:

Egain =  Σ (1,n) { ∫ (t_ai, t_bi) {∫ {∫ (0, π/2)  {{{T_cmbr /{{1/{[1 – [(v_i/C) ²]] ^1/2}}[1 + [(v_i/C) cos θ]]}} ⁴} σ e}dθ} dA}dt}    

where t_ai and t_bi and dt are the times in the background reference frame.

Now for constant acceleration ship time, T₀ = (c/g) ln {{[[ (C²) + (V₀ ²)] ^1/2]   –   [V₀/[[1 – [(V₀/C) ²]] ^1/2 ]]} { [(C ²) + [[(g)(t)  + [V₀ /[1 – [(V₀/C) ²]] ^1/2 ] ²]] ^1/2] + [(g)(t)] +  [V₀/[[1 – [(V₀/C) ²]] ^1/2]]} / (C ²)}. We can incorporate the expression for T₀ prefaced by the notation Delta to indicate the time steps,  ship time,  of uniform duration ship frame.

For computation in terms of T₀, we obtain:

Egain = Σ (0,n)    {{ ∫  (y₁, y₂){ ∫  (x₁,x₂){ ∫ (0,  π/2) {{{T_cmbr /{{{1/{[1 – [(v_i/C) ²]] ^1/2}}}[1 + [(v_i/C) cos θ]]}} ⁴} σ e}dθ}dx}dy} {(Delta) {(c/g) ln {{[[ (C²) + (V_0i ²)] ^1/2]   –   [V_0i/[[1 – [(V_0i/C) ²]] ^1/2 ]]} { [(C ²) + [[(g_i)(t_i)  + [V_0i /[1 – [(V_0i/C) ²]] ^1/2 ] ²]] ^1/2] + [(g_i)(t_i)] +  [V₀/[[1 – [(V_0i/C) ²]] ^1/2]]} / (C ²)}}} {1/{[1 – [(v_i/C) ²]] ^1/2}}}  .     

where t_i is the time in the background reference frame and g_i is the ship acceleration in the ship’s reference frame.

Note that the above formulas provide precise calculations for many numerical iterations involving small increments for velocity increase and small time steps in the ship’s frame.

Alternatively, we can use the following series:

Egain =  Σ (1,n) { {∫ {∫ (0, π/2)  {{{T_cmbr /{{1/{[1 – [(v_i/C) ²]] ^1/2}}[1 + [(v_i/C) cos θ]]}} ⁴} σ e}dθ} dA} {(Delta) {(c/g) ln {{[[ (C²) + (V_0i ²)] ^1/2]   –   [V_0i/[[1 – [(V_0i/C) ²]] ^1/2 ]]} { [(C ²) + [[(g_i)(t_i)  + [V_0i /[1 – [(V_0i/C) ²]] ^1/2 ] ²]] ^1/2] + [(g_i)(t_i)] +  [V_0i/[[1 – [(V_0i/C) ²]] ^1/2]]} / (C ²)}}} {1/{[1 – [(v_i/C) ²]] ^1/2}}}             

Another method entails integration with respect to space craft velocity with respect to the background and integration with respect to time as follows:

E_gain = ∫ (v₁, v₂)  {{∫  (t₁, t₂) { ∫ (y₁, y₂){ ∫ (x₁,x₂){ ∫ (0,  π/2) {{{T_cmbr {1/{[1 – [(v/C) ²]] ^1/2}}[1 + [(v/C) cos θ]]} ⁴} σ e}dθ}dx}dy} dt}/v}dv

Or alternatively,

E_gain =  ∫(v₁,v₂) {∫ (t₁,t₂){∫  {∫ (0,  π/2) {{{_Tcmbr/{{{1/{[1 – [(v/C) ²]] ^1/2}}[1 + [(v/C) cos θ]]}}⁴} σ e} dθ} dA}dt}/v}dv

where t₁ and t₂ and dt are the times in the background reference frame.

Now, E_gain in practice needs to take into account the radiative temperature of the sail.

Now, given that

P_net = A σ e (T⁴ – T₀⁴)

 

where T is the body temperature and T₀ is the surrounding temperature, we can re-interpret T as the impinging radiation’s black body temperature and T₀ as the emitted thermal radiation black body temperature. So in other words, if the impinging temperature is 10 times higher in Kelvins then the thermal radiative temperature, the net power input into the sail is 10⁴ or 10,000 times greater than the power loss through radiative emissions.

 

The net power delivered to the  sail will be equal to the power intake minus the power thermally radiated as

P = {∫(y₁,y₂) {∫(x₁,x₂) {∫ (0, π/2) {{{(T_cmbr) /{γ [1 + [(v/C) cos θ]]}}⁴} σ e} dθ}dx}dy} – {∫(y₁,y₂) {∫(x₁,x₂) (T₀⁴ σ e) dx}dy}

= {∫(y₁,y₂) {∫(x₁,x₂) {∫ (0, π/2) {{{(T_cmbr) /{{1/{[1 + [(v/C)² ]] ^1/2}}  [1 + [(v/C) cos θ]]}}⁴} σ e} dθ}dx}dy}  – {∫(y₁,y₂) {∫(x₁,x₂) (T₀⁴ σ e) dx}dy}

= { ∫ {∫ (0, π/2) {{{(T_cmbr) /{{1/{[1 – [(v/C)² ]] ^1/2}}  [1 + [(v/C) cos θ]]}}⁴} σ e} dθ} dA} -

- {∫(T₀⁴ σ e) dA}

The following expression can be used to compute relativistic energy gain by the ship in consideration of the black body emissions from the sail heated by CMBR.

From computation in terms of t, we obtain:

Egain  = {Σ (0,n)   { ∫ (t_ai, t_bi) { ∫  (y₁, y₂){ ∫  (x₁,x₂){ ∫ (0,  π/2) {{{T_cmbr /{{{1/{[1 – [(v_i/C) ²]] ^1/2}}}[1 + [(v_i/C) cos θ]]}} ⁴} σ e}dθ}dx}dy} dt}}   – {Σ (0,n) {∫ (t_ai, t_bi) {∫(y₁,y₂) {∫(x₁,x₂) (T⁴_0i σ e) dx}dy}dt}}     

where t_ai and t_bi and dt are the times in the background reference frame.

Now ship time = T₀ = {(c/g_n) ln {[[ (C²) + (V₀ ²)] ^1/2]   –   [V₀/[[1 – [(V₀/C) ²]] ^1/2 ]]} { [(C ²) + [[(g_n)(t_n)  + [V₀ /[1 – [(V₀/C) ²]] ^1/2 ] ²]] ^1/2] + [(g_n)(t_n)] +  [V₀/[[1 – [(V₀/C) ²]] ^1/2]]} / (C ²)}}

Computation in terms of T₀, we obtain:

Egain  = {Σ (0,n)   {{ ∫  (y₁, y₂){ ∫  (x₁,x₂){ ∫ (0,  π/2) {{{T_cmbr /{{{1/{[1 – [(v_i/C) ²]] ^1/2}}}[1 + [(v_i/C) cos θ]]}} ⁴} σ e}dθ}dx}dy} {(Delta) {(c/g_i) ln {{[[ (C²) + (V_0i ²)] ^1/2]   –   [V_0i/[[1 – [(V_0i/C) ²]] ^1/2 ]]} { [(C ²) + [[(g_i)(t)  + [V_0i /[1 – [(V_0i/C) ²]] ^1/2 ] ²]] ^1/2] + [(g_i)(t)] +  [V_0i/[[1 – [(V_0i/C) ²]] ^1/2]]} / (C ²)}}} {1/{[1 – [(v_i/C)² ]] ^1/2}}}}    – {Σ (0,n)  {{∫(y₁,y₂) {∫(x₁,x₂) (T⁴_0i σ e) dx}dy}    {(Delta) {(c/g_i) ln {{[[ (C²) + (V_0i ²)] ^1/2]   –   [V_0i/[[1 – [(V_0i/C) ²]] ^1/2 ]]} { [(C ²) + [[(g_i)(t_i)  + [V_0i /[1 – [(V_0i/C) ²]] ^1/2 ] ²]] ^1/2] + [(g_i)(t_i)] +  [V_0i/[[1 – [(V_0i/C) ²]] ^1/2]]} / (C ²)}}} {1/{[1 – [(v_i/C)² ]] ^1/2}} }} 

where T₀ is the ship time.

Alternatively, we can use the following series calculated with  t:

Egain  =  {Σ (1,n) { ∫ (t_ai, t_bi) {∫ {∫ (0, π/2)  {{{T_cmbr /{{1/{[1 – [(v_i/C) ²]] ^1/2}}[1 + [(v_i/C) cos θ]]}} ⁴} σ e}dθ} dA}dt}}   -  {Σ (1,n) ∫ (t_ai, t_bi) {∫ (T⁴ _0i σ e) dA}dt}   

where t_ai and t_bi and dt are the times in the background reference frame.

Calculating with respect to T₀, we obtain:

Egain =  {Σ (1,n)  {∫ {∫ (0, π/2)  {{{T_cmbr /{{1/{[1 – [(v_i/C) ²]] ^1/2}}[1 + [(v_i/C) cos θ]]}} ⁴} σ e}dθ} dA}}   -  {Σ (1,n) {∫ (T⁴ _0i σ e) dA}   {(Delta) {(c/g_i) ln {{[[ (C²) + (V_0i ²)] ^1/2]   –   [V_0i/[[1 – [(V_0i/C) ²]] ^1/2 ]]} { [(C ²) + [[(g_i)(t_i)  + [V_0i /[1 – [(V_0i/C) ²]] ^1/2 ] ²]] ^1/2] + [(g_i)(t_i)] +  [V_0i/[[1 – [(V_0i/C) ²]] ^1/2]]} / (C ²)}}} {1/{[1 – [(v_i/C)² ]] ^1/2}}}.

Integrating with respect to time and velocity;

the formulas for total kinetic energy  gain are:

E_gain = {∫ (v₁, v₂)  {{∫  (t₁, t₂) { ∫ (y₁, y₂){ ∫ (x₁,x₂){ ∫ (0,  π/2) {{{T_cmbr {1/{[1 – [(v/C) ²]] ^1/2}}[1 + [(v/C) cos θ]]} ⁴} σ e}dθ}dx}dy} dt}/v}dv} -  E_{rad lost}

or alternatively,

E_gain =  {∫(v₁,v₂) {{∫ (t₁,t₂){∫  {∫ (0,  π/2) {{{_Tcmbr/{{1/{[1 – [(v/C) ²]] ^1/2}}[1 + [(v/C) cos θ]]}}⁴} σ e} dθ} dA}dt}/v}dv} -  E_{rad lost}

 

 

where t_ai and t_bi , t_i, and dt are the times in the background reference frame, g_i is the ship acceleration in the ship’s reference frame, and V_0i is the starting velocity at the beginning of each time of Delta T₀,  or ship time.

Now, the CMBR incident on the light sail from behind will generally require either a monolithic light sail of near nanometer thickness or perhaps a grid like sail with a cross-weave for which the lines or fibers are separated by less than 0.25 millimeters in order to reflect the vast majority of the incident CMBR for space craft traveling at mildly relativistic velocities. For grid like sails, the advantage of sail porosity enables much higher mass specific capture areas. Since the Doppler blue shifted light incident from directly in front of the sail or nearly so will be much shorter in wavelength than the backwardly incident light for high gamma factor sails, the forwardly incident light can largely pass through the sail openings providing a means for the backwardly incident light to push the sail efficiently forward for cases where the sail is transmissive from front to back to a suitable degree.

Now radiation pressure is equal to σT⁴/C and {2 [σT⁴/C]} for reflected radiation. However, for a space craft traveling through a black body radiation field, the apparent temperature of the radiation increases in proportion to γ and so the black body power impinging on the space craft from directly in front grows in proportion to T⁴ and thus  to γ⁴.

The temperature of a black body is T = {P/[(A)(σ)(e)]}^1/4 = {P/{(A)[5.670400(40) x 10^-8 W m^-2 K^-4]} ^1/4}. Therefore, the cosmic microwave background radiation pressure on a perfectly reflective flat bow  relativistic space craft is roughly equal to  {2 [σT_cmbr ⁴/C]} γ⁴ = {2 [σT_cmbr ⁴/C]} { {1/{1 – [(v/C)²]}^1/2}  ⁴} =   {2 [σT_cmbr ⁴/C]} {1/{1 – [(v/C)²]}²} where γ is constant and T_cmbr is constant. However, the light pressure incident from directly behind will be approximately equal to {2 [σT_cmbr ⁴/C]}/{1/{1 – [(v/C)²]}²}. In actuality, not all of the light is directly incident from the back and so there will be angular affects that result in loss of driving power. However, we will assume that all of the radiation is absorbed and then re-cycled and released as a perfect backwardly directed laser beam.

Assuming that the velocity of the sail starts out at (Zero) C, the optical pressure will be equal to {2 [σT_cmbr ⁴/C]}/γ⁴ = {2 [σT_cmbr ⁴/C]}/{ {1/{1 – [(v/C)²]}^1/2} ⁴} = {2{[5.670400(40) x 10^-8 W m^-2 K^-4][(2.725 K)⁴]/(300,000,000 m/s)}}/(1²) = 2.0844  x 10^-14 Newtons/m². For a 10,000 km by 10,000 km sail, the drive force will be 2.0844 Newtons.

Now, how are we going to deploy such a sail in a meaningful manner? The solution is obvious my dear Watson! Use a grid.

Consider that a monolithic one nanometer thick sail made of STP H₂O density carbonaceous materials would have a mass of  100,000 thousand metric tons, assuming that the space craft plus her sail had a mass of 208,440 metric tons, the craft would start out with an acceleration of F/M = a = 2.0844 N/208,440,000 kg = 10^-8 meter/s². After traveling 6 x 10¹⁵ seconds or about 200,000,000 years, the velocity of the space craft will be 0.20 C and the relativistic Lorentz transformation factor will be 1.0206 thus permitting the above Newtonian formula to apply.

For such a space craft that deployed a linear series of 1,000 tethered sails where each sail was separated by an efficient 10 sail widths, a space craft having a total mass of 208, 440,000 metric tons could be identically accelerated. The mass of the crew quarters would be 108,440,000 metric tons.

For such a space craft that deployed a linear series of 1,000,000 tethered sails where each sail was separated by an efficient 10 sail widths, a space craft having a total mass of 208, 440,000,000  metric tons could be identically accelerated. The mass of the crew quarters would be 108,440,000,000  metric tons. For cosmic journeys, this is not bad.

Some supermaterials already in laboratory existence such as carbon nanotubes can in theory be used to construct large space elevators that would extend from the surface of the Earth near the Equator to locations significantly father than geosynchronous orbit. Such tethers would perhaps have the equivalent of 0.1 G or 1m/s² acceleration based force pulling on it which would be commensurate with a cable roughly 100,000 km long accelerated at 1 m/s². Thus,  a cable that is 10¹³ km long or one light-year long could in theory withstand 10^-8 m/s² levels of acceleration. A linear series of tethered leading sails numbering 1,000,000 where each sail would have a width of 10,000 kilometers and be serially spaced a distance of 100,000 kilometers would have a length of 10¹¹ kilometers.  Thus, a series of 100 million tethered sails might conceivably pull a sail craft combination having a mass of 20,844,000,000,000 metric tons and a crew quarters having a mass of 10,844,000,000,000 metric tons.

Some high-end carbonaceous super-materials include:

1) carbon nano-tubes;
2) boron-nitride nanotubes;
3) buckyball-sheets;
4) layered sheet arrangements of graphene;
5) graphene-oxide paper;
6) fabrics composed of a weave or knit on carbon atom chains;
7) diamond fiber-based fabric;
8) carbon nitride fiber-based fabric;
9) combinations of two or more of the above, and the like material

Metalization would help in these regards.

The sails could have nanotech self-repair mechanisms. An ideal mechanism would entail sails constructed of metallic hydrogen where the hydrogen would be captured from interstellar space and incorporated into the sail membrane(s) in order to re-supply sail atoms knocked loose by interstellar atom and molecular species.

However, much higher sail velocities are anticipatable with much greater accelerations as will be covered in the next post in this series.

However, we can also deploy gridded sails. For example, consider a sail that is comprised on one nanometer wide fibers in a cross-weave where adjacent parallel  fibers are separated by 200 microns. Also consider situations where the fibers are one side reflective and one side transmissive. A sail comprised of such a material will have a mass specific capture area that is 1/100,000 that of a one nanometer thick monolithic sail.

Considering that such a sail that is gridded with the above  one nanometer thick sail fiber construction made of STP H₂O density carbonaceous materials would have a mass of  one metric ton for a sail area of 10⁸ square kilometers, assuming that the space craft plus her sail had a mass of 208,440 metric tons, the craft would start out with an acceleration of F/M = a = 2.0844 N/208,440,000 kg = 10^-8 meter/s². After traveling 6 x 10¹⁵ seconds or about 200,000,000 years, the velocity of the space craft will be 0.20 C and the relativistic Lorentz transformation factor will be 1.0206 thus permitting the above Newtonian formula to apply.

For such a space craft that deployed a linear series of 1,000 tethered sails where each sail was separated by an efficient 10 sail widths, a space craft having a total mass of 208, 440,000 metric tons could be identically accelerated. The mass of the crew quarters would be 208, 439,000 metric tons.

For such a space craft that deployed a linear series of 1,000,000 tethered sails where each sail was separated by an efficient 10 sail widths, a space craft having a total mass of 208, 440,000,000  metric tons could be identically accelerated. The mass of the crew quarters would be 208, 439,000,000 metric tons. For cosmic journeys, this is not bad.

A series of 100 million tethered sails might conceivably pull a sail craft combination having a mass of 20,844,000,000,000 metric tons and a crew quarters having a mass of 20,843,900,000,000 metric tons.

Consider again that such sails which  are gridded with the above  one nanometer thick sail fiber construction made of STP H₂O density carbonaceous materials would have a mass of  one metric ton each, assuming that the space craft plus her sail had a mass of 208,440 metric tons, the craft would start out with an acceleration of F/M = a = 2084.4 N/208,440,000 kg = 10^-5 meter/s² for cases where the craft would utilized 1,000 tethered driving sails. After traveling 6 x 10¹²  seconds or about 200,000 years, the velocity of the space craft will be 0.20 C.

Now consider a space craft having a mass of 208,440 metric tons driven by 10,000 such one metric tons sails. For such a space craft that deployed a linear series of 10,000 tethered sails where each sail was separated by an efficient 10 sail widths, the space craft having a total mass of 208, 440 metric tons would start out with an acceleration of F/M = a = 2084.4 N/208,440,000 kg = 10^-4  meter/s². After traveling 6 x 10¹¹ seconds or about 20,000 years, the velocity of the space craft will be 0.20 C.

We can consider more robust gridded sails such as those made from 10 nanometer diameter fibers spaced 200 microns apart. Each such sail would have a mass of 100 metric  tons. Thus, a space craft having a total mass of 208,440 metric tons that is driven by 1,000 such sails would too start out with an acceleration of F/M = a = 2084.4 N/208,440,000 kg = 10^-5 meter/s² and achieve a velocity of 0.20 C after 200,000 years.

Cnsider a sail that is comprised on 316.2  nanometer wide fibers in a cross-weave where adjacent parallel  fibers are separated by 200 microns. Also consider situations where the fibers are one side reflective and one side transmissive. A sail comprised of such a material will have a mass specific capture area that is equal to that of a one nanometer thick monolithic sail.

Consider that such a sail which is gridded with the above  316.2  nanometer thick sail fiber construction made of STP H₂O density carbonaceous materials would have a mass of  100,000 metric tons for a capture area of 10⁸ square kilometers. Assuming that the space craft plus her sail had a mass of 208,440 metric tons, the craft would start out with an acceleration of F/M = a = 2.0844 N/208,440,000 kg = 10^-8 meter/s². After traveling 6 x 10¹⁵ seconds or about 200,000,000 years, the velocity of the space craft will be 0.20 C and the relativistic Lorentz transformation factor will be 1.0206 thus permitting the above Newtonian formula to apply.

For such a space craft that deployed a linear series of 1,000 tethered sails where each sail was separated by an efficient 10 sail widths, a space craft having a total mass of 208, 440,000 metric tons could be identically accelerated. The mass of the crew quarters would be 208, 439,000 metric tons.

For such a space craft that deployed a linear series of 1,000,000 tethered sails where each sail was separated by an efficient 10 sail widths, a space craft having a total mass of 208, 440,000,000  metric tons could be identically accelerated. The mass of the crew quarters would be 208, 439,000,000 metric tons. For cosmic journeys, this is not bad.

A series of 100 million tethered sails might conceivably pull a sail craft combination having a mass of 20,844,000,000,000 metric tons and a crew quarters having a mass of 20,843,900,000,000 metric tons.

The background interstellar and intergalactic matter might not erode even many of highly relativistic sail of sub-micron thickness.

The diametrical cross-sectional area of our observable universe is close to 10 ⁴⁷  square kilometers and the mass of the total mass energy of the observable universe is only about 10 ⁵⁰ metric tons of which only 4 percent is baryonic.  Thus,  an average column spanning the diameter of the entire visible universe would have an H2O STP matter thickness of only 25 micrometers for reactive matter.

However,  this is not a concern for the following reasons.

First, the sails could be replaceable grid sails and driven by optical, IR, microwave or rf radiation. The mass of such sails can be reduced by many orders of magnitude relative to monolithic sails that are only micrometer scales in thickness.

Second, sails having a very thick cable or thread like construction are conceivable where the cables or wires would be many times if not several orders of magnitude thicker than 25 microns. The sails could be mostly empty space to almost entirely empty space to reflect long wave rF phased array beams.

As for concerns about over burdening the conductive or super-conductive wires or cables used for such sails by extremely intense rF beams, note that such reflective members could be very conductive to superconductive to thereby yield near perfect reflection. The EM energy that was not reflected would largely pass through the openings in the sail grid.

Second, a magnetic and/or electric field based scoop or anti-scoop could divert the chargons away from the sail just as an extended electrodynamic scoop for an interstellar ramjet would. Electro-dynamic-hydro-dynamic-plasma-drive features could utilize the diverted plasma in a reactive and gainful manner.

The sail might be deployed in a manner that is orthogonal to the ship’s velocity vector.  The sail might be parallel to the space craft velocity vector and driven obliquely from behind. This way, the effective thickness of the sail could be thousands of miles and the sail could include electro-dynamic-hydro-dynamic-plasma-drive features.

Fourth, the above parallel sail could conceivably be made of negative refraction index materials that would be pulled forward by incident star light and highly blue-shifted CMBR, far infrared, and non-CMBR radio sources.

Fifth, the sail can simply be a deployed mag-sail or M2P2 type of sail or any other magnetic or plasma bottle sail. It is possible that a plasma affixed to the space craft to be driven by rf radation, and even source based laser light upon attainment of extreme space craft gamma factors could be easily reflected by such sails. Plasma makes an excellent rF reflector even at very small densities.

I have done a lot of writing on parallel sails such as negative refraction index monolithic and grid sails capable of extreme gamma factors.

Sixth, some sail materials such as any future forms of super-strong very conductive to super-conductive metallic hydrogen can be used as nuclear fusion fuel for fusion rockets upon degradation to useless levels.

Seventh, it has been proposed that very thin,  metallic,  very low gas density containing balloons might be used for nuclear warhead decoys and which could survive 100 meter proximity detonation to a one kiloton neutron bomb in the vacuum of space. The rate of radiative cooling would be tens of billions of Kelvins per second due to the extreme thinness of the balloon membranes and most of the neutrons would pass right through the balloon without interacting or by only depositing a very small portion of the particles kinetic energy into the balloon and enclosed gas. Interstellar chargons are more reactive to electronic shell structures but not by that much.

The general idea for obliquely oriented beams involves the beamed energy incident on both sides of the sail. The sail could include a surface of hair like cilia or any other surface contour that would work so as to much more effectively grab ahold of the light.

In addition, the sail could be fabricated from photovoltaic materials in order to provide power for electro-dynamic-hydrodynamic-plasma-drives or chargon rockets, or perhaps even photon rockets.

For extreme gamma factors, the CMBR and starlight will be highly blue-shifted and will be relativistically abberated to what would approach a point source in front of the space craft at gamma = infinity. A sail parallel to the space craft velocity vector made of a suitable negative electromagnetic refraction index material will be pulled forward even by light incident on the sail at a very shallow angle from in front of the space craft.

To enhance the negative refraction index sails capture of EM energy, the sails may have negative index hairs or cilia distributed along its length.

Negative refraction index materials have actually been measured to be pulled on by incident light. Duke University and other academic and government labs are researching the various aspects of negative refraction index materials.

I have no problem with space craft being pulled forward by forward incident light. After all, the paradigm of light speed velocity limits may or may not have been shattered with any future validation or not of the CERN superluminal neutrino results. The big bang may have been the most recent free lunch. There is no reason why the big bang could not have started with miniscule quantities of mass-energy.

A good abstract for a great paper on negative super-pressure of light acting on a negative refractive index material is

Henri Lezec
(Center for Nanoscale Science and Technology, NIST)

Forty years ago, V. Veselago derived the electromagnetic properties of a hypothetical material having simultaneously-negative values of electric permittivity and magnetic permeability [1]. Such a material, denominated “left-handed”, was predicted to exhibit a negative index of refraction, as well as a number of other counter-intuitive optical properties. For example, it was hypothesized that a perfect mirror illuminated with a plane wave would experience a negative radiation pressure (pull) when immersed in a left-handed medium, as opposed to the usual positive radiation pressure experienced when facing a dielectric medium such as air or glass. Since left-handed materials are not available in nature, considerable efforts are currently under way to implement them under the form of artificial “metamaterials” — composite media with tailored bulk optical characteristics resulting from constituent structures which are smaller in both size and density than the effective wavelength in the medium. Here we show how surface-plasmon modes propagating in a stacked array of metal-insulator-metal (MIM) waveguides can be harnessed to yield a volumetric left-handed metamaterial characterized by an in-plane-isotropic negative index of refraction over a broad frequency range spanning the blue and green. By sculpting this material with a focused-ion beam we realize prisms and micro-cantilevers which we use to demonstrate, for the first time, (a) in-plane isotropic negative-refraction at optical frequencies, and (b) negative radiation pressure. We predict and experimentally verify a negative “superpressure”, the magnitude of which exceeds the photon pressure experienced by a perfect mirror by more than a factor of two. 1) V. Veselago, \textit{ Sov. Phys. Usp. }10, p.509 (1968).

Available at:

http://meetings.aps.org/Meeting/MAR09/Event/93172

The sail might not need to  be held by guy lines. A strong magnetic field based coupling or electrical charged based connection might work.

Another option is to fabricate the sail guy lines out of graphene, carbon nanotubes, boron nitride nanotubes, graphene oxide paper, and the like. A cable constructed from such materials could stretch for about 20 to 50 kilometers yet still handle tens to hundreds of Earth G’s. The tensile strength of graphene is close to 18 million PSI for perfect forms.

Materials such as solid quarkoniums and somehow stabilized neutroniums, and perhaps even Higgsiniums would be better yet, but such materials may only exist in nature in extreme mass quantity states as of the present cosmic era.

The collection area of the sail can be very, very, large. A large electro-dynamic scoop could extent very far out from the sail.

Regarding nanotech self-assembly mechanisms, just simply greatly increase the capture area of a electrodynamic scoop to collect enough interstellar materials and use most of the collected interstellar material as an EHPD, an MHPD, or a combination of the two and use the rest of the materials for sail repair.

Regarding holding M2P2 plasma affixed to the ship under high gamma factor condition, simply increase the strength of the fastening fields.

Now regarding interstellar matter density near our solar system of one particle for every 10 cm³, the density would  work out to be a layer of hydrogen or helium atoms about one atom thick for a column that is one light-year long. Not a show stopper for light sails or sails that are electro-dynamically shielded or protected.

If extreme materials are used with excellent reflectance, we could simply use a sail that has a thickness of one millimeter or more and which is monolithic, or better yet,  use a sail with grid lines that are one millimeter or perhaps much greater in thickness. This way, a sail that has an area of only one square kilometer can intercept a beam having an equivalent black body temperature of several thousand Kelvins provided it is constructed of suitably refractive materials.

We could simply use electrodynamic methods of grabbing ahold of the interstellar gas and diverting around the space craft and sail. The power to operate the electrodynamic mechanisms can be supplied by beams. The electrodynamic methods can include lasers for ionization, or rf radiation where the gamma factors are suitably large, magnetic fields, electric fields, plasma fields affixed to the space craft, and the like.

Then there is always the possibilities for sails comprised of truly exotic materials such as somehow stabilized neutroniums, quarkoniums, higgsiniums, monopoliums, and perhaps even raw space-time-mass-energy forms such as the “Yelm” of mid-20th Century big bang theory.

Since one cubic meter of neutronium would have a mass of about 10¹⁵ tons. A 1,000 kilometer long thread of the stuff that has a cross-sectional area of 1,000,000 neutrons would have a mass of only one kilogram. A 1 kilometer long thread having a cross-sectional area of 1 billion neutrons would have a mass of only 1 kilogram. Lines made of quarkoniums could have the same length and cross-section but would be 10 to 1,000 times more massive. Higgsiniums would be all the more massive.

Provided such extreme materials could be developed, they could also serve as electric current carrying magnetic sail components. Anyhow magnetic sails can be made of any ordinary conducting or superconducting period table materials.

It is also conceivable that a hybrid sail can be used where a current carrying magsail would deflect plasma away from a monolithic and grid like light sail or rf sail.

Now, regarding the subject of sail erosion by exposure to interstellar or intergalactic gas, we must realize that the kinetic energy of a gas atom traveling at a velocity of 86.7 percent of the speed of light with respect to the sail would be equal to the binding energy of roughly 10 billion atoms within a sail of micron thickness. Thus, the fact that 10 billion atoms could be dislodged should all of the energy of the gas atom be deposited within the sail. Incident gas atoms having even higher associated gamma factors with respect to the star ship sail could potentially knock loose even more atoms. Perhaps, there is no reason to worry about sail erosion in spite of this for the following reasons.

First, extremely relativistic particles would likely deposit only a small portion of its energy within the sail thereby greatly lessening the number of atoms that would be knocked loose. This fact would apply to chargons as well as neutral incident particles.

Second, for sails of near micron thickness, atoms that were knocked loose would likely simply be re-assimilated by the bulk sail materials. Perhaps the only chance for an atom to be knocked loose would include atoms located on the backward side of the sail.  Atoms for which bonds where broken within the bulk sail material would tend to simply re-bond with adjacent atoms.

Third, since the incident gas or plasma particle would deposit only a small portion of its energy within the sail, the kinetic energy per particle for particles that are knocked loose may be only slightly in excess of the binding energy of the dislodged atoms. Basically, the kinetic energy of the dislodged atoms could likely be re-absorbed and/or radiated away thereby promoting rebinding of the dislodged atoms.

Fourth, for cases where the sail would completely absorb the kinetic energy of the incident gas or plasma particles such as an alpha particle, for the case of a one micron thick sail, the sail would obviously be able to complete stop the chargon without losing it. Thus, any atoms disbonded by the incident chargon would also likely be captured and prevented from leaving the sail material.

Fifth, for grid like sails, the grid lines might be positively chargeable so that incident interstellar or intergalactic ions are pushed away from the grid lines and through the openings within the grid like sails. The effect would be similar to the Vander walls force that keeps neutral atoms from being squeezed together to tightly.

We now perform a reality check on the above formulations.

Consider the space craft at a stationary state. The CMBR appears equally bright from all directions within about 1 part in 30,000.

Now, the apparent angle, θ_s,  of CMBR pre-incident on the space craft at an angle of 90 degrees or with respect to the length of the space craft relative to the source reference frame at v = zero C will appear to be incoming at an angle, θ_o,  of 90 degrees with respect to the space craft,  ship’s reference frame.

If we consider the effects of relativistic aberration, the general formula for apparent shift in angle of incidence of the CMBR from the ship’s perspective is

Cos θ_o = {[cos θ_s] – (v/C)}/{1 – [(v/C) cos θ_s]}

Now say we desire to find the range of CMBR angles incident on the space craft with respect to the space craft reference frame for space craft velocities of 0.20 C.

Now since we are considering an angle of θ_o = π/2, cos θ_o = zero. Using the above formula, we achieve Cos θ_o = {[cos θ_s] – (v/C)}/{1 – [(v/C) cos θ_s]} = Cos π/2 = {[cos θ_s] – (0.20)}/{1 – [(0.20) cos θ_s]} = zero = {[cos θ_s] – (0.20)}/{1 – [(0.20) cos θ_s]}.

Thus, (zero) {1 – [(0.20) cos θ_s]} = {[cos θ_s] – (0.20)} = zero.

Therefore, cos θ_s = 0.20 — > θ_s  = 78.463 degrees. We will make a first order assumption that the incident CMBR from behind has a frequency of f’ = f / {γ [1 + (β cosine θ)]} = f / {1.02062 [1 + [0.2 cosine ( 0)]]} = (0.816497161) f. Thus, we will assume that θ = 0 degrees for the following 5 scenarios where we assume that the CMBR is directly incident from behind.

The radiated power received by the sail will be [(78.463)²/(90²)] f’ = [(78.463)²/(90²)] f / {γ [1 + (β cosine θ)]} = [(78.463)²/(90²)] f / {1.02062 [1 + [0.2 cosine ( 0)]]} = [(78.463)²/(90²)] (0.816497161) f =

Once again, the temperature of a black body is T = {P/[(A)(σ)(e)]}^1/4 = {P/{(A)[5.670400(40) x 10^-8 W m^-2 K^-4]} ^1/4}. The light pressure incident from directly behind will be approximately equal to [(θ_s)²/(90²)] {2 {σ {{(T_cmbr)/{γ [1 + (β cosine θ)]}}}⁴/C}} =  [(78.463)²/(90²)] {2 {[5.670400(40) x 10^-8 W m^-2 K^-4] {[(T_cmbr) (0.816497161) ]⁴}/C}} = 4.632092076  x 10^-15 Newtons/m². In actuality, not all of the light is directly incident from the back and so there will be angular affects that result in loss of driving power. However, we will assume that all of the radiation is absorbed and then re-cycled and released as a perfect backwardly directed laser beam.

Now  E_gain = ʃF^odx = ʃ(0,10²⁵) F^odx = ʃ(0,10²⁵)(10¹⁴) [4.632092076  x 10^-15 N] ^odx = 4.632092076 x 10²⁴ Joules.

Now, a 208,440 metric invariant mass space craft traveling at a starting velocity of 0.2 C has a kinetic energy of {1.02062[M C²]} – [M C²] = {1.02062[208,440,000  C²]} – [208,440,000  C²] =  1.9146 x 10²⁵ Joules – 1.87596 x 10²⁵ Joules = 3.864 x 10²³ Joules. When  4.632092076 x 10²⁴ Joules is added, the total gamma factor becomes [5.01849 x 10²⁴ Joules + 1.87596 x 10²⁵ Joules]/ [1.87596 x 10²⁵ Joules] = 1.2675. The associated space craft velocity will be equal to 0.6142 C.

Likewise doing iterated numerical approximations with v = 0.6142 C to obtain another higher velocity and then repeating the steps over and over again will give a first order approximation for space craft terminal velocity.

So we have reasonably demonstrated that CMBR sails can drive very large space arks to velocities considered fast by interstellar propulsion physicists. Typically, fast interstellar travel occurs at a better part of the speed of light.

However, a much finer scale is needed to produce results for many such steps where the computed velocity would not significantly diverge from the actual velocity obtained.

Note that here, I neglect the effects of mass based astrodynamic drag. I have come up with several mechanisms by which massive astrodynamic drag can be almost entirely eliminated and will post on this subject later this month.

 

The total kinetic energy gain for the craft will be

E _totalgain = ʃF ₁^odx₁  +  ʃF ₂^odx₂ + ʃF ₃^odx₃ + … +ʃF _n^odx_n

= {{ʃ{[(θ_s1)²/ ((90 degrees) ²)] {2 {σ {{(T_cmbr)/{γ₁ [1 + (β₁ cosine θ)]}}}⁴/C}}}^odx₁}(A)}+  {{ʃ{[(θ_s2)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{γ₂ [1 + (β₂ cosine θ)]}}}⁴/C}}} ^odx₂}(A)} + {{ʃ{[(θ_s3)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{γ₃ [1 + (β₃ cosine θ)]}}}⁴/C}}} ^odx₃}(A)} + … +{{ʃ{[(θ_sn)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{γ_n [1 + (β_n cosine θ)]}}}⁴/C}}} ^odx_n}(A)}

 

= ʃ{[(θ_s1)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{{1/{1 – [(v₁/C)²]}^1/2} [1 + (β₁ cosine θ)]}}}⁴/C}}}^odx₁  +  ʃ{[(θ_s2)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{ {1/{1 – [(v₂/C)²]}^1/2}  [1 + (β₂ cosine θ)]}}}⁴/C}}} ^odx₂ + ʃ{[(θ_s3)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{ {1/{1 – [(v₃/C)²]}^1/2}  [1 + (β₃ cosine θ)]}}}⁴/C}}} ^odx₃ + … +ʃ{[(θ_sn)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{ {1/{1 – [(v_n/C)²]}^1/2}  [1 + (β_n cosine θ)]}}}⁴/C}}} ^odx_n

 

= Σ (i = 1, i = n) ʃF _i^odx_i   = Σ (i = 1, i = n) ʃ{[(θ_si)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{γ_i [1 + (β_i cosine θ)]}}}⁴/C}}}^odx_i

=   Σ (i = 1, i = n) ʃ{[(θ_si)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{ {1/{1 – [(v_i/C)²]}^1/2}  [1 + (β_i cosine θ)]}}}⁴/C}}} ^odx_i

 

The following numerical formula offers a first order approximation of space craft gamma factor  gain;

{[E_KEtotalgain] + [M_restC²]}/[M_restC²]= {[ʃF ₁^odx₁]  +  [ʃF ₂^odx₂]  + [ʃF ₃^odx₃ ] + … + [ʃF _n^odx_n] + [M_restC²]}/[M_restC²] 

= {{{ʃ{[(θ_s1)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{γ₁ [1 + (β₁ cosine θ)]}}}⁴/C}}}^odx₁}(A)}+  {{ʃ{[(θ_s2)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{γ₂ [1 + (β₂ cosine θ)]}}}⁴/C}}} ^odx₂ }(A)}  + {{ʃ{[(θ_s3)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{γ₃ [1 + (β₃ cosine θ)]}}}⁴/C}}} ^odx₃ }(A)} + … + {{ʃ{[(θ_sn)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{γ_n [1 + (β_n cosine θ)]}}}⁴/C}}} ^odx_n}(A)}+ [M_restC²]}/[M_restC²] 

 

= {{{ʃ{[(θ_s1)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{{1/{1 – [(v₁/C)²]}^1/2} [1 + (β₁ cosine θ)]}}}⁴/C}}}^odx₁  }(A)}  +  {{ʃ{[(θ_s2)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{ {1/{1 – [(v₂/C)²]}^1/2}  [1 + (β₂ cosine θ)]}}}⁴/C}}} ^odx₂ }(A)} +   {{ʃ{[(θ_s3)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{ {1/{1 – [(v₃/C)²]}^1/2}  [1 + (β₃ cosine θ)]}}}⁴/C}}} ^odx₃ }(A)} + … +  {{ʃ{[(θ_sn)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{ {1/{1 – [(v_n/C)²]}^1/2}  [1 + (β_n cosine θ)]}}}⁴/C}}} ^odx_n}(A)}+ [M_restC²]}/[M_restC²] 

 

= {{Σ (i = 1, i = n) ʃF _i^odx_i }+ [M_restC²]}/[M_restC²]   = {{Σ (i = 1, i = n) {{ʃ{[(θ_si)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{γ_i [1 + (β_i cosine θ)]}}}⁴/C}}}^odx_i}(A)}}+ [M_restC²]}/[M_restC²] 

=   {{Σ (i = 1, i = n) ʃ{[(θ_si)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{ {1/{1 – [(v_i/C)²]}^1/2}  [1 + (β_i cosine θ)]}}}⁴/C}}} ^odx_i}+ [M_restC²]}/[M_restC²] 

Now, v = C{[-[1/γ²] + 1]^1/2} according to Special Relativity. Consequently, the following formulas can be used to compute v by numerical trial and error.

v = C{{-{1/{{[E_KEtotalgain] + [M_restC²]}/[M_restC²]}²} – 1}^1/2}  

 

=  C{{-{1/{{[ʃF ₁^odx₁]  + [ʃF ₂^odx₂]  + [ʃF ₃^odx₃ ] + ʃF _n^odx_n]} + [M_restC²]}/[M_restC²]}  ²}} + 1}^1/2}

=  C{{-{1/{{{{ʃ{[(θ_s1)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{γ₁ [1 + (β₁ cosine θ)]}}}⁴/C}}}^odx₁}(A)}+   {{ʃ{[(θ_s2)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{γ₂ [1 + (β₂ cosine θ)]}}}⁴/C}}} ^odx₂ }(A)} +  {{ʃ{[(θ_s3)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{γ₃ [1 + (β₃ cosine θ)]}}}⁴/C}}} ^odx₃ }(A)}   + … + {{ʃ{[(θ_sn)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{γ_n [1 + (β_n cosine θ)]}}}⁴/C}}} ^odx_n}(A)}+ [M_restC²]}/[M_restC²]}  ²}} + 1}^1/2}

=  C{{-{1/{{{{ʃ{[(θ_s1)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{{1/{1 – [(v₁/C)²]}^1/2} [1 + (β₁ cosine θ)]}}}⁴/C}}}^odx₁  }(A)} +  {{ʃ{[(θ_s2)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{ {1/{1 – [(v₂/C)²]}^1/2}  [1 + (β₂ cosine θ)]}}}⁴/C}}} ^odx₂ }(A)} +  {{ʃ{[(θ_s3)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{ {1/{1 – [(v₃/C)²]}^1/2}  [1 + (β₃ cosine θ)]}}}⁴/C}}} ^odx₃ }(A)} + … +  {{ʃ{[(θ_sn)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{ {1/{1 – [(v_n/C)²]}^1/2}  [1 + (β_n cosine θ)]}}}⁴/C}}} ^odx_n}(A)}+ [M_restC²]}/[M_restC²]}²}} + 1}^1/2}.   .

=  C{{-{1/{{{{Σ (i = 1, i = n) ʃF _i^odx_i }+ [M_restC²]}/[M_restC²]}   ²}} + 1}^1/2} 

=    C{{-{1/{{{{Σ (i = 1, i = n) {{ʃ{[(θ_si)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{γ_i [1 + (β_i cosine θ)]}}}⁴/C}}}^odx_i}(A)}}+ [M_restC²]}/[M_restC²]}  ²}} + 1}^1/2} 

=   C{{-{1/{{{{Σ (i = 1, i = n) {{ʃ{[(θ_si)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{ {1/{1 – [(v_i/C)²]}^1/2}  [1 + (β_i cosine θ)]}}}⁴/C}}} ^odx_i}(A)}}+ [M_restC²]}/[M_restC²]}  ²}} + 1}^1/2}

When the to two sides of the above equations are equal, we will have thus computed relativistic velocity, v.   

As you can see, for cases where there is much natural variation in acceleration with respect to the space craft frame, and for travel over very long distances, many iterations or steps need to be used in numerical algorithms to get mil spec and super-mil-spec results. Such precision is needed when traveling near light speed otherwise mission disaster could happen. In actuality, the above formulations would not be fit for mil spec computations because of the mere approximation to the actual vehicular performance.

We now consider scenarios where the photon angle of incidence from behind is considered and where drag effects are neglected for total space craft energy gains, accrued gamma factors, and accrued velocities. Here, we consider only angular values of radiation incident on the sail for which the radiation exerts forward pressure. In otherwords, we only consider values of θ₀ less than or equal to 90 degrees or π/2 radians. We also assume perfect backward sail reflectivity or trivially imperfect backward reflectivity and trivial massive astrodynamic drag.

The total kinetic energy gain for the craft will be

E _totalgain = ʃF ₁^odx₁  +  ʃF ₂^odx₂ + ʃF ₃^odx₃ + … +ʃF _n^odx_n

= {Σ(i = 1, i = n) {{{[[(θ_01i,1²) - (θ_02i,1²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,1 , θ_s2i,1)}^-1}{{[dr_bi,1/dr_ai,1]}│(r_b1i,1 , r_b2i,1)}[cos [(θ_01i,1 +  θ_02i,1)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ₁ [1 + [β₁cosine [(θ_01i,1 + θ_02i,1)/2]]]}}}⁴/C}}}^odx₁}/n}(A)}}}  

+  {Σ(i = 1, i = n) {{{[[(θ_01i,2²) - (θ_02i,2²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,2 , θ_s2i,2)}^-1}{{[dr_bi,2/dr_ai,2]}│(r_b1i,2 , r_b2i,2)}[cos [(θ_01i,2 +  θ_02i,2)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ₂ [1 + [β₂cosine [(θ_01i,2 + θ_02i,2)/2]]]}}}⁴/C}}}^odx₂}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{[[(θ_01i,3²) - (θ_02i,3²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,3 , θ_s2i,3)}^-1}{{[dr_bi,3/dr_ai,3]}│(r_b1i,3 , r_b2i,3)}[cos [(θ_01i,3 +  θ_02i,3)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ₃ [1 + [β₃cosine [(θ_01i,3 + θ_02i,3)/2]]]}}}⁴/C}}}^odx₃}/n}(A)}}} 

+ … +    {Σ(i = 1, i = n) {{{[[(θ_01i,m²) - (θ_02i,m²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,m , θ_s2i,m)}^-1}{{[dr_bi,m/dr_ai,m]}│(r_b1i,m , r_b2i,m)}[cos [(θ_01i,m +  θ_02i,m)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ_m[1 + [β₂cosine [(θ_01i,m + θ_02i,m)/2]]]}}}⁴/C}}}^odx_m}/n}(A)}}} 

= {Σ(i = 1, i = n) {{{[[(θ_01i,1²) - (θ_02i,1²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,1 , θ_s2i,1)}^-1}{{[dr_bi,1/dr_ai,1]}│(r_b1i,1 , r_b2i,1)}[cos [(θ_01i,1 +  θ_02i,1)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{{1/{1 – [(v₁/C)²]}^1/2}  [1 + [(v₁/C)cosine [(θ_01i,1 + θ_02i,1)/2]]]}}}⁴/C}}}^odx₁}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{[[(θ_01i,2²) - (θ_02i,2²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,2 , θ_s2i,2)}^-1}{{[dr_bi,2/dr_ai,2]}│(r_b1i,2 , r_b2i,2)}[cos [(θ_01i,2 +  θ_02i,2)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v₂/C)²]}^1/2}  [1 + [(v₂/C)cosine [(θ_01i,2 + θ_02i,2)/2]]]}}}⁴/C}}}^odx₂}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{[[(θ_01i,3²) - (θ_02i,3²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,3 , θ_s2i,3)}^-1}{{[dr_bi,3/dr_ai,3]}│(r_b1i,3 , r_b2i,3)}[cos [(θ_01i,3 +  θ_02i,3)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v₃/C)²]}^1/2}  [1 + [(v₃/C)cosine [(θ_01i,3 + θ_02i,3)/2]]]}}}⁴/C}}}^odx₃}/n}(A)}}} 

+ … +    {Σ(i = 1, i = n) {{{[[(θ_01i,m²) - (θ_02i,m²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,m , θ_s2i,m)}^-1}{{[dr_bi,m/dr_ai,m]}│(r_b1i,m , r_b2i,m)}[cos [(θ_01i,m +  θ_02i,m)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v_m/C)²]}^1/2} [1 + [(v_m/C)cosine [(θ_01i,m + θ_02i,m)/2]]]}}}⁴/C}}}^odx_m}/n}(A)}}} 

=  Σ(i = 1, i = m)   {Σ(i = 1, i = n) {{{[[(θ_01i,j²) - (θ_02i,j²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,j , θ_s2i,j)}^-1}{{[dr_bi,j/dr_ai,j]}│(r_b1i,j , r_b2i,j)}[cos [(θ_01i,j +  θ_02i,j)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ_j [1 + [β_jcosine [(θ_01i,j + θ_02i,j)/2]]]}}}⁴/C}}}^odx_j}/n}(A)}}} 

= Σ(i = 1, i = m)   {Σ(i = 1, i = n) {{{[[(θ_01i,j²) - (θ_02i,j²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,j , θ_s2i,j)}^-1}{{[dr_bi,j/dr_ai,j]}│(r_b1i,j , r_b2i,j)}[cos [(θ_01i,j +  θ_02i,j)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v_j/C)²]}^1/2}  [1 + [(v_j/C)cosine [(θ_01i,j + θ_02i,j)/2]]]}}}⁴/C}}}^odx_j}/n}(A)}}} 

= {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_sli,1]}}}

²} – {{cos^-1 {{[cos θ_s2i,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_s2i,1]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v₁/C)}/{1 – [(v₁/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,1 , θ_s2i,1)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v₁ /C)}/{1 – [(v₁/C) cos θ_s]}}}}│[cos  θ_s1i,1 ,  cos θ_s2i,1]}{cos {{{cos^-1 {{[cos θ_sli,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_sli,1]}}}+  {cos^-1 {{[cos θ_s2i,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_s2i,1]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ₁ {1 + {β₁cosine {{{cos^-1 {{[cos θ_sli,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_sli,1]}}}+ {cos^-1 {{[cos θ_s2i,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_s2i,1]}}}}/2}}}}}}⁴/C}}}^odx₁}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_sli,2]}}}

²} – {{cos^-1 {{[cos θ_s2i,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_s2i,2]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v₂/C)}/{1 – [(v₂/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,2 , θ_s2i,2)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v₂ /C)}/{1 – [(v₂/C) cos θ_s]}}}}│[cos  θ_s1i,2 ,  cos θ_s2i,2]}{cos {{{cos^-1 {{[cos θ_sli,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_sli,2]}}}+  {cos^-1 {{[cos θ_s2i,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_s2i,2]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ₂ {1 + {β₂cosine {{{cos^-1 {{[cos θ_sli,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_sli,2]}}}+ {cos^-1 {{[cos θ_s2i,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_s2i,2]}}}}/2}}}}}}⁴/C}}}^odx₂}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_sli,3]}}}

²} – {{cos^-1 {{[cos θ_s2i,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_s2i,3]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v₃/C)}/{1 – [(v₃/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,3 , θ_s2i,3)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v₃ /C)}/{1 – [(v₃/C) cos θ_s]}}}}│[cos  θ_s1i,3 ,  cos θ_s2i,3]}{cos {{{cos^-1 {{[cos θ_sli,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_sli,3]}}}+  {cos^-1 {{[cos θ_s2i,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_s2i,3]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ₃ {1 + {β₃cosine {{{cos^-1 {{[cos θ_sli,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_sli,3]}}}+ {cos^-1 {{[cos θ_s2i,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_s2i,3]}}}}/2}}}}}}⁴/C}}}^odx₃}/n}(A)}}} 

+ … +   {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_sli,m]}}}

²} – {{cos^-1 {{[cos θ_s2i,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_s2i,m]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v_m/C)}/{1 – [(v_m/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,m , θ_s2i,m)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v_m /C)}/{1 – [(v_m/C) cos θ_s]}}}}│[cos  θ_s1i,m ,  cos θ_s2i,m]}{cos {{{cos^-1 {{[cos θ_sli,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_sli,m]}}}+  {cos^-1 {{[cos θ_s2i,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_s2i,m]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ_m {1 + {β_mcosine {{{cos^-1 {{[cos θ_sli,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_sli,m]}}}+ {cos^-1 {{[cos θ_s2i,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_s2i,m]}}}}/2}}}}}}⁴/C}}}^odx_m}/n}(A)}}} 

= {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_sli,1]}}}

²} – {{cos^-1 {{[cos θ_s2i,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_s2i,1]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v₁/C)}/{1 – [(v₁/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,1 , θ_s2i,1)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v₁ /C)}/{1 – [(v₁/C) cos θ_s]}}}}│[cos  θ_s1i,1 ,  cos θ_s2i,1]}{cos {{{cos^-1 {{[cos θ_sli,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_sli,1]}}}+  {cos^-1 {{[cos θ_s2i,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_s2i,1]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v₁/C)²]}^1/2}   {1 + {(v₁/C)cosine {{{cos^-1 {{[cos θ_sli,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_sli,1]}}}+ {cos^-1 {{[cos θ_s2i,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_s2i,1]}}}}/2}}}}}}⁴/C}}}^odx₁}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_sli,2]}}}

²} – {{cos^-1 {{[cos θ_s2i,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_s2i,2]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v₂/C)}/{1 – [(v₂/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,2 , θ_s2i,2)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v₂ /C)}/{1 – [(v₂/C) cos θ_s]}}}}│[cos  θ_s1i,2 ,  cos θ_s2i,2]}{cos {{{cos^-1 {{[cos θ_sli,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_sli,2]}}}+  {cos^-1 {{[cos θ_s2i,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_s2i,2]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v₂/C)²]}^1/2}   {1 + {(v₂/C)cosine {{{cos^-1 {{[cos θ_sli,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_sli,2]}}}+ {cos^-1 {{[cos θ_s2i,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_s2i,2]}}}}/2}}}}}}⁴/C}}}^odx₂}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_sli,3]}}}

²} – {{cos^-1 {{[cos θ_s2i,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_s2i,3]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v₃/C)}/{1 – [(v₃/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,3 , θ_s2i,3)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v₃ /C)}/{1 – [(v₃/C) cos θ_s]}}}}│[cos  θ_s1i,3 ,  cos θ_s2i,3]}{cos {{{cos^-1 {{[cos θ_sli,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_sli,3]}}}+  {cos^-1 {{[cos θ_s2i,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_s2i,3]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v₃/C)²]}^1/2}   {1 + {(v₃/C)cosine {{{cos^-1 {{[cos θ_sli,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_sli,3]}}}+ {cos^-1 {{[cos θ_s2i,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_s2i,3]}}}}/2}}}}}}⁴/C}}}^odx₃}/n}(A)}}} 

+ … +   {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_sli,m]}}}

²} – {{cos^-1 {{[cos θ_s2i,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_s2i,m]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v_m/C)}/{1 – [(v_m/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,m , θ_s2i,m)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v_m /C)}/{1 – [(v_m/C) cos θ_s]}}}}│[cos  θ_s1i,m ,  cos θ_s2i,m]}{cos {{{cos^-1 {{[cos θ_sli,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_sli,m]}}}+  {cos^-1 {{[cos θ_s2i,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_s2i,m]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v_m/C)²]}^1/2}   {1 + {(v_m/C)cosine {{{cos^-1 {{[cos θ_sli,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_sli,m]}}}+ {cos^-1 {{[cos θ_s2i,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_s2i,m]}}}}/2}}}}}}⁴/C}}}^odx_m}/n}(A)}}} 

Σ ( j= 1, j = m) {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}

²} – {{cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v_j/C)}/{1 – [(v_j/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,j , θ_s2i,j)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v_j /C)}/{1 – [(v_j/C) cos θ_s]}}}}│[cos  θ_s1i,j ,  cos θ_s2i,j]}{cos {{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}+  {cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ_j {1 + {β_jcosine {{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}+ {cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}}/2}}}}}}⁴/C}}}^odx_j}/n}(A)}}} 

= Σ ( j= 1, j = m) {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}

²} – {{cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v_j/C)}/{1 – [(v_j/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,j , θ_s2i,j)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v_j /C)}/{1 – [(v_j/C) cos θ_s]}}}}│[cos  θ_s1i,j ,  cos θ_s2i,j]}{cos {{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}+  {cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v_j/C)²]}^1/2}   {1 + {(v_j/C)cosine {{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}+ {cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}}/2}}}}}}⁴/C}}}^odx_j}/n}(A)}}} 

 

 

The following numerical formula offers a first order approximation of space craft gamma factor  gain;

{[E_KEtotalgain] + [M_restC²]}/[M_restC²]= {[ʃF ₁^odx₁]  +  [ʃF ₂^odx₂]  + [ʃF ₃^odx₃ ] + … + [ʃF _n^odx_n] + [M_restC²]}/[M_restC²] 

 

 

= {{{Σ(i = 1, i = n) {{{[[(θ_01i,1²) - (θ_02i,1²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,1 , θ_s2i,1)}^-1}{{[dr_bi,1/dr_ai,1]}│(r_b1i,1 , r_b2i,1)}[cos [(θ_01i,1 +  θ_02i,1)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ₁ [1 + [β₁cosine [(θ_01i,1 + θ_02i,1)/2]]]}}}⁴/C}}}^odx₁}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{[[(θ_01i,2²) - (θ_02i,2²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,2 , θ_s2i,2)}^-1}{{[dr_bi,2/dr_ai,2]}│(r_b1i,2 , r_b2i,2)}[cos [(θ_01i,2 +  θ_02i,2)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ₂ [1 + [β₂cosine [(θ_01i,2 + θ_02i,2)/2]]]}}}⁴/C}}}^odx₂}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{[[(θ_01i,3²) - (θ_02i,3²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,3 , θ_s2i,3)}^-1}{{[dr_bi,3/dr_ai,3]}│(r_b1i,3 , r_b2i,3)}[cos [(θ_01i,3 +  θ_02i,3)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ₃ [1 + [β₃cosine [(θ_01i,3 + θ_02i,3)/2]]]}}}⁴/C}}}^odx₃}/n}(A)}}} 

+ … +    {Σ(i = 1, i = n) {{{[[(θ_01i,m²) - (θ_02i,m²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,m , θ_s2i,m)}^-1}{{[dr_bi,m/dr_ai,m]}│(r_b1i,m , r_b2i,m)}[cos [(θ_01i,m +  θ_02i,m)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ_m[1 + [β₂cosine [(θ_01i,m + θ_02i,m)/2]]]}}}⁴/C}}}^odx_m}/n}(A)}}}}  + [M_restC²]}/[M_restC²] 

= {{{Σ(i = 1, i = n) {{{[[(θ_01i,1²) - (θ_02i,1²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,1 , θ_s2i,1)}^-1}{{[dr_bi,1/dr_ai,1]}│(r_b1i,1 , r_b2i,1)}[cos [(θ_01i,1 +  θ_02i,1)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{{1/{1 – [(v₁/C)²]}^1/2}  [1 + [(v₁/C)cosine [(θ_01i,1 + θ_02i,1)/2]]]}}}⁴/C}}}^odx₁}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{[[(θ_01i,2²) - (θ_02i,2²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,2 , θ_s2i,2)}^-1}{{[dr_bi,2/dr_ai,2]}│(r_b1i,2 , r_b2i,2)}[cos [(θ_01i,2 +  θ_02i,2)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v₂/C)²]}^1/2}  [1 + [(v₂/C)cosine [(θ_01i,2 + θ_02i,2)/2]]]}}}⁴/C}}}^odx₂}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{[[(θ_01i,3²) - (θ_02i,3²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,3 , θ_s2i,3)}^-1}{{[dr_bi,3/dr_ai,3]}│(r_b1i,3 , r_b2i,3)}[cos [(θ_01i,3 +  θ_02i,3)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v₃/C)²]}^1/2}  [1 + [(v₃/C)cosine [(θ_01i,3 + θ_02i,3)/2]]]}}}⁴/C}}}^odx₃}/n}(A)}}} 

+ … +    {Σ(i = 1, i = n) {{{[[(θ_01i,m²) - (θ_02i,m²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,m , θ_s2i,m)}^-1}{{[dr_bi,m/dr_ai,m]}│(r_b1i,m , r_b2i,m)}[cos [(θ_01i,m +  θ_02i,m)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v_m/C)²]}^1/2} [1 + [(v_m/C)cosine [(θ_01i,m + θ_02i,m)/2]]]}}}⁴/C}}}^odx_m}/n}(A)}}}}  + [M_restC²]}/[M_restC²] 

 

 

=  {{Σ(i = 1, i = m)   {Σ(i = 1, i = n) {{{[[(θ_01i,j²) - (θ_02i,j²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,j , θ_s2i,j)}^-1}{{[dr_bi,j/dr_ai,j]}│(r_b1i,j , r_b2i,j)}[cos [(θ_01i,j +  θ_02i,j)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ_j [1 + [β_jcosine [(θ_01i,j + θ_02i,j)/2]]]}}}⁴/C}}}^odx_j}/n}(A)}}}}  + [M_restC²]}/[M_restC²] 

= {{Σ(i = 1, i = m)   {Σ(i = 1, i = n) {{{[[(θ_01i,j²) - (θ_02i,j²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,j , θ_s2i,j)}^-1}{{[dr_bi,j/dr_ai,j]}│(r_b1i,j , r_b2i,j)}[cos [(θ_01i,j +  θ_02i,j)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v_j/C)²]}^1/2}  [1 + [(v_j/C)cosine [(θ_01i,j + θ_02i,j)/2]]]}}}⁴/C}}}^odx_j}/n}(A)}}} + [M_restC²]}/[M_restC²]   

 

 

 

 

= {{{Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_sli,1]}}}

²} – {{cos^-1 {{[cos θ_s2i,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_s2i,1]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v₁/C)}/{1 – [(v₁/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,1 , θ_s2i,1)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v₁ /C)}/{1 – [(v₁/C) cos θ_s]}}}}│[cos  θ_s1i,1 ,  cos θ_s2i,1]}{cos {{{cos^-1 {{[cos θ_sli,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_sli,1]}}}+  {cos^-1 {{[cos θ_s2i,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_s2i,1]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ₁ {1 + {β₁cosine {{{cos^-1 {{[cos θ_sli,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_sli,1]}}}+ {cos^-1 {{[cos θ_s2i,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_s2i,1]}}}}/2}}}}}}⁴/C}}}^odx₁}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_sli,2]}}}

²} – {{cos^-1 {{[cos θ_s2i,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_s2i,2]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v₂/C)}/{1 – [(v₂/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,2 , θ_s2i,2)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v₂ /C)}/{1 – [(v₂/C) cos θ_s]}}}}│[cos  θ_s1i,2 ,  cos θ_s2i,2]}{cos {{{cos^-1 {{[cos θ_sli,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_sli,2]}}}+  {cos^-1 {{[cos θ_s2i,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_s2i,2]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ₂ {1 + {β₂cosine {{{cos^-1 {{[cos θ_sli,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_sli,2]}}}+ {cos^-1 {{[cos θ_s2i,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_s2i,2]}}}}/2}}}}}}⁴/C}}}^odx₂}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_sli,3]}}}

²} – {{cos^-1 {{[cos θ_s2i,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_s2i,3]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v₃/C)}/{1 – [(v₃/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,3 , θ_s2i,3)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v₃ /C)}/{1 – [(v₃/C) cos θ_s]}}}}│[cos  θ_s1i,3 ,  cos θ_s2i,3]}{cos {{{cos^-1 {{[cos θ_sli,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_sli,3]}}}+  {cos^-1 {{[cos θ_s2i,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_s2i,3]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ₃ {1 + {β₃cosine {{{cos^-1 {{[cos θ_sli,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_sli,3]}}}+ {cos^-1 {{[cos θ_s2i,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_s2i,3]}}}}/2}}}}}}⁴/C}}}^odx₃}/n}(A)}}} 

+ … +   {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_sli,m]}}}

²} – {{cos^-1 {{[cos θ_s2i,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_s2i,m]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v_m/C)}/{1 – [(v_m/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,m , θ_s2i,m)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v_m /C)}/{1 – [(v_m/C) cos θ_s]}}}}│[cos  θ_s1i,m ,  cos θ_s2i,m]}{cos {{{cos^-1 {{[cos θ_sli,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_sli,m]}}}+  {cos^-1 {{[cos θ_s2i,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_s2i,m]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ_m {1 + {β_mcosine {{{cos^-1 {{[cos θ_sli,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_sli,m]}}}+ {cos^-1 {{[cos θ_s2i,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_s2i,m]}}}}/2}}}}}}⁴/C}}}^odx_m}/n}(A)}}}} + [M_restC²]}/[M_restC²]   

= {{{Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_sli,1]}}}

²} – {{cos^-1 {{[cos θ_s2i,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_s2i,1]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v₁/C)}/{1 – [(v₁/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,1 , θ_s2i,1)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v₁ /C)}/{1 – [(v₁/C) cos θ_s]}}}}│[cos  θ_s1i,1 ,  cos θ_s2i,1]}{cos {{{cos^-1 {{[cos θ_sli,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_sli,1]}}}+  {cos^-1 {{[cos θ_s2i,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_s2i,1]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v₁/C)²]}^1/2}   {1 + {(v₁/C)cosine {{{cos^-1 {{[cos θ_sli,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_sli,1]}}}+ {cos^-1 {{[cos θ_s2i,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_s2i,1]}}}}/2}}}}}}⁴/C}}}^odx₁}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_sli,2]}}}

²} – {{cos^-1 {{[cos θ_s2i,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_s2i,2]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v₂/C)}/{1 – [(v₂/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,2 , θ_s2i,2)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v₂ /C)}/{1 – [(v₂/C) cos θ_s]}}}}│[cos  θ_s1i,2 ,  cos θ_s2i,2]}{cos {{{cos^-1 {{[cos θ_sli,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_sli,2]}}}+  {cos^-1 {{[cos θ_s2i,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_s2i,2]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v₂/C)²]}^1/2}   {1 + {(v₂/C)cosine {{{cos^-1 {{[cos θ_sli,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_sli,2]}}}+ {cos^-1 {{[cos θ_s2i,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_s2i,2]}}}}/2}}}}}}⁴/C}}}^odx₂}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_sli,3]}}}

²} – {{cos^-1 {{[cos θ_s2i,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_s2i,3]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v₃/C)}/{1 – [(v₃/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,3 , θ_s2i,3)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v₃ /C)}/{1 – [(v₃/C) cos θ_s]}}}}│[cos  θ_s1i,3 ,  cos θ_s2i,3]}{cos {{{cos^-1 {{[cos θ_sli,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_sli,3]}}}+  {cos^-1 {{[cos θ_s2i,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_s2i,3]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v₃/C)²]}^1/2}   {1 + {(v₃/C)cosine {{{cos^-1 {{[cos θ_sli,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_sli,3]}}}+ {cos^-1 {{[cos θ_s2i,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_s2i,3]}}}}/2}}}}}}⁴/C}}}^odx₃}/n}(A)}}} 

+ … +   {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_sli,m]}}}

²} – {{cos^-1 {{[cos θ_s2i,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_s2i,m]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v_m/C)}/{1 – [(v_m/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,m , θ_s2i,m)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v_m /C)}/{1 – [(v_m/C) cos θ_s]}}}}│[cos  θ_s1i,m ,  cos θ_s2i,m]}{cos {{{cos^-1 {{[cos θ_sli,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_sli,m]}}}+  {cos^-1 {{[cos θ_s2i,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_s2i,m]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v_m/C)²]}^1/2}   {1 + {(v_m/C)cosine {{{cos^-1 {{[cos θ_sli,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_sli,m]}}}+ {cos^-1 {{[cos θ_s2i,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_s2i,m]}}}}/2}}}}}}⁴/C}}}^odx_m}/n}(A)}}}}  [M_restC²]}/[M_restC²]   

 

 

 

 

{{Σ ( j= 1, j = m) {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}

²} – {{cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v_j/C)}/{1 – [(v_j/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,j , θ_s2i,j)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v_j /C)}/{1 – [(v_j/C) cos θ_s]}}}}│[cos  θ_s1i,j ,  cos θ_s2i,j]}{cos {{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}+  {cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ_j {1 + {β_jcosine {{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}+ {cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}}/2}}}}}}⁴/C}}}^odx_j}/n}(A)}}}} + [M_restC²]}/[M_restC²]     

= {{Σ ( j= 1, j = m) {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}

²} – {{cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v_j/C)}/{1 – [(v_j/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,j , θ_s2i,j)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v_j /C)}/{1 – [(v_j/C) cos θ_s]}}}}│[cos  θ_s1i,j ,  cos θ_s2i,j]}{cos {{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}+  {cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v_j/C)²]}^1/2}   {1 + {(v_j/C)cosine {{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}+ {cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}}/2}}}}}}⁴/C}}}^odx_j}/n}(A)}}}} + [M_restC²]}/[M_restC²]    

For total accrued velocity, v, we have

 

v = C{{-{1/{{{Σ(i = 1, i = m)   {Σ(i = 1, i = n) {{{[[(θ_01i,j²) - (θ_02i,j²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,j , θ_s2i,j)}^-1}{{[dr_bi,j/dr_ai,j]}│(r_b1i,j , r_b2i,j)}[cos [(θ_01i,j +  θ_02i,j)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ_j [1 + [β_jcosine [(θ_01i,j + θ_02i,j)/2]]]}}}⁴/C}}}^odx_j}/n}(A)}}}}  + [M_restC²]}/[M_restC²]}  ²}} + 1}^1/2}

= C{{-{1/{{{Σ(i = 1, i = m)   {Σ(i = 1, i = n) {{{[[(θ_01i,j²) - (θ_02i,j²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,j , θ_s2i,j)}^-1}{{[dr_bi,j/dr_ai,j]}│(r_b1i,j , r_b2i,j)}[cos [(θ_01i,j +  θ_02i,j)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v_j/C)²]}^1/2}  [1 + [(v_j/C)cosine [(θ_01i,j + θ_02i,j)/2]]]}}}⁴/C}}}^odx_j}/n}(A)}}} + [M_restC²]}/[M_restC²]} ²}} + 1}^1/2}

= C{{-{1/{{{Σ ( j= 1, j = m) {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}

²} – {{cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v_j/C)}/{1 – [(v_j/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,j , θ_s2i,j)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v_j /C)}/{1 – [(v_j/C) cos θ_s]}}}}│[cos  θ_s1i,j ,  cos θ_s2i,j]}{cos {{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}+  {cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ_j {1 + {β_jcosine {{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}+ {cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}}/2}}}}}}⁴/C}}}^odx_j}/n}(A)}}}} + [M_restC²]}/[M_restC²]}     

²}} + 1}^1/2}

= C{{-{1/{{{Σ ( j= 1, j = m) {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}

²} – {{cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v_j/C)}/{1 – [(v_j/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,j , θ_s2i,j)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v_j /C)}/{1 – [(v_j/C) cos θ_s]}}}}│[cos  θ_s1i,j ,  cos θ_s2i,j]}{cos {{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}+  {cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v_j/C)²]}^1/2}   {1 + {(v_j/C)cosine {{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}+ {cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}}/2}}}}}}⁴/C}}}^odx_j}/n}(A)}}}} + [M_restC²]}/[M_restC²]  ²}} + 1}^1/2}

As you can see, attempts at analytic solutions and even non-computational numerical solutions would pose a proverbial night-mare.

Now consider again that radiation pressure is equal to σT⁴/C and {2 [σT⁴/C]} for reflected radiation. However, for a space craft traveling through a black body radiation field, the apparent temperature of the radiation increases in proportion to γ and so the black body power impinging on the space craft from directly in front grows in proportion to T⁴ and thus  to γ⁴.

The temperature of a black body is T = {P/[(A)(σ)(e)]}^1/4 = {P/{(A)[5.670400(40) x 10^-8 W m^-2 K^-4]} ^1/4}. Therefore, the cosmic microwave background radiation pressure on a perfectly reflective flat bow  relativistic space craft is approximately equal to  {2 [σT_cmbr ⁴/C]} γ⁴ = {2 [σT_cmbr ⁴/C]} { {1/{1 – [(v/C)²]}^1/2}  ⁴} =   {2 [σT_cmbr ⁴/C]} {1/{1 – [(v/C)²]}²} where γ is constant and T_cmbr is constant. However, the light pressure incident from directly behind will be approximately equal to {2 [σT_cmbr ⁴/C]}/{1/{1 – [(v/C)²]}²}. In actuality, not all of the light is directly incident from the back and so there will be angular affects that result in loss of driving power. However, we will assume that all of the radiation is absorbed and then re-cycled and released as a perfect backwardly directed laser beam. We will assume that CMBR light which is forwardly incident completely passes through the sail.

Assuming that the velocity of the sail starts out at (Zero) C, the optical pressure will be equal to {{2 [σT_cmbr⁴/C]}/γ⁴} = {{2 [σT_cmbr⁴/C]}/ { {1/{1 – [(v/C)²]}^1/2} ⁴} } = {{2{[5.670400(40) x 10^-8 W m^-2 K^-4][(2.725 K)⁴]/(300,000,000 m/s)}}/(1²)} = [2.0844355 x 10^-14] Newtons/m². For a 10,000 km by 10,000 km sail, the drive force will be 2.0844 Newtons. A 100,000 km by 100,000 km sail will produce a driving force of 208.44 Newtons.

Now assume that the sail is monolithic, made of one nanometer thick carbonaceous, STP water density materials. The sail would have a mass of 10,000,000 thousand metric tons. Assuming that the space craft plus her sail had a mass of 20,844,000 metric tons, the craft would start out with an acceleration of F/M = a = 208.44 N/20,844,000,000 kg = 10^-8 meter/s². After traveling 6 x 10¹⁵ seconds or about 200,000,000 years, the velocity of the space craft will be 0.20 C and the relativistic Lorentz transformation factor will be 1.0206 thus permitting the above Newtonian formula to apply as a reasonable approximation.

Assume that the background gas and dust that contacts the sail over a path length of 1 light year has an invariant  mass of (0.06667 kg)( 10¹⁴){[ 3 x 10¹⁰]^-1} = 222.2 kg. The momentum of the gas and dust with respect to the sail will be (m)(v) = (222.2 kg)(50,000,000 m/s) =1.111 x 10¹⁰  kg m s. Now Force equal dP/dt. Therefore, the force on the sail is on average equal to F_0.05C  = dP_0.2C/dt = 71.677 Newtons.. For a velocity of 0.02 C, the net propulsive force is 208.44 N – 71.67 N = 136.76 N which will still obviously permit 0.2 C velocities.

For such a space craft that deployed a linear series of 1,000 tethered sails where each sail was separated by an efficient 10 sail widths, a space craft having a total mass of 208, 440,000 metric tons could be identically accelerated. The mass of the crew quarters would be 108,440,000 metric tons. For such a space craft that deployed a linear series of 1,000,000 tethered sails where each sail was separated by an efficient 10 sail widths, a space craft having a total mass of 208, 440,000,000  metric tons could be identically accelerated. The mass of the crew quarters would be 108,440,000,000  metric tons. For cosmic journeys, this is not bad. A series of 100 million tethered sails might conceivably pull a sail craft combination having a mass of 20,844,000,000,000 metric tons and a crew quarters having a mass of 10,844,000,000,000 metric tons. For a velocity of 0.2 C, each of the latter massed space craft would have the same ratio of backward driving force and massive drag force. The caveat is simply the deployment of commensurate numbers of sails simultaneously in a spatial series along the space craft velocity vector.

Now assume that the sail is a gridded fabric or net made of STP water density conducting nanometer wide carbonaceous fibers that are separated by 0.0005 meters such as in a judicious cross weave spacing. A one square meter portion of the net will have a mass of 2 x 10^-12 kilograms. A 0.2 kilogram sail will have an plan form area of 10⁵ square kilometers. A 20,000 kilogram sail will have an plan form area of 10¹⁰ square kilometers and will have an acceleration of F/M = A = 208.44 Newtons/20,000 kg = 0.010422 m/s².  A space craft having a total mass of  20,000 metric tons will have an initial acceleration of 0.000010422 m/s².   In 200,000 years, the velocity of the 20,000 metric ton  system will be about 0.215388 C assuming Newtonian approximations.

Now, the 10¹⁰ square kilometer plan form area gridded sail will have a massive species contact area of [10¹⁰km²]/500,000 = 20,000 km². So the background gas and dust that contacts the sail over a path length of 1 light year has an invariant  mass of (0.06667 kg)( 10¹⁴){[ 3 x 10¹⁰]^-1}/(500,000) = 0.0004444 kg. The momentum of the gas and dust with respect to the sail will be (m)(v) = (0.0004444 kg)(50,000,000 m/s) =22,220 kg m s. Now Force equal dP/dt. Therefore, the force on the sail is on average equal to F_0.05C  = dP_0.2C/dt = 0.000143354 Newtons.. For a velocity of 0.02 C, the ratio of the driving force to massive drag force is [208.44 N/ 0.000143354 N] = 1,454,000.

Regards;

Jim

Copyright James M. Essig January 26, 2012 All Rights Reserved.

A Heads Up On Some Upcoming Really Cool New (At Least To My Writing) CMBR Interstellar Sailing Concepts That Should Work In Theory. Also, My Apology For The Posting Of Several Unworkable Concepts Under The “Interstellar CMBR Sailing Ships” Series Of Posts And Notice Of My Deletion Of The Subject Erroneous Posts.

You may have read or glanced through some of my “Interstelllar CMBR Sailing Ships” articles. Most of the subject anticipated  concepts would not work. However, I have condensed a summary of actual workable concepts in the previous post “Interstellar CMBR Surfing” for traditional CMBR sails where by traditional, I assume sails that are orthogonally oriented to the space craft velocity vector and which involve more or less materials with ordinary optical properties.

 

While attempting to determine how to make the concepts work, I have discovered a whole host of methods and configurations far better than the would be possible failed concepts and will be posting these concepts in the days and weeks ahead. These concepts just morphed into my understanding thereof, one after another. I am pleased with how many configurational solutions and methods occurred to me over a time span of only a few minutes.

 

But first, I will post  a revised version of “Interstellar CMB Surfing” by sometime this afternoon, EST, USA. Then, I will progressively disclose the new concepts over the days and weeks to follow.

 

Regards;

 

Jim

Interstellar CMBR Surfing: 1st Edition.

You ever wonder whether or not physicists and theoretical engineers will at some point in time determine how to obtain a free lunch? Well, for all practical purposes, we have a free lunch. It is called the cosmic microwave background energy or CMBR and may be available in infinite quantities given that our entire universe may have an infinite volume and spatial extent, and perhaps also forward potential time extension. The CMBR will always be available provided no further phase changes or symmetric breaking events will convert the background photonic radiations to another useless form. As such, photons and electromagnetic waves are theoretically perfectly stable. As a Catholic and affectionato for the Holy Bible, I like to muse at times on the metaphor that light was the first element of creation in at least some translations. Now, the actual meaning of light is most likely a metaphor, but given that our universe in the Big Bang may have started out from pure energy where such energy was embodied in the start of the initial space-time and mass energy forms in a kind of space-time-energy unification, perhaps the Bible has a deeper meaning here that was somehow preserved from antiquity.

That space and time are intimately tied to electromagnetic radiation is obvious when one considered the ubiquitous inclusion of the speed of light in vacuu as a constant in virtually all special and general relativistic formulations. Even in classical electromagnetic theory, the velocity of light is intimately related to the properties of space time including the magnetic permeability and electric permittivity of free space by the formula C = {1/[μ₀ ɛ₀]}^1/2.

I am sure that most of the concepts expressed within this post have been contemplated by others before.

By now the reader is aware of the concept of light sail(s) driven space craft that can reach relativistic velocities. A space craft traveling at extreme gamma factors using an ordinary beam sail will experience extreme astro-dynamic drag, and the sail would likely be ionized by the drag induced friction. This is largely due to the fact that most beam sail space craft contemplate beam sails that are orthogonally spread  with respect to the craft velocity vector and thus which have a very large surface area to experience forward drag.

Suppose a relativistic rocket was powered by energy captured by an attached square or rectangular CMBR  sail that is  oriented in a perpendicular to the velocity vector of the space craft. The equation for Doppler shifting of  CMBR acting on the sail would then be:  

1 + z = {1 + [ ν (cos θ)/C]}/{[1 - [(v/C)²]]^1/2}

or,

z  = {1 + [ ν (cos θ)/C]}/{[1 - [(v/C)²]]^1/2} – 1

f’ = f / {γ [1 + (β cosine θ)]}

which reduces to F’ = f/γ for a radiation source and space craft moving in a direction perpendicular to the line connecting these reference frames with respect to a space craft observer since cos (π/2) = zero where f represents frequency. Here, θ is the angle of view with respect to the space craft velocity vector or the perceived angle of  radiation incidence on the sail with respect to the direction of space craft travel,  with respect to the space craft.

Now,  the energy of a photon is as follows:

E = [h/(2 π)] ω = hf = hC/λ 

where h is the Planck Constant and λ  is the photon wave-length.

Therefore, the energies of the individual CMBR photons impinging on the light sail oriented in a direction perpendicular to it from the space craft’s perspective from directly behind are equal to:

E + =  hf/{γ [1 + (β cos  θ)]} = hf /{γ [1 + (β cos  (0)]}

which reduces to;

hf /{γ [1 + β ]}.

Now,  the CMBR power impinging on the space craft sail per differential unit of time element (space craft reference frame), per differential unit of angle of pre-incidence (space craft reference frame), per differential element of sail area (space craft reference frame) for black body radiation is a function of γ ⁴. This is because the black body radiation frequency curve peak is proportional to black body source temperature and an incident source photon’s frequency is proportional gamma. Since black body total power emission per unit of surface area is proportional to the  fourth power of the temperature of the black body, the above differential area element of the sail will receive a total power that scales with γ ⁴. Black body emitter frequency distribution scales as a function of gamma relative to a moving observer traveling at a factor of γ with respect to the source for directly approaching observers and 1/ γ for directly receding observers.

Planck’s Law states that

 

I(ѵ,T)dѵ = {[2hѵ³]/C²}{1/{[e^[(hѵ)/(kT)]] -1}}dѵ

 

λ_max = b/T

 

 

 

 

where λ max,  is a function only of the temperature.

P_net = P_emit – P_absorbed

Applying the Stefan–Boltzmann law,

P_net = A σ e (T⁴ – T₀⁴)

 

 

where sigma =  σ = (2π⁵k_B⁴)/(15 h³ C²) = (π²k_B⁴)/(60 ђ³ C²)

 

 

 

 

or  where sigma =  σ = 5.670400(40) x 10^-8 W m^-2 K^-4

Therefore, the apparent spectral temperature of the CMBR radiation incident on the sail per unit angle of CMBR incidence for a stationary sail is:

{[P_cmbr/(A σ e)] ^1/4}

The apparent spectral temperature of the CMBR radiation incident on the sail per unit of apparent angle of incidence of the CMBR with respect to the space craft reference frame-based observer(s) for a sail traveling at a given velocity for backwardly impinging radiation is:

T_app = {∫(0, π/2){{{[P_cmbr/(e σ)]^1/4}/{γ [1 +  [(v/C) cos θ]]}}⁴}{{∫(y₁,y₂){ ∫(x₁,x₂) dx} dy}^-1} dθ}^1/4

 

= {∫(0, π/2){{{[P_cmbr/(e σ)]^1/4} /{{1/{[1 – [(v/C)² ]] ^1/2}} [1 +  [(v/C) cos θ]]}}⁴}{{∫(y₁,y₂){ ∫(x₁,x₂) dx} dy}^-1} dθ}^1/4

 

 

= {∫(0, π/2){{{[Pcmbr/(e σ)]^1/4}/{{1/{[1 – [(v/C)² ]] ^1/2}} [1 + [(v/C) cos θ]]}}⁴}[(∫d A)^-1] dθ}^1/4

where P_cmbr is the background CMBR power incident on the sail, dA is the differential element of sail area with respect to the space craft reference frame, v is the velocity of the space craft with respect to the background, and θ is the angle of radiation incidence on the sail with respect to a sail based observer. Theta ranges from π/2 radians for radiation traveling in an orthogonal direction with respect to the ship velocity vector to zero radians for radiation traveling in a parallel direction with respect to the ship velocity vector.

The total power backwardly incident upon the sail with respect to the sail’s reference frame for a given gamma factor  is  therefore:

P = ∫(y₁,y₂) {∫(x₁,x₂) {∫ (0, π/2) {{{(T_cmbr) /{γ [1 + [(v/C) cos θ]]}}⁴} σ e} dθ}dx}dy

= ∫(y₁,y₂) {∫(x₁,x₂) {∫ (0, π/2) {{{(T_cmbr) /{{1/{[1 + [(v/C)² ]] ^1/2}}  [1 + [(v/C) cos θ]]}}⁴} σ e} dθ}dx}dy

= ∫ {∫ (0, π/2) {{{(T_cmbr) /{{1/{[1 – [(v/C)² ]] ^1/2}}  [1 + [(v/C) cos θ]]}}⁴} σ e} dθ} dA

Here, T_cmbr is the background CMBR temperature.

Note that in the above calculations and the ones that follow, all of the relevant backwardly incident background energies are assumed to be initially absorbed by the sail even if the sail acquires a temperature significantly above absolute zero and thereby produces thermal electromagnetic black body emissions. I describe potential methods of the absorption of nearly all incident radiations even in cases where relativistic aberration would otherwise cause the bulk of the impinging radiation to easily reflect off the sail because of increasingly shallow angles of incidence. The forwardly incident radiation is assumed to completely pass through the sail without exchange of momentum.

We can numerically integrate the relativistic  energy growth of the ship in small time steps as follows:

∫P₁dt₁ + ∫P₂dt₂ + ∫P₃dt₃ +, …, + ∫P_ndt_n

Thus, the following expression can be used to compute relativistic energy gain by the ship in terms of t.

Egain  = Σ (0,n)    { ∫ (t_ai, t_bi) { ∫  (y₁, y₂){ ∫  (x₁,x₂){ ∫ (0,  π/2) {{{T_cmbr /{{{1/{[1 – [(v_i/C) ²]] ^1/2}}}[1 + [(v_i/C) cos θ]]}} ⁴} σ e}dθ}dx}dy} dt}      

Here,  t_ai, t_bi, and dt are the times in the background reference frame.

Note, the reason why I assume the latter three times are background reference frame times is such that for a space craft traveling at a velocity of just under 1 C, where gamma is held constant, the energy gain for the space craft will be proportional to the length of the path traveled by the space craft according to the background reference frame. The distance of space craft travel  is proportional to the time of space craft travel with respect to the background reference frame. The same is true for a space craft traveling at any velocity held constant, thus the reason for the performance of the numerical integration for each time step where the velocity is incrementally increased but held constant for each time step.

Alternatively, we can use the following series:

Egain =  Σ (1,n) { ∫ (t_ai, t_bi) {∫ {∫ (0, π/2)  {{{T_cmbr /{{1/{[1 – [(v_i/C) ²]] ^1/2}}[1 + [(v_i/C) cos θ]]}} ⁴} σ e}dθ} dA}dt}    

where t_ai and t_bi and dt are the times in the background reference frame.

Now for constant acceleration ship time, T₀ = (c/g) ln {{[[ (C²) + (V₀ ²)] ^1/2]   –   [V₀/[[1 – [(V₀/C) ²]] ^1/2 ]]} { [(C ²) + [[(g)(t)  + [V₀ /[1 – [(V₀/C) ²]] ^1/2 ] ²]] ^1/2] + [(g)(t)] +  [V₀/[[1 – [(V₀/C) ²]] ^1/2]]} / (C ²)}. We can incorporate the expression for T₀ prefaced by the notation Delta to indicate the time steps,  ship time,  of uniform duration ship frame.

For computation in terms of T₀, we obtain:

Egain = Σ (0,n)    {{ ∫  (y₁, y₂){ ∫  (x₁,x₂){ ∫ (0,  π/2) {{{T_cmbr /{{{1/{[1 – [(v_i/C) ²]] ^1/2}}}[1 + [(v_i/C) cos θ]]}} ⁴} σ e}dθ}dx}dy} {(Delta) {(c/g) ln {{[[ (C²) + (V_0i ²)] ^1/2]   –   [V_0i/[[1 – [(V_0i/C) ²]] ^1/2 ]]} { [(C ²) + [[(g_i)(t_i)  + [V_0i /[1 – [(V_0i/C) ²]] ^1/2 ] ²]] ^1/2] + [(g_i)(t_i)] +  [V₀/[[1 – [(V_0i/C) ²]] ^1/2]]} / (C ²)}}} {1/{[1 – [(v_i/C) ²]] ^1/2}}}  .     

where t_i is the time in the background reference frame and g_i is the ship acceleration in the ship’s reference frame.

Note that the above formulas provide precise calculations for many numerical iterations involving small increments for velocity increase and small time steps in the ship’s frame.

Alternatively, we can use the following series:

Egain =  Σ (1,n) { {∫ {∫ (0, π/2)  {{{T_cmbr /{{1/{[1 – [(v_i/C) ²]] ^1/2}}[1 + [(v_i/C) cos θ]]}} ⁴} σ e}dθ} dA} {(Delta) {(c/g) ln {{[[ (C²) + (V_0i ²)] ^1/2]   –   [V_0i/[[1 – [(V_0i/C) ²]] ^1/2 ]]} { [(C ²) + [[(g_i)(t_i)  + [V_0i /[1 – [(V_0i/C) ²]] ^1/2 ] ²]] ^1/2] + [(g_i)(t_i)] +  [V_0i/[[1 – [(V_0i/C) ²]] ^1/2]]} / (C ²)}}} {1/{[1 – [(v_i/C) ²]] ^1/2}}}             

Another method entails integration with respect to space craft velocity with respect to the background and integration with respect to time as follows:

E_gain = ∫ (v₁, v₂)  {{∫  (t₁, t₂) { ∫ (y₁, y₂){ ∫ (x₁,x₂){ ∫ (0,  π/2) {{{T_cmbr {1/{[1 – [(v/C) ²]] ^1/2}}[1 + [(v/C) cos θ]]} ⁴} σ e}dθ}dx}dy} dt}/v}dv

Or alternatively,

E_gain =  ∫(v₁,v₂) {∫ (t₁,t₂){∫  {∫ (0,  π/2) {{{_Tcmbr/{{{1/{[1 – [(v/C) ²]] ^1/2}}[1 + [(v/C) cos θ]]}}⁴} σ e} dθ} dA}dt}/v}dv

where t₁ and t₂ and dt are the times in the background reference frame.

Now, E_gain in practice needs to take into account the radiative temperature of the sail.

Now, given that

P_net = A σ e (T⁴ – T₀⁴)

 

where T is the body temperature and T₀ is the surrounding temperature, we can re-interpret T as the impinging radiation’s black body temperature and T₀ as the emitted thermal radiation black body temperature. So in other words, if the impinging temperature is 10 times higher in Kelvins then the thermal radiative temperature, the net power input into the sail is 10⁴ or 10,000 times greater than the power loss through radiative emissions.

 

The net power delivered to the  sail will be equal to the power intake minus the power thermally radiated as

P = {∫(y₁,y₂) {∫(x₁,x₂) {∫ (0, π/2) {{{(T_cmbr) /{γ [1 + [(v/C) cos θ]]}}⁴} σ e} dθ}dx}dy} – {∫(y₁,y₂) {∫(x₁,x₂) (T₀⁴ σ e) dx}dy}

= {∫(y₁,y₂) {∫(x₁,x₂) {∫ (0, π/2) {{{(T_cmbr) /{{1/{[1 + [(v/C)² ]] ^1/2}}  [1 + [(v/C) cos θ]]}}⁴} σ e} dθ}dx}dy}  – {∫(y₁,y₂) {∫(x₁,x₂) (T₀⁴ σ e) dx}dy}

= { ∫ {∫ (0, π/2) {{{(T_cmbr) /{{1/{[1 – [(v/C)² ]] ^1/2}}  [1 + [(v/C) cos θ]]}}⁴} σ e} dθ} dA} -

- {∫(T₀⁴ σ e) dA}

The following expression can be used to compute relativistic energy gain by the ship in consideration of the black body emissions from the sail heated by CMBR.

From computation in terms of t, we obtain:

Egain  = {Σ (0,n)   { ∫ (t_ai, t_bi) { ∫  (y₁, y₂){ ∫  (x₁,x₂){ ∫ (0,  π/2) {{{T_cmbr /{{{1/{[1 – [(v_i/C) ²]] ^1/2}}}[1 + [(v_i/C) cos θ]]}} ⁴} σ e}dθ}dx}dy} dt}}   – {Σ (0,n) {∫ (t_ai, t_bi) {∫(y₁,y₂) {∫(x₁,x₂) (T⁴_0i σ e) dx}dy}dt}}     

where t_ai and t_bi and dt are the times in the background reference frame.

Now ship time = T₀ = {(c/g_n) ln {[[ (C²) + (V₀ ²)] ^1/2]   –   [V₀/[[1 – [(V₀/C) ²]] ^1/2 ]]} { [(C ²) + [[(g_n)(t_n)  + [V₀ /[1 – [(V₀/C) ²]] ^1/2 ] ²]] ^1/2] + [(g_n)(t_n)] +  [V₀/[[1 – [(V₀/C) ²]] ^1/2]]} / (C ²)}}

Computation in terms of T₀, we obtain:

Egain  = {Σ (0,n)   {{ ∫  (y₁, y₂){ ∫  (x₁,x₂){ ∫ (0,  π/2) {{{T_cmbr /{{{1/{[1 – [(v_i/C) ²]] ^1/2}}}[1 + [(v_i/C) cos θ]]}} ⁴} σ e}dθ}dx}dy} {(Delta) {(c/g_i) ln {{[[ (C²) + (V_0i ²)] ^1/2]   –   [V_0i/[[1 – [(V_0i/C) ²]] ^1/2 ]]} { [(C ²) + [[(g_i)(t)  + [V_0i /[1 – [(V_0i/C) ²]] ^1/2 ] ²]] ^1/2] + [(g_i)(t)] +  [V_0i/[[1 – [(V_0i/C) ²]] ^1/2]]} / (C ²)}}} {1/{[1 – [(v_i/C)² ]] ^1/2}}}}    – {Σ (0,n)  {{∫(y₁,y₂) {∫(x₁,x₂) (T⁴_0i σ e) dx}dy}    {(Delta) {(c/g_i) ln {{[[ (C²) + (V_0i ²)] ^1/2]   –   [V_0i/[[1 – [(V_0i/C) ²]] ^1/2 ]]} { [(C ²) + [[(g_i)(t_i)  + [V_0i /[1 – [(V_0i/C) ²]] ^1/2 ] ²]] ^1/2] + [(g_i)(t_i)] +  [V_0i/[[1 – [(V_0i/C) ²]] ^1/2]]} / (C ²)}}} {1/{[1 – [(v_i/C)² ]] ^1/2}} }} 

where T₀ is the ship time.

Alternatively, we can use the following series calculated with  t:

Egain  =  {Σ (1,n) { ∫ (t_ai, t_bi) {∫ {∫ (0, π/2)  {{{T_cmbr /{{1/{[1 – [(v_i/C) ²]] ^1/2}}[1 + [(v_i/C) cos θ]]}} ⁴} σ e}dθ} dA}dt}}   -  {Σ (1,n) ∫ (t_ai, t_bi) {∫ (T⁴ _0i σ e) dA}dt}   

where t_ai and t_bi and dt are the times in the background reference frame.

Calculating with respect to T₀, we obtain:

Egain =  {Σ (1,n)  {∫ {∫ (0, π/2)  {{{T_cmbr /{{1/{[1 – [(v_i/C) ²]] ^1/2}}[1 + [(v_i/C) cos θ]]}} ⁴} σ e}dθ} dA}}   -  {Σ (1,n) {∫ (T⁴ _0i σ e) dA}   {(Delta) {(c/g_i) ln {{[[ (C²) + (V_0i ²)] ^1/2]   –   [V_0i/[[1 – [(V_0i/C) ²]] ^1/2 ]]} { [(C ²) + [[(g_i)(t_i)  + [V_0i /[1 – [(V_0i/C) ²]] ^1/2 ] ²]] ^1/2] + [(g_i)(t_i)] +  [V_0i/[[1 – [(V_0i/C) ²]] ^1/2]]} / (C ²)}}} {1/{[1 – [(v_i/C)² ]] ^1/2}}}.

Integrating with respect to time and velocity;

the formulas for total kinetic energy  gain are:

E_gain = {∫ (v₁, v₂)  {{∫  (t₁, t₂) { ∫ (y₁, y₂){ ∫ (x₁,x₂){ ∫ (0,  π/2) {{{T_cmbr {1/{[1 – [(v/C) ²]] ^1/2}}[1 + [(v/C) cos θ]]} ⁴} σ e}dθ}dx}dy} dt}/v}dv} -  E_{rad lost}

or alternatively,

E_gain =  {∫(v₁,v₂) {{∫ (t₁,t₂){∫  {∫ (0,  π/2) {{{_Tcmbr/{{1/{[1 – [(v/C) ²]] ^1/2}}[1 + [(v/C) cos θ]]}}⁴} σ e} dθ} dA}dt}/v}dv} -  E_{rad lost}

 

 

where t_ai and t_bi , t_i, and dt are the times in the background reference frame, g_i is the ship acceleration in the ship’s reference frame, and V_0i is the starting velocity at the beginning of each time of Delta T₀,  or ship time.

Now, the CMBR incident on the light sail from behind will generally require either a monolithic light sail of near nanometer thickness or perhaps a grid like sail with a cross-weave for which the lines or fibers are separated by less than 0.25 millimeters in order to reflect the vast majority of the incident CMBR for space craft traveling at mildly relativistic velocities. For grid like sails, the advantage of sail porosity enables much higher mass specific capture areas. Since the Doppler blue shifted light incident from directly in front of the sail or nearly so will be much shorter in wavelength than the backwardly incident light for high gamma factor sails, the forwardly incident light can largely pass through the sail openings providing a means for the backwardly incident light to push the sail efficiently forward for cases where the sail is transmissive from front to back to a suitable degree.

Now radiation pressure is equal to σT⁴/C and {2 [σT⁴/C]} for reflected radiation. However, for a space craft traveling through a black body radiation field, the apparent temperature of the radiation increases in proportion to γ and so the black body power impinging on the space craft from directly in front grows in proportion to T⁴ and thus  to γ⁴.

The temperature of a black body is T = {P/[(A)(σ)(e)]}^1/4 = {P/{(A)[5.670400(40) x 10^-8 W m^-2 K^-4]} ^1/4}. Therefore, the cosmic microwave background radiation pressure on a perfectly reflective flat bow  relativistic space craft is roughly equal to  {2 [σT_cmbr ⁴/C]} γ⁴ = {2 [σT_cmbr ⁴/C]} { {1/{1 – [(v/C)²]}^1/2}  ⁴} =   {2 [σT_cmbr ⁴/C]} {1/{1 – [(v/C)²]}²} where γ is constant and T_cmbr is constant. However, the light pressure incident from directly behind will be approximately equal to {2 [σT_cmbr ⁴/C]}/{1/{1 – [(v/C)²]}²}. In actuality, not all of the light is directly incident from the back and so there will be angular affects that result in loss of driving power. However, we will assume that all of the radiation is absorbed and then re-cycled and released as a perfect backwardly directed laser beam.

Assuming that the velocity of the sail starts out at (Zero) C, the optical pressure will be equal to {2 [σT_cmbr ⁴/C]}/γ⁴ = {2 [σT_cmbr ⁴/C]}/{ {1/{1 – [(v/C)²]}^1/2} ⁴} = {2{[5.670400(40) x 10^-8 W m^-2 K^-4][(2.725 K)⁴]/(300,000,000 m/s)}}/(1²) = 2.0844  x 10^-14 Newtons/m². For a 10,000 km by 10,000 km sail, the drive force will be 2.0844 Newtons.

Now, how are we going to deploy such a sail in a meaningful manner? The solution is obvious my dear Watson! Use a grid.

Consider that a monolithic one nanometer thick sail made of STP H₂O density carbonaceous materials would have a mass of  100,000 thousand metric tons, assuming that the space craft plus her sail had a mass of 208,440 metric tons, the craft would start out with an acceleration of F/M = a = 2.0844 N/208,440,000 kg = 10^-8 meter/s². After traveling 6 x 10¹⁵ seconds or about 200,000,000 years, the velocity of the space craft will be 0.20 C and the relativistic Lorentz transformation factor will be 1.0206 thus permitting the above Newtonian formula to apply.

For such a space craft that deployed a linear series of 1,000 tethered sails where each sail was separated by an efficient 10 sail widths, a space craft having a total mass of 208, 440,000 metric tons could be identically accelerated. The mass of the crew quarters would be 108,440,000 metric tons.

For such a space craft that deployed a linear series of 1,000,000 tethered sails where each sail was separated by an efficient 10 sail widths, a space craft having a total mass of 208, 440,000,000  metric tons could be identically accelerated. The mass of the crew quarters would be 108,440,000,000  metric tons. For cosmic journeys, this is not bad.

Some supermaterials already in laboratory existence such as carbon nanotubes can in theory be used to construct large space elevators that would extend from the surface of the Earth near the Equator to locations significantly father than geosynchronous orbit. Such tethers would perhaps have the equivalent of 0.1 G or 1m/s² acceleration based force pulling on it which would be commensurate with a cable roughly 100,000 km long accelerated at 1 m/s². Thus,  a cable that is 10¹³ km long or one light-year long could in theory withstand 10^-8 m/s² levels of acceleration. A linear series of tethered leading sails numbering 1,000,000 where each sail would have a width of 10,000 kilometers and be serially spaced a distance of 100,000 kilometers would have a length of 10¹¹ kilometers.  Thus, a series of 100 million tethered sails might conceivably pull a sail craft combination having a mass of 20,844,000,000,000 metric tons and a crew quarters having a mass of 10,844,000,000,000 metric tons.

Some high-end carbonaceous super-materials include:

1) carbon nano-tubes;
2) boron-nitride nanotubes;
3) buckyball-sheets;
4) layered sheet arrangements of graphene;
5) graphene-oxide paper;
6) fabrics composed of a weave or knit on carbon atom chains;
7) diamond fiber-based fabric;
8) carbon nitride fiber-based fabric;
9) combinations of two or more of the above, and the like material

Metalization would help in these regards.

The sails could have nanotech self-repair mechanisms. An ideal mechanism would entail sails constructed of metallic hydrogen where the hydrogen would be captured from interstellar space and incorporated into the sail membrane(s) in order to re-supply sail atoms knocked loose by interstellar atom and molecular species.

However, much higher sail velocities are anticipatable with much greater accelerations as will be covered in the next post in this series.

However, we can also deploy gridded sails. For example, consider a sail that is comprised on one nanometer wide fibers in a cross-weave where adjacent parallel  fibers are separated by 200 microns. Also consider situations where the fibers are one side reflective and one side transmissive. A sail comprised of such a material will have a mass specific capture area that is 1/100,000 that of a one nanometer thick monolithic sail.

Considering that such a sail that is gridded with the above  one nanometer thick sail fiber construction made of STP H₂O density carbonaceous materials would have a mass of  one metric ton for a sail area of 10⁸ square kilometers, assuming that the space craft plus her sail had a mass of 208,440 metric tons, the craft would start out with an acceleration of F/M = a = 2.0844 N/208,440,000 kg = 10^-8 meter/s². After traveling 6 x 10¹⁵ seconds or about 200,000,000 years, the velocity of the space craft will be 0.20 C and the relativistic Lorentz transformation factor will be 1.0206 thus permitting the above Newtonian formula to apply.

For such a space craft that deployed a linear series of 1,000 tethered sails where each sail was separated by an efficient 10 sail widths, a space craft having a total mass of 208, 440,000 metric tons could be identically accelerated. The mass of the crew quarters would be 208, 439,000 metric tons.

For such a space craft that deployed a linear series of 1,000,000 tethered sails where each sail was separated by an efficient 10 sail widths, a space craft having a total mass of 208, 440,000,000  metric tons could be identically accelerated. The mass of the crew quarters would be 208, 439,000,000 metric tons. For cosmic journeys, this is not bad.

A series of 100 million tethered sails might conceivably pull a sail craft combination having a mass of 20,844,000,000,000 metric tons and a crew quarters having a mass of 20,843,900,000,000 metric tons.

Consider again that such sails which  are gridded with the above  one nanometer thick sail fiber construction made of STP H₂O density carbonaceous materials would have a mass of  one metric ton each, assuming that the space craft plus her sail had a mass of 208,440 metric tons, the craft would start out with an acceleration of F/M = a = 2084.4 N/208,440,000 kg = 10^-5 meter/s² for cases where the craft would utilized 1,000 tethered driving sails. After traveling 6 x 10¹²  seconds or about 200,000 years, the velocity of the space craft will be 0.20 C.

Now consider a space craft having a mass of 208,440 metric tons driven by 10,000 such one metric tons sails. For such a space craft that deployed a linear series of 10,000 tethered sails where each sail was separated by an efficient 10 sail widths, the space craft having a total mass of 208, 440 metric tons would start out with an acceleration of F/M = a = 2084.4 N/208,440,000 kg = 10^-4  meter/s². After traveling 6 x 10¹¹ seconds or about 20,000 years, the velocity of the space craft will be 0.20 C.

We can consider more robust gridded sails such as those made from 10 nanometer diameter fibers spaced 200 microns apart. Each such sail would have a mass of 100 metric  tons. Thus, a space craft having a total mass of 208,440 metric tons that is driven by 1,000 such sails would too start out with an acceleration of F/M = a = 2084.4 N/208,440,000 kg = 10^-5 meter/s² and achieve a velocity of 0.20 C after 200,000 years.

Cnsider a sail that is comprised on 316.2  nanometer wide fibers in a cross-weave where adjacent parallel  fibers are separated by 200 microns. Also consider situations where the fibers are one side reflective and one side transmissive. A sail comprised of such a material will have a mass specific capture area that is equal to that of a one nanometer thick monolithic sail.

Consider that such a sail which is gridded with the above  316.2  nanometer thick sail fiber construction made of STP H₂O density carbonaceous materials would have a mass of  100,000 metric tons for a capture area of 10⁸ square kilometers. Assuming that the space craft plus her sail had a mass of 208,440 metric tons, the craft would start out with an acceleration of F/M = a = 2.0844 N/208,440,000 kg = 10^-8 meter/s². After traveling 6 x 10¹⁵ seconds or about 200,000,000 years, the velocity of the space craft will be 0.20 C and the relativistic Lorentz transformation factor will be 1.0206 thus permitting the above Newtonian formula to apply.

For such a space craft that deployed a linear series of 1,000 tethered sails where each sail was separated by an efficient 10 sail widths, a space craft having a total mass of 208, 440,000 metric tons could be identically accelerated. The mass of the crew quarters would be 208, 439,000 metric tons.

For such a space craft that deployed a linear series of 1,000,000 tethered sails where each sail was separated by an efficient 10 sail widths, a space craft having a total mass of 208, 440,000,000  metric tons could be identically accelerated. The mass of the crew quarters would be 208, 439,000,000 metric tons. For cosmic journeys, this is not bad.

A series of 100 million tethered sails might conceivably pull a sail craft combination having a mass of 20,844,000,000,000 metric tons and a crew quarters having a mass of 20,843,900,000,000 metric tons.

The background interstellar and intergalactic matter might not erode even many of highly relativistic sail of sub-micron thickness.

The diametrical cross-sectional area of our observable universe is close to 10 ⁴⁷  square kilometers and the mass of the total mass energy of the observable universe is only about 10 ⁵⁰ metric tons of which only 4 percent is baryonic.  Thus,  an average column spanning the diameter of the entire visible universe would have an H2O STP matter thickness of only 25 micrometers for reactive matter.

However,  this is not a concern for the following reasons.

First, the sails could be replaceable grid sails and driven by optical, IR, microwave or rf radiation. The mass of such sails can be reduced by many orders of magnitude relative to monolithic sails that are only micrometer scales in thickness.

Second, sails having a very thick cable or thread like construction are conceivable where the cables or wires would be many times if not several orders of magnitude thicker than 25 microns. The sails could be mostly empty space to almost entirely empty space to reflect long wave rF phased array beams.

As for concerns about over burdening the conductive or super-conductive wires or cables used for such sails by extremely intense rF beams, note that such reflective members could be very conductive to superconductive to thereby yield near perfect reflection. The EM energy that was not reflected would largely pass through the openings in the sail grid.

Second, a magnetic and/or electric field based scoop or anti-scoop could divert the chargons away from the sail just as an extended electrodynamic scoop for an interstellar ramjet would. Electro-dynamic-hydro-dynamic-plasma-drive features could utilize the diverted plasma in a reactive and gainful manner.

The sail might be deployed in a manner that is orthogonal to the ship’s velocity vector.  The sail might be parallel to the space craft velocity vector and driven obliquely from behind. This way, the effective thickness of the sail could be thousands of miles and the sail could include electro-dynamic-hydro-dynamic-plasma-drive features.

Fourth, the above parallel sail could conceivably be made of negative refraction index materials that would be pulled forward by incident star light and highly blue-shifted CMBR, far infrared, and non-CMBR radio sources.

Fifth, the sail can simply be a deployed mag-sail or M2P2 type of sail or any other magnetic or plasma bottle sail. It is possible that a plasma affixed to the space craft to be driven by rf radation, and even source based laser light upon attainment of extreme space craft gamma factors could be easily reflected by such sails. Plasma makes an excellent rF reflector even at very small densities.

I have done a lot of writing on parallel sails such as negative refraction index monolithic and grid sails capable of extreme gamma factors.

Sixth, some sail materials such as any future forms of super-strong very conductive to super-conductive metallic hydrogen can be used as nuclear fusion fuel for fusion rockets upon degradation to useless levels.

Seventh, it has been proposed that very thin,  metallic,  very low gas density containing balloons might be used for nuclear warhead decoys and which could survive 100 meter proximity detonation to a one kiloton neutron bomb in the vacuum of space. The rate of radiative cooling would be tens of billions of Kelvins per second due to the extreme thinness of the balloon membranes and most of the neutrons would pass right through the balloon without interacting or by only depositing a very small portion of the particles kinetic energy into the balloon and enclosed gas. Interstellar chargons are more reactive to electronic shell structures but not by that much.

The general idea for obliquely oriented beams involves the beamed energy incident on both sides of the sail. The sail could include a surface of hair like cilia or any other surface contour that would work so as to much more effectively grab ahold of the light.

In addition, the sail could be fabricated from photovoltaic materials in order to provide power for electro-dynamic-hydrodynamic-plasma-drives or chargon rockets, or perhaps even photon rockets.

For extreme gamma factors, the CMBR and starlight will be highly blue-shifted and will be relativistically abberated to what would approach a point source in front of the space craft at gamma = infinity. A sail parallel to the space craft velocity vector made of a suitable negative electromagnetic refraction index material will be pulled forward even by light incident on the sail at a very shallow angle from in front of the space craft.

To enhance the negative refraction index sails capture of EM energy, the sails may have negative index hairs or cilia distributed along its length.

Negative refraction index materials have actually been measured to be pulled on by incident light. Duke University and other academic and government labs are researching the various aspects of negative refraction index materials.

I have no problem with space craft being pulled forward by forward incident light. After all, the paradigm of light speed velocity limits may or may not have been shattered with any future validation or not of the CERN superluminal neutrino results. The big bang may have been the most recent free lunch. There is no reason why the big bang could not have started with miniscule quantities of mass-energy.

A good abstract for a great paper on negative super-pressure of light acting on a negative refractive index material is

Henri Lezec
(Center for Nanoscale Science and Technology, NIST)

Forty years ago, V. Veselago derived the electromagnetic properties of a hypothetical material having simultaneously-negative values of electric permittivity and magnetic permeability [1]. Such a material, denominated “left-handed”, was predicted to exhibit a negative index of refraction, as well as a number of other counter-intuitive optical properties. For example, it was hypothesized that a perfect mirror illuminated with a plane wave would experience a negative radiation pressure (pull) when immersed in a left-handed medium, as opposed to the usual positive radiation pressure experienced when facing a dielectric medium such as air or glass. Since left-handed materials are not available in nature, considerable efforts are currently under way to implement them under the form of artificial “metamaterials” — composite media with tailored bulk optical characteristics resulting from constituent structures which are smaller in both size and density than the effective wavelength in the medium. Here we show how surface-plasmon modes propagating in a stacked array of metal-insulator-metal (MIM) waveguides can be harnessed to yield a volumetric left-handed metamaterial characterized by an in-plane-isotropic negative index of refraction over a broad frequency range spanning the blue and green. By sculpting this material with a focused-ion beam we realize prisms and micro-cantilevers which we use to demonstrate, for the first time, (a) in-plane isotropic negative-refraction at optical frequencies, and (b) negative radiation pressure. We predict and experimentally verify a negative “superpressure”, the magnitude of which exceeds the photon pressure experienced by a perfect mirror by more than a factor of two. 1) V. Veselago, \textit{ Sov. Phys. Usp. }10, p.509 (1968).

Available at:

http://meetings.aps.org/Meeting/MAR09/Event/93172

The sail might not need to  be held by guy lines. A strong magnetic field based coupling or electrical charged based connection might work.

Another option is to fabricate the sail guy lines out of graphene, carbon nanotubes, boron nitride nanotubes, graphene oxide paper, and the like. A cable constructed from such materials could stretch for about 20 to 50 kilometers yet still handle tens to hundreds of Earth G’s. The tensile strength of graphene is close to 18 million PSI for perfect forms.

Materials such as solid quarkoniums and somehow stabilized neutroniums, and perhaps even Higgsiniums would be better yet, but such materials may only exist in nature in extreme mass quantity states as of the present cosmic era.

The collection area of the sail can be very, very, large. A large electro-dynamic scoop could extent very far out from the sail.

Regarding nanotech self-assembly mechanisms, just simply greatly increase the capture area of a electrodynamic scoop to collect enough interstellar materials and use most of the collected interstellar material as an EHPD, an MHPD, or a combination of the two and use the rest of the materials for sail repair.

Regarding holding M2P2 plasma affixed to the ship under high gamma factor condition, simply increase the strength of the fastening fields.

Now regarding interstellar matter density near our solar system of one particle for every 10 cm³, the density would  work out to be a layer of hydrogen or helium atoms about one atom thick for a column that is one light-year long. Not a show stopper for light sails or sails that are electro-dynamically shielded or protected.

If extreme materials are used with excellent reflectance, we could simply use a sail that has a thickness of one millimeter or more and which is monolithic, or better yet,  use a sail with grid lines that are one millimeter or perhaps much greater in thickness. This way, a sail that has an area of only one square kilometer can intercept a beam having an equivalent black body temperature of several thousand Kelvins provided it is constructed of suitably refractive materials.

We could simply use electrodynamic methods of grabbing ahold of the interstellar gas and diverting around the space craft and sail. The power to operate the electrodynamic mechanisms can be supplied by beams. The electrodynamic methods can include lasers for ionization, or rf radiation where the gamma factors are suitably large, magnetic fields, electric fields, plasma fields affixed to the space craft, and the like.

Then there is always the possibilities for sails comprised of truly exotic materials such as somehow stabilized neutroniums, quarkoniums, higgsiniums, monopoliums, and perhaps even raw space-time-mass-energy forms such as the “Yelm” of mid-20th Century big bang theory.

Since one cubic meter of neutronium would have a mass of about 10¹⁵ tons. A 1,000 kilometer long thread of the stuff that has a cross-sectional area of 1,000,000 neutrons would have a mass of only one kilogram. A 1 kilometer long thread having a cross-sectional area of 1 billion neutrons would have a mass of only 1 kilogram. Lines made of quarkoniums could have the same length and cross-section but would be 10 to 1,000 times more massive. Higgsiniums would be all the more massive.

Provided such extreme materials could be developed, they could also serve as electric current carrying magnetic sail components. Anyhow magnetic sails can be made of any ordinary conducting or superconducting period table materials.

It is also conceivable that a hybrid sail can be used where a current carrying magsail would deflect plasma away from a monolithic and grid like light sail or rf sail.

Now, regarding the subject of sail erosion by exposure to interstellar or intergalactic gas, we must realize that the kinetic energy of a gas atom traveling at a velocity of 86.7 percent of the speed of light with respect to the sail would be equal to the binding energy of roughly 10 billion atoms within a sail of micron thickness. Thus, the fact that 10 billion atoms could be dislodged should all of the energy of the gas atom be deposited within the sail. Incident gas atoms having even higher associated gamma factors with respect to the star ship sail could potentially knock loose even more atoms. Perhaps, there is no reason to worry about sail erosion in spite of this for the following reasons.

First, extremely relativistic particles would likely deposit only a small portion of its energy within the sail thereby greatly lessening the number of atoms that would be knocked loose. This fact would apply to chargons as well as neutral incident particles.

Second, for sails of near micron thickness, atoms that were knocked loose would likely simply be re-assimilated by the bulk sail materials. Perhaps the only chance for an atom to be knocked loose would include atoms located on the backward side of the sail.  Atoms for which bonds where broken within the bulk sail material would tend to simply re-bond with adjacent atoms.

Third, since the incident gas or plasma particle would deposit only a small portion of its energy within the sail, the kinetic energy per particle for particles that are knocked loose may be only slightly in excess of the binding energy of the dislodged atoms. Basically, the kinetic energy of the dislodged atoms could likely be re-absorbed and/or radiated away thereby promoting rebinding of the dislodged atoms.

Fourth, for cases where the sail would completely absorb the kinetic energy of the incident gas or plasma particles such as an alpha particle, for the case of a one micron thick sail, the sail would obviously be able to complete stop the chargon without losing it. Thus, any atoms disbonded by the incident chargon would also likely be captured and prevented from leaving the sail material.

Fifth, for grid like sails, the grid lines might be positively chargeable so that incident interstellar or intergalactic ions are pushed away from the grid lines and through the openings within the grid like sails. The effect would be similar to the Vander walls force that keeps neutral atoms from being squeezed together to tightly.

We now perform a reality check on the above formulations.

Consider the space craft at a stationary state. The CMBR appears equally bright from all directions within about 1 part in 30,000.

Now, the apparent angle, θ_s,  of CMBR pre-incident on the space craft at an angle of 90 degrees or with respect to the length of the space craft relative to the source reference frame at v = zero C will appear to be incoming at an angle, θ_o,  of 90 degrees with respect to the space craft,  ship’s reference frame.

If we consider the effects of relativistic aberration, the general formula for apparent shift in angle of incidence of the CMBR from the ship’s perspective is

Cos θ_o = {[cos θ_s] – (v/C)}/{1 – [(v/C) cos θ_s]}

Now say we desire to find the range of CMBR angles incident on the space craft with respect to the space craft reference frame for space craft velocities of 0.20 C.

Now since we are considering an angle of θ_o = π/2, cos θ_o = zero. Using the above formula, we achieve Cos θ_o = {[cos θ_s] – (v/C)}/{1 – [(v/C) cos θ_s]} = Cos π/2 = {[cos θ_s] – (0.20)}/{1 – [(0.20) cos θ_s]} = zero = {[cos θ_s] – (0.20)}/{1 – [(0.20) cos θ_s]}.

Thus, (zero) {1 – [(0.20) cos θ_s]} = {[cos θ_s] – (0.20)} = zero.

Therefore, cos θ_s = 0.20 — > θ_s  = 78.463 degrees. We will make a first order assumption that the incident CMBR from behind has a frequency of f’ = f / {γ [1 + (β cosine θ)]} = f / {1.02062 [1 + [0.2 cosine ( 0)]]} = (0.816497161) f. Thus, we will assume that θ = 0 degrees for the following 5 scenarios where we assume that the CMBR is directly incident from behind.

The radiated power received by the sail will be [(78.463)²/(90²)] f’ = [(78.463)²/(90²)] f / {γ [1 + (β cosine θ)]} = [(78.463)²/(90²)] f / {1.02062 [1 + [0.2 cosine ( 0)]]} = [(78.463)²/(90²)] (0.816497161) f =

Once again, the temperature of a black body is T = {P/[(A)(σ)(e)]}^1/4 = {P/{(A)[5.670400(40) x 10^-8 W m^-2 K^-4]} ^1/4}. The light pressure incident from directly behind will be approximately equal to [(θ_s)²/(90²)] {2 {σ {{(T_cmbr)/{γ [1 + (β cosine θ)]}}}⁴/C}} =  [(78.463)²/(90²)] {2 {[5.670400(40) x 10^-8 W m^-2 K^-4] {[(T_cmbr) (0.816497161) ]⁴}/C}} = 4.632092076  x 10^-15 Newtons/m². In actuality, not all of the light is directly incident from the back and so there will be angular affects that result in loss of driving power. However, we will assume that all of the radiation is absorbed and then re-cycled and released as a perfect backwardly directed laser beam.

Now  E_gain = ʃF^odx = ʃ(0,10²⁵) F^odx = ʃ(0,10²⁵)(10¹⁴) [4.632092076  x 10^-15 N] ^odx = 4.632092076 x 10²⁴ Joules.

Now, a 208,440 metric invariant mass space craft traveling at a starting velocity of 0.2 C has a kinetic energy of {1.02062[M C²]} – [M C²] = {1.02062[208,440,000  C²]} – [208,440,000  C²] =  1.9146 x 10²⁵ Joules – 1.87596 x 10²⁵ Joules = 3.864 x 10²³ Joules. When  4.632092076 x 10²⁴ Joules is added, the total gamma factor becomes [5.01849 x 10²⁴ Joules + 1.87596 x 10²⁵ Joules]/ [1.87596 x 10²⁵ Joules] = 1.2675. The associated space craft velocity will be equal to 0.6142 C.

Likewise doing iterated numerical approximations with v = 0.6142 C to obtain another higher velocity and then repeating the steps over and over again will give a first order approximation for space craft terminal velocity.

So we have reasonably demonstrated that CMBR sails can drive very large space arks to velocities considered fast by interstellar propulsion physicists. Typically, fast interstellar travel occurs at a better part of the speed of light.

However, a much finer scale is needed to produce results for many such steps where the computed velocity would not significantly diverge from the actual velocity obtained.

Note that here, I neglect the effects of mass based astrodynamic drag. I have come up with several mechanisms by which massive astrodynamic drag can be almost entirely eliminated and will post on this subject later this month.

 

The total kinetic energy gain for the craft will be

E _totalgain = ʃF ₁^odx₁  +  ʃF ₂^odx₂ + ʃF ₃^odx₃ + … +ʃF _n^odx_n

= {{ʃ{[(θ_s1)²/ ((90 degrees) ²)] {2 {σ {{(T_cmbr)/{γ₁ [1 + (β₁ cosine θ)]}}}⁴/C}}}^odx₁}(A)}+  {{ʃ{[(θ_s2)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{γ₂ [1 + (β₂ cosine θ)]}}}⁴/C}}} ^odx₂}(A)} + {{ʃ{[(θ_s3)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{γ₃ [1 + (β₃ cosine θ)]}}}⁴/C}}} ^odx₃}(A)} + … +{{ʃ{[(θ_sn)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{γ_n [1 + (β_n cosine θ)]}}}⁴/C}}} ^odx_n}(A)}

 

= ʃ{[(θ_s1)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{{1/{1 – [(v₁/C)²]}^1/2} [1 + (β₁ cosine θ)]}}}⁴/C}}}^odx₁  +  ʃ{[(θ_s2)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{ {1/{1 – [(v₂/C)²]}^1/2}  [1 + (β₂ cosine θ)]}}}⁴/C}}} ^odx₂ + ʃ{[(θ_s3)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{ {1/{1 – [(v₃/C)²]}^1/2}  [1 + (β₃ cosine θ)]}}}⁴/C}}} ^odx₃ + … +ʃ{[(θ_sn)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{ {1/{1 – [(v_n/C)²]}^1/2}  [1 + (β_n cosine θ)]}}}⁴/C}}} ^odx_n

 

= Σ (i = 1, i = n) ʃF _i^odx_i   = Σ (i = 1, i = n) ʃ{[(θ_si)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{γ_i [1 + (β_i cosine θ)]}}}⁴/C}}}^odx_i

=   Σ (i = 1, i = n) ʃ{[(θ_si)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{ {1/{1 – [(v_i/C)²]}^1/2}  [1 + (β_i cosine θ)]}}}⁴/C}}} ^odx_i

 

The following numerical formula offers a first order approximation of space craft gamma factor  gain;

{[E_KEtotalgain] + [M_restC²]}/[M_restC²]= {[ʃF ₁^odx₁]  +  [ʃF ₂^odx₂]  + [ʃF ₃^odx₃ ] + … + [ʃF _n^odx_n] + [M_restC²]}/[M_restC²] 

= {{{ʃ{[(θ_s1)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{γ₁ [1 + (β₁ cosine θ)]}}}⁴/C}}}^odx₁}(A)}+  {{ʃ{[(θ_s2)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{γ₂ [1 + (β₂ cosine θ)]}}}⁴/C}}} ^odx₂ }(A)}  + {{ʃ{[(θ_s3)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{γ₃ [1 + (β₃ cosine θ)]}}}⁴/C}}} ^odx₃ }(A)} + … + {{ʃ{[(θ_sn)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{γ_n [1 + (β_n cosine θ)]}}}⁴/C}}} ^odx_n}(A)}+ [M_restC²]}/[M_restC²] 

 

= {{{ʃ{[(θ_s1)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{{1/{1 – [(v₁/C)²]}^1/2} [1 + (β₁ cosine θ)]}}}⁴/C}}}^odx₁  }(A)}  +  {{ʃ{[(θ_s2)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{ {1/{1 – [(v₂/C)²]}^1/2}  [1 + (β₂ cosine θ)]}}}⁴/C}}} ^odx₂ }(A)} +   {{ʃ{[(θ_s3)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{ {1/{1 – [(v₃/C)²]}^1/2}  [1 + (β₃ cosine θ)]}}}⁴/C}}} ^odx₃ }(A)} + … +  {{ʃ{[(θ_sn)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{ {1/{1 – [(v_n/C)²]}^1/2}  [1 + (β_n cosine θ)]}}}⁴/C}}} ^odx_n}(A)}+ [M_restC²]}/[M_restC²] 

 

= {{Σ (i = 1, i = n) ʃF _i^odx_i }+ [M_restC²]}/[M_restC²]   = {{Σ (i = 1, i = n) {{ʃ{[(θ_si)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{γ_i [1 + (β_i cosine θ)]}}}⁴/C}}}^odx_i}(A)}}+ [M_restC²]}/[M_restC²] 

=   {{Σ (i = 1, i = n) ʃ{[(θ_si)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{ {1/{1 – [(v_i/C)²]}^1/2}  [1 + (β_i cosine θ)]}}}⁴/C}}} ^odx_i}+ [M_restC²]}/[M_restC²] 

Now, v = C{[-[1/γ²] + 1]^1/2} according to Special Relativity. Consequently, the following formulas can be used to compute v by numerical trial and error.

v = C{{-{1/{{[E_KEtotalgain] + [M_restC²]}/[M_restC²]}²} – 1}^1/2}  

 

=  C{{-{1/{{[ʃF ₁^odx₁]  + [ʃF ₂^odx₂]  + [ʃF ₃^odx₃ ] + ʃF _n^odx_n]} + [M_restC²]}/[M_restC²]}  ²}} + 1}^1/2}

=  C{{-{1/{{{{ʃ{[(θ_s1)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{γ₁ [1 + (β₁ cosine θ)]}}}⁴/C}}}^odx₁}(A)}+   {{ʃ{[(θ_s2)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{γ₂ [1 + (β₂ cosine θ)]}}}⁴/C}}} ^odx₂ }(A)} +  {{ʃ{[(θ_s3)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{γ₃ [1 + (β₃ cosine θ)]}}}⁴/C}}} ^odx₃ }(A)}   + … + {{ʃ{[(θ_sn)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{γ_n [1 + (β_n cosine θ)]}}}⁴/C}}} ^odx_n}(A)}+ [M_restC²]}/[M_restC²]}  ²}} + 1}^1/2}

=  C{{-{1/{{{{ʃ{[(θ_s1)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{{1/{1 – [(v₁/C)²]}^1/2} [1 + (β₁ cosine θ)]}}}⁴/C}}}^odx₁  }(A)} +  {{ʃ{[(θ_s2)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{ {1/{1 – [(v₂/C)²]}^1/2}  [1 + (β₂ cosine θ)]}}}⁴/C}}} ^odx₂ }(A)} +  {{ʃ{[(θ_s3)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{ {1/{1 – [(v₃/C)²]}^1/2}  [1 + (β₃ cosine θ)]}}}⁴/C}}} ^odx₃ }(A)} + … +  {{ʃ{[(θ_sn)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{ {1/{1 – [(v_n/C)²]}^1/2}  [1 + (β_n cosine θ)]}}}⁴/C}}} ^odx_n}(A)}+ [M_restC²]}/[M_restC²]}²}} + 1}^1/2}.   .

=  C{{-{1/{{{{Σ (i = 1, i = n) ʃF _i^odx_i }+ [M_restC²]}/[M_restC²]}   ²}} + 1}^1/2} 

=    C{{-{1/{{{{Σ (i = 1, i = n) {{ʃ{[(θ_si)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{γ_i [1 + (β_i cosine θ)]}}}⁴/C}}}^odx_i}(A)}}+ [M_restC²]}/[M_restC²]}  ²}} + 1}^1/2} 

=   C{{-{1/{{{{Σ (i = 1, i = n) {{ʃ{[(θ_si)²/(((90 degrees)²)] {2 {σ {{(T_cmbr)/{ {1/{1 – [(v_i/C)²]}^1/2}  [1 + (β_i cosine θ)]}}}⁴/C}}} ^odx_i}(A)}}+ [M_restC²]}/[M_restC²]}  ²}} + 1}^1/2}

When the to two sides of the above equations are equal, we will have thus computed relativistic velocity, v.   

As you can see, for cases where there is much natural variation in acceleration with respect to the space craft frame, and for travel over very long distances, many iterations or steps need to be used in numerical algorithms to get mil spec and super-mil-spec results. Such precision is needed when traveling near light speed otherwise mission disaster could happen. In actuality, the above formulations would not be fit for mil spec computations because of the mere approximation to the actual vehicular performance.

We now consider scenarios where the photon angle of incidence from behind is considered and where drag effects are neglected for total space craft energy gains, accrued gamma factors, and accrued velocities. Here, we consider only angular values of radiation incident on the sail for which the radiation exerts forward pressure. In otherwords, we only consider values of θ₀ less than or equal to 90 degrees or π/2 radians. We also assume perfect backward sail reflectivity or trivially imperfect backward reflectivity and trivial massive astrodynamic drag.

The total kinetic energy gain for the craft will be

E _totalgain = ʃF ₁^odx₁  +  ʃF ₂^odx₂ + ʃF ₃^odx₃ + … +ʃF _n^odx_n

= {Σ(i = 1, i = n) {{{[[(θ_01i,1²) - (θ_02i,1²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,1 , θ_s2i,1)}^-1}{{[dr_bi,1/dr_ai,1]}│(r_b1i,1 , r_b2i,1)}[cos [(θ_01i,1 +  θ_02i,1)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ₁ [1 + [β₁cosine [(θ_01i,1 + θ_02i,1)/2]]]}}}⁴/C}}}^odx₁}/n}(A)}}}  

+  {Σ(i = 1, i = n) {{{[[(θ_01i,2²) - (θ_02i,2²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,2 , θ_s2i,2)}^-1}{{[dr_bi,2/dr_ai,2]}│(r_b1i,2 , r_b2i,2)}[cos [(θ_01i,2 +  θ_02i,2)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ₂ [1 + [β₂cosine [(θ_01i,2 + θ_02i,2)/2]]]}}}⁴/C}}}^odx₂}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{[[(θ_01i,3²) - (θ_02i,3²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,3 , θ_s2i,3)}^-1}{{[dr_bi,3/dr_ai,3]}│(r_b1i,3 , r_b2i,3)}[cos [(θ_01i,3 +  θ_02i,3)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ₃ [1 + [β₃cosine [(θ_01i,3 + θ_02i,3)/2]]]}}}⁴/C}}}^odx₃}/n}(A)}}} 

+ … +    {Σ(i = 1, i = n) {{{[[(θ_01i,m²) - (θ_02i,m²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,m , θ_s2i,m)}^-1}{{[dr_bi,m/dr_ai,m]}│(r_b1i,m , r_b2i,m)}[cos [(θ_01i,m +  θ_02i,m)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ_m[1 + [β₂cosine [(θ_01i,m + θ_02i,m)/2]]]}}}⁴/C}}}^odx_m}/n}(A)}}} 

= {Σ(i = 1, i = n) {{{[[(θ_01i,1²) - (θ_02i,1²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,1 , θ_s2i,1)}^-1}{{[dr_bi,1/dr_ai,1]}│(r_b1i,1 , r_b2i,1)}[cos [(θ_01i,1 +  θ_02i,1)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{{1/{1 – [(v₁/C)²]}^1/2}  [1 + [(v₁/C)cosine [(θ_01i,1 + θ_02i,1)/2]]]}}}⁴/C}}}^odx₁}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{[[(θ_01i,2²) - (θ_02i,2²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,2 , θ_s2i,2)}^-1}{{[dr_bi,2/dr_ai,2]}│(r_b1i,2 , r_b2i,2)}[cos [(θ_01i,2 +  θ_02i,2)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v₂/C)²]}^1/2}  [1 + [(v₂/C)cosine [(θ_01i,2 + θ_02i,2)/2]]]}}}⁴/C}}}^odx₂}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{[[(θ_01i,3²) - (θ_02i,3²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,3 , θ_s2i,3)}^-1}{{[dr_bi,3/dr_ai,3]}│(r_b1i,3 , r_b2i,3)}[cos [(θ_01i,3 +  θ_02i,3)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v₃/C)²]}^1/2}  [1 + [(v₃/C)cosine [(θ_01i,3 + θ_02i,3)/2]]]}}}⁴/C}}}^odx₃}/n}(A)}}} 

+ … +    {Σ(i = 1, i = n) {{{[[(θ_01i,m²) - (θ_02i,m²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,m , θ_s2i,m)}^-1}{{[dr_bi,m/dr_ai,m]}│(r_b1i,m , r_b2i,m)}[cos [(θ_01i,m +  θ_02i,m)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v_m/C)²]}^1/2} [1 + [(v_m/C)cosine [(θ_01i,m + θ_02i,m)/2]]]}}}⁴/C}}}^odx_m}/n}(A)}}} 

=  Σ(i = 1, i = m)   {Σ(i = 1, i = n) {{{[[(θ_01i,j²) - (θ_02i,j²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,j , θ_s2i,j)}^-1}{{[dr_bi,j/dr_ai,j]}│(r_b1i,j , r_b2i,j)}[cos [(θ_01i,j +  θ_02i,j)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ_j [1 + [β_jcosine [(θ_01i,j + θ_02i,j)/2]]]}}}⁴/C}}}^odx_j}/n}(A)}}} 

= Σ(i = 1, i = m)   {Σ(i = 1, i = n) {{{[[(θ_01i,j²) - (θ_02i,j²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,j , θ_s2i,j)}^-1}{{[dr_bi,j/dr_ai,j]}│(r_b1i,j , r_b2i,j)}[cos [(θ_01i,j +  θ_02i,j)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v_j/C)²]}^1/2}  [1 + [(v_j/C)cosine [(θ_01i,j + θ_02i,j)/2]]]}}}⁴/C}}}^odx_j}/n}(A)}}} 

= {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_sli,1]}}}

²} – {{cos^-1 {{[cos θ_s2i,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_s2i,1]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v₁/C)}/{1 – [(v₁/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,1 , θ_s2i,1)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v₁ /C)}/{1 – [(v₁/C) cos θ_s]}}}}│[cos  θ_s1i,1 ,  cos θ_s2i,1]}{cos {{{cos^-1 {{[cos θ_sli,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_sli,1]}}}+  {cos^-1 {{[cos θ_s2i,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_s2i,1]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ₁ {1 + {β₁cosine {{{cos^-1 {{[cos θ_sli,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_sli,1]}}}+ {cos^-1 {{[cos θ_s2i,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_s2i,1]}}}}/2}}}}}}⁴/C}}}^odx₁}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_sli,2]}}}

²} – {{cos^-1 {{[cos θ_s2i,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_s2i,2]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v₂/C)}/{1 – [(v₂/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,2 , θ_s2i,2)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v₂ /C)}/{1 – [(v₂/C) cos θ_s]}}}}│[cos  θ_s1i,2 ,  cos θ_s2i,2]}{cos {{{cos^-1 {{[cos θ_sli,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_sli,2]}}}+  {cos^-1 {{[cos θ_s2i,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_s2i,2]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ₂ {1 + {β₂cosine {{{cos^-1 {{[cos θ_sli,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_sli,2]}}}+ {cos^-1 {{[cos θ_s2i,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_s2i,2]}}}}/2}}}}}}⁴/C}}}^odx₂}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_sli,3]}}}

²} – {{cos^-1 {{[cos θ_s2i,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_s2i,3]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v₃/C)}/{1 – [(v₃/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,3 , θ_s2i,3)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v₃ /C)}/{1 – [(v₃/C) cos θ_s]}}}}│[cos  θ_s1i,3 ,  cos θ_s2i,3]}{cos {{{cos^-1 {{[cos θ_sli,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_sli,3]}}}+  {cos^-1 {{[cos θ_s2i,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_s2i,3]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ₃ {1 + {β₃cosine {{{cos^-1 {{[cos θ_sli,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_sli,3]}}}+ {cos^-1 {{[cos θ_s2i,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_s2i,3]}}}}/2}}}}}}⁴/C}}}^odx₃}/n}(A)}}} 

+ … +   {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_sli,m]}}}

²} – {{cos^-1 {{[cos θ_s2i,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_s2i,m]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v_m/C)}/{1 – [(v_m/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,m , θ_s2i,m)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v_m /C)}/{1 – [(v_m/C) cos θ_s]}}}}│[cos  θ_s1i,m ,  cos θ_s2i,m]}{cos {{{cos^-1 {{[cos θ_sli,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_sli,m]}}}+  {cos^-1 {{[cos θ_s2i,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_s2i,m]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ_m {1 + {β_mcosine {{{cos^-1 {{[cos θ_sli,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_sli,m]}}}+ {cos^-1 {{[cos θ_s2i,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_s2i,m]}}}}/2}}}}}}⁴/C}}}^odx_m}/n}(A)}}} 

= {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_sli,1]}}}

²} – {{cos^-1 {{[cos θ_s2i,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_s2i,1]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v₁/C)}/{1 – [(v₁/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,1 , θ_s2i,1)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v₁ /C)}/{1 – [(v₁/C) cos θ_s]}}}}│[cos  θ_s1i,1 ,  cos θ_s2i,1]}{cos {{{cos^-1 {{[cos θ_sli,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_sli,1]}}}+  {cos^-1 {{[cos θ_s2i,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_s2i,1]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v₁/C)²]}^1/2}   {1 + {(v₁/C)cosine {{{cos^-1 {{[cos θ_sli,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_sli,1]}}}+ {cos^-1 {{[cos θ_s2i,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_s2i,1]}}}}/2}}}}}}⁴/C}}}^odx₁}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_sli,2]}}}

²} – {{cos^-1 {{[cos θ_s2i,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_s2i,2]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v₂/C)}/{1 – [(v₂/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,2 , θ_s2i,2)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v₂ /C)}/{1 – [(v₂/C) cos θ_s]}}}}│[cos  θ_s1i,2 ,  cos θ_s2i,2]}{cos {{{cos^-1 {{[cos θ_sli,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_sli,2]}}}+  {cos^-1 {{[cos θ_s2i,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_s2i,2]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v₂/C)²]}^1/2}   {1 + {(v₂/C)cosine {{{cos^-1 {{[cos θ_sli,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_sli,2]}}}+ {cos^-1 {{[cos θ_s2i,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_s2i,2]}}}}/2}}}}}}⁴/C}}}^odx₂}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_sli,3]}}}

²} – {{cos^-1 {{[cos θ_s2i,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_s2i,3]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v₃/C)}/{1 – [(v₃/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,3 , θ_s2i,3)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v₃ /C)}/{1 – [(v₃/C) cos θ_s]}}}}│[cos  θ_s1i,3 ,  cos θ_s2i,3]}{cos {{{cos^-1 {{[cos θ_sli,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_sli,3]}}}+  {cos^-1 {{[cos θ_s2i,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_s2i,3]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v₃/C)²]}^1/2}   {1 + {(v₃/C)cosine {{{cos^-1 {{[cos θ_sli,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_sli,3]}}}+ {cos^-1 {{[cos θ_s2i,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_s2i,3]}}}}/2}}}}}}⁴/C}}}^odx₃}/n}(A)}}} 

+ … +   {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_sli,m]}}}

²} – {{cos^-1 {{[cos θ_s2i,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_s2i,m]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v_m/C)}/{1 – [(v_m/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,m , θ_s2i,m)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v_m /C)}/{1 – [(v_m/C) cos θ_s]}}}}│[cos  θ_s1i,m ,  cos θ_s2i,m]}{cos {{{cos^-1 {{[cos θ_sli,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_sli,m]}}}+  {cos^-1 {{[cos θ_s2i,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_s2i,m]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v_m/C)²]}^1/2}   {1 + {(v_m/C)cosine {{{cos^-1 {{[cos θ_sli,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_sli,m]}}}+ {cos^-1 {{[cos θ_s2i,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_s2i,m]}}}}/2}}}}}}⁴/C}}}^odx_m}/n}(A)}}} 

Σ ( j= 1, j = m) {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}

²} – {{cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v_j/C)}/{1 – [(v_j/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,j , θ_s2i,j)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v_j /C)}/{1 – [(v_j/C) cos θ_s]}}}}│[cos  θ_s1i,j ,  cos θ_s2i,j]}{cos {{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}+  {cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ_j {1 + {β_jcosine {{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}+ {cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}}/2}}}}}}⁴/C}}}^odx_j}/n}(A)}}} 

= Σ ( j= 1, j = m) {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}

²} – {{cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v_j/C)}/{1 – [(v_j/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,j , θ_s2i,j)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v_j /C)}/{1 – [(v_j/C) cos θ_s]}}}}│[cos  θ_s1i,j ,  cos θ_s2i,j]}{cos {{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}+  {cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v_j/C)²]}^1/2}   {1 + {(v_j/C)cosine {{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}+ {cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}}/2}}}}}}⁴/C}}}^odx_j}/n}(A)}}} 

 

 

The following numerical formula offers a first order approximation of space craft gamma factor  gain;

{[E_KEtotalgain] + [M_restC²]}/[M_restC²]= {[ʃF ₁^odx₁]  +  [ʃF ₂^odx₂]  + [ʃF ₃^odx₃ ] + … + [ʃF _n^odx_n] + [M_restC²]}/[M_restC²] 

 

 

= {{{Σ(i = 1, i = n) {{{[[(θ_01i,1²) - (θ_02i,1²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,1 , θ_s2i,1)}^-1}{{[dr_bi,1/dr_ai,1]}│(r_b1i,1 , r_b2i,1)}[cos [(θ_01i,1 +  θ_02i,1)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ₁ [1 + [β₁cosine [(θ_01i,1 + θ_02i,1)/2]]]}}}⁴/C}}}^odx₁}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{[[(θ_01i,2²) - (θ_02i,2²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,2 , θ_s2i,2)}^-1}{{[dr_bi,2/dr_ai,2]}│(r_b1i,2 , r_b2i,2)}[cos [(θ_01i,2 +  θ_02i,2)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ₂ [1 + [β₂cosine [(θ_01i,2 + θ_02i,2)/2]]]}}}⁴/C}}}^odx₂}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{[[(θ_01i,3²) - (θ_02i,3²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,3 , θ_s2i,3)}^-1}{{[dr_bi,3/dr_ai,3]}│(r_b1i,3 , r_b2i,3)}[cos [(θ_01i,3 +  θ_02i,3)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ₃ [1 + [β₃cosine [(θ_01i,3 + θ_02i,3)/2]]]}}}⁴/C}}}^odx₃}/n}(A)}}} 

+ … +    {Σ(i = 1, i = n) {{{[[(θ_01i,m²) - (θ_02i,m²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,m , θ_s2i,m)}^-1}{{[dr_bi,m/dr_ai,m]}│(r_b1i,m , r_b2i,m)}[cos [(θ_01i,m +  θ_02i,m)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ_m[1 + [β₂cosine [(θ_01i,m + θ_02i,m)/2]]]}}}⁴/C}}}^odx_m}/n}(A)}}}}  + [M_restC²]}/[M_restC²] 

= {{{Σ(i = 1, i = n) {{{[[(θ_01i,1²) - (θ_02i,1²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,1 , θ_s2i,1)}^-1}{{[dr_bi,1/dr_ai,1]}│(r_b1i,1 , r_b2i,1)}[cos [(θ_01i,1 +  θ_02i,1)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{{1/{1 – [(v₁/C)²]}^1/2}  [1 + [(v₁/C)cosine [(θ_01i,1 + θ_02i,1)/2]]]}}}⁴/C}}}^odx₁}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{[[(θ_01i,2²) - (θ_02i,2²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,2 , θ_s2i,2)}^-1}{{[dr_bi,2/dr_ai,2]}│(r_b1i,2 , r_b2i,2)}[cos [(θ_01i,2 +  θ_02i,2)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v₂/C)²]}^1/2}  [1 + [(v₂/C)cosine [(θ_01i,2 + θ_02i,2)/2]]]}}}⁴/C}}}^odx₂}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{[[(θ_01i,3²) - (θ_02i,3²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,3 , θ_s2i,3)}^-1}{{[dr_bi,3/dr_ai,3]}│(r_b1i,3 , r_b2i,3)}[cos [(θ_01i,3 +  θ_02i,3)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v₃/C)²]}^1/2}  [1 + [(v₃/C)cosine [(θ_01i,3 + θ_02i,3)/2]]]}}}⁴/C}}}^odx₃}/n}(A)}}} 

+ … +    {Σ(i = 1, i = n) {{{[[(θ_01i,m²) - (θ_02i,m²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,m , θ_s2i,m)}^-1}{{[dr_bi,m/dr_ai,m]}│(r_b1i,m , r_b2i,m)}[cos [(θ_01i,m +  θ_02i,m)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v_m/C)²]}^1/2} [1 + [(v_m/C)cosine [(θ_01i,m + θ_02i,m)/2]]]}}}⁴/C}}}^odx_m}/n}(A)}}}}  + [M_restC²]}/[M_restC²] 

 

 

=  {{Σ(i = 1, i = m)   {Σ(i = 1, i = n) {{{[[(θ_01i,j²) - (θ_02i,j²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,j , θ_s2i,j)}^-1}{{[dr_bi,j/dr_ai,j]}│(r_b1i,j , r_b2i,j)}[cos [(θ_01i,j +  θ_02i,j)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ_j [1 + [β_jcosine [(θ_01i,j + θ_02i,j)/2]]]}}}⁴/C}}}^odx_j}/n}(A)}}}}  + [M_restC²]}/[M_restC²] 

= {{Σ(i = 1, i = m)   {Σ(i = 1, i = n) {{{[[(θ_01i,j²) - (θ_02i,j²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,j , θ_s2i,j)}^-1}{{[dr_bi,j/dr_ai,j]}│(r_b1i,j , r_b2i,j)}[cos [(θ_01i,j +  θ_02i,j)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v_j/C)²]}^1/2}  [1 + [(v_j/C)cosine [(θ_01i,j + θ_02i,j)/2]]]}}}⁴/C}}}^odx_j}/n}(A)}}} + [M_restC²]}/[M_restC²]   

 

 

 

 

= {{{Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_sli,1]}}}

²} – {{cos^-1 {{[cos θ_s2i,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_s2i,1]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v₁/C)}/{1 – [(v₁/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,1 , θ_s2i,1)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v₁ /C)}/{1 – [(v₁/C) cos θ_s]}}}}│[cos  θ_s1i,1 ,  cos θ_s2i,1]}{cos {{{cos^-1 {{[cos θ_sli,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_sli,1]}}}+  {cos^-1 {{[cos θ_s2i,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_s2i,1]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ₁ {1 + {β₁cosine {{{cos^-1 {{[cos θ_sli,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_sli,1]}}}+ {cos^-1 {{[cos θ_s2i,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_s2i,1]}}}}/2}}}}}}⁴/C}}}^odx₁}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_sli,2]}}}

²} – {{cos^-1 {{[cos θ_s2i,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_s2i,2]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v₂/C)}/{1 – [(v₂/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,2 , θ_s2i,2)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v₂ /C)}/{1 – [(v₂/C) cos θ_s]}}}}│[cos  θ_s1i,2 ,  cos θ_s2i,2]}{cos {{{cos^-1 {{[cos θ_sli,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_sli,2]}}}+  {cos^-1 {{[cos θ_s2i,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_s2i,2]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ₂ {1 + {β₂cosine {{{cos^-1 {{[cos θ_sli,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_sli,2]}}}+ {cos^-1 {{[cos θ_s2i,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_s2i,2]}}}}/2}}}}}}⁴/C}}}^odx₂}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_sli,3]}}}

²} – {{cos^-1 {{[cos θ_s2i,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_s2i,3]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v₃/C)}/{1 – [(v₃/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,3 , θ_s2i,3)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v₃ /C)}/{1 – [(v₃/C) cos θ_s]}}}}│[cos  θ_s1i,3 ,  cos θ_s2i,3]}{cos {{{cos^-1 {{[cos θ_sli,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_sli,3]}}}+  {cos^-1 {{[cos θ_s2i,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_s2i,3]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ₃ {1 + {β₃cosine {{{cos^-1 {{[cos θ_sli,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_sli,3]}}}+ {cos^-1 {{[cos θ_s2i,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_s2i,3]}}}}/2}}}}}}⁴/C}}}^odx₃}/n}(A)}}} 

+ … +   {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_sli,m]}}}

²} – {{cos^-1 {{[cos θ_s2i,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_s2i,m]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v_m/C)}/{1 – [(v_m/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,m , θ_s2i,m)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v_m /C)}/{1 – [(v_m/C) cos θ_s]}}}}│[cos  θ_s1i,m ,  cos θ_s2i,m]}{cos {{{cos^-1 {{[cos θ_sli,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_sli,m]}}}+  {cos^-1 {{[cos θ_s2i,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_s2i,m]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ_m {1 + {β_mcosine {{{cos^-1 {{[cos θ_sli,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_sli,m]}}}+ {cos^-1 {{[cos θ_s2i,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_s2i,m]}}}}/2}}}}}}⁴/C}}}^odx_m}/n}(A)}}}} + [M_restC²]}/[M_restC²]   

= {{{Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_sli,1]}}}

²} – {{cos^-1 {{[cos θ_s2i,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_s2i,1]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v₁/C)}/{1 – [(v₁/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,1 , θ_s2i,1)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v₁ /C)}/{1 – [(v₁/C) cos θ_s]}}}}│[cos  θ_s1i,1 ,  cos θ_s2i,1]}{cos {{{cos^-1 {{[cos θ_sli,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_sli,1]}}}+  {cos^-1 {{[cos θ_s2i,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_s2i,1]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v₁/C)²]}^1/2}   {1 + {(v₁/C)cosine {{{cos^-1 {{[cos θ_sli,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_sli,1]}}}+ {cos^-1 {{[cos θ_s2i,1] – (v₁/C)}/{1 – [(v₁/C) cos θ_s2i,1]}}}}/2}}}}}}⁴/C}}}^odx₁}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_sli,2]}}}

²} – {{cos^-1 {{[cos θ_s2i,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_s2i,2]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v₂/C)}/{1 – [(v₂/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,2 , θ_s2i,2)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v₂ /C)}/{1 – [(v₂/C) cos θ_s]}}}}│[cos  θ_s1i,2 ,  cos θ_s2i,2]}{cos {{{cos^-1 {{[cos θ_sli,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_sli,2]}}}+  {cos^-1 {{[cos θ_s2i,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_s2i,2]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v₂/C)²]}^1/2}   {1 + {(v₂/C)cosine {{{cos^-1 {{[cos θ_sli,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_sli,2]}}}+ {cos^-1 {{[cos θ_s2i,2] – (v₂/C)}/{1 – [(v₂/C) cos θ_s2i,2]}}}}/2}}}}}}⁴/C}}}^odx₂}/n}(A)}}} 

+  {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_sli,3]}}}

²} – {{cos^-1 {{[cos θ_s2i,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_s2i,3]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v₃/C)}/{1 – [(v₃/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,3 , θ_s2i,3)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v₃ /C)}/{1 – [(v₃/C) cos θ_s]}}}}│[cos  θ_s1i,3 ,  cos θ_s2i,3]}{cos {{{cos^-1 {{[cos θ_sli,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_sli,3]}}}+  {cos^-1 {{[cos θ_s2i,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_s2i,3]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v₃/C)²]}^1/2}   {1 + {(v₃/C)cosine {{{cos^-1 {{[cos θ_sli,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_sli,3]}}}+ {cos^-1 {{[cos θ_s2i,3] – (v₃/C)}/{1 – [(v₃/C) cos θ_s2i,3]}}}}/2}}}}}}⁴/C}}}^odx₃}/n}(A)}}} 

+ … +   {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_sli,m]}}}

²} – {{cos^-1 {{[cos θ_s2i,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_s2i,m]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v_m/C)}/{1 – [(v_m/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,m , θ_s2i,m)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v_m /C)}/{1 – [(v_m/C) cos θ_s]}}}}│[cos  θ_s1i,m ,  cos θ_s2i,m]}{cos {{{cos^-1 {{[cos θ_sli,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_sli,m]}}}+  {cos^-1 {{[cos θ_s2i,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_s2i,m]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v_m/C)²]}^1/2}   {1 + {(v_m/C)cosine {{{cos^-1 {{[cos θ_sli,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_sli,m]}}}+ {cos^-1 {{[cos θ_s2i,m] – (v_m/C)}/{1 – [(v_m/C) cos θ_s2i,m]}}}}/2}}}}}}⁴/C}}}^odx_m}/n}(A)}}}}  [M_restC²]}/[M_restC²]   

 

 

 

 

{{Σ ( j= 1, j = m) {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}

²} – {{cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v_j/C)}/{1 – [(v_j/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,j , θ_s2i,j)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v_j /C)}/{1 – [(v_j/C) cos θ_s]}}}}│[cos  θ_s1i,j ,  cos θ_s2i,j]}{cos {{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}+  {cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ_j {1 + {β_jcosine {{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}+ {cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}}/2}}}}}}⁴/C}}}^odx_j}/n}(A)}}}} + [M_restC²]}/[M_restC²]     

= {{Σ ( j= 1, j = m) {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}

²} – {{cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v_j/C)}/{1 – [(v_j/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,j , θ_s2i,j)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v_j /C)}/{1 – [(v_j/C) cos θ_s]}}}}│[cos  θ_s1i,j ,  cos θ_s2i,j]}{cos {{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}+  {cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v_j/C)²]}^1/2}   {1 + {(v_j/C)cosine {{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}+ {cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}}/2}}}}}}⁴/C}}}^odx_j}/n}(A)}}}} + [M_restC²]}/[M_restC²]    

For total accrued velocity, v, we have

 

v = C{{-{1/{{{Σ(i = 1, i = m)   {Σ(i = 1, i = n) {{{[[(θ_01i,j²) - (θ_02i,j²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,j , θ_s2i,j)}^-1}{{[dr_bi,j/dr_ai,j]}│(r_b1i,j , r_b2i,j)}[cos [(θ_01i,j +  θ_02i,j)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ_j [1 + [β_jcosine [(θ_01i,j + θ_02i,j)/2]]]}}}⁴/C}}}^odx_j}/n}(A)}}}}  + [M_restC²]}/[M_restC²]}  ²}} + 1}^1/2}

= C{{-{1/{{{Σ(i = 1, i = m)   {Σ(i = 1, i = n) {{{[[(θ_01i,j²) - (θ_02i,j²)] /((90 degrees)²)]  {{[dθ₀/dθ_s]│(θ_s1i,j , θ_s2i,j)}^-1}{{[dr_bi,j/dr_ai,j]}│(r_b1i,j , r_b2i,j)}[cos [(θ_01i,j +  θ_02i,j)/2]]}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v_j/C)²]}^1/2}  [1 + [(v_j/C)cosine [(θ_01i,j + θ_02i,j)/2]]]}}}⁴/C}}}^odx_j}/n}(A)}}} + [M_restC²]}/[M_restC²]} ²}} + 1}^1/2}

= C{{-{1/{{{Σ ( j= 1, j = m) {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}

²} – {{cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v_j/C)}/{1 – [(v_j/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,j , θ_s2i,j)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v_j /C)}/{1 – [(v_j/C) cos θ_s]}}}}│[cos  θ_s1i,j ,  cos θ_s2i,j]}{cos {{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}+  {cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{γ_j {1 + {β_jcosine {{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}+ {cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}}/2}}}}}}⁴/C}}}^odx_j}/n}(A)}}}} + [M_restC²]}/[M_restC²]}     

²}} + 1}^1/2}

= C{{-{1/{{{Σ ( j= 1, j = m) {Σ(i = 1, i = n) {{{{{{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}

²} – {{cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}²}} /((90 degrees)²)} {{{d{cos^-1 {{[cos θ_s] – (v_j/C)}/{1 – [(v_j/C) cos θ_s]}}}

/dθ_s}│(θ_s1i,j , θ_s2i,j)}^-1}{{[Δ (cos θ_s )]/{Δ {{[cos θ_s] – (v_j /C)}/{1 – [(v_j/C) cos θ_s]}}}}│[cos  θ_s1i,j ,  cos θ_s2i,j]}{cos {{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}+  {cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}}/2}}}} {{{ʃ{{2 {σ {{(T_cmbr)/{ {1/{1 – [(v_j/C)²]}^1/2}   {1 + {(v_j/C)cosine {{{cos^-1 {{[cos θ_sli,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_sli,j]}}}+ {cos^-1 {{[cos θ_s2i,j] – (v_j/C)}/{1 – [(v_j/C) cos θ_s2i,j]}}}}/2}}}}}}⁴/C}}}^odx_j}/n}(A)}}}} + [M_restC²]}/[M_restC²]  ²}} + 1}^1/2}

As you can see, attempts at analytic solutions and even non-computational numerical solutions would pose a proverbial night-mare.

 

I will post further on this subject later today.

Regards;

Jim

Copyright James M. Essig  January 26, 2011  All Rights Reserved.

Singularities Of Objective Time Dependent Quantitative Derivatives Of Human Will As A Function Of Thought Or Of d(d Will/d Thought)/dt.

 

 

Non-zero orders of differentiation of Soul state of the Soul’s will with respect to thought with respect to objective time plausibly range from of order 1 to order Aleph i where i = 0, 1,2,3, ….,Omega, …,Aleph 0,…, Aleph 1, … Aleph 2, …, Aleph Omega, …, Aleph (Aleph 0),…, Aleph (Aleph 1), .., Aleph (Aleph 2),…, Aleph (Aleph (Omega)), …, Aleph (Aleph (Aleph 0)),…, Aleph (Aleph (Aleph 1)), .., Aleph (Aleph (Aleph 2)), and so on utterly ad infinitum, worlds without end amen.  Any existence of such infinite order double thought time derivatives obviously implies that the human soul is infinitely complex and perfectly continuous to super-continuous in its state change with respect to time.

 

A good mathematical scenario of non-zero infinite order time derivatives of state change of  will with respect to thought includes dynamics where the change of soul-will-though state is described by a finite or infinite series of trigonometric functions such as those expressible as a partial or full Fourier Series. Another scenario includes soul-will-though states defined by exponential functions such as functions of will-thought including but not limited to: f(will) = (h)[e^{[g(will-though)]}] or perhaps f(will) = {(h)[e^{[g(will-though)]}]} + d where h and d can be functions of will and/or thought , or any other parameters, and g(will-thought) is a function of will and/or thought. For functions of will expressible as a Fourier Series, one or more or all of the summation terms can be functions of will and/or thought. The series of similar trigonometric or exponential functions might  alternatively be a product series or a series of exponents, a series of tetrations, 4,  a series of pentations, 5, a series of hexations, 6, 7, 8, ensemble, …, infinity scrapper, …, Omega, …,Aleph 0,…, Aleph 1, … Aleph 2, …, Aleph Omega, …, Aleph (Aleph 0),…, Aleph (Aleph 1), .., Aleph (Aleph 2),…, Aleph (Aleph (Omega)), …, Aleph (Aleph (Aleph 0)),…, Aleph (Aleph (Aleph 1)), .., Aleph (Aleph (Aleph 2)), and so on utterly ad infinitum, worlds without end amen.

 

Note that tetration is defined as follows:

 

From our friend of Wikipedia;

 

“As we can see from the definition, when evaluating tetration expressed as an “exponentiation tower”, the exponentiation is done at the deepest level first (in the notation, at the highest level). In other words:”

 

⁴2 = 2 EXP (2 EXP (2 EXP 2))) = 2 EXP (2 EXP 4) = 2 EXP 16 = 65,536.

 

Pentation is the next higher level and is defined as in the following examples:

 

2↑³2 = ²2 = 4

 

2↑³2 = ²2₂ = ⁴2 = 65,536

 

2↑³4 = ⁴2 = ^65,5362 which is far too large to be written in conventional notation.

 

Likewise, the higher levels of hexatation, septation, octation and so-on are mathematically definable.

 

 

 

 

For cases where the function or states of will- thought are expressible as a trigonometric series, the number of dimensions in each term can be equal to 1 and perhaps as great as Aleph i where i = 0, 1,2,3, ….,Omega, …,Aleph 0,…, Aleph 1, … Aleph 2, …, Aleph Omega, …, Aleph (Aleph 0),…, Aleph (Aleph 1), .., Aleph (Aleph 2),…, Aleph (Aleph (Omega)), …, Aleph (Aleph (Aleph 0)),…, Aleph (Aleph (Aleph 1)), .., Aleph (Aleph (Aleph 2)), and so on utterly ad infinitum, worlds without end amen.

 

Now regarding objective time dependent evolution of the time derivative of  the thought derivatives of will state with respect to objective and/or subjective time, the slope of the curve defining such evolution can be extra-ordinarily abrupt and localized in time such that the time limits of the curve would be localized between say -1 and 1, or between any finite real numbers, m and n, where m and n can be but need not be equal and which can be either positive or negative but where the area under the curve is normalized to infinite numbers of square units where the infinite number can be Ω,…,f₁Ω, …, Aleph 0, …, f₂(Aleph 0), …,  Aleph 1, …,  f₃(Aleph 1), …, Aleph 2, …, f₄(Aleph 2),  and so-on ad infinitum. Alternatively, the area under the curve can be normalized to one square unit or any finite numbers of square units less than or greater than one where the limits of integration are -1/Ω,…,-1/[f₁Ω], …, -1/[Aleph 0], …, -1/[f₂(Aleph 0)], …,  -1/[Aleph 1], …,  -1/[f₃(Aleph 1)], …, -1/[Aleph 2], …, -1/[f₄(Aleph 2)] and so-on ad infinitum to 1/Ω,…,1/[f₁Ω], …, 1/[Aleph 0], …, 1/[f₂(Aleph 0)], …,  1/[Aleph 1], …,  1/[f₃(Aleph 1)], …, 1/[Aleph 2], …, 1/[f₄(Aleph 2)] ,  and so-on ad infinitum. Here f_i are suitable finite or infinite non-dimensional factors.

 

An analogous  normalization can be obtained for objective time dependent functions of will with respect to thought of 3 dimensions where the region under the normalized curve is bounded along the x₁ and x₂ axes such that along the x₁ and x₂ axes, the time limits of the curve would be localized between say -1 and 1, or between any finite real numbers, m and n, where m and n can be but need not be equal and which can be either positive or negative but where the 3-D volume under the curve is normalized to infinite numbers of 3-D cubic units where the infinite number can be Ω,…,f₁Ω, …, Aleph 0, …, f₂(Aleph 0), …,  Aleph 1, …,  f₃(Aleph 1), …, Aleph 2, …, f₄(Aleph 2),  and so-on ad infinitum but where the function is well behaved in the sense that for zero centered functions, the x₁ and x₂ coordinates of any point along the bounding curve surface are finite. Alternatively, the volume under the curve can be normalized to one 3-D cubic unit or any finite numbers of such cubic units less than or greater than one where the limits of integration along x₁ and x₂ axes are -1/Ω,…,-1/[f₁Ω], …, -1/[Aleph 0], …, -1/[f₂(Aleph 0)], …,  -1/[Aleph 1], …,  -1/[f₃(Aleph 1)], …, -1/[Aleph 2], …, -1/[f₄(Aleph 2)] and so-on ad infinitum to 1/Ω,…,1/[f₁Ω], …, 1/[Aleph 0], …, 1/[f₂(Aleph 0)], …,  1/[Aleph 1], …,  1/[f₃(Aleph 1)], …, 1/[Aleph 2], …, 1/[f₄(Aleph 2)]   and so-on ad infinitum but where the function is well behaved in the sense that for zero centered functions, the x₁ and x₂ coordinates of any point along the bounding curve surface are finite. Here f_i are suitably finite or infinite non-dimensional factors.

 

An analogous  normalization can be obtained for time dependent functions of will with respect to thought of 4 dimensions where the region under the normalized curve is bounded along the x₁, x₂, and x₃ axes such that along the x₁, x₂, and x₃ axes, the time limits of the curve would be localized between say -1 and 1, or between any finite real numbers, m and n, where m and n can be but need not be equal and which can be either positive or negative but where the 4-D volume under the curve is normalized to infinite numbers of 4-D hyper-cubic units where the infinite number can be Ω,…,f₁Ω, …, Aleph 0, …, f₂(Aleph 0), …,  Aleph 1, …,  f₃(Aleph 1), …, Aleph 2, …, f₄(Aleph 2),  and so-on ad infinitum but where the function is well behaved in the sense that for zero centered functions, the x₁, x₂, and x₃ coordinates of any point along the bounding curve surface are finite. Alternatively, the volume under the curve can be normalized to one 4-D hyper-cubic unit or any finite numbers of such 4-D hyper-cubic units less than or greater than one where the limits of integration along x₁, x₂, and x₃ axes are -1/Ω,…,-1/[f₁Ω], …, -1/[Aleph 0], …, -1/[f₂(Aleph 0)], …,  -1/[Aleph 1], …,  -1/[f₃(Aleph 1)], …, -1/[Aleph 2], …, -1/[f₄(Aleph 2)] and so-on ad infinitum to 1/Ω,…,1/[f₁Ω], …, 1/[Aleph 0], …, 1/[f₂(Aleph 0)], …,  1/[Aleph 1], …,  1/[f₃(Aleph 1)], …, 1/[Aleph 2], …, 1/[f₄(Aleph 2)]   and so-on ad infinitum but where the function is well behaved in the sense that for zero centered functions, the x₁, x₂, and x₃ coordinates of any point along the bounding curve surface are finite. Here f_i are suitable finite or infinite non-dimensional factors.

 

An analogous  normalization can be obtained for time dependent functions of will with respect to thought of 5 dimensions where the region under the normalized curve is bounded along the x₁, x₂, x₃, and x₄  axes such that along the x₁, x₂, x₃, and x₄  axes, the time limits of the curve would be localized between say -1 and 1, or between any finite real numbers, m and n, where m and n can be but need not be equal and which can be either positive or negative but where the 5-D volume under the curve is normalized to infinite numbers of 5-D hyper-cubic units where the infinite number can be Ω,…,f₁Ω, …, Aleph 0, …, f₂(Aleph 0), …,  Aleph 1, …,  f₃(Aleph 1), …, Aleph 2, …, f₄(Aleph 2),  and so-on ad infinitum but where the function is well behaved in the sense that for zero centered functions, the x₁, x₂, x₃, and x₄  coordinates of any point along the bounding curve surface are finite. Alternatively, the volume under the curve can be normalized to one 5-D hyper-cubic unit or any finite numbers of such 5-D hyper-cubic units less than or greater than one where the limits of integration along x₁, x₂, x₃, and x₄  axes are -1/Ω,…,-1/[f₁Ω], …, -1/[Aleph 0], …, -1/[f₂(Aleph 0)], …,  -1/[Aleph 1], …,  -1/[f₃(Aleph 1)], …, -1/[Aleph 2], …, -1/[f₄(Aleph 2)] and so-on ad infinitum to 1/Ω,…,1/[f₁Ω], …, 1/[Aleph 0], …, 1/[f₂(Aleph 0)], …,  1/[Aleph 1], …,  1/[f₃(Aleph 1)], …, 1/[Aleph 2], …, 1/[f₄(Aleph 2)]   and so-on ad infinitum but where the function is well behaved in the sense that for zero centered functions, the x₁, x₂, x₃, and x₄  coordinates of any point along the bounding curve surface are finite. Here f_i are suitable finite or infinite non-dimensional factors.

 

In general, an analogous  normalization can be obtained for time dependent functions of will with respect to thought of (n + 1) dimensions where the region under the normalized curve is bounded along the x₁, x₂, x₂, …, and x_n  axes such that along the x₁, x₂, x₂, …, and x_n  axes, the time limits of the curve would be localized between say -1 and 1, or between any finite real numbers, m and n, where m and n can be but need not be equal and which can be either positive or negative but where the (n + 1)-D volume under the curve is normalized to infinite numbers of (n + 1)-D hyper-cubic units where the infinite number can be Ω,…,f₁Ω, …, Aleph 0, …, f₂(Aleph 0), …,  Aleph 1, …,  f₃(Aleph 1), …, Aleph 2, …, f₄(Aleph 2),  and so-on ad infinitum but where the function is well behaved in the sense that for zero centered functions, the x₁, x₂, x₂, …, and x_n  coordinates of any point along the bounding curve surface are finite. Alternatively, the volume under the curve can be normalized to one (n + 1)-D hyper-cubic unit or any finite numbers of such (n + 1)-D hyper-cubic units less than or greater than one where the limits of integration along x₁, x₂, x₂, …, and x_n  axes are -1/Ω,…,-1/[f₁Ω], …, -1/[Aleph 0], …, -1/[f₂(Aleph 0)], …,  -1/[Aleph 1], …,  -1/[f₃(Aleph 1)], …, -1/[Aleph 2], …, -1/[f₄(Aleph 2)] and so-on ad infinitum to 1/Ω,…,1/[f₁Ω], …, 1/[Aleph 0], …, 1/[f₂(Aleph 0)], …,  1/[Aleph 1], …,  1/[f₃(Aleph 1)], …, 1/[Aleph 2], …, 1/[f₄(Aleph 2)]   and so-on ad infinitum but where the function is well behaved in the sense that for zero centered functions, the x₁, x₂, x₂, …, and x_n  coordinates of any point along the bounding curve surface are finite. Here f_i are suitable finite or infinite non-dimensional factors.

 

Note that the integrated volume under the above normalized curves need not necessarily be continuous, smooth, and or symmetrical. The conic sections bounding the regions defining the functions can be curvy, bumpy, lumpy, have a high degree or torsion, of rough contours, and/or may perhaps even have contours that are of arbitrarily rough fractal patterns and arbitrary forms of fractal patterns in one, more than one, or all dimensions including along the temporal dimension.

 

Since an act of will is well defined, a given species of act will either be performed or not performed. The state of an act of will upon its completion or upon the formation of a fully free and deliberate intention to the precursor state immediately preceding the act will be discontinuous as described by the following ratios: k₁/Ω, [k _{i + 2_}]/(Aleph i) where i = 0, 1,2,3, ….,Omega, …,Aleph 0,…, Aleph 1, … Aleph 2, …, Aleph Omega, …, Aleph (Aleph 0),…, Aleph (Aleph 1), .., Aleph (Aleph 2),…, Aleph (Aleph (Omega)), …, Aleph (Aleph (Aleph 0)),…, Aleph (Aleph (Aleph 1)), .., Aleph (Aleph (Aleph 2)), and so on utterly ad infinitum worlds without end amen. For the latter formulation, k₁ is finite, k_{(I +2)} is either finite or suitably infinite. Here the numerator is the absolute values of the quantitative state(s) variable(s) immediately before the start of the free act and the denominator is the absolute value of the state(s) variable(s) immediately upon realizations or development of the act.

 

 

In order to introduce a complexity to the morphology of the surface contours of the above delta Dirac function analogues, the continuum background abstracted as a spatial volume can be positively or negatively curved or combinations of both forms of curvature. The curvature may be so convoluted that it is marked by a topology that is curvy, bumpy, lumpy, having a high degree or torsion, roughly contoured, and/or may perhaps even have a curvature that is defined by arbitrarily rough fractal patterns and arbitrary forms of fractal patterns in one, more than one, or all dimensions including along the temporal dimension.

 

When we superpose conic sections defined by intra-space functions that are curvy, bumpy, lumpy, have a high degree or torsion, of rough contours, and/or perhaps even have contours that are of arbitrarily rough fractal patterns and arbitrary forms of fractal patterns in one, more than one, or all dimensions including along the temporal dimension with spaces having curvatures defined by functions that are curvy, bumpy, lumpy, have a high degree or torsion, of rough contours, and/or perhaps even contours that are of arbitrarily rough fractal patterns and arbitrary forms of fractal patterns in one, more than one, or all dimensions including along the temporal dimension, we come up with a real epistemological and morphological mess. However, such mess is of the essence of the tangled workings of the Human Heart which only GOD alone can fully comprehend and judge.

 

Even for situations where the resolution of objective time for human volitional behavior is finitely quantized at the Planck Time = {[h/(2π)] G/[C⁵]}^1/2 = 5.39 x 10^-44 second or perhaps less, the before and after will act states for the will are abrupt thereby automatically indicating a singularity in time dependent will  states of the Human Soul.

 

Since the human soul is a unity in terms of its substantial, semi-substantial, facultative, and accidental aspects, and in terms of its vegetative, sensitive, and intellectual life  aspects and that  thus the human psyche is a unity in terms of its conscious, semi-conscious, sub-conscious, and unconscious aspects, and indeed in terms of its ego, ID and superego, every completed and objectively abrupt act of human free volition, has abrupt and immediate effects of the intellectual life of a human person even in cases where such thought or thought change is not or cannot be abruptly or immediately recognized in objective and/or subjective time by the person so producing the act of will.

 

Our thoughts may evolve in manners consistent with the above singularities in objective and even subjective time even if we cannot perceive such fine grained or continuous or super-continuous objective or subjective time dependent emotion change or perceive objective and subjective time at such continuous or super-continuous manners. As for me, I can perhaps distinguish the temporal distance of sound between firecrackers that explode about 1/30 of a second apart but at the same distance from me. Any slightly smaller temporal distances become very rapidly hard for me to distinguish.

 

Thought is truly awesome and has been exalted to a primary status by we in the Western world who have a cultural tendancy to extol the virtues of the academic intellect over our emotional life.

 

Now thought, intellectual understanding, intellectual and/or abstract wisdom when possessed to the fullest degree possible regarding a given subject for a given person is in a sense something that we either have or do not have. Even if our awareness of our own understanding waxes and wanes in generally continuous ways in a manner commensurate with our finite ability to perceive the resolution of subjective and objective time, a development of a full and clear understanding of an idea, concept, notion, fact, situation, subject, topic or whatever,  with respect to a previous state of imprecise understanding involves a singularity from imprecise understanding to perfect understanding, even though self-perception or self-awareness of the transition boundary between  imperfect understanding and perfect understanding in real objective and subjective time during which the transition takes place has a finite level of objective and subjective temporal resolution.

 

From a purely epistemological and ontological standpoint, such a cognitive transition between complete understanding and lack of complete understanding is abstractly affirmable if for no other reason than that truth is what is true. Something is either true or false and correctly understood or perfectly understood or intellectually abstractly or intuitively clear or it isn’t. Perfection is an absolute state even if the level, mode, or type of perfection is limited. Even in cases where the evolution from imperfect understanding or lack of perfect understanding to perfect or full understanding is continuous, the local finite region of the time dependent evolution of understanding with respect to either objective or subjective time is asymptotic along the dimension of understanding where the asymptotic rise of the time dependent understanding along the objective or subjective temporal axis occurs at the times of transition.

 

In practice, at least for me, the transition from complete and full understanding or knowing from lack of complete and full understanding or knowing, is blurred in terms of my awareness or experience of such a transition. Maybe I am just a mood or emotional thinker, but even my conscious perception of objective or subjective time passage as such relates to my awareness of a personal understanding of something from a previous imperfect or perhaps outright non-understanding of something is seemingly often continuously morphing even  at times when I am struggling to understand a concept that I am writing about such as the subject of this article. Even when I have a sudden flash of insight when a subject is personally first fully understood, it seems that I can sense or intuitively perceive that I am about to understand or beginning to understand the self-aware aspects of such understanding only at a temporal level of resolution of at least 1/10^th of a second if the idea becomes consciously clear to me in an obvious and clear matter. Usually, the evolution of personal imperfect or lack of understanding to complete personal understanding takes anywhere from a better part of a second to a few seconds for me.

 

Just as our conscious moods and thoughts can continually morph, so too can our mental images, mental abstractions, and understandings,  especially our conscious visceral awareness of such intellective activity. Oddly, this is even true for understandings wrought from  purely abstract or deductive cognitive and logical cognitive processes. For those ultra-rationalist folks who deny their emotionality and perhaps even outright attempt to always repress their emotionality, even in cases where some such folks are really emotionally low key and perhaps out-right calm to the point of being emotionally cold, they would be loathed to try to perceive the temporal time steps of developing conscious understanding, in either subjective or objective time, down to a level of one millisecond. Ask them to try to perceive the time flow of such a transition region from lack of perfect understanding to perfect understanding down to a level of one microsecond, one nano-second, or how about one Planck Time Unit and they could only say that’s impossible. In terms of the existence of any continuous subjective time or subjective time resolution at a level of the infinitesimal, which obviously no human on Earth can consciously perceive or recognize,  asking the above most rationalist and intellectual persons to try to perceive such would only end in their utter frustration even if they put all of their effort into trying to do so.

 

However, since any truth is an absolute, even if the value of a truth, the significance of a truth, the purpose of a truth, the goodness of a truth, and/or the reason for a truth is limited with respect to another, the state of abstractly or intuitively objectively internalized truth in an existential and ontological manner with respect to the temporally nearest state of lack of such internalized truth must be held to be a singularity.

 

Now, from an ontological and existential perspective, there does seem to exist singularities of the above understanding realization types. Such singularities generally do precede in objective and subjective time, free, deliberate, and rational acts of free will. However, such singularities being a subset of human behavior and also a subset of human psychodynamic structures and elements also couple with human mood, attitude, and emotion. Since we can all agree that mood, emotion, feeling, affect,  and to some degree attitude are in constant objective and subjective time varying flux, such fluxes also exists along-side understanding singularities and can both effect and be effected by experienced acquisition of  new understandings regardless of whether or not the new understandings are fully within conscious realization and perception or whether or not the understandings are semi-conscious, sub-conscious, and perhaps even unconscious.

 

Because such time dependent understandings occurs within the context of a real and concretely existing human psyche and more generally, within a given human soul, such singularities are related in objective and subjective time to moods, feelings, emotions, affect, attitude, and even with other thoughts. The significance of the previous statement will become clear to reader below.

 

Imagine that a conscious realization of understanding type of singularity is plotted above an abstract number line or perhaps two number lines that run more or less parallel to each other and horizontally. The numbers lines are the subjective and objective past, present, and future dimensions defining human psychodynamic movements. The location of the understanding singularity a slight distance above the number line can serve as a proxy for the fact that the singularity occurs mainly in the intellect and is  thus located somewhat existentially externally to the sensitive life in the sense that the intellect is not precisely identical to the sensitive life although obviously related to and coupled to the sensitive life.

 

Because of the existential distance between the understanding singularity and the proximate sensitive life, when one considers a third sensitive axis running parallel to the horizontal temporal axes, one can draw radial lines from the singularity to different positions along either of the three axes. Thus, lines can be drawn to arbitrary points nearly under and ahead of the singularity of arbitrary length thereby permitting the formation of angles between any two radial lines  having arbitrary measures. No matter how finitely small the angle, it can always be bisected. In fact for a perfectly dynamically continuous human psyche, or more generally, human soul, the measure of the angles produced can be as small as n/Ω radians where n is positive and finite and Ω is the least transfinite or infinite ordinal. For level 1 super-continuous  psyches or souls, the measure can be as small as n/(Aleph 0) radians. For level 2 super-continuous psyches or souls, the measure can be as small as n/(Aleph 1) radians. For level 3 super-continuous psyches or souls, the measure can be as small as n/(Aleph 2) radians. One can  continue angles of measure n/(Aleph i) radians for (i-1) level super-continuities where i can be 4, 5, 6, …,Omega, …,Aleph 0,…, Aleph 1, … Aleph 2, …, Aleph Omega, …, Aleph (Aleph 0),…, Aleph (Aleph 1), .., Aleph (Aleph 2),…, Aleph (Aleph (Omega)), …, Aleph (Aleph (Aleph 0)),…, Aleph (Aleph (Aleph 1)), .., Aleph (Aleph (Aleph 2)), and so on utterly ad infinitum worlds without end amen.

 

Since all such angles remain open until they reach the very center of the point defining the singularity, they are open when they cross the external boundary of the singularity because even at the boundary of such an infinitesimal abstraction, the radial lines have not yet converged. Since the singularity is a real and concrete objective event, perhaps the external singularity boundary values of the separations of the lines indicate individual points or sub-points along the eternal surface of the singularity. Each such boundary location would definitely serve as a proxy for a bit of existential and ontological information about the singularity. In fact, each possible angular divergence of the radial lines from both the boundary surface of the singularity and the very heart of the singularity would serve as a data bit describing and indicating an existential and ontological feature within the singularity. Moreover, each point along a given line as it passes through the boundary of the singularity to the heart of the singularity can be said to represent an ontological or existential character or feature data bit defining the singularity. The number of individual points and sub-points that are possible within the singularity-sensitive life-temporal axis system can be represented as a summation of m_1i, f(Ω) terms for continuous psyches or souls; m_2i f(Aleph 0) terms for level 1 super-continuous psyches or souls; m_3i f(Aleph 1) terms for level 2 super-continuous psyches or souls; m_4i f(Aleph 2) terms for level 1 super-continuous psyches or souls; and indeed; m_{(i +1)i} f(Aleph i) terms for level (i + 1) super-continuous psyches or souls, where i can be 4, 5, 6, …,Omega, …,Aleph 0,…, Aleph 1, … Aleph 2, …, Aleph Omega, …, Aleph (Aleph 0),…, Aleph (Aleph 1), .., Aleph (Aleph 2),…, Aleph (Aleph (Omega)), …, Aleph (Aleph (Aleph 0)),…, Aleph (Aleph (Aleph 1)), .., Aleph (Aleph (Aleph 2)), and so on utterly ad infinitum worlds without end amen.

 

In reality, the number of infinite functional terms, m_i scales with the degree of continuity or super-continuity of the human psyche or within at least the singularity-sensitive life-temporal axis system. This is because the number of points or sub-points on each line scales with the ultimate scale of resolution for each degree of super continuity. Since each such point involves a particular location along a given radial line, the distance between each point and its angular coordinate with respect to the location of the heart of the singularity defines a relation which in the context of a real entity such as the human soul, must also represent a real character or feature or distinct aspect of a given singularity-sensitive life-temporal axis system, and more generally, of the overall human psyche or soul.

 

Since there is an objective set, S₀,  defining each point, sub-point, and angle thus formed in the singularity-sensitive life-temporal axis system, the set, S₁,  of all subsets of  the elements in the former  set further defines real relations or features within the singularity-sensitive life-temporal axis system. The set,  S₂, of all subsets of S₁, still further defines real relations or features with the singularity-sensitive life-temporal axis system. The set,  S₃, of all subsets of S₂, still further defines real relations or features with the singularity-sensitive life-temporal axis system. Likewise, we can go on to form sets, S_i, where i = 4, 5, 6, …,Omega, …,Aleph 0,…, Aleph 1, … Aleph 2, …, Aleph Omega, …, Aleph (Aleph 0),…, Aleph (Aleph 1), .., Aleph (Aleph 2),…, Aleph (Aleph (Omega)), …, Aleph (Aleph (Aleph 0)),…, Aleph (Aleph (Aleph 1)), .., Aleph (Aleph (Aleph 2)), and so on utterly ad infinitum worlds without end amen.

 

Thus, the number of associated features or characters within the singularity-sensitive life-temporal axis system for continuous psyches or souls is roughly

{{2 EXP {Σ[i = 1, f(Ω)] m_1i, f(Ω)}} -1} +  {{2 EXP {2 EXP {Σ[i = 1, f(Ω)] m_1i, f(Ω)}} -1} – 1} + {{ 2 EXP {2 EXP {2 EXP {Σ[i = 1, f(Ω)] m_1i, f(Ω)}} -1}}  - 1} + {{2 EXP { 2 EXP {2 EXP {2 EXP {Σ[i = 1, f(Ω)] m_1i, f(Ω)}} -1}}  – 1}} and so-on forever.

 

The number of associated features or characters within the singularity-sensitive life-temporal axis system for level 1 super-continuous psyches or souls is roughly abstracted as {{2 EXP {Σ[i = 1, f(Aleph 0)] m_1i, f(Aleph 0)}} -1} +  {{2 EXP {2 EXP {Σ[i = 1, f(Aleph 0)] m_1i, f(Aleph 0)}} -1} – 1} + {{ 2 EXP {2 EXP {2 EXP {Σ[i = 1, f(Aleph 0)] m_1i, f(Aleph 0)}} -1}}  – 1} + {{2 EXP { 2 EXP {2 EXP {2 EXP {Σ[i = 1, f(Aleph 0)] m_1i, f(Aleph 0)}} -1}}  – 1}} and so-on forever. In reality, the actual number of features and characters is {2 EXP {{{2 EXP {Σ[i = 1, f(Aleph 0)] m_1i, f(Aleph 0)}} -1} +  {{2 EXP {2 EXP {Σ[i = 1, f(Aleph 0)] m_1i, f(Aleph 0)}} -1} – 1} + {{ 2 EXP {2 EXP {2 EXP {Σ[i = 1, f(Aleph 0)] m_1i, f(Aleph 0)}} -1}}  – 1} + {{2 EXP { 2 EXP {2 EXP {2 EXP {Σ[i = 1, f(Aleph 0)] m_1i, f(Aleph 0)}} -1}}  – 1}} and so-on forever}} -1 .

 

The number of associated features or characters within the singularity-sensitive life-temporal axis system for level 2 super-continuous psyches or souls is roughly {{2 EXP {Σ[i = 1, f(Aleph 1)] m_1i, f(Aleph 1)}} -1} +  {{2 EXP {2 EXP {Σ[i = 1, f(Aleph 1)] m_1i, f(Aleph 1)}} -1} – 1} + {{ 2 EXP {2 EXP {2 EXP {Σ[i = 1, f(Aleph 1)] m_1i, f(Aleph 1)}} -1}}  – 1} + {{2 EXP { 2 EXP {2 EXP {2 EXP {Σ[i = 1, f(Aleph 1)] m_1i, f(Aleph 1)}} -1}}  – 1}} and so-on forever. In reality, the actual number of features and characters is {2 EXP {{{2 EXP {Σ[i = 1, f(Aleph 1)] m_1i, f(Aleph 1)}} -1} +  {{2 EXP {2 EXP {Σ[i = 1, f(Aleph 1)] m_1i, f(Aleph 1)}} -1} – 1} + {{ 2 EXP {2 EXP {2 EXP {Σ[i = 1, f(Aleph 1)] m_1i, f(Aleph 1)}} -1}}  – 1} + {{2 EXP { 2 EXP {2 EXP {2 EXP {Σ[i = 1, f(Aleph 1)] m_1i, f(Aleph 1)}} -1}}  – 1}} and so-on forever }} -1

 

The number of associated features or characters within the singularity-sensitive life-temporal axis system for level 3 super-continuous psyches or souls is roughly {{2 EXP {Σ[i = 1, f(Aleph 2)] m_1i, f(Aleph 2)}} -1} +  {{2 EXP {2 EXP {Σ[i = 1, f(Aleph 2)] m_1i, f(Aleph 2)}} -1} – 1} + {{ 2 EXP {2 EXP {2 EXP {Σ[i = 1, f(Aleph 2)] m_1i, f(Aleph 2)}} -1}}  – 1} + {{2 EXP { 2 EXP {2 EXP {2 EXP {Σ[i = 1, f(Aleph 2)] m_1i, f(Aleph 2)}} -1}}  – 1}} and so-on forever. In reality, the actual number of features and characters is {2 EXP {{{2 EXP {Σ[i = 1, f(Aleph 2)] m_1i, f(Aleph 2)}} -1} +  {{2 EXP {2 EXP {Σ[i = 1, f(Aleph 2)] m_1i, f(Aleph 2)}} -1} – 1} + {{ 2 EXP {2 EXP {2 EXP {Σ[i = 1, f(Aleph 2)] m_1i, f(Aleph 2)}} -1}}  – 1} + {{2 EXP { 2 EXP {2 EXP {2 EXP {Σ[i = 1, f(Aleph 2)] m_1i, f(Aleph 2)}} -1}}  – 1}} and so-on forever }} -1

 

In general, the number of associated features or characters within the singularity-sensitive life-temporal axis system j level one super-continuous psyches or souls is roughly {{2 EXP {Σ[i = 1, f(Aleph (j -1) )] m_1i, f(Aleph (j -1))}} -1} +  {{2 EXP {2 EXP {Σ[i = 1, f(Aleph (j -1))] m_1i, f(Aleph (j -1))}} -1} – 1} + {{ 2 EXP {2 EXP {2 EXP {Σ[i = 1, f(Aleph (j -1))] m_1i, f(Aleph (j -1))}} -1}}  – 1} + {{2 EXP { 2 EXP {2 EXP {2 EXP {Σ[i = 1, f(Aleph (j -1))] m_1i, f(Aleph (j -1))}} -1}}  – 1}} and so-on forever. In reality, the actual number of features and characters is {2 EXP {{{2 EXP {Σ[i = 1, f(Aleph (j -1) )] m_1i, f(Aleph (j -1))}} -1} +  {{2 EXP {2 EXP {Σ[i = 1, f(Aleph (j -1))] m_1i, f(Aleph (j -1))}} -1} – 1} + {{ 2 EXP {2 EXP {2 EXP {Σ[i = 1, f(Aleph (j -1))] m_1i, f(Aleph (j -1))}} -1}}  – 1} + {{2 EXP { 2 EXP {2 EXP {2 EXP {Σ[i = 1, f(Aleph (j -1))] m_1i, f(Aleph (j -1))}} -1}}  – 1}} and so-on forever }} -1 where j = 4, 5, 6, …,Omega, …,Aleph 0,…, Aleph 1, … Aleph 2, …, Aleph Omega, …, Aleph (Aleph 0),…, Aleph (Aleph 1), .., Aleph (Aleph 2),…, Aleph (Aleph (Omega)), …, Aleph (Aleph (Aleph 0)),…, Aleph (Aleph (Aleph 1)), .., Aleph (Aleph (Aleph 2)), and so on utterly ad infinitum worlds without end amen.

 

Now since each human psyche, or more generally each human soul, has all manner of forms and types of feelings which evolve, intermingle, interact, and intra-act with each other and themselves, the number of parallel horizontal axes and thus the richness of the human heart, sensitive life, and soul is commensurately super-abundantly infinitely greater yet.

 

I even say this as a large bulky middle aged man whose moods good and bad seem to slowly evolve and come and go. When my mood is good and even manic as a result of excessive caffeine use, this is great fun which can last quite a while. When my mood is flat, life can be a real bore. When my mood is depressed which it can be at times, I tend to turtle under my covers and sleep the daylight hours away. So much for cyclothymic physicist and amateur armchair theologian with sluggish moods! At least, I am no longer physically as sluggish as I used to be. After all, I did a 88  minute cross-county style walk today at a weight of 365 pounds in hilly terrain without a single break. My mood is a little elevated tonight, and so I should hold off on using any more diet Coke this evening.

 

The human heart and mind is so complex that even in Heaven after the Final Resurrection, we may never even begin to fully understand the existential and ontological richness and sizes of our souls, hearts, and minds. However, we have all eternity to grow and evolve existentially and ontologically and to contemplate our internal wonders, those we love by special familial, marriage, or non-familial friendship bonds, and indeed also among all of the elect in Heaven.

 

Our heart life and emotions, affects, feelings, moods, attitudes, are sacred and awesomely existentially and ontologically rich and by corollary, even far more so is our overall psyche and soul by which the former are contained or a sub-portion thereof.

 

So enjoy and respect your emotions, affects, feelings, moods, attitudes. They will be with you and a part of who you are for all eternity and will be Resurrected in an exalted manner in nature and in grace at the Final Resurrection.

 Regards;

Jim

Copyright James M. Essig January 24, 2011  All Rights Reserved

 

 

THE HUMAN SOUL IN 77 CHAPTERS. Seventy-Seven Chapters On The Dignity And Granduer Of Every Human Soul For Those Looking To See The Sacredness Of Every Human Soul As A Reason To Forgive The Biblical Metaphorical “Not Seven Times! Not Seven Times Seven! But Seventy-Times Seven!”

THE HUMAN SOUL IN 77 CHAPTERS.

 

 

 

This very long post is a summary of my thoughts on the Human Soul over the past 6 years. I hope you will enjoy reading or browsing through it as much as I enjoy thinking about the Human Soul.

 

In this very long post, you will likely be exposed to ideas that are new and novel to you, even those of you who are faith abiding Catholic Clergymen or Religious.

 

Eventhough I am a physicist by training, one that works of interstellar propulsion concept theories, I have a deep love for the human soul, and for the salvation of all human souls if such would be possible. I simply love all human souls and respect them with a deep reverence, even the souls in Hell. The sanctity and sacredness of each human soul is that important to me.

 

This is not to imply that I am a Saint. I have done just about the entire range of human sins. My at times habitual sin ranged from sins of sexual impurity, to gluttony, to excessive anger, to blasphemous speech, to idile gossip, lying, cheating and the like. In fact, even today as a mature almost 50 year old (I will turn 50 this January 25), I still see the need to avail myself the opportuinity of Sacramental absolution in the Confessional twice per month on average. So do not worry that I think I am better than anyone else. I am keenly aware of my capacity and disposition for sinning.

 

To give you an idea of how much I love and respect the human soul in each instance, I would during my teenage years and early adulthood frequently break down and bitterly silently weep in my bed at night because I wanted to know certain things I wanted to believe about the human soul so badly that I would become distraught with despair upon hearing clergymen here in the Diocese of Arlington say things about the human soul that I found objectionable.

 

In a nut shell, I longed with all of my being to know that the human soul is naturally immortal and incorruptible per addends and per se instead of being merely immortal by grace. To the best of my knowledge,  I and  no other Catholic, Clergyman, Religious, or Layperson has definitely stated or definitely knows or understands in what way and manner is the Human Soul immortal.

 

However, as I matured and even philosophically contemplated natural mechanisms that might be capable of destroying the human soul, or at the very least the human energy or spirit body, which I believe is not the human soul and is of a less refined or sublime nature of the human soul, I began to look for ways and means by which to know and understand how each and every human soul would nonetheless be all the more sacred, special, sublime, transcendent, existentially and ontologically large, good, and valuable, and how ironically, the glory of the human soul would nonetheless, be all the greater in some ways in the event that the human soul is not naturally immortal.

 

However, fear not, it is an absolute truth that each human soul will last utterly forever in Heaven, Hell, or any Limbo because even in the case that it is not immortal by its very nature, GOD has definitively declared that each human  soul will ultimately live utterly forever. GOD’s will is utterly unshakeable in this regards, and so the ultimate immortality of every human soul is as utterly unshakeable as GOD’s will power in this regard.

 

Now, the human soul may indeed be immortal by its very nature. It is just that no one to the best of my knowledge in this life has ever proven it to be true in a defacto manner that can witstand all philosophical and logical scruitiny.

 

However, as I say again, fear not! Scholastic Theology may be correct regarding its assertion of the natural immortality of the Human Soul, and even if the approach is not correct, the human soul is supremely great as you will see by reading this long post and is meant for and will last utterly forever, in each and every case.

 

I have always had a fascination with the concept of the Human Soul from my pre-school age years onward.

 

As a 12 year old, I remember doing a lot of reading of articles about the human soul, the human mind, psychology, psychiatry, and the like. Most of these articles where available and read from the 1964 Edition of Collier’s Encyclopedia that my father bought for the family, with the intention of providing me and my five siblings an opportuinity to learn by reading and to assist us with our academic life.

 

I however, was indeed the proverbial black sheep of the family, and in fact did not enjoy going to school as a young boy. I was very shy and introverted during my elementary school age years, but eventually blossomed into an extravert. While most of my brothers and sisters were busy obtaining straight As for the most part, I was content to ride my bike, through a ball, work out, and more to the point, indulge in reading about the Human Soul, and other topics unusual for 5^th through 11^th graders such as UFO space alien abduction accounts and other psuedo-scientific topics.

 

I had developed a strong love of future human space flight scenarios and eventually fell in love with physics. As a physicist, I am primarily interested in prospects for interstellar flight, although thinking and writing on the topic of human nature especially with regard to Catholic notion of a spiritual and immortal soul is a great joy for me.

 

 

Now, I know we have a body also that will be Ressurected at the End Of Time, immortal and incorruptible, and so do not be lead astray when you delve into this article thinking that after you die, you will never get your self-same identical body back which will arise a spiritual body yet a physical body. Now that is a whimsically far out and cool concept.

 

However, I have a special place in my heart for thinking about the human soul. This comes from my early childhood as you will soon read about below.

 

 

I thought that you would enjoy this writing on the great dignity of the human soul.  This article offers a sharp contrast to the main topics on which I tend to post, and was written and compiled from my heart. I have often posted articles on extreme manned star ship technologies, and as a physicist, I will continue to do such. However,  I offer this rather long article as a sharing of my personal belief in the transcendent dignity of every human person, and by corollary, that of any of our ETI brothers and sisters.

 

With modern technological capabilities to monitor the various emotional and mental states of test subjects, and the ability to measure and experimentally probe the electric and magnetic fields generated within the human body, we sometimes are tempted to view the human soul as some form of corruptible energy field.  We long  for a rekindling of a sense of mystery regarding the ephemeral reality of the human soul.

 

Below is a personal attempt to restore a sense of mystery in the minds and  hearts of any and all persons who will read this post regarding that aspect of our human nature that seems to be beyond validation by modern science, technology, and medicine, and which seems to defy certain and precise explanation by philosophers, theologians, and clergyman alike.

 

In this article, I focus mainly on the traditionally held higher faculties of the human soul, but in future posts and re-edited versions of this article, I will discuss the awesome scope of the so-called vegetative and sensitive aspects of the human soul which may entail deeper mystique and intrigue, and mystery in general, then the conscious rational aspects of the human soul.

 

1)  The Creation Of The Human Soul Is Like GOD’s Blowing Living Bubbles.

 

 

2)  Ever Wonder How Complex The Human Heart Is, The Human Soul Is, the Human Psyche In Its Conscious, Sub-Conscious, And Unconscious Aspects Is?

 

 

3)  The Who, What, Where, When, Why, And How Of The Human Soul.

 

 

 

A) The Who Of The Human Soul

 

B)  The What Of The Human Soul

 

C)  The Where Of The Human Soul

 

D)  The When Of The Human Soul

 

E)  The Why Of The Human Soul.

 

F)  The How  Of The Human Soul

 

 

 

4)  Natural Accidental Nature Of The Human Soul Can Grow Without Limit

 

 

 

5)  Soul, Accidents Verses Substance

 

 

 

6)  The Great Dignity Of The Human Soul Even If It Would Be Immortal By Grace

 

 

 

7) The Soul As The Substantial Form Of The Body And What This Implies For The Sublime And Transcendent Dignity Of The Human Soul.

 

 

 

8]  WHAT IS THIS BEING CALLED YOU?

 

 

 

9)  THE HUMAN PERSON AS A MICROCOSM

 

 

 

10)  MYSTERIES OF THE HUMAN BODY

 

 

 

11)  SOULS

 

 

 

12)  THE JOYS OF CONTEMPLATING THE HUMAN SOUL: PART 1

 

 

 

A) The Wonders and Transcendent Reality of the Human Heart

 

 

 

B) The Natural Immortality of the Human Soul and its Non-materiality for Those Who are Looking For Some Higher Meaning of Natural Human Dignity.

 

 

 

C) Musings on the Incorruptibility of the Positive Truth Value of the Goodness of all Rational Spiritual Creatures including but Perhaps not Limited to Human Persons, Angels, any and all Damned Human Souls, all Fallen Angels including Satan, and any Spiritual and Rational Extraterrestrial Beings on Other Planets including all Those that have Died.

 

 

 

13)  THE JOYS OF CONTEMPLATING THE HUMAN SOUL: PART 2

 

14)  WHAT IS THIS THING CALLED FREE WILL?

 

 

 

15)  COULD THERE EXIST A HUMAN ENERGY BODY THAT IS DISTINCT FROM THE HUMAN SOUL?

 

 

 

16)  THE NOTION OF A REAL INTERFACE BETWEEN THE HUMAN SOUL AND THE HUMAN BODY

 

 

 

17)  The Human Soul As Made In The Image And Likeness Of The TRIUNE GOD.

 

 

18)  Personal Musings On The Menagerie Of Planets: There Are Likely More Planets Within Just The Visible Portion Of Our Universe Than There Are Drops Of Water In The Combined Volume Of All Oceans, Rivers, Lakes, Aquifers, Etc., On Planet Earth. An Unlimited Number Of Specific ETI Psychodynamic Personality Trait Spectrums Is Possible Assuming That A Similar  Unlimited Number Exists Of The Same For We Humans.

 

 

19) THE OPPORTUINITY FOR ETERNAL GROWTH OF THE HUMAN SOUL

 

20) TIME AND THE SOUL

 

21) THE VEGETATIVE AND SENSITIVE ASPECTS OF THE HUMAN SOUL

 

 

22) Non-academic Forms Of Intelligence

 

23)  There Is Just Something Magnificently Immutably Eternal About The Human Soul.

 

24) The Great Dignity Of The Human Soul Even If It Would Be Immortal By Grace, Only. But Not To Worry, All Human Souls Are Immortal, And Saint Thomas Aquinas Held That Each Human Soul Is Naturally Immortal, And He Did Not Become A Saint And Earn The Title Of Angelic Doctor Of The Church For No Reason At All.

 

25) Perhaps The Human Soul Grows Substantially And Accident-Wise For All Eternity As It Travels Its World Line In This Life And Then In The Next Life In An Ontological Process Analogous To The Growth Of Physical Objects In 4-D Spatial-Temporal Volume As They Age.

 

26) The Unique And Unrepeatable Human Soul.

 

27) The Human Soul As Real Information, More Properly,  As A Simple And Non-Composite Information.

 

28) Just A Shadow Of A Glimpse Of The Utterly Limitless Number Derivatives of Human Emotion With Respect To Time, Thought, Volition, Affect, Memory, Instinct, And Emotion  Where These Latter 6 Psychodynamic Parameter Are Likely Just An Infinitesimal Fraction Of The Number Of Possible Psychodynamic Parameters, Of Which In This Life, We Have  A Glimpse Of Relatively Few.

 

 

 

29) Just A Shadow Of A Glimpse Of The Utterly Limitless Number Derivatives of Human Affect With Respect To Time, Thought, Volition, Affect, Memory, Instinct, And Emotion  Where These Latter 6 Psychodynamic Parameter Are Likely Just An Infinitesimal Fraction Of The Number Of Possible Psychodynamic Parameters, Of Which In This Life, We Have  A Glimpse Of Relatively Few.

 

 

30) Just A Shadow Of A Glimpse Of The Utterly Limitless Number Derivatives of Human Instinct  With Respect To Time, Thought, Volition, Affect, Memory, Instinct, And Emotion  Where These Latter 6 Psychodynamic Parameter Are Likely Just An Infinitesimal Fraction Of The Number Of Possible Psychodynamic Parameters, Of Which In This Life, We Have  A Glimpse Of Relatively Few.

 

 

33) Just A Shadow Of A Glimpse Of The Utterly Limitless Number Derivatives of Human Memory  With Respect To Time, Thought, Volition, Affect, Memory, Instinct, And Emotion  Where These Latter 6 Psychodynamic Parameter Are Likely Just An Infinitesimal Fraction Of The Number Of Possible Psychodynamic Parameters, Of Which In This Life, We Have  A Glimpse Of Relatively Few.

 

 

 

34) Just A Shadow Of A Glimpse Of The Utterly Limitless Number Derivatives of Human Thought  With Respect To Time, Thought, Volition, Affect, Memory, Instinct, And Emotion  Where These Latter 6 Psychodynamic Parameter Are Likely Just An Infinitesimal Fraction Of The Number Of Possible Psychodynamic Parameters, Of Which In This Life, We Have  A Glimpse Of Relatively Few.

 

 

35) Just A Shadow Of A Glimpse Of The Utterly Limitless Number Derivatives of Will  With Respect To Time, Thought, Volition, Affect, Memory, Instinct, And Emotion  Where These Latter 6 Psychodynamic Parameter Are Likely Just An Infinitesimal Fraction Of The Number Of Possible Psychodynamic Parameters, Of Which In This Life, We Have  A Glimpse Of Relatively Few.

 

 

36) A Human Soul That Can Change Says Something Transcendently Remarkable About The Human Soul

 

 

 

37) The Soul As An Eternal Form.

 

38) The Soul As Self Transcendent.

 

39) The Human Soul Ever New

 

 

40) The Soul Intra-Reactivity

 

 

41)  The Continuous Refreshment Of The Human Soul

 

 

42)  GOD KNEW US BEFORE HE FORMED US IN OUR MOTHER’S WOMB

 

43)  ALL HUMAN PERSONS,  ALIVE AND DECEASED,  SHARE A COMMON SOLIDARITY AS FREE AND RATIONAL SPIRITUAL PERSONS WHO EACH HAVE A SPIRITUAL AND IMMORTAL, DIRECTLY AND IMMEADIATELY CREATED SOUL.

 

 

44) An Ontological Simplicity To The Human Soul? Yes! An Organic Internal Ontological Structure To The Human Soul? Perhaps, And A Way To Arrive At The Great Mystery Of The Human  Heart!

 

45) The Self In The Soul

 

46) A Human Soul Can Substantially Survive Destruction Of Its Faculties And Purely Accidental Features.

 

47) The Glories For The Human Soul To Come.

 

48) Created Relationships

 

49) The Created Spiritual Fireworks Of Human Souls.

 

50) Heaven Is Analogous To An  Eighth Sacrament

 

51) The Plausible Nebulousity Of The Human Soul And How Such Would Actually Entail Something Profoundly Transcendent And Perhaps Incomprehensible For Us

In This Life About The Human Soul.

 

52) Taking A Humorous Breather

 

53) THE HUMAN SOUL: A BEING OF LIGHT, A PERSON OF LIGHT.

 

54) Perhaps A Substantial Self Transcendance Of The Human Soul As An Abstract Eternal Ideal Or Form

 

55) The Morality Of Absolutely Each And Every Human Soul As A Transcendent Aspect Of The Soul As Form

 

56) An Energy Body As Distinct From The Human Soul: A Sort Of Little Philosophically Understoood Middle Ground Between Soul And Body

 

57) The Fire Of The Experiential Life Of The Human Soul And Its Capacity For Self Transcendence

 

58) Time And Souls

 

60)  Emotions Are Great

 

61)  Emotions: What Are They Made Of?

 

62)  What Color Is Your Soul?

 

63) Married Couples Of Fertile Age, Give A Soul The Ultimate Gift Of Being Created. Conceive A Child Before Or During Christmas.

 

64) Does The Human Soul Have A Charge?

 

65)  Anecdotal Musings On The Nature Of The Human Soul By Reflections On The Very Speculative Concept Of Proton Fission.

 

66)  Does The Human Soul Have A Spin?

 

67)  The Many Unique Degrees Of Human Soul Spins

 

68) The Human Soul As The Substantial Form Of Body Defining Quantum And Thermodynamic Energy States And Informations.

 

69) The Dynamic Life Of The Human Soul: Another Spiritual Dimension

 

70) The Entropy Of The  Human Soul And Its Objective Temporal Extension And Eternal Existential Growth

 

71) The Subjective Time Dependent Growth Of The Human Soul And How The Human Soul Grows Itself Along The Axis Of Subjective Time.

 

72)  Eternal Growth Of The Human Soul In And By Eternal Growth Of The Human Soul’s Vegetative Life

 

72) Taking A Humorous Breather

 

73) The Underappreciated  Vegetative Life Of The Human Soul

 

74) Singularities Of  Objective Time Dependent Quantitative Derivatives Of Human Will States

 

75)  Singularities Of  Objective Time Dependent Quantitative Derivatives Of Human Will As A Function Of Emotion Or Of d(d Will/d Emotion)/dt.

 

76) Singularities Of  Objective Time Dependent Quantitative Derivatives Of Human Will As A Function Of Thought  Or Of d(d Will/d Thought)/dt.

 

77) Taking A Humorous Breather

 

Introduction.

 

I remember as a 4 year old boy, while I was living with my family in Arlington Virginia right outside of Washington D.C., asking my Mom where my  Soul was located within my body, and what did  the human soul like, to which my Mom, if my memory serves me correctly, said it is a form. At the time I first clearly recall asking her this question, I was playing with my toy “Colorforms” template by which one would take small rubber like material based, variously colored and shaped renditions of articles of clothing and place them over a black colored template whereby one could dress the template with the  self-adhesively removable stickers. I think I may have actually had some idea at that very day, about the human soul, that is not too far removed from how it is commonly summarized in theology classes. I had thus sort of arrived at the notion; even then, that the soul did not have a geometric shape, but nonetheless, was some sort of ideal in the sense that my young but very limited mind could comprehend. I have not lost the sense of wonderment regarding the sublime nature of the human soul since then, and the personal sense of mystique about the topic has only deepened and grown over the years since my childhood.

 

Now here is just a summary of my life long quest to understand the human soul.

 

 

1)  The Creation Of The Human Soul Is Like GOD’s Blowing Living Bubbles.

 

 

The disordered conduct of child abuse and abuse of women will only largely come to a halt when all human persons, from the moment of conception onward are respected as rational, free, and unique individuals with a great reverential sense and respect of the sacredness and of the mystery and transcendent dignity of the spiritual and immortal human soul. A discussion of the spiritual and immortal soul seems to becoming gradually lost as human persons are more and more viewed as solely physical, and as worthy of love and respect commensurate with their visible existential characteristics such as wealth, psychological health, academic intelligences, social-economic standing, and the like consumerist mentality based criteria that mean nothing to GOD and which will mean nothing to us and which are of no importance in the eternal scheme of things.

 

Scripture describes the creation of Man as a process by which GOD formed Man from the dust of the Earth and then blew into Him the breath of life. These are not the exact words of Sacred Scripture but they are nonetheless, somewhat representative of a generalization that could be made by summarizing the respective accounts of the creation of the Human Person in the books of Genesis its various translations.

 

Now what does it mean for a person such as a young child to blow bubbles, or for a young parent and his or her child or children to have fun blowing bubbles?

 

A) First, a wand or other loop is dipped into a soap suds like solution that is made of ordinary molecular soap like matter whereupon the parent or child then pulls the wand out of the solution and then blows into the loop to form the bubble.

 

B) As the bubble is created, it grows and then eventually separates from the loop.

 

C) As a separate entity the, bubble floats freely and travels in a somewhat erratic path.

 

D) As the bubble travels, it takes on various beautiful colored patterns. This occurs as light is refracted by passing through the bubbles membrane, and also as a result of positive and negative reinforcement of the various frequencies of background light as the light passes through one side of a differential area element of the bubble’s wall and is then reflected back by the opposing surface of the differential area element of the wall, due to the differences in the indices of refraction and the discontinuities between the area element of the bubble and the adjacent air. The colored patterns of the bubbles continues to change and evolve in a time dependent and space dependent manner as the bubbles floats around and approaches and exits various environments with frequency dependent light flux distributions.

 

Now, for the analogy of GOD’s creation of the Human Soul.

 

A) The creation of the Human Soul involves a special act of GOD’s creation and therefor is a not an ordinary act of GOD’s creation. We can even speculate as to whether the process of GOD’s creating the Human Soul is ontologically different or metaphysically different in a qualitative sense from the creation of say a physical object by GOD or the working of the physical miracle. The new Catechism of the Catholic Church implies that the creation of the human soul by GOD involves a Special Creative Act that puts the soul or more generally, the Human Person, forever in a Special Relation to His or Her creator.

 

The human parent or child’s breath is in an intimate relationship between his or her bodily composition as being a partial product of exhaled bodily metabolites, some of which were previously a part of the materials or baryonic mass composition of the body. Such exhalants include carbon in the form of Carbon Dioxide, as well water vapor derived from the water composition of the body, and the specific forms and ratios of pheromones, portions of personal DNA and RNA, and other unique chemical identifiers of the particular human parent or child’s body. Consequently each bubble is filled with air that uniquely identifies the person who blew the bubble and that air is contained within the bubble and prevents the bubble from collapsing by keeping it whole and inflated. The bodily metabolites even become enmeshed or contained within the bubble wall by molecular and atomic diffusion of the air of the person’s initial breath and the air within the bubble into the bubble membranous material.

 

In an analogous manner, the metaphorical breath of GOD or the breathing into a man or a women’s just conceived body, the breath of life or the breath of GOD’s spirit, according to the paraphrased Scriptural accounts, denotes an intimate relationship between each directly, immediately created spiritual and immortal human soul created by GOD, with respect to GOD’s causative or generative creative act.

 

Now the human breath of the parent or child who blows the bubbles undergoes subtle time and space dependent changes in its specific equations of state, which is a fancy way of essentially stating that its temperature, density, chemical composition, pressure, and the like, change slightly from one breath to another. One breath of air blown into a bubble is always slightly differing from another breath blown into another bubble, even from the same person.

 

Likewise, all human souls that are metaphorically blown into existence, are all equally essentially human by virtue of the analogous identical composition of the soap materials and virtually identical material gas that holds each bubble up from collapse (except for the above subtle variations) for each soap bubble blown. All human persons are thereby of the same morally equality before GOD as stated in the new Catechism of the Catholic Church. Yet each soul has its unique calling and vocation, and when united to its human body, each human soul develops its unique set of accidental attributes and characteristics as its own internal and externally generated experiences, and actions, including instinctual as well as partial and fully free acts modify its accidental form. Thus, each created human soul is marked by a personal, and even by distinct metaphysical relationships with its Creator by virtue of the distinction of each soul as a unique and unrepeatable spiritual and immortal vital or life principle. Each human soul constitutes each human person as a unique and autonomous individual who is radically endowed with free will. This reality can be inferred from the concept that each human soul is the unique, vital, or life principle, or the principle of individuality, identity, unity, and uniqueness that constitutes each human person as an autonomous and free individual.

 

B) As the bubble grows, it is eventually separated and becomes a fully created and free bubble. By analogy, the soul is said to be created in an instant, however, relativistic quantum field theorists hold that time progresses in discreet steps of finite size and resolution or at the level of the Planck Time = Tp = {[h/(2π)]G/[C⁵]}^1/2 = 5.39 x 10 ^-44 seconds, a finite time but very small indeed! Note that the smallest period of time ever measured by the most sophisticated human laboratory apparatus is much longer than the Planck Time units or roughly on the order of 10 EXP ^{– 18} second. The difference between these two extremes is roughly of the same magnitude as the difference between one year, and one millionth of trillionth of a second. In terms of the process of spiritual creation of the human soul as to its essential nature, perhaps the smallest unit of resolution of GOD’s creative time is the interval over which the soul is created. Here, perhaps time periods or durations of creative actions by GOD are not metaphysically defined for shorter periods and perhaps there does not exist and sub-routines, or sub-processes, in the human soul’s creation by GOD. Perhaps the finite granularity of physical space time and any such fundamental analogues to the creation of the human soul by GOD at conception can be reconciled by analogy, although perhaps rationalized methods by which this can be accomplished have not been given over to human understanding in this point in human history on Earth. Note that relativistic quantum field theorists also; in some cases, contemplate a spatial temporal structure below the level of the finite units of the Planck Length and Planck Time Units or {[h/(2π)]G/[C³]}^1/2 ~ 10 ^-35 meters and {[h/(2π)]G/[C⁵]}^1/2 = 5.39 x 10 ^-44 seconds respectively, but generally hold that such fine grained structure may otherwise by inaccessible to direct observational scrutiny at the classical level of space and time. We simply might not be capable of understanding the details of any sub-structures to the process of GOD’s creation of the Human Soul at the so-called point in time of conception through rationalized algorithms at this point in human history. However, the metaphorical process of blowing each human soul into existence is a creative act or process by GOD which is directed by GOD, aka by HIS Almighty Will, and is done so with deliberation, care, and infinite personal love. Just as a human child delights with squeals and giggles at blowing bubbles with his or her parent(s), GOD must certainly delight in creating each human soul, a delight which is compounded by GOD’s infinite childlike humility. Moreover, the bubbles GOD blows are eternal and immortal and thus will last forever.

 

C) As a separate entity, the bubble floats freely and travels in a somewhat erratic path. And so the created human soul bubbles with life, and is a dynamic and free agent from the time it is created. It is free to choose its actions, and to grow in a myriad of ways. It is free to learn what it wants to and can learn. It is free to cooperate in its divinely inspired and given vocation. It is free to enter interpersonal relationships with other human persons with various degrees of intimacy and interpersonal warmth. In short, it is free to be itself and to become who and what it wants to be.

 

D) Yes indeed, as the bubble travels, it takes on various beautiful colored patterns as light.

 

An so the human soul upon its creation blossoms with the nuances and colors of life, experience, vitality, virtue, wisdom, love, warmth and the like, in short in the dynamic and shimmering vital life activity of its accidental form. Such a dynamism most likely per dues into and throughout all eternity since the human soul will be reunited with the human body in all cases at the Final Resurrection of the Dead at the End of Time.

 

Regardless of whether the human soul in immortal by its very created nature, immortal by universal grace, or a somehow combination of the two, it has a beauty both ontologically and substantially, accidentally and existentially, and morally, that transcends its immortality. Therefore, regardless of whether the human soul is naturally and/or immortal by universal grace, it has inherent qualities that transcend or go beyond this immortality. Since GOD is love, He fashions each human soul with infinite personal childlike humility and love, and regardless of whether the human soul is naturally and/or gratuitously immortal, in each and every case, it will last forever. This is GOD’s promise and this is GOD’s will, and GOD never takes back a created substantial principle that is personal.

 

Note that I personally believe that each human soul is naturally immortal as I am traditionally Scholastic in orientation, but I am open minded to the opinions of those who argue immortality of the human soul in other ways. Regardless, the human soul not only has the ontological transcendent characteristic of beauty, but also those of purpose, reason for existing, value, worth, goodness (and all souls are greatly ontologically good even any souls that are in Hell or any existent Limbo). Perhaps the set of similar attributes is infinite beyond human reckoning of which we are only currently given the ability to form abstractions of the above few members of any such set.

 

The care and love and transcendent dignity of the human soul is the reason why we should love all human persons and respect the sanctity of all human life, just as assuredly as GOD has lovingly created each human person and looks after each human person with child-like humble infinite love and delight. In a world amassed with scientific weapons systems that could perhaps destroy the human race and more, can we not afford to treat each other any differently from how GOD treats us and loves us.

 

 

Note that I personally believe that each human soul is naturally immortal as I am traditionally Scholastic in orientation, but I am open minded to the opinions of those who argue immortality of the human soul in other ways. Regardless, the human soul not only has the ontological transcendent characteristic of beauty, but also those of purpose, reason for existing, value, worth, goodness (and all souls are greatly ontologically good even any souls that are in Hell or any existent Limbo). Perhaps the set of similar attributes is infinite beyond human reckoning of which we are only currently given the ability to form abstractions of the above few members of any such set.

The care and love and transcendent dignity of the human soul is the reason why we should love all human persons and respect the sanctity of all human life, just as assuredly as GOD has lovingly created each human person and looks after each human person with child-like humble infinite love and delight. In a world amassed with scientific weapons systems that could perhaps destroy the human race and more, can we not afford to treat each other any differently from how GOD treats us and loves us.

 

 

2)  Ever Wonder How Complex The Human Heart Is, The Human Soul Is, the Human Psyche In Its Conscious, Sub-Conscious, And Unconscious Aspects Is?

 

Here is an article I thoughtfully composed this Sunday Afternoon on the subject of the human heart. Psychologists, Psychiatrists, Theologians, Anthropologists, Sociologists, Sinners and Saints have pondered at the incomprehensible complexity of the human heart and its tangled workings, and in some sense, this incomprehensibly is irrevocable. Ultimately, only GOD can judge the human heart and perhaps the only way for the SECOND PERSON OF THE HOLY TRINITY  to comprehend and relate to we humans in the tangled workings of our hearts was to take on a human nature Himself.

 

Ever wonder how complex the human heart is, the human soul is, the human psyche in its conscious, sub-conscious, and unconscious aspects is?

 

To paraphrase the Holy Bible and the Jewish Torah, “Who but the LORD GOD HIMSELF can fathom the complexity of the human heart, or judge the actions of a human being!”

 

Now,  modern physics is familiar with the concept of the atomization and quantization of matter, electric charge, electromagnetic radiation, and theoretically, even space and time, at the level of the finite Planck Length and Planck Time at Lp = {[h/(2 pi)] G/[C EXP 3]} EXP (1/2) and Tp = {[h/(2 pi)] G /[C EXP 5]} EXP (1/2) ~ (10 EXP – 35) meter and [5.4 x (10 EXP – 44)] second respectively.

 

Modern mathematics is familiar with the concept of the infinitesimal and the infinite in terms of numerical values and quantitative values and is even familiar with the concept of greater and lesser cardinalities of infinity or of sets with greater or lesser infinite numbers of elements.

 

The Cardinality of Aleph 0 is the smallest transfinite aleph number and is the number of elements within the set of integers. If one accepts the Continuum Hypothesis which has defied proof, then Aleph 1 is the number of real numbers which is a set that is infinitely in greater in number of its elements than the number of integers regardless of whether or not the Continuum Hypothesis is correct. Regardless, the mathematical philosophical methods developed by the great mathematician Georg Cantor near the late 19th Century hold that ever higher transfinite Aleph ordinals exist such as Aleph 2, Aleph 3, Aleph 4, … , Aleph Omega, … and that just as there can exist no highest integer, there can be no highest Aleph number. Any one for Aleph(Aleph 0), or Aleph (Aleph 1), or Aleph (Aleph(Aleph 0)), or Aleph(Aleph(Aleph 0)), or Aleph(Aleph(Aleph(Aleph(Aleph 0)))) or Aleph(Aleph(Aleph(Aleph  ….infinite number of Aleph word iterations and of associated nested parenthesis…))), and so on ad infinitum.

 

Now we can imagine a value of zero = 1/(infinity) = 1/(Aleph 0). But what about 1/(Aleph 1) or 0/(Aleph 0). Or perhaps 1/(Aleph 2) or 0/(Aleph 2) or even 0/ Aleph(Aleph(Aleph(Aleph(Aleph 0))))) or perhaps even {0/ Aleph(Aleph(Aleph(Aleph(Aleph 0)))))}/{ Aleph(Aleph(Aleph(Aleph(Aleph 0))))} and so on.

 

What about numbers with absolute values that are infinitely smaller than the absolute value of zero, or numbers with absolute values that equal l0l/(Aleph 0), or l0l/(Aleph 1), or even l0l/{ Aleph(Aleph(Aleph(Aleph(Aleph 0))))} or even l0l/{ Aleph (Aleph (Aleph (Aleph  ….infinite number of Aleph word iterations and of associated nested parenthesis…)))}, and so on ad infinitum.

 

Note that the concept of a value or quantity having an absolute value of less than zero is alien to most in not all applied and theoretical mathematics conventions and paradigms, but mathematics is an evolving endeavor just as science and technology is an ever involving endeavor, and in principle, mathematics can never be completed as to its applied, theoretical, and philosophical forms. No complete self-consistent and self-referenced mathematical systems are possible. This is good news, since we will have all eternity to ponder mathematics, numbers, shapes, dimensions, and the like.

 

Scholastic theological interpretations of the belief in immortal human souls hold that the soul: 1) is naturally immortal, that it does not survive bodily death because of the grace of God nor through the incurrence of the sacraments of the Catholic Church, but rather is inherently immortal of its own nature; 2) has no extension in space; 3) has no shape; 4) has no spatial size; 5) has no separate components into which it can decay or be divided; 6) is simple; 7) is  unextended; 8] is spiritual and not dependent on matter in any way for its existence; 9) is a first created principle meaning that it is not dependent on any other created being for its existence, not even the human body or brain; 10) is directly created by GOD as the first and only cause for its existence; 11) is incorruptible per addends and per se meaning that it has no pieces or extension into which it could decay and that it cannot be created nor destroyed by any natural forces nor by God through the use of any natural forces and agents; 12) is rational; 13) is radically endowed with free will and so on.

 

The Catholic Church’s Tradition which is rich with Encyclicals regarding human nature and its fundamental dignity holds that the each Human Soul is the vital or life principle that constitutes each individual human person as a unique and unrepeatable individual, and as such is the fundamental principle of unity, individuality, and identity in each human person.

 

However the Human Person in this life is not just simply a Soul, but a substantial union of a Body and a Soul. Scholasticism holds that the Human Soul is the substantial form of the Body, not in a geometric shape sense, but rather in the sense of the Eternal Platonic and Aristotelian Forms of ancient Greek philosophy.

 

The Catholic Church is currently somewhat ambivalent about the extreme spiritualism of Saint Thomas Aquinas and currently does not seek so much to explain the immortality of the human soul, but nonetheless, holds as a matter of faith that the human soul is immortal and that each human person whether consigned to Hell, in Purgatory, or in Heaven will be Resurrected as a full and complete human being at the Final Resurrection of the Dead, and then so to a nature that will be incorruptible

 

Now read through these quotations from the new Catechism of the Catholic Church.

Part 1, Section 1, Chapter 1, SubSection 2

 

33 The human person: with his openness to truth and beauty, his sense of moral goodness, his freedom and the voice of his conscience, with his longings for the infinite and for happiness, man questions himself about God’s existence. In all this he discerns signs of his spiritual soul. The soul, the “seed of eternity we bear in ourselves, irreducible to the merely material”, 9 can have its origin only in God.

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 1

 

360 Because of its common origin the human race forms a unity, for “from one ancestor [God] made all nations to inhabit the whole earth”: 226

 

O wondrous vision, which makes us contemplate the human race in the unity of its origin in God. . . in the unity of its nature, composed equally in all men of a material body and a spiritual soul; in the unity of its immediate end and its mission in the world; in the unity of its dwelling, the earth, whose benefits all men, by right of nature, may use to sustain and develop life; in the unity of its supernatural end: God himself, to whom all ought to tend; in the unity of the means for attaining this end;. . . in the unity of the redemption wrought by Christ for all. 227.

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 2

 

363 In Sacred Scripture the term “soul” often refers to human life or the entire human person. 230 But “soul” also refers to the innermost aspect of man, that which is of greatest value in him, 231 that by which he is most especially in God’s image: “soul” signifies the spiritual principle in man.

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 2

 

366 The Church teaches that every spiritual soul is created immediately by God – it is not “produced” by the parents – and also that it is immortal: it does not perish when it separates from the body at death, and it will be reunited with the body at the final Resurrection. 235

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 2

 

367 Sometimes the soul is distinguished from the spirit: St. Paul for instance prays that God may sanctify his people “wholly”, with “spirit and soul and body” kept sound and blameless at the Lord’s coming. 236 The Church teaches that this distinction does not introduce a duality into the soul. 237 “Spirit” signifies that from creation man is ordered to a supernatural end and that his soul can gratuitously be raised beyond all it deserves to communion with God. 238.

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 4

 

382 “Man, though made of body and soul, is a unity” (GS 14 # 1). The doctrine of the faith affirms that the spiritual and immortal soul is created immediately by God.

 

Part 1, Section 2, Chapter 3, Article 11, SubSection 1, Heading 2

997 What is “rising”? In death, the separation of the soul from the body, the human body decays and the soul goes to meet God, while awaiting its reunion with its glorified body. God, in his almighty power, will definitively grant incorruptible life to our bodies by reuniting them with our souls, through the power of Jesus’ Resurrection.

 

Part 1, Section 2, Chapter 3, Article 12, SubSection 6

1052 “We believe that the souls of all who die in Christ’s grace . . . are the People of God beyond death. On the day of resurrection, death will be definitively conquered, when these souls will be reunited with their bodies” (Paul VI, CPG § 28].

 

Part 2, Section 2, Chapter 1, Article 1, SubSection 7, Heading 5

1280 Baptism imprints on the soul an indelible spiritual sign, the character, which consecrates the baptized person for Christian worship. Because of the character Baptism cannot be repeated (cf. DS 1609 and DS 1624).

 

Part 2, Section 2, Chapter 1, Article 2, SubSection 3

1304 Like Baptism which it completes, Confirmation is given only once, for it too imprints on the soul an indelible spiritual mark, the “character,” which is the sign that Jesus Christ has marked a Christian with the seal of his Spirit by clothing him with power from on high so that he may be his witness. 121

 

Part 3, Section 1, Chapter 1, Article 1

 

1705 By virtue of his soul and his spiritual powers of intellect and will, man is endowed with freedom, an “outstanding manifestation of the divine image.” 8

 

Part 3, Section 1, Chapter 1, Article 1

 

1711 Endowed with a spiritual soul, with intellect and with free will, the human person is from his very conception ordered to God and destined for eternal beatitude. He pursues his perfection in “seeking and loving what is true and good” (GS 15 § 2).

 

Part 3, Section 1, Chapter 2, Article 3, SubSection 2

 

1934 Created in the image of the one God and equally endowed with rational souls, all men have the same nature and the same origin. Redeemed by the sacrifice of Christ, all are called to participate in the same divine beatitude: all therefore enjoy an equal dignity.

 

The soul is the very vital life principle of individuality, unity, uniqueness, and identity of the human person. In a way, it is a created version of an individual personalized life incarnate that exists, as such, as GOD, as the created image and likeness of GOD.

 

If the soul is so simple, than it cannot have any fine grained sub-components or separate parts. But the human soul does have aspects and characteristics as well as accidents which are numerous beyond enumeration. Since there is no granular structure or separable divisions within the human soul from the ontological and existential standpoint, we are left to conclude that perhaps the features of the human soul such as its accidents in the form of thoughts, feelings, emotions, instincts, acts of will or volition, are infinitely continuous, as to their integration into the psyche or the power aspects of the human soul such as the human heart, intellect, memory, will, and the like including the conscious, subconscious, and unconscious mind. The human soul may have no smallest metric measurement or part in which it can be partially considered or defined unlike space and time and mass and energy which is quantized at small but finite levels.

 

Could the continuity of the human soul, heart, mind, psyche, etc, be at the level of 1/(Aleph 0) for psychodynamic metrics that define its essence and/or its accidents. What about at the level of 1/(Aleph 1) or 0/(Aleph 0). Or perhaps at the level of  1/(Aleph 2) or 0/(Aleph 2) or even 0/ Aleph(Aleph(Aleph(Aleph(Aleph 0))))) or perhaps even {0/ Aleph(Aleph(Aleph(Aleph(Aleph 0)))))}/{ Aleph(Aleph(Aleph(Aleph(Aleph 0))))} and so on.

 

What about metrics with a fine grained structure that are objectively definable, in principle,  with ordinal quantities or ordinal qualities having  absolute values that are infinitely smaller than the absolute value of zero, or defined by numbers with absolute values that equal l0l/(Aleph 0), or l0l/(Aleph 1), or even l0l/{ Aleph(Aleph(Aleph(Aleph(Aleph 0))))} or even l0l/{ Aleph (Aleph (Aleph (Aleph  ….infinite number of Aleph word iterations and of associated nested parenthesis…)))}, and so on ad infinitum.

 

If we take Sacred Scripture at face value, then we must hold that only GOD HIMSELF can comprehend the tangled workings of the Human Heart, or comprehend the depths of the Human Heart. This means that no; angel, saint,  intelligent extra-terrestrial,  or intelligent ultra-terrestrial persons can comprehend the complexity of the Human Heart.

 

The Catechism states that the human heart is the innermost aspect of the human person where He or She decides for or against GOD and to which He or She and GOD alone have access.

 

Since the Human Heart has a complexity that defies comprehension by all except GOD HIMSELF, then perhaps the Human Heart, the Human Psyche, the Human Intellect, The Human Will, and the Human; Intuition, Instinctive Intelligence, Social Intelligence, Sensibility, Emotional Intelligence, and Affect, can grow without limit, being that the set of imprinted features or accidents within the Human Soul and Human Heart can grow without limit. I propose this as a possibility because part of the size, whether quantitative or qualitative or “whatevertative” of any systems is defined by the degree and number of states, features, aspects, characteristics, and accidents contained within such systems.  We hold our universe to be huge in part because of the number of galaxies and stars that it contains is absolutely huge, perhaps even infinite. Likewise, a super-continuous Human Soul, Heart, Psyche, Intellect etc., is huge and hugely complex, perhaps to a degree known and comprehended only by GOD.

 

For all of you artist types who work in the field of perception, and artistic experience, and complexity, there is a very real degree of sophistication and spirituality possessed by you that the rest of us lack to some degree. For all of  you married folks or romantic partners who  live out your daily lives; with a degree of interpersonal relation with your beloved, you represent in the complexity of your hearts, the depths and the magnitude, in quality, the LIFE of THE HOLY TRINITY.  When you procreate children, you are in a very real sense, directly responsible for the creation of a brand new Human Person, Body and Soul, and Heart and thus your procreative acts from this alone are sacred and have tremendous dignity.

 

As a interstellar space craft propulsion physicist who currently has effectively signed up for the cause that we humans will one day roam the universe black in ever more capable manned space craft, I often muse, even poetically, and definitely, romantically, at the infinitely vast universe, which may be just one universe among enumerable universes. But perhaps I should step back from time to time from all of this far out interstellar astronautics and cosmology, and look at the infinity within each and every one of us as an individual, whether the individual is myself, you, your loved ones, your friends, my friends, and even my enemies and your enemies. After all, I cannot judge any of my enemies any more than I can comprehend the tangled workings and the awesome complexity of their hearts.

 

You who have received this email from me are greatly appreciated by me and you, your loved ones, and your friends are thus greatly honored by me, not only due to familiar ties, but also because of the infinity that you embody and which defines your value and self-worth. GOD holds to these notions infinitely more than I because HE is the One in HIS SON JESUS CHRIST who walked to Calvary and Died on the Cross for You, and who would do so again, just for you, if it were necessary.

 

 

 

 

 

 

 

 

 

 

 

3)  The Who, What, Where, When, Why,  And How Of The Human Soul.

 

A) The Who Of The Human Soul

 

 

 

Once again, note that Scholastic theologian interpretations of the belief in immortal human souls hold that the soul: 1) is naturally immortal, that it does not survive bodily death because of the grace of God nor through the incurrence of the sacraments of the Catholic Church, but rather is inherently immortal of its own nature; 2) has no extension in space; 3) has no shape; 4) has no spatial size; 5) has no separate components into which it can decay or be divided; 6) is simple; 7) is unextended; 8] is spiritual and not dependent on matter in any way for its existence; 9) is a first created principle meaning that it is not dependent on any other created being for its existence, not even the human body or brain; 10) is directly created by GOD as the first and only cause for its existence; 11) is incorruptible per addends and per’ se meaning that it has no pieces or extension into which it could decay and that it cannot be created nor destroyed by any natural forces nor by God through the use of any natural forces and agents; 12) is rational; 13) is radically endowed with free will and so on.

 

The New Catechism of the Catholic Church basically indorses the spirit of the above mindset with a greater or lesser degree of emphasis on the particular arguments for such.

 

Scholastics have traditionally made a distinction between the faculties of the human soul and its essence or substance (the ontological meaning of the word). The faculties of the human soul are more or less viewed as accidental properties of the soul whose operation in this life depends extrinsically on the human body/brain. Every experience of the human person is said to modify its accidental properties.

 

The human soul is said to be of a multiplicity in nature meaning that it is multiplied in its relation to the body by being completely present in and completely and totally united to each and every differential portion of the human body.  Since  the human soul is said to be substantially united to the body in this life, and then again to the resurrected human body at the Final Resurrection, such multiplicity is a good aspect of the human soul.  In a real way, such multiplicity adds to the existential or ontological size of the soul for lack of a better word.

 

The Catholic Church’s Tradition which is rich with Encyclicals regarding human nature and its fundamental dignity holds that the each Human Soul is the vital or life principle that constitutes each individual human person as a unique and unrepeatable individual, and as such is the fundamental principle of unity, individuality, and identity in each human person.

 

Once again, from the new Catechism of the Catholic Church, we know the following.

Part 1, Section 1, Chapter 1, SubSection 2

 

33 The human person: with his openness to truth and beauty, his sense of moral goodness, his freedom and the voice of his conscience, with his longings for the infinite and for happiness, man questions himself about God’s existence. In all this he discerns signs of his spiritual soul. The soul, the “seed of eternity we bear in ourselves, irreducible to the merely material”, 9 can have its origin only in God.

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 1

 

360 Because of its common origin the human race forms a unity, for “from one ancestor [God] made all nations to inhabit the whole earth”: 226

 

O wondrous vision, which makes us contemplate the human race in the unity of its origin in God. . . in the unity of its nature, composed equally in all men of a material body and a spiritual soul; in the unity of its immediate end and its mission in the world; in the unity of its dwelling, the earth, whose benefits all men, by right of nature, may use to sustain and develop life; in the unity of its supernatural end: God himself, to whom all ought to tend; in the unity of the means for attaining this end;. . . in the unity of the redemption wrought by Christ for all. 227.

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 2

 

363 In Sacred Scripture the term “soul” often refers to human life or the entire human person. 230 But “soul” also refers to the innermost aspect of man, that which is of greatest value in him, 231 that by which he is most especially in God’s image: “soul” signifies the spiritual principle in man.

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 2

 

366 The Church teaches that every spiritual soul is created immediately by God – it is not “produced” by the parents – and also that it is immortal: it does not perish when it separates from the body at death, and it will be reunited with the body at the final Resurrection. 235

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 2

 

367 Sometimes the soul is distinguished from the spirit: St. Paul for instance prays that God may sanctify his people “wholly”, with “spirit and soul and body” kept sound and blameless at the Lord’s coming. 236 The Church teaches that this distinction does not introduce a duality into the soul. 237 “Spirit” signifies that from creation man is ordered to a supernatural end and that his soul can gratuitously be raised beyond all it deserves to communion with God. 238.

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 4

 

382 “Man, though made of body and soul, is a unity” (GS 14 # 1). The doctrine of the faith affirms that the spiritual and immortal soul is created immediately by God.

 

Part 1, Section 2, Chapter 3, Article 11, SubSection 1, Heading 2

997 What is “rising”? In death, the separation of the soul from the body, the human body decays and the soul goes to meet God, while awaiting its reunion with its glorified body. God, in his almighty power, will definitively grant incorruptible life to our bodies by reuniting them with our souls, through the power of Jesus’ Resurrection.

 

Part 1, Section 2, Chapter 3, Article 12, SubSection 6

1052 “We believe that the souls of all who die in Christ’s grace . . . are the People of God beyond death. On the day of resurrection, death will be definitively conquered, when these souls will be reunited with their bodies” (Paul VI, CPG § 28].

 

Part 2, Section 2, Chapter 1, Article 1, SubSection 7, Heading 5

1280 Baptism imprints on the soul an indelible spiritual sign, the character, which consecrates the baptized person for Christian worship. Because of the character Baptism cannot be repeated (cf. DS 1609 and DS 1624).

 

Part 2, Section 2, Chapter 1, Article 2, SubSection 3

1304 Like Baptism which it completes, Confirmation is given only once, for it too imprints on the soul an indelible spiritual mark, the “character,” which is the sign that Jesus Christ has marked a Christian with the seal of his Spirit by clothing him with power from on high so that he may be his witness. 121

 

Part 3, Section 1, Chapter 1, Article 1

 

1705 By virtue of his soul and his spiritual powers of intellect and will, man is endowed with freedom, an “outstanding manifestation of the divine image.” 8

 

Part 3, Section 1, Chapter 1, Article 1

 

1711 Endowed with a spiritual soul, with intellect and with free will, the human person is from his very conception ordered to God and destined for eternal beatitude. He pursues his perfection in “seeking and loving what is true and good” (GS 15 § 2).

 

Part 3, Section 1, Chapter 2, Article 3, SubSection 2

 

1934 Created in the image of the one God and equally endowed with rational souls, all men have the same nature and the same origin. Redeemed by the sacrifice of Christ, all are called to participate in the same divine beatitude: all therefore enjoy an equal dignity.

 

We now ask Who is the soul nonetheless bearing in mind that the human person in this life is not just a soul, but rather is a profound union of the body and soul. However, we must realize that those who have passed on to the next life, as well as the souls in Purgatory and any Souls in Hell, continue to exist with their own psychodynamic characteristics and accidental properties. These souls are not just things but rather are persons.

 

When asking Who is the soul, we can more fully appreciate that each soul is the fundamental, natural, directly and immediately created, spiritual and immortal life principle or vital principle within the human person that constitutes each person as a unique, free, autonomous, individual; in other words the soul is the fundamental, natural, directly and immediately created, spiritual and immortal life or vital principle of individuality, uniqueness, identity, and unity within the human person. Thus,  the reality that a Human Person is a person and not simply a being flows primarily from the fact of the above characteristics of the Human Soul.

 

We naturally intuit the human personality as equivalent to the psyche not only in daily living but also from antiquity in terms of philosophical and theological thought and in the modern and postmodern era, with the development of the science of psychology, and the disciplines of applied social science such as psychology, psychiatry, social work, psychotherapy, and psycho-analysis which has largely fallen out of favor as a treatment for psychological disorders.

 

Thus, by lexicographical and heuristic association of the concept of the human soul with the modern psyche of social science and the concept of personality in terms of daily relationships and character assessment, given that the human soul is the principle of individuality, unity, uniqueness, and identity within the human person, it is intuitively easy to make the case that the human soul is also that fundamental principle of personality that constitutes each person’s personality or personhood or personal identity.

 

No doubt that the human person in this life has a brain and that most if not all of ordinary daily conscious experiences are extrinsically dependent on the operation of the human body, especially the human central nervous system, we nonetheless do not speak of the human  psyche nor of human emotions, thoughts, feelings, acts of will, attitudes, experiences, memories,  drives, instincts, and the like as possessing spin orbital angular momentum, kinetic energy, electrical charge, inertia, inertial force based acceleration of a mass, a physical cross section, and the like nor do we describe such psychodynamic personality elements or attributes by equations such as the Schrödinger Equation, matrix mechanics, the famous special relativistic mass energy relation of E = M[C EXP 2] and the like.

 

Thus, it would seem to be the case that the human person’s conscious identity, regardless of whether such an identity is perceived by a given human person flows from the very spiritual and immortal principle of identity which is the human soul.

 

Note that the reality that the human soul is the life principle of identity within the human person has a fundamentally deeper meaning than the simple notion or experience of self-consciousness or personal conscious identity. The latter sense can be interrupted by sleep, head injury, certain mental or physical illnesses and the like.

 

It is therefore the human soul that gives us the “Who” of who we are and this spiritual and immortal principle is so ontologically simple in nature to a degree commensurate with its being the principle of unity, oneness, identity, uniqueness, and individually of the fundamental autonomous individuals we call the human person.

 

B)  The What Of The Human Soul

 

The What of the human soul is that fundamental aspect by which it is what it is isn’t what it isn’t.

 

Even if there were two or more persons that were created with the exact same nervous system and body, and that the souls were an exact copy of each other, thus wherein these two or more human persons where thermodynamically utterly identical and placed in utterly identical environments such that the statistical mechanical states defining the body and soul combination of such more than one identical human persons where identical to each other in every manner, each of these two or more individuals would be distinct persons and the existence and attributes of one such person would not depend on the existence or attributes of the other such person(s).

 

The reason for this reality is that each human soul is a first created spiritual principle meaning that it is directly and immediately created by GOD and as such its existence is directly a result of GOD’s act of creating it and GOD’s act of sustaining it in being as a first created principle. It would not matter if GOD had created an infinite number of such identical human persons who were placed in identical environments, each such person by virtue of his or her spiritual and immortal soul would be an ontologically separate and distinct individual if only simply because the human soul is the principle of autonomy and distinction within the human person.

 

It is often said that in the thermodynamics and in the statistical mechanics of phenomenon at the quantum mechanical level, that two identical bosons can exist in the same energy state and thus two identical bosons which are particles with a quantum spin number of an even number of fundamental spin units are indistinguishable. This is not so in the case of identical human souls wherein each human soul would have a sustaining act of GOD’s will as its own unique existential and ontological underpinning or existential underwriting.

 

An analogous example would be the qualitative situation wherein I would somehow blow two identical soap bubbles into existence at the same time say with two toy soap bubble wands. Note that as a 6 or 7 year old, my Mother would often buy me and my siblings a bottle of non-toxic soap solution that came with a dipper with an approximately  ½ inch diameter loop which was called a  wand wherein the bubble forming solution was sold under the name “Bubble Stuff”. One would simply dip the wand into the little bottle of solution to form a soap film membrane spanning the inner area of the loop and then blow gently onto the soap film thereby causing the soap film to become distended and stretched to the point that the film would break free of the wand and form an enclosure that we commonly know to be a soap bubble. The funny thing is, I use to think about human souls as I blew such bubbles into existence and the bubbles thus formed would sometimes impart the mental image of the abstract concept of the human soul although I definitely lacked the intellectual maturity or sophistication as a young elementary school age child to know what I was really contemplating.

 

The point is that this What of the human soul is such a fundamental property of the Human Soul to the extent that utterly qualitatively identical human souls would each be completely distinct entities and would not depend on the existence of any qualitatively identical human souls for its existence. Since the human soul can be said to be a substance or an essence, even if perhaps an incomplete one when separated from the human body, it is nonetheless its own principle to an extent commensurate with being the fundamental principle of union, identity, individuality, ontological and existential distinctness, separateness, and the like within the human person.

 

Truly, the What of the human soul or the What is the human soul in every instance of the existence of individual human souls transcends in a fundamental existential and ontological manner any situation whereby GOD would and could create multiple absolutely qualitatively identical human souls and/or create such human souls united to absolutely thermodynamically and statistical mechanically identical human bodies.

 

C)  The Where Of The Human Soul

 

The human soul is created at the moment of conception which is the moment when the human embryo can be first considered as conceived of as a viable individual.

 

The human soul is accordingly infused with the embryo and is completely and totally present and substantially united to every differential volumetric element and every differential mass-energy element of the human body wherein; accordingly, the soul is said to be multiply present.

 

Even though the human soul has no size, shape, or spatial extension, it can be said to be present to every differential element of the human body to which it is united in the sense of substantial union wherein the soul is present to the dimensionless substantial or ontological nature of the human  body’s composing mass-energy.

 

In a certain sense, the human soul can be said to be located in the world in this life in the sense that the concrete accidental properties of the human soul are highly effected and changeable by virtue of the transformative experiences that the human person in this life undergoes. According to modern spiritual theology of the human soul, every experience adds to the accidental form and properties of the human soul.

 

Thus, the human soul can improve or grow not only in terms of its accidental natural properties, but also in terms of the life of grace. Moreover, each of three Sacraments of Baptism, Confirmation, and Holy Orders bestow an inherent supernatural property within or imprint on the souls of the recipients of these Sacraments which cannot be repeated and which cannot be erased, not even by any personal mortal sins of the recipients nor by the fires of Hell. Once a Catholic, always a Catholic even if the only Sacrament ever bestowed on you is the Sacrament of Baptism. Once a Priest, always a Priest.

 

To the extent that the human soul in this life is united to the human body is the extent to which the human soul in this life can be said to be located within the world.

 

However, after death which is the natural process whereby the soul is separated from the human body upon bodily death, the human undergoes a particular judgment and then goes to either the state, or state and place referred to as Heaven, Hell, or Purgatory.

 

Souls that must first be cleansed of the effects of personal sins but who nonetheless are saved must first be cleansed by the metaphorical fires of Purgatory.

 

As for Hell, the souls who end up in this state or state and place nonetheless are still naturally alive, and in fact are likely extraordinarily naturally alive to a degree commensurate with their being able to experience the pains and sufferings of Hell of which the personal knowledge of the loss of the opportunity to go to Heaven is the chief suffering.

 

Rather than somehow losing their existence, the souls who go to Hell, must be said to be naturally alive to the extent that they are capable of experiencing suffering wherein this state of being alive is full in the sense that it is completely natural since the souls in Hell do not possess the life of grace in the sense that they do not possess sanctifying grace. However, even in the cases where the Baptized, or Baptized and Confirmed, or the Baptized,  Confirmed, and Clericized souls go to Hell, these souls nonetheless retain their supernatural characters bestowed on them for all eternity.

 

Ultimately, the reason and purpose for the existence of Hell is a great mystery for which we on Earth and perhaps even any creatures in Heaven are not yet given a full understanding of its purpose. The usual run of the mill philosophical answer as to why there is a Hell given by clerics when the clergymen are asked by children as to why it exists in the form of statements of response such as “People who are real bad all of their life up until the time they die and never tell God their sorry must be held eternally accountable for their actions because GOD is fair and just.”,  simply does not satisfy the older more advanced thinker. However, we know that GOD would not permit personal moral and material evil in His creatures if He was not so all powerful so as to draw an even greater good from such evils.

 

The souls who end up in Purgatory are nonetheless in GOD’s full friendship although they must still undergo a purification before they can enter Heaven, but in absolutely all instances, the souls who must first go to the state, or the state and place of Purgatory, eventually are released into the full Glories of the Kingdom of Heaven where they behold the face of GOD in the BEATIFIC VISION.

 

Some souls such as the Souls of Canonized Saints go directly to Heaven without the need for temporary detention in Purgatory.

 

When a little child ask you where his soul is located, I hope these musings will or can be of use if you feel that otherwise, you are unable to provide an adequate response to the child’s question.

 

D)  The When Of The Human Soul

 

When is the human soul created? The famous Baltimore Catechism in at least some of its version states at the moment of conception. The human soul is accordingly not some sort of fire that goes from life to life or from body to body as supposed in the false doctrine of reincarnation such as is the subject of belief in Buddhist Teachings, certain aspects of Hindu, and now most recently, in dubious space alien UFO based religious cults.

 

The human soul is indeed created only once and is substantially united to only one human body that it is meant to inform and have close union with in this life, and then again after the Final Resurrection of the Dead at the End of Time. Even the bodies of the souls who go to Hell will be Resin Incorruptible although such bodies will have to undergo eternal punishment which can include certain types of deprivation, but either way,  punishment in ways for which the details of such remain veiled to our complete understanding in this life.

 

As just a personal reflection, to the extent that the Human Soul not only has accidental properties, but also has an essence or substantial nature, I have come to believe that the Human soul has a timeless nature in some respects to the extent that its essence is immutable in a manner commensurate with the soul being the vital, spiritual, and immortal principle of identity, union, individuality, autonomy, and distinctness of the human person. Even the souls in Hell because of Hell’s eternal duration will last forever and such souls must remain and do in fact remain the spiritual and immortal principles of identity, union, individuality, autonomy, and distinctness of any human persons who unfortunately may end up in Hell. If Hell is indeed eternal, then the Human Persons who end up in Hell must also have an aspect of eternal duration thus one reason out of many why the human soul in absolutely all cases is timeless in terms of its nature or essence. In short, aside from its initial creation at the moment of embryonic conception, there may not be a when for the Essence of the Human Soul to the extent the such an essence is eternally immutable.

 

As for the accidental nature of the human soul, the accidental form of the human soul is malleable and as such, the human soul in this life, and presumably in the dynamic, ultimately fun, and ultimately enjoyable afterlife in Heaven must also have a malleable accidental form whereby apart from the fundamental possession of the Beatific Vision, the Human Soul can and may still eternally grow in accidental virtue, and perhaps even grow for all eternity in an ever deeper and more comprehensive vision of GOD since only GOD can know HIMSELF in a perfect and utterly exhaustively limitless infinite manner since only GOD in HIS INTELLECT is utterly and exhaustively limitlessly infinite, all knowing, and all wise.

 

E)  The Why Of The Human Soul.

 

Why the human soul exists is a question that can be asked with different types of answers in mind.

 

For instance, we can ask why does GOD create human souls but we can also ask why does GOD’s sustaining presence or HIS WILL which holds the soul in existence as it also does every other creature, actually sustain such souls in existence. We can ask why did GOD choose to manifest creatures, including the Human soul as being in need of HIS Sustaining might and Will in order for such creatures to exist, or to continue to exist, whatever continuance means for substantially timeless realities such as the essence or the substantial nature of the Human Soul.

 

Perhaps one answer to this above question is that GOD chooses to express HIMSELF as HE does simply because that is HIS FREE CHOICE. However, this does not answer the question of why GOD has made the personal choices HE has made in terms of the modality of HIS SELF EXPRESSED NATURE not to mention the creation of HIS creatures including but not limited to the Human Soul, each and all of which depend on HIS all sustaining might to remain in existence.

 

A plausible answer as to why GOD did not somehow create self-existent creatures that where somehow emanations or derivations of HIS BEING or HIS DIVINE NATURE might lie in the reality that HE desired that we have our own identity, individuality, uniqueness,  unity, and autonomy that is existentially and ontologically distinct form HIS. Perhaps GOD somehow saw that the creation of creatures as their own selves is a much better gift than to create entities that would not have separate and distinct existence from HIM in terms of HIS DIVINE BEING or NATURE and /or from HIM in terms of either of HIS THREE DIVINE PERSONS and/or in terms of HIMSELF AS THE HOLY TRINITY, THRICE HOLY.

 

There is something to be said regarding the remarkable but perhaps almost trivially sounding self-evident notion that we Human Persons are free and autonomous individuals and that we each have our own existence, nature, essence, individuality, separate identity, distinction, union, oneness and the like, and all of these aspects of the Human Person flow by definition primarily from the spiritual, immortal, vital or life principle we refer to in spiritual psychology as the Human Soul.

 

F)  The How  Of The Human Soul

 

How did GOD create the Human Soul while parting with nothing of  HIS existence or nature in doing such is perhaps one of the biggest mysteries of the Cosmos or of all creation. Since the Human Person is so much like GOD as being created in HIS IMAGE and LIKENESS, a fundamental attribute that flows primarily from the separate, distinct, and autonomous, spiritual and immortal vital or life principle known as the Human Soul, wherein the mystery of the entire Human Person, especially with regards to the creation of the Human Soul as such that is ontologically and essentially separate from GOD, yet by which it is not nothing, points to a remarkable and loving attribute of GOD wherein GOD would choose to create beings, especially rational persons such as Human Persons, Angels, and any bodily  extraterrestrial persons that might live on other planets orbiting other stars or any bodily extraterrestrial persons that might inhabit other dimensions, both of which would most likely also possess spiritual and immortal souls, wherein GOD would thus lovingly and humbly remove HIMSELF from the situation whereby the only and sole reality would be GOD HIMSELF.

 

Since the sum total of all being and reality is not in the absolute sense, only and simply GOD, but rather includes the  reality of the set of GOD, THE THREE DIVINE PERSONS who are in fact each and completely totally GOD,  GOD’s first principle creations such as Human Souls, Angels, and any existent ETI Souls, and the various forms of matter such as the Human Body, atoms, molecules, sub-atomic particles, sub-nuclear particles, stars, planets, animals, black holes, universes if there is more than one universe and the like, GOD has ever so slightly removed HIMSELF from the situation wherein HE is the sum total of everything that exists or that has reality.

 

For all of these reasons, we as Catholic Clergyman, Religious, and Laypersons should speak out all the more against the process of abortion, and not only abortion, but also with regards to the practice of artificial contraception, Given that the practice of artificial contraception is so widely adopted, in fact as many as 90 percent or more of married Catholic Couples have practiced it at times, we need to present arguments as to why such a practice is wrong but then so in a kind, understanding, and non-judgmental manner. We need to argue in a positive and proactive manner that each human person who is determinably on tract to be conceived is not simply a potentially physical germ like embryonic entity, and do not get me wrong, I believe that the human body has great dignity also and a discussion of such great dignity will be the subject of another similar article, but rather is a beautiful union of body and soul, and that when a conception that is determinably on track to occur is prevented, the Human Soul that would otherwise have been created may never able have the opportunity to come into existence, at least not in any way currently known to humanity.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4)  Natural Accidental Nature Of The Human Soul Can Grow Without Limit

 

Note yet again that Scholastic theologian interpretations of the belief in immortal human souls hold that the soul: 1) is naturally immortal, that it does not survive bodily death because of the grace of God nor through the incurrence of the sacraments of the Catholic Church, but rather is inherently immortal of its own nature; 2) has no extension in space; 3) has no shape; 4) has no spatial size; 5) has no separate components into which it can decay or be divided; 6) is simple; 7) is unextended; 8] is spiritual and not dependent on matter in any way for its existence; 9) is a first created principle meaning that it is not dependent on any other created being for its existence, not even the human body or brain; 10) is directly created by GOD as the first and only cause for its existence; 11) is incorruptible per addends and perse meaning that it has no pieces or extension into which it could decay and that it cannot be created nor destroyed by any natural forces nor by God through the use of any natural forces and agents; 12) is rational; 13) is radically endowed with free will and so on.

 

The New Catechism of the Catholic Church basically indorses the spirit of the above mindset with a greater or lesser degree of emphasis on the particular arguments for such.

 

Scholastics have traditionally made a distinction between the faculties of the human soul and its essence or substance (the ontological meaning of the word). The faculties of the human soul are more or less viewed as accidental properties of the souls whose operation in this life depends extrinsically on the human body/brain. Every experience of the human person is said to modify its accidental properties.

 

The human soul is said to be of a multiplicity in nature meaning that it is multiplied in its relation to the body by being completely present in and completely and totally united to each and every differential portions of the human body.  Since  the human soul is said to be substantially united to the body in this life, and then again to the resurrected human body at the Final Resurrection, such multiplicity is a good aspect of the human soul.  In a real way, such multiplicity adds to the existential or ontological size of the soul for lack of a better word.

 

The Catholic Church’s Tradition which is rich with Encyclicals regarding human nature and its fundamental dignity holds that the each Human Soul is the vital or life principle that constitutes each individual human person as a unique and unrepeatable individual, and as such is the fundamental principle of unity, individuality, and identity in each human person.

 

However the Human Person in this life is not just simply a Soul, but a substantial union of a Body and a Soul. Scholasticism holds that the Human Soul is the substantial form of the Body, not in a geometric shape sense, but rather in the sense of the Eternal Platonic and Aristotelian Forms of ancient Greek philosophy.

 

Yet once again note the following quotations from the new Catechism of the Catholic Church.

Part 1, Section 1, Chapter 1, SubSection 2

 

33 The human person: with his openness to truth and beauty, his sense of moral goodness, his freedom and the voice of his conscience, with his longings for the infinite and for happiness, man questions himself about God’s existence. In all this he discerns signs of his spiritual soul. The soul, the “seed of eternity we bear in ourselves, irreducible to the merely material”, 9 can have its origin only in God.

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 1

 

360 Because of its common origin the human race forms a unity, for “from one ancestor [God] made all nations to inhabit the whole earth”: 226

 

O wondrous vision, which makes us contemplate the human race in the unity of its origin in God. . . in the unity of its nature, composed equally in all men of a material body and a spiritual soul; in the unity of its immediate end and its mission in the world; in the unity of its dwelling, the earth, whose benefits all men, by right of nature, may use to sustain and develop life; in the unity of its supernatural end: God himself, to whom all ought to tend; in the unity of the means for attaining this end;. . . in the unity of the redemption wrought by Christ for all. 227.

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 2

 

363 In Sacred Scripture the term “soul” often refers to human life or the entire human person. 230 But “soul” also refers to the innermost aspect of man, that which is of greatest value in him, 231 that by which he is most especially in God’s image: “soul” signifies the spiritual principle in man.

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 2

 

366 The Church teaches that every spiritual soul is created immediately by God – it is not “produced” by the parents – and also that it is immortal: it does not perish when it separates from the body at death, and it will be reunited with the body at the final Resurrection. 235

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 2

 

367 Sometimes the soul is distinguished from the spirit: St. Paul for instance prays that God may sanctify his people “wholly”, with “spirit and soul and body” kept sound and blameless at the Lord’s coming. 236 The Church teaches that this distinction does not introduce a duality into the soul. 237 “Spirit” signifies that from creation man is ordered to a supernatural end and that his soul can gratuitously be raised beyond all it deserves to communion with God. 238.

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 4

 

382 “Man, though made of body and soul, is a unity” (GS 14 # 1). The doctrine of the faith affirms that the spiritual and immortal soul is created immediately by God.

 

Part 1, Section 2, Chapter 3, Article 11, SubSection 1, Heading 2

997 What is “rising”? In death, the separation of the soul from the body, the human body decays and the soul goes to meet God, while awaiting its reunion with its glorified body. God, in his almighty power, will definitively grant incorruptible life to our bodies by reuniting them with our souls, through the power of Jesus’ Resurrection.

 

Part 1, Section 2, Chapter 3, Article 12, SubSection 6

1052 “We believe that the souls of all who die in Christ’s grace . . . are the People of God beyond death. On the day of resurrection, death will be definitively conquered, when these souls will be reunited with their bodies” (Paul VI, CPG § 28].

 

Part 2, Section 2, Chapter 1, Article 1, SubSection 7, Heading 5

1280 Baptism imprints on the soul an indelible spiritual sign, the character, which consecrates the baptized person for Christian worship. Because of the character Baptism cannot be repeated (cf. DS 1609 and DS 1624).

 

Part 2, Section 2, Chapter 1, Article 2, SubSection 3

1304 Like Baptism which it completes, Confirmation is given only once, for it too imprints on the soul an indelible spiritual mark, the “character,” which is the sign that Jesus Christ has marked a Christian with the seal of his Spirit by clothing him with power from on high so that he may be his witness. 121

 

Part 3, Section 1, Chapter 1, Article 1

 

1705 By virtue of his soul and his spiritual powers of intellect and will, man is endowed with freedom, an “outstanding manifestation of the divine image.” 8

 

Part 3, Section 1, Chapter 1, Article 1

 

1711 Endowed with a spiritual soul, with intellect and with free will, the human person is from his very conception ordered to God and destined for eternal beatitude. He pursues his perfection in “seeking and loving what is true and good” (GS 15 § 2).

 

Part 3, Section 1, Chapter 2, Article 3, SubSection 2

 

1934 Created in the image of the one God and equally endowed with rational souls, all men have the same nature and the same origin. Redeemed by the sacrifice of Christ, all are called to participate in the same divine beatitude: all therefore enjoy an equal dignity.

 

In addition to these wonderful quotations, we have the Wisdom of Saint Thomas Aquinas, who held that the Human Soul is naturally immortal, spiritual, simple, unextended, incorruptible per addends and per se.

 

When Saint Thomas said that the Human Soul is the substantial form of the body, he was not saying that it physically looked like the body, rather he was using the Platonic or Aristotelian concept of eternal, immaterial, and perfect forms as the reified abstract ideal ideas that things represent.

 

Some pretty heavy duty stuff here regarding the great dignity and mysterious human soul!

 

Now what about the accidental properties of the human soul such  as individual memories, psychological, intellectual, emotional, social, and spiritual abilities, thoughts, attitudes, psychological characteristics, psychodynamic traits and personality spectrum profiles and the like.

 

Accidental forms and aspects our souls, and indeed, the accidents  of our souls, are of great dignity in their own rights and it is through such accidental realities by which we are most directly aware, conscious, sentient, and by which we move, will, feel, act, think, love, have memories, and the like.

 

Each human conscious personality, which is an amalgamation of the given human person’s soul’s accidental  properties has great dignity in its own right. Moreover, since there is in principle, no concept which can be understood at the natural level of created persons given all of physical eternity to learn and develop, and indeed, no limit to the growth of intellect, memory, will, emotions, feelings, thoughts and the like in both quality and number thereof, there is essentially, no limit to the number of accidental elements or accidental individual characteristics that a given soul may acquire or be imbued with.

 

Although the basic essence or ontological substantial properties of the human soul seemed fixed as to the substantial nature of the soul, there is essentially no limit to the ability of the human soul to grow and develop with regards to its accidental nature.

 

The accidental properties of each and every human soul have great dignity, as such forms the core of our daily waking conscious and sentient identity.

 

Now given that the human soul is directly and immediately created by GOD and is held in existence by GOD through a direct act of His sustaining decree, which is a onetime and eternal degree, (and yes I do not think that GOD is consciously deciding every second in a temporal manner to hold a given  human soul in existence since GOD’s acts of will are eternal and one time and final decisions regarding His intentions to create a first principle creation such as a human soul) and that the accidental properties of the Human Soul subsist or exist in an existential dependent relation to the essence or substance of the human soul, in a sense, these accidental properties of the Human Soul are one step removed and thus one step independent for their existence from GOD.

 

Now obviously, the accidental properties and elements of the Human Soul would not and could not exist without the essence or substance of the human soul, nonetheless to the extent that they subsist in or exist because of the sustaining influence of the essence or substance of the human soul, which in turn is sustained in existence by GOD because of GOD’s eternal decision to create a given soul, even though there exist the following chain of dependency (GOD) — > (Soul Essence or Substance)  —- > (Soul Accidental Elements, Properties, and Form), where the series starts at complete independence and self-existence from the left side, the middle link of the chain in at least some limited sense, separates the accidental properties, elements, and features of the Human Soul from GOD’s direct sustaining might.

 

This makes intuitive sense, since we can act independently of GOD or to freely choose to except or disobey Him, in acts of will of which GOD permits to operate independently of His Will. GOD did not make us puppets, but rather gave us free will, and a capacity for free and independent creative and vital self-expression at the level of  the natural created realities of our souls.

 

The cool thing about all of this is that we can in theory, improve, develop, evolve, and grow for all eternity with respect to the accidental forms of our souls. There is no hard and set finite limit to the ability of we humans to grow in terms of the accidental form and accidental elements of our souls. We can continue to naturally grow without limit, in Heaven, in Limbo, and perhaps even in some mysterious and currently unknown manner as yet known only to GOD , in Hell also.

 

Perhaps in the depths of future physical eternity, there exists a very large finite number, an ensemble, an infinity scrapper, an Aleph 0, an Aleph 1, an Aleph 2, and Aleph 3, and/or so on acts of will, accidental features, thoughts, perceptions, feelings, acts of love, social interactions, memories, and the like which can be acquired by a human soul. It might also be the case that the number of human persons yet to be created is, an ensemble, an infinity scrapper, an Aleph 0, an Aleph 1, an Aleph 2, and Aleph 3, and/or so on if the creation of human persons somehow continues after the Final Resurrection of the Dead at the End of Time. At the very least, there might already exist; an ensemble, an infinity scrapper, an Aleph 0, an Aleph 1, an Aleph 2, and Aleph 3, and/or so on, number of extraterrestrial bodily person souls and ultra-terrestrial bodily person souls.

 

For all of you who enjoy social interaction, and we all do at some level and extent or another, think of the huge opportunity for social growth and development. For all of you psychologists, sociologists, therapists, social workers, and the like whose very occupation involves the study and healing of the tangled social  workings of the human personality, think of the rich development that can occur within your own personalities as well as those of your clients as you interact with each other on the other side of the Post Final Resurrection Era.

 

Note that Aleph 0 is the infinite number of integers,  Aleph 1 is the infinite number of real numbers which is larger than the infinite number of integers by a factor of infinity if one accepts the Continuum Hypothesis, Aleph 2 is commensurately larger than Aleph 1, Aleph 3 is commensurately larger than Aleph 2. According to the developer of the concept of Cardinalities, the series of ever higher Cardinal infinite values never ends and proceeds up to Aleph Omega and eternal beyond Aleph Omega, where Omega is at least as great as the least infinite ordinal value. Any body for Aleph (Aleph Omega), Aleph (Aleph (Aleph Omega)), Aleph (Aleph (Aleph (Aleph Omega))) and so on!

 

Truly, there is no limit to the objective and subjective growth we can undergo with regards to the accidental properties, aspects, and features of our spiritual and immortal Human Souls.

 

Let us foster the growth of  the human soul of all  persons we come in contact with today by issuing a kind word, gesture, or deed, even for those persons who we would be naturally repulsed by. We are all in this together, and thus, we can, should, and must all grow together.

 

I will thus continue my vocation to advocate for the cause of manned interstellar space travel as a physics geek, in the hope that we can colonize ever greater reaches of our universe and perhaps beyond as interact with any bodily ET or UT persons and their civilizations we may encounter in our Exodus out into the wonderful, and perhaps ever growing cosmos, a cosmos that might be just one of an Aleph (Aleph (Aleph (Aleph Omega))) and so on cosmoses in a set of cosmoses that will grow in elements for all eternity through GOD’s  Almighty Creative Will.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5)  Soul, Accidents Verses Substance

 

Note that in some of my past writings, I have expressed concern regarding the possibility that the ultra-high temperatures and thermodynamic gradients near the heart of nuclear explosions might somehow injure or somehow temporarily destroy human souls.

 

My tendency is to believe that the human soul is naturally indestructible and naturally immortal in the spirit of the teachings of Saint Thomas Aquinas, however, even in the case that the accidental form of the soul could somehow be annihilated by a nuclear explosion, the substantial nature or essence of the soul likely could never be annihilated by anything but GOD acting directly.

 

Since the new Catechism of the Catholic Church teaches that all human persons share a fundamental moral equality before our Creator, and are all equally composed of a body and a soul, my feeling is that in this life, our daily waking conscious identity with respect to our souls is analogous to the consciousness of a new born baby with respect to its spiritual and immortal soul.

 

Even in the event that souls who end up in Hell may suffer eternally, the state of their suffering conscious identity may only be a tip of the ice burg regarding their complete and entire soul much as the crying of a baby  cannot be said to detract from the natural dignity and sacredness of the baby’s truest natural self of its spiritual and immortal soul.

 

I am convinced that President Obama’s Nuclear Posture Review and His desire to rid humanity of nuclear weapons is a good and noble goal. I am also absolutely convinced that in the off chance that human or ET souls could be destroyed by nuclear weapons and in some unfortunate circumstances, might be, all such persons will be Resurrected body and soul on the last day to Eternal Glory for having gone through the martyrdom of any soul death. One thing we can be absolutely sure of is that we will all be Resurrected complete and whole on the last day. Even the souls who do not make it  to Heaven will be reunited with their bodies made incorruptible although such persons will undergo unspecified suffering to the extent and nature for which  we have no certain knowledge, but they will last forever, body and soul.

 

I tend to believe in the incorruptibility of the human soul per addends and per se, and such a paradigm has been held in traditional Catholic interpretations of the immortality of the soul. As a result, I believe you do not have to worry about your soul being destroyed by a nuclear weapon. Even if it by some remote offbeat chance that has not been considered by theologians, it is sure to be Resurrected utterly incorruptible on the last day to a degree all the more glorified having undergone such a martyrdom. But not to worry, the Catholic Church holds as a doctrinal matter that every human soul is spiritual and immortal.

 

One great spiritual writer of the late 19th early 20th century held an expressed written belief that our daily conscious life and identity in this life bellies a vast infinite ocean of existence which is our spiritual and immortal soul in each and every one of us. This ocean of existence is unfathomably infinite in extent and in depth, and accordingly in this life we catch just a surface glimmer of an ocean surface ripple or wave of the infinite ocean of existence that is our souls. Perhaps this surface glimmer is the accidental form or surface glimmer of our souls in the form of our conscious waking identity in this life. If this is the case, and I believe it to be so, then we can bear all things with a little more confidence and hope in an eternal future where we will have access to the wonders of GOD, HIS THREE PERSONS, the Angels, Saints, All Human Persons in Heaven, All ET Persons in Heaven, and any and All so called Ultra-terrestrial Persons in Heaven, as well as the Wonders within Our Selves and Our Loved Ones, as well as of the Rest of Creation.

 

Another way of looking at daily waking conscious life in this world is to make the analogy that daily waking consciousness relative to the substance or essence of the human soul is more or less similar to the relationship between a person watching a movie in a movie theater and the person’s his or her own self. Even if the movie is suddenly interrupted or stops playing, the person still exists in all of his or her existential integrity with the conscious experience of watching and affectively engaging the movie being more or less akin to the daily waking consciousness or perhaps even the accidental properties of the human soul such as might exist in their totality in the form of the unconscious, sub-conscious, and/or conscious psyche.

 

Perhaps another way of making the analogy is to consider the concept of a light bulb whereby the illuminated state of the light bulb represents our daily conscious psychic activities or perhaps at least a portion of our soul’s accidental properties  as distinct from the substantial or essence-wise ontological properties of our spiritual and immortal souls..

 

The substantial or essential aspects of our souls continue to exist naturally incorruptible per addends and per se even if the accidental state of the metaphorical illuminated light bulb is turned off.

 

Yet another way of perhaps making the analogy is to consider the concept of a garden hose that is spraying water into a garden wherein the water transmissive state of the hose corresponds to the daily working conscious life of the human person or perhaps at least in part, the accidental properties of the human soul whereas the hose itself continues to exist just fine regardless of whether or not it is transmitting water. One could say that the hose is being more useful if it is transmitting water to water a garden relative to its state while not being used and make such an analogy with regard to a human soul in this life being in the habitual state of mortal sin verses another soul being useful in a practical applied manner such as a devout person who works for a charitable non for profit corporation and yet who does volunteer work such as helping out in a homeless shelter or who visits the imprisoned or institutionalized. In both cases, the ontological good of the substance or essence of the soul remains incorrupt and continues to exist just fine.

 

Given the sad reality of Hell, and the fact that GOD loves all of His creatures especially created persons, regardless of whether such persons are in Heaven, on Earth in this life, are of the form of  any extraterrestrial or so called ultra-terrestrial persons that might exist, are in Purgatory or perhaps in Hell, I cannot logically see how the relationship between the accidental properties of the soul and our conscious daily working psyches and the substance or essence-wise properties of our souls could be otherwise interrelated.

 

A modern popular Catholic encyclopedic dictionary that I purchased from a local Catholic book store states in an entry on the subject related to what is Good and subject of  the Divine Economy that Satan has a nature that is essentially very good although he uses his nature for the morally evil purpose of furthering his agenda.

 

Now the sad reality of Hell and eternal separation from GOD that results is no triviality and we must do all in our power to avoid going there, but we must remember that GOD’s love shines on the just as well as the unjust and we are all morally equal in this life before GOD.

 

We have forgotten this fact as a result of modern psychodynamic existentialism and other crap that has entered the halls of even seminary formation programs for the Priesthood. I will even hazard a guess that the ubiquitous-ness  of the sin of abortion is the result of the loss of belief in the sanctity of the human soul in every instance. It is not quit so much the sin of a poor hurting young adolescent girl who obtains an abortion for herself as it is the sin of affluent politicians and health care workers who do not speak out on this issue and who support groups like Planned Parenthood and other trashy organizations.

 

Most assuredly, the Lord looks more kindly on the poor hurting emotionally disturbed adolescent girl who feels she must have an abortion just has he had mercy on the adulterous women about to be stoned by the elite establishment in the Gospels than on even the affluent white collar psychiatrists and therapists who may feign compassion for the hurting woman while suggesting to her that it is OK to have an abortion if she feels she needs one while at the same time perhaps looking down on such emotionally disturbed young women thinking that such women are primitive or primitive drive motivated and all of this other psychodynamic Freudian existentialist crap that has even made its way into formation programs within many of modern day Catholic seminaries.

 

Part of the signs that a civilization is coming close to its end is how the so called devout Catholics who feign conservatism look down on, discriminate against, or otherwise display a self-righteous attitude toward those who are viewed as unfit or unworthy because they are emotionally, psychologically, and/or intellectually disabled, or because perhaps they are poor, unemployed or undereducated, or perhaps who have a hatred for those on death row and support the death penalty in an overzealous manner when the late Pope John Paul II stated that there is virtually no case where the death penalty needs to be administered and that we have the technology to keep even the most severe felons safely separated from society.

 

Remember, such hateful attitudes had developed in NAZI Germany before World War II and we are already well underway in the process of America’s Holocaust, the results of the supreme court ruling of Roe Verses Wade. One it tempted to think that perhaps the start of eternal punishment is at least in part the natural result of Suns falling down from the sky in the form of high yield  nuclear warhead detonations over our metropolitan areas. The Miracle of the Sun at Fatima is truly meant to be a message of peace, but to the extent that we live in self-righteous hate and indignation for those of lesser degrees of intellectual, psychological, social, emotional, and/or social economic prowess should be a wakeup call to us that perhaps there is yet another more serious warning in the Miracle of the Sun.  For those who do not believe me, please be advised to read the accounts of the Church Approved Apparitions of Akita Japan.

 

I can see that a main calling of mine if not my sole occupational calling  is to assist with the development of interstellar propulsion technologies that are safe and effective so that the human race can expand outward into our universe and perhaps beyond. The production of all the more families which are the fundamental unit of human civilization permits the size of the spiritual cosmos to grow irrevocably via the creation of every new soul at the moment of conception and a body that in all cases is destined to arise incorruptible on the last day.  I feel utterly compelled to give human life a chance to exist in cases where it does not such as promoting my pro-life views.

 

I see that giving children a chance to exist and to be born is a great calling that each and every one of us can practice regardless of our state of life.

 

As a conservative Catholic, I can state with utmost certainty that long, long after the last Mass is sail, the last Confession is heard, the last portions of the Sacred Species of the Holy Eucharist are brought into being during the prayers of consecration, long after the last Baptisms occur, each and every one of us will indelibly and irrevocably still be GOD’s children, and together we and the rest of the faithful will each be a member of the Mystical Body of Christ, not simply members of the Body of Christ, but members of the “Mystical Body of Christ”.

 

 

 

We are all predestined by GOD to be irreplaceable and unique citizens of the civilization of love. This applies to all of us regardless of whether we are Catholic, Baptist,  Evangelical, Jewish, Muslim, Hindu, Buddhist, Taoist, practitioners of Shinto, Professed Atheists, Professed Agnostics, New Agers, Married, Single, Virgins or not,  Celibate, Clergymen, Consecrated Religious, Convicts, Disabled Mentally, Emotionally, Intellectually, and/or Physically, Rock hard U.S. NAVY SEALS, or as physically frail as the great physicist Stephen Hawking, Burly and Robust Construction Workers, Custodians, Electricians, Engineers, Beautiful Female Models, Gay, Straight, Bisexual, or what have you. We all share a fundamental moral equality before GOD and are all called to partake in the City Of God, that Eternal Beacon of Divine Light and Created Light. For those who are looking for a pecking order in Heaven, you may still get their but you will be disappointed. In Heaven, there cannot and will not be a pecking order, and each person in Heaven will be an irreplaceable member of the Mystical Body of Christ.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6)  The Great Dignity Of The Human Soul Even If It Would Be Immortal By Grace

 

Note that in some of my past writings, I have expressed concern regarding the possibility that the ultra-high temperatures and thermodynamic gradients near the heart of nuclear explosions might somehow injure or somehow temporarily destroy human souls.

 

My tendency is to believe that the human soul is naturally indestructible and naturally immortal in the spirit of the teachings of Saint Thomas Aquinas, however, even in the case that the accidental form of the soul could somehow be annihilated by a nuclear explosion, the substantial nature or essence of the soul likely could never be annihilated by anything but GOD acting directly.

 

Since the new Catechism of the Catholic Church teaches that all human persons share a fundamental moral equality before our Creator, and are all equally composed of a body and a soul, my feeling is that in this life, our daily waking conscious identity with respect to our souls is analogous to the consciousness of a new born baby with respect to its spiritual and immortal soul.

 

Even in the event that souls who end up in Hell may suffer eternally, the state of their suffering conscious identity may only be a tip of the ice burg regarding their complete and entire soul much as the crying of a baby  cannot be said to detract from the natural dignity and sacredness of the baby’s truest natural self of its spiritual and immortal soul.

 

I am convinced that President Obama’s Nuclear Posture Review and His desire to rid humanity of nuclear weapons is a good and noble goal. I am also absolutely convinced that in the off chance that human or ET souls could be destroyed by nuclear weapons and in some unfortunate circumstances, might be, all such persons will be Resurrected body and soul on the last day to Eternal Glory for having gone through the martyrdom of any soul death. One thing we can be absolutely sure of is that we will all be Resurrected complete and whole on the last day. Even the souls who do not make it  to Heaven will be reunited with their bodies made incorruptible although such persons will undergo unspecified suffering to the extent and nature for which  we have no certain knowledge, but they will last forever, body and soul.

 

One great spiritual writer of the late 19th early 20th century held an expressed written belief that our daily conscious life and identity in this life bellies a vast infinite ocean of existence which is our spiritual and immortal soul in each and every one of us. This ocean of existence is unfathomably infinite in extent and in depth, and accordingly in this life we catch just a surface glimmer as of an ocean surface ripple or wave of the infinite ocean of existence that is our souls. Perhaps this surface glimmer is the accidental form or surface glimmer of our souls in the form of our conscious waking identity in this life. If this is the case, and I believe it to be so, then we can bear all things with a little more confidence and hope in an eternal future where we will have access to the wonders of GOD, HIS THREE PERSONS, the Angels, Saints, All Human Persons in Heaven, All ET Persons in Heaven, and any and All so called Ultra-terrestrial Persons in Heaven, as well as the Wonders within Our Selves and Our Loved Ones, as well as of the Rest of Creation.

 

Another way of looking at daily waking conscious life in this world is to make the analogy that daily waking consciousness relative to the substance or essence of the human soul is more or less similar to the relationship between a person watching a movie in a movie theater and the person’s his or her own self. Even if the movie is suddenly interrupted or stops playing, the person still exists in all of his or her existential integrity with the conscious experience of watching and affectively engaging the movie being more or less akin to the daily waking consciousness or perhaps even the accidental properties of the human soul such as might exist in their totality in the form of the unconscious, sub-conscious, and/or conscious psyche.

 

Perhaps another way of making the analogy is to consider the concept of a light bulb whereby the illuminated state of the light bulb represents our daily conscious psychic activities or perhaps at least a portion of our soul’s accidental properties  as distinct from the substantial or essence-wise ontological properties of our spiritual and immortal souls.

 

The substantial or essential aspects of our souls continue to exist naturally incorruptible per addends and per se even if the accidental state of the metaphorical illuminated light bulb is turned off.

 

Yet another way of perhaps making the analogy is to consider the concept of a garden hose that is spraying water into a garden wherein the water transmissive state of the hose corresponds to the daily working conscious life of the human person or perhaps at least in part, the accidental properties of the human soul whereas the hose itself continues to exist just fine regardless of whether or not it is transmitting water. One could say that the hose is being more useful if it is transmitting water to water a garden relative to its state while not being used and make such an analogy with regard to a human soul in this life being in the habitual state of mortal sin verses another soul being useful in a practical applied manner such as the case of a devout person who works for a charitable non for profit corporation and yet who does volunteer work such as helping out in a homeless shelter or who visits the imprisoned or institutionalized. In both cases, the ontological good of the substance or essence of the soul remains incorrupt and continues to exist just fine.

 

Given the sad reality of Hell, and the fact that GOD loves all of His creatures especially created persons, regardless of whether such persons are in Heaven, on Earth in this life, are of the form of  any extraterrestrial or so called ultra-terrestrial persons that might exist, are in Purgatory or perhaps in Hell, I cannot logically see how the relationship between the accidental properties of the soul and our conscious daily working psyches and the substance or essence-wise properties of our souls could be otherwise interrelated.

 

A modern popular Catholic encyclopedic dictionary that I purchased from a local Catholic book store states (in an entry on the subject related to what is Good and the subject of  the Divine Economy) that Satan has a nature that is essentially very good although he uses his nature for the morally evil purpose of furthering his agenda.

 

Now the sad reality of Hell and eternal separation from GOD that results is no triviality and we must do all in our power to avoid going there, but we must remember that GOD’s love shines on the just as well as the unjust and we are all morally equal in this life before GOD.

 

We have forgotten this fact as a result of modern psychodynamic existentialism and other crap that has entered the halls of even seminary formation programs for the Priesthood. I will even hazard a guess that the ubiquitous-ness  of the sin of abortion is the result of the loss of belief in the sanctity of the human soul in every instance. It is not quit so much the sin of a poor hurting young adolescent girl who obtains an abortion for herself as it is the sin of affluent politicians and health care workers who do not speak out on this issue and who support groups like Planned Parenthood and other trashy organizations.

 

Most assuredly, the Lord looks more kindly on the poor hurting emotionally disturbed adolescent girl who feels she must have an abortion just as he had mercy on the adulterous women about to be stoned by the elite establishment in the Gospels than on even the affluent white collar psychiatrists and therapists who may feign compassion for the hurting woman while suggesting to her that it is OK to have an abortion if she feels she needs one while at the same time perhaps looking down on such emotionally disturbed young women thinking that such women are primitive or primitive drive motivated and all of this other psychodynamic Freudian existentialist crap that has even made its way into formation programs within many of modern day Catholic seminaries.

 

Part of the signs that a civilization is coming close to its end is how the so called devout Catholics who feign conservatism look down on, discriminate against, or otherwise display a self-righteous attitude toward those who are viewed as unfit or unworthy because they are emotionally, psychologically, and/or intellectually disabled, or because perhaps they are poor, unemployed or undereducated, or perhaps who have a hatred for those on death row and support the death penalty in an overzealous manner when the late Pope John Paul II stated that there is virtually no case where the death penalty needs to be administered and that we have the technology to keep even the most severe felons safely separated from society.

 

Remember, such hateful attitudes had developed in NAZI Germany before World War II and we are already well underway in the process of America’s Holocaust, the results of the Supreme Court ruling of Roe Verses Wade. One it tempted to think that perhaps the start of eternal punishment is at least in part the natural result of Suns falling down from the sky in the form of high yield nuclear warhead detonations over our metropolitan areas. The Miracle of the Sun at Fatima is truly meant to be a message of peace, but to the extent that we live in self-righteous hate and indignation for those of lesser degrees of intellectual, psychological, social, emotional, and/or social-economic prowess should be a wakeup call to us that perhaps there is yet another more serious warning in the Miracle of the Sun.  For those who do not believe me,  please be advised to read the accounts of the Church Approved Apparitions of Akita Japan.

 

I can see that a main calling of mine if not my sole occupational calling  is to assist with the development of interstellar propulsion technologies that are safe and effective so that the human race can expand outward into our universe and perhaps beyond. The production of all the more families which are the fundamental unit of human civilization permits the size of the spiritual cosmos to grow irrevocably via the creation of every new soul at the moment of conception and a body that in all cases is destined to arise incorruptible on the last day.  I feel utterly compelled to give human life a chance to exist in cases where it does not, such as promoting my pro-life views.

 

I see that giving children a chance to exist and to be born is a great calling that each and every one of us can practice regardless of our state of life.

 

As a conservative Catholic, I can state with utmost certainty that long, long after the last Mass is sail, the last Confession is heard, the last portions of the Sacred Species of the Holy Eucharist are brought into being during the prayers of consecration, long after the last Baptisms occur, each and every one of us will indelibly and irrevocably still be GOD’s children, and together we and the rest of the faithful will each be a member of the Mystical Body of Christ, not simply members of the Body of Christ, but members of the “Mystical Body of Christ”.

 

 

 

We are all predestined by GOD to be irreplaceable and unique citizens of the civilization of love. This applies to all of us regardless of whether we are Catholic, Baptist,  Evangelical, Jewish, Muslim, Hindu, Buddhist, Taoist, practitioners of Shinto, Professed Atheists, Professed Agnostics, New Agers, Married, Single, Virgins or not,  Celibate, Clergymen, Consecrated Religious, Convicts, Disabled Mentally, Emotionally, Intellectually, and/or Physically, Rock hard U.S. NAVY SEALS, or as physically frail as the great physicist Stephen Hawking, Burly and Robust Construction Workers, Custodians, Electricians, Engineers, Beautiful Female Models, Health Care Workers and/or Professionals, Politicians, Gay, Straight, Bisexual, or what have you. We all share a fundamental moral equality before GOD and are all called to partake in the City Of God, that Eternal Beacon of Divine Light and Created Light. For those who are looking for a pecking order in Heaven, you may still get their but you will be disappointed. In Heaven, there cannot and will not be a pecking order, and each person in Heaven will be an irreplaceable member of the Mystical Body of Christ.  This is not to suggest that some folks will be rewarded in some ways more than others, however, each person will have his or her unique role to play that is and will remain indispensable to the Resurrected Mystical Body of Christ. Will some folks who spend time, perhaps even a lot of time in Purgatory, have a level or levels of various Resurrected graces equal to the top Canonized Saints? Perhaps. To the best of my knowledge, the Church has never taken any formal doctrinal position on this issue. But either way, regardless of your state of life, ask GOD to give you the grace so that you can become a Saint, even a Canonized Saint. GOD’s grace is free for the asking.

 

 

 

Regardless of whether or not the Human Soul is Naturally Immortal or immortal by grace only, each and every human soul that has ever existed, regardless of whether one goes to Heaven or not is meant forever, and will last forever. Since the basic un-augmented by grace nature of the Human soul is immutable, it is thus eternal in its very essence.

 

Now suppose the human soul is only immortal because of GOD’s grace by the merits of Christ Conception, Birth, Life, Passion, Death on the Cross, and Resurrection. The Human Soul’s existence would not be caused by itself or due to itself. Thus, in a sense, the soul would be independent of itself for its existence. The soul would not need its existence to be based on itself. This is a sort of ultimate transcendence for a creature.

 

Even if the Human Soul is immortal by grace only, this really does not matter since God holds all creatures in existence by His Almighty and sustaining will. Even the Angels would lapse into non-existence if it were not for GOD maintaining them in existence.

 

If indeed the Human Soul is immortal by grace only, then perhaps the Human Soul does not need this direct existence sustaining power of GOD, at least to the extent that it would need such in the case that it was immortal by nature. The reason for this kind of self-existence of the Human Soul in the event that it is immortal by grace only is that it is the supernatural life or aspect of the natural created soul that would then seem to be the mechanism for the continued existence of the Soul. This grace, which would come from GOD would not be identical with GOD since we creatures are in no way a part of GOD nor are we GOD.

 

So imagine that! A Human Soul that exist forever after death in a manner such that it does not need its own self caused mechanism to continue to exist but rather exists perhaps because of itself wherein this “itself” is partly a supernatural character or attribute by which the soul is not required to exist by its natural powers nor by some form of natural immortality, both of the latter of which would still require GOD’s all sustaining power to hold the Human Soul in existence.

 

Thus, a human soul that is immortal by grace might not need GOD to directly hold it in existence as a first created principle, but rather at the very least, the Soul would continue to exist indirectly by GOD, and more likely be held in existence after death by its own grace. After all, why would a soul need to be directly held in existence by GOD, if its immortality was rather a consequence of grace.  It would seem that GOD would not duplicate His efforts by requiring both mechanisms of immortality to be operative.

 

In a way, the existence of the state of immortality of the human soul might be far more independent for the case of gratuitous immortality than for natural immortality, including immortality that is independent from the soul’s nature or independent from the natural soul itself.

 

Even in the rare cases such that Human Souls might somehow be injured or destroyed by ways and means known only to GOD at this point in time, such as perhaps close proximity to the energy scrambling heart of a nuclear explosion, or perhaps as a result of a human person falling into a black hole, and the like, rest assure that any such souls will be Resurrected on the last day with all the more glory, having gone through the natural martyrdom and cross of natural soul death. With the cross, comes all the more eternal glory.

 

Regardless, it is true that even those who do not make it to Heaven will still have their bodies reunited to their immortal souls wherein their bodies will also be resin incorruptible on the last day and reunited to their spiritual and immortal soul.

 

However, for those of you who want to believe in the natural immortality and natural incorruptibility of the soul, the great theologian of Saint Thomas Aquinas strongly and logically argued in favor of the natural immortality and incorruptibility of the soul. His writings on the subject are still in widespread teaching in formation programs and the new Catholic Catechism does not make counter arguments to Saint Thomas’ teachings, and in fact, it  seems to indorse the spirit of His teachings, although in not as great of detail in terms of the explanation of the immortality of the Human Soul.

 

Note, once again, I also prefer to believe that the Human Soul is naturally immortal, and as a result, not immortal by grace. I make the above argument so that everyone can be satisfied that the human soul possesses great and transcendent dignity.

 

Also, once again, note the Scholastic interpretation as promulgated by Saint Aquinas of the nature of the human soul, that is the human soul is:  1) Spiritual, 2) Naturally immortal, 3) Incorruptible per addends and per se, 4) Simple, 5) Unextended, 6) Without shape or size, 7) Non-material,   8]   Non-corporeal, 9) Rational, 10) Free,  11) A first created principle, 12) An essence or a being which exist per se, 13) Independent of the body for its existence and to some extent its operations in this life, 14) The substantial form of the body in the Ancient Greek philosophical sense of the word, 15) Directly created by God, 16) Immediately created by God, and if I am not mistaken, 17) Multiple meaning that it is completely and totally present and united to every portion of the human body that is alive.

 

The modern Catholic approach to the immortality of the soul is somewhat ambivalent about the spiritualistic extreme ideologies of Saint Thomas Aquinas described above, however its modern viewpoint backed by the full weight of the highest levels of the Church Hierarchy is that the human soul is: 1) Immortal, 2) Spiritual, 3) Rational, 4) Does not die when separated from its body at death, 4) Immediately created, 5) According to the index of the first addition of the new Catechism of the Catholic Church, directly created by God; 6) The seed of eternity we bear within ourselves, 7) Not reducible to the mere material world;   8]   The form of the body.

 

 

 

Here are some things that you can be assured are true regarding the Human Soul, that seemingly intangable innermost aspect of our natural being that has perplexed philosophers and theologians from antiquity.

 

Rest assure, some of the poor souls in purgatory who have no one to pray for them because, of phrases, such as “May they Rest in Peace” and similar phrases, when used by clergyman, and others, to indicate views points, such as “We really cannot know what happens after death.” or “The dead have fallen asleep to be awakened on the last day”, are of no consolation to these poor forgotten souls, who I assure every living adult human, are the very same persons they knew on Earth, and who I can assure everyone, are most fully alive, alert, conscious, affective, feeling, and sadly suffering.

 

Now; once again, read through these quotations from the new Catechism of the Catholic Church which was approved by the very highest levels of the Vatican during 1980s.

Part 1, Section 1, Chapter 1, SubSection 2

 

33 The human person: with his openness to truth and beauty, his sense of moral goodness, his freedom and the voice of his conscience, with his longings for the infinite and for happiness, man questions himself about God’s existence. In all this he discerns signs of his spiritual soul. The soul, the “seed of eternity we bear in ourselves, irreducible to the merely material”, 9 can have its origin only in God.

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 1

 

360 Because of its common origin the human race forms a unity, for “from one ancestor [God] made all nations to inhabit the whole earth”: 226

 

O wondrous vision, which makes us contemplate the human race in the unity of its origin in God. . . in the unity of its nature, composed equally in all men of a material body and a spiritual soul; in the unity of its immediate end and its mission in the world; in the unity of its dwelling, the earth, whose benefits all men, by right of nature, may use to sustain and develop life; in the unity of its supernatural end: God himself, to whom all ought to tend; in the unity of the means for attaining this end;. . . in the unity of the redemption wrought by Christ for all. 227.

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 2

 

363 In Sacred Scripture the term “soul” often refers to human life or the entire human person. 230 But “soul” also refers to the innermost aspect of man, that which is of greatest value in him, 231 that by which he is most especially in God’s image: “soul” signifies the spiritual principle in man.

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 2

 

366 The Church teaches that every spiritual soul is created immediately by God – it is not “produced” by the parents – and also that it is immortal: it does not perish when it separates from the body at death, and it will be reunited with the body at the final Resurrection. 235

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 2

 

367 Sometimes the soul is distinguished from the spirit: St. Paul for instance prays that God may sanctify his people “wholly”, with “spirit and soul and body” kept sound and blameless at the Lord’s coming. 236 The Church teaches that this distinction does not introduce a duality into the soul. 237 “Spirit” signifies that from creation man is ordered to a supernatural end and that his soul can gratuitously be raised beyond all it deserves to communion with God. 238.

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 4

 

382 “Man, though made of body and soul, is a unity” (GS 14 # 1). The doctrine of the faith affirms that the spiritual and immortal soul is created immediately by God.

 

Part 1, Section 2, Chapter 3, Article 11, SubSection 1, Heading 2

997 What is “rising”? In death, the separation of the soul from the body, the human body decays and the soul goes to meet God, while awaiting its reunion with its glorified body. God, in his almighty power, will definitively grant incorruptible life to our bodies by reuniting them with our souls, through the power of Jesus’ Resurrection.

 

Part 1, Section 2, Chapter 3, Article 12, SubSection 6

1052 “We believe that the souls of all who die in Christ’s grace . . . are the People of God beyond death. On the day of resurrection, death will be definitively conquered, when these souls will be reunited with their bodies” (Paul VI, CPG § 28].

 

Part 2, Section 2, Chapter 1, Article 1, SubSection 7, Heading 5

1280 Baptism imprints on the soul an indelible spiritual sign, the character, which consecrates the baptized person for Christian worship. Because of the character Baptism cannot be repeated (cf. DS 1609 and DS 1624).

 

Part 2, Section 2, Chapter 1, Article 2, SubSection 3

1304 Like Baptism which it completes, Confirmation is given only once, for it too imprints on the soul an indelible spiritual mark, the “character,” which is the sign that Jesus Christ has marked a Christian with the seal of his Spirit by clothing him with power from on high so that he may be his witness. 121

 

Part 3, Section 1, Chapter 1, Article 1

 

1705 By virtue of his soul and his spiritual powers of intellect and will, man is endowed with freedom, an “outstanding manifestation of the divine image.” 8

 

Part 3, Section 1, Chapter 1, Article 1

 

1711 Endowed with a spiritual soul, with intellect and with free will, the human person is from his very conception ordered to God and destined for eternal beatitude. He pursues his perfection in “seeking and loving what is true and good” (GS 15 § 2).

 

Part 3, Section 1, Chapter 2, Article 3, SubSection 2

 

1934 Created in the image of the one God and equally endowed with rational souls, all men have the same nature and the same origin. Redeemed by the sacrifice of Christ, all are called to participate in the same divine beatitude: all therefore enjoy an equal dignity.

 

Thus, we have at the very least, the above 13 aspects of the transcendent dignity of the Human Soul. In addition to these wonderful quotations, we have the Wisdom of Saint Thomas Aquinas, who held that the Human Soul is naturally immortal, spiritual, simple, unextended, incorruptible per addends and per se.

 

When Saint Thomas said that the Human Soul is the substantial form of the body, he was not saying that it physically looked like the body, rather he was using the Platonic or Aristotelian concept of eternal, immaterial, and perfect forms as the reified abstract ideal ideas that things represent.

 

Saint Thomas referred to the Soul as the substantial form of the body, ‘substantial” meaning a first created principle of being that is intrinsically independent of the body for its existence and for some of its more advanced operations.

 

Now once again, given the Scholastic interpretation of the nature of the human soul, that is the human soul is:  1) Spiritual, 2) Naturally immortal, 3) Incorruptible per addends and per se, 4) Simple, 5) Unextended, 6) Without shape or size, 7) Non-material,   8]   Non-corporeal, 9) Rational, 10) Free,  11) A first created principle, 12) An essence or a being which exist per se, 13) Independent of the body for its existence and to some extent its operations in this life, 14) The substantial form of the body in the Ancient Greek philosophical sense of the word, 15) Directly created by God, 16) Immediately created by God, and if I am not mistaken, 17) Multiple meaning that it is completely and totally present and united to every portion of the human body that is alive, we have much grounding through the use of natural reasoning that the human soul is naturally immortal and naturally indestructible. In all, we have at least the above 17 transcendent dignities of the human soul if Saint Thomas Aquinas is to be believed.

 

Now, I try to aim for the utmost objectivity in my reasoning and speculations regarding the subject of the human soul since this subject is so dear to me, and perhaps because even though I am a large framed, iron pumping, near 500 pound, big guy, and a little too obese and corpulent, I was nonetheless slight of build and thin during my elementary school years and I got picked on and teased a lot by my class mates because of my formerly shy temperament and lack of sports playing athletic ability. As a result, even after the onset of adolescence when I started lifting weights and I became an extroverted, stocky, and slightly above average height, young man, I had developed a love of the soul over the body, simply because, my body was once small and somewhat fragile in build until I hit puberty.

 

Since I try for such extreme objectivity in this subject of soul immortality, I must cover all bases and including the remote but nonetheless, possible scenarios, that perhaps at the very least, situations such a very close proximity to a nuclear explosion and other extreme events such as bodily falling into a black hole, onto a neutron star, or perhaps even onto a white dwarf, might at the very least, be able to destroy the accidental form of the soul, even if it be the case, that the essence or substance of the soul might be utterly naturally incorruptible to any created forces, agents, or persons.

 

Even if my hopes in complete human soul natural immortality are proved false, but I doubt they can be, I can assure the reader that it is my utmost Holy Rosary reciting, frequent daily mass attending, and frequent Sacramental Confession attending conservative Catholic personhood, that any souls that might thus be destroyed or injured will be Resurrected at least no later than the End of Time at the Final Resurrection of the Dead to Eternal Glory for having undergone the Cross and Crucifixion of any possible soul death, just as Christ was Resurrected and has Ascended into the Glory of sitting at the proverbial Right Hand of the Father and just as Christ will become the proverbial  Father of the World to Come after the Final Resurrection of the Dead. This Final Resurrection of the Dead is open to all persons of all faiths and belief systems or lack thereof, and I am obliged to believe that many, many, if not most persons who are not Catholic do in fact attain eternal salvation. The teachings of the Catholic Faith coupled with common sensible reason all point extremely affirmative to this reality. The late Pope John Paul II, in the title of His book, “Be Not Afraid”, applies to each and every person alive today on this good planet Earth.

 

Now here is some really freaky conjecture that occurred to me as I was out running errands last evening. The notions involve the speculations that we humans might not only have either purely naturally based, natural coupled with supernatural grace based, or purely graced based immortality of the soul, but perhaps our souls have immortality like analogues or parallel qualities that are of the same class as any immortality of the soul as such but which are fundamentally different. The concept is analogous to the speculation that their might exist higher dimensions alongside or in parallel with the 4-D ordinary Einsteinian space time that we are familiar with in everyday life but which also is the primary foundation of current applied and theoretical physics paradigms.

 

We can speculate that such immortality analogues might be referred to as para-immortality, meta-immortality, trans-immortality, or super-immortality. If such analogues exist, then even though such qualities would have to be said to have been given to the soul, perhaps at the very natural level, at the time of the soul’s creation at the moment of embryonic conception, if it be the case that the soul could be destroyed at least in terms of its accidental form or accidental properties, perhaps by close proximity to the heart of a nuclear explosion, then perhaps, just perhaps, the soul would continue to exist, or para-exist, in an irrevocable manner in the given soul’s para-immortality, meta-immortality, trans-immortality, or super-immortality characteristics.

 

My reasoning here flows from the commonly understood Catholic Teaching that the Human Person, especially the Human Soul, is made in GOD’s Image and Likeness. Just as GOD has the eternal I AM THAT I AM BEING AND ESSENSE, and has a NATURE that is absolutely simple ontologically speaking, but yet this same ONE and ABSOLUTELY SIMPLE GOD has THREE DIVINE PERSONS and who is thus TRICE HOLY, and where JESUS the SON OF GOD, THE SECOND PERSON OF THE HOLY TRINITY died on the CROSS yet continued to exist in HIS  DIVINE NATURE and  in HIS HUMAN NATURE of HIS immortal Human Soul and His deceased and presumably decaying Body and once Sentient Brain, we humans might thus have multiple levels of Immortality, and perhaps even non-immortality analogues such as the proposed para-immortality, meta-immortality, trans-immortality, or super-immortality fundamental and essential characteristics. After all, if we are made in GOD’s image and likeness, then we can in a sense be considered in the nature and essence of our immortal souls, to be created versions or analogues of that YEHWAY or created versions or analogues of that I AM THAT I AM.

 

The point is that we have just scratched the surface of what and who beautiful and transcendent Human Souls are even at the level of the Soul’s Natural attributes, both essential and substantial attributes and even the more accidental and ancillary attributes and characteristics of the Human Soul. Each Human Soul is of infinite worth to GOD AS THE HOLY TRINITY OR DIVINE BEING OR ESSENSE and to GOD, AS AND IN EACH OF HIS THREE DIVINE PERSONS, THE FATHER, THE SON, AND THE HOLY SPIRIT. You don’t believe me? Then consider that JESUS, the combination the SECOND DIVINE PERSON AND HIS  Human Nature, was called  by GOD THE FATHER to take on a Human Nature, and to suffer, and die on the Cross, for the Eternal Salvation of all Human  Persons, regardless of the religious faith, believe system, state of life, vocation, or lack thereof that a given human person has. Christ lovingly did so out of obedience to HIS ETERNAL FATHER, but perhaps more significantly for us, out of love for us, the same love for us that the ETERNAL FATHER has for us.

 

So when we bemoan our physical frailty and the fact that we cannot seem to run, jump, skip, and hop like we could when we were young children, know that you are special and are meant for and will last forever.

 

 

 

 

 

 

 

 

 

7) The Soul As The Substantial Form Of The Body And What This Implies For The Sublime And Transcendent Dignity Of The Human Soul.

 

Yet still once again, note the that Scholastic theologian interpretations of the belief in immortal human souls hold that the soul: 1) is naturally immortal, that it does not survive bodily death because of the grace of God nor through the incurrence of the sacraments of the Catholic Church, but rather is inherently immortal of its own nature; 2) has no extension in space; 3) has no shape; 4) has no spatial size; 5) has no separate components into which it can decay or be divided; 6) is simple; 7) is unextended; 8] is spiritual and not dependent on matter in any way for its existence; 9) is a first created principle meaning that it is not dependent on any other created being for its existence, not even the human body or brain; 10) is directly created by GOD as the first and only cause for its existence; 11) is incorruptible per addends and perse meaning that it has no pieces or extension into which it could decay and that it cannot be created nor destroyed by any natural forces nor by God through the use of any natural forces and agents; 12) is rational; 13) is radically endowed with free will and so on.

 

The New Catechism of the Catholic Church basically indorses the spirit of the above mindset with a greater or lesser degree of emphasis on the particular arguments for such.

 

Scholastics have traditionally made a distinction between the faculties of the human soul and its essence or substance (the ontological meaning of the word). The faculties of the human soul are more or less viewed as accidental properties of the souls whose operation in this life depends extrinsically on the human body/brain. Every experience of the human person is said to modify its accidental properties.

 

The human soul is said to be of a multiplicity in nature meaning that it is multiplied in its relation to the body by being completely present in and completely and totally united to each and every differential portions of the human body.  Since  the human soul is said to be substantially united to the body in this life, and then again to the resurrected human body at the Final Resurrection, such multiplicity is a good aspect of the human soul.  In a real way, such multiplicity adds to the existential or ontological size of the soul for lack of a better word.

 

The Catholic Church’s Tradition which is rich with Encyclicals regarding human nature and its fundamental dignity holds that the each Human Soul is the vital or life principle that constitutes each individual human person as a unique and unrepeatable individual, and as such is the fundamental principle of unity, individuality, and identity in each human person.

 

However the Human Person in this life is not just simply a Soul, but a substantial union of a Body and a Soul. Scholasticism holds that the Human Soul is the substantial form of the Body, not in a geometric shape sense, but rather in the sense of the Eternal Platonic and Aristotelian Forms of ancient Greek philosophy.

 

Now Catholic Theologians that study the metaphysics of material being often refer to something known as Prime Matter or Prime Matters. Prime matter or matters is a Scholastic Theological Concept promulgated in the philosophical writings of Saint Thomas Aquinas that held that the ultimate physical levels of physical reality, the physical cosmos, or of physical material (and by corollary physical energy and space and time) are naturally indestructible and non-transmutable meaning that no created agent by itself, and no created agent being used by GOD, can destroy or transmute prime matters. Accordingly, only GOD by HIMSELF directly can destroy such prime matters by withdrawing his sustaining presence (in the ontological sense of the word rather than the spatial temporal sense) thus causing the prime matter(s) to immediately lapse into nothing or negation, in other words, to immediately cease to exist. Since GOD is All Powerful, GOD can create or destroy or transform or change anything HE desires by an utterly effortless act of HIS all-powerful will.

 

Perhaps between the visible levels of space and time, and matter and energy, there exists a very large finite number, an ensemble, an infinity scrapper, an Aleph 0, an Aleph 1, an Aleph 2, and Aleph 3, and/or so on levels of ever finer, ever more primitive underpinnings of known and currently observable physical matter, energy, space, and time, until the ultimate prime matters are reached. It might also be the case that the number of species of prime matters is very large, an ensemble, an infinity scrapper, an Aleph 0, an Aleph 1, an Aleph 2, and Aleph 3, and/or so on.

 

Note that Aleph 0 is the infinite number of integers,  Aleph 1 is the infinite number of real numbers which is larger than the infinite number of integers by a factor of infinity, Aleph 2 is commensurately larger than Aleph 1, Aleph 3 is commensurately larger than Aleph 2. According to the developer of the concept of Cardinalities, the series of ever higher Cardinal infinite values never ends and proceeds at least up to Aleph Omega where Omega is at least as great as the least infinite ordinal value. Anybody for Aleph (Aleph Omega), Aleph (Aleph (Aleph Omega)), Aleph (Aleph (Aleph (Aleph Omega))) and so on!

 

Now if the Human Soul is the substantial form of the human body, and the Human Soul is substantially united to the Human Body, than presumably the ultimate material underpinnings or constituents out of which the human body is composed must be substantial in a sense commensurate with the possibility of such a substantial union. Whether this substantiality is of a prime matter composition or substance like, or a para-substantial, accidental form of prime matter or as such is derived from prime matter(s), the Human Soul must be said from this notion alone to be wonderfully sublime and transcendent being that it would accordingly, be the substantial form, in the ancient Greek Eternal Forms sense of the word form, of some entity that already embodies prime matter of substantiality.

 

It might be the case that what we currently observe as mass and energy, electrical charge, space-time, bosons, fermions, momentum, atoms, molecule, and all things composed of such, are simply accidental properties, albeit, very stable accidental properties, of more refined and primitive levels of physical accidental being or reality for which the number of levels might well be infinite as conjectured about above. Note that we are willing to except the notion that the universe may be infinite in extent, or that there might exist an infinite number of universes wherein each universe started with its own Big Bang, or that the number of Angels might be infinite or that the number of any extraterrestrial bodily persons on other planets in the universe might be infinite. So why not consider that the richness or the numbers of any levels of hierarchies of ever more sublime and primitive accidental, or substance like accidental levels of being, exist between the currently scientifically visible portion of our universe and also the physical visible constitution or the physical form of our mortal and naturally destructible Human Bodies and any prime matters on which the existence of the cosmos for which we have scientific access is based.

 

If the Human Soul is truly the substantial form of the Body, then it would seem likely to also be the substantial form in some very significant manner(s) to any prime matters on which each human body ultimately rests, even if the mortal nature and constitution of the human body as an organic unit is based on purely scientifically visible and accidental material reality.

 

Note that according to the Standard Model of particle physics and fields,  the still theoretical Higgs Field via its quanta, the Higgs Boson(s), is the mechanism for the generation of mass within our universe. Accordingly, any bodies that have inertia or non-zero rest mass do so as a result of the pervading presence of the Higgs Field which if it exists, would act as a kind of molasses that slows particles with non-zero rest mass down below the speed of light, the speed at which they would travel where it not for the existence of the Higgs Field. We accordingly do not notice the Higgs Field pulling or pushing on anything since it is a scalar field with zero gradient on the level of ordinary atomic and nuclear microscopic scales through the ordinary observable macroscopic spatial and temporal scales.

 

What’s more, the Minimally Supersymmetric Standard Model or MSSM predicts the existence of 5 species of Higgs Bosons thus making the Higgs Field more rich than in the Standard Model.

 

Note that theoretical particles physicists and high energy physicists in general view the discovery and confirmation of the Higgs Field and its field quanta, the Higgs Boson(s) as very likely at the European Large Hadron Collider as it is ramped up to its design collision energy levels sometime next year. The search for the Higgs Boson(s) was the main reason why such a facility was designed and constructed at a cost of about 10 billion Euros which is roughly 10 billion U.S. dollars.

 

Just an aside, if we discover the Higgs Field and learn how to manipulate it, the ramification of technological applications may  go far beyond the alleged technologies of space alien piloted UFOs or Star Trek Science Fiction methods in scope and in wonderment. But such applications, if possible, would not likely become manifest for many years after any broad and detailed study of the Higgs Field(s) and its characterization has been rigorously made.

 

The point to this digression, is that if the Human Soul is the substantial form of the human body, then it in and of itself is by definition a substance or spiritual analogue of prime matter and as such is commensurately more sublime and transcendent that physical prime matter(s). Moreover, the Human Soul as the substantial form of the Human Body would have within itself a huge infinite ocean of existence, to borrow the language of a late 19th century/early 20th century renowned theologian and spiritual writer.  This includes a substantiality of form of any prime matter underpinnings of the human body. Imagine that! The soul as the substantial form of a physical substance or first principle of physical prime matter as well as that all of the physical accidental levels that are derived from any such prime matters and which are embodied in levels of accidental physical being that immediately constitute the living flesh composition of the Human Body.

 

Truly, in spite of the fact that modern science has learned how to manipulate the visible and tangible aspects of the human person and human embryos, and to reap horrible destruction on all human life in the form of body soul unions by modern scientific weaponry, we can take solace that there is still profound mystery in the metaphysics of the human person, and much that we are likely to never be able to comprehend about such in this life. As the late 19th Century/ early 20th Century spiritual writer stated, in this life we see just a surface glimmer of the reality of our souls which are each like an infinitely vast ocean of unfathomable depth.

 

It is good to get back to our spiritual roots and make the case for our Pro-life agenda by focusing more on the fantastic spiritual realities, even natural spiritual realities within the Human Person, and place not so much emphasis the dignity of the Human Person from materialist spiritually minimalist explanations such as the uniqueness of each human genome, the independence of the human embryonic code in just conceived babies, the complexity of the Human Body and Brain and the like nonsense arguments. Rest assure in terms of the number of components and in general nano-circuits, computers will one day out class the human brain in complexity in terms of the numbers of human brain cells and intercellular connections of the human brain with respect to quantum computers, and future supercomputers based on nano-technological circuits.

 

I may be way off base in these speculations, however I hope Saint Thomas Aquinas is happy and proud that I would attempt to delve deeper into the ontology of the human person in the light of modern physics and cosmological theory based speculation.

 

 

 

 

 

 

 

 

 

 

 

8]  WHAT IS THIS BEING CALLED YOU?

 

We are all familiar with the common calling by name of you, or the statement  Someone is manipulating You, or You can do this or that, or the question What happened to You?, or perhaps the question, What is wrong with you/

 

A profound truth is that only You can be You and You cannot be anyone but You. But what is this You of You?

 

We are all familiar of the concepts of Heaven, Hell, Purgatory, and many of us have heard of the place and/or state called Limbo. We can be assured of the Eternity of Heaven and Hell, the temporary reality of Purgatory, and perhaps the eternal reality of Limbo providing that any existent Limbo does not morph into or is not transformed into some higher type of reality whose nature and existence has not yet been disclosed to we humans of Earth.

 

The truth is that each one of us will be our selves regardless of where we spend eternity.

 

One assumes that the condemned souls will last forever or spend literally an eternity in Hell, however, even such being the case, these souls will be the exact same persons as they were on Earth. They will not be someone else. The condemned souls aka persons will remain the individuals they are with the full brunt of the stability of identity as such identity is commensurate with the moral reality that they are eternally punished.

 

A person or a soul cannot become someone else, or a different soul or a different type of being, in short anything that is not who the soul is even in the fires of Hell, otherwise, the concept of eternal punishment would not be valid. If a soul could somehow become something other than the soul or condemned person it is originally, then how could the original person remain in existence or remain real so as to be punished with the particular punishments that are meant for the given soul or person.

 

I do not believe that the fires of Hell can destroy a soul any more than I do not believe in the eternity of Hell. The eternity of Hell is eternal to an extent commensurate with the person or soul in Hell remaining the same soul or person as always. The moral truth of the validity of GOD’s judgment requires that the person or soul thus judged exist as long as the soul or person is being punished, otherwise upon the cessation of the state of the person being the soul or person that the person originally was, the result would be that the original person or soul would no longer be punished since the original person or soul entity would no longer exists as the moral entity for which the punishment was decreed or administered by GOD. Eternal punishment requires by necessity, the eternal existence of the person or entity being punished and the eternal existence or endurance of the person or entity so originally judged.

 

Now since the rigors of the eternal punishment of the souls in Hell cannot destroy such souls, nothing will.

 

A similar argument can be made for a soul still substantially united to its body here on Earth wherein the soul repeatedly falls from the state of grace. The person who falls from the state of grace is still the same person that recovers from the state of mortal sin via the sacrament of confession or other ordinary means, or any extra-ordinary means.  Thus at least while one exists on Earth, the soul or identity of the person remains even after the fall from and through the process of recovery of the state of grace no matter how frequently such occurs.

 

The human soul is the very life principle or vital principle of individuality, identity,   and uniqueness that constitutes who that person is as they are the person that they are. The soul is the very life principle of individuality, identity, and uniqueness by which a human person is a unique individual.

 

Even in Heaven, the souls of the persons judged worthy of Heaven upon bodily death, will remain the same souls they were while they were on Earth just as assuredly as the persons living on Earth now who will go to Heaven will remain as the persons they are currently as to the continuance of their personal identity no matter to what extent they enter into Heavenly Glory or reward. If this were not the case, then the souls that go to Heaven could not be so rewarded because the personal identity of the persons to be or that are so rewarded would not continue indefinitely, a requirement in order for the everlasting glory to be administered. This reality is a kind of compound fact or compound truth with both metaphysical aspects and moral aspects.

 

A similar argument can be made for the case of souls that go to Limbo if Limbo exists, the existence of which is a subject of controversy among theologians of the Catholic Church.

 

Now if the human soul can last to remain the same soul that it is, regardless of the condition of the state of grace or lack thereof, the rewards or punishments dispensed upon judgment after death, and the like, should we not do more to promote the coming into existence of all the more souls such as by being open to the possibility of life and procreation by not using artificial contraception in order to avoid pregnancy.

 

When we use artificial contraception, especially agents that abort the process of contraception that is determinably on track to occur, we cause the soul that would have been directly and immediately created by GOD not to come into existence. In other words, we destroy the potential for the soul to come into existence.

 

Guys need to step up to the plate also and avoid sinful behaviors such as fornication, cohabitation, adultery, oral sex, petting and necking to the point of sexual arousal in pre-marital and extra-marital situations and the like. We will only see an end to abortions when such behaviors are no longer the norm or at the very least, no longer common.

 

Even if it were the case that due to some philosophical inconsistencies, we were lead into the would be conventional erroneous thinking that the entire human soul or the essence of the human soul is  naturally indestructible, and in such a case, the human soul or at least some of its accidental forms might somehow be naturally destroyed or injured in cases such as a living person’s very close proximity to the super intense physical energy and matter scrambling effects at the heart of the nuclear explosion, or in the remote chance that some sort of black hole would swallow a living human person alive an immediately subject the bodily remains of the person so swallowed to such violence to the point where the laws of physics that operate on the physical mattergy of the body would be scrambled along with the body’s matter and energy near the central singularity of the black hole, I am convinced that all such souls in their full essential and accidental forms would be recreated as the exact same souls or persons they once were and that upon recreation, the souls as such would be created incorruptible.

 

Just as all of the dead will rise incorruptible at the end of time in terms of the reunion of the immortal soul with the physical body wherein the physical body will be made incorruptible, any souls that would somehow by ways perhaps known only to GOD himself be completely or at least partially destroyed or injured by any such natural means will also be Resin Incorruptible. Any such souls undergoing such a soul death or injury such as a result of a nuclear war, or exotic natural disaster,  would be all the more glorified at the end of time by Divine power due to the martyrdom of their very existence or life.

 

I do not speak for the Catholic Faith by the speculations in the previous paragraph, and I tend to believe that the human soul is naturally immortal and naturally incorruptible, however, if I am wrong in my assumptions and extreme natural processes can and sometimes do take out souls by ways known only to GOD, I can assure the reader that all such souls would be re-created by GOD in such an incorruptible manner as commensurate with the concept and the reality of the Resurrection of the Dead and the entrance into eternal glory and utter immortality, for which Christ Resurrected human nature is the prototype. Even those condemned to Hell will have their full nature Resurrected Immortal, as a union of body and soul, although the condemned will have to undergo some form of suffering or deprivation whose nature we cannot definitely know at the present in any comprehensive manner since the details of such are not open to human scrutiny at present.

 

The point of all of this conjecture is once again to make the point as to how sinful artificial contraception is especially in cases where the use of such means prevents the conception of a child that is already determinably on track to occur. In such cases, we do not simply injure a soul that already exists, but rather we destroy its ability to come into existence by preventing the process of conception. A human person conceived is decreed by GOD to exist forever no matter where the person spends his or her afterlife. A would be human person whose conception is prevented never even has the chance to come into existence. This is really the ultimate kind of death.

 

 

 

 

 

 

 

9)  THE HUMAN PERSON AS A MICROCOSM

 

 

 

We as human persons are often to tempted to think of ourselves as GODs or as a part of GOD, an aspect of GOD and the like. In reality, we human persons, although being able to partake in the super natural life of grace are not part of GOD, nor are we an aspect of GOD. Assuming that GOD and the universe or more broadly the cosmos are one and the same is in error according to the teaching of the Catholic Faith.

 

Well then, how are we to view are selves as having any real significance in the midst of our daily crosses and toils when there seems to be so much disrespect for the sanctity of human life and persons as made in the image and likeness of GOD?

 

An answer to such a question that should give all of us humans, and presumably any bodily extraterrestrial persons that may exist on other planets, is such that we created bodily human persons are according to the Catechism of the Catholic Church are each like a universe or a cosmos unto ourselves since we possess all of the basic elements of creation in our constitution.

 

First, we have a physical body that is comprised of atoms and molecules which in turn is composed of quarks that form the protons and neutrons in the atomic nuclei and the electrons in the electronic atomic shell structures of the atoms that make up our bodies. From these considerations alone, we know that the force of electromagnetism as embodied in atomic and molecular magnetic moments, electric field via electrical charge, and the electromagnetic radiations emitted and absorbed by atoms and molecules, is definitely represented within our  bodies composition.

 

The strong nuclear force is an essential component  of the protons and neutrons that comprise the atomic nuclei of the atoms the compose our bodies thus the gluons as strong force carriers that bind the quarks together in the subject nuclei are representative of the presence of quantum-chromo-dynamics level of physics that is ubiquitous throughout the atomic nuclei in our bodies.

 

The weak force is also present, not only be virtue of the presence of certain radio-isotopes in trace amounts that comprise our bodies, some of which decay by the weak interaction which is mediated by the W+, W-, and Zo weak force bosons, but also by virtue of the  weak force’s association with the electromagnetic force via the electroweak unification or unified field theory for which the formulation of and its discovery was the subject of a Nobel Prize in Physics in the latter half of the 20th Century.

 

Since all known matter has in effect a gravitational charge, and reacts to gravitation, the fundamental force of gravity is inherent in the constitution of our bodies.

 

Throw in the still theoretical Higgs Fields also since the Higgs field is the Standard Model Field that supposedly results in massive bodies having inertia and mass instead of the material incorporated into massive particles existing as the pure light speed energy equivalence of the inertial mass. Since theoretical super symmetric particles and fields would be related to the known fermions and bosons, throw in super-symmetric mattergy as well, which is a good bet since nature seems to be a unity in terms of operative principles.

 

Second, we share the vegetative life principles operative in plants, bacteria, viruses, and the like as a result of the basic physical and thermodynamic life metabolic activities that operate within our bodies.

 

Third, we share the sensitive, instinctual, visceral perceptive abilities, and abilities for associative learning present in the many fine animal species that populate the Earth. One aspect of our sensitive life that is highly esteemed in modern culture is the instinctual and pleasurable nature of human sexuality, which in its most raw and primitive form is similar to the sexual urges of animals. Yet this same fundamental characteristic of humanity has advanced emotional, affective, intellectual, and even spiritual characteristics that perhaps model the non-sexual intimate discourse that must ashuredly marks the lives of the pure spirits called angels. We must not assume that angels cannot have emotions, or emotional and social affection, in ways that are more advanced then we humans experience it. In fact, since angels are pure spirits, perhaps their emotions although of a purely spiritual and/or intellectual type of nature, are far richer, more intense, and vibrant then human emotions here on Earth because angels are not limited in their psychodynamic processes by a brain or a body, which they do not possess.

 

Fourth; we humans have an advanced brain and advanced cognitive capacities which we most assuredly would share with any existent advanced extra-terrestrial persons and their civilizations, if such beings exist. We have the ability of informed reason, memory, executive level cognitive functions, perceptual filtering, planning, symbolic and abstract thinking, mathematical, verbal, artistic, creative, and advanced intuitional skills.

 

Fifth, we humans possess a spiritual and immortal soul that is free, directly and immediately created, and rational that is gifted with the immaterial aspects of intellect, will, heart, and memory. By virtue of our spiritual and immortal souls, we share the nature of the angels which are pure spirits. We also have powerful faculties within our souls such as the non-corporeal reality based intellect, free will, heart, and memory.

 

Sixth, we humans can share the supernatural life of GOD while in the state of grace and some theological thinkers hold that perhaps all human persons share the supernatural life somehow wrought by Christ’s Incarnation, Life, Sufferings, Passion, Death on the Cross, Resurrection, and Ascension into the Glory of Heaving. In the event that the immortality of the human soul is only such by gratuitous effects such as is the speculation of some modern and postmodern theological perspectives, then even the condemned souls in Hell would in some fundamental sense share in this ubiquitous grace since the Catholic Church has proclaimed the Eternity of Hell. If the human soul is gratuitously immortal, then since all human souls are immortal, all human souls in the next life must possess some measure of supernatural grace.

 

I will not speculate too much on the notion of gratuitous immortality of the human soul since the concept as such is still very controversial.

 

Seventh, for we Catholics, and other Christian denominations for which the Sacraments of Baptism, Confirmation, and Holy Orders are still valid, we are aware that each of these three Sacraments instills a sacramental seal or character in the souls of the recipients of these sacraments which is no mere garment, but which actually imbues the subject souls with a certain supernatural character. Even the souls of those who have received only the Sacrament of Baptism have such a sacramental seal or supernatural characteristic.

 

Note however, that those who are called to the married life and for which the sacrament of Holy Orders in not a possibility, should not despair at not being able to receive the Sacrament of Holy Orders since the vocation of Holy Matrimony according to the Catholic Teaching should not be considered and must not be considered as inferior or less worthy then the Sacrament of Holy Orders, because each of these two vocations has its unique focus and graces associated with it. In fact, the highest creature, the Queen of Heaven, The Queen of the Universe, the Mother of GOD, is none other than the Blessed Virgin Mary who was in fact married to Saint Joseph under the customs of Jewish Law. Heck, she even became pregnant by the power of GOD as she conceived the Child Jesus in Her womb. Mary far exceeds in grace and supernatural life that of any Catholic Priest, Bishop, Archbishop, Cardinal, or Pope, and some theologians would say that she is holier than the entirety of the rest of creation combined. She is truly most full of grace And so even though I have chosen not to enter the Sacrament of Holy Matrimony, for all of those who feel called to do such, or who have already done such, have not fear or regrets, for your calling is truly a magnificent one.

 

Since we so broadly possess the above basic elements of creation, the Catechism of the Catholic Church reassures us that each of we humans is like a universe or a cosmos all unto itself, possessing in some measure the full array of created aspects in the unity we refer to as the human person.

 

We are not GOD or parts of GOD, but we are unique and in some profound respects free and autonomous individuals that are who we are and not anyone else. I say this especially for all of you rugged individualists who long for a sense of ontological identity in a world that has used empirical science as an excuse to remain blinded to the above realities. No doubt, we humans as well as all other creatures depend on GOD for our existence and salvation, however, we possess a unique and unrepeatable individuality and identity commensurate in glory to being in a sense, a whole microcosm to itself.

 

Our very souls, whether naturally immortal or immortal by grace, are the simple, spiritual, rational, free, directly and immediately created vital or life principles of identity and individuality that constitute each one of us as a human person, so much so that it is primarily our souls that constitute each one of we humans as a unique, free, an unrepeatable person.

 

In closing, the point I am trying to make, is that given the above realities of the constitution of the human person, should we not do all the more to respect and promote the dignity of all human life until natural death. Yes, we should even love terrorists, and convicts as assuredly as Christ has called us to love our neighbors and to love our enemies. If we do not visit the imprisoned, comfort the afflicted, clothe the naked, feed the hungry, give drink to the thirsty, our Lord will tell us at the End of Time, that so long as we refused to do such for these least of our brethren, we refused to do so for Him. This is a tough message in a modern civilization that measures a  person’s worth strictly in terms of occupational, psychological, and conventional academic intellectual prowess. Modern existentialism has blinded us the reality that all human persons share a fundamental moral equality before GOD. Don’t believe me? Then read the Catechism where such a statement in clearly made.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

10)  MYSTERIES OF THE HUMAN BODY

 

 

 

As someone who is partial to think about the human soul in preference to thinking about the human body, for whatever particular psychodynamic personality structures I have that might predispose my to prefer the human soul over the body, I thought this morning that it would be enjoyable to compose my a description of my attitudes toward the human body, which those who have a tendency to focus more on the body in preference to the human soul, will probably enjoy reading.

 

It is interesting to consider the marvelous mysteries of the human body that constitute the qualities of the human body that make it a human body.

 

We know of the high degree of complexity of the human body as evidenced from the fact that the human body is comprised of trillions of cells whereupon each cell is composed on average of quadrillions of atoms.

 

When consideration is made at the fundamental biochemical level, the number of statistical quantum mechanical states of the human body is stupendous. The number of types of chemical reactions that occur within the human body, both known and unknown, is enough to be the subject matter of thousands upon thousands of PhD research thesis.

 

Simply considering the complexity of the various human tissues and organs and the self-regulatory feedback mechanisms that maintain the bodies health and equilibrium is amazing and such mechanisms will be material for  PhD research thesis for generation to come.

 

Now we can contemplate the empirical aspects of the human body as known to medical science and bio-chemistry and still not arrive at a full consideration of the mysteries of the human body.

 

We need to delve deeper yet into the world of metaphysics and ultimately religious faith based systems to fully appreciate the meaning and nature of the human body and the mysteries that it presents us.

 

The human body is according to The Catholic Catechism united to a spiritual and immortal soul. This soul is accordingly directly and immediately created, is spiritual, and not reducible to the mere material world. The soul is the seed of eternity we bear within ourselves. Other qualities of the human soul are that it is rational and radically endowed with free will. It is not produced by the parents, nor any form of spiritual semen or any other pre-existing material.

 

Saint Thomas Aquinas held that the human soul in created ex-nihilo or directly and immediately out of nothing. The human soul is accordingly independent of the human body for its existence and to some extent its operations and does not ceased to exist when separated from the human body at the time of death. It is spiritual, simple, and unextended and thus has no separate parts, shape, or other forms of spatial extension. It is accordingly incorruptible per addends and per se. The human soul is also considered by Saint Thomas to be a first created principle meaning that there is no intermediate element or agent that stands between the existence of the human soul and GOD’s creative act of will that caused it to come into being and which maintains it in being.

 

 

Now what qualities of the human body exist by which such an sublime and transcendent reality of the human soul can be substantially united whereupon the substantial union between the human body and the human soul in this life constitutes a complete, full, and autonomous human person.

 

There is some ineffable quality or aspect of the human body by which such a union cannot only take place, but by which such a union is natural to produce.

 

The human body remains a human body even though much of its atomic and/or molecular constituents and even its cellular constituents are replaced over a relatively small faction of an adult human lifetime, yet the human body does not cease being human and maintains a substantial union with the human soul that animates it.

 

There is just something marvelous and perhaps over looked by many spiritual anthropologists regarding mysteries of the human body such as these.

 

The human body is said to be the temple of the HOLY SPIRIT and as such, there is something sacred about the human body. The HOLY SPIRIT would not choose junk for His temple.

 

The human mind brain is strongly effected by neurological states in this life including neural electrical energy patterns, bio-electrical-chemical states, chemical states, and perhaps even by the magnetic and electromagnetic field generated by the electrical activity within the human brain.

 

There is something ineffable about even the primitive emotions, drives, sensory perceptions, moods, and other primal sentient psychodynamic activities and processes that occur within what we call the human mind brain. Since such processes are so strongly coupled to the human brain and its various thermodynamic states, even in consideration that the human brain is substantially united to the human soul as well as is every other portion of the human body, there is some aspect of human brain thermodynamic micro-states, mesoscale states, and macrostates that generates the sentient psychodynamic activities and processes from both an objective and subjective standpoint.

 

This aspect of human ontology that we refer to as the mind, or daily working psyche with all of its qualities of sensual experiences, emotional experiences, conscious thinking, conscious volition, conscious drives, impulses, appetites, and attitudes seems to reside in a “never never land” somewhere between the human body and the human soul, yet which depends on both the human  body and the human soul. There is just something about the physical material, physical states, and physical substance of the human body especially the human brain that helps generate such conscious, sentient, psychodynamic elements of the human psyche. Since the human body continues to live and thrive often even as the human person sleeps or is under general anesthesia such as for surgical procedures, perhaps the human body and/or brain has in at least a limited sense, a sort of primacy over such psychodynamic microstates, mesoscale states, and macrostates.

 

Some thinking in the field of the fundamental aspects of physical  matter and physical energy has held that perhaps pure physical matter and energy has or is somehow conscious, feeling, experiencing etc. This consciousness or feeling may be another aspect of physical mattergy or it may be a fundamental reality that somehow parallels the physical mattergy cosmos but yet which is not the same thing or same reality as the human soul that animates the human body and which is substantially united to the human body in this life. In the event that any such consciousness of physical mattergy exists, it may rather exist as another aspect to mattergy in a manner analogous to the properties of electrical charge, spin, charmness, strangeness, bottomness, and topness, and other fundamental quantum-electro-dynamic and quantum-chromo-dynamic aspects of fundamental baryonic and mesonic matter and its fundamental standard model composition.

 

That faith based organizations especially the Catholic Church hold that a given person’s body is not that of another seems obvious at first, however when one considers that the human body as such is a unity despite the intermingling of the material and energy fields composing the human body with the its surrounding environment, it is easy to develop a sense of mystery as to why  a given human body is precisely one human body and not that of another person as well as a sense of mystery of why the human body, despite such intermingling with its environment is precisely one human body and has only one human soul substantially united to it.

 

A real mystery is how scientifically speaking and therefore factually speaking can the spiritual and immortal soul be so united substantially to the human body wherein the human soul is totally and substantially united to ever differential portion of the human body that is alive. That such a union can take place, even though the union as such is brought about by Divine Power points to a profound mystery as to the ultimate substantial and existential nature of the human body.

 

Ultimately, the human body and the mysteries that surround it obtain their highest form when consideration of the eternal destiny of every human body to be Resurrected at the End of Time, the good to the Beatitude of Heaven, and for those who have definitively chosen to remain separate from God, the sufferings of Hell, of which we have no clear or certain knowledge of the nature of this suffering.

 

Come to think of it, our very own mortal physical bodies will be Resurrected Incorruptible with the same characteristics as Christ Resin body and will be reunited with our glorified spiritual and immortal souls at the Final Resurrection.

 

Our brains are part of our bodies and so all of the powers that our brains currently have will be greatly amplified and exalted in a manner commensurate with our overall Resurrected and Glorified Spiritualized bodies that will still be physical bodies but also spiritualized  bodies at the same time. Wow! What an exalted state of the already stable and conservative properties of mass and energy the compose the human body as it exist before the Final Resurrection in this life..

 

In addition to being reunited to our souls, I believe if I am not mistaken, that The New Catholic Catechism mentions that the Resurrected Human bodies will have their own immortal life definitively granted to them or something similar. I am still trying to find out what that means.

 

What will the Resurrected Human Body be like in Heaven? Many theologians who study the topic would state that the Resurrected Human bodies in Heaven will look absolutely brilliantly radiant and be in perfect Health and of a most beautiful form in terms of shape and features. The glorified human body will no longer be able to or at least will no longer suffer in any way. It will be free from every defect or infirmity regardless of whether or not it suffered from disease in this life in the form of physical or mental, emotional, or psychological disturbances. For all you folks who suffer from brain based illnesses such as bipolar disorder, schizophrenia, major depression, schizoaffective disorder, obsessive compulsive disorder, post-traumatic stress disorder, multiple personality disorder and the like, your mind brain is pre-destined to be exalted in health, power, and function in ways that you simply cannot comprehend in this life. Just as you have been given the cross of your condition, I believe that you are predestined to be glorified in an exemplar manner since with the Cross come the reward of Eternal Glory.

 

The human body will be incorruptible and able to move about from place to place at the speed of though and will otherwise be a perfect instrument of the human soul. The powers of brain based reason, logic, sentient awareness, emotion, and even the five senses will be exalted and enhanced in a manner commensurate with having a glorified body.

 

Part of my quest for my interest in physics is a reflective if only philosophical type of insight into the physical world and by extension, a means to provide a heuristic and epistemological ability to question exactly what our glorified bodies and brains will be like.

 

Not to sound greedy, but Post Resurrection Heaven is there for the asking. No one will have any sense of diss-satisfaction in Heaven. The Catechism states that we all share a fundamental moral equality before GOD. The road to Heaven in this life has its ups and downs but nonetheless can be enjoyable.

 

11)  SOULS

 

 

 

Scholastic theologian interpretations of the belief in immortal human souls hold that the soul is naturally immortal, that it does not survive bodily death because of the grace of God nor through the incurrence of the sacraments of the Catholic Church, but rather is inherently immortal of its own nature. The Scholastics hold that the human soul has no extension in space, has no shape, size, nor separate components into which it can decay or be divided. It is said to be simple and unextended. Thus, it is said to be spiritual and not dependent on matter in any way for its existence.

 

The scholastics also hold that the soul is a first created principle meaning that it is not dependent on any other being for its existence, not even the human body or brain, and that it is directly created by God as its first and only cause for existence.

 

 

Scholastics hold that the human soul is incorruptible per addends and perse meaning that it has no pieces or extension into which it could decay and that it cannot be created nor destroyed by any natural forces nor by God through the use of any natural forces and agents. It is said that only God by a direct act of his will could destroy the human soul but that he would never do so because he never takes back what he has given in his first principle creatures.

 

The New Catechism of the Catholic Church basically indorses the above mindset with a greater or lesser degree of emphasis on the particular arguments for such.

 

Moreover, the Catholic Catechism states that each human soul is endowed to a radical degree with free will and that the human soul is rational.

 

Scholastics have traditionally made a distinction between the faculties of the human soul and its essence or substance (the ontological meaning of the word). The faculties of the human soul are more or less viewed as accidental properties of the souls whose operation in this life depends extrinsically on the human body/brain. Every experience of the human person is said to modify its accidental properties.

 

I believe that the human soul is said to be of a multiplicity in nature meaning that it is multiplied in its relation to the body by being completely present in and completely and totally united to each and every differential portions of the human body. Since the human soul is said to be substantially united to the body in this life, and then again to the resurrected human body at the Final Resurrection, such multiplicity is a good aspect of the human soul. In a real way, such multiplicity adds to the existential or ontological size of the soul for lack of a better word.

 

Some theologians hold that the human free will can almost be viewed as a separate ontological or substantial principle in its self because of its profound ability to produce actions that are not determined by God nor  by the actions’ causes.

 

Thus, for all of you have chosen or will choose marriage and the resultant call to procreation as a corollary, be mindful of the great dignity of your vocation and try not to shun the hassle of day to day provisions for your families. Your children would not have come into existence if it were not for your vocation. This wonderful creature called the human person, body and soul, who is destined to be Glorified and completely resurrected at the Second Coming of Christ has come into existence in part by you who have made the choice to bear children. These children, in fact, any and all descendants in your future family lineages will be incredibly grateful and  respectful of the vocation you have chosen that has led to their creation.

 

So when it comes to election day, vote pro-life. Only you can make the decision to do such according to the dictates of your reasoned arguments. However, remember that untold future numbers of babies and human persons who will be able to grow to maturity just as your kids have or are doing such. There will be untold numbers of thankful persons in heaven to greet you for your actions.

 

The Catholic Catechism also states in line with Catholic Teaching that each human soul is created by a special act of God’s will and immediately. In the original version of the New Catechism of the Catholic Church, the term directly created is used within the table of contents of this brilliant work. The history of the meaning of direct creation is creation completely and entirely directly be God using no pre-existing matter or agents. This is creation directly out of nothing by God. When a child is allowed to be conceived, it is a great victory for the child’s guardian angel and  those who will have the privilege to raise the child to maturity.

 

If you know of anybody who is contemplating an abortion, feel free to pass this article on to them with or without my name attached. My personal authorship of this article is not important. What is important is the giving of all the more souls the life of being created and for those souls who have already been conceived, a right to grow to maturity and the opportunity to become great canonized Saints. You never know, perhaps you yourselves each will  become a Canonized Saint and a great one at that as well as the same for your children.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

12)  THE JOYS OF CONTEMPLATING THE HUMAN SOUL: PART 1

 

 

 

In our modern scientific culture that ever attempts perfected economic efficiency and consumerism of material wealth where having lots of money, a big house, a trophy wife, and a sometimes almost obsessive desire to see one’s children progress beyond their peers in intelligence, intellectual and psychological prowess and in athletic competitions, many have seemed to have lost the sense of the mystery of all human persons as well as the loss of the sense of the existence of spiritual created realities such as human souls and angels. Perhaps even modern theological movements that have put so much emphasis on the body in an attempt to counter extreme spiritualism are partly to blame. It is clear to me that human souls exist in a perfectly happy state in Heaven even though they are not united to their deceased bodies. Even souls that need purging of sin after death in order to reach their eternal reward, in purgatory, I am sure, have full affective and cognitive functionality, in all probability, to a far greater extent than the human persons that are still living in the Earthly realm of everyday life. Is it any wonder that with the loss of respect for the spiritual realms, we would grow to callously disregard the integrity of our physical environment with little concern over the welfare of the integrity of nature and of the other feeling creatures or species we share the planet with? Yes, the New Catholic Catechism does in fact teach that God looks after the animals of planet Earth with His providential care and concern.

 

Regarding the sense of mystery that we seem to have lost regarding our own ontological makeup in its aspects that cannot be seen with the optical vision of our eyes nor with any of our other sensible senses, I would like to offer the above personal thoughts of encouragement that I have come to cherish as a Catholic  middle aged man, although my views do not necessarily represent the official views of the Vatican and Church tradition.

 

A) The Wonders and Transcendent Reality of the Human Heart

 

The human heart, in terms of not only the workings of the affective life of our psyche, but that irreducible inner sanctuary of our being where only we as individuals can be alone with God, that innermost aspect of our being by which we ultimately choose for or against God, is one of the most awesome mysteries of creation. The Holy Bible states in a rhetorical question format something like, “Who but the Lord God Almighty Himself can understand or comprehend the depths of and the tangled workings of the human heart?”

 

As we see behaviors of fellow humans with free will that defy reason, such as criminal acts that defy rationality, acts of bravery on the battlefield that seem to exude super natural courage, and the seemingly intractable complexity of human relationships, from the untreatable paranoid babbling of flagrantly psychotic persons in the dark wards of mental hospitals, to the complexities of the day to day interactions of spouses, that of parents and children, of siblings amongst themselves, and the consciously deeply felt love between husband and wife, girlfriend and boyfriend, that seems to defy rationalization and even takes on a deeply spiritual affectivity that somehow cannot be framed by rational science, we see the wonderful beings we are as made in the image and likeness of God.

 

This intangible yet consciously experienced part of our innermost being, the human heart, is ultimately something that only God can fully comprehend, The human heart, in its natural growth in maturity and its ever ongoing acquisition of new experiences that modify its accidental form, and its supernatural growth in the life of sanctifying grace seems to have been forgotten in our modern life of scientific rationality and economic engines that push for ever greater and more efficient economic output that seems to blind us to higher realities within and amongst ourselves with temptations to make consumerism and having things or accumulating possessions into our God.

 

In a modern scientific society that has advanced so far in its ability to theorize that we have come up with scientific explanations that are mathematically based regarding the birth of the universe or the ability to manipulate and even genetically engineer human embryos, we are tempted to view human life as just another object in this vast, perhaps infinitely spatially extending cosmos, to the point where we have lost a sense of mystery and wonderment, not only about the incomprehensible vastness of the universe, but the intangible aspects that make us human.

 

It has been theorized by cosmologists that what we call the Big Bang might simply be one of innumerable Big Bangs in an ever growing fractal like tree of parent and baby universes. What’s more, its been conjectured that there might by innumerable fractal like trees or fractal-verses, and God only knows where the hierarchy levels stop. Perhaps there is innumerable hierarchies beyond the level of any fractal-verse or multiverse level.

 

Likewise, its been said that each human being is like a microcosm, in short like a separate cosmos because we possess a physical but living body and a spiritual and immortal soul that is of the same level as that of the pure bodiless spirits called angels. Just as our human minds can acquire factual knowledge, abstract understanding, and the prowess of cerebral reasoning skills, let us not forget about the eternal growth capacity of our human hearts.

 

It has been said by logicians that a statement is either true or false, in other words defined as to its truth or falseness by the rules of logic . But there is a higher form of truth that transcends this mathematical logic and that truth is the truth of morality, the truth of the ultimate good, the truth of the human free will, the truth of the purpose for creation and each and every one of us. Ultimately, that truth is accessible by us humans and any other rational beings within the cosmos only within the reality of our hearts.

 

In a society that has become so scientifically motivated, even ironically to the technologicalization, computerization, and rationalization of our base urges to kill our fellow humans by the cold steely destructive power of multi-billion dollar nuclear submarines which perhaps can end all life on the planet, lets take a break and look inward, and amongst each other at those aspects of our nature that we somehow seem to have forgotten. Science and technological progress are good and so is the development of our rational intellectual abilities. As someone trained within the field of physics, I certainly do enjoy science and technology and also the increasing of my own scientific and technical aptitude and abilities. However, let us not let our technical wizardry enslave us in the material world by our ability to manipulate and destroy human life and wreak havoc on mother nature. I am confident that we can and will continue our legacy of scientific and technological progress, however, let us build a civilization of love also. With God’s grace, all things are possible.

 

As we strive to reach out and explore the vastness of our cosmos, let us realize that there is an ever higher truth or to use a phrase borrowed from modern physics, higher dimensions that cannot be quantified. These dimensions are not spatial, not temporal, not spatial-temporal, nor are they intelligible through mathematics. They are the realities of goodness, the ultimate good, purposefulness, the ultimate purpose, love and charity, the ultimate love and charity, morality and righteousness. Who knows, at the sunset of our life here on Earth, when we pass on to the other side, we might find out that there is an infinite number of such non spatial, non-temporal, non-spatial temporal, and non-mathematical dimensions or transcendent realities. We might even find that there exists such a multitude of such realities that not even all of the creatures God has ever created could symbolically define the cardinality of infinity of such higher principles. Perhaps the number is so vast that the concept of cardinality has no meaning or effectiveness at defining the multitude of such transcendent aspects.

 

But first things first. We have a whole solar system to explore with man’s return to the Moon by 2020 according to NASAs plans and the plans of the space programs of other nations, and then onward to Mars and beyond. As we reach out into the vast solar system and ultimately out into our Milky Way Galaxy and beyond, I somehow get a feeling that we will have plenty of opportunity to speculate and theorize on the ultimate meaning of things, perhaps also with any of our intelligent extraterrestrial brothers and sisters as well as to ponder the mysteriously infinite depths of the here and now of our physical universe.

 

B) The Natural Immortality of the Human Soul and its Non-materiality for Those Who are Looking For Some Higher Meaning of Natural Human Dignity.

 

My posting on my own blog site earlier last year offered a materialistic view of the human soul. I have decided to argue the reverse position which is the one chiefly held by Catholic Theologians and which is in line with the statements contained within the new Catholic Catechism of the Catholic Church and its Revised Edition.

 

Scholastic theologian interpretations of the belief in immortal human souls hold that the soul is naturally immortal, that it does not survive bodily death because of the grace of God nor through the incurrence of the sacraments of the Catholic Church, but rather is inherently immortal of its own nature. The Scholastics hold that the human soul has no extension in space, has no shape, size, nor separate components into which it can decay or be divided. It is said to be simple and un-extended. Thus, it is said to be spiritual and not dependent on matter in any way for its existence.

 

The scholastics also hold that the soul is a first created principle meaning that it is not dependent on any other being for its existence, not even the human body or brain, and that it is directly created by God as its first and only cause for existence.

 

 

Scholastics hold that the human soul is incorruptible per addends and per se meaning that it has no pieces or extension into which it could decay and that it cannot be created nor destroyed by any natural forces nor by God through the use of any natural forces and agents. It is said that only God by a direct act of his will could destroy the human soul but that he would never do so because he never takes back what he has given in his first principle creatures.

 

The human soul is said to be that transcendent principle of the makeup of the human person that constitutes him/her as a unique and individual person.

 

The New Catechism of the Catholic Church basically endorses the above mindset with a greater or lesser degree of emphasis on the particular arguments for such. Moreover, the Catholic Catechism states that each human soul is endowed to a radical degree with free will and that the human soul is rational.

 

Scholastics have traditionally made a distinction between the faculties of the human soul and its essence or substance (the ontological meaning of the word). The faculties of the human soul are more or less viewed as accidental properties of the souls whose operation in this life depends extrinsically on the human body/brain. Every experience of the human person is said to modify its accidental properties.

 

I believe that the human soul is said to be of a multiplicity in nature meaning that it is multiplied in its relation to the body by being completely present in and completely and totally united to each and every differential portion of the human body. Since the human soul is said to be substantially united to the body in this life, and then again to the resurrected human body at the Final Resurrection, such multiplicity is a good aspect of the human soul. In a real way, such multiplicity adds to the existential or ontological size of the soul for lack of a better word.

 

Some theologians hold that the human free will can almost be viewed as a separate ontological or substantial principle in its self because of its profound ability to produce actions that are not determined by God nor  by the actions’ causes. God certainly does not will humans to go to Hell or some terrorist with a suicide belt to blow dozens of small children, newlyweds, grandparents etc., to pieces. These children’s guardian angels watch over their subjects just as intensely as our guardian angels watched over us when we were children as well as the various Popes and Saints throughout the millennia. To say that everything happens exactly according to God’s will is simplistic and naive. Part of our greatness as human persons endowed radically with free will (also according the New Catechism) is our ability to interact dynamically with God and make choices for better or for worse. God did not make us deterministic puppets.

 

Thus, for all of you have chosen or will choose marriage and the resultant call to procreation as a corollary, be mindful of the great dignity of your vocation and try not to shun the hassle of day to day provisions for your families. Your children would not have come into existence if it were not for your vocation. This wonderful creature called the human person, body and soul, who is destined to be Glorified and completely resurrected at the Second Coming of Christ has come into existence in part by you who have made the choice to bear children. These children, in fact, any and all descendants in your future family lineages will be incredibly grateful and  respectful of the vocation you have chosen that has led to their creation.

 

So when it comes to election days, for those within the United States, vote pro-life. Only you can make the decision to do such according to the dictates of your reasoned arguments. However, remember that untold future numbers of babies and human persons  will be able to grow to maturity just as your kids have or are doing such. There will be untold numbers of thankful persons in heaven to greet you for your actions.

 

The Catholic Catechism also states in line with Catholic Teaching that each human soul is created by a special act of God’s will and immediately. In the original version of the New Catechism of the Catholic Church, the term directly created is used within the table of contents of this brilliant work. The history of the meaning of direct creation is creation completely and entirely directly be God using no pre-existing matter or agents. This is creation directly out of nothing by God. When a child is allowed to be conceived, it is a great victory for the child’s guardian angel and  those who will have the privilege to raise the child to maturity.

 

The heart of man is referred to as that innermost aspect of the human person by which we ultimately decide for or against God

 

If you know of anybody who is contemplating an abortion, feel free to pass this article on to them with or without my name attached. My personal authorship of this article is not important. What is important is the giving of all the more souls the life of being created and for those souls who have already been conceived, a right to grow to maturity and the opportunity to become great canonized Saints. You never know, perhaps you yourselves each will  become a Canonized Saint and a great one at that as well as the same for your children.

 

C) Musings on the Incorruptibility of the Positive Truth Value of the Goodness of all Rational Spiritual Creatures including but Perhaps not Limited to Human Persons, Angels, any and all Damned Human Souls, all Fallen Angels including Satan, and any Spiritual and Rational Extraterrestrial Beings on Other Planets including all Those that have Died.

 

I am glad to share my further thoughts below on the dignity of the human person.

 

It occurred to me to mention another inherently incorruptible aspect of the human person, the angels, and even the natural good of the damned, the fallen angels, and even Satan himself although the latter beings who have made definitive evil choices use their inherently ontologically good nature for evil purposes. Modern Catholic theology generally holds that all creatures are good and that even Satan, who accordingly has a nature that is inherently very good, although he uses his nature for profoundly evil motives and agendas, has a greatly good nature having been created with perhaps the highest nature of all of the Angels. The reason why it is a sin to curse even Satan in a vengeful way such as wishing God to annihilate him or somehow ontologically tear him to shreds is that like all rational spiritual creatures, he and all other rational creatures by their very spiritual and immortal nature represent God’s creative act in a manner that is special. All created rational and spiritual creatures including all human souls and all humans souls that ever will be created involve a special act of God’s creative genius to be brought into existence out of nothing.

 

Regarding the incorruptibility of each and every rational creatures goodness, although I am Catholic but am not speaking for the Catholic Church, I firmly believe that not even God, who by his very nature of being Truth itself in the form of a GOD with the perfection of personality, can reduce the positive truth value of the goodness of a spiritual rational creature to nothing or change it in any manner at the creature’s natural level of being; neither directly by His Will nor indirectly through the use of another creature or other creatures. Yes, GOD can deprive any natural rational and spiritual creature and any creature no matter how great its state of grace of its existence by reducing it to nothing, but GOD’s memory of having produced the creature and the Goodness of the would be one time existent creature would still per due including the positive truth value of the goodness of the rational spiritual creature as it once existed. God, who is truth itself, cannot erase any form of ontological or eternal truth, and the truth is, all rational spiritual creatures in Heaven, Hell, Purgatory, on Earth, or out on other planets in the cosmos are ontologically inherently good in their nature.

 

Analogous positive truth values of created spiritual rational beings that at least in some sense are absolutely incorruptible and immutably true, even in the event of the annihilation of the creature possessing such by God, involve the concepts of positive truth values for purpose, value, meaning and the like. Who knows where the series of lexicographically defined analogous terms would end. Perhaps we are just on the first stepping stone in an eternal ongoing discovery of such concepts for positive truth values.

 

All of us Catholics, whether or not we profess that faith as we grow older or abandon it altogether, are blessed with the sacramental characters incurred by the power of the Holy Spirit in the Sacraments of Baptism and for those who have received the sacrament of Confirmation, that also. This sacramental seal is no mere garment, but is an indelible supernatural quality that is imprinted or produced within the human soul that per dues forever, regardless of whether or not one spends eternity in Hell or in Heaven. This is why, in part, we must not call down anger in vengeance on any human being whatsoever, especially our fellow Catholics. For all of the readership of this blog who are Catholics, be secure that your baptism and confirmation mark you forever, under absolutely all situations, in a special relationship with GOD. It does not matter whether or not you have turned completely away from the Catholic Faith, you are special in GOD’s eyes and are not inferior to anyone else on the planet. These sacramental seals cannot be erased and mark all Catholics forever as Catholics. The same type of sacramental seal is also imprinted at another level to those who have validly received the sacrament of Holy Orders and obtains it full perfection in those consecrated as Bishops of the Church.

 

For all those who are not Catholic but would like to become Catholic, find a good parish Catholic Priest to talk to, but be secure that while you are not yet Catholic, no matter what your religious faith, you are in no way inferior persons to those of the Catholic Faith. We are all of equal fundamental moral equality before GOD, and that includes all of those who practice any Faith at all, all those who are professed atheists or agnostics, all of those in comatose vegetative states, etc.. Absolutely every human being on Earth is of fundamentally moral equality before the Eternal Father, before Your Eternal Father. This fact is also clearly stated in the New Catholic Catechism of the Catholic Church.

 

For those of other faiths who do not profess Christianity or for those of non- Catholic Christian denominations, realize that the Catholic Church fully holds that you can obtain eternal salvation without being Catholic. I must say that as a Conservative Roman Catholic who believes there is something absolutely special and unique about the Catholic Faith, I will be judged more harshly and vigorously when I pass on to the next life than those who happily and peacefully practice their non-Catholic and even non-Christian faiths. I believe I will be judged more vigorously than even atheists, even professed atheists, who do to no fault of their own have not been able to come to a belief in God yet who nonetheless, guided by grace, in some ways, perhaps by ways known only to God, stand for the dignity and progress of the human race and the human person. Some of these persons may, and I suspect, there some who go straight to Heaven, and perhaps become great Saints although such Saints will probably never be officially be recognized as such in the official process of Canonization.

 

For all of us Catholics, whether Clergyman, religious, single, married, divorced, we must reach out and let the world see the mystery of the Catholic Faith in us so that they can be inspired. Yes, there are objective sins that we all commit, but we must not allow others faults to make us become judgmental or hateful of those who sin, no matter how horribly they sin. The Bible clearly states that there is more rejoicing in Heaven among the angels over one repentant sinner than over 99 who have no need of repentance. We have many lost brothers and sisters out there and we must do our best to lead them back to God. To do such is the ultimate vocation that a Catholic can have.

 

We can build a civilization of love wherein not only the integrity of the natural order of all creation is respected, but also wherein each and every one of us is respected as a Child of God

 

As I was out driving early one morning, say at around 1 AM, I thought that I would take a drive to see the house that I spent some of my earliest years, a house that is located about 12 miles from where I currently live. As I was driving toward this former residence, for which I have very fond childhood memories, I begin to think about just how significant human free will is and the existential and ontological dignity associated with human free will.

 

I began to formulate some thoughts in a mentally articulated manner that I have never really thought before regarding the dignity, and transcendent nature and power of the human free will.

 

First, I reflected on the power of human free will to operate independently of the causes of the choices it produces. This freedom does not simply mean that we are not forced by others to do what we do and that we merely can do what we feel and/or think is appropriate. According to Catholic Theology, it is the ability of the human free will to transcend deterministic behavior, to act in an non-deterministic manner in which the human will can produce acts that are independent, and not determined by the actions causes.

 

Although I have long held a belief in the ability of human free will to act independently of the causes of its actions, another idea occurred to me. Essentially, this idea arose out of the idea that the human free will can do what it was not meant to do by God, in other words, it can simply act in ways it was not meant to do.

 

We can all agree that human free will choices such as murder, terrorist acts, reckless driving, rape, embezzlement of Church funds and the like are human choices that were not meant by God to occur. Some may say that God’s will is always accomplished but I retort in response, not so fast. It is never God’s will that human beings sin. God would never have willed the murder of millions of Jews, his chosen people, at the hands of the NAZI Gestapo, nor the 25 million Russian military troops and brave civilians who died fighting NAZI troops who invaded Russia. God never intended a situation that would arise by which dozens of nuclear submarines from the U.S. and Russia, and several from the U.K., France, and China would ply the depths of Earth’s oceans in a cold calculating manner wherein some of these subs have on an individual basis, perhaps enough nuclear warheads to end the human race if not all life on the surface of the Earth from the combined primary and secondary effects of targeting hundreds of large cities. God never intended Fundamentalists Islamic terrorists to start using woman as suicide bombers to kill dozens of innocent civilians, many of them young children who as young children, their angels go before the Lord on the children’s behalf, to paraphrase Sacred Scripture. The list of examples is huge.

 

What can we make of this human free will wherein even God’s will for us can be thwarted or disobeyed. I am not glorifying evil, but instead suggest that just as we humans have the ability for profoundly evil and un meant to be acts, perhaps with God’s grace we have the ability to go beyond the call of duty as we carry our life’s crosses and pray that ,our loved ones, and even our enemies grow all the more in the state of grace. There just may be some cases, wherein an individual human being desiring to do good to the extent that he or she was not called to do such good by God, or originally not meant to do such good, actually guided somehow in a mysterious way by God’s own grace, goes the extra mile and goes beyond the call of duty. Some folks might say that such cannot happen, at least in any normal sense or times, but we live in extraordinary times and I say, because God has chosen to let us humans make free choices on our behalf and on the behalf of others,  all bets are off on this one.

 

Another concept that occurred to me is the concept of violating the purpose of one’s life by his or her free choices and then coming back with flying colors to do good in the process of conversion. We all know of many instances of individuals who have sinned profoundly but who have come back to the life of grace with flying colors. A good example is that of Saint Paul of the early Church who personally was involved in the death sentences of perhaps hundreds of thousands of early Christians who were persecuted by the authorities for professing and practicing their faith.

 

I believe that God can provide a means for salvific atonement in cases where one takes his own life in a mortally sinful manner by ways known only to God. This notion seems to be clearly implied in the New Catechism of the Catholic Church. Note that the Catholic Catechism says that in many cases of suicide, culpability is reduced and that the chief hindrances to full culpability are mental disorders, fear, torture, etc. For cases where the culpability is reduced and the person who takes their own life is not in the state of mortal sin when he dies, then no means for salvific atonement known only to God is required since a stay in purgatory will then be the means of purification, a means which is known by every practicing Catholic. I personally believe that in some cases, persons who take their own lives go straight to heaven especially those as such who were the unfortunate victims of alleged CIA mind control experiments involving massive doses of LSD and perhaps even brain implants because such persons were martyred in the most horrible way, by the grave attacks on what we in modern civilization view as are inner sanctum, our very psyches. I just cannot see God punishing a poor bedraggled elderly street bag lady that commits suicide in a stupor of depression who has been rejected by her husband, raped, and abandoned by her children as insane who nonetheless stops by a Catholic Church some days and puts a quarter in the poor basket. Only a hypocritical, pretentious,  and self-righteous aristocratic snob could envision God punishing such a woman, and much worse, have a desire that God should punish such a woman.

 

One form of going beyond the call of duty is to make a so-called Heroic Act of Charity daily by which one offers any time up he will spend in Purgatory for the salvation of others and even for others to become Saints, even Canonized Saints, especially for family members and enemies. God will surely not let such Heroic Acts go unrewarded. I cannot think of a more selfless act than to essentially volunteer to spend time in purgatory, even while aiming at a state of sanctity in this life, for ones enemies to become Saints.

 

Even when we use our free will to transcend cause and effect or simply causality, and to in an ironic sense, perhaps by some level of God’s providence,  to transcend the purpose for which we were created, and perform acts that were not meant by God for us to do, we can make the initial choice to come back to God, and then come back into the fullness of Gods grace with the help of God’s grace.

 

Just as we have all inherited a state of original sin, we will be Resurrected at the end of time by the power of God. I believe we will actually be of an incredibly more exalted state because of original sin than we would have had we never sinned thru Adam and Eve. Just as Christ’s Human Nature was exalted and glorified in His Resurrection from the Dead after His Life’s suffering and Passion and death on the Cross, so will all of us as we struggle to overcome sin, sickness, persecution, the hassles of daily life in the life of a working family (a life in modern America which can be among the biggest of crosses due to the anti-life, anti-family culture that has spread through our civilization), the hassles of dealing with other motorists on our highways who treat us rudely, and the list goes on and on.

 

This wonderful thing, we call the human free will, is perhaps far more profound than even our intellects. Let us use our free will to harness our intellects and our hearts for the good of humanity. Only then, guided by God’s grace, will we build a civilization of love.

 

It is interesting to consider the ontological make up of our souls, or to use a more modern term, that of our psyches or personalities.

 

Traditional psychodynamic personality theory held that the human psyche is divided into several main spheres or aspects, but nonetheless. retains its fundamental unity. These aspects were the unconscious, the sub-conscious, and the conscious minds, as well as the id, the self, and the superego.

 

According to Freud, the vast depository of information within the human psych was somehow contained within the unconscious mind, while the sub-conscious mind more or less contained information that was more accessible than the information contained within the unconscious mind and wherein the information contained within the sub-conscious mind was more or less a form of working non-conscious memory that stored information that was more or less readily recallable when needed.

 

The Id was essentially the instinctual or repository for drives, especially the sex drive, while the superego was essentially a guiding principle or set of values that moderates the expression of the Id. The ego or conscious self was essentially what we would refer to as our personalities or our conscious self.

 

Modern neuro-psychology, biopsychology, bio-sociology, and neuroscience have largely done away with the emphasis of Freudian Psychodynamic personality theory, however, the existence of the neuro-physical substrates of our unconscious physical and mental processes, of our drives, instincts, emotions, and memories is still the  subject of ongoing refinement and further knowledge acquisition about human conscious experience. The existence of a neuro-physical substrate for our conscious experiences, memories, thinking processes, behavioral self-regulation, cognition, and acts of volition is also the current paradigm by which that latter processes are interpreted.

 

However, could Freud have been correct?

 

Scholastic theologians have argued for the existence of an vegetative soul in plants that guides and directs the growth of plants and their other life processes. The animalistic soul in animals would involve the emotional and instinctive as well as the sensory perception processes of animals. The animal souls would accordingly also possess a vegetative component commensurate with growth and maintenance of  the life processes of animal bodies. The human soul would be naturally immortal, spiritual, simple, un-extended, and non-material, but would also contain the animalistic soul aspects as well as the vegetative soul aspects.

 

Given that subconscious imagery such as subliminal advertisement processes, public consciousness altering political ads and the like seem to have proven highly effective at altering the attitudes of the general citizenry, perhaps Freud was onto something.

 

 

The prevalence of the interest in sex by adolescents and adults, and the fact that the huge proportion of the adult human population has either married or has had extramarital relations seems to indicate the strong influence that psychic processes that are considered the domain of the Id, have on human behavior and expression. The ubiquitous aspect of marriage, family, and other aspects of human civilization that promote human sexuality as a positive thing seem to indicate the great extent of the influence of human sexuality and related affective aspects of our psychodynamic make-up.

 

Even the Catholic Church, which many erroneously believe to be puritanical, holds fast to the belief that human sexuality is sacred and deeply made in the image and likeness of God. In fact, modern theologians hold in general that the conjugal act in marriage represents the passionate love that the Three Persons of the Holy Trinity as one God have among themselves as well as direct toward we creatures, regardless of whether or not we believe in God, an no matter how badly we sin.

 

In fact, even formation programs for seminarians and candidates for the Ordained Catholic Priesthood are rigorously scrutinized in order to make sure they have a healthy sexuality. The vow of celibacy is not viewed as a way to rid oneself of sexuality, but is rather a means by which Priests, consecrate their sexuality in the service of sacrifice for others. Thus, the Church places strong emphasis that the sexuality of Catholic priests is an integral part of their ministry. After all, Christ himself has and has had while on Earth, a great sensitivity, concern, and respect for woman, especially for  the most sinful woman such as the adulteress who loving came to His assistance and sprinkled olive oil on His feet and who sought His forgiveness.

 

The point is, there seems to be some aspect of us humans, a sort of life force for lack of a better word, that permeates our entire psyche. Modern psychologists tell us that even very young children have a sexuality although it is largely not consciously and/or volitionally expressed in a free manner until puberty or adolescence.

 

At another level, given that modern Catholic theologians hold that the human soul is the vital principle that constitutes each human as unique and un-repeatable.  perhaps this identity constituting aspect of the human souls is completely unconscious since the human personality continues in its fully conscious state even after deep nocturnal sleep, general anesthesia, awakening from a coma, and the fact that our personality and personal sense of identity per dues throughout life even though our memories and other conscious experiences change and vary throughout the waking day, and during dream inducing rem sleep.

 

This identity continuity forming aspect of the human soul might be related to the non-conscious aspects of the soul, and perhaps if the Scholastic Theologians have any sense, the vegetative aspects of the human soul.

 

The Id like aspects of human motivation such as the ubiquitous human sexuality, seems to validate some of Freud’s psychodynamic notions. The Catholic Church has endorsed human sexuality as a fundamental aspect of our makeup, regardless of whether or not we are single, married, or celibate. This being created in the image and likeness of God, to quote the Bible, “male and female” might in some way be related to the principle of our souls whereby our souls constitute us as unique individuals.

 

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We, in a modern scientific culture that demands a rational observational proof of everything created we can think of, are truly amazed at the great pictures taken by the Hubble Space Telescope of Galaxies containing hundreds of billions of star each that are billions of light years distant from Earth. We are rightly impressed and in awe and wonderment about the mysteries of the physical universe and should become ever more so. However, we need to regain a sense of the mystery of our selves, in terms of a belief in the spiritual and immortal souls we have, and also of the pure spirits we refer to as angels. We should recognize that perhaps the spiritual realm by far, is existentially and ontologically, larger than the physical cosmos.

 

For instance, the Bible seems to use a word, if I am not mistaken, to describe the number of angels that God has created, and the word, I believe translates into utterly countless, a sort of crude version of the modern mathematical set theory concept of infinity. Each time a human soul is created, the natural existential, ontological, size of the spiritual cosmos increases, and the number of spiritual elements in the set of spiritual beings in the cosmos likewise increases.

 

When we think about such deep mysteries such as that of our sublime souls, we can get a sense of reverential awe and respect of the created spiritual nature we are all endowed with, and such mystery will no doubt translate into a sense of wonderment in all other aspects of our psychic make-up including the often abused but mysterious aspects of human sexuality.

 

The following arguments may put the process of the sin of abortion and contraception, including sterilization, and the use of the morning after pill, the so-called RU-486 pill in better light.

 

Rather than justifying the murder of the Holy Innocents in abortion, these arguments show the transcendent dignity of the human beings being killed, and perhaps the prevention of God’s creation of a particular human soul (that was determinably on track to be created but perhaps never will because of an act of artificial contraception brought on by the RU-486 pill usage.)

 

The following quotations from the Catechism of the Catholic Church should prove to any Catholic beyond a shadow of a doubt that the Human Soul: is created by God, immediately; and that it is spiritual; immortal; not reducible to the mere material world, but rather can have its origin only in God; it does not die or cease to exist after separation from the body at death; is rational; is radically endowed with free will; is eternal; it is not produced by the parents; and in every case upon coming of age, is capable of receiving the sacraments of baptism and confirmation, both of which, each imprint an indelible sign, seal, or character within the soul.

 

The fact that every such spiritual and immortal soul is open to the possibility of receiving the fantastic sacramental character imprinted in Baptism and in Confirmation should cause every Catholic who would interrupt a conception, prevent a conception that is determinably on track to occur, or to abort a child already conceived, to see how utterly unfair and wrong such an act is.

 

There can be no wavering among Catholic theologians, Catholic priests, catechists, and Catholic Bishops on these facts.

 

Yes, we do indeed have a body which is good and also made in the image and likeness of God, however, I have come to view the arguments such as; “The observation; of the process of conception, the unique DNA of each individual embryo, by modern scientific observational processes proves the embryo to be a full human person”, and other physicalist or spiritual minimalists so-called proofs that the embryo is probably a full human person have gone way too far.

 

We have gradually dissolved our knowledge in the belief of the spiritual, and now try to explain the transcendent dignity of the human person in terms of the body and/or brain alone. I believe this is one of the grave modern errors that Our Lady has warned us of in some of the various Church approved Marian Apparitions over the past several centuries.

 

With large amounts of money being put into research and development of technologies that might one day, in more advanced forms, lead to nanometer scale molecular self-assembly, and computers, that are more complex, by far, then the human brain, we need to rediscover our roots as a species grounded in the belief of spiritual created realities, especially that of ourselves in terms of our spiritual and immortal souls.

 

Rest assure, some of the poor souls in purgatory who have no one to pray for them because, of phrases, such as “May they Rest in Peace” and similar phrases, when used by clergyman, and others, to indicate views points, such as “We really can not know what happens after death.” or “The dead have fallen asleep to be awakened on the last day”, are of no consolation to these poor forgotten souls, who I assure every living adult human, are the very same persons they knew on Earth, and who I can assure everyone, are most fully alive, alert, conscious, affective, feeling, and sadly suffering.

 

Now read through these quotations.

Part 1, Section 1, Chapter 1, SubSection 2

 

33 The human person: with his openness to truth and beauty, his sense of moral goodness, his freedom and the voice of his conscience, with his longings for the infinite and for happiness, man questions himself about God’s existence. In all this he discerns signs of his spiritual soul. The soul, the “seed of eternity we bear in ourselves, irreducible to the merely material”, 9 can have its origin only in God.

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 1

 

360 Because of its common origin the human race forms a unity, for “from one ancestor [God] made all nations to inhabit the whole earth”: 226

 

O wondrous vision, which makes us contemplate the human race in the unity of its origin in God. . . in the unity of its nature, composed equally in all men of a material body and a spiritual soul; in the unity of its immediate end and its mission in the world; in the unity of its dwelling, the earth, whose benefits all men, by right of nature, may use to sustain and develop life; in the unity of its supernatural end: God himself, to whom all ought to tend; in the unity of the means for attaining this end;. . . in the unity of the redemption wrought by Christ for all. 227.

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 2

 

363 In Sacred Scripture the term “soul” often refers to human life or the entire human person. 230 But “soul” also refers to the innermost aspect of man, that which is of greatest value in him, 231 that by which he is most especially in God’s image: “soul” signifies the spiritual principle in man.

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 2

 

366 The Church teaches that every spiritual soul is created immediately by God – it is not “produced” by the parents – and also that it is immortal: it does not perish when it separates from the body at death, and it will be reunited with the body at the final Resurrection. 235

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 2

 

367 Sometimes the soul is distinguished from the spirit: St. Paul for instance prays that God may sanctify his people “wholly”, with “spirit and soul and body” kept sound and blameless at the Lord’s coming. 236 The Church teaches that this distinction does not introduce a duality into the soul. 237 “Spirit” signifies that from creation man is ordered to a supernatural end and that his soul can gratuitously be raised beyond all it deserves to communion with God. 238.

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 4

 

382 “Man, though made of body and soul, is a unity” (GS 14 # 1). The doctrine of the faith affirms that the spiritual and immortal soul is created immediately by God.

 

Part 1, Section 2, Chapter 3, Article 11, SubSection 1, Heading 2

997 What is “rising”? In death, the separation of the soul from the body, the human body decays and the soul goes to meet God, while awaiting its reunion with its glorified body. God, in his almighty power, will definitively grant incorruptible life to our bodies by reuniting them with our souls, through the power of Jesus’ Resurrection.

 

Part 1, Section 2, Chapter 3, Article 12, SubSection 6

1052 “We believe that the souls of all who die in Christ’s grace . . . are the People of God beyond death. On the day of resurrection, death will be definitively conquered, when these souls will be reunited with their bodies” (Paul VI, CPG § 28].

 

Part 2, Section 2, Chapter 1, Article 1, SubSection 7, Heading 5

1280 Baptism imprints on the soul an indelible spiritual sign, the character, which consecrates the baptized person for Christian worship. Because of the character Baptism cannot be repeated (cf. DS 1609 and DS 1624).

 

Part 2, Section 2, Chapter 1, Article 2, SubSection 3

1304 Like Baptism which it completes, Confirmation is given only once, for it too imprints on the soul an indelible spiritual mark, the “character,” which is the sign that Jesus Christ has marked a Christian with the seal of his Spirit by clothing him with power from on high so that he may be his witness. 121

 

Part 3, Section 1, Chapter 1, Article 1

 

1705 By virtue of his soul and his spiritual powers of intellect and will, man is endowed with freedom, an “outstanding manifestation of the divine image.” 8

 

Part 3, Section 1, Chapter 1, Article 1

 

1711 Endowed with a spiritual soul, with intellect and with free will, the human person is from his very conception ordered to God and destined for eternal beatitude. He pursues his perfection in “seeking and loving what is true and good” (GS 15 § 2).

 

Part 3, Section 1, Chapter 2, Article 3, SubSection 2

 

1934 Created in the image of the one God and equally endowed with rational souls, all men have the same nature and the same origin. Redeemed by the sacrifice of Christ, all are called to participate in the same divine beatitude: all therefore enjoy an equal dignity.

 

In addition to these wonderful quotations, we have the Wisdom of Saint Thomas Aquinas, who held that the Human Soul is naturally immortal, spiritual, simple, unextended, incorruptible per addends and per se.

 

When Saint Thomas said that the Human Soul is the substantial form of the body, he was not saying that it physically looked like the body, rather he was using the Platonic or Aristotelian concept of eternal, immaterial, and perfect forms as the reified abstract ideal ideas that things represent.

 

Saint Thomas referred to the Soul as the substantial form of the body, ‘substantial” meaning a first created principle of being that is intrinsically independent of the body for its existence and some of its more advanced operations.

 

I would like to suggest that given the modern paradigms of physics such as the conservation of mass-energy, conservation of electric charge, conservation of baryon number, conservation of momentum, etc, all of which apply in the physical realm, including the human body, that, the human soul represents these ideals in the matter and energy that makes up the human body, even though the human body is corruptible, the mass energy content, electrical charge of the particles that comprise it, seem to obey conservative laws, even after the past three decades of progress in theoretical physics and cosmology.

 

If the human soul represents the eternal substantial form of the human body, it must also represent the conservative aspects of the prime matter that comprises the human body, except in a yet more exulted and elevated manner commensurate with its being an eternal form.

 

I get a feeling if matter and physical energy as to their equivalence cannot be created or destroyed by any natural created process, or at least not by any natural processes that are ordinarily available to harness technologically, then the human soul as the substantial form of the body must ontologically and existentially excel at incorruptibility.

 

When we prevent conceptions that would otherwise occur, we in a, ironically, real sense are killing the human being that would be created in perhaps a more horrible manner than in the abortion of a embryo, or a fetus. To prevent a soul from ever being created by God seems unspeakably horrible to me. Perhaps God, in ways known only to Him, can create such a soul, or a soul/body union as a human person by ways known only to Him, but I am certainly unaware of any such creational mechanism.

 

Some folks who read this posting, might consider me off base, or not modern, or not with the program of modern science, however, I will offer a rebuttal by saying that I hold an undergraduate degree in physics, and have had a few graduate level courses in physics and one in math, and am co-inventor and co-holder of a number of U.S. patents, and am patent pending on dozens of additional patent application in foreign jurisdictions.

 

I do not intend to make this a brag session, however, my training in physics, and work as an inventor in the field of portable renewable energy equipment, insitu resource acquisition systems, and disaster and humanitarian relief equipment, has not blinded me to the reality that some things, although viewable in the light of natural reason, are beyond the scope of experimental and observational science.

 

Ultimately, I feel that we will find that we can never experimentally discover the human soul. But such sublimity of the human soul should not prevent us from using mathematical-like, logical and philosophical reasoning to prove that it exists, or to make reasonable arguments for its existence.

 

I think that the whole Roe verses Wade fiasco and the artificial contraception and sterilization liberal movement started in the 1960s will only be remedied when we rediscover a belief in created spiritual entities, and that includes the belief in a immediately and directly created, spiritual, and immortal human soul.

 

I am not trying to talk over anyone’s head in this posting, but am trying to instill a sense of wonderment and mystery, in all of those who read this posting but who long for a sense of mystery, wonderment, and reverential awe regarding their own selves, in those of others such as in newlyweds, spouses, those who have recently fallen in love, and even clergymen, Deacons, Ordained Priests, Bishops, and Cardinals who have lost a sense of the marvelous thing that a human soul is, each of which that was ever created will last utterly forever, long after the last Sacred Host is consecrated during Mass and long after the very last sacramental confession is heard.

 

One can consider  the power, strength properties, or functional strengths of the human soul and the transcendent higher aspects of the human soul.

 

First, we must realize that for each act of conception God creates a human soul and units this soul to the new human body.

 

As the reader will now find evident, I tend to believe as Saint Thomas Aquinas believed that nothing created whatsoever can destroy the human soul. I tend to view the human soul as spiritual, eternal, naturally immortal, incorruptible per addends and per se, intrinsically independent of the human body including the human brain for both its existence and to some extent its operations, simple, un-extended, immaterial, and which is a first created essential or substantial principle.

 

For those of us who are Catholics,  from any reasonable interpretation of the New Catholic Catechism of the Catholic Church, we know that the human soul is: spiritual, immortal, the principle of unity within the human person that constitutes each human as an individual, free, radically endowed with free will; the seed of eternity which we bear within ourselves; immediately and directly created; rational; and not reducible to the mere material world and that it is created by a special act of God which puts the soul forever in a special relationship to its creator.

 

In addition, we know from Catholic Tradition that the human soul is multiply and completely present in every differential portion of the human body that is alive. We know that it is created Ex Nihilo, out of nothing directly from God and that it is not produced by the parents nor through some sort of spiritual semen or spiritual seed.

 

As mentioned above, some great Catholic theologian near the turn of the 19th century stated that the human soul is an immortal person that no one but ourselves has access to, not even the Almighty God in the real sense, that only we can make the free choices we make for good or for evil by ourselves. Only we can touch our souls in this sense because only we can make our own free will choices.

 

The power of the radically free human will which can make mortally sinful choices and then make a perfect act of contrition the next hour and/or a sacramental contrition in the confessional says something about the power of our spiritual identity, vital life principle of personal identity, or our souls: The ability to act in radical and in unpredictable manners in ways that are radically undetermined in their causes.

 

Yes, our freedom to sin and come back to the state of grace again and again is indeed profound. If sinless bodily ETI life forms or UTI life forms cannot not have the freedom to sin, we are in a sense more free and have more powerful freedom of will then they have. The power of our human free will is astounding and so is the transcendent property of our souls by which we are vested with such power.

 

This same late 19th century theologian stated that each human soul, each human person that has ever existed has his or her current experiences, thoughts, feelings, acts of will, whether on Earth, in Heaven, in Purgatory, in Hell, and in any form of Limbo state.  Each such human soul is an immortal being that only that very same soul has access to.

 

Baring some unknown philosophical inconsistency in human and Church teaching on the Human soul such as the remote chance it could be destroyed by the furious bodily matter and energy form scrambling capability of a nuclear explosion, a notion I brought up in a previous posting, simply to make the point that we will all be resurrected incorruptible on the last day, no matter what happens or could remotely happen, we will and are meant for eternity and will live eternity in Heaven or Hell, even if by some remote chance as might be  known only to God that our souls might somehow conceivably be naturally destroyed on a temporary basis.

 

Any such destroyed souls would be, I am sure, Resurrected on the last day, and in the off chance as perhaps known only to God, in any such cases, such souls I believe would be Resurrected with an increased level of both natural and supernatural glory, nature, and characteristics at both the essence-wise or substantial level and at the accidental level for having gone through the martyrdom of the cross of the temporary nature of annihilation.

 

The point is regardless of whether the human soul is naturally immortal or not, it will last for all eternity and this fact  is decreed by God’s unalterable and Almighty Providence: The soul is indeed Immortal.

 

The Bible speaks of the whole human person, body and soul as being Resurrected at the end of time, and that even the damned will be resurrected incorruptible although they will have to undergo some unspecified suffering which we at present really cannot not know about as to the nature of this suffering and how the suffering will vary with time in the depths of eternity. However, we will all be Resurrected incorruptible, no if, and, or buts, no exceptions what so ever.

 

By the way, if the human soul is so transcendent, then why would anyone want to prevent the conception of a human being whereupon in the process of conception, God directly and immediately creates a human immortal soul.

 

Each time anyone conceives, a new human person is brought into being, body and soul, and the soul comes into being by a special creative act by God. Thus, procreation by human persons literally leads to the increase in the size of the cosmos, in terms of the spiritual cosmos by permitting a new spirit or a new human soul, to come into existence.

 

 No! The human soul does not somehow cease to exist and await recreation at the end of time through its union with the body. I assure the reader that each soul in Heaven is perfectly naturally and supernaturally happy and is perfectly naturally and supernaturally alive.

 

Those spiritual minimalists who want to downgrade the status of the human soul as only having meaning or existence when united to a human body, I assure the reader, are doing a great diss-service to the Poor Souls suffering in Purgatory by ignoring or trivializing the nature of the Poor Souls in Purgatory who I assure you are most fully alive, fully conscious, and fully suffering.

 

Now the above discussion of the human soul in terms of its nature as: spiritual, eternal, naturally immortal, incorruptible per addends and per se, intrinsically independent of the human body including the human brain for both its existence and to some extent its operations, simple, un-extended, immaterial,  a first created essential or substantial principle; are what I will refer to as the power or strength properties of the human soul. What I will discuss below are the transcendent properties of the human soul.

 

We know that human nature, although wounded by original sin, is inherently good, for God created all things good. When we think of goodness, we sometimes tend to think of some eternal abstract principle of goodness, a sort of Platonic Eternal Form, and since we are told from our childhood that God is Good and that God is Goodness Incarnate, goodness in our minds takes on some sort of ineffable transcendent nature that goes beyond the fact with reference to our souls, of the power or strength properties of our human souls. We see the reflection, the image and likeness of God, in our spiritual and immortal souls as well as in our physical living bodies. I believe this image and likeness of God goes beyond the power or strength properties of the human soul although such power and strength properties of our souls are inherently very good in and of themselves.

 

For we who are Catholics, one way that we can get a grip on the distinction between power and strength properties verses transcendent properties in terms of Goodness is to take the example of the Holy Eucharist which Catholics belief is the body of Christ. Catholics hold that the bread of the Sacred Host and the wine, when consecrated at in the Holy Mass, are the Body and Blood of Our Lord Jesus Christ. As such, the consecrated host and wine having become the Body and Blood of Christ take on an infinite level of goodness or infinite value as becoming substantially the Body and Blood of Our Lord Jesus Christ.

 

Note however, the great deal of corruptibility of the Consecrated Sacred Species. The Sacred Host can be dissolved within the human digestive track and in fact is so dissolved in about 10 to 15 minutes after reception of the Sacrament of the Holy Eucharist. The Sacred Host and Sacred Wine can be destroyed by fire, other natural elements, etc. For us Catholics, we see the infinite goodness of the consecrated sacred species yet we see the mechanical, and chemical frailty of the Sacred Species.

 

Another example that I can give is our intellectual assent to the goodness of some 100 year old lady that has lived a full life, and which was known by her children to have been devoutly religious, whatever her faith may have been, yet who falls into a state wherein her cognitive powers are greatly weakened, or perhaps becomes bed ridden and so weak that she could not even defend herself from a diminutive house cat. Many of the readership I am sure can relate to personal knowledge of some special elderly person in their lives that stood out as particularly virtuous in terms of the manner in which he or she lived life, but which at the sunset of his/her life on Earth, fell into the state of cognitive weakness and physical frailty due to common illnesses such as dementia, stroke, cancer, and the like. Yet, we do not think any less of them in their goodness. We therefore hold that the principle of goodness within our elderly relatives as such continues to exist even though the elderly become very weak and frail, mentally and/or physically.

 

Another transcendent principle to consider is one of value or worth. As Catholics, we hold that God the Father loves us so much that He sent His only Son to die on the Cross for us in order to redeem us. We even hold that Jesus would have Suffered His Passion and Death on the Cross for each and every one of us over and over again, for as many times as there are or will exist human beings if such was necessary to save us. Thus, since God would have and in fact did Sacrifice His only Begotten Son for us and for our Eternal Salvation, we are left to conclude that God views each one of we human beings or human persons as having infinite value or worth, and as worthy of His Infinite Love.

 

It has even been said by some historical figure within the Catholic Church or some devout person, I cannot remember the exact circumstances, that Christ still grieves over the rebellion of Satan. If Christ can be so loving so as to grieve over the loss of friendship with Satan, and also to willingly die on the Cross for each and every one of us, our spiritual and immortal souls must have infinite value and by association, so must our physical bodies.

 

That we can have infinite worth and yet consider God to be Infinite is not a contradiction. We can from the mathematical theories of George Cantor see that there exist greater and lesser infinite numerical values.

 

We can start out with the concept of Aleph 0 which is the infinite number of the number of counting numbers, followed by the concept of Aleph 1, which is the infinite number of the number of real numbers which is much greater than Aleph 0.  Simply think of the infinite number of real numbers that exists between, say the numbers one and   two on the real number line including all decimal numbers; all such numbers including rational, and irrational numbers.

 

Likewise, we can consider a sequence of ever greater cardinalities that exist as defined by the infinite series Aleph 2, Aleph 3,…

 

As a review, we will note that the Cardinality of Aleph 1 is the Cardinality of the Continuum according to the Continuum Hypothesis and is equal to c = 2 EXP (Aleph 0). Beth 1 is equal to Aleph 1 and Beth 2 is equal to 2 EXP c = 2 EXP (Aleph 1) = 2 EXP  [2 EXP (Aleph 0)]. Beth 2 is equal in number to the elements within the power set of R (where R is the set of real numbers) or the total number of all subsets of R. Thus, Beth 2 = 2 EXP R > Aleph 1 = c.

 

The point is that if we can consider ever greater numerical or quantitative infinite values, why not consider ever greater qualitative, moral, ontological, metaphysical, or existential values. I believe that Jesus did as implicit in His Life, Passion, and death on the Cross for each and every one of us. Thus, we have now considered the qualities of the infinite value and infinite worth of  each and every human soul.

 

Now we move on to the transcendent aspect of the human person as having purpose. Purpose is another Platonic Eternal Form that seems to transcend but which includes the power or strength characteristics of the human soul. Because God went through the special unique creative process by directly and immediately creating each and every one our spiritual and immortal souls, he has a purpose in mind for us each on an individual level. This purpose in a very real sense is an inherent property of our human spiritual and immortal souls which are the principles of identity, unity, and individuality within each and every one of us human persons that constitutes each and every one of we human persons as a distinct, and unique individual. This inherent purpose for our being is our inherent meant to be aspect of our existence and exist forever regardless of whether we end up in Hell or Heaven. If those souls in Hell and the fallen angels including Satan did not have any purpose, God would simply let them lapse into nothingness by withdrawing these fallen persons from existence. Even though the Eternity of Hell is held as a central truth of the Catholic Faith, I do not think that we are given the whole story about and purpose for Hell by God as of yet. Perhaps no creature, including the souls of the Saints in Heaven, the good angels in Heaven, and perhaps not even the Blessed Virgin Mary has been given the full story about the reality of Hell and its purpose as may only be known by God the Father. The Divine Economy is ultimately a great mystery which will take all eternity to unfold because it is part of God’s eternal plans.

 

Regarding the subject of Goodness, all creatures are said to possess ontological goodness. Even Satan who was created as such a great or high angel retains most or all of his natural strength or power and intelligence and since he is such a great creature in terms of the level of his created nature, he perhaps has the highest level of natural ontological goodness relative to any of the other creatures God has created including all of the Saints, and all of the good Angels. However, Satan and his fellow fallen angels now use their good natures for evil purposes in spiritual behavior that is morally wrong. Likewise, all human souls that were ever created possess a great deal on ontological goodness even the souls in Hell.

 

Moral Goodness, which is possessed by all human persons on Earth to a certain extent, and to a great extent by the Souls in Heaven and Purgatory as well as the good angels, is distinct from ontological goodness. Moral goodness seems to be predominantly lived out in the accidental properties of the human soul, in particular, lived out chiefly within the faculty of the human soul of the human free will. Thus, moral goodness is possessed to a great extent by the human souls in purgatory and in Heaven, and by the good angels, and perhaps to extents known only to God, the souls in Hell and also perhaps by the fallen angels.

 

There also might exist additional categories of goodness for God ‘s creatures, other than ontological goodness and moral goodness, that God has not yet revealed to any of His creatures, certainly not yet to we humans here on Earth. Perhaps there is an indefinably infinitely ordinal valued Cardinality of Infinity of such distinct forms or aspects of Goodness just waiting to be gradually revealed to us as we live out eternity having access to the wonders of all creation and also the wonders of God.

 

Now we have described several so-called ontological transcendent aspects of the human soul. These are value, worth, purpose, ontological goodness, and moral goodness. Other such ineffable transcendent aspects are meaning, truth, etc. In fact, there may exist, and I suspect there is, an indefinably infinitely ordinal valued Cardinality of Infinity of such distinct so-called ontological transcendent aspects  or realities just waiting to be gradually revealed to us as we live out eternity having access to the wonders of all creation and also the wonders of God.

 

Note that the strength or power aspects of the human soul such as its characteristics of being: spiritual, eternal, naturally immortal, incorruptible per addends and per se, intrinsically independent of the human body including the human brain for both its existence and to some extent its operations, simple, un-extended, immaterial,  a first created essential or substantial principle and perhaps other characteristics of equally broad scope which we are not yet aware of are inherently good, worthy, valuable, purposeful, and meaningful to a great extent and together with the human soul’s ontologically and existentially transcendent aspects, make the human soul and all the more wonderful creation. This is precisely why any act of conception or procreation which is determinably on  track to occur must be allowed to occur and not be prevented such as through the use of the so-called morning after pill or the RU- 486 agent.

 

I remember having an argument with my Father well over a decade ago who is been deceased for about 3 ½ year now, but who also is Catholic whereby I was trying to make the point that if a conception that was meant to be did not happen, then God could simply still permit the human being to come into being with another body to which the soul that would have been created and united to the would have been human body could still be created and united into another different body. My Father quickly pointed out to my dismay that the to be created human being would then not still be the same person because the human person is a unity of body and soul wherein the human soul is created in uniform to the body it will inform or is or was meant to inform. Perhaps God in special extraordinary circumstances can create a meant to be human person whose procreation was aborted in the form of another body by ways known only to GOD. However, such it would seem would be no ordinary circumstance and would imply GOD acting outside the bounds of the Catholic Theology of the Body. GOD can nonetheless act and create as He pleases, and the Catholic Church cannot put any limits on GOD’s creative power as much as the Church Hierarchy might like to determine artificial bounds on GOD’s Almighty Creative Power.

 

But my Dad’s insightful opinion offered about 2 decades ago has led me over the past few months to consider the following concepts.

 

Since the human soul is the human soul that it is for each given instance of the human soul, and since the very nature of the human soul is to be the principle of identity, individuality, and unity of the human person possessing the soul, and since the human soul we know by the New Catholic Catechism of the Catholic Church is spiritual, and immortal, and not reducible to the material, we can be assured that the qualities of a particular human soul at the substantial or essential level of the given human soul cannot be separated from the soul, cannot be destroyed without GOD’s destroying the human soul, and as a result, assume a certain level of utter indestructibility in the sense that the soul cannot be the soul that it is without these substantial or essential characteristics that make a particular human soul the human soul that it is.

 

This argument can be made based on the premise that the characteristics of the human soul that are of the most significance and of the most basic, primitive, and fundamental nature of a given human soul are the ontological attributes that make a given human soul the exact substantial principle of unity, identity, and individuality of the human person possessing the soul. According to the Catholic Catechism, each human soul is unique and unrepeatable.

 

Since the human soul of a person possessing that particular human soul cannot be the soul of another person being that such a given human soul is the spiritual, immortal, principle of identity, uniqueness, and individuality of the given human person possessing the soul, this soul can only be the soul that it is and not another soul. This attribute of the human soul cannot be erased or destroyed; otherwise, the soul possessing such an attribute would be changed or substantially destroyed thus effectively implying the destruction of the human soul as it would otherwise be substantially changed. In a sense, this principle of identity, unity, uniqueness, and individuality of a given human soul cannot be destroyed and this principle nature of the human soul is not some mere accidental nor  even an ancillary substantial characteristic of the given human soul, but is rather what it means for the soul to be a soul and what it means for the soul to be the unique soul that it is. If ever there was a most essential principle of a given human soul, it is its characteristics as an absolutely unique definer of the individuality, unity, and identity of the person it comprises.

 

Since the soul is the very life or vital principle of the human person in terms of the human person’s non-material aspects, this life principle or vital principle of the human person is by definition identical with the human soul. Thus, the fact that the human soul is the natural spiritual vital or life principle of the human person who possesses the given human soul, the quality of the soul as being ontologically identical with the vital or life principle of the human person possessing the given human soul cannot be separated from the soul. Such a vital principle is the soul itself by definition and so  the only way that the vital principle of the human soul can be destroyed is for GOD to destroy the whole and entire human soul altogether.

 

In a sense, the ontological aspect of the interface of both the principle of the human soul by which it is the principle of identity, unity, and individuality of the human person possessing such a soul and the principle by which the human soul is the spiritual vital principle  or life principle of the person possessing the given human soul with the substance or essence of the soul itself, is utterly indestructible in the sense that the existence of a given human soul necessary implies such an ontological interface at the deepest natural levels of human spiritual composition. Perhaps such an interface is not merely an abstraction, but has real existence or being as some sort of super-ontological or super-existential reality associated with the human soul.

 

The fact that the human soul is created in uniform with the body it will inform may entail that perhaps  even the secondary aspects of the human soul such as a person’s given faculties of his or her particular intellect, will, heart, and memory etc., may be inseparable from a particular soul that possesses the given set of faculties.

 

Perhaps the accidental properties that are stored as experiences within the unconscious and subconscious minds of the faculty of the personality or psyche of a given human soul cannot be erased from the soul either. This would be fact, if indeed it is a fact, might somehow be related to the concept that only we can make our own free choices by definition of our own free choices. In a sense, not even GOD can make our free choices for us, since our choices that are free are by definition made with full freedom, deliberation, and self-possession by our own wills.

 

Thus, our very own free wills might not be separable from our spiritual and immortal souls. It has been said that folks who definitively have chosen Hell after death have chosen Hell such that not even the punishments of Hell in all of its potential fury can cause the person not to choose the Hell that He or She chooses for His or Her self. If the fires of Hell cannot separate the Human power of free volition which is the human free will from its soul, then perhaps absolutely nothing can. The soul would have to cease to exist for the will to no longer exist.

 

Regarding the human free will, it by definition can act in manners that  are undetermined in their causes. Thus, the human free will can act independently of GOD’s will and even act contrary to GOD’s will. Yes folks, we have that much power in our free will. It has been said by some Catholic Theologians that the human will can thus in a valid sense be considered as if it were a complete and entire nature in itself. Let us use the wonderful free will that we have for charitable and loving purposes.

 

The concept of the Human Soul is in a way a great mystery. As mentioned above, for those of us including myself who adhere to the traditional Catholic Scholastic concept of the human soul, the human soul is: spiritual, immortal, independent in its existence from the human body including the brain and to some extent its operations, naturally immortal, incorruptible per addends and per se, simple, un-extended, eternal, rational, free, immediately and directly created, substantial, a first created principle, endowed with the faculties of intellect, will, heart, and memory and the list of wonderfuls goes on.

 

From the New Catholic Catechism, we know that the soul is immortal, free, rational, spiritual, eternal, directly and immediately created, not reducible to the mere material world, the seed of eternity we bear within ourselves, radically endowed with free will etc.

 

But yet we note that in this life the soul is substantially united to the human body and according to the New Catholic Catechism, has to be considered the form of the body, not in the geometric shape sense, but in the Platonic and Aristotelian sense of the meaning of eternal abstract forms.

 

Thus, the human soul remains for philosophers and theologians a great enigma. On one hand, it is capable of existing independently of the human body after bodily death and indeed is perfectly happy in Heaven and in Limbo if such a state exists and so does not need the human body to exist and be fully happy. One the other hand, it is substantially united to the human body in this life and so has the capability of substantial unity with a physical entity and as a result, in addition to being spiritual, it has an ability to be oriented toward the physical in terms of its very substance or essence.

 

Perhaps the above enigmatic quality of the human soul  somehow makes it a more rich or larger type of spiritual or created entity in the existential, substantial, or ontological sense that the pure spirits known as angels who do not have bodies nor are united to bodies.

 

To be a spiritual substance and yet have a quality by which the human soul can be substantially united to the human body and be effected in terms of its faculties of heart, intellect, will, and memory by the human body and the accidental properties of these faculties in a sense makes the human soul a fuller and larger substantial and perhaps even accident-wise principle than the pure spirits referred to as Angels.

 

Note that the following paraphrase of Sacred Scripture, “Who but the Lord God alone can comprehend the tangled workings of the Human Heart”, points to the immense complexity of the Human Heart, but with complexity come existential size and existential variety.

 

Some Catholic Theologians would say that; since the human soul is naturally meant to be united to a human body, it is an incomplete substance. Perhaps any such incompleteness in substance of the human soul points to the fact that it may be the most pure form and simple form (in the ontological sense of the word) of created substance because it does not have the existential or ontological baggage of being weighed down by having the form of a complete substance such as exists in the form of the pure spirits known as angels. In a real sense, the human soul may be more ontologically simple, and by a long shot and I am going out on a limb here, perhaps more exemplar of natural incorruptibility and natural immortality that are the pure spirits of angels.

 

The following notion may be somewhat of a play on words, but the human soul being that it is the substantial vital or life principle of identity, individuality, and unity within the human person, perhaps it is in a way, more of a raw or pure form of created existence than the pure spirits of angels. This principle of identity, oneness, individuality, and unity within the human person might be more one and more simple than even the angels being that the human soul is precisely the substantial principle of identity, oneness, individuality and unity within the human person.

 

What’s more, the human person, in the form of a body and soul union appears to be able to  grow without limit in terms of the life of grace, at least in this life, and appears to be able to acquire knowledge and evolve in terms of the accidental forms regarding the human psyche or mind without limit as each human person acquires knowledge, memories, talents, and wisdom.

 

No doubt, angels being pure spirits are more intelligent, strong, and powerful in will than we humans since they are not limited by the bondage of having a body, but they cannot in theory grow naturally in wisdom, mind, will, and heart, since they are given all of their natural knowledge, wisdom, and talents from the beginning of their creation.

 

We humans can in theory grow without limit in terms of intelligence, mind, heart, will, memories, and even in the life of grace, not only in this life, but perhaps also after the Final Resurrection of the Dead when we get our bodies back: Bodies that will be mysteriously spiritualized, immortal, incorruptible, and which will have their own life definitively granted to them.

 

Given the wonderful thing that the human person is, who could in their right mind desire to prevent a conception that is determinably on track to occur or abort a human embryo of fetus growing in its mother’s womb.

 

The concept of the Human Soul is in a way a great mystery. For those of us including myself who adhere to the traditional Catholic Scholastic concept of the human soul, the human soul is: spiritual, immortal, independent in its existence from the human body including the brain and to some extent its operations, naturally immortal, incorruptible per addends and per se, simple, un-extended, eternal, rational, free, immediately and directly created, substantial, a first created principle, endowed with the faculties of intellect, will, heart, and memory and the list of wonderfuls goes on.

 

From the New Catholic Catechism, we know that the soul is immortal, free, rational, spiritual, eternal, directly and immediately created, not reducible to the mere material world, the seed of eternity we bear within ourselves, radically endowed with free will etc.

 

But yet we note that in this life the soul is substantially united to the human body and according to the New Catholic Catechism, has to be considered the form of the body, not in the geometric shape sense, but in the Platonic and Aristotelian sense of the meaning of eternal abstract forms.

 

Thus, the human soul remains for philosophers and theologians a great enigma. On one hand, it is capable of existing independently of the human body after bodily death and indeed is perfectly happy in Heaven and in Limbo if such a state exists and so does not need the human body to exist and be fully happy. One the other hand, it is substantially united to the human body in this life and so has the capability of substantial unity with a physical entity and as a result, in addition to being spiritual, it has an ability to be oriented toward the physical in terms of its very substance or essence.

 

Perhaps the above enigmatic quality of the human soul  somehow makes it a more rich or larger type of spiritual or created entity in the existential, substantial, or ontological sense that the pure spirits known as angels who do not have bodies nor are united to bodies.

 

To be a spiritual substance and yet have a quality by which the human soul can be substantially united to the human body and be effected in terms of its faculties of heart, intellect, will, and memory by the human body and the accidental properties of these faculties in a sense makes the human soul a fuller and larger substantial and perhaps even accident-wise principle than the pure spirits referred to as Angels.

 

Note that the following paraphrase of Sacred Scripture, “Who but the Lord God alone can comprehend the tangled workings of the Human Heart”, points to the immense complexity of the Human Heart, but with complexity come existential size and existential variety.

 

Some Catholic Theologians would say that; since the human soul is naturally meant to be united to a human body, it is an incomplete substance. Perhaps any such incompleteness in substance of the human soul points to the fact that it may be the most pure form and simple form (in the ontological sense of the word) of created substance because it does not have the existential or ontological baggage of being weighed down by having the form of a complete substance such as exists in the form of the pure spirits known as angels. In a real sense, the human soul may be more ontologically simple, and by a long shot and I am going out on a limb here, perhaps more exemplar of natural incorruptibility and natural immortality that are the pure spirits of angels.

 

The following notion may be somewhat of a play on words, but the human soul being that it is the substantial vital or life principle of identity, individuality, and unity within the human person, perhaps it is in a way, more of a raw or pure form of created existence than the pure spirits of angels. This principle of identity, oneness, individuality, and unity within the human person might be more one and more simple than even the angels being that the human soul is precisely the substantial principle of identity, oneness, individuality and unity within the human person.

 

What’s more, the human person, in the form of a body and soul union appears to be able to  grow without limit in terms of the life of grace, at least in this life, and appears to be able to acquire knowledge and evolve in terms of the accidental forms regarding the human psyche or mind without limit as each human person acquires knowledge, memories, talents, and wisdom.

 

No doubt, angels being pure spirits are more intelligent, strong, and powerful in will than we humans since they are not limited by the bondage of having a body, but they cannot in theory grow naturally in wisdom, mind, will, and heart, since they are given all of their natural knowledge, wisdom, and talents from the beginning of their creation.

 

We humans can in theory grow without limit in terms of intelligence, mind, heart, will, memories, and even in the life of grace, not only in this life, but perhaps also after the Final Resurrection of the Dead when we get our bodies back: Bodies that will be mysteriously spiritualized, immortal, incorruptible, and which will have their own life definitively granted to them.

 

Given the wonderful thing that the human person is, who could in their right mind desire to prevent a conception that is determinably on track to occur or abort a human embryo of fetus growing in its mother’s womb.

 

As someone who is partial to think about the human soul in preference to thinking about the human body, for whatever particular psychodynamic personality structures I have that might predispose my to prefer the human soul over the body, I thought this morning that it would be enjoyable to compose my a description of my attitudes toward the human body, which those who have a tendency to focus more on the body in preference to the human soul, will probably enjoy reading.

 

It is interesting to consider the marvelous mysteries of the human body that constitute the qualities of the human body that make it a human body.

 

We know of the high degree of complexity of the human body as evidenced from the fact that the human body is comprised of trillions of cells whereupon each cell is composed on average of quadrillions of atoms.

 

When consideration is made at the fundamental biochemical level, the number of statistical quantum mechanical states of the human body is stupendous. The number of types of chemical reactions that occur within the human body, both known and unknown, is enough to be the subject matter of thousands upon thousands of PhD research thesis.

 

Simply considering the complexity of the various human tissues and organs and the self-regulatory feedback mechanisms that maintain the bodies health and equilibrium is amazing and such mechanisms will be material for  PhD research thesis for generation to come.

 

Now we can contemplate the empirical aspects of the human body as known to medical science and bio-chemistry and still not arrive at a full consideration of the mysteries of the human body.

 

We need to delve deeper yet into the world of metaphysics and ultimately religious faith based systems to fully appreciate the meaning and nature of the human body and the mysteries that it presents us.

 

The human body is according to The Catholic Catechism united to a spiritual and immortal soul. This soul is accordingly directly and immediately created, is spiritual, and not reducible to the mere material world. The soul is the seed of eternity we bear within ourselves. Other qualities of the human soul are that it is rational and radically endowed with free will. It is not produced by the parents, nor any form of spiritual semen or any other pre-existing material.

 

Saint Thomas Aquinas held that the human soul in created ex-nihilo or directly and immediately out of nothing. The human soul is accordingly independent of the human body for its existence and to some extent its operations and does not ceased to exist when separated from the human body at the time of death. It is spiritual, simple, and unextended and thus has no separate parts, shape, or other forms of spatial extension. It is accordingly incorruptible per addends and per se. The human soul is also considered by Saint Thomas to be a first created principle meaning that there is no intermediate element or agent that stands between the existence of the human soul and GOD’s creative act of will that caused it to come into being and which maintains it in being.

 

 

Now what qualities of the human body exist by which such an sublime and transcendent reality of the human soul can be substantially united whereupon the substantial union between the human body and the human soul in this life constitutes a complete, full, and autonomous human person.

 

There is some ineffable quality or aspect of the human body by which such a union cannot only take place, but by which such a union is natural to produce.

 

The human body remains a human body even though much of its atomic and/or molecular constituents and even its cellular constituents are replaced over a relatively small faction of an adult human lifetime, yet the human body does not cease being human and maintains a substantial union with the human soul that animates it.

 

There is just something marvelous and perhaps over looked by many spiritual anthropologists regarding mysteries of the human body such as these.

 

The human body is said to be the temple of the HOLY SPIRIT and as such, there is something sacred about the human body. The HOLY SPIRIT would not choose junk for His temple.

 

The human mind brain is strongly effected by neurological states in this life including neural electrical energy patterns, bio-electrical-chemical states, chemical states, and perhaps even by the magnetic and electromagnetic field generated by the electrical activity within the human brain.

 

There is something ineffable about even the primitive emotions, drives, sensory perceptions, moods, and other primal sentient psychodynamic activities and processes that occur within what we call the human mind brain. Since such processes are so strongly coupled to the human brain and its various thermodynamic states, even in consideration that the human brain is substantially united to the human soul as well as is every other portion of the human body, there is some aspect of human brain thermodynamic micro-states, mesoscale states, and macrostates that generates the sentient psychodynamic activities and processes from both an objective and subjective standpoint.

 

This aspect of human ontology that we refer to as the mind, or daily working psyche with all of its qualities of sensual experiences, emotional experiences, conscious thinking, conscious volition, conscious drives, impulses, appetites, and attitudes seems to reside in a “never never land” somewhere between the human body and the human soul, yet which depends on both the human  body and the human soul. There is just something about the physical material, physical states, and physical substance of the human body especially the human brain that helps generate such conscious, sentient, psychodynamic elements of the human psyche. Since the human body continues to live and thrive often even as the human person sleeps or is under general anesthesia such as for surgical procedures, perhaps the human body and/or brain has in at least a limited sense, a sort of primacy over such psychodynamic microstates, mesoscale states, and macrostates.

 

Some thinking in the field of the fundamental aspects of physical  matter and physical energy has held that perhaps pure physical matter and energy has or is somehow conscious, feeling, experiencing etc. This consciousness or feeling may be another aspect of physical mattergy or it may be a fundamental reality that somehow parallels the physical mattergy cosmos but yet which is not the same thing or same reality as the human soul that animates the human body and which is substantially united to the human body in this life. In the event that any such consciousness of physical mattergy exists, it may rather exist as another aspect to mattergy in a manner analogous to the properties of electrical charge, spin, charmedness, strangeness, bottomness, and topness, and other fundamental quantum-electro-dynamic and quantum-chromo-dynamic aspects of fundamental baryonic and mesonic matter and its fundamental standard model composition.

 

That faith based organizations especially the Catholic Church hold that a given person’s body is not that of another seems obvious at first, however when one considers that the human body as such is a unity despite the intermingling of the material and energy fields composing the human body with the its surrounding environment, it is easy to develop a sense of mystery as to why  a given human body is precisely one human body and not that of another person as well as a sense of mystery of why the human body, despite such intermingling with its environment is precisely one human body and has only one human soul substantially united to it.

 

A real mystery is how scientifically speaking and therefore factually speaking can the spiritual and immortal soul be so united substantially to the human body wherein the human soul is totally and substantially united to ever differential portion of the human body that is alive. That such a union can take place, even though the union as such is brought about by Divine Power points to a profound mystery as to the ultimate substantial and existential nature of the human body.

 

Ultimately, the human body and the mysteries that surround it obtain their highest form when consideration of the eternal destiny of every human body to be Resurrected at the End of Time, the good to the Beatitude of Heaven, and for those who have definitively chosen to remain separate from God, the sufferings of Hell, of which we have no clear or certain knowledge of the nature of this suffering.

 

Come to think of it, our very own mortal physical bodies will be Resurrected Incorruptible with the same characteristics as Christ Resin body and will be reunited with our glorified spiritual and immortal souls at the Final Resurrection.

 

Our brains are part of our bodies and so all of the powers that our brains currently have will be greatly amplified and exalted in a manner commensurate with our overall Resurrected and Glorified Spiritualized bodies that will still be physical bodies but also spiritualized  bodies at the same time. Wow! What an exalted state of the already stable and conservative properties of mass and energy the compose the human body as it exist before the Final Resurrection in this life..

 

In addition to being reunited to our souls, I believe if I am not mistaken, that The New Catholic Catechism mentions that the Resurrected Human bodies will have their own immortal life definitively granted to them or something similar. I am still trying to find out what that means.

 

What will the Resurrected Human Body be like in Heaven? Many theologians who study the topic would state that the Resurrected Human bodies in Heaven will look absolutely brilliantly radiant and be in perfect Health and of a most beautiful form in terms of shape and features. The glorified human body will no longer be able to or at least will no longer suffer in any way. It will be free from every defect or infirmity regardless of whether or not it suffered from disease in this life in the form of physical or mental, emotional, or psychological disturbances. For all you folks who suffer from brain based illnesses such as bipolar disorder, schizophrenia, major depression, schizoaffective disorder, obsessive compulsive disorder, post-traumatic stress disorder, multiple personality disorder and the like, your mind brain is pre-destined to be exalted in health, power, and function in ways that you simply cannot comprehend in this life. Just as you have been given the cross of your condition, I believe that you are predestined to be glorified in an exemplar manner since with the Cross come the reward of Eternal Glory.

 

The human body will be incorruptible and able to move about from place to place at the speed of though and will otherwise be a perfect instrument of the human soul. The powers of brain based reason, logic, sentient awareness, emotion, and even the five senses will be exalted and enhanced in a manner commensurate with having a glorified body.

 

Part of my quest for my interest in physics is a reflective if only philosophical type of insight into the physical world and by extension, a means to provide a heuristic and epistemological ability to question exactly what our glorified bodies and brains will be like.

 

Not to sound greedy, but Post Resurrection Heaven is there for the asking. No one will have any sense of diss-satisfaction in Heaven. The Catechism states that we all share a fundamental moral equality before GOD. The road to Heaven in this life has its ups and downs but nonetheless can be enjoyable.

 

In consideration of pseudoscientific belief systems and new age eastern types of spiritualism wherein it is claimed be certain psychics that they can somehow travel out of their physical body in some sort of spiritual body as well as considerations of the new age space alien UFO cult that there exist extraterrestrials on Earth that have the same abilities, I would like to present a contrasting focus by saying that those who cannot leave their physical body as such may represent a higher state or at least prefigure a higher state of being with respect to their soul body relationship than any transiency of soul location or energy body location or soul or energy body to  physical body relationship.

 

To further clarify my point, we do not say that God leaves His body and that GOD is free to roam around the universe, or pass through solid objects. Indeed, GOD is not defined by space and time matter and energy, nor by any aspect of creation. GOD does not need a place to travel into or an entity to be separable from such as a body, because GOD created all of space and time, matter and energy, all of Heaven, and indeed all of creation, and all of creation past, present, and future, cannot contain GOD. In a sense, GOD is outside of all creation since creation cannot define GOD. Indeed, each and every creation, in fact all of creation depends on GOD’s sustaining might to be kept into existence. GOD is neither bounded by creation nor does HE need creation for HIS GLORY or existence.

 

Indeed, GODs DIVINE NATURE cannot move around because the entire Cosmos cannot contain HIM. In a very real sense, even HEAVEN cannot contain GOD because GOD Created “Heaven and Earth”. GOD in each of HIS THREE DIVINE PERSONS cannot  be contained and cannot move or be moved because GOD is absolutely changeless and is not definable nor containable by space and time.

 

GOD cannot move about or pass through walls etc., because GOD is not definable by motion. GOD is utterly immovable and is unchangeable. In short, GOD is immutable in  the utmost absolute sense.

 

Now we humans, or non-psychic humans who obey the Church’s teaching by not dabbling into the occult, spiritism, the phenomenon of clairvoyance and all this other crap might be looked down on others that do, however, we must realize that we have a spiritual, naturally immortal, naturally incorruptible per addends and perse, directly and immediately created, simple, unextended, independently existing of the body and brain, eternal soul. The human soul is that seed of eternity we bear within ourselves that is not reducible to the mere material world and which  requires a special act of GOD to be created which forever marks it in a unique relationship with its creator.

 

The fact that we so-called ordinary humans cannot leave our bodies shows that Our Human Souls have  a permanency or un-changeability in this life as to the essence or existence of the substantial properties of the soul to the extent that the soul cannot be separated from the body in this life. While any so-called astral projecting psychic human and perhaps any ETs with such alleged powers claim or secretly possess such a capacity of out of body travel, we body-bound humans have a relation of permanency or immutability with respect to the physical world via our physical bodies by virtue of the fact that our spiritual and immortal souls are substantially united to our bodies in an inseparable manner until natural death. Thus, we display and have a certain form of immovability with respect to the physical cosmos that is representative and commensurate with having a soul that is  substantially and existentially immovable with respect to the human body. We not only are unable to separate from our body in this life, but we do not need to nor have to in order to produce our free acts of will.

 

This substantial and ontological immovability of ours in a real sense prefigures our substantial and immovable soul traits at the Final Resurrection of the Dead when our Souls, both in terms of the essence or substance of our souls, the faculties of our souls of intellect, heart, will, and memory, as well as the accidental properties of our souls will be exalted and glorified beyond imagining. It is often said that what is represented as a virtue here on Earth in our human body soul relation will be exalted beyond imaging at the Final Resurrection and Glorification of the Dead. The immovable relationship between our human Souls and our human bodies in this life is going to be enhanced. We will have a substantially absolutely immovable existence in our souls with respect to our human bodies and through extension, with respect to the entire rest of creation.

 

For those who dabble in the Occult or the phenomenon of clairvoyance and who look down on the rest of us Catholics who do not and who claim to have no psychic abilities, bear in mind that any lack of power we may appear to have, will be more than made up at the Final Resurrection of the Dead, wherein our mortal bodies will be Resurrected Incorruptible on the last day and spiritualized to such an extent that they will be far more spiritual and ephemeral than any energy body or spirit bodies that psychics claim to be able to travel out of and away from their physical bodies in. In short, what is sown in dishonor will rise in incorruptibility. What is sown in mortality will arise in immortality. Our mortal physical bodies will arise incorruptible and spiritualized on the last day with the same incorruptibility and immortality of the Resin and Glorified human body of Our Lord Jesus Christ.

 

Note that the Final Resurrection and Glorification of the Body is meant for every one including those who dabble in the occult or who claim either validly or under the influence of Satan, or perhaps delusionally, to be able to leave their physical bodies and perform out of body travel. So if you are one such person, please do not take offense at my writing. We are all called to the Final Resurrection of the Dead and the Glory of the World to come. However, we must if we are Catholics, submit to the Ordinary and Supreme Magisterial teachings, the Traditional Teaching of, and the Sacred Scripture of the Catholic Church.

 

By the way, I have some theories about what any energy bodies or so-called spirit bodies are made of and that I believe such spirit or energy bodies that so-called psychics or perhaps ETs, if they exist, have  can be destroyed in nuclear explosions of nuclear weapons and other similar super-hot and super intense energy scrambling events. But I will not discuss such concepts here in my post so as to not induce fear. These respective concepts are scary and to frighten the readership of my blog is not my intent. Rather, my intent is always to build people up rather than tear them down.

 

By now, the readership of my blog will not that I am a champion of the underdog, the afflicted, the weak, the poor, and the oppressed. There is a reason for this. There is no greater cross than to be the underdog, the afflicted, the weak, the poor, or the oppressed especially when persons as such speak up for the truths of the Catholic Church and Judea-Christian morals and ethics. Truly, the last will be first, and many (but not all) of the first will be last. Our crosses and momentary afflictions are preparing for us a glory beyond imagining.  I am keenly aware, that when I meet my creator at the End of Time, Jesus will I hope tell me that “I was hungry and you fed me, naked and you clothes me, thirsty and you gave me to drink, in prison and you visited me, was sick and you comforted me, was sorrowing and you consoled me, etc. I will then ask, Lord when did I see you naked, hungry, thirsty, in prison, sick, or sorrowful. The Lord will then say, so long as you did such for the least of my brothers and sisters, you did so for me. And this included sticking up for the poorest, weakest, and most vulnerable, that is the newly conceived and the fetuses growing within their mother’s wombs.

 

 

 

 

 

 

 

 

13)  THE JOYS OF CONTEMPLATING THE HUMAN SOUL: PART 2

 

Note again the Scholastic interpretation of the nature of the human soul, that is the human soul is:  1) Spiritual, 2) Naturally immortal, 3) Incorruptible per addends and per se, 4) Simple, 5) Unextended, 6) Without shape or size, 7) Non-material,   8]   Non-corporeal, 9) Rational, 10) Free,  11) A first created principle, 12) An essence or a being which exist per se, 13) Independent of the body for its existence and to some extent its operations in this life, 14) The substantial form of the body in the Ancient Greek philosophical sense of the word, 15) Directly created by God, 16) Immediately created by God, and if I am not mistaken, 17) Multiple meaning that it is completely and totally present and united to every portion of the human body that is alive.

 

 

The modern Catholic approach to the immortality of the soul is somewhat ambivalent about the spiritualistic extreme ideologies of Saint Thomas Aquinas described above, however its modern viewpoint backed by the full weight of the highest levels of the Church Hierarchy is that the human soul is: 1)Immortal, 2) Spiritual, 3) Rational, 4) Does not die when separated from its body at death, 4) Immediately created; 5) According to the index of the first addition of the new Catechism of the Catholic Church, directly created by God; 6) The seed of eternity we bear within ourselves, 7) Not reducible to the mere material world;   8]   The form of the body.

 

Now as a modern scientific  and technologically advanced civilization, we have grown much in our heuristic, epistemological, and ordered approach to knowledge; a reality that has given us new words, new concepts, in short, a whole new language in which to approach concepts such as the nature, existence, and reality of the human soul, the nature and existence of the physical world, the origin of our universe, etc.

 

As someone trained in physics, I am aware of the notion and concept of fermions and bosons. Fermions are particles  with a spin of (1/2) h/(2 pi) or odd integer multiples of the respective value such as 1{(1/2) h/(2 pi)}, 3{(1/2) h/(2 pi)}, 5{(1/2) h/(2 pi)}, … whereas Bosons are particles with an even integer multiple of spin such as 0{(1/2) h/(2 pi)}, 2{(1/2) h/(2 pi)}, 4{(1/2) h/(2 pi)},… .

 

Fermions obey the Pauli Exclusion Principle meaning that they cannot exist in the same spatial place at the same time with the same energy as another fermion. Bosons are able to exist in the same place at the same time with the same energy as another boson.

 

Fermions, in statistical mechanics language parlance obey what is referred to as Fermi-Dirac statistics whereas bosons obey Bose-Einstein Statistics.

 

The Fermi Distribution or probability that a fermion will be in a given energy state for a system of fermions at a temperature T of absolute zero is given by:

 

f(E) = 1/{{(e) EXP [(E - Ef)/(kT)]} – 1}

 

where Ef is the Fermi Energy, E is the energy state of the particle, k is the Boltzman constant, and T is the system temperature.

 

As one can see, the probability for an energy state below the Fermi Energy is one while the probability of an energy state of a particle being above the Fermi Energy is zero for T = absolute zero.

 

The Bose Einstein Distribution is defined as follows:

 

f(E) = 1/{{ (A){e EXP [E/(kT)]}} – 1},

 

where E is the energy of the particle, A is a constant which for photons equals one, k is the Boltzman Constant, and T is the temperature of the system.

 

Now, we can, those of us who are Catholics, be absolutely certain that what is written within the Catholic Catechism of the Catholic Church about the human soul is endorsed by the Catholic Church Hierarchy. I feel that the writings of Saint Thomas Aquinas in regard to the nature and characteristics of the human soul are quite worthy also.

 

Now given that the human soul is completely and totally present to every differential portion of the human body it is substantially united to that is alive, in fact completely and totally substantially united to every differential portion of the human body as such, we can in a sense say that the human soul is completely and totally united to every particle, in fact, every sub-atomic particle also that comprises living portions of the human body wherein such particles are quarks, any sub-components of quarks, protons, neutrons, electrons, and any sub-components of electrons, as well as all of the bosonic energy fields of the human body, presumably even the zero point vacuum energy fields included in the composition of the human body.

 

As such, we can be assured that the human soul is probably not some sort of fermion or of fermionic composition since if it was, it would not naturally have an affinity for or the natural ability to be united to the human body. No doubt, GOD could supernaturally unite the human soul to the human body if the human soul was of fermionic composition, but GOD does not work harder than HE needs to and does not duplicate efforts regarding individual creatures where one set of efforts is adequate.

 

If the human soul was composed of fermionic forms of ethereal material such a fermionic ectoplasm and was generally extended with the same shape as the human body, such as is alleged by many of those claiming to have near death experiences or by certain psychics that claim to be able to travel out of their body in the form of an energy body, then the human soul and its differential volumetric elements could not naturally be substantially united to the human body due to the degeneracy pressure and the Pauli Exclusion Principle that would be active to prevent such a close union. In fact, one would tend to think that if the human soul, with such fermionic properties and extendedness, would be as close in space and in time to each portion or each fermionic constituent particle of the human body as possible, i.e., at least as close in space and time, as the smallest spatial and temporal unit scales of the Planck Length and Planck Time Units or about 10 EXP – 35 meters and 5.3 x 10 EXP – 44 seconds respectively, it would either be transmuted or instantly repelled with tremendous pressure, or degeneracy pressure. More likely, is that the fermionic constituents of the soul would need to be precisely enmeshed and superposed over and within the fermionic and bosonic composition of the human body in order for the soul to be so united to the human body such that the human soul could be considered substantially united to the human body.

 

Now do not get me wrong! I am not discounting the potential validity of those alleged near death experiences nor the so called possibility of out of body astral travel. However, it is my opinion that any such experiences do not involve substantial disconnection of the human soul from the body even though those who claim to have such experiences might  disagree with me. I believe that indeed, if such experiences are real, the soul remains fully and completely united to the human body throughout the duration of such experiences,  however, I am open minded to the fact that perhaps we humans as well as any intelligent extraterrestrial and/or intelligent ultra-terrestrial persons may have an energy body or some form of body made of a more refined material, which might be completely physical, but which is not the same thing as the human, ETI, or UTI soul. Perhaps it is with this secondary body, which I am convinced is not our Resurrected Physical Body that will be Resurrected and Glorified Incorruptible after the Final Judgment at the  End of Time, that we are able to interact with each other and perceive our environment upon bodily death in the meantime. I am also certain that if such an energy body exists, it exists in each and every one of us, i.e., each of us has our own energy body, and that such an energy body will also be Resurrected Incorruptible on the Last Day for each and every one of us humans, and presumably any ETI and UTI to the extent that GOD permits.

 

These leads us to another question, if the human soul is so simple and completely and substantially united to each portion of the human body, each bosonic and fermionic portion of the human body, could  the human soul be essentially bosonic or boson like. If it is so, it would have to be a spiritual bosonic form of soul since the soul by Catholic dogma, even according to the new Catechism is spiritual. The human soul would likely have no physical extension at all or at least be limited in extent to distance scales no greater than the Planck Length at 10 EXP – 35 meters. More likely, it would have zero extension in space so as to be substantially united to and somehow commensurately enmeshed with each bosonic and fermionic component of the living human body.

 

 

That such a bosonic constitution of the human soul might be plausible seems to flow with the idea that the human soul has to have some properties by which it can be substantially united to the human body and every differential fermionic and bosonic portion of the human body that is alive. Perhaps the perceived energy body experienced by those who claim out of body experiences is nothing more than the totality of superposition states of the human soul as it interfaces with each differential bosonic and fermionic portion of the living human body in that such totality of superposition states takes the form of a holographic accidental property of the soul that is projected away from the physical body without the substantial union of the soul with the living human body being disrupted or terminated.

 

The human soul, nonetheless, is not simply a thing or an object, but is rather the vital, life principle of each and every created person that defines the person as an individual, unique, and unrepeatable, person. The Human Soul and any ETI and UTI souls are the vital life principles of identity that constitute each one of us as human, ETI, or UTI if that later two classed of being exist. The soul is deeper and more profoundly us then even our sub-conscious and unconscious psychological or mind-brain states, and the Soul is the essence or core of our being, most especially our spiritual being. In a sense, Our Soul is the real us. Each human, ETI, and UTI person has their very own soul, and is their very own soul.

 

The main point to the last few paragraphs above, is that, if the human souls is bosonic or bosonic like in nature, then even though this property would be part of the substantial properties of the human soul, it would only be one limited facet or aspect of the substance of the human soul. The human soul goes much deeper in its existence then to be merely only substantially united to the human body, or to be merely only bosonic or boson-like in nature. For the human soul is the core and substantial vital life principle that contains the identity of our of our psyches, our unconscious, subconscious, and conscious minds, or Id and sexuality, our Superego, our Ego. The human soul not only contains and is comprised of the above, but it is the above, and even more sublime is that the human soul is the spiritual essence of us, our deepest natural selves. It is that simple and unitary life principle of ourselves and by which  we are who we are. Your Soul is most truly and perfectly you and my soul is most truly and perfectly me. You are your soul and I am my soul.

 

But we have a body also. For those of you who follow the so-called cult of the body, or who spend much time and effort developing and focusing on your body, I would like to state, that even though I am a die-hard soul freak, I am sure that your bodies, as well as my body will be Resurrected on the Last Day and take on the same Incorruptibility and Glory as Jesus Christ’s Resin and Glorified Body. Our Resurrected Physical Bodies will be both physical and spiritual bodies. How our mortal physical body will be spiritualized is currently beyond our comprehension. But just as such is currently beyond our comprehension, so will the lowly physical bodies we possess in this life be Resin Incorruptible in Eternal Glory. I believe that the Catholic Catechism states that not only will our glorified souls be reunited to our human bodies on the Last Day, but if I am not mistaken, the Catechism also states that our Glorified Human Bodies will definitively have their own Incorruptible life granted to them.

 

Now if our bodies are to be so glorified and exalted, it is my utmost opinion that our souls will be also but to a much, much greater degree. Just as the soul according to the Catholic Catechism is that aspect of us by which we are most closely made in the image of GOD, so will the soul receive commensurately more glory and exaltation in Heaven at the Final Resurrection of the Dead.

 

Now for those who are upset by this article, bear in mind that I strongly favor the Scholastic Interpretation of the Human Soul as promulgated by Saint Thomas Aquinas and that is that the human soul is accordingly:  1) Spiritual, 2) Naturally immortal, 3) Incorruptible per addends and per se, 4) Simple, 5) Unextended, 6) Without shape or size, 7) Non-material,   8]   Non-corporeal, 9) Rational, 10) Free,  11) A first created principle, 12) An essence or a being which exist per se, 13) Independent of the body for its existence and to some extent its operations in this life, 14) The substantial form of the body in the Ancient Greek philosophical sense of the word, 15) Directly created by God, 16) Immediately created by God, and if I am not mistaken, 17) Multiple meaning that it is completely and totally present and united to every portion of the human body that is alive.

 

It is my opinion that the Catholic Church has lost something at least as its daily faith is lived out by many Catholic theologians, clergymen, Bishops, and Cardinals when it de-emphasized the Scholastic viewpoint during the latter half of the 20th Century.

 

 

Regardless of whether Scholastism holds to the correct formulation of the human soul, and presumably by extension, the souls of any ETI and UTI persons that might exist, we can be absolutely assured that the human soul has at least the following great properties as irrevocably described and cast in stone by the Catholic Catechism which has approval at the highest level of the Church hierarchy on Earth, Pope Benedict XVI. These great qualities are as follows. The human soul is accordingly: 1)Immortal, 2) Spiritual, 3) Rational, 4) Does not die when separated from its body at death, 4) Immediately created; 5) According to the index of the first addition of the new Catechism of the Catholic Church, directly created by God; 6) The seed of eternity we bear within ourselves, 7) Not reducible to the mere material world;   8]   The form of the body.

 

For all of you fellow soul freaks who long for the certainly of Saint Thomas Aquinas, and who are also a little dismayed by the Church’s de-emphasis of the spiritually maximalist viewpoints of Saint Thomas Aquinas, I say take heart. In some of the reported apparitions of The Blessed Mother Mary, she supposedly predicted, and warned future generations about, the spiritual minimalistic trash that has been introduced in many of our adolescent CCD programs and in many of formation programs for religious and seminarians studying for the priesthood. If there are any clergyman or bishops who doubt this last statement that read this post, I recommend that you look back at the writings and messages of the Blessed Virgin Mary in all of Her Church approved apparitions in a comprehensive manner and I think you will find the references that I am talking about.

 

I say take heart, all you fellow soul freaks, because it is my opinion that regarding the many great but still unknown general qualities our souls here and now even before the Final Resurrection, You ain’t seen nothing yet.

 

 

 

 

 

14)  WHAT IS THIS THING CALLED FREE WILL?

 

Why is abortion, artificial contraception, and the like sinful behaviors that came out of the 1960s so wrong?

 

First, in order to provide one answer that it is indeed so wrong that is evident from purely philosophical arguments, we ask the next question.

What is this thing called Free Will?

 

We have all wondered in admiration as many of us have seen or known relatives with chronic illness hold on to their struggle to live right up to the point of death.

 

We have witnessed on TV or in a combat situations of cases where brave young men and women fight to the very death with a determination that does not wane even in their dying moments.

 

We have heard of brave men and women who do not yield secrets even to the point of being tortured to death.

 

We have heard of heroic acts of will wherein certain Canonized Saints would hold on to their faith even as they stand tied to a stake and burned to death.

 

Some of us have seen persons who are chronically mentally ill with almost incomprehensibly bazaar and socially grotesque symptoms who despite being often discouraged by their mental health care providers to stop perseverating on their faith and become more down to Earth, maintain their virginity or purity despite the whole plethora of Freudian trash that they were told by their mental health care providers and the cultural influences that could well lead anyone to habitual sins of the flesh including decorated war heroes.

 

We have seen persons climb Mount Everest who display natural but almost inhuman stamina as they struggle to get to the top of the summit amidst well below freezing temperatures and very thin high altitude air.

 

We have seen persons run Marathon races, Triathlons, and the like until they are utterly exhausted, and yet complete the race again at some later date, only to run to the point of utter exhaustion again and repeat the process many times over their running careers.

 

We have seen people lost at sea swim for days while they barely maintain consciousness until the point that they are rescued by Coast Guardsmen, or other search and rescue units.

 

We have heard of stories of horrible accident victims determined to become fully functional in society again and in fact do so.

 

We have all seen horrible images of emaciated NAZI death camp survivors who survived the brutal conditions of their prisons and yet fully recover to have a relatively normal well-adjusted life.

 

But sadly, we are aware of probably the most ironically profound but sad acts of will by which one chooses to be eternally separated by GOD for all eternality, perhaps even upon or immediately after death after being shown some form of Final Mercy by GOD, a concept that is not taught by the Catholic Church that nonetheless, I like to believe in as a Mercy offered to some of the worst sinners who remained stepped in mortal sin right up to the point of passing, but where by ways known only to GOD, they are given the opportunity to spend eternity in Heaven, if perhaps only through a stay in Purgatory beforehand.

 

This thing called Free Will seems to defy all other aspects of natural psychodynamic make-up of the human person.

 

Just look at all of the acts of Will by which habitual serious sinners and pious folks alike repeatedly attend the Sacrament of Confession. Some of these folks when they are knocked down by mortal sin or serious venial sins, get right back up over and over again.

 

It seems that this Free Will lasts and per dues in the life of a sinner in a manner by which a sinner can keep coming back to Sacramental Absolution even in cases where the person has effectively lost the state of grace.

 

In the now famous alleged apparitions of Our Lady in Medjugorie, Our Lady is said to have confided to the visionaries that the souls in Hell choose to remain in Hell and hate GOD even more in Hell than they did on Earth. Clergymen, religious, and laypersons alike who study mystical theology seem to agree that it is possible that some persons could be so hardened in their anger and hatred that they being already in Hell after death would rather remain in Hell then to repent and love GOD.

 

Truly this thing called Free Will can almost be called or referred to as a nature in the substantial sense of the word, and perhaps it is effectively a nature as such.

 

It is a great mystery in a profound way that the will can remain confirmed in resolute hatred that per dues into eternity, or that a habitually sinful life style can exist wherein the person with such a lifestyle appears to struggle with sin while at the same time coming back to the Sacrament of Confession time and time again in an attempt to come to a deeper faith, and love of GOD, GOD IN HIS THREE PERSONS, and the Human Nature, Body, Blood, Soul, and The Supernatural Life of CHRIST’s Body and Soul which is inferred to exist just as we can have supernatural life within our Souls yet at the same time, our Souls are mere creations although exalted spiritual creations.

 

That such poor sinners who make repeated and predictable choices to come back to confession time and time again exist with certainty is evidenced by that fact that I am one among many of such poor sinners.

 

Human Free Will is profound in that it still exists even when the personality of a person has been somewhat corrupted by habitual sinful lifestyles, and that it exists presumably forever, in Heaven, Purgatory then Heaven, Limbo if such a state or state and place exists, and Hell.

 

Now do not get me wrong when I refer to personalities as being corrupted. I am not referring to the personalities of those who are seriously mentally ill such as persons with Schizophrenia, treatment resistant Bipolar Disorder, Schizo-effective Disorder, Major Depression, Multiple Personality Disorder, and Post Traumatic Stress Disorder. I have met many of such persons in my life, and many of such persons are the most tormented, dejected, rejected, and depressed individuals one could imagine while at the same time they are often devoutly religious, many of whom pray the daily Rosary. These persons are not the false, manipulative, maladjusted, free loafers that many well to do affluent persons think they are, and I assure any such persons who want to rush to judgment on these poor souls that you should be so grateful that you do not have any of the above conditions. Yet I have seen many cases of such persons who attend Mass, recite the Daily Rosary and Read Sacred Scripture which is perhaps the only thing that keeps some such persons from going postal at times.

 

The point is that even given the overall psycho-social deterioration that these chronically mentally suffer, their wills are often resolutely set like an iron trap on what really matters, the spiritual things in life that neither money, status, or privilege can buy.

 

Truly, this thing we call free will is a fundamental aspect of our being with power to do great things, and when augmented by the grace of GOD, is capable of profoundly good Free Choices.

 

The Human Free Will which is a faculty of the Human Soul can in a sense be considered a nature in itself since its scope is so far reaching and is evident in every free decision or act of Will that we make.

 

Given this knowledge of our Free Will, we should treat our Free Will with respect and not abuse this faculty or insult it by choosing to participate in sinful lifestyles. When we kill an unborn baby or prevent the complete conception of a child, we are killing a person who would otherwise have had the chance to live out His/Her life on Earth and enjoy use of His/Her Free Will, or interrupt the process by which a child would be conceived thus preventing a Human Soul with its Free Will from coming into being, at least by any methods ordinarily known and/or intelligible to Human Persons on Earth.

 

This is why the promoting of the right for women to have an abortion, not speaking out against the practice of legalized abortion, and the use of artificial contraception especially casual use of the morning after pill or the so-called RU-486 pill must be stopped. GOD has been merciful to modern civilization, but we cannot anymore remain complacent with regards to these sins against humanity and natural law thinking that the status quo is just fine with GOD. I think Our Lady Of Fatima has warned us about such complacency, and the picture isn’t pretty.

 

The truth is that artificial contraception, particularly when it aborts the conception process that is already determinably on track to occur, kills the potential existence of another spiritual and immortal soul, another body that is destined to be Resurrected at the End of Time, and another will that would otherwise experience the joy of acting as the most significant faculty of the Human Soul, even to the extent that the Human Will is said to be superior to the intellect and memory. After all, it is through the will that we accomplish everything we choose to do in life.

 

For GOD’s sake, let stop the slaughter of the unborn, over 50 million of which have died at the permission of the U.S. constitution. A truly great nation would never permit this Holocaust, and GOD’s patience is limited in this regard.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

15)  COULD THERE EXIST A HUMAN ENERGY BODY THAT IS DISTINCT FROM THE HUMAN SOUL?

 

 

 

I have a theory that the human energy body that certain so-called psychics say that they can travel out of body in and that which persons involved in so-called near death experiences claim to have is simply a body made of a material, perhaps super cooled non-relativistic neutrino material that is produced by the electroweak unification between the electromagnetic force and the weak nuclear force. As one might be aware, the neutrino is the particle with zero electric charge but which interacts with matter through the weak nuclear force reaction. A beam of pure neutrinos can accordingly travel thru light years of lead and remain largely unattenuated.

 

My theory in another version is that the material out of which human and extraterrestrial energy bodies are made is composed of photo-neutrinos which would be a hybrid force particle with characteristics of both the electromagnetic photon and the weak force neutrino. My theory would explain why energy bodies appear or at least are reported to pass through material objects by those having near death experiences. Whichever version of my theory is correct, the electroweak unification in physics, the basic form of the theory for which a Nobel Prize was awarded, is the basis for suggesting that super cooled neutrinos, or photo-neutrinos, can interact by electric fields or electronic like fields and thus form the continuous material that energy bodies and auras appear to be made of in the form of aggregates of massive numbers of cooled neutrinos or photo-neutrinos in bound states.

 

Alternatively, perhaps some sort of very long half-life millicharged fermion might comprise any such energy bodies. One might go on to suggest the possible existence of microcharged, nanocharged, picocharged, etc., particles as the source of such energy bodies. No attempt is being made to advocate pseudoscience here, but given the anecdotal accounts of so-called energy bodies and the alleged neutrino or cold dark matter like  qualities of such energy bodies, perhaps another venue for looking for exotic fermions might involve studying the electrodynamics and quantum-electrodynamics of the low intensity energy fields known to be emitted from human and animal bodies.

 

Since these alleged energy bodies seem to float or hover weightlessly, one is tempted to think, if they exist at all, that they couple very weakly with gravity at ordinary one Earth G levels, but at the same time have some sort of massive inertial characteristics, for otherwise, they would simply not float around in hospital rooms for several minutes for persons allegedly having such experiences. Since these energy bodies remain close by to their “dead” physical bodies, it seems that they are coupled to their spatial temporal environment, perhaps via the local space time fabric by the local Higgs Field. This sounds far out, but we as scientists and space heads should investigate every avenue in our search to understand CDM, HDM, and the like.

 

The reason for suggesting that energy bodies are made of a material that has inertial mass properties and that the energy bodies are coupled to the space time fabric in the location where the persons have “died” is that the energy bodies do not seem to go flying off as if being dislodged from a rotor due to the centripetal acceleration of the Earth’s rotation as well as due to Earth’s orbital motion around the Sun and other motions with respect to any background reference frame which might include the cosmic microwave background radiation.

 

Another possibility is that the energy bodies could electro-dynamically, electro-weakly, magnetically, electrically, or electromagnetically couple to the baryonic matter within the atmosphere, solid materials, etc., that exist within the environment where the person died which would interact as sort of a molasses to hold the energy body relatively fixed just after it separates from the physical body.

 

Another option for the composition of any human energy body or spirit body and by corollary those of any intelligent extraterrestrial persons is that perhaps such energy bodies are formed out of stabilized or bound states of electromagnetic waves. Such a mechanism might imply that low frequency and even infrared photons can form some form of a bound state by which the electric and/or magnetic field components of such waves are aligned or oriented on a wave per wave basis such that the assemblage of waves so organized forms a bound state or stationary state of electromagnetic energy. According to this concept, the EM waves would attract or both attract and repel each other in such a manner that a bound low energy state of EM waves would be produced that would be immune from collapse and also from  radiating away or dissolution at least under ordinary circumstances.

 

Such a mechanism may operate along with other mechanisms wherein electric and magnetic  fields produced within the human body become self-contained or bound within with respect to differential volumetric elements of such electric and/or electric fields or perhaps the electric field and magnetic field components of an energy body so composed are the sole processes by which the energy body is formed and/or evolves along with the growth and metabolic activities of the living  person’s human body.

 

One might then ask if some process of entanglement of electromagnetic waves or photons and/or some process of entanglement of any composition of electric and magnetic fields comprising any energy bodies results in the formation and development in this life , and continued existence of the energy body in the next life . Such a process of entanglement could conceivably take the form of one or two different meanings of the phrase entanglement. First, the entanglement may be of a classical mechanics types of entanglement wherein the EM waves and/or electro-dynamic fields are tied together in a mechanical or topological manner that obeys the principles of applied classical electrodynamics or yet to be developed classical electrodynamic concepts. Second, perhaps the form of entanglement is of a whole different form such as quantum mechanical entanglement wherein the EM waves and/or the physical bodies’ electric and magnetic fields become mutually entangled in a manner similar to the entanglement of laboratory experiments wherein two photons are made to be entangled but not in the classical mechanical sense of the word. However, the effects of such entanglement might be analogous to the case of classical mechanical entanglement where the correlation of the energy states, spin states, polarity states, and momentum etc., of the waves and/or fields causes them to be locked in place by themselves and/or locked in place with any fermionic atomic particle states that produce these waves and/or fields.

 

At this point, it is worth considering whether or not the human person and by corollary, any extraterrestrial person species energy bodies, if composed of a more rarified and fine grained atomistic material with finite divisibility obeys the principles of not only conservation of energy but also of entropy as well, whether or not the individual atomistic components of such energy bodies or spirit bodies obey the particle wave duality that physical particles obey. Perhaps each atomistic component of an energy body has associated with it a wave-function which may or may not be describable by the Schrödinger Equation in any or all of its various forms. Also, it might be the case that each such atomistic component obeys the Heisenberg Uncertainty Principle.

 

If such atomistic components of any human or ETI species energy bodies obey the above physical principles that are conjectured to apply, then one wonders if there is a temperature or other thermodynamic properties associated with such energy bodies. Assuming such properties apply to energy bodies, perhaps energy bodies have a slight momentum, energy density,  and/or  mass-energy or physical energy – immaterial energy equivalence principle operative in their composition. Such energy bodies may or may not be destructible by processes manifested by such equivalences by either or both of natural means or supernatural means.

 

Energy bodies if they exist and have real spatial extent might have higher dimensional and/or parallel dimensional spatial, spatial temporal, and/or temporal components or characteristics in a manner similar to or analogous to such characteristics proposed to be operative or existent within the physical world. These higher dimensional aspects may be either manifested at the level of any atomistic composition of an energy body, any differential volumetric element of a continuous non-atomistic composition of the energy body, or at the level of the entire  energy body regardless of whether or not the energy body is comprised of  a finite atomistic sub composition at finite spatial and/or temporal extension scales.

 

If there exists any form of energy bodies in human, ETI, or animal life-forms, perhaps their exist additional higher levels of bodies within our make-up, perhaps several to many such bodies of ascending characteristics, perhaps even an ensemble or a given cardinality of infinity of such potential bodies, perhaps an indefinably large cardinality of such energy bodies or potential energy bodies. Who knows the exact extent of human and any ETI higher natures!

 

Since a renowned Catholic theologian near the turn of the 19th century once indicated his belief in various published literature that within each immortal human soul exists a vast ocean of existence which is infinite in depth and extent and of which we see just a surface glimmer in this life as if a reflection of light off of a ripple of a wave on the surface of a vast ocean, infinite and incomprehensible.

 

Regarding created spirits such as human souls, any existent ETI bodily being souls, and the pure spirits called angels, one can question as to whether there is an even higher level of being or for lack of a better word, higher material than pure spirit. One concept of such a material or principle that really occurred to me for the first time ever last year  is what I will call the principle of identity, or the principle of individuality, by which a spiritual being is constituted as a completely distinct individual with an eternal identity. This principle of identity would seem to constitute every soul or spirit as a distinct person and so we can speculate as to whether this ontological principle of identity is a real, unique, substantial, immortal, incorruptible, super-spiritual principle in each instance such as for each person and whether or not it can have accidental forms just as the soul and body can have accidental characteristics.

 

Perhaps each of the Three Persons of the HOLY TRINITY, although being of one and the same uncreated pure spiritual nature, also have this higher principle, yet, of pure, uncreated, eternal, Identity or Individuality by which each Divine Person is constituted as unique and individual and wherein each Identity or Individuality is unique as opposed to Identity or Individuality being some abstract dis-personalized principle such as the abstract principles of goodness, worth, purposefulness etc.

 

Regarding the possible existence of energy bodies, I am inclined to think that if they exist, then they might not be identical with the principle or any existent principle that theologians and metaphysics refer to as the soul.

 

I get a feeling that if the human soul actually exists, then it is a directly created ex nihilo, spiritual, immortal, incorruptible, simple, non-extended, non-geometric, free, rational, and substantial principle, although my tendency to adhere to such extreme dualist views even puts me at odds with many contemporary theologians who favor a less spiritualist explanation of the human soul.

 

My feeling is that the existence of any energy bodies or so-called spirit bodies is defined at least in part by these bodies materiality, thus, I hold that natural effects produce and/or cause such energy bodies to change or evolve during life on Earth or on other planets, and that such bodies in theory could be destroyed by natural forces such as extreme physical temperatures, radiation fluxes, gravitational tidal forces such as near black holes and neutron stars etc., although speaking from a purely philosophical perspective with no intention of trying to convert anyone, perhaps any would be God, prevents or forbids deceased persons from venturing to close to dangerous situations, at least in the normal scheme of things.

 

Now if this super cooled neutrino material, photo neutrino material, milli-charged, micro-charged etc., material, or whatever energy body material exists, then perhaps inanimate bulk forms of such material can be created artificially. Perhaps as some level, any such bulk materials can occupy the same space at the same time or be in the same energy state thus perhaps allowing the materials so comprising the bulk material to be volumetrically layered in such a manner that very dense forms of such materials can be produced, perhaps materials as such with the density of white dwarfs, neutron stars, quark nuggets, and perhaps even black holes.

 

If such material exists and/or can be artificially produced, perhaps such material can travel faster than light, or perhaps mechanical deformations, so-called acoustic vibrations, or other effects can propagate through such bulk material faster than light with obvious implications for manned interstellar space craft.

 

Another possibility for the nature of materials out of which any existent energy bodies could be made of involves the concept that perhaps at the level of thermodynamic, electrochemical, or electro-dynamic activity energy events and complexity that occurs within human, animal, or and ETI bodies, a sort of residue is built up over time as a result of some impression left by the thermodynamic states as such, in fact wherein each thermodynamic state leaves a spatial-temporal impression of its previous existence. Accordingly, the energy body would be gradually built up by the layered or aggregated bound state or state of cohesion by each such impression. The number of possible impressions would be huge since the number of quantum thermodynamic states that a human body acquires in just one year is tremendous, if fact, many orders of magnitude greater than the number of electrons and quarks that make of the atoms of a given human body. This might explain the pseudo-scientific notion that the energy bodies are made of a much more tenuous or refined kind of material than the baryonic matter out of which our physical bodies are made.

 

Perhaps the energy body is made of past states as such wherein each thermodynamic event that leaves a memory that composes, in part, energy bodies, actually exist in the past as a real event even though the human energy body, if the pseudo-science has any truth to it, exists as a concrete item within the present. Thus, the past so-called “memory layers” would conserve the information of the past thermodynamic states and possibly also  the spatial temporal residues of such states within the present state of the energy body. The energy body accordingly would be built up from residues that exist in the past or at least have some extension into the past from the present.

 

It might be the case that the inter-relation of adjacent individual quantum thermodynamic events composing any such energy bodies are much more important in determining the shape of the energy body than the random position changes that a given human or ETI body experiences as the person goes about their day to day living activities. If the relative positions of the arms, legs or head, for example, of the physical body where most important in producing the thermodynamic event residues that might produce an energy body or modify it, then the human and ETI energy bodies would seem, philosophically, to exist as some smeared out amorphous blob rather than having a distinct shape that people who experience so-called out of body near death experiences recognize as the forms of their deceased loved ones, friends, and acquaintances.

 

If such energy bodies exist, and are naturally produced and/or modified, it begs the question as to whether inanimate forms of material of the same kind can be artificially produced for space craft or transport construction and whether of not there exist whole unexplored material realms or universes made of such material.

 

Perhaps the physical thermodynamic states of the human body interact with, aid in the production of, or otherwise modify the zero point mattergy fields in such a manner that the zero point mattergy fields are incorporated in part into any existent energy bodies. It might even be the case that any energy bodies are built up from residues or shadow presences of such zpf fluctuations in much the same manner as the conjectured similar process involving real mattergy quantum thermodynamic and/or small scale classical dynamic states might. These zpf thermodynamic states might also be partially or fully linked to the past or exist in the past, or be partially or fully extended into the past from the present state of any energy bodies.

 

Another possibility is that the energy body might be composed of parallel history or parallel world layers of quantum level thermodynamic states and/or small scale classical level dynamic states. The operational mechanism as such may either be parallel layers of global aggregate states as such, parallel history or parallel worlds layers of large sub set portions of such global states, and/or parallel layers of quantum level thermodynamic states and/or small scale classical level thermodynamic states. Such parallel history or world states might involve the states as such within the zpf fluctuations and/or real mattergy fluctuations. Another option is that any of these parallel states might involve past parallel state residues or shadows in manners similar to the above speculations on past influences or residues from the one world version.

 

All of these various conjectures of the formation of any energy bodies might not be mutually exclusive, but rather might be complementary explanations or different aspects of the same underlying global phenomena leading to any energy body formation or evolution.

 

I just wish I could ask any scientists from any 10 billion year old ETI intergalactic space faring civilizations questions regarding the above conjectures. If the ETI could not answer such questions, I would love to ask any pure spirits or angels questions related to the above conjectures. I would love to spend days talking with such beings about this stuff.

 

I continue my comments on energy body material with a conjecture as to whether or not any artificially manufactured inanimate energy body like material could be created by artificial culture from physical organisms such a plants, vats of bacteria, algae, or fungi, or live-stock in forms that are optimized to produce energy body like material. Perhaps any conditions by which any human energy body material is produced could be duplicated by micro-electronic or nano-electronic, or micro or nano-scale mechanical, electromechanical, or electro-chemical-mechanical systems.

 

If such material can be created and produced in dense enough form, perhaps it can be used as an energy source or for the construction of civil infrastructure and transport systems for a future galactic or extragalactic human civilization. If any energy bodies form without the depletion of real particle and zpf virtual energy from the baryonic, CDM, or Dark Energy forms of such within our universe or other universes, perhaps this situation can imply the creation of mattergy in the form of energy body material from essentially nothing, in other words, implying an eternal and ultimate free lunch in terms of construction materials for an ever expanding human civilization and the required infrastructure including interstellar and intergalactic transportation systems.

 

If energy body material can be produced out of normal matter, be the normal matter baryonic matter, CDM, or super-symmetric matter particles, could an antimatter energy body material form exist wherein interaction between a sample of normal energy body like material with that of an antimatter version of energy body like material result in Fermi-Dirac annihilation thus leading to the possibility of producing inanimate energy body matter and inanimate energy body antimatter for use as compact high density energy storage mechanisms perhaps to power interstellar manned space craft? If this material could essentially be created out of nothing i.e., without conversion of normal mattergy or normal anti-mattergy into it, we might have an ultimate free lunch to power human civilization eternally into the future.

 

Could it be that such energy body materials actually have a mass that is less than, equal to, greater than, or much, much greater than E/[C EXP 2]? If energy body material has mass, could its latent energy be equal to E = f(E) + M[C EXP 2] or E = f(E){M[C EXP 2]} where f(E) is a nomial, polynomial, series, product, exponential, transcendental, trigonometric, complex, and/or the like function in whole or in part and wherein the value of f(E) might range from much, much less than unity to much, much greater than unity?

 

It might be the case that any energy body materials are a great energy storage mechanism that does not have mass, in other words, an energy equivalency that does not involve mass. Perhaps this energy exists as and/or can be converted into electromagnetic, strong nuclear, weak nuclear, and/or gravitational energy and/or any associated fermions. Alternatively, perhaps energy body material can be converted into super-symmetric bosonic energy such as sleptonic, squarkonic, or sneutrinic energy and/or the associated super-symmetric fermions. I ask the reader to excuse the three latter apparent cases of creative lexicography.

 

Or perhaps any energy body materials can be converted into unknown types of physically operational energy such as negative energy, imaginary energy, and/or other types of energy for which  we have not yet developed the lexicography and scientific processes to mathematically explain or intuit.

 

If energy body material has no mass, might it as a result, not affect the curvature of space time. Alternatively, perhaps energy body material affects space time in unknown types of ways. My intuition leads me to believe that because of the unity of nature and the apparent geometrical spatial shape of energy bodies as they are reported to exist by those having near death experiences, they do effect general relativistic space time curvature and can be effected by such.

 

In my above comments on the possible mechanisms for the formation of energy bodies, I conjectured as to whether quantum scale and/or small scale classical level thermodynamic processes based at least in part on atomic and molecular events and processes within the human, animal, and/or any ETI physical bodies could lead to the formation of any energy bodies.

 

 Now I would like to conjecture on any possible operative principles for the formation of energy body materials based on the scale of nuclear matter distances, densities, and strong nuclear force and nucleonic electromagnetic processes.

 

 Perhaps such nuclear scale processes can be used to produce a more dense, more refined, and/or more durable form of artificial energy body material. Perhaps the energy body materials so produced would be of a qualitatively different type than any energy body materials produced by the human physical body. This conjecture begs the question as to whether any nuclear matter scale environments that might lead to the formation of animal or ETI life forms with the bodily density of nuclear matter, such as perhaps on the surface of neutrons stars and the like, might also lead to the formation of exotic energy bodies and perhaps also be utilized in the formation of artificial forms of associated energy body material.

 

 Perhaps the gluonic strong nuclear reaction among the nucleons, and more specifically, among the quarks composing in part such nucleons can result in the formation of super intense, super dense, or super strong energy bodies or similar artificial material.

 

It is possible that energy body material has no fine grained atomistic or molecular-like structure and that such material is perfectly continuous even down to at least the scale of the Planck length and  time unit scales which are about 10 EXP – 35 meters and 5 x 10 EXP – 44 seconds respectively. If energy bodies are perfectly continuous, perhaps they are continuous at levels well below the Planck distance and time scale and so all the way down to literally the scale of mathematical or geometric points which have zero dimension and zero volume. If the energy body so constructed is infinity continuous, then perhaps it is indestructible at least to ordinary natural forces or agents.

 

If there are multiple finite or infinite numbers of higher energy bodies which in totality might  comprise the human soul, perhaps the higher energy bodies are made from a hard to intuit super continuity in their material composition wherein the level of continuity would proceed below that of a mathematical or geometric point to levels commensurate with the notion of scales below 1/(Aleph 0) where Aleph 0 is the number of integers according to the renown late 19th century mathematician Georg Cantor. It might be possible that such energy bodies might be continuous on the scale of 1/(Aleph 1) wherein Aleph 1 is accordingly the number of real numbers which is a much larger set then the number of integers. Like-wise according to Cantor, there exists Cardinal Values of Aleph i where i = 2,3,…, all the way up to values of i at least as great as the least infinite ordinal value.  One can speculate as to whether energy bodies exist within a human person wherein successively finer or higher forms of energy bodies are composed of successively finer levels of super-continuity wherein the levels of continuity would manifest themselves on the scale of 1/(Aleph i) wherein i can be any arbitrary finite or infinite ordinal value and even any infinite cardinal value such as i = Aleph 1, Aleph 2, …, Aleph (Aleph 0),…

 

One can also speculate as to whether or not, as conjectured previously, there exists in arbitrarily large infinite or cardinal numbers of energy bodies or spirit bodies that have an ever more refined type of nature or existence wherein the infinite or cardinal numbers can be defined as Aleph i where i = 0, 1, 2, …, Aleph 0, Aleph 1, Aleph 2, …, Aleph (Aleph 0), Aleph (Aleph 1), Aleph (Aleph 2), … and so on.

 

Perhaps what we refer to as the totality of the human soul is the unification and totality of such huge numbers of ever more refined energy or spirit bodies. Such a view of the human soul would seem to explain a mechanism wherein the human soul could include the vegetative, animalistic, and rational aspects of human life or vital principle composition as promulgated by Saint Thomas Aquinas in his description of the human soul. Another way of interpreting such an unending series of energy bodies as comprising the human soul is to view the lowest levels of such energy bodies as the least substantial aspects of the human soul or the most accidental or lowest forms of characteristics of the human soul.

 

In the event that such an huge finite or infinite series of energy bodies comprises the human soul, perhaps it is through the lowest or least refined levels of such energy bodies that that human soul comprised of such energy bodies is united substantially to the physical body since these lower levels of energy bodies would be most closely related in characteristics to the physical carbon based human body and which therefore could bridge the gap between the physical body and the higher levels of human spiritual composition to form the human person in this life as a unity of body and soul.

 

 Now, although I am not trying to advance the cause of pseudoscience, New Age belief systems, and the like, but any physical effects by which any energy bodies are created or evolved might also be used to destroy energy bodies. However, being of the Catholic Faith, I am a firm believer that all aspects of the Human Person will be glorified, exalted, and risen incorruptible at the Final Resurrection. This, I believe, also includes any energy bodies whether or not the energy bodies are damaged or destroyed beforehand by accident etc.. Now, once again,  I am not trying to convert anyone here, but rather am encouraging the readership to consider the possibilities I have discussed here and realize, the there are many possible belief systems that one can choose from in order for one to be assured of  their ultimate and totally secure future.

 

If we as a civilization learn how to manipulate our energy bodies or produce artificial forms of energy body materials, then it remains possible that such technology might be used to medically enhance our energy bodies, repair them, or otherwise improve them.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

16)  THE NOTION OF A REAL INTERFACE BETWEEN THE HUMAN SOUL AND THE HUMAN BODY

 

 

 

Now given the Catholic Scholastic notion that the human soul and the human body are substantially united in this life and that the human soul is the substantial form of the body it will inform, and the more modern existential approach outlined in the new Catechism Of The Catholic Church that the human soul, although spiritual and immortal, directly and immediately created, is the form of the human body, we can be left pondering whether or not there is some ontological or existential transition zone that marks the boundary between the body and the soul, the transition between the substance of the soul with the substance of the human body, or the transition between what is the soul which is not the body and what is the body that is not the soul.

 

As a physicist type who has taken many college courses in physics including several graduate level physics courses, I can attest that anyone with at least a BS degree in Physics and some graduate level physics courses under his/her belt is keenly aware of the notion of transition zones in the electromagnetic properties of various optical media, in the mechanical properties of elastic and acoustic media, in the magnetization patterns in permanent magnets and the like. These transition zones mark or define the boundaries where the dielectric properties of optical materials, the mechanical acoustic properties of solid, liquid, or gaseous materials, and the magnetic properties of permanent magnets, change in an abrupt manner. The entire systems under consideration often consist of one or more of such transition zones and thus the entire system although a unity has a form of composition that does not necessarily imply discontinuous spatial, or spatial temporal separation of the various sub-components, and thus allows for the schema of understanding the system as a whole unit.

 

We also see evidence of perhaps more loosely defined transition zones in the formulations of physical laws especially as developed during the early 20th Century. The transition from the highly accurate Newtonian approximations at non-relativistic velocities to the need for Special and General Relativistic theories to describe classical systems involving relative velocities that are close to the speed of light, and gravitational systems in the extreme spatial temporal distortions that exist within the vicinity of black holes and even the less extreme environments of neutron stars.

 

Many of my fellow physics geeks as well as is myself are familiar with the quantum gravitational concepts of the Planck Length and Planck Time Units, {[h/(2 pi)]G/[C EXP 3]} EXP 2 and {[h/(2 pi)]G/[C EXP 5]} EXP 2 or ~ 10 EXP – 35 meter and 5.4 x 10 EXP – 44 second respectively, whereby the fabric of space and time theoretically takes on a discreetized form of fundamental scale units below which the meaning of space and time is absent, in other words, the Planck Length and the Planck Time being the smallest possible spatial and temporal units, but yet where the sub-Planck scale structure might take the form of a metaphorical roiling, bubbling, arching, bridging, froth where the integrity of traditionally understood deterministic cause and effect, and even the integrity of cause and effect at ordinary quantum scales does not exist below the Planck scales, all the while the fabric of space time and the vacuum energy state of space time remains a unity.

 

Many of us are also familiar with the notion of the perceived need to unify the classical realm of macroscopic phenomenon and the general relativistic notion that gravity is a manifestation of curved or distorted space time with the quantum mechanical realm of quantized mass and energy, and quantized space and time including that of space time distortion.

 

Some of us who follow the developments of physics more closely are familiar with the notion that the five basic forms of string theory are really alternate but equivalent ways of looking at the reality of the ultra-small and the unification of the four known fundamental forces. The unified frame work that umbrellas these five basic different formulations is often referred to M-Theory, where according to some accounts of the relevant lexicography, the word stands for Meta-Theory.

 

And finally as a last example I give, we are familiar with the validity of classical electromagnetic theory and the extremely accurate and as yet still undefeated formulations of quantum-electro-dynamics or QCD.

 

I can give many more examples of holistic physical systems and theoretical paradigms that have a composition yet which have aspects that are unique on either side of a transition zone, and in some cases, the precise extent or nature of the transition zone is not fully defined if at all, not understood, and/or which might point to a finer and more sublime set of operative physical principles or possible mathematical/lexicographical formulations.

 

Regarding the conjectured transition zone between the substantial nature of the soul, and the substantial nature of the human body, this transition zone might be defined as the principle of the unitedness between the human soul and the human body in this life, and after the Final Resurrection of the Dead by which the unity of the Soul and the Human Body is casually, existentially, and ontologically derived or operative.

 

We can all agree that the human soul is not the human body nor is it the human body’s brain, and that the human body including its brain is not the human soul. Yet we commonly understand that the human soul and the human body in their substantial union form the human person in this life, and also after the reunion of every human soul with its body at the Final Resurrection of The Dead.

 

This hard to grasp no man’s land within the ontological aspects of the Human Person seems to be the ontological and existential cause of the concrete form of the Human Person as a substantial union of body and soul. If such a transition zone did not exist, then perhaps the Human Person could not be so constituted as a substantial union between body and soul.

 

We can now ponder what might be the causal, generative, ontological, existential, and the like nature of this transition zone that seems to have such broad reaching aspects in the constitution of the human person  Perhaps this transition zone is somewhat loosely, or perhaps even absolutely definable as the Heart of the Human Person (not in the physical organ sense). Another heuristic interpretation is that perhaps this transition zone could somehow be viewed as the unconscious mind or unconscious and sub-conscious mind of the Human Person. Alternatively, perhaps such a transition zone has relevance to the concept of human sexuality or the Scriptural Male and Female fundamental nature of the Human Person as being created in the image and likeness of GOD. Or perhaps this transition zone can be considered to be the human libido as conceptually referring to the meaning of the term in psychodynamic personality theory. Yet another plausible aspect of such a transition zone is that it might somehow be the core of our being, an essential principle that is neither our soul nor our body, that is neither physical nor material, nor spiritual. Could metaphysics deal with a third ontological substantial mode aside from the two that we intuit such as the physical and the spiritual?

 

I am perhaps treading on some deep water potentially in these last paragraphs, but what’s an unemployed physics geek have to do with his spare time.

 

Many years ago as I was having great personal difficulties, my sister Mary would console me gently but firmly with the profound but  simple statement, “Jim, this life is a just as stepping stone in eternity!” I now strive to live daily by my sisters profound words looking ahead to the wonders and potential of the future with a personal motto of “What Dreams May Come!” after the title of a popular movie that was released about a decade ago with afterlife themes that can give us all a feeling of hope.

 

I strongly feel that a main aspect of my concrete calling in this life as a physics geek is to promote and advocate for the bold vision that humanity will one day travel among the stars and perhaps meet any of our extra-terrestrial brothers and sisters. This personal quest of mine is kept alive in part by and in conjunction with my decision to remain single and to offer up my sexuality as a kind of motivation and inner energy source which seeks to nonetheless find some bonding in friendship with all women including any extraterrestrial females, and by corollary and in conjunction, also the promotion of the great dignity of marriage in general, which is elevated to the level of  the Sacrament of Holy Matrimony within the Catholic Church and commensurately the great dignity of family life as a union between husband and wife, and the great precious little ones we call children.

 

When we are quite honest with ourselves, each one of us  mature adult age  humans wonders if there might exist extraterrestrial persons or ultra terrestrial persons living on other worlds in this vast physical cosmos. Part of the yearning to know or to be intrigued by such a mystery is derived from a desire for a deeper intimacy and sharing with our fellow creatures, the ones we know of such as our family members, spouses, and friends and coworkers, our loved ones who have left this world, and the countless angelic pure spirit beings that exist beyond the realm of space and time, and most especially our desire for intimate union with the Almighty GOD HIMSELF.

 

17)    The Human Soul As Made In The Image And Likeness Of The TRIUNE GOD.

 

The Human Soul resembles that HOLY TRINITY in terms of intra-enumeration of fundamental aspects. Just as the ONE TRIUNE GOD, has THREE DIVINE PERSONS, THE FATHER, THE SON, and THE HOLY SPIRIT,  one can think of the Human Soul as having 3 power aspects, The Heart, The Intellect, and The Will. Each one of these power aspects of the Human Soul is truly the Human Soul.

 

Now a Catholic Church written document refers to the TRIUNE GOD, in HIS THREE PERSONS as being THRICE HOLY. Well, perhaps we can refer to the Human Soul as being Thrice Psychological, or Thrice Intra-personal.

 

From Freudian Psychodynamic Personality Theory, we can refer to the Human Psyche as tri-partite in terms of the Conscious, Sub-Conscious, and Unconscious. The Conscious has the least amount of data, knowledge and experience, the Sub-Conscious, the next greater amount of data, knowledge, and experience, and the Unconscious, the bulk of the data, knowledge, and experience. Likewise using the perhaps outmoded but still philosophically relevant Freudian Psychodynamic Personality Theory, we can categorize the Human Psyche by the Ego, Super Ego, and the Id.

 

Regarding the Human Intellect, we can classify its nature in terms of Abstract Thought and Processes, Experiential or Intuitive Thought Processes, and the Memory.

 

We can classify abstract reasoning into three commonly made distinctions as; Mathematical Reasoning, Verbal Reasoning, and Creative Reasoning which can include either or both of the former forms of abstract reasoning.

 

Regarding the memory, it is commonly classified into three broad categories such as the long term memory, the short term memory, and the working memory, the later of which is routinely active in our daily working schedule and which involves the pre-frontal cortex as one of its principle mediators.

 

We can classify the Human Heart into the Instinctive Appetites or Drives, the Emotions, and The Refined Spiritual Sentiments and Consolations such as authentic spiritual joy. Unfortunately, I seem to be stuck in the Instinctive Appetites or Drives mode because of my multiple vices, which require me to feel the need to attend the Sacrament of Confession frequently, especially with regard, at least as of before I recently started the South Beach Diet, the vice of gluttony. Too many Wendy’s Triple Baconator Combo Large meal I suppose. Grins and Giggles!  We can classify the Instinctive Appetites in  three commonly made distinctions as the erotic sexual drive, the drive to eat and drink, and the drive to sleep or rest. Of the drives that are ubiquitously active in every conscious and fully functioning person; Saint, Sinner, Celibate, Married, Single, Adult or Child, alike, we have the drive to eat and drink, the drive to rest, relax, and/or sleep, and the drive to eliminate bodily waste. I suppose breathing can be considered a drive, but as it is regulated by the autonomic central nervous system and since most of the time, it is occurs unconsciously, as one goes about their daily activities, it is not included in this listing.

 

We can classify the Will in terms of Rational and Fully Deliberative Acts, Semi-Deliberative Acts, and Instinctive Volitional Reactions. One aspect of such volition classification involves moral culpability, as in  acts that are; Mortal Sins, Venial Sins, or Non-Sinful and Morally Good Acts.

 

From an ontological consideration, we can classify the metaphysical properties of the Human Soul in terms of three categories; Its Substantial nature or its Essence, Its Power Aspects of Heart, Intellect or Will which are otherwise often referred to as its Faculties, and its Purely Accidental Properties such as individual experiences, daily working and living activities, sensations, and the like, from a conscious, subconscious, and/or unconscious stand point.

 

Since we are made in GOD’s image and likeness with our Souls being the aspect of we humans that is of greatest importance and by which we are most made in GOD’s Image and Likeness, and since GOD is a TRIUNE GOD, we can expect that at some ontological and existential levels, we resemble in our Soul’s the TRIUNE NATURE of GOD. We will not likely fully understand this aspect of our Souls being in the Image and Likeness of GOD until we behold GOD in Heaven where after the Final Resurrection of the Dead at the End of Time, we will have access to the wonders of all creation for eternity.

 

Now within the Holy Trinity, there is commonly said to be six interpersonal relations: 1) between the Father and the Son; 2) between the Father and the Holy Spirit;  3) between the Son and the Holy Spirit; 4) between the Father and the Son, and the Holy Spirit; 5) between the Father and the Holy Spirit, and the Son; 6) between the Son and the Holy Spirit, and the Father.

 

Now within the human soul, there is lexicographically six intra-personal facultative relations: 1) between the Will and the Heart; 2) between the Will and the Intellect;  3) between the Heart  and the Intellect; 4) between the Will and the Heart, and the Intellect; 5) between the Will and the Intellect, and the Heart; 6) between the Heart and the Intellect, and the Will.

 

The Father, to which the act of generative creation is attributed as well as the begotten-ness of the Son, we might logically pair with the Will. In fact, the Son in Sacred Scripture says He only does the Will of the Father. To the Son, we might logically pair with the Heart; since, the Human Heart is where one ultimately decides for or against GOD. The Heart is associated with Love, the love of a Human Person doing the Will of another Human Person, or the Son doing the Will of the Father. The Holy Spirit, we might pair with the Intellect, since the Holy Spirit is often referred to as the Wisdom of GOD, and who is associated with the Sacramental Graces of Baptism, Confirmation, and Holy Orders, as well as the graces afforded and produced by the other Sacraments.

 

Now just as we can speculate about an ontological or existential substantial interface between the substance of the Human Soul with the substance of the Human Body, perhaps given the unity and simplicity of the Human Soul from an ontological or substantial point of view, we can denote or lexicographically reify, the interfaces between the three primary faculties of the Human Soul which are the Will, Intellect, and Heart.

 

Now we might ask as to whether or not these lexicographically defined interfaces are real, perhaps even substantial, or para-substantial, and as such, whether or not they imply characteristics of the Human Soul or aspects of the Human Soul that have not yet been studied, or at least not yet addressed in any great detail in a rigorous manner.

 

If such interfaces do not exist, then how would each of the individual three faculties of the Human Soul interact with each other as a unity, and yet remain in tacked as individual psychic spheres of the Human Personality. It seems to me there must exist a transition boundary, by which what constitutes the existence and properties of each faculty is maintained, wherein each of the  three faculties retain their identity, but wherein they form a pseudo-substantial unity, in the form of the Human Personality, which to me seems to be a form of  a metaphysical mid-level between the very substantial or essence-wise aspects of the Human Soul and its transitory, or malleable accidental properties such as individual memories, sensations, thoughts, acts of volition, experiences, and other objective psychodynamic data, elements, and activities.

 

These facultative transition zones or boundaries might imply the existence of an even greater existential or ontological size of the Human Soul, and if such transitions zones or boundaries exist, perhaps the implications are profound regarding the study of ontological psychology or spiritual psychology, especial spiritual anthropology.

 

Now for the HOLY TRINITY, each of THE THREE DIVINE PERSONS has the same nature and is completely GOD, yet each person is distinguishable even though each PERSON is Consubstantial. Thus, there must be something to distinguish each of the THREE DIVINE PERSONS. The FATHERNESS  of the FATHER,  the SON-NESS  of the SON,  and the HOLY SPIRIT-NESS  of the HOLY SPIRIT are some perhaps exotic ontological DIVINE ASPECTS, that do not involve qualitative and substantial differences in the DIVINE  NATURE  of each of the THREE DIVINE PERSONS,  since They are Consubstantial. Thus we are left to speculate on the subject distinguishing characteristics of the each of the THREE DIVINE PERSONS.

 

In a more limited manner, the Will-ness of the Human Will, the Intellect-ness of Human Intellect, and the Heart-ness of the Human Heart can constitute an abstraction by which each of these three faculties are distinguished, while at the same time, each of these faculties of the Human Soul are truly the Human Soul.

 

Note that a much deeper elaboration on these notions will be posted in yet another revised version of this article to be posted sometime tomorrow or this Saturday, but wherein the Doctrine of the HOLY TRINITY is maintained in its full integrity, thus where it is assumed that each of the THREE DIVINE PERSONS is truly and completely GOD, and that each of the THREE DIVINE PERSONS is completely Consubstantial or that THEY equally share ONE DIVINE NATURE.

 

18)  Personal Musings On The Menagerie Of Planets: There Are Likely More Planets Within Just The Visible Portion Of Our Universe Than There Are Drops Of Water In The Combined Volume Of All Oceans, Rivers, Lakes, Aquifers, Etc., On Planet Earth. An Unlimited Number Of Specific ETI Psychodynamic Personality Trait Spectrums Is Possible Assuming That A Similar  Unlimited Number Exists Of The Same For We Humans.

 

I can imagine what a beautiful novel vantage point future human settlers and explorers will have, if say, they travel to a two star or a three star system that has at least one Earth like planet in a stable orbit around one of the stars. More specifically, image a triple system that included a G-2 star like the Sun, a red dwarf, and a deep orange K-class star. Throw in a habitable moon in orbit around a gas giant planet in such a stable orbit, and the view from the surface of the moon could be just plain and simply awesome.

 

I did a rough mental calculation in my head just now for which I assumed that one out of every ten stars has a planet that could be habitable or terraformable. on average. This works out to be 10 EXP 23 planets in just the visible portion of the universe alone.

 

Put it this way, imagine the very small end grains of flower such as from a bag of Gold Medal Brand Flower typically sold in supermarkets here within the United States. I assume that such low end range flower grains are only 100 micrometers across. Well then, the number of such planets would be equal to the number of such low end flower grains that would completely fill a 100 cubic kilometer volume. Ever take just a pinch of Gold Meadow Flower and throw it up into the air and notice the cloud that results which has far too many dust grains to ever count. I do not know about you folks, but I am lucky if I can keep a clear mental image of 10 mentally countable red dots in my mind at the same time.

 

Put another way, 10 EXP 23 is roughly equal to the number of drops of water within the combined hydrospheric water content on the entire planet Earth: all oceans, lakes, rivers, aquifers, and ponds combined.

 

This boggles my mind. We space-head; astronautical, physics, cosmology, and astronomy types are no stranger to dealing with numbers on the order of 10 EXP 23 in an abstract manner, but it is sometimes helpful to put such numbers in a concretely framed and tangible context. Just as assuredly as there is an esthetic and visceral artistic appeal in trying to grasp huge numbers, which are still only miniscule in comparison to much larger numbers such as those referred to as ensembles, the beauty we will discover on other worlds without end, can only spur us on to advocate for more bold space based observatory platforms for studying exo-planetary systems. The potential number of species of life forms is perhaps even more staggering.

 

Whether or not double or triple systems can have planets where such stars orbit each other closely enough to produce the above whimsically beautiful scenario  is another question, but my guess that that there are probably numerous systems right here in the Milky Way where the stars are far enough away from each other such that one star can have planets in stable orbit around it.

 

In short, we absolutely must go out and explore the cosmos. I am sure that all of you humanities types, some of who prefer to focus on the inner space of the human psyche such as many a sociologists, and psychologists, instead of the great unending eternal blackness of outer space, will agree,  if for no other reason than that of the ramifications of the potential numbers of intelligent ETI person species and civilizations that may adorn the Heavens. We will likely find that each civilization has its unique culture, and even in the event that evolution tends to favor the development of humanoid looking ETI persons, each species will likely have its unique statistical spread of associated psychodynamic, and psychogenic, personality trait spectrums that would likely include intelligence, temperament, emotionality, sociality, sexuality, sensuality, and all of the other fun and interesting aspects of created bodily intelligent life forms or bodily persons.

 

Now, the following  set of very broad psychodynamic or psychogenic traits and abilities exist within the human person.

 

Verbal intelligence, mathematical reasoning ability, artistic intelligence, interpersonal intelligence, social intelligence, emotional intelligence, sexual intelligence, motor skills, mechanical aptitude, creative ability, logical thinking ability, abstract thinking ability, volitional intelligence,  moral intelligence, short term memory, working memory, long term memory, autobiographical memory, the personality trait of anger, the personality trait of gentleness, the personality trait of bitterness, the personality trait of affection-ness, the personality trait of introversion, the personality trait of extroversion, the personality trait of paranoia, the personality trait of suggestibility, the personality trait of laziness, the personality trait of fun-loving-ness, the personality trait of intellectualism, the personality trait of emotionality, the personality trait of sensitivity, the personality trait of sensuality, the personality trait of perceptibility, the personality trait of emotional coldness, the personality  trait of emotional warmth, the personality trait of level of erotic sex drive, the personality trait of erotic effectionality, the personality trait of level of erotic sexual excitability, the personality trait of sexual endurance and efficiency, the personality trait of friendliness, the personality trait of being loving, the personality trait of being prideful, the personality trait of narcissism, the personality trait of trill and danger seeking, the personality trait of stimulatability, the personality trait of interior level or emotional, affective, or physic arousal or arousability, the personality trait of under-arousability, the personality trait of will power, the personality trait of interpersonal openness, the personality trait of truthfulness, the personality trait of being detailed oriented, the personality trait of multi-tasking ability, the personality trait of restlessness, the personality trait of level of emotion energy, the personality trait of mental energy, the personality trait of volitional energy, the personality trait of sexual energy, the personality trait of level or urgic tension, the personality trait of having a flat affect, the personality trait of schizothymic tendencies, the personality trait of cyclothymiic tendencies, the personality trait of goal orientedness, the personality trait of artistic temperament, the personality trait of purposefulness, and the list goes on and on.

 

Above, we have listed 64 specific personality and psychogenic traits, but the this set is far from being complete, even at the above level of general abstraction.

 

We can divide each of these traits or characteristics into very numerous sub-traits, which can likely be sub-categorized even further.

 

But we also have psychodynamic traits of specific personal interests. We also have the set of unique specific personal experiences, specific unique learned behaviors and talents, specific interpretations of one’s religious belief systems, specific likes and dislikes, specific interpersonal experiences, specific sexual experiences and behaviors, and the list goes on and on.

 

Now, imagine that each of the above specific 64 traits can be labeled on a relative scale by a real number, or by a level and quality ordinal that has a unique real number identifying label. Then the number of possible combinations of the traits is equal to R EXP 64 where R is the number of real numbers. This assumes that each trait exist on a perfectly continuous scale.

 

Since the human person is a unity from the psychic standpoint and is thus a simple, unextended, immaterial, non-corporeal, and spiritual being in terms of the entirety of his or her spiritual and immortal soul, we would not expect that time dependent change of psychodynamic states within the human psyche or soul to be finitely quantized.

 

Since the human soul is spiritual and simple, we might expect that each such trait exist perhaps not only in a non-finitely quantized varying manner, but perhaps at the level super-continuity of level 0 where the differential fundamental units of variation of each psychic trait is approximated by dx/(Aleph 0) where dx in the fundamental unit of difference between one real number having an unlimited decimal expansion and the next highest real number of unlimited decimal expansion.

 

Alternatively such psychic traits may vary at level  1 super-continuity where the differential fundamental units of variation of each psychic trait is approximated by dx/(Aleph 1) where dx in the fundamental unit of difference between one real number having an unlimited decimal expansion and the next highest real number of unlimited decimal expansion.

 

Yet alternatively still, such psychic traits may vary at level 2 super-continuity where the differential fundamental units of variation of each psychic trait is approximated by dx/(Aleph 2) where dx in the fundamental unit of difference between one real number having an unlimited decimal expansion and the next highest real number of unlimited decimal expansion.

 

Yet alternatively still, such psychic traits may vary at level 3 super-continuity where the differential fundamental units of variation of each psychic trait is approximated by dx/(Aleph 3) where dx in the fundamental unit of difference between one real number having an unlimited decimal expansion and the next highest real number of unlimited decimal expansion.

 

Yet alternatively still, such psychic traits may vary at level i super-continuity where the differential fundamental units of variation of each psychic trait is approximated by dx/(Aleph i) where dx in the fundamental unit of difference between one real number having an unlimited decimal expansion and the next highest real number of unlimited decimal expansion.

 

Note that here, i = 4,5,6, …, Aleph 0, …, Aleph 1, …, Aleph 2, …, Aleph (Aleph 0),…, Aleph (Aleph 1), …, Aleph (Aleph 2), …, and so on.

 

Note that Aleph 0 is the number of integers according to the renowned late 19th Century mathematician Georg Cantor. Aleph 1 is the number of real numbers which is infinitely greater than the number of integers by a factor of infinity. Heck, just between the numbers one and two on the real number line, their exist and infinite number of real numbers. Likewise, Cantor proposed an unlimited series of ever higher transfinite Aleph numbers, Aleph i, where i = 2, 3, 4, …

 

Factor in the range of possible unique specific experiences, mental and emotional images that are subjectively-experienced-time-dependent, unique emotional and affective states and nuances involved in our daily and remembered  subjectively-experienced-time varying personal experiences, and the number of possible psychic states is equal to perhaps R EXP (Aleph 1) even under the condition that the metric continuums are not super-continuous but are rather just plain continuous at the classical level of dx = 1/(classical number line infinity). Here, I assume that the number of possible specific experience forms under non-super-continuous but perfectly continuous metrics is equal to the number of real numbers.

 

Now what if, since the human psyche in its emotionality and sensuality and capability of interpersonal feelings, affections, act of love etc. is primarily defined on a non-numeric scale or a qualitative scale, these associated qualitative metrics perhaps are variable at a hyper-numerical discreetized level. Note that the concept of hyper-numeric here is associated with the notion of a hyper-extended abstract number line where there exists numerical values quantitatively and/or qualitatively greater than infinity on or along the hyper extended number line, or a number line that extends beyond infinity.

 

Given the uniqueness of everyones body and the fact that the human soul is created in uniform with the body it will be united to and that the human soul is in an ontological sense, the substantial form of the body it is united to, and the potential numbers of what it is like for one to be himself or herself is perhaps not clearly symbolically definable.

 

Sacred Old Testament Scripture rhetorically ask something like “Who but the Lord God Himself can judge the intensions of the Human Heart!”” Who but the Lord God Himself can comprehend the complexity and the tangled workings of the Human Heart!”

 

Now given that the number of types of ETI persons’ body forms is equal to at least the number of combinations of specific atoms that would comprise a body of similar size to an adult human body, the number of what it is like to be a specific ETI person given all of the possible genotypes and environmentally influenced ETI body and central nervous system forms is beyond comprehension.

 

Now if we further assume that each form of matter may have its own primitive type of consciousness or feeling as a kind of hidden variable that gets amplified in the brain in order to produce brain states that have a particular experienciality to the person having said brain, the numbers of what it is like to have a certain brain form, is absolutely astounding.

 

Consider that each universe may have its own unique relative physical constant values, relative masses of fundamental simple and fundamental composite particle, levels of space time curvature, and the like, and the numbers of potential forms of mass consciousnesses,  mass-energy consciousnesses, or energy consciousnesses goes to utterly infinite values in the limit that the number distinctive universes goes to utterly infinite values. And  this does not include the number of possible distinctively amplified matter, energy, or matter-energy consciousness states which are unique to every bodily person.

 

For the above reasons alone, all of you artist types, social scientists, and anyone else who contemplates the marvels of human nature and human interpersonal relationships should delight in the potential prospects of humans traveling to other extra-solar worlds and befriending any ETI persons and the civilizations to which the subject ET persons are citizens.

 

The cool thing is that we live at a time when the discovery of an Earth like planet having an  electromagnetic optical spectral signature of possessing a biosphere may occur within a decade or two from now. If we develop the technology and launch space telescopes that can detect one such planet, then in all likelihood, a plethora of additional such detections will follow.

 

As a friend of mine named Jason would say, “Cool Beans!” to which I would add, “Cool Beings!”

 

19) THE OPPORTUINITY FOR ETERNAL GROWTH OF THE HUMAN SOUL

 

 

 

The human soul according to traditional Catholic mindsets has substantial properties and accidental properties. The substantial properties of the human soul are viewed in main paradigms as being fixed or inalterable. However, the accidental properties of the human soul can increase or grow without limit. Even though accidents subsist in a created substantial principle, accidents are nonetheless real. As a result, human experiences, memories, thoughts, emotions, feelings, acts of will, instincts, drives, attitudes, and the like are real and have objective being.

 

Since it is possible for the human soul to exist forever, and  to be re-united with its Resurrected body forever, the possibility of the number and varieties of experienced events is utterly unlimited. The number of memories that the human soul can have is consequently, equally unlimited. Add the subjective intra-psychic reaction and the subjective interpretation of the future human person’s experiences and memories of events and the number of associated psychodynamic nuances in terms of conscious, sub-conscious, unconscious, emotions, feelings, attitudes, thoughts, sensations, intuitions, acts of will, drives, motives, motivations, social experiences, interpersonal experiences, intrapersonal experiences, romantic experiences such as may exist in some form of special spiritual bonding between husband and wife, or between boyfriend and girlfriend, perhaps even in the afterlife for all eternity, and the number of features, intra-psychic elements, experiences, and the like within the human soul can grow to an ever greater extent that is utterly unbounded in quantity, quality, and in variety.

 

In a real sense, the human soul can grow with respect to its natural accidental properties to an absolutely unbounded extent. These accidental properties can modify the faculties of the human soul including those of the intellect, will, heart, sensitive life, and memory.

 

Thus,  by the fact that each and every one of us possesses a spiritual and immortal soul, the opportunity for natural spiritual growth for all eternity awaits us in the next life.

 

20) TIME AND THE SOUL

 

Now back to some more pleasant topics including that of the human soul, which is of truly eternal importance and significance for each one of us. I hope I did not spook anybody with my previous post on the possibility of distant future Galaxy Scale Nukes that can produce Super-Planck Energy densities. Such devices are of truly miniscule importance in the eternal scheme of things for us on the level of the individual and our families and loved ones since we are destined to live forever, and we are all destined to arise incorruptible as a full union of our Resurrected mortal bodies and our immortal souls. The body will be definitively granted its own incorruptible life at the Final Resurrection and will be a perfect body in look, form, and function just as Jesus’s Resurrected Body is such.

 

For all women who read my blog who may have issues with anorexia and/or bulimia, or who struggle with body image, the Lord wants you to know that He deeply beholds the beauty of your female body, and you will have a body that infinitely surpasses the beauty of the most gorgeous bodies on Earth at present, and which will be radiant beyond belief with natural and supernatural beauty at the substantial and accidental level. Your body will be spiritualized in a manner that is currently unknowable. And this spiritualized body will not be the same as any spirit body or energy body that those having near death experiences claim to experience, but rather will be both a real physical body and a real spiritual body that has unimaginably more depth to its existence that any temporary spirit or energy body could ever have.

 

But you also have an immortal and spiritual soul that will also be glorified at the Final Resurrection. The Catechism of the Catholic Church also refers to the human heart as the inner core of our being that only we and GOD alone have access to and by which we decide for or against GOD.

 

 

Ever wonder about the deep  meaning of the statement, “Time is all we got!”

 

Well consider that our souls are created at the point in time of our conception and that according to the new Catechism of the Catholic Church and also in its Revised Version, the human soul is immortal, spiritual, rational, radically endowed with free will, immediately created by GOD, and in the index of the original edition, directly created by GOD, and not reducible to the mere material world, the principle of unity and identity by which we most resemble GOD, and the list of wonderfuls goes on and on.

 

It seems likely that the past states of the human soul in terms of experiences, whether of a mental, volitional, emotional, effective, sensitive, romantic, or whatever level are conserved in the present state of each human soul, and so even in the subjective sense of personal identity, the human soul continues to grow with time and will always grow with subjective dynamically experienced  consciousness from a mental, volitional, emotional, effective, and sensitive standpoint, even in the next life, regardless of where we end up.

 

Since the human soul is simple and unextended in a metaphysical sense, might the objective nature, essence, substance, and existentiality of the human soul also grow for all eternity?

 

I am proposing that just as our physical universe may evolve and grow forever, or just as our multiverse may evolve and grow forever, as a unity in a present that evolves without temporal future limits, perhaps the human soul as a substantial unity simply grows along its own world line of subjectively experienced time, and thus since the soul is its own principle of life and identity at least as far as its spiritual aspects are concerned, perhaps it self grows for all of future subjectively experienced times steps in all cases, if not in a consciously controlled manner, then perhaps in an autonomous, automatic manner.

 

I know that life can be difficult in the culture that is obsessed with being thin, and model like in appearance, but remember you are wonderfully and beautifully made by GOD, and you will be infinitely gorgeous by all objective and subjective metrics upon your complete Resurrection at the End of Time.

 

I am especially speaking to all of you women and girls who have body image issues. Trust me, you are not alone, I have known folks with such conditions and I have a relative who has been hospitalized for eating disorders. I find that some of the most attractive and beautiful women have serious body image issues.

 

As a large guy, in fact a 425 pound husky large framed guy, although morbidly obese, because I am a guy, I am not as effected by body image if for no other reason than society is more forgiving of guys who are overweight  then of women.

 

Still the thought and realization that I need to respect my body since it will be a part of me for all eternity, has lead me back into a regular weight training and walking program. I took a 1 ½ mile walk last in under full sun-light and found the walk very refreshing.

 

For all those of you who are depressed about your body or your state of life, give a gentle outdoor walk for about 45 minutes a try. Do not over exercise, but try to get some sunlight every day. I have been making an effort to walk on most sunny days and my mood is more joyful yet calmer because of it.

 

21) THE VEGETATIVE AND SENSITIVE ASPECTS OF THE HUMAN SOUL

 

Classical ontological interpretation of the human soul holds that it has three major qualitative aspects; 1) the vegetative, 2) the sensitive, and 3) the rational. The vegetative aspect is viewed as the aspect of our souls that interacts with our bodies and which keeps our bodies alive and vital. The sensitive aspect of our soul or the animalistic aspect of our soul is the aspect that we share with animals and which involves feelings, sensations, emotions, drives, and instincts. The rational aspect of our souls involves the higher faculties of spiritual heart, intellect, and free will.

 

Perhaps we have overlooked the vegetative and sensitive aspects of our soul in importance as we have from ancient times attempted to define ourselves above the animals that roam the planet. It might be the case that the vegetative aspect of our soul is akin or related to its essence in the sense that it is the overarching primitive first principle of our souls that is identical with the aspect of our soul by which the soul is the principle of unity, individuality, identity, and uniqueness that makes us who we are. Thus, the great portion if not the almost entirety of the vegetative aspect of our soul might not be experienced, understood, or even known by us as individuals as we go about our daily lives. The vegetative aspect of our soul may be similar or analogous to the Freudian concept of the Unconsciousness.

 

Ever notice how at times we almost seem to feel the personality of persons especially those that strongly affect us emotionally, for better or for worse. Sometimes we have insights about other people almost as if we can feel some aspects of their personality that they seem to be unaware of.

 

For instance, we may have experienced a situation of being in the presence of a person of the opposite sex who we find extremely attractive in looks, figure, and in personality and temperament and upon having a sense that such a person is really hot, have somehow became involved in a discussion about ourselves where the person we find very attractive will state that he or she is not into romance, or that he or she is gay or lesbian, or that he or she in very calm and unemotional. I have experienced such discourse with certain beautiful women who strongly appear to be people persons and who are very expressive emotionally, and for which I am tempted to judge the person by thinking to myself, “RRRrrriight!”

 

Now for all of you liberated women out there, do not misunderstand me here. I am in no way a chauvinist or anti-female. I am merely offering an anecdotal account of how it seems at times that we can almost feel the personality, perhaps even the unconsciousness of certain persons that we are attracted to, or who perhaps we have a strong aversion to, or who intimidate us. It is almost as if we can sense some aspect of their vegetative souls that even they are not consciously aware of and which perhaps they are incapable of being consciously aware of at least in this life, yet which is central to the core of their spiritual constitution.

 

A similar situation can perhaps be said for the sensitive life or sensitive principle of the human soul. We at times have experienced being in the presence of someone who we find especially attractive and who we may have  flirted with, and for which they responded mutually in kind. It seems at times as if we can almost read an aspect of their conscious or subconscious emotions. Most theologians, psychologists, sociologists, biologists, psychiatrists, medical doctors, and the like will write these casual if only temporary strong feelings of sexual attraction off as primitive casual animalistic instincts, or as the result of primitive body language interpretation, or perhaps as a result of unconscious signals transmitted by chemicals referred to as pheromones. However, we all have likely felt that at times, there was a person of the opposite sex that was at the right place at the right time to give us some sort of affirmation almost as if there was a spiritual aspect and mysterious reason why the encounter occurred, even in the case that we will likely never meet or see this person again in this life.

 

The reason for these anecdotal personal accounts  is to leave the reader with a sense of mystery regarding the vegetative and sensitive aspects of the human soul which in the long run are just as important and mysterious as the rational aspects. It is through the ability to experience and through intuitive perception that we experience ourselves, our loved ones, and very attractive strangers that we seem to encounter if only in a passing and fleeting manner, that seems to be of most importance in human relations and in human bonding. Those engaged or newly married on honeymoons tend to be in love with their partners, and this romance would not be possible for those they dislike even if they loved the person they dislike out of sorrow or empathy for the person such as a personal object of their dislike that may have unpleasant personality traits or dispositions yet which may be suffering in some sad manner.

 

However, there seems to be some even more primitive aspect of the human soul, that makes the given human soul itself or the soul that it is and no one other person’s soul and which per dues no matter how the life and personality of a given person evolves. Even given the bazaar mental disorder of multiple personality disorder, we are bound by faith to believe that each human person and each human body has only one distinct and substantial spiritual and immortal principle united to it, and that is the person’s or body’s spiritual and immortal soul. Could this even more primitive aspect of the human soul, if I am correct in my speculations be somehow related to a pre-unconsciousness, or an ultra-unconsciousness: a sort of principle that is the soul itself, but which is the very ontological essence of the soul, or principle that makes the soul a soul or the soul itself?

 

Regardless, to any persons who has read the entirely of this article, in all of its 129 pages in Time New Roman 12 point font, you can be absolutely sure that even if the entire content of this article is true, there is so much more yet to learn about our souls, that we will likely learn new things about our souls for all eternity in the next life. Part of having access to the wonders of all creation is to have access to the wonders of ourselves, our souls, the souls of those we love, and the souls of those beautiful strangers that are sometimes placed within our midst, but which leave a permanent impression on us, even though we may never see them again in this life.

 

 

 

 

 

22) Non-academic Forms Of Intelligence

 

As I was driving to Chincoteague Virginia for a vacation on the Eastern Shore of Virginia relatively recently, I was thinking about the topic of emotion, feeling, affect, instinct, sensuality, sexuality, and romance.

 

As I became deeper in thought, it occurred to me how emotions and moods can morph in a continuous manner in many cases, which is in stark contrast to the process of algorithmic reasoning whereby one solves a math or other problem in a step by step discretized manner. It is of course also true that conscious thought and other so-called higher level intellectual process can undergo similar continuous morphing and typically does so.

 

I had begun to look objectively at the Platonic and Aristotelian notion that the higher faculties of reason and will  are spiritual and are therefore independent of matter and which are allegedly evidence of, and due to,  a spiritual and immortal soul. The theological system of Saint Thomas Aquinas also holds to such a mindset.

 

However, something seemed wrong with the above lower/higher level distinction between emotion, feeling, affect, instinct, sensuality, sexuality, and romance on the one hand and algorithmic reasoning processes and volition on the other hand. After all, emotions, feelings, affect, instinct, sensuality, sexuality, and romance continue can  be present even in situations where algorithmic reasoning and free volitional processes are impaired or disabled such as by chemical intoxication, mental exhaustion, brain injury, certain neurological, mental, emotional, or psychological conditions and the like.

 

It seems that the very last vestige of consciousness to undergo corruption in this life is the instinctual, affective, and sensual, such as for persons on their deathbed who have been in so-called minimally conscious states, or who have suffered several years of progressing dementia.

 

Upon consideration of the ubiquitous-ness of human sexual expression, even among those who are most intelligent among us such as Albert Einstein who was known at the time to have been somewhat of a womanizer, and the numerous instances of Catholic clergymen who have violated their vows of celibacy, as some do, and who  have consequently ended up leaving the Priesthood, I mused that even those who are most psychologically astute among us have a psychodynamic nature that is infused with sexuality.

 

Such psychodynamic sexual infusement seems to be ubiquitous, from the undergraduate college curriculum attending young woman who was raised Catholic who becomes sexually involved with her boyfriend, to the high school age intelligent and inhibited young studious women who claims to have no sexual feelings nor romantic inclinations but who falls in love and gets married after college and who then feels the subjective need to forsake her Catholic faith by using artificial contraception to avoid unwanted or untimely pregnancy.

 

I am by no means being judgmental here. The point is that the instinctual, affective, emotional, sensual, sexual, romantic, and intuitive aspects of our psychodynamic make-up are every bit a part of our personalities as our algorithmic reasoning abilities, and our free will.

 

Contrary to what extreme rationalists claim or would like to claim, the above sensitive aspects of our personalities provide meaning and context for what we do, as well as motivations. Our free wills would not make a choice if they were not presented with a motive, and motives are essentially derived from emotions, feelings, acts of will, sexuality, romance, and sensations.

 

Extreme rationalists would like to disagree with me on these accounts, but I must say that even persons who are doing Christian deeds that cause him or her mental, emotional, intellectual, or sensual pain, are doing such acts because they have a motive that many of  such personal acts depend on to be freely generated. Most likely, for those who are competitive or who like to view themselves as intelligent, such acts are primarily the result of a desire for enhanced self-esteem, enhanced sense of self-worth, a compassionate love for those who are less fortunate, or a sense of duty which often has strong conscious, subconscious, and/or unconscious affective underpinnings.

 

The reality of human affective life thus seems just as important if not more important than the reality of algorithmic reasoning abilities, working memory for such algorithmic reasoning abilities, and the like. Ask any two PhDs  who are newlyweds and I am sure that if they are psychologically healthy, sex and romance are top on their list of priorities. The fact that so many otherwise perhaps inhibited Catholic newlywed couples often take to using artificial contraception, or feel a need to do so after they have a few children shows just how important human sexual expression is to them. For those professional white collar workers who  want to view themselves as independent but who are involved in cohabitative and/or serial romantic relationships, the same argument can be applied. Even high school age Catholic or Christian girls often become involved in necking or heavy petting under the false guise that such behavior is not sexual.

 

Now I am not trying to be overly Freudian here, but perhaps Freud was onto something about the power and ubiquitous nature of the human ID.

 

Regarding Sacred Scripture, we are said to be required to love GOD with our whole mind, soul, heart, and will. Such love will necessarily have affective influences even if such influences are not consciously perceived by the Christian.

 

The new Catechism of the Catholic Church refers to the human heart almost in seeming distinction to the human soul where the heart is that innermost aspect of our being by which we decide for or against GOD. Here, the heart is not synonymous with the blood pumping organ referred by the same word, but rather seems to indicate that deep inner psychic life that makes us the alive and experience capable personal beings we are.

 

Now,  I do not mean to insult any of you rationalists who may be put off by the contents of this writing, but if you consider carefully and objectively, the various emotions you experience throughout the day, and the manner in which you react to them, you will become aware of the effects of such emotions on your behavior. Such emotionally driven behavior takes the form of gasps of disgust or anger at hearing the news of the rape and murder of a little girl, the actions of pedophile clergyman or high school teachers, the impersonation of military officers by those who have never served, the anger and unkind words often expressed toward homeless folks begging for money on the street corner and the like. All of these reactions are motivated by affective elements within the psyche of the human person experiencing them.

 

Now, I am not intending to insult or demean any persons who are shy, quiet, introverted, laid back, or otherwise socially and emotionally inexpressive. I have found that such persons tend to be humble and in actuality, tend to be affectively and emotionally warm internally as well as being highly intelligent. In fact, psychological studies seem to indicate that such persons are reserved because they have a higher level of internal arousal and feel a subjective, although perhaps sub-conscious or unconscious need, to be calm or remain calm. Some mental illnesses such as schizophrenia are associated with higher levels of internal arousal as are persons of Asian descent.  In fact,  the populations of the countries of North and South Korea, China, Japan, the Philippines and the like tend to have a higher prevalence  of the disorders of schizophrenia compared to western cultures and also tend to have higher levels of internal arousal and higher metabolisms.

 

Thus, emotionality, sensuality, romance, affectivity, and the like are vitally important dimensions in all cultures and persons. Some of the most intelligent and rational persons are among the most sensitive and romantic.

 

There seems to exist other forms of intelligences not measured by IQ tests, SATs, or college entrance exams. Some such forms of intelligence are emotional intelligence, affective intelligence, sensitivity or acuities intelligence, social intelligence, romantic intelligence, sexual intelligence, social intelligence, interpersonal intelligence, creative intelligence, intuitive intelligence, moral intelligence, and spiritual intelligence, and some would say paranormal intelligence.

 

Since the life of Heaven among the Blest is primarily lived out in interpersonal relationships and in cooperative and unitive love, one can argue that at least a limited portion of the above non-academic intelligences are primary within the abode of the Blest in Heaven. In fact, the life of the HOLY TRINITY has the absolute perfection of being a life of pure mutual interrelationship. Since love is said to be above all else, and love exist in the context of personal entities as such entities share with themselves as well as with others, the HOLY TRINITY can therefore be said to possess absolute, utterly unbounded, super-infinite, interpersonal intelligence. The ONE, TRIUNE GOD, THRICE HOLY, can be said to have the utter absolute and unbounded perfection of personality. Moreover, this perfection of personalities is possessed by each of the THREE DIVINE PERSONS, FATHER, SON, AND HOLY SPIRIT  by virtue of their consubstantiality as being each totally and completely GOD, as well as by virtue of the relations  that constitute each DIVINE PERSON as a separate PERSON.

 

Since we model GOD as being made in HIS IMAGE and LIKENESS, we will share in that DIVINE LIFE of PERSONALITY PERFECTION  and PURE MUTUAL INTER-RELATIONSHIP  in a much more full manner than we can on Earth.

 

However, once again, I mean no disrespect or disappointment to those possessing very strong academic or algorithmic reasoning talents as every noble aspect of our nature in this life will be enhanced beyond our currently ability to comprehend, and this enhancement also includes brain based academic intelligence which is live out most fully in this life by algorithmic reasoning in its concrete, abstract, mathematical, logical, and verbal forms, as well as in the intellective faculties of short term, long term, and working memories.

 

Regardless of whether or not we are extreme cyclothymic extroverts as I am; or pensive, reserved, type B, introverts who are folks that can be annoyed by my occasional seemingly prideful bantering and rightfully so at times (comes from my upbringing within a large family),  our affective and sensitive life is vitally important and will be a part of our psychodynamic constitution for all eternity.

 

When we extoll the life of academic rational intelligence over that of affective, emotional, social, interpersonal, and the like non-academic intelligence, we fail to prepare the next generation to deal with matters of sexual morality and emotional soundness and resilience which are needed in this fast pace modern civilization where temptations to immoral behavior of the sensitive life are ever present and which can be succumbed to if we are not careful.

 

Just as we can ponder the huge number, essentially a huge infinity of possible forms of thought, or intellective thoughts in general, we can also ponder the huge number, perhaps equally infinite, if not much more so, of the possible feelings, emotions, affective experiences, sensations, acts of platonic, romantic, erotic, and sexual love and intimacy, that are possible to experience. It is therefore, the purely rational algorithmic forms of though and expression, combined with volitional ability or free will, combined with the affective or sensitive life, that determines the shear hugeness of the accidental nature of every human soul in all of its faculties, intelligences, and abilities.

 

We should teach the youngest generation which is now in grade school a deep respect for their affective and sensitive life instead of teaching them that such fundamental aspects of our being are to be suppressed or stamped out. Only with such self-knowledge will they be able to deal with temptations of the flesh and to give authentic examples of ways to live that are truly pro-life. An end to the legalized and widespread practice of abortion, the use of artificial contraception, and other actions that effectively unjustly terminate the lives of human persons will most likely require such a new approach.

 

 

 

23)  There Is Just Something Magnificently Immutably Eternal About The Human Soul.

 

 

Towards the end of offering up the petty annoyances we can at times experience from family, relatives, friends, co-workers, and colleagues, I have the following of what I hope will be an inspirational short digression into the need to have a certain humility before all of GOD’s rational creatures, philosophically typically referred to as created persons.

In these times of modern scientific reductionism, our bodily vulnerability and weakness has been made so clear in the tragic deaths resulting from the sudden and ongoing disaster in Japan. We long for a sense of human transcendence in a time when it seems that even the existence of a spiritual and immortal human soul seems uncertain in the minds of many of clergymen.

 

 

When Saint Thomas said that the Human Soul is the substantial form of the body, he was not saying that it physically looked like the body, rather he was using the Platonic or Aristotelian concept of eternal, immaterial, and perfect forms as the reified abstract ideal ideas that things represent.

 

 

Saint Thomas referred to the Soul as the substantial form of the body, ‘substantial” meaning a first created principle of being that is intrinsically independent of the body for its existence and for some of its more advanced operations.

 

 

Now once again, given the Scholastic interpretation of the nature of the human soul, that is the human soul is: 1) Spiritual, 2) Naturally immortal, 3) Incorruptible per addends and per se, 4) Simple, 5) Unextended, 6) Without shape or size, 7) Non-material, 8] Non-corporeal, 9) Rational, 10) Free, 11) A first created principle, 12) An essence or a being which exist per se, 13) Independent of the body for its existence and to some extent its operations in this life, 14) The substantial form of the body in the Ancient Greek philosophical sense of the word, 15) Directly created by God, 16) Immediately created by God, and if I am not mistaken, 17) Multiple meaning that it is completely and totally present and united to every portion of the human body that is alive, we have much grounding through the use of natural reasoning that the human soul is naturally immortal and naturally indestructible. In all, we have at least the above 17 transcendent dignities of the human soul if Saint Thomas Aquinas is to be believed.

 

 

Now read through these quotations from the new Catechism of the Catholic Church which was approved by the very highest levels of the Vatican during 1980s.

 
Part 1, Section 1, Chapter 1, SubSection 2

 

 

33 The human person: with his openness to truth and beauty, his sense of moral goodness, his freedom and the voice of his conscience, with his longings for the infinite and for happiness, man questions himself about God’s existence. In all this he discerns signs of his spiritual soul. The soul, the “seed of eternity we bear in ourselves, irreducible to the merely material”, 9 can have its origin only in God.

 

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 1

 

 

360 Because of its common origin the human race forms a unity, for “from one ancestor [God] made all nations to inhabit the whole earth”: 226

O wondrous vision, which makes us contemplate the human race in the unity of its origin in God. . . in the unity of its nature, composed equally in all men of a material body and a spiritual soul; in the unity of its immediate end and its mission in the world; in the unity of its dwelling, the earth, whose benefits all men, by right of nature, may use to sustain and develop life; in the unity of its supernatural end: God himself, to whom all ought to tend; in the unity of the means for attaining this end;. . . in the unity of the redemption wrought by Christ for all. 227.

 

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 2

 

 

363 In Sacred Scripture the term “soul” often refers to human life or the entire human person. 230 But “soul” also refers to the innermost aspect of man, that which is of greatest value in him, 231 that by which he is most especially in God’s image: “soul” signifies the spiritual principle in man.

 

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 2

 

 

366 The Church teaches that every spiritual soul is created immediately by God – it is not “produced” by the parents – and also that it is immortal: it does not perish when it separates from the body at death, and it will be reunited with the body at the final Resurrection. 235

 

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 2

 

 

367 Sometimes the soul is distinguished from the spirit: St. Paul for instance prays that God may sanctify his people “wholly”, with “spirit and soul and body” kept sound and blameless at the Lord’s coming. 236 The Church teaches that this distinction does not introduce a duality into the soul. 237 “Spirit” signifies that from creation man is ordered to a supernatural end and that his soul can gratuitously be raised beyond all it deserves to communion with God. 238.

 

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 4

 

 

382 “Man, though made of body and soul, is a unity” (GS 14 # 1). The doctrine of the faith affirms that the spiritual and immortal soul is created immediately by God.

 

 

Part 1, Section 2, Chapter 3, Article 11, SubSection 1, Heading 2

 
997 What is “rising”? In death, the separation of the soul from the body, the human body decays and the soul goes to meet God, while awaiting its reunion with its glorified body. God, in his almighty power, will definitively grant incorruptible life to our bodies by reuniting them with our souls, through the power of Jesus’ Resurrection.

 

 

Part 1, Section 2, Chapter 3, Article 12, SubSection 6

 
1052 “We believe that the souls of all who die in Christ’s grace . . . are the People of God beyond death. On the day of resurrection, death will be definitively conquered, when these souls will be reunited with their bodies” (Paul VI, CPG § 28].

 

 

Part 2, Section 2, Chapter 1, Article 1, SubSection 7, Heading 5

 
1280 Baptism imprints on the soul an indelible spiritual sign, the character, which consecrates the baptized person for Christian worship. Because of the character Baptism cannot be repeated (cf. DS 1609 and DS 1624).

 

 

Part 2, Section 2, Chapter 1, Article 2, SubSection 3

 
1304 Like Baptism which it completes, Confirmation is given only once, for it too imprints on the soul an indelible spiritual mark, the “character,” which is the sign that Jesus Christ has marked a Christian with the seal of his Spirit by clothing him with power from on high so that he may be his witness. 121

 

 

Part 3, Section 1, Chapter 1, Article 1

 

 

1705 By virtue of his soul and his spiritual powers of intellect and will, man is endowed with freedom, an “outstanding manifestation of the divine image.” 8

 

 

Part 3, Section 1, Chapter 1, Article 1

 

 

1711 Endowed with a spiritual soul, with intellect and with free will, the human person is from his very conception ordered to God and destined for eternal beatitude. He pursues his perfection in “seeking and loving what is true and good” (GS 15 § 2).

 

 

Part 3, Section 1, Chapter 2, Article 3, SubSection 2

 

 

1934 Created in the image of the one God and equally endowed with rational souls, all men have the same nature and the same origin. Redeemed by the sacrifice of Christ, all are called to participate in the same divine beatitude: all therefore enjoy an equal dignity.

However, from Sacred Scripture, we are warned not to worry about those who can kill the body but cannot destroy the Soul, but rather fear HIM who can destroy both body and soul in Hell. Even among spiritual anthropologists, there is some disagreement over whether or not the Soul is immortal by grace only, and even in some cases, whether or not the human soul can and may ceased to exist in Hell, at least after a while.

 

 

However, the Church Teaching on the Human Soul is that it is indeed immortal. The Church teaches that Hell is eternal, most especially a state of eternal separation from GOD. I still struggle with what such statements imply in the utmost rigorous sense given the mysterious and currently veiled ultimate plans of GOD in HIS Divine Economy.

Now, assuming that Hell is eternal, especially in eternal separation from GOD, we can come to an agreement that such eternal separation signifies a lack of Sanctifying Grace, even in the case that Souls in Hell last or live naturally forever because of any absolutely universal grace of immortality bestowed on the condemned and saved alike.

 

 

What we can be assured of is that the Supernatural Grace or Life of every human soul still on this side of the curtain of death can be corrupted by free and even semi-free sinful acts. We can also likely assume that the accidental properties of the human soul can become corrupted, including those of Saintly and wise old folks who become ill with dementia such as Alzheimer’s decease, strokes, and other age related problems. Severe mental disorders such as Schizophrenia can result in a partial disintegration of the personality of those afflicted with such conditions especially in the 1/3 of the cases that are notoriously hard to treat even with the best medications.

 

 
However, assuming that the punishment of Hell is eternal, the Souls who unfortunately end up in Hell, remain precisely the Souls and Persons they are, regardless of the accidental and perhaps even substantial degrading or even at least partially corrupting effects of material agents referred to as Hell Fire even if such materials are non-physical.

In order for a Soul to be forced to undergo everlasting punishment, there must be an utterly eternally lasting personal identity of the condemned that is as utterly naturally immutable as the morally binding state of the Soul that merits eternal punishment and separation from GOD.

 

 

GOD cannot non-contradictorily punish a Soul in an eternally binding matter if the punished human soul cannot undergo eternal punishment in a morally binding manner that presupposes the eternal existence of the personal identity of the condemned souls.

In order for eternal punishment to even be plausible, eternal personal responsibility of the eternally punished presupposes the utterly eternal existence and immutability of the characteristics of the condemned soul that make the condemned soul the person that it is, and not, not the soul or person that it is.

 

 

This aspect of the Soul is the very heart of its identity and existence, even in cases where the accidental properties and at least some secondary substantial properties of the condemned souls can be and in at least some cases, perhaps are corrupted in eternal damnation.

 

 

A person must always be his or her person and a human soul must always be itself and nothing else, in such a manner that the nature, existence, and essence of the person being his or her person and the nature, existence, and essence of the soul always being itself cannot ever be corrupted otherwise, the morally binding judgment of GOD in the manifestation of eternal punishment would have no reason for being real or existing.

 

 

Perhaps the above argument points to some sort of essence of the substance of the soul which in turn supports its accidental properties. What this property or meta-substantial or super-substantial entity is may remain a veiled mystery, but if such a reality exist in or for the human soul, it is certainly immutably what it is.

 

 

 

God will never take back what HE has created, especially with regards to the existence of human souls, even those that unfortunately end up in Hell. The same argument can also be applied to the angels including the fallen angels. IMHO, since the punishment of Hell is severe, the souls that go there are most assuredly fully naturally alive and will remain so for all eternity. Otherwise, they could not experience the effects of severe punishment.

 

 

 

Now we can and should rebuke maleficent evil spirits as enemies of GOD when we fall under their attacks, but we must never curse either condemned human souls nor fallen angels including Satan out of vengeful hatred or out of an angry desire or hateful desire for GOD to harm them. Such evil spirits are miserable enough, and as fellow rational creatures, we thus share a solidarity with them as fellow created persons, even though such persons will never appreciate this fact. For in a real sense, the Love of GOD shines on the just as well as the unjust.

 

 

Now do not get me wrong, I am in no way advocating collusion with, worship of, or even moral praise for evil spirits, although I am certain that to hate such persons and to vengefully call down GOD’s wrath on them is a strong sign of personal undue pride or lack of humility. Besides, when we give into the temptation to vengefully curse evil spirits, we travel down the road a little closer to Hell ourselves.

 

 

By all means, rebuke the attacks of Satan and His followers and pray daily for protection from them, but then so in a spirit of humility, the same humility expressed in the phrase “we humbly pray” in the famous prayer to Saint Michael the Archangel where we ask for His protection “from the wickedness and snares of the Devil”.

 

 

 

IMHO, there are many mysteries, both philosophical and theological about the human soul, and we will have all eternity in Heaven to ponder them in utter joy and peace and with an utter sense of delight in the whimsical. Let us strive to love all GOD’s creatures and put aside the hate. Our former World War II enemies in Japan, now our friends, offer us a lesson on civility and chivalry as they band together to support their fellow country men and women in the unfolding tragedy that has stricken Japan.

 

 

If a 1980′s militaristic redneck son of a career nuclear Navy man such as my former self can come to express a certain humility with regards to the worst of enemies of the human race, although I admit that I am far from sainthood and will in fact be attending the Sacrament of Reconcilliation within a week of today, then perhaps all of us can feel more confident in a developing ability and grace to offer up our daily trials and tribulations at the hands of others still living.

 

24)  The Great Dignity Of The Human Soul Even If It Would Be Immortal By Grace, Only. But Not To Worry, All Human Souls Are Immortal, And Saint Thomas Aquinas Held That Each Human Soul Is Naturally Immortal, And He Did Not Become A Saint And Earn The Title Of Angelic Doctor Of The Church For No Reason At All.

 

 

Note that in some of my past writings, I have expressed concern regarding the possibility that the ultra-high temperatures and thermodynamic gradients near the heart of nuclear explosions might somehow injure or somehow temporarily destroy human souls. Since I have been a follower of some of the occult-like literature regarding extraterrestrial and ultra-terrestrial space alien and UFO encounters from a sociological perspective as well as from the perspective of a postmodern physicist with an open mind, I am aware of some of the reported accounts of persons who claim telepathic contact with such ET and UT bodily persons where such extraterrestrials have made claims at times that the human or for that matter, any souls can be destroyed by close proximity to a nuclear explosion, even the souls and spirits of astral travelers. Among other threats posed by nuclear weapons, the so-called ability of such devices to allegedly destroy souls is one of the reasons such ETs believe that nuclear weapons use can be  horribly evil.

 

Now please do not worry that Jim has gone off on some sort of a New Age conspiracy theory mode. I simply believe in utilizing all resources of potential knowledge for the betterment of human civilization. I have for a very long time tried to prove to myself that the human soul is naturally incorruptible per addends and per se and thus utterly naturally immortal and it may well be so in the spirit of the writings of Saint Thomas Aquinas, however I have never been able to prove such to myself beyond a shadow of a doubt. The claim by modern Catholic Theologians that the human person is not complete without the human body as well some of their claims that the Catholic Church’s formally approved teachings on the human soul do not so much seek to explain the immortality of the human soul so as to merely assert it, makes my job all the more difficult in my attempts to prove the natural indestructability of the human soul.

 

However, we can assert with absolute certainty that all human souls will be reunited with their Resurrected and Incorruptible bodies, even so for the souls who go to Hell. The condemned will have to undergo some form of suffering and deprivations in eternity but they will never cease to exist, not even after the Final Resurrection of the Dead. Thus, if the human soul is immortal by grace only, we can be assured that at some level or another, all human persons have some form of grace by virtue of any gratuitous immortality of the soul, and all human persons will partake of the Final Resurrection of the Dead, even persons who go to Hell. These are premises which I feel we are absolutely safe in assuming as least bounding conditions on the nature of effective human immortality

 

My tendency is to believe that the human soul is naturally indestructible and naturally immortal in the spirit of the teachings of Saint Thomas Aquinas, however, even in the case that the accidental form of the soul could somehow be annihilated by a nuclear explosion, the substantial nature or essence of the soul likely could never be annihilated by anything but GOD acting directly.

 

Since the new Catechism of the Catholic Church teaches that all human persons share a fundamental moral equality before our Creator, and are all equally composed of a body and a soul, my feeling is that in this life, our daily waking conscious identity with respect to our souls is analogous to the consciousness of a new born baby with respect to its spiritual and immortal soul.

 

Even in the event that souls who end up in Hell suffer eternally, the state of their suffering conscious identity may only be a tip of the ice burg regarding their complete and entire soul much as the crying of a baby  cannot be said to detract from the natural dignity and sacredness of the baby’s truest natural self of its spiritual and immortal soul.

 

I am convinced that President Obama’s Nuclear Posture Review and His desire to rid humanity of nuclear weapons is a good and noble goal. I am also absolutely convinced that in the off chance that human or ET souls could be destroyed by nuclear weapons and in some unfortunate circumstances, might be, all such persons will be Resurrected body and soul on the last day to Eternal Glory for having gone through the martyrdom of any soul death. One thing we can be absolutely sure of is that we will all be resurrected complete and whole on the last day. Even the souls who do not make it to Heaven will be reunited with their bodies made incorruptible although such persons will undergo unspecified suffering to an extent and nature for which  we have no certain knowledge, but they will last forever, body and soul.

 

One great spiritual writer of the late 19th early 20th century held an expressed written belief that our daily conscious life and identity in this life bellies a vast infinite ocean of existence which is our spiritual and immortal soul in each and every one of us. This ocean of existence is unfathomably infinite in extent and in depth, and accordingly in this life we catch just a surface glimmer as of an ocean surface ripple or wave of the infinite ocean of existence that is our souls. Perhaps this surface glimmer is the accidental form or surface glimmer of our souls in the form of our conscious waking identity in this life. If this is the case, and I believe it to be so, then we can bear all things with a little more confidence and hope in an eternal future where we will have access to the wonders of GOD, HIS THREE PERSONS, the Angels, Saints, All Human Persons in Heaven, All ET Persons in Heaven, and any and All so called Ultra-terrestrial Persons in Heaven, as well as the Wonders within Our Selves and Our Loved Ones, as well as of the Rest of Creation.

 

Another way of looking at daily waking conscious life in this world is to make the analogy that daily waking consciousness relative to the substance or essence of the human soul is more or less similar to the relationship between a person watching a movie in a movie theater and the person’s his or her own self. Even if the movie is suddenly interrupted or stops playing, the person still exists in all of his or her existential integrity with the conscious experience of watching and affectively engaging the movie being more or less akin to the daily waking consciousness or perhaps even the accidental properties of the human soul such as might exist in their totality in the form of the unconscious, sub-conscious, and/or conscious psyche.

 

Perhaps another way of making the analogy is to consider the concept of a light bulb whereby the illuminated state of the light bulb represents our daily conscious psychic activities or perhaps at least a portion of our soul’s accidental properties  as distinct from the substantial or essence-wise ontological properties of our spiritual and immortal souls.

 

The substantial or essential aspects of our souls continue to exist naturally incorruptible per addends and per se even if the accidental state of the metaphorical illuminated light bulb is turned off.

 

Yet another way of perhaps making the analogy is to consider the concept of a garden hose that is spraying water into a garden where the water transmissive state of the hose corresponds to the daily working conscious life of the human person or perhaps at least in part, the accidental properties of the human soul whereas the hose itself continues to exist just fine regardless of whether or not it is transmitting water. One could say that the hose is being more useful if it is transmitting water to water a garden relative to its state while not being used and make such an analogy with regard to a human soul in this life being in the habitual state of mortal sin verses another soul being useful in a practical applied manner such as the case of a devout person who works for a charitable non for profit corporation and yet who does volunteer work such as helping out in a homeless shelter or who visits the imprisoned or institutionalized. In both cases, the ontological good of the substance or essence of the soul remains incorrupt and continues to exist just fine.

 

Given the sad reality of Hell, and the fact that GOD loves all of His creatures especially created persons, regardless of whether such persons are in Heaven, on Earth in this life, are of the form of  any extraterrestrial or so called ultra-terrestrial persons that might exist, are in Purgatory or perhaps in Hell, I cannot logically see how the relationship between the accidental properties of the soul and our conscious daily working psyches and the substance or essence-wise properties of our souls could be otherwise interrelated.

 

A modern popular Catholic encyclopedic dictionary that I purchased from a local Catholic book store states (in an entry on the subject related to what is Good and the subject of  the Divine Economy) that Satan has a nature that is essentially very good although he uses his nature for the morally evil purpose of furthering his agenda.

 

Now the sad reality of Hell and eternal separation from GOD that results is no triviality and we must do all in our power to avoid going there, but we must remember that GOD’s love shines on the just as well as the unjust and we are all morally equal in this life before GOD.

 

We have forgotten this fact as a result of modern psychodynamic existentialism and other crap that has entered the halls of even seminary formation programs for the Priesthood.  I will even hazard a guess that the ubiquitous-ness  of the sin of abortion is the result of the loss of belief in the sanctity of the human soul in every instance. It is not quit so much the sin of a poor hurting young adolescent girl who obtains an abortion for herself as it is the sin of affluent politicians and health care workers who do not speak out on this issue and who support groups like Planned Parenthood and other trashy organizations.

 

Most assuredly, the Lord looks more kindly on the poor hurting emotionally disturbed adolescent girl who feels she must have an abortion just as he had mercy on the adulterous women about to be stoned by the elite establishment in the Gospels than on even the affluent white collar psychiatrists and therapists who may feign compassion for the hurting woman while suggesting to her that it is OK to have an abortion if she feels she needs one while at the same time perhaps looking down on such emotionally disturbed young women thinking that such women are primitive or primitive drive motivated and all of this other psychodynamic Freudian existentialist crap that has even made its way into formation programs within many of modern day Catholic seminaries.

 

Part of the signs that a civilization is coming close to its end is how the so called devout Catholics who feign conservatism look down on, discriminate against, or otherwise display a self-righteous attitude toward those who are viewed as unfit or unworthy because they are emotionally, psychologically, and/or intellectually disabled, or because perhaps they are poor, unemployed or undereducated, or perhaps who have a hatred for those on death row and support the death penalty in an overzealous manner when the late Pope John Paul II stated that there is virtually no case where the death penalty needs to be administered and that we have the technology to keep even the most severe felons safely separated from society.

 

Remember, such hateful attitudes had developed in NAZI Germany before World War II and we are already well underway in the process of America’s Holocaust, the results of the Supreme Court ruling of Roe Verses Wade. One is tempted to think that perhaps the start of eternal punishment is at least in part the natural result of Suns falling down from the sky in the form of high yield nuclear warhead detonations over our metropolitan areas. The Miracle of the Sun at Fatima is truly meant to be a message of peace, but to the extent that we live in self-righteous hate and indignation for those of lesser degrees of intellectual, psychological, social, emotional, and/or social-economic prowess should be a wakeup call to us that perhaps there is yet another more serious warning in the Miracle of the Sun.  For those who think my above conjecture is utterly implausible,  please be advised to read the accounts of the Church Approved Apparitions of Akita Japan. This apparition does not explicitly refer to a nuclear war, however, it does refer to the possibility of fire raining down from Heaven and wiping out a great portion of humanity, in a punishment that would be worse than the deluge of Noah’s time.

 

I can see that a main calling of mine if not my sole occupational calling  is to assist with the development of interstellar propulsion technologies that are safe and effective so that the human race can expand outward into our universe and perhaps beyond. The production of all the more families which are the fundamental unit of human civilization permits the size of the spiritual cosmos to grow irrevocably via the creation of every new soul at the moment of conception and a body that in all cases is destined to arise incorruptible on the last day.  I feel utterly compelled to give human life a chance to exist in cases where it does not, such as promoting my pro-life views.

 

I see that giving children a chance to exist and to be born is a great calling that each and every one of us can practice regardless of our state of life.

 

As a conservative Catholic, I can state with utmost certainty that long, long after the last Mass is sail, the last Confession is heard, the last portions of the Sacred Species of the Holy Eucharist are brought into being during the prayers of consecration, long after the last Baptisms occur, each and every one of us will indelibly and irrevocably still be GOD’s children, and together we and the rest of the faithful will each be a member of the Mystical Body of Christ, not simply members of the Body of Christ, but members of the “Mystical Body of Christ”.

 

 

 

We are all predestined by GOD to be irreplaceable and unique citizens of the civilization of love. This applies to all of us regardless of whether we are: Catholic, Baptist,  Evangelical, Jewish, Muslim, Hindu, Buddhist, Taoist, practitioners of Shinto, Professed Atheists, Professed Agnostics, New Agers, Married, Single, Consecrated Virgins or not,  Celibate, Clergymen, Consecrated Religious, Convicts, Disabled Mentally, Emotionally, Intellectually, and/or Physically, Rock hard U.S. Navy Seals,  physically frail as the great physicist Stephen Hawking, Burly and Robust Construction Workers, Custodians, Electricians, Engineers, Beautiful Female Models, Health Care Workers and/or Professionals, Politicians, Gay, Straight, Bisexual, or what have you. We all share a fundamental moral equality before GOD and are all called to partake in the City Of God, that Eternal Beacon of Divine Light and Created Light. For those who are looking for a pecking order in Heaven, you may still get their but you will be disappointed. In Heaven, there cannot and will not be a pecking order, and each person in Heaven will be an irreplaceable member of the Mystical Body of Christ.  This is not to suggest that some folks will be rewarded in some ways more than others, however, each person will have his or her unique role to play that is and will remain indispensable to the Resurrected Mystical Body of Christ. Will some folks who spend time, perhaps even a lot of time in Purgatory, have a level or levels of various Resurrected graces equal to the top Canonized Saints?  Perhaps. To the best of my knowledge, the Church has never taken any formal doctrinal position on this issue. But either way, regardless of your state of life, ask GOD to give you the grace so that you can become a Saint, even a Canonized Saint. GOD’s grace is free for the asking.

 

 

 

Regardless of whether or not the Human Soul is Naturally Immortal or immortal by grace only, each and every human soul that has ever existed, regardless of whether one goes to Heaven or not, is meant forever, and will last forever. Since the basic un-augmented by grace nature of the Human soul is immutable, it is thus eternal in its very essence.

 

Now suppose the human soul is only immortal because of GOD’s grace by the merits of Christ Conception, Birth, Life, Passion, Death on the Cross, and Resurrection. The Human Soul’s existence would not be caused by itself or due to itself. Thus, in a sense, the soul would be independent of itself for its existence. The soul would not need its existence to be based on itself. This is a sort of ultimate self-transcendence for a creature.

 

Even if the Human Soul is immortal by grace only, this really does not matter since God holds all creatures in existence by His Almighty and sustaining will. Even the Angels would lapse into non-existence if it were not for GOD maintaining them in existence.

 

If indeed the Human Soul is immortal by grace only, then perhaps the Human Soul does not need this direct existence sustaining power of GOD, at least to the extent that it would need such in the case that it was immortal by nature. The reason for this kind of self-existence of the Human Soul in the event that it is immortal by grace only is that it is the supernatural life or aspect of the natural created soul that would then seem to be the mechanism for the continued existence of the Soul. This grace, which would come from GOD would not be identical with GOD since we creatures are in no way a part of GOD nor are we GOD.

 

So imagine that! A Human Soul that exist forever after death in a manner such that it does not need its own self caused mechanism to continue to exist but rather exists perhaps because of itself wherein this “itself” is partly a supernatural character or attribute by which the soul is not required to exist by its natural powers nor by some form of natural immortality, both of the latter of which would still require GOD’s all sustaining power to hold the Human Soul in existence.

 

Thus, a human soul that is immortal by grace might not need GOD to directly hold it in existence as a first created principle, but rather at the very least, the Soul would continue to exist indirectly by GOD, and more likely be held in existence after death by its own grace. After all, why would a soul need to be directly held in existence by GOD, if its immortality was rather a consequence of grace.  It would seem that GOD would not duplicate His efforts by requiring both mechanisms of immortality to be operative.

 

In a way, the existence of the state of immortality of the human soul might be far more independent for the case of gratuitous immortality than for natural immortality, including immortality that is independent from the soul’s nature or independent from the natural soul itself.

 

Even in the rare cases such that Human Souls might somehow be injured or destroyed by ways and means known only to GOD at this point in time, such as perhaps close proximity to the energy scrambling heart of a nuclear explosion, or perhaps as a result of a human person falling into a black hole, and the like, rest assure that any such souls will be Resurrected on the last day with all the more glory, having gone through the natural martyrdom and cross of natural soul death. With the cross, comes all the more eternal glory.

 

Regardless, it is true that even those who do not make it to Heaven will still have their bodies reunited to their immortal souls wherein their bodies will also be resin incorruptible on the last day and reunited to their spiritual and immortal soul.

 

However, for those of you who want to believe in the natural immortality and natural incorruptibility of the soul, the great theologian of Saint Thomas Aquinas strongly and logically argued in favor of the natural immortality and incorruptibility of the soul. His writings on the subject are still in widespread teaching in formation programs and the new Catholic Catechism does not make counter arguments to Saint Thomas’ teachings, and in fact, it  seems to indorse the spirit of His teachings, although in not as great of detail in terms of the explanation of the immortality of the Human Soul.

 

Note, once again, I also prefer to believe that the Human Soul is naturally immortal, and as a result, not immortal by grace. I make the above argument so that everyone can be satisfied that the human soul possesses great and transcendent dignity.

 

Also, once again, note the Scholastic interpretation as promulgated by Saint Aquinas of the nature of the human soul, that is the human soul is:  1) Spiritual, 2) Naturally immortal, 3) Incorruptible per addends and per se, 4) Simple, 5) Unextended, 6) Without shape or size, 7) Non-material,   8]   Non-corporeal, 9) Rational, 10) Free,  11) A first created principle, 12) An essence or a being which exist per se, 13) Independent of the body for its existence and to some extent its operations in this life, 14) The substantial form of the body in the Ancient Greek philosophical sense of the word, 15) Directly created by God, 16) Immediately created by God, and if I am not mistaken, 17) Multiple meaning that it is completely and totally present and united to every portion of the human body that is alive.

 

The modern Catholic approach to the immortality of the soul is somewhat ambivalent about the spiritualistic extreme ideologies of Saint Thomas Aquinas described above, however its modern viewpoint backed by the full weight of the highest levels of the Church Hierarchy is that the human soul is: 1) Immortal, 2) Spiritual, 3) Rational, 4) Does not die when separated from its body at death, 4) Immediately created, 5) According to the index of the first addition of the new Catechism of the Catholic Church, directly created by God; 6) The seed of eternity we bear within ourselves, 7) Not reducible to the mere material world;   8]   The form of the body.

 

 

 

Here are some things that you can be assured are true regarding the Human Soul, that seemingly intangible innermost aspect of our natural being that has perplexed philosophers and theologians from antiquity.

 

Some of the poor souls in purgatory may  have no one to pray for them. Such phrases as “May they Rest in Peace” and similar phrases, when used by clergyman, and others, to indicate views points, such as “We really cannot know what happens after death.” or “The dead have fallen asleep to be awakened on the last day”, are of no consolation to these poor forgotten souls, who I assure every living adult human, are the very same persons they knew on Earth, and who I can assure everyone, are most fully alive, alert, conscious, affective, feeling, and sadly suffering.

 

Now; once again, read through these quotations from the new Catechism of the Catholic Church which was approved by the very highest levels of the Vatican during 1980s.

Part 1, Section 1, Chapter 1, SubSection 2

 

33 The human person: with his openness to truth and beauty, his sense of moral goodness, his freedom and the voice of his conscience, with his longings for the infinite and for happiness, man questions himself about God’s existence. In all this he discerns signs of his spiritual soul. The soul, the “seed of eternity we bear in ourselves, irreducible to the merely material”, 9 can have its origin only in God.

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 1

 

360 Because of its common origin the human race forms a unity, for “from one ancestor [God] made all nations to inhabit the whole earth”: 226

 

O wondrous vision, which makes us contemplate the human race in the unity of its origin in God. . . in the unity of its nature, composed equally in all men of a material body and a spiritual soul; in the unity of its immediate end and its mission in the world; in the unity of its dwelling, the earth, whose benefits all men, by right of nature, may use to sustain and develop life; in the unity of its supernatural end: God himself, to whom all ought to tend; in the unity of the means for attaining this end;. . . in the unity of the redemption wrought by Christ for all. 227.

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 2

 

363 In Sacred Scripture the term “soul” often refers to human life or the entire human person. 230 But “soul” also refers to the innermost aspect of man, that which is of greatest value in him, 231 that by which he is most especially in God’s image: “soul” signifies the spiritual principle in man.

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 2

 

366 The Church teaches that every spiritual soul is created immediately by God – it is not “produced” by the parents – and also that it is immortal: it does not perish when it separates from the body at death, and it will be reunited with the body at the final Resurrection. 235

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 2

 

367 Sometimes the soul is distinguished from the spirit: St. Paul for instance prays that God may sanctify his people “wholly”, with “spirit and soul and body” kept sound and blameless at the Lord’s coming. 236 The Church teaches that this distinction does not introduce a duality into the soul. 237 “Spirit” signifies that from creation man is ordered to a supernatural end and that his soul can gratuitously be raised beyond all it deserves to communion with God. 238.

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 4

 

382 “Man, though made of body and soul, is a unity” (GS 14 # 1). The doctrine of the faith affirms that the spiritual and immortal soul is created immediately by God.

 

Part 1, Section 2, Chapter 3, Article 11, SubSection 1, Heading 2

997 What is “rising”? In death, the separation of the soul from the body, the human body decays and the soul goes to meet God, while awaiting its reunion with its glorified body. God, in his almighty power, will definitively grant incorruptible life to our bodies by reuniting them with our souls, through the power of Jesus’ Resurrection.

 

Part 1, Section 2, Chapter 3, Article 12, SubSection 6

1052 “We believe that the souls of all who die in Christ’s grace . . . are the People of God beyond death. On the day of resurrection, death will be definitively conquered, when these souls will be reunited with their bodies” (Paul VI, CPG § 28].

 

Part 2, Section 2, Chapter 1, Article 1, SubSection 7, Heading 5

1280 Baptism imprints on the soul an indelible spiritual sign, the character, which consecrates the baptized person for Christian worship. Because of the character Baptism cannot be repeated (cf. DS 1609 and DS 1624).

 

Part 2, Section 2, Chapter 1, Article 2, SubSection 3

1304 Like Baptism which it completes, Confirmation is given only once, for it too imprints on the soul an indelible spiritual mark, the “character,” which is the sign that Jesus Christ has marked a Christian with the seal of his Spirit by clothing him with power from on high so that he may be his witness. 121

 

Part 3, Section 1, Chapter 1, Article 1

 

1705 By virtue of his soul and his spiritual powers of intellect and will, man is endowed with freedom, an “outstanding manifestation of the divine image.” 8

 

Part 3, Section 1, Chapter 1, Article 1

 

1711 Endowed with a spiritual soul, with intellect and with free will, the human person is from his very conception ordered to God and destined for eternal beatitude. He pursues his perfection in “seeking and loving what is true and good” (GS 15 § 2).

 

Part 3, Section 1, Chapter 2, Article 3, SubSection 2

 

1934 Created in the image of the one God and equally endowed with rational souls, all men have the same nature and the same origin. Redeemed by the sacrifice of Christ, all are called to participate in the same divine beatitude: all therefore enjoy an equal dignity.

 

Thus, we have at the very least, the above 13 aspects of the transcendent dignity of the Human Soul. In addition to these wonderful quotations, we have the Wisdom of Saint Thomas Aquinas, who held that the Human Soul is naturally immortal, spiritual, simple, unextended, incorruptible per addends and per se.

 

When Saint Thomas said that the Human Soul is the substantial form of the body,  he was not saying that it physically looked like the body, rather he was using the Platonic or Aristotelian concept of eternal, immaterial, and perfect forms as the reified abstract ideal ideas that things represent.

 

Saint Thomas referred to the Soul as the substantial form of the body, ‘substantial” meaning a first created principle of being that is intrinsically independent of the body for its existence and for some of its more advanced operations.

 

Now once again, given the Scholastic interpretation of the nature of the human soul, that is the human soul is:  1) Spiritual, 2) Naturally immortal, 3) Incorruptible per addends and per se, 4) Simple, 5) Unextended, 6) Without shape or size, 7) Non-material,   8]   Non-corporeal, 9) Rational, 10) Free,  11) A first created principle, 12) An essence or a being which exist per se, 13) Independent of the body for its existence and to some extent its operations in this life, 14) The substantial form of the body in the Ancient Greek philosophical sense of the word, 15) Directly created by God, 16) Immediately created by God, and if I am not mistaken, 17) Multiple meaning that it is completely and totally present and united to every portion of the human body that is alive, we have much grounding through the use of natural reasoning that the human soul is naturally immortal and naturally indestructible. In all, we have at least the above 17 transcendent dignities of the human soul if Saint Thomas Aquinas is to be believed.

 

Now, I try to aim for the utmost objectivity in my reasoning and speculations regarding the subject of the human soul since this subject is so dear to me, and perhaps because even though I am a large framed, static resistance training, near 412 pound, big guy, and a little too obese and corpulent, I was nonetheless slight of build and thin during my elementary school years and I got picked on and teased a lot by my class mates because of my formerly shy temperament and lack of sports playing athletic ability. As a result, even after the onset of adolescence when I started lifting weights and I became an extroverted, stocky, and slightly above average height, young man, I had developed a love of the soul over the body, simply because, my body was once small and somewhat fragile in build until I hit puberty.

 

Since I try for such extreme objectivity in this subject of soul immortality, I must cover all bases and including the remote but nonetheless, possible scenarios, that perhaps at the very least, situations such a very close proximity to a nuclear explosion and other extreme events such as bodily falling into a black hole, onto a neutron star, or perhaps even onto a white dwarf, might at the very least, be able to destroy the accidental form of the soul, even if it be the case, that the essence or substance of the soul might be utterly naturally incorruptible to any created forces, agents, or persons.

 

Even if my hopes in complete human soul natural immortality are proved false, but I doubt they can be, I can assure the reader that it is my utmost Holy Rosary reciting, frequent daily mass attending, and frequent Sacramental Confession attending conservative Catholic personhood, that any souls that might thus be destroyed or injured will be Resurrected at least no later than the End of Time at the Final Resurrection of the Dead to Eternal Glory for having undergone the Cross and Crucifixion of any possible soul death, just as Christ was Resurrected and has Ascended into the Glory of sitting at the proverbial Right Hand of the Father and just as Christ will become the proverbial  Father of the World to Come after the Final Resurrection of the Dead. This Final Resurrection of the Dead is open to all persons of all faiths and belief systems or lack thereof, and I am obliged to believe that many, many, if not most persons who are not Catholic do in fact attain eternal salvation. The teachings of the Catholic Faith coupled with common sensible reason all point extremely affirmative to this reality. The late Pope John Paul II, in the title of His book, “Be Not Afraid”, applies to each and every person alive today on this good planet Earth.

 

Now here is some really freaky conjecture that occurred to me as I was out running errands one evening. The notions involve the speculations that we humans might not only have either purely naturally based, natural coupled with supernatural grace based, or purely graced based immortality of the soul, but perhaps our souls have immortality like analogues or parallel qualities that are of the same class as any immortality of the soul as such but which are fundamentally different. The concept is analogous to the speculation that their might exist higher dimensions alongside or in parallel with the 4-D ordinary Einsteinian space time that we are familiar with in everyday life but which also is the primary foundation of current applied and theoretical physics paradigms.

 

We can speculate that such immortality analogues might be referred to as para-immortality, meta-immortality, trans-immortality, or super-immortality. If such analogues exist, then even though such qualities would have to be said to have been given to the soul, perhaps at the very natural level, at the time of the soul’s creation at the moment of embryonic conception, if it be the case that the soul could be destroyed at least in terms of its accidental form or accidental properties, perhaps by close proximity to the heart of a nuclear explosion, then perhaps, just perhaps, the soul would continue to exist, or para-exist, in an irrevocable manner in the given soul’s para-immortality, meta-immortality, trans-immortality, or super-immortality characteristics.

 

My reasoning here flows from the commonly understood Catholic Teaching that the Human Person, especially the Human Soul, is made in GOD’s Image and Likeness. Just as GOD has the eternal I AM THAT I AM BEING AND ESSENSE, and has a NATURE that is absolutely simple ontologically speaking, but yet this same ONE and ABSOLUTELY SIMPLE GOD has THREE DIVINE PERSONS and who is thus TRICE HOLY, and where JESUS the SON OF GOD, THE SECOND PERSON OF THE HOLY TRINITY died on the CROSS yet continued to exist in HIS  DIVINE NATURE and  in HIS HUMAN NATURE of HIS immortal Human Soul and His deceased and presumably decaying Body and once Sentient Brain, we humans might thus have multiple levels of Immortality, and perhaps even non-immortality analogues such as the proposed para-immortality, meta-immortality, trans-immortality, or super-immortality fundamental and essential characteristics. After all, if we are made in GOD’s image and likeness, then we can in a sense be considered in the nature and essence of our immortal souls, to be created versions or analogues of that YEHWAY or created versions or analogues of that I AM THAT I AM.

 

The point is that we have just scratched the surface of what and who beautiful and transcendent Human Souls are even at the level of the Soul’s Natural attributes, both essential and substantial attributes and even the more accidental and ancillary attributes and characteristics of the Human Soul. Each Human Soul is of infinite worth to GOD AS THE HOLY TRINITY OR DIVINE BEING OR ESSENSE and to GOD, AS AND IN EACH OF HIS THREE DIVINE PERSONS, THE FATHER, THE SON, AND THE HOLY SPIRIT. You don’t believe me? Then consider that JESUS, the combination the SECOND DIVINE PERSON AND HIS  Human Nature, was called  by GOD THE FATHER to take on a Human Nature, and to suffer, and die on the Cross, for the Eternal Salvation of all Human  Persons, regardless of the religious faith, believe system, state of life, vocation, or lack thereof that a given human person has. Christ lovingly did so out of obedience to HIS ETERNAL FATHER, but perhaps more significantly for us, out of love for us, the same love for us that the ETERNAL FATHER has for us.

 

Now the human soul is the vital, simple, life principle, principle of identity, principle of unity, principle of uniqueness, that constitutes each one of us as human. Thus, even in the case that the human soul would be naturally destructible, and even in the case that some souls might be naturally destroyed, these souls still possess transcendent dignity based on their ontological goodness including natural substantial, essential, facultative and accidental ontological goodness , natural capacity for morally informed behavior, purpose, reason for being created, inherent value, essential beauty, substantial beauty, accidental beauty, GOD’s permanent memory of them, the fact that they once existed which can never be erased, the effects of their one time existence which would propagate into eternity forever, and perhaps an utterly non-definable list of transcendent ontological properties.

 

In fact, a soul that has such extreme transcendent ontological properties but which can be naturally destroyed might be in a greater proportion, such transcendent ontological properties with respect to its existence, whether the existence being contemplated is of the souls accidental forms, facultative forms, substantial forms, or very basic and most primitive essential forms. In short, the transcendent ontological properties of each and every human soul, each and every extra-terrestrial’s soul, each and every ultra-terrestrial’s soul, might be of greater portions, perhaps much greater portions of the reality or nature of the human soul than the soul’s immortality, especially relative to souls that would be immortal or naturally indestructible. Once again, such proposed transcendent ontological properties are: natural substantial, essential, facultative and accidental ontological goodness , natural capacity for morally informed behavior, purpose, reason for being created, inherent value, essential beauty, substantial beauty, accidental beauty, GOD’s permanent memory of them, the fact that they once existed which can never be erased, and perhaps indefinably more attributes, including a perhaps ironically ever growing and super abounding set of such attributes. Moreover, perhaps each soul naturally improves in each such transcendent ontological property if for no other reason than that it continues to exist, thus building up its past history or past cosmos line, or past afterlife line.

 

Quite simply put, the more destructible a human, ET, or UT soul is in nature, perhaps the greater the proportion of its being or reality is the reality of the transcendent ontological properties. In other words, such would be naturally corruptible human souls would be all the more self-transcendent, or transcendent of their natural corruptibility since they would be in a greater proportional reality, their transcendent ontological properties.

 

 

Now, we know in fact, that effectively, each and every human soul is immortal, even any souls that would by some fortuitous event be naturally destroyed such as in cases known only to GOD, or at least not known to any humans on this side of life. Since all of the Dead will arise as complete body soul unions at the Final Resurrection, and  then so in incorruptibility, we know that all human persons whether they go to Hell, any Limbo, or Heaven, will be Resurrected as complete persons. In my own humble opinion, any souls that are so destroyed will be Resurrected with all the more natural, and supernatural glory, commensurate with having gone through the martyrdom of soul death. Any souls that are somehow  accidentally or accidently and substantially effectively destroyed or injured in a nuclear weapon explosion will be Resurrected with all the greater glory having gone through such martyrdom.

 

Now if the human soul is immortal by grace only, then every single human soul is effectively immortal by grace, regardless of whether they go to Hell, Heaven, Purgatory then to Heaven, or directly to Heaven. This grace is bestowed as an effectively supernatural character permanently instilled within each and every human soul and since all souls are eternal, this character per dues into eternity and can never end. I would hazard a guess that any such immortality by grace is bestowed by virtue of Christ’s life, Passion, Crucifixion, Resurrection, and Ascension at the Right Hand Of The Father in Glory, and even more so, by  HIS destiny to be the Father of the World To Come.

 

The fact that the human soul has realities that might be self-transcendent might be a degenerate or at least a pseudo-degenerate aspect or quality with respect to the reality by which the soul in each and every instance has grace. Even in cases where the self-transcendence of the human soul such as in the above transcendental ontological properties is not identical with grace, such natural self-transcendence can serve as a proxy for the implication of universal human grace of any gratuitous immortality.

 

One aspect of such natural self-transcendence is the natural ability inherent in every soul to have Divine Grace bestowed on it. Every soul is ontologically capable of supporting grace, and if the human soul is immortal by grace, then by corollary, even the souls of those in Hell can support grace and indeed do support grace.

 

Thus, even in the case where the human soul is immortal by grace only, all human souls are naturally ordained to ontologically to a bestowing of Divine Grace, yes, this includes even the souls who go to Hell.

 

Even the souls who go to Hell have great, beauty, value, purpose, and great ontological dignity. Because the reward of those who go to Heaven must be based on accepting and living a life in the state of grace, except in cases of death bed conversions, or perhaps somehow in the transition of Divine Judgment such as the Lord presenting the soul with a final opportunity to get to Heaven, or a Final Mercy, such acceptance must be relative to something else, and in my own humble opinion, that something else is the passing of this life into the next in the form of a chronically lived life of mortal sin without any final remorse. The reward of Heaven as a morally binding consequence must have its opposite if characters such as the gifts of the Holy Spirit, the fruits of the Holy Spirit, and the three theological virtues are to have meaning. After all, the distinction of Eternal Reward in Heaven may be meaningless if it has no opposite or possibility for an opposite. Think of the analogous cases of: matter and antimatter, positive and negative electrical charge, positive and negative energy, actual and potential energy, positive and negative velocity, positive and negative acceleration, financial debits and credits, and the like. Everything that has a positive would seem to have its opposite.

 

It is my opinion that such existential, and reality based polarizations, may be one reason but by far not the only reason, why the souls in Hell who will live forever in a natural state, have great value, dignity, ontological goodness, and which serve a great purpose even if such souls in at least some cases will be so motivated by hatred for GOD that they will never feel remorse for making the ultimate choice of choosing Hell over Heaven.

Only human souls have such a power of choice regarding the use of their radically free will to make morally informed decisions or choices. Much of the literature on so-called UFO space alien abductions and telepathic communications if it was true , or if in some cases, perhaps has a grain of truth to it all,  would strongly suggest that the human will is so free that even the most technologically, scientifically, and evolutionally, advanced extraterrestrials and ultraterrestrials have great difficulty predicting human behavior, to such an extent that even reasonable attempts at approximate predictions are very often completely thrown off by human free acts. To see why,  think of how difficult it is for the human institution of the U.S. Central Intelligence Agency and its predecessor organizations to predict the outcome of leaders of rogue regimes such as Kaddafi, Osama Bin Laden, Adolf Hitler and the very large numbers of other dictators that have displayed motives and strategies that defy prediction.

 

So next time you feel the urge to curse a soul of someone you knew in this life who treated you horribly and who you might feel is in Hell, please forgo the hate and realize that even the souls of those in Hell have great goodness in the mind and heart of GOD, and also have great dignity and even great beauty in the eyes of GOD, and GOD is the ultimate reference frame. These poor condemned souls may never consciously feel joy with respect to their great natural dignity, ontological goodness, and purpose etc, and etc., but they are nonetheless fellow free and rational spiritual created persons, and as such, we share a certain solidarity with all of them even though they may never appreciate this fact. However, we can and so we must not curse the condemned and even never curse the fallen angels out of hate or vengeance, because such hatred in unbecoming of morally wise creatures and is a sin against our fellow unfortunate spiritual created persons who will never share the peace and joy of Heaven with us.

 

So when we bemoan our physical frailty and the fact that we cannot seem to run, jump, skip, and hop like we could when we were young children, we should remind ourselves that we special and are meant for and will last forever.

 

25) Perhaps The Human Soul Grows Substantially And Accident-Wise For All Eternity As It Travels Its World Line In This Life And Then In The Next Life In An Ontological Process Analogous To The Growth Of Physical Objects In 4-D Spatial-Temporal Volume As They Age.

 

Here is an interesting conjecture regarding the human soul. These following general ideas first occurred to me this morning as I was driving home after attending a Mass at a local parish in the Catholic Diocese of Arlington.

 

Some of you may be familiar with the concept of a world line such as promulgated by those who study Special and General Relativity. Such a notion involves the travel of an object or a person on a trajectory through 4-D space time, three spatial dimensions unified with one temporal dimension. Thus, as an object continues to exist, its 4-dimensional space time volume increases in the case where the object’s spatial changes would not negate the 4-D growth along the temporal axis.

 

Now consider the Catholic Teaching that there is no re-incarnation and there is no previous existence or previous life of the human person. Each human person in no way had substantial existence before conception. Each human spiritual and immortal soul is created ex-nihilo according to conventional Catholic Wisdom which is affirmed by modern Catholic teaching and approaches to understanding the human soul. Thus, each human soul, as an entity whose accidental nature can and does evolve with time, even in terms of the effects of non-free actions, has a time dependent state. To the extent that the human soul experiences dynamic interaction in Heaven, Hell, Purgatory, any Limbo, or perhaps in any ghost like state that may exist due to the seeming inability of the Church to absolutely rebuttal the phenomenon of hauntings, each human soul has or lives out its world line for eternity wherever it ultimately ends up, and each human soul will be permanently and irrevocably reunited to an immortalized and incorruptible body for all eternity, wherever it ultimately ends up.

 

Now what can you the reader, and I, the writer of these proses take away from this fact? Well, since a physical object that exist in 4-D space time continues to become larger and larger along the 4th dimension of time, as well as with respect to its 4-D spatial volume, an analogous effect might progress in terms of the human soul.

 

For example, each human soul from the time it was created changes and evolves as to its accidental nature by involuntary and voluntary processes. Thus, there are grounds for stating a time dependent function of state for the human soul both in this life and in the next life, and definitely upon re-union with its eventually immortalized and incorruptible body to be. Thus, we can affirm the growth of the human soul along the dimension of experienced time or experienced change, which in this life is coupled to temporal flow of physical mass-energy states. Thus, in a very real sense, the human soul keeps getting larger and larger, and will continue  to do so no matter where he or she ultimately ends up. This soul growth is essentially utterly eternal and can never cease. Thus, each of our souls keeps getting bigger and bigger in an irrevocable and utterly unstoppable manner simply because each soul is immortal.

 

A degenerate form of this general argument involves the consideration of the soul’s accidental growth through accidental form modifying experiences and interior psychodynamic processes, whether conscious, sub-conscious, or unconscious. Each such manifestation adds to the accidental form of the human soul, and to the extent that dynamic experiences and internal processes within the soul occur for all eternity, which they will, the growth in the accidental form of the human soul will continue for all eternity, at least as far as its accidental form is concerned.

 

 

Now since the soul comes into being at a particular point in time upon its creation ex-nihilo by GOD, so does its sub-composition in the form of its substance. Thus, since the creation of the soul in all of its nature and glory occurs immediately and directly, we can wonder as to whether its substance, even if changeless in nature at the level of the souls natural attributes, can nonetheless continue to grow or become larger and larger in an irrevocable and utterly eternal manner. It would seem that if the soul can grow in size along its world line in accidental form, by symmetry, it should also  grow along its world line in substantial or essential form.

 

The Catholic contemporary thinking as well as much of the Catholic Church’s previous mindset is that GOD maintains all creation in existence or that HE sustains it in being by HIS proverbial Almighty Arm. Now how does  this assumption help with the analysis of an ever growing soul along its world line?

 

In order to answer the latter question, we might note that the human soul is continually being held in existence, as are all other creatures, living and non-living, physical, spiritual, or both. This continuous creation might be degenerate with the human soul being continually  re-created without any loss of identity or continuity of identity. IMHO, I would hazard a guess that this act of continually being recreated involves a continually evolving or changing substance, or perhaps secondary substantial nature of the soul. Perhaps, this ongoing act of the souls creation or its continuous recreation implies a time dependent dynamic to the souls creation, thus serving the interpretation that the soul is substantial changing or essentially changing in a changeless manner. Such an interpretation might indicate that the soul continues to grow for all eternity in terms of such a dynamism based world line, and by analogy and corollary, also in terms of its accidental properties and its faculties which seem to reside along a continuum somewhere between the purely accidental or experience based form of the human soul and its substance or essence.

 

If the human soul is changing in a changeless manner as to its substance, then it would then beg the question as to whether or not there is an aspect of the human soul that transcends this dynamically but changelessly evolving state of its existence. Could this property or very ephemeral aspect of the human soul have something to do with the fact that each human soul remains itself and does not  become someone else, even though in principle GOD could create any finite or any infinite number of souls having identical characteristics, and experiences, and which could remain so-identically throughout all eternity, but yet be completely distinct substantially, and even more to the point completely distinct identity-wise.

 

Now comes the difficult part, and so if I offend anyone by the below speculations, it is not out of ill-will nor poor intention by any means. I have speculated as to whether the human soul might under some circumstances be able to be destroyed by natural causes such as unfortunate location near the very heart of  a nuclear explosion, or perhaps partially destroyed or corrupted such as perhaps taking on some poltergeist or ghost form similar to the accounts of the fringe paranormal or occult culture. That some souls might somehow be trapped in a neither here nor there state as ghosts does not seem to have been absolutely rebutted by even the Catholic Church. There are so many accounts of hauntings, even ones that will not stop as a result of blessings or prayers by Catholic Clergyman that we need to consider that at least some reported hauntings might represent real phenomenon that are not satanically deceptive nor demonic in nature.

 

The new Catechism Of The Catholic Church is paraphrased by the statement that the Church prays for those who have taken their own lives but that in many cases, culpability for such acts is reduced or eliminated altogether thus resulting in any required atonement after death being expiated on the way to Heaven via detention in Purgatory. However, the Catechism also states that GOD can provide a means for salvific atonement by ways and means known only to Him. This would seem to imply that in cases where the suicide, perhaps rarely, is finally mortally sinful, GOD can provide a means for the soul to be saved. If the means and ways of such salvific atonement are known only to GOD, then by corollary, it would seem that such methods do not involve detention in Purgatory since Purgatory is a known mechanism for atonement and purification. The notion that such a known only to GOD means of salvific atonement might simply be a particular punishment in Purgatory, does not make sense, because most likely, there are many forms of  particular punishment in Purgatory, most assuredly unknown to we humans in this life. Besides, if the deceased person who took their own life was saved upon entering the presence and judgment of GOD, then the phrase salvific atonement would have no meaning because any souls that go to Purgatory or straight to heaven are in the state of grace upon death. There would be no need for salvific atonement after death if the soul was already judged to be effectively saved by GOD.

 

So for all of you folks who have had loved ones commit serious crimes followed by suicide, have hope. In many cases, the loved one was psychotically delusional or psychotically depressed  and thus was not capable of committing a mortal sin. In cases where the loved might have been so capable and where the act was extreme in proportion, have hope as well for your loved one. For indeed, GOD can and I believe HE does call all such persons to salvation upon their deaths. GOD’s love shines on the hurting and tormented and who could be more hurting and tormented than someone who takes their own life, and even more so someone who commits mass murder than suicide. I am by no means condoning such acts, but I merely iterate that the last will be first, and many of the first will be last. Who could not be more last in this life than a person tormented with uncontrollable rage and psychotic depression for years and years and who takes desperate actions to put it all behind themselves(s).

 

 

Now if partial or virtually complete natural destruction of the human soul can rarely occur, be absolutely assured that any and all such souls will be re-created as the exact very same soul that they were before destruction. This is evident from Sacred Scripture where the Holy Bible clearly states that all will arise at the End Of Time, and that all human souls, including any such souls that would have been temporarily destroyed or naturally injured, will be re-united with an immortalized and incorruptible body. This is true even for the souls that end up in Hell. Thus, we can be absolutely assured that any souls that might somehow be destroyed partially or in full, will be recreated in full at a point in future cosmic history no later than the time of the Final Resurrection.

 

How does this argument pertain to the discussion at hand? The answer is that if a soul where to somehow be injured or destroyed in cases known only to GOD, the subsequent re-creation of these souls might imply a dynamic of double creation, where the soul is created not just once, but twice. Thus, such souls might have all the more size or depth upon recreation having been repeated as themselves twice. Anyhow, IMHO, any souls who are so destroyed are doing an effective extreme penance by such destruction and are undergoing the greatest possible cross for a human person, that of soul death. With the Cross comes Resurrection into Eternal Glory, and IMHO, such souls will be all the more glorified having done their penance to extreme extents.

 

Now I present the above soul destruction argument immediately above for purposes of absolute philosophical rigorousness. In all likelihood, no created agent or effect could ever destroy or annihilate any human soul, ever.

 

 

To the latter end,  once again note the Scholastic interpretation as promulgated by Saint Aquinas of the nature of the human soul, that is the human soul is:  1) Spiritual, 2) Naturally immortal, 3) Incorruptible per addends and per se, 4) Simple, 5) Unextended, 6) Without shape or size, 7) Non-material,   8]   Non-corporeal, 9) Rational, 10) Free,  11) A first created principle, 12) An essence or a being which exist per se, 13) Independent of the body for its existence and to some extent its operations in this life, 14) The substantial form of the body in the Ancient Greek philosophical sense of the word, 15) Directly created by God, 16) Immediately created by God, and if I am not mistaken, 17) Multiple meaning that it is completely and totally present and united to every portion of the human body that is alive.

 

The modern Catholic approach to the immortality of the soul is somewhat ambivalent about the spiritualistic extreme ideologies of Saint Thomas Aquinas described above, however its modern viewpoint backed by the full weight of the highest levels of the Church Hierarchy is that the human soul is: 1) Immortal, 2) Spiritual, 3) Rational, 4) Does not die when separated from its body at death, 4) Immediately created, 5) According to the index of the first addition of the new Catechism of the Catholic Church, directly created by God; 6) The seed of eternity we bear within ourselves, 7) Not reducible to the mere material world;   8]   The form of the body.

 

 

 

Here are some things that you can be assured are true regarding the Human Soul, that seemingly intangible innermost aspect of our natural being that has perplexed philosophers and theologians from antiquity.

 

Some of the poor souls in purgatory may  have no one to pray for them. Such phrases as “May they Rest in Peace” and similar phrases, when used by clergyman, and others, to indicate views points, such as “We really cannot know what happens after death.” or “The dead have fallen asleep to be awakened on the last day”, are of no consolation to these poor forgotten souls, who I assure every living adult human, are the very same persons they knew on Earth, and who I can assure everyone, are most fully alive, alert, conscious, affective, feeling, and sadly suffering.

 

Now; once again, read through these quotations from the new Catechism of the Catholic Church which was approved by the very highest levels of the Vatican during 1980s.

Part 1, Section 1, Chapter 1, SubSection 2

 

33 The human person: with his openness to truth and beauty, his sense of moral goodness, his freedom and the voice of his conscience, with his longings for the infinite and for happiness, man questions himself about God’s existence. In all this he discerns signs of his spiritual soul. The soul, the “seed of eternity we bear in ourselves, irreducible to the merely material”, 9 can have its origin only in God.

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 1

 

360 Because of its common origin the human race forms a unity, for “from one ancestor [God] made all nations to inhabit the whole earth”: 226

 

O wondrous vision, which makes us contemplate the human race in the unity of its origin in God. . . in the unity of its nature, composed equally in all men of a material body and a spiritual soul; in the unity of its immediate end and its mission in the world; in the unity of its dwelling, the earth, whose benefits all men, by right of nature, may use to sustain and develop life; in the unity of its supernatural end: God himself, to whom all ought to tend; in the unity of the means for attaining this end;. . . in the unity of the redemption wrought by Christ for all. 227.

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 2

 

363 In Sacred Scripture the term “soul” often refers to human life or the entire human person. 230 But “soul” also refers to the innermost aspect of man, that which is of greatest value in him, 231 that by which he is most especially in God’s image: “soul” signifies the spiritual principle in man.

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 2

 

366 The Church teaches that every spiritual soul is created immediately by God – it is not “produced” by the parents – and also that it is immortal: it does not perish when it separates from the body at death, and it will be reunited with the body at the final Resurrection. 235

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 2

 

367 Sometimes the soul is distinguished from the spirit: St. Paul for instance prays that God may sanctify his people “wholly”, with “spirit and soul and body” kept sound and blameless at the Lord’s coming. 236 The Church teaches that this distinction does not introduce a duality into the soul. 237 “Spirit” signifies that from creation man is ordered to a supernatural end and that his soul can gratuitously be raised beyond all it deserves to communion with God. 238.

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 4

 

382 “Man, though made of body and soul, is a unity” (GS 14 # 1). The doctrine of the faith affirms that the spiritual and immortal soul is created immediately by God.

 

Part 1, Section 2, Chapter 3, Article 11, SubSection 1, Heading 2

997 What is “rising”? In death, the separation of the soul from the body, the human body decays and the soul goes to meet God, while awaiting its reunion with its glorified body. God, in his almighty power, will definitively grant incorruptible life to our bodies by reuniting them with our souls, through the power of Jesus’ Resurrection.

 

Part 1, Section 2, Chapter 3, Article 12, SubSection 6

1052 “We believe that the souls of all who die in Christ’s grace . . . are the People of God beyond death. On the day of resurrection, death will be definitively conquered, when these souls will be reunited with their bodies” (Paul VI, CPG § 28].

 

Part 2, Section 2, Chapter 1, Article 1, SubSection 7, Heading 5

1280 Baptism imprints on the soul an indelible spiritual sign, the character, which consecrates the baptized person for Christian worship. Because of the character Baptism cannot be repeated (cf. DS 1609 and DS 1624).

 

Part 2, Section 2, Chapter 1, Article 2, SubSection 3

1304 Like Baptism which it completes, Confirmation is given only once, for it too imprints on the soul an indelible spiritual mark, the “character,” which is the sign that Jesus Christ has marked a Christian with the seal of his Spirit by clothing him with power from on high so that he may be his witness. 121

 

Part 3, Section 1, Chapter 1, Article 1

 

1705 By virtue of his soul and his spiritual powers of intellect and will, man is endowed with freedom, an “outstanding manifestation of the divine image.” 8

 

Part 3, Section 1, Chapter 1, Article 1

 

1711 Endowed with a spiritual soul, with intellect and with free will, the human person is from his very conception ordered to God and destined for eternal beatitude. He pursues his perfection in “seeking and loving what is true and good” (GS 15 § 2).

 

Part 3, Section 1, Chapter 2, Article 3, SubSection 2

 

1934 Created in the image of the one God and equally endowed with rational souls, all men have the same nature and the same origin. Redeemed by the sacrifice of Christ, all are called to participate in the same divine beatitude: all therefore enjoy an equal dignity.

 

Thus, we have at the very least, the above 13 aspects of the transcendent dignity of the Human Soul. In addition to these wonderful quotations, we have the Wisdom of Saint Thomas Aquinas, who held that the Human Soul is naturally immortal, spiritual, simple, unextended, incorruptible per addends and per se.

 

26) The Unique And Unrepeatable Human Soul.

 

 

Now, the Catholic Church holds that each Human Soul is unique and unrepeatable. Thus, each human soul has unique properties. However, we can see some initial conflict with this notion based on the possibility that our universe is infinite in extent where the size of the infinity is arbitrarily large or not yet properly and empirically defined.

 

The reason for the latter statement is none-other than the possibility that in an infinitely large universe, the number of times the identical ordering of mass-energy-space-time states that can repeated is commensurately infinite, thereby resulting in an infinite duplicity of states that define our local light cone or our visible portion of the universe and even finite portions thereof of much greater extent.

 

The paradox of the Many World’s Interpretation of quantum theory might simply be a proxy for the fact that identical orderings of our local light cone, or sub-universe portion beyond our light cone, are simply duplicities in the chance arrangements of mass-energy-space-time that have no relation to the notion of the production of a separate history by the process of quantum decoherence. For each change in our universe, the change would provide a differentiation characteristic that results in formerly identical portions of the cosmos there-afterward  having different characteristics, not by the portions’ creation ex-nihilo, but rather through  becoming differentiated by the process of relative changes.

 

The same notions of duplicity can be contemplated with respect to repetitions of universes within a larger multiverse where such repetitions occur by chance and imply identical physical orderings of thermodynamic and statistical mechanical mass-energy-space-time states relative to our universe. In an infinite multiverse, provided that the subject infinity is large enough, the number of identical orderings should be infinite to an unknown extent. Each time a person in our universe performs an action, or an event occurs in our universe, the result would be a differentiation of our universe from the previously identical universes, not by casual mechanisms, but by shear relative evolutionary histories between our universe and the other universes within our multiverse.

 

The same notions of duplicity can be contemplated with respect to repetitions of  any local multiverse within a larger forest where such repetitions occur by chance and imply identical physical orderings of thermodynamic and statistical mechanical mass-energy-space-time states relative to our multiverse. In an infinite forest, provided that the subject infinity is large enough, the number of identical orderings should be infinite to an unknown commensurate extent. Each time a person in our multiverse, or an event occurs in our multiverse, the result would be a differentiation of our multiverse from the previously identical multiverses, not by casual mechanisms, but by shear relative evolutionary histories for our multiverse and many other previously identical multiverses within our forest.

 

The same notions of duplicity can be contemplated with respect to repetitions of our forest  within a larger biosphere where such repetitions occur by chance and imply identical physical orderings of thermodynamic and statistical mechanical mass-energy-space-time states relative to our forest. In an infinite biosphere, provided that the subject infinity is large enough, the number of identical orderings should be infinite to an unknown extent. Each time a person in our forest performs an action, or an event occurs in our forest, the result would be a differentiation of our forest from the previously identical forests, not by casual mechanisms, but by shear relative evolutionary histories for our forest and many other previously identical  forests within our biosphere.

 

The same notions of duplicity can be contemplated with respect to repetitions of our biosphere within a larger “solar system” where such repetitions occur by chance and imply identical physical orderings of thermodynamic and statistical mechanical mass-energy-space-time states relative to our biosphere. In an infinite “solar system”, provided that the subject infinity is large enough, the number of identical orderings should be infinite to an unknown extent. Each time a person in our biosphere makes a free choice, or an event occurs in our biosphere, the result would be a differentiation of our biosphere from the previously identical biospheres, not by casual mechanisms, but by shear relative evolutionary histories between our biosphere and the other biospheres within our “solar system”.

 

And the number of hierarchies might simply progress eternally, where eternally is used to qualify the eternity defines the continuum of the perhaps utterly infinite numbers of hierarchies.

 

Now could there exist more than one eternity or eternities that are identical, non-identical, of the same species, not of the same species, of the same class, not of the same class, of the same category, not of the same category and so-on ad infinitum where said similarities and differences are qualitative and/or quantitative, in existential, accidental, ontological, or substantial in nature? Do to GOD’s all powerful capacity to create, we simply should never answer the above question negatively.

 

Since the cosmos might be ever superabundantly growing in size, there may be all the more regions within our universe, universes, multiverses, forests biosphere, solar systems and so on and so on, ad infinitum, coming into being by GOD’s creative providence.

 

Thus, the opportunities for souls to be created and united to bodies that are embryonic and which are identical to our bodily state upon our conception presents the possibility of utterly unfathomable infinite numbers of souls united to identical embryos. The possibility of utterly infinite numbers of souls remaining united to utterly infinite numbers of bodies whereby said bodies will by chance live out infinite numbers of identical local world lines cannot be dismissed.

 

Now, if we can take the Catholic Church’s opinions and statements that the Human Soul is unique and unrepeatable, meaning that GOD only produces unique human souls, then even given the utterly unlimited numbers of human souls that can be created and the possibility that Human Souls might be united to a human body that lives out its world line in an exact spatial temporal mass-energy state and pattern that is case specific and duplicated over and over again, each human soul would necessarily have distinct qualities and characteristics. This remains the case even though identical human body states to which human souls are united would be forever repeated in ever more infinite numbers.

 

In my humble opinion, a distinguishing feature of each such soul, considering that each soul is the substantial form of the body to which it is united, is the self-personality or self-feel of each human soul. By this I mean the “what it is like for a soul to be itself to the soul” and even the mere “what it is like to be the soul that a soul is”. Another way of approaching the general aspect of distinction is to consider the “what it is like for the soul to have its identity” or the “what it is like for the soul to have its identity to itself”.

 

If you are like me, you may have noticed at times an extremely attractive member of the opposite sex where you and this attractive person would seem to connect at first glance, perhaps by mutual attraction in  the mystique of the feeling that you would make good soul mates even though you are complete strangers and most likely would never meet again in this life. This has happened to me rather frequently over the years. When it does happen, I could almost swear that I can feel the personality and psyche of the beautiful woman that I seem to connect with.

 

This may simply be a normal psychological and sexual attraction, but perhaps one that might involve subtle clairvoyant phenomenon that cannot be measured or analyzed by current scientific methods.

 

Many of you might have had similar experiences, but either way, I bring all of this up for the purpose of the preceding argument for the unrepeatable uniqueness of every Human Soul.

 

Perhaps I am in some way perceiving a given Human Soul as I behold the object of my attraction even if the method of perceiving is only hard wired natural 5 sense based interpretation of body language such as may be due to an  inherent as a form of intelligence in all human persons that is part of our common genetic legacy built up over several to many thousands of years of human evolution.

 

Regardless, we or at least I seem to feel the personalities of certain people I meet especially strongly, to much of my immediate delight  and sense of mystery.

 

The point of this digression on human intuition is that perhaps even souls that are united to human bodies that have identical world line histories and identical world line external environments from conception until natural death have a distinguishing feature in the form of primal levels of self-awareness, emotions, feelings, instincts, in short, of the aspects of their personalities that are a manifestation of the unrepeatable uniqueness of their souls. Even souls that have bodies that are always identical in this life and which live out identical world lines, might not only have their unique “what it is like to be the soul that they are” or “what it is like to be the soul that the given soul is” from the standpoint of ontological identity, but also in nature, feeling, experience, perception, and the like from a conscious, sub-conscious, and unconscious standpoint.

 

Since the number of possible human souls is absolutely unboundedly infinite in an non-abstractly labelable or precise symbolic sense, this reality must also take into consideration the fact that in a given infinite universe, multiverse, forest, biosphere, solar system and so on ad infinitum, the number of times that a given human body mass-energy-space-time world line will be locally duplicated is an ever growing infinite number

.

This points to the awesome simplicity and super-continuity of each and every human soul in its substance, faculties, and accidental characteristics. An absolutely beautiful aspect of the human soul is that such unrepeatable natures can never be diminished in uniqueness. Since the number of human souls can grow utterly without limit, and since the number of identical human body world lines can grow without limit, such unlimited growth on both fronts seems to indicate that each human soul will grow in accidental if not also in facultative, and substantial nature for all eternity. Such growth would seem necessary in the DIVINE ECONOMY if each Human Soul is destined to have an un-repeatable nature amidst the ever growing set of duplicate body mass-energy-space-time world line states and identical mass-energy-space-time local environments.

 

Thus, the above arguments might simply serve as a proxy that each human soul will grow ontologically, existentially, substantially, facultatively, and accidently for all eternity. It also indicates an utter infinitely super-continuous aspect of the substance and accidental properties of each human soul. Each human soul IMHO is absolutely awesome and beautiful to contemplate. Each human soul can be created by GOD during the conjugal act must be given a chance to without the interruptive aspects of artificial birth control. All young married couples should be open to having large families. I  use the word young herein because middle aged newlyweds might not have many if any biological fertile years left due to menopausal or post-menopausal states. A couple can only crank out children so fast, and so older fertile couples will most likely find the ability to procreate large families greatly diminished even in cases where contraception and natural family planning methods are not utilized.

 

 

27) The Human Soul As Real Information, More Properly,  As A Simple And Non-Composite Information

 

The Human Soul is the substantial form of the body according to the Scholastic Theology promulgated by the pre-imminent Doctor of the Church, Saint Thomas Aquinas. According to the new Catechism of the Catholic Church, the Soul is to be considered the form of the body because of the extreme union of the Soul with the body. Nonetheless, in either circumstance, the Human Soul in said to be immortal and spiritual and immediately created.

 

Now, how do we reconcile the extremely close union of the Human Soul with the Human Body where the union is so extreme, that the composition of the Human Person is not a union of two natures, but rather one nature in two principles?

 

Yet the Human Soul exists just fine in the afterlife without the Human Body, whether in  Heaven, Hell, Purgatory, Limbo, or perhaps in some indeterminate state such as is in the subject of ghosts or poltergeists studied by paranormal enthusiasts.

 

We have never scientifically proven the existence of a Human Soul, and by no means have we ever observed it or measured it. Much of Catholic emphasis on the beginning of human life at the point of conception focuses on the scientifically observable union of  a sperm cell and an egg and where the distinct DNA and embryo is therefore said to be necessarily a complete human person, all the while the notion of a directly created, spiritual, and immortal human soul is rarely ever mentioned anymore. For me, this latter fact is a great folly of modern theology and philosophy, and has actually lead to a devaluation of the esteem that we humans in general have for one another and especially for the unwanted and unborn.

 

I would like to introduce a concept that involves the interpretation of the very essence of the Human Soul as reified information. This reified information would have a certain level of  an accidental and substantial embodiment but might continue to exist even if the substantial and accidental spiritual embodiment of the subject information at another level was destroyed, compromised, condemned to the eternal fires of Hell, or perhaps destroyed by some natural process such as close proximity to the heart of a nuclear weapon explosion which is a mechanism that is considered to be possible by various alleged telepathic communications with by space alien extra-terrestrials by some practitioners of the UFO-space alien culture.

 

By substantial and accidental embodiment of the human soul, I am not referring to the actual human body, but rather instead am referring to a spiritual substantial principle that would have facultative spiritual organs often referred to as the heart, the intellect, the will, and the memory as well as accidental properties such as feelings, emotions, thoughts, individuals memories, experiences and the like.

 

The human soul as such would as a total substantial principle include both a pure information as well as an embodying substantial principle that has both the facultative organs of heart, intellect, will, memory, an also purely accidental aspects.

 

Accordingly, one aspect of the infomations that are human souls might be the purely quantum-mechanical information that defines the human body in its mass-energy-space-time form. Perhaps this quantum information, when considered purely information instead of mass, energy, space, and time, can be said to be the non-corporeal or non-physical vegetative aspect of the Human Soul. Note that Scholastic Theology is familiar with the notion that the Human Soul has three chief divisions: 1) The rational or intellective aspect which is considered the highest and most spiritual aspect of the Human Soul; 2) The animalistic aspect which is considered to be in common with other animal life-forms and which includes the emotions, intuition, feelings, instincts, drives, sensibilities and sensitivities and the like; and 3) The vegetative aspect which includes the vital and unconscious life principles that maintain and sustain the Human Body’s unconscious life processes.

 

Another aspect of the informations of the human soul might be the higher analogue  to  the speculative quantum-mechanical information that defines the human body in its mass-energy-space-time form. This second higher level of information might be the information that defines the emotional, affective, moody, instinctive, intuitive, passionate, and the like aspects of our daily waking and sleeping consciousness without actually being the subject emotions, affective states, feelings, instincts, moods, intuitive experiences, and passions and the like.

 

Yet another aspect of the informations of the human soul might be a still yet higher analogue to the speculative quantum-mechanical information that defines the human body in its mass-energy-space-time form. This third higher level of information might be the information that defines the logical, free-volitional, rational, imaginative, cognitive, and experienced intellectual truth  states that are manifest while the human persons conducts higher order cognitive behaviors and executive functions such as during the work day and   the like.

 

We can go one step further and speculate as to whether yet another aspect of the informations of the Human Soul exist such as those that define moral goodness or the capacity for moral goodness as well as the states of grace that are super-added to the substantial and accidental nature embodiments of the human soul. This fourth level of informations might exist in absolutely every human person as an aspect of their Souls and which comes into being at the moment of conception whether or not this fourth level is universally bestowed on human nature as a result of the merits and graces wrought by Christ’s Incarnation, Life on Earth, Passion, Death On The Cross, Resurrection, and Ascension into Heaven. If the human soul is immortal by grace in terms of its spiritual substantial and spiritual accidental embodiment, then even the Human Soul’s that end up in Hell have a perpetual and inerasable degree of the eternal life of grace in the sense that they have gratuitous substantial and accidental immortality with respect to any such substantial and accidental embodiment.

 

Now typical theologians will assent to the reality that the metaphorical fires of Hell cannot effect the substance of the Soul, but rather only affect the accidental form of the Soul. I would like to suggest that the subject informations which are conjectured to be the very core of the human soul would continue to exist as the identity, unity, and individuality of the Human Soul in an incorruptible manner even if the Human Soul’s accidental embodying form and perhaps even if its substantial embodying form was at least partially if not fully corrupted. My reasoning behind this conjecture is none-other than the fact that each Human Soul will last utterly forever, regardless of whether it ends up in Heaven, Purgatory then Heaven, Hell, Limbo, or perhaps in any exotic but nonetheless temporary ghost or poltergeist like state, the latter state most certainly terminating in the Resurrection of the subject persons as a complete Body Soul Union at the End of Time. Perhaps by ways and means known only to GOD,  any such Souls trapped in a ghost like state are most likely doing  their penance and in my humble opinion, most likely will be exceedingly well rewarded for the current cross they are bearing.

 

 

Now, any spiritual information that defines what I will refer to as the super-essence or meta-essence of the human soul will necessary be a complete unity that is a whole and entire simple entity meaning that it would necessarily not have any separate parts or sub-composition. Thus, such information must be viewed as a complete unity and not sub-divided ontologically or existentially divided into parts in any real manner.

 

Because of the above would be complete oneness, unity, and individuality of the super-essence of the set of the human soul, I will refer to such a mode of reality not as information, but rather as an information, so as to distinguish the entity from the erroneous belief that I am merely referring to the Human Soul as a non-simple entity or a mere collection of facts, and much less, a mere corruptible collection of such facts.

 

Note that the above concepts seem perhaps a little viable to me giving that the Human Soul is so closely united and related to the Human Body in this life that it is according to the new Catechism of the Catholic Church, to be considered the form of the Body.

 

Now by the phrase, form of the Body, I am not referring to the soul actually being shaped like a body, nor resembling the human body in its nature and accidents, but am rather using the actual intended meaning of the word eternal form as promulgated by Plato, Socrates, and Aristotle in ancient Greek philosophy. These brilliant folks held more or less similar beliefs in eternal forms. For example, the eternal form of a circle would actually be a real entity but would be the absolute ideal of what a circle represents in terms of a figure for which every point on the  two dimensional figure would be exactly the same distance away from its center, even more precisely than the limiting uncertainty in the resolution of real space-time below the levels of the Planck Length and Planck Time Units. Likewise, abstract but real properties of goodness and love would have their eternal forms of Divine Goodness and Divine Love.

 

Now since the human body is wonderfully made and has a thinking, feeling, and volitionally operating human brain and indeed is the temple of the HOLY SPIRIT,  how much better and more glorious is the substantial and accidental embodiment of any super-essence of the Human Soul as aspects of the ideal substantial form of the Human Body,  and even how much more glorious yet is any would be any super-essence of the Human Soul as aspects of the ideal substantial form of our daily working psyche or personality.

 

The daily waking human consciousness has all but shown to be dependent on Human Brain electrodynamic-chemical information states, but such consciousness must have a way of existing after the mortal Human Body has died. Perhaps these information states are included in the absolutely holistic but simple set called the information which might in some aspects be the Substantial Form of the Human Body or the Form of the Human Body as the abstract ideal of the Human Body or perhaps even the abstract ideal of the quantum mechanical information that defines the Human Body, Furthermore, perhaps the information states that define the vegetative, sensitive, and intellective and rational states of our daily waking conscious activity are ontologically expressed in an abstract ideal or form that is even higher than the form of the mere  quantum information set that defines the mass-energy-space-time set of the living Human Body. An analogue might also exist for the capacity for moral goodness or the capacity for supernatural grace that is present in every Human Person. After all, there has got to be some reason why the Catholic Catechism states that we are all of fundamentally equal moral equality before GOD. By this, I will assert, that each Human Soul is just as much a Human Soul in its ability for free and rational acts and indeed is considered by GOD to be just as important and good as any other Human Soul.

 

Regarding  the above conjecture on the aspect of the Human Soul as having a super-essence that defines the information states of the Human Body,  Vegetative Life, Sensitive Life, Rational and Intellective Life, and Moral Capacity for Goodness, for daily life in this world, such a super-essence would be an eternal form that is extra-ordinarily ontologically simple with no separate composition or parts.

 

The above speculations are a summary of my best guess as to how the continuity of the human personality can continue upon human bodily death, and also how the otherwise apparent extrinsic dependence of human sensitive, intellective, rational, and volitional, and working capacity for moral goodness on the living human brain in this life can be explained.

 

Note that even though human sensitive, intellective, rational, and volitional life, and working capacity for moral goodness in this life are extrinsically dependent on the human brain,  these activities are in themselves, by no means, physical nor material. To me, this is yet a great philosophical mystery that we also need to accept. The depths and mystery of the Human Person in my own humble opinion are much greater than the Theology of Saint Thomas and even much greater than the truths expressed within the new Catechism of the Catholic Church even if such works were claimed to be an exhaustive account of the mysteries of the Human  Person.

 

Note that I will be posting a more comprehensive version of this article in the coming days, perhaps even today, as I get my thoughts more focused on this particular subject after I get my brain jump started by getting a Double Big Gulp of Diet Coke from 7/11. By the way, I am a really big fan of 7/11 convenience stores because they tend to be open all night and day. I would buy stock in their parent corporation in a heartbeat if I had the money, and just might do so in the future.

 

Note that I am a rather strange physicist being that I feel equally at home contemplating spiritual ontological realities as I do the purely physical. However, for those of you who are put off by my occasional spiritualistic speculations as being unreal, false, or impractical, never fear, for I assure you I am not losing my mind, and will continue with my main and primary work as a physicist whose primary objective is to work as an interstellar propulsion system concept developer.

 

 

28) Just A Shadow Of A Glimpse Of The Utterly Limitless Number Derivatives of Human Emotion With Respect To Time, Thought, Volition, Affect, Memory, Instinct, And Emotion  Where These Latter 6 Psychodynamic Parameter Are Likely Just An Infinitesimal Fraction Of The Number Of Possible Psychodynamic Parameters, Of Which In This Life, We Have  A Glimpse Of Relatively Few.

 

Emotion  as such can be a function or partially a function of emotion, will, affect, instinct, emotion and/or memory; and thought as such can be expressed as follows:

 

 

E(t), E(w), E(a), E(i), E(m), E(t,w), E(t,a), E(t,i), E(t,m), E(w,a), E(w,i), E(w,m), E(a,i), E(a,m), E(i,m), E(t,w,a), E(t,w,i), E(t,w,m), E(t,a,i), E(t,a,m), E(t,i,m), E(w,a,i), E(w,a,m), E(w,i,m), E(a,i,m), E(t,w,a,i), E(t,w,a,m), E(t,w,i,m), E(t,a,i,m), E(w,a,i,m), E(t,w,a,i,m), E(t,e), E(w,e), E(a,e), E(i,e), E(m,e), E(t,w,e), E(t,a,e), E(t,i,e), E(t,m,e), E(w,a,e), E(w,i,e), E(w,m,e), E(a,i,e), E(a,m,e), E(i,m,e), E(t,w,a,e), E(t,w,i,e), E(t,w,m,e), E(t,a,i,e), E(t,a,m,e), E(t,i,m,e), E(w,a,i,e), E(w,a,m,e), E(w,i,m,e), E(a,i,m,e), E(t,w,a,i,e), E(t,w,a,m,e), E(t,w,i,m,e), E(t,a,i,m,e), E(w,a,i,m,e), E(t,w,a,i,m,e).

 

Note that some differential expressions involving  the form of functions of will, or E,  as a function of emotion, e, by itself, or in conjunction with any sub-set of the parameters of t,w,a,i,m, are not included to the same extent as many similar expressions including E, and these other parameters denoted by the small letters, t,w,a,i, and/or m in this section. A more comphrensive post will include the currently omitted explicit formulas incorporating the parameter, e. Note that capital e, or E, is a parameter that is often included in the differential equations herein, but then so in a slightly different context than e would have be included. The difference between e and E will become clear from the context of the specific formulas.

 

In all, there are (2 EXP n) – 1 = (2 EXP 6) – 1 = 63 expressions as such if one assumes the previous five dimensions of will.

 

Assuming that each of the above function f(E) is perfectly continuous, the number of forms that the general emotion function, f(E), can have is plausibly equal to П(1,62)R where R is the number of real numbers.

 

Assuming that each of the above functions f(E) is super-continuous at the level of 0/(Aleph 0) where Aleph 0 is the number of integers, the number of forms that the general emotion function, f(E), can have is plausibly equal to П(1,62)[R x (Aleph 0)] where R is the number of real numbers.

 

Assuming that each of the above functions f(E) is super-continuous at the level of 0/(Aleph 1) where Aleph 1 is the number of real numbers according to the Continuum Hypotheses, the number of forms that the general emotion function, f(E), can have is plausibly equal to П(1,62)[R x (Aleph 1)] where R is the number of real numbers.

 

Assuming that each of the above functions f(E) is super-continuous at the level of 0/(Aleph 2) where Aleph 2 is is greater than Aleph 1 by a factor of infinity (the exact details of this infinity of which are a little more involve than the latter simple statement), the number of forms that the general emotion function, f(E), can have is plausibly equal to П(1,62)[R x (Aleph 2)] where R is the number of real numbers.

 

Assuming that each of the above functions f(E) is super-continuous at the level of 0/(Aleph 3) where Aleph 3 is is greater than Aleph 2 by a factor of infinity (the exact details of this infinity of which are a little more involve than the latter simple statement), the number of forms that the general emotion function, f(E), can have is plausibly equal to П(1,62)[R x (Aleph 3)] where R is the number of real numbers.

 

… and so on ad infinitum to, through, and beyond the following product series, П(1,62)[R x (Aleph 4)],   П(1,62)[R x (Aleph 5)],  П(1,62)[R x (Aleph 6)],…,  П(1,62)[R x (Aleph Ω)], …,  П(1,62)[R x (Aleph (Aleph 0))], …, П(1,62)[R x (Aleph (Aleph 1))], …, П(1,62)[R x (Aleph (Aleph 2))], … , П(1,62)[R x (Aleph (Aleph Ω))], …, П(1,62)[R x (Aleph (Aleph (Aleph 0)))] and so on perhaps in an ever lasting series even a  the latter level of abstraction.

 

Assuming that each of the above functions f(E) is super-continuous at the level of 0/(Aleph 2) where Aleph 2 is is greater than Aleph 1 by a factor of infinity (the exact details of this infinity of which are a little more involve than the latter simple statement), the number of forms that the general emotion function, f(E), can have is plausibly equal to П(1,62)[R x (Aleph 2)] where R is the number of real numbers.

 

 

We can summarize all of these combinations as follows in compact symbolism that is intuitively clear to follow:

 

 

E = E(t and/or w and/or a and/or i and/or m)

 

 

We can express E as a function of time as follows: E(T) =  E[(t and/or w and/or a and/or i and/or m),(T)] or perhaps the following notation can be more appropriate in certain circumstances.

 

 

E(T) = E{[t(T)] and/or [w(T)] and/or [a(T)] and/or [i(T)] and/or [m(T)]}.

 

 

Thus the following first order derivatives of emotion with respect to time are possible.

 

 

dE(t)/dT, dE(w)/dT, dE(a)/dT, dE(i)/dT, dE(m)/dT, dE(t,w)/dT, dE(t,a)/dT, dE(t,i)/dT, dE(t,m)/dT, dE(w,a)/dT, dE(w,i)/dT, dE(w,m)/dT, dE(a,i)/dT, dE(a,m)/dT, dE(i,m)/dT, dE(t,w,a)/dT, dE(t,w,i)/dT, dE(t,w,m)/dT, dE(t,a,i)/dT, dE(t,a,m)/dT, dE(t,i,m)/dT, dE(w,a,i)/dT, dE(w,a,m)/dT, dE(w,i,m)/dT, dE(a,i,m)/dT, dE(t,w,a,i)/dT, dE(t,w,a,m)/dT, dE(t,w,i,m)/dT, dE(t,a,i,m)/dT, dE(w,a,i,m)/dT, dE(t,w,a,i,m)/dT.

 

 

Or more succinctly,  dE/dT = dE(t and/or w and/or a and/or i and/or m)/dT

 

 

Or perhaps dE(T)/dT =d E{[t(T)] and/or [w(T)] and/or [a(T)] and/or [i(T)] and/or [m(T)]}/dT.

 

 

Likewise, we can take the second time derivatives of  E as follows:

 

 

 

d[dE(t)/dT]/dT, d[dE(w)/dT]/dT, d[dE(a)/dT]/dT, d[dE(i)/dT]/dT, d[dE(m)/dT]/dT, d[dE(t,w)/dT]/dT, d[dE(t,a)/dT]/dT, d[dE(t,i)/dT]/dT, d[dE(t,m)/dT]/dT, d[dE(w,a)/dT]/dT, d[dE(w,i)/dT]/dT, d[dE(w,m)/dT]/dT, d[dE(a,i)/dT]/dT, d[dE(a,m)/dT]/dT, d[dE(i,m)/dT/dT, d[dE(t,w,a)/dT]/dT, d[dE(t,w,i)/dT]/dT, d[dE(t,w,m)/dT]/dT, d[dE(t,a,i)/dT]/dT, d[dE(t,a,m)/dT]/dT,  d[dE(t,i,m)/dT]/dT, d[dE(w,a,i)/dT]/dT, d[dE(w,a,m)/dT]/dT, d[dE(w,i,m)/dT]/dT, d[dE(a,i,m)/dT]/dT, d[dE(t,w,a,i)/dT]/dT, d[dE(t,w,a,m)/dT/dT, d[dE(t,w,i,m)/dT]/dT, d[dE(t,a,i,m)/dT]/dT, d[dE(w,a,i,m)/dT]/dT, d[dE(t,w,a,i,m)/dT]/dT..

 

 

or more succinctly, as d(dE/dT)/dT = d[d E(t and/or w and/or a and/or i and/or m)/dT]/dT = E2

 

 

or as

 

 

d[dE(T)/dT]/dT  = d[d E{[t(T)] and/or [w(T)] and/or [a(T)] and/or [i(T)] and/or [m(T)]}/dT]/dT = E2.

 

 

 

Likewise, we can take the third time derivatives of  E as follows:

 

 

 

d[d[dE(t)/dT]/dT]/dT, d[d[dE(w)/dT]/dT]/dT, d[d[dE(a)/dT]/dT]/dT, d[d[dE(i)/dT]/dT]/dT, d[d[dE(m)/dT]/dT]/dT, d[d[dE(t,w)/dT]/dT]/dT, d[d[dE(t,a)/dT]/dT]/dT, d[d[dE(t,i)/dT]/dT]/dT, d[d[dE(t,m)/dT]/dT]/dT, d[d[dE(w,a)/dT]/dT]/dT, d[d[dE(w,i)/dT]/dT]/dT, d[d[dE(w,m)/dT]/dT]/dT, d[d[dE(a,i)/dT]/dT]/dT, d[d[dE(a,m)/dT]/dT]/dT, d[d[dE(i,m)/dT/dT]/dT, d[d[dE(t,w,a)/dT]/dT]/dT, d[d[dE(t,w,i)/dT]/dT]/dT, d[d[dE(t,w,m)/dT]/dT]/dT, d[d[dE(t,a,i)/dT]/dT]/dT, d[d[dE(t,a,m)/dT]/dT]/dT,  d[d[dE(t,i,m)/dT]/dT]/dT, d[d[dE(w,a,i)/dT]/dT]/dT, d[d[dE(w,a,m)/dT]/dT]/dT, d[d[dE(w,i,m)/dT]/dT]/dT, d[d[dE(a,i,m)/dT]/dT]/dT, d[d[dE(t,w,a,i)/dT]/dT]/dT, d[d[dE(t,w,a,m)/dT/dT]/dT, d[d[dE(t,w,i,m)/dT]/dT]/dT, d[d[dE(t,a,i,m)/dT]/dT]/dT, d[d[dE(w,a,i,m)/dT]/dT]/dT, d[d[dE(t,w,a,i,m)/dT]/dT]/dT.

 

 

or more succinctly, as d[d(dE/dT)/dT]/dT = d[d[d E(t and/or w and/or a and/or i and/or m)/dT]/dT]/dT = E3

 

 

or as

 

 

d[d[dE(T)/dT]/dT]/dT  = d[d[d E{[t(T)] and/or [w(T)] and/or [a(T)] and/or [i(T)] and/or [m(T)]}/dT]/dT]/dT = E3.

 

 

We can also form the expressions;

 

 

d[d[f(E)]/dT]/dT = d{d [E[t(T)]]/dT and/or d[E[w(T)]]/dT and/or d[E[a(T)]]/dT and/or d[E[i(T)]]/dT and/or d[E[m(T)]]/dT}/dT  = f(E)2

 

 

and

 

 

d[d[d[f(E)]/dT]/dT]/dT = d{d{ d [E[t(T)]]/dT and/or d[E[w(T)]]/dT and/or d[E[a(T)]]/dT and/or d[E[i(T)]]/dT and/or d[E[m(T)]]/dT}/dT}/dT  = f(E)3A, where A stands for type A differentiation which is not to be confused with the meaning of so-called Type A personality as A is used as an ordinal in a totally different context here.

 

 

and

 

 

d[d[d[f(E)]/dT]/dT]/dT = d{d[d [E[t(T)]]/dT]/dT  and/or d[d [E[w(T)]]/dT]/dT  and/or d[d [E[a(T)]]/dT]/dT  and/or d[d [E[i(T)]]/dT]/dT  and/or d[d [E[m(T)]]/dT]/dT }/dT = f(E)3B, where B stands for type B differentiation which is not to be confused with the meaning of so-called Type  B personality as B is used as an ordinal in a totally different context here .

 

 

In fact, one can form yet higher order time derivatives of emotions with respect to time as follows.

 

 

E5 = d E4/dT = d[dE3/dT]/dT

 

 

 

E5 = d E4/dT =  d[d[d[d[d E{[t(T)] and/or [w(T)] and/or [a(T)] and/or [i(T)] and/or [m(T)]}/dT]/dT]/dT]/dT]/dT.

 

 

 

f(E)5A = d[f(E)4A]/dT = d[d [f(E)3A]/dT]/dT =  d{d{d{d{ d [E[t(T)]]/dT and/or d[E[w(T)]]/dT and/or d[E[a(T)]]/dT and/or d[E[i(T)]]/dT and/or d[E[m(T)]]/dT}/dT}/dT]/dT]/dT

 

 

 

 

E6 = d E5/dT = d[d E4/dT]/dT = d[d[dE3/dT]/dT]/dT

 

 

 

E6 = dE5/dT = d[d[d[d[d[d E{[t(T)] and/or [w(T)] and/or [a(T)] and/or [i(T)] and/or [m(T)]}/dT]/dT]/dT]/dT]/dT]/dT

 

 

 

f(E)6A = d[f(E)5A]/dT = d{ d{d{d{d{ d [E[t(T)]]/dT and/or d[E[w(T)]]/dT and/or d[E[a(T)]]/dT and/or d[E[i(T)]]/dT and/or d[E[m(T)]]/dT}/dT}/dT]/dT]/dT]/dT

 

 

 

 

E7 = dE6/dT

 

f(E)7A = d[f(E)6A]/dT

 

 

E8 = d E7/dT

 

f(E)8A = d[f(E)7A]/dT

 

 

 

E9 = d E8/dT

 

f(E)9A = d[f(E)8A]/dT

 

 

E10…, E11…, E12 … etc.

 

 

Anyone for E ensemble, or E infinity scrapper, or E (Aleph 0), or E(Aleph 1), or E(Aleph 2), or how about E Aleph (Aleph 0), or E Aleph (Aleph 1) , or E Aleph (Aleph 2), or even E Aleph (Aleph (Aleph 0)), or E Aleph (Aleph (Aleph 1)), or E Aleph (Aleph (Aleph 2)), and so on?

 

 

Thus, for the set of the sets of derivatives of E1 through E(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}.

 

For the set of the sets of derivatives of E1 through E(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)},…, {П(0,31)[R]}_{(Aleph 1)}.

 

For the set of the sets of derivatives of E1 through E(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}.

 

For the set of the sets of derivatives of E1 through E(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the derivative states in the set of the sets of derivatives of E1 through E(Aleph 0) is plausible equal to:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of E1 through E(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of E1 through E(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}}}.

 

For the set of the sets of derivatives of E1 through E(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous E(Aleph 0) derivative space at the level of 0/(Aleph 0), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of E1 through E(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of E1 through (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of E1 through E(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of E1 through E(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of E1 through E(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of E1 through E(Aleph 1), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of E1 through  E(Aleph 2), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of E1 through E(Aleph 3), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous E(Aleph 0) derivative space at the level of 0/(Aleph 1), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of E1 through E(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of E1 through E(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of E1 through E(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of E1 through  E(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations  for the set of the sets of derivatives of E1 through E(Aleph 0) is plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of E1 through E(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of E1 through E(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of E1 through E(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

 

For super-continuous E(Aleph 0) derivative space at the level of 0/(Aleph 2), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of E1 through E(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of E1 through E(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of E1 through E(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of E1 through E(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of E1 through E(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of E1 through E(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of E1 through E(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of E1 through E(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

Similar series can be developed for super-continuity at any applicable level such as 0/(Aleph 3), 0/(Aleph 4), 0/(Aleph 5),…, 0/(Aleph Ω), 0/(Aleph (Aleph 0)), …, 0/(Aleph (Aleph 1)), …, 0/(Aleph (Aleph 2)), …, 0/(Aleph (Aleph 3)),…, 0/(Aleph (Aleph Ω)),…, 0/(Aleph (Aleph (Aleph 0))), …, 0/(Aleph (Aleph (Aleph 1))),…, 0/(Aleph (Aleph (Aleph 2))),…, 0/(Aleph (Aleph (Aleph 3))),…, 0/(Aleph (Aleph  (Aleph Ω))), …

 

An so-on ad infinitum.

 

 

In addition to these numerical functions of E as functions of summation series of product series functions, in order to really appreciate the enourmous complexity of the human soul in terms of its potential to evolve and be differentiated from all other souls in its characteristics, we would need to consider how every single category and even every single species of emotions of the form E can very. Since there may exist an arbitrarily high infinite number species of E, the number of numerical functions of E is utterly beyond recogning. I will cover such notions in terms of mathematical notation in yet another series of articles I will write on this general concept.

 

 

Perhaps these numbers are applicable when one considers that the human soul, in its accidental form and perhaps even in its substantial form stores all experience and other psychodynamics based phenomenon. Every experience adds to the accidental form of the human soul and this includes the souls of all those still alive on Earth, all those in Purgatory, all those in Heaven, all those in Hell, and all those in any Limbo.

Since the human soul can grow without limit in terms of its psychodynamic time –flow world line, such a consideration offers another mechanism where the number of derivative states, combinations of derivative states, and even super-continuity of the derivative state space can grow forever.

 

Folks, for those of you who might balk at me for including literally all souls in the above consideration, including the souls in Hell, as well as bodily extraterrestrial souls and the souls of so-called bodily ultraterrestials sometimes referred to as etherians in the new age UFO buff culture, my reply is that we simply do not understand the full scope of GOD’s Divine Economy. We may never fully comprehend the scope of the Divine Economy because such an utterly eternal scheme, is, well, eternal and never ending.

We can also express emotion qualitatively, statistically, and perhaps with the use of some forms of real analyses as a derivative of thought or of t.

 

Given that E(t) =  E(t and/or w and/or a and/or i and/or m), the following first order derivatives of emotion with respect to thought are possible.

 

 

dE(t)/dt, dE(w)/dt, dE(a)/dt, dE(i)/dt, dE(m)/dt, dE(t,w)/dt, dE(t,a)/dt, dE(t,i)/dt, dE(t,m)/dt, dE(w,a)/dt, dE(w,i)/dt, dE(w,m)/dt, dE(a,i)/dt, dE(a,m)/dt, dE(i,m)/dt, dE(t,w,a)/dt, dE(t,w,i)/dt, dE(t,w,m)/dt, dE(t,a,i)/dt, dE(t,a,m)/dt, dE(t,i,m)/dt, dE(w,a,i)/dt, dE(w,a,m)/dt, dE(w,i,m)/dt, dE(a,i,m)/dt, dE(t,w,a,i)/dt, dE(t,w,a,m)/dt, dE(t,w,i,m)/dt, dE(t,a,i,m)/dt, dE(w,a,i,m)/dt, dE(t,w,a,i,m)/dt.

 

 

Or more succinctly,  dE/dt = dE(t and/or w and/or a and/or i and/or m)/dt

 

 

Or perhaps dE(t)/dt =d E{[t(t)] and/or [w(t)] and/or [a(t)] and/or [i(t)] and/or [m(t)]}/dt.

 

 

Likewise, we can take the second thought derivatives of  E as follows:

 

 

 

d[dE(t)/dt]/dt, d[dE(w)/dt]/dt, d[dE(a)/dt]/dt, d[dE(i)/dt]/dt, d[dE(m)/dt]/dt, d[dE(t,w)/dt]/dt, d[dE(t,a)/dt]/dt, d[dE(t,i)/dt]/dt, d[dE(t,m)/dt]/dt, d[dE(w,a)/dt]/dt, d[dE(w,i)/dt]/dt, d[dE(w,m)/dt]/dt, d[dE(a,i)/dt]/dt, d[dE(a,m)/dt]/dt, d[dE(i,m)/dt/dt, d[dE(t,w,a)/dt]/dt, d[dE(t,w,i)/dt]/dt, d[dE(t,w,m)/dt]/dt, d[dE(t,a,i)/dt]/dt, d[dE(t,a,m)/dt]/dt,  d[dE(t,i,m)/dt]/dt, d[dE(w,a,i)/dt]/dt, d[dE(w,a,m)/dt]/dt, d[dE(w,i,m)/dt]/dt, d[dE(a,i,m)/dt]/dt, d[dE(t,w,a,i)/dt]/dt, d[dE(t,w,a,m)/dt/dt, d[dE(t,w,i,m)/dt]/dt, d[dE(t,a,i,m)/dt]/dt, d[dE(w,a,i,m)/dt]/dt, d[dE(t,w,a,i,m)/dt]/dt..

 

 

or more succinctly, as d(dE/dt)/dt = d[d E(t and/or w and/or a and/or i and/or m)/dt]/dt = Et2

 

 

or as

 

 

d[dE(t)/dt]/dt  = d[d E{[t(t)] and/or [w(t)] and/or [a(t)] and/or [i(t)] and/or [m(t)]}/dt]/dt = Et2.

 

 

 

Likewise, we can take the third thought derivatives of  E as follows:

 

 

 

d[d[dE(t)/dt]/dt]/dt, d[d[dE(w)/dt]/dt]/dt, d[d[dE(a)/dt]/dt]/dt, d[d[dE(i)/dt]/dt]/dt, d[d[dE(m)/dt]/dt]/dt, d[d[dE(t,w)/dt]/dt]/dt, d[d[dE(t,a)/dt]/dt]/dt, d[d[dE(t,i)/dt]/dt]/dt, d[d[dE(t,m)/dt]/dt]/dt, d[d[dE(w,a)/dt]/dt]/dt, d[d[dE(w,i)/dt]/dt]/dt, d[d[dE(w,m)/dt]/dt]/dt, d[d[dE(a,i)/dt]/dt]/dt, d[d[dE(a,m)/dt]/dt]/dt, d[d[dE(i,m)/dt/dt]/dt, d[d[dE(t,w,a)/dt]/dt]/dt, d[d[dE(t,w,i)/dt]/dt]/dt, d[d[dE(t,w,m)/dt]/dt]/dt, d[d[dE(t,a,i)/dt]/dt]/dt, d[d[dE(t,a,m)/dt]/dt]/dt,  d[d[dE(t,i,m)/dt]/dt]/dt, d[d[dE(w,a,i)/dt]/dt]/dt, d[d[dE(w,a,m)/dt]/dt]/dt, d[d[dE(w,i,m)/dt]/dt]/dt, d[d[dE(a,i,m)/dt]/dt]/dt, d[d[dE(t,w,a,i)/dt]/dt]/dt, d[d[dE(t,w,a,m)/dt/dt]/dt, d[d[dE(t,w,i,m)/dt]/dt]/dt, d[d[dE(t,a,i,m)/dt]/dt]/dt, d[d[dE(w,a,i,m)/dt]/dt]/dt, d[d[dE(t,w,a,i,m)/dt]/dt]/dt.

 

 

or more succinctly, as d[d(dE/dt)/dt]/dt = d[d[d E(t and/or w and/or a and/or i and/or m)/dt]/dt]/dt = Et3

 

 

or as

 

 

d[d[dE(t)/dt]/dt]/dt  = d[d[d E{[t(t)] and/or [w(t)] and/or [a(t)] and/or [i(t)] and/or [m(t)]}/dt]/dt]/dt = Et3.

 

 

We can also form the expressions;

 

 

d[d[f(E)]/dt]/dt = d{d [E[t(t)]]/dt and/or d[E[w(t)]]/dt and/or d[E[a(t)]]/dt and/or d[E[i(t)]]/dt and/or d[E[m(t)]]/dt}/dt  = f(Et)2

 

 

and

 

 

d[d[d[f(E)]/dt]/dt]/dt = d{d{ d [E[t(t)]]/dt and/or d[E[w(t)]]/dt and/or d[E[a(t)]]/dt and/or d[E[i(t)]]/dt and/or d[E[m(t)]]/dt}/dt}/dt  = f(Et)3A, where A stands for type A differentiation which is not to be confused with the meaning of so-called Type A personality as A is used as an ordinal in a totally different context here.

 

 

and

 

 

d[d[d[f(E)]/dt]/dt]/dt = d{d[d [E[t(t)]]/dt]/dt  and/or d[d [E[w(t)]]/dt]/dt  and/or d[d [E[a(t)]]/dt]/dt  and/or d[d [E[i(t)]]/dt]/dt  and/or d[d [E[m(t)]]/dt]/dt }/dt = f(Et)3B, where B stands for type B differentiation which is not to be confused with the meaning of so-called Type  B personality as B is used as an ordinal in a totally different context here .

 

 

In fact, one can form yet higher order derivatives of emotions with respect to thought as follows.

 

 

Et5 = d Et4/dt = d[dEt3/dt]/dt

 

 

 

Et5 = dEt4/dt =  d[d[d[d[d E{[t(t)] and/or [w(t)] and/or [a(t)] and/or [i(t)] and/or [m(t)]}/dt]/dt]/dt]/dt]/dt.

 

 

 

f(Et)5A = d[f(tE)4A]/dt = d[d [f(Et)3A]/dt]/dt =  d{d{d{d{ d [E[t(t)]]/dt and/or d[E[w(t)]]/dt and/or d[E[a(t)]]/dt and/or d[E[i(t)]]/dt and/or d[E[m(t)]]/dt}/dt}/dt]/dt]/dt

 

 

 

 

Et6 = d Et5/dt = d[d Et4/dt]/dt = d[d[dEt3/dt]/dt]/dt

 

 

 

Et6 = dEt5/dt = d[d[d[d[d[d E{[t(t)] and/or [w(t)] and/or [a(t)] and/or [i(t)] and/or [m(t)]}/dt]/dt]/dt]/dt]/dt]/dt

 

 

 

f(Et)6A = d[f(Et)5A]/dt = d{ d{d{d{d{ d [E[t(t)]]/dt and/or d[E[w(t)]]/dt and/or d[E[a(t)]]/dt and/or d[E[i(t)]]/dt and/or d[E[m(t)]]/dt}/dt}/dt]/dt]/dt]/dt

 

 

 

 

Et7 = dEt6/dt

 

f(Et)7A = d[f(Et)6A]/dt

 

 

Et8 = d Et7/dt

 

f(Et)8A = d[f(Et)7A]/dt

 

 

 

Et9 = d Et8/dt

 

f(Et)9A = d[f(Et)8A]/dt

 

 

Et10…, Et11…, Et12 … etc.

 

 

Anyone for Et ensemble, or Et infinity scrapper, or Et (Aleph 0), or Et(Aleph 1), or Et(Aleph 2), or how about Et Aleph (Aleph 0), or Et Aleph (Aleph 1) , or Et Aleph (Aleph 2), or even Et Aleph (Aleph (Aleph 0)), or Et Aleph (Aleph (Aleph 1)), or Et Aleph (Aleph (Aleph 2)), and so on?

 

 

 

 

 

 

 

 

 

Thus, for the set of the sets of derivatives of Et1 through Et(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Et1 through Et(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)},…, {П(0,31)[R]}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Et1 through Et(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Et1 through Et(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the derivative states in the set of the sets of derivatives of Et1 through Et(Aleph 0) is plausible equal to:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Et1 through Et(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Et1 through Et(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}}}.

 

For the set of the sets of derivatives of Et1 through Et(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Et(Aleph 0) derivative space at the level of 0/(Aleph 0), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Et1 through Et(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Et1 through Et (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Et1 through Et(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Et1 through Et(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Et1 through Et(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Et1 through Et(Aleph 1), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Et1 through  Et(Aleph 2), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Et1 through Et(Aleph 3), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Et(Aleph 0) derivative space at the level of 0/(Aleph 1), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Et1 through Et(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Et1 through Et(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Et1 through Et(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Et1 through  Et(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations  for the set of the sets of derivatives of Et1 through Et(Aleph 0) is plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Et1 through Et(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Et1 through Et(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Et1 through Et(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

 

For super-continuous Et(Aleph 0) derivative space at the level of 0/(Aleph 2), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Et1 through Et(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Et1 through Et(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Et1 through Et(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Et1 through Et(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Et1 through Et(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Et1 through Et(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Et1 through Et(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Et1 through Et(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}}}

 

and so on ad infinitum.

 

 

Similar series can be developed for super-continuity at any applicable level such as at the levels of: 0/(Aleph 3), 0/(Aleph 4), 0/(Aleph 5),…, 0/(Aleph Ω), 0/(Aleph (Aleph 0)), …, 0/(Aleph (Aleph 1)), …, 0/(Aleph (Aleph 2)), …, 0/(Aleph (Aleph 3)),…, 0/(Aleph (Aleph Ω)),…, 0/(Aleph (Aleph (Aleph 0))), …, 0/(Aleph (Aleph (Aleph 1))),…, 0/(Aleph (Aleph (Aleph 2))),…, 0/(Aleph (Aleph (Aleph 3))),…, 0/(Aleph (Aleph  (Aleph Ω))), …

 

An so-on ad infinitum.

 

In addition to these numerical functions of Et as functions of summation series of product series functions, in order to really appreciate the enourmous complexity of the human soul in terms of its potential to evolve and be differentiated from all other souls in its characteristics, we would need to consider how every single category and even every single species of emotions of the form Et can very. Since there may exist an arbitrarily high infinite number species of Et, the number of numerical functions of Et is utterly beyond recogning. I will cover such notions in terms of mathematical notation in yet another series of articles I will write on this general concept.

 

 

Perhaps these numbers are applicable when one considers that the human soul, in its accidental form and perhaps even in its substantial form stores all experience and other psychodynamics based phenomenon. Every experience adds to the accidental form of the human soul and this includes the souls of all those still alive on Earth, all those in Purgatory, all those in Heaven, all those in Hell, and all those in any Limbo.

Since the human soul can grow without limit in terms of its psychodynamic time –flow world line, such a consideration offers another mechanism where the number of derivative states, combinations of derivative states, and even super-continuity of the derivative state space can grow forever.

 

Folks, for those of you who might balk at me for including literally all souls in the above consideration, including the souls in Hell, as well as bodily extraterrestrial souls and the souls of so-called bodily ultraterrestials sometimes referred to as etherians in the new age UFO buff culture, my reply is that we simply do not understand the full scope of GOD’s Divine Economy. We may never fully comprehend the scope of the Divine Economy because such an utterly eternal scheme, is, well, eternal and never ending.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The general meaning of thought derivatives of emotion can be viewed as the manner in which the qualitative and/or quantitative aspects of emotion as a function of thought very with thought. The manner in which emotions very with thought may be multi-thought dimensional wherein the dimensions of derivations can be multiple, and wherein the derivations can be taken in parallel, series parallel or serial manner The differentials can be partial or non-partial derivatives, or both partial and non-partial for a given computation.

 

In fact, since there is in theory, no limit to the numbers of qualitatively and quantitatively different thoughts, and perhaps no limit to the number of possible different types or classes of thoughts, wherein each person has his or her own unique thoughts, the number of thought dimensions that can effect emotions is literally infinite, given the entirety of the set of created persons, and perhaps also literally infinite for each person as an individual, although we can not intellectually and intuitively understand this infinite number.

 

It is interesting to consider the ramifactions of being able to perform realistic calculations involving thought derivatives of emotion from a mathematical, theoretical, scientific,  and philosophical perspective.

 

Persons for which one or more nth order derivatives of emotion with respect to thought that have large absolute values would tend to have their emotions highly influenced by thought, or at least at least for the emotions under consideration with respect to the dimension of the specific thought type(s) or class(es) for which the differentiation(s) are performed. Perhaps a strong coupling between emotion and thought indicates a well integrated personality and commensurately, a high degree of emotional capacity and a high degree of emotional intelligence.

 

We would expect that disembodied human souls, ETI souls, and/or UTI souls in Heaven, Limbo, highly evolved bodily ETI persons, highly evolved UTI persons, and angels to have emotions of all kinds and intensities which are highly subject to thought.

 

 

We can also consider two dimensional nth ordered derivatives of emotion with respect to thought and time, or with respect to t and T, respectively.

 

Given that E[(t)(T)] =  E[(t and/or w and/or a and/or i and/or m)(t)(T)], the following first order two dimensional derivatives of emotion with respect to thought and Time are possible.

 

 

d[dE[(t)(T)]/dt]/dT, d[dE[(w)(T)]/dt]/dT, d[dE[(a)(T)]/dt]/dT, d[dE[(i)(T)]/dt]/dT, d[dE[(m)(T)]/dt]/dT, d[dE[(t,w)(T)]/dt]/dT, d[dE[(t,a)(T)]/dt]/dT, d[dE[(t,i)(T)]/dt]/dT, d[dE[(t,m)(T)]/dt]/dT, d[dE[(w,a)(T)]/dt]/dT, d[dE[(w,i)(T)]/dt]/dT, d[dE[(w,m)(T)]/dt]/dT, d[dE[(a,i)(T)]/dt]/dT, d[dE[(a,m)(T)]/dt]/dT, d[dE[(i,m)(T)]/dt]/dT, d[dE[(t,w,a)(T)]/dt]/dT, d[dE[(t,w,i)(T)]/dt]/dT, d[dE[(t,w,m)(T)]/dt]/dT, d[dE[(t,a,i)(T)]/dt]/dT, d[dE[(t,a,m)(T)]/dt]/dT, d[dE[(t,i,m)(T)]/dt]/dT, d[dE[(w,a,i)(T)]/dt]/dT, d[dE[(w,a,m)(T)]/dt]/dT, d[dE[(w,i,m)(T)]/dt]/dT, d[dE[(a,i,m)(T)]/dt]/dT, d[dE[(t,w,a,i)(T)]/dt]/dT, d[dE[(t,w,a,m)(T)]/dt]/dT, d[dE[(t,w,i,m)(T)]/dt]/dT, d[dE[(t,a,i,m)(T)]/dt]/dT, d[dE[(w,a,i,m)(T)]/dt]/dT, d[dE[(t,w,a,i,m)(T)]/dt]/dT.

 

 

Or more succinctly,  d[dE(T)/dt]/dT = d[dE[(T)(t and/or w and/or a and/or i and/or m)]/dt]/dT

 

or

 

d[dE(T)/dT]/dt = d[dE[(T)(t and/or w and/or a and/or i and/or m)]/dT]/dt

 

 

 

 

 

Or perhaps d[d E[(t)(T)]/dt]/dT  = d[d E [{[t(t)] and/or [w(t)] and/or [a(t)] and/or [i(t)] and/or [m(t)]}(T)]/dt]/dT

 

or

 

Or perhaps d[d E[(t)(T)]/dT]/dt  = d[d E [{[t(t)] and/or [w(t)] and/or [a(t)] and/or [i(t)] and/or [m(t)]}(T)]/dT]/dt

 

 

 

Likewise, we can take the second dual dimensioned thought-time derivatives of  E as follows:

 

d[d[d[dE[(t)(T)]/dt]/dT]/dt]/dT, d[d[d[dE[(w)(T)]/dt]/dT]/dt]/dT, d[d[d[dE[(a)(T)]/dt]/dT]/dt]/dT, d[d[d[dE[(i)(T)]/dt]/dT]/dt]/dT, d[d[d[dE[(m)(T)]/dt]/dT]/dt]/dT, d[d[d[dE[(t,w)(T)]/dt]/dT]/dt]/dT, d[d[d[dE[(t,a)(T)]/dt]/dT]/dt]/dT, d[d[d[dE[(t,i)(T)]/dt]/dT]/dt]/dT, d[d[d[dE[(t,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dE[(w,a)(T)]/dt]/dT]/dt]/dT, d[d[d[dE[(w,i)(T)]/dt]/dT]/dt]/dT, d[d[d[dE[(w,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dE[(a,i)(T)]/dt]/dT]/dt]/dT, d[d[d[dE[(a,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dE[(i,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dE[(t,w,a)(T)]/dt]/dT]/dt]/dT, d[d[d[dE[(t,w,i)(T)]/dt]/dT]/dt]/dT, d[d[d[dE[(t,w,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dE[(t,a,i)(T)]/dt]/dT]/dt]/dT, d[d[d[dE[(t,a,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dE[(t,i,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dE[(w,a,i)(T)]/dt]/dT]/dt]/dT, d[d[d[dE[(w,a,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dE[(w,i,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dE[(a,i,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dE[(t,w,a,i)(T)]/dt]/dT]/dt]/dT, d[d[d[dE[(t,w,a,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dE[(t,w,i,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dE[(t,a,i,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dE[(w,a,i,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dE[(t,w,a,i,m)(T)]/dt]/dT]/dt]/dT.

 

or as:

 

 

 

d[d[d[dE[(t)(T)]/dt]/dT]/dT]/dt, d[d[d[dE[(w)(T)]/dt]/dT]/dT]/dt, d[d[d[dE[(a)(T)]/dt]/dT]/dT]/dt, d[d[d[dE[(i)(T)]/dt]/dT]/dT]/dt, d[d[d[dE[(m)(T)]/dt]/dT]/dT]/dt, d[d[d[dE[(t,w)(T)]/dt]/dT]/dT]/dt, d[d[d[dE[(t,a)(T)]/dt]/dT]/dT]/dt, d[d[d[dE[(t,i)(T)]/dt]/dT]/dT]/dt, d[d[d[dE[(t,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dE[(w,a)(T)]/dt]/dT]/dT]/dt, d[d[d[dE[(w,i)(T)]/dt]/dT]/dT]/dt, d[d[d[dE[(w,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dE[(a,i)(T)]/dt]/dT]/dT]/dt, d[d[d[dE[(a,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dE[(i,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dE[(t,w,a)(T)]/dt]/dT]/dT]/dt, d[d[d[dE[(t,w,i)(T)]/dt]/dT]/dT]/dt, d[d[d[dE[(t,w,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dE[(t,a,i)(T)]/dt]/dT]/dT]/dt, d[d[d[dE[(t,a,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dE[(t,i,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dE[(w,a,i)(T)]/dt]/dT]/dT]/dt, d[d[d[dE[(w,a,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dE[(w,i,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dE[(a,i,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dE[(t,w,a,i)(T)]/dt]/dT]/dT]/dt, d[d[d[dE[(t,w,a,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dE[(t,w,i,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dE[(t,a,i,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dE[(w,a,i,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dE[(t,w,a,i,m)(T)]/dt]/dT]/dT]/dt.

 

or as:

 

d[d[d[dE[(t)(T)]/dT]/dt]/dt]/dT, d[d[d[dE[(w)(T)]/dT]/dt]/dt]/dT, d[d[d[dE[(a)(T)]/dT]/dt]/dt]/dT, d[d[d[dE[(i)(T)]/dT]/dt]/dt]/dT, d[d[d[dE[(m)(T)]/dT]/dt]/dt]/dT, d[d[d[dE[(t,w)(T)]/dT]/dt]/dt]/dT, d[d[d[dE[(t,a)(T)]/dT]/dt]/dt]/dT, d[d[d[dE[(t,i)(T)]/dT]/dt]/dt]/dT, d[d[d[dE[(t,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dE[(w,a)(T)]/dT]/dt]/dt]/dT, d[d[d[dE[(w,i)(T)]/dT]/dt]/dt]/dT, d[d[d[dE[(w,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dE[(a,i)(T)]/dT]/dt]/dt]/dT, d[d[d[dE[(a,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dE[(i,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dE[(t,w,a)(T)]/dT]/dt]/dt]/dT, d[d[d[dE[(t,w,i)(T)]/dT]/dt]/dt]/dT, d[d[d[dE[(t,w,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dE[(t,a,i)(T)]/dT]/dt]/dt]/dT, d[d[d[dE[(t,a,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dE[(t,i,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dE[(w,a,i)(T)]/dT]/dt]/dt]/dT, d[d[d[dE[(w,a,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dE[(w,i,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dE[(a,i,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dE[(t,w,a,i)(T)]/dT]/dt]/dt]/dT, d[d[d[dE[(t,w,a,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dE[(t,w,i,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dE[(t,a,i,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dE[(w,a,i,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dE[(t,w,a,i,m)(T)]/dT]/dt]/dt]/dT.

 

 

or as;

 

 

 

 

d[d[d[dE(t)/dt]/dt]/dT]/dT, d[d[d[dE(w)/dt]/dt]/dT]/dT, d[d[d[dE(a)/dt]/dt]/dT]/dT, d[d[d[dE(i)/dt]/dt]/dT]/dT, d[d[d[dE(m)/dt]/dt]/dT]/dT, d[d[d[dE(t,w)/dt]/dt]/dT]/dT, d[d[d[dE(t,a)/dt]/dt]/dT]/dT, d[d[d[dE(t,i)/dt]/dt]/dT]/dT, d[d[d[dE(t,m)/dt]/dt]/dT]/dT, d[d[d[dE(w,a)/dt]/dt]/dT]/dT, d[d[d[dE(w,i)/dt]/dt]/dT]/dT, d[d[d[dE(w,m)/dt]/dt]/dT]/dT, d[d[d[dE(a,i)/dt]/dt]/dT]/dT, d[d[d[dE(a,m)/dt]/dt]/dT]/dT, d[d[d[dE(i,m)/dt]/dt]/dT]/dT, d[d[d[dE(t,w,a)/dt]/dt]/dT]/dT, d[d[d[dE(t,w,i)/dt]/dt]/dT]/dT, d[d[d[dE(t,w,m)/dt]/dt]/dT]/dT, d[d[d[dE(t,a,i)/dt]/dt]/dT]/dT, d[d[d[dE(t,a,m)/dt]/dt]/dT]/dT,  d[d[d[dE(t,i,m)/dt]/dt]/dT]/dT, d[d[d[dE(w,a,i)/dt]/dt]/dT]/dT, d[d[d[dE(w,a,m)/dt]/dt]/dT]/dT, d[d[d[dE(w,i,m)/dt]/dt]/dT]/dT, d[d[d[dE(a,i,m)/dt]/dt]/dT]/dT, d[d[d[dE(t,w,a,i)/dt]/dt]/dT]/dT, d[d[d[dE(t,w,a,m)/dt/dt, d[d[d[dE(t,w,i,m)/dt]/dt]/dT]/dT, d[d[d[dE(t,a,i,m)/dt]/dt]/dT]/dT, d[d[d[dE(w,a,i,m)/dt]/dt]/dT]/dT, d[d[d[dE(t,w,a,i,m)/dt]/dt]/dT]/dT..

 

or as:

 

d[d[d[dE(t)/dT]/dt]/dT]/dt, d[d[d[dE(w)/dT]/dt]/dT]/dt, d[d[d[dE(a)/dT]/dt]/dT]/dt, d[d[d[dE(i)/dT]/dt]/dT]/dt, d[d[d[dE(m)/dT]/dt]/dT]/dt, d[d[d[dE(t,w)/dT]/dt]/dT]/dt, d[d[d[dE(t,a)/dT]/dt]/dT]/dt, d[d[d[dE(t,i)/dT]/dt]/dT]/dt, d[d[d[dE(t,m)/dT]/dt]/dT]/dt, d[d[d[dE(w,a)/dT]/dt]/dT]/dt, d[d[d[dE(w,i)/dT]/dt]/dT]/dt, d[d[d[dE(w,m)/dT]/dt]/dT]/dt, d[d[d[dE(a,i)/dT]/dt]/dT]/dt, d[d[d[dE(a,m)/dT]/dt]/dT]/dt, d[d[d[dE(i,m)/ dT]/dt]/dT]/dt, d[d[d[dE(t,w,a)/dT]/dt]/dT]/dt, d[d[d[dE(t,w,i)/dT]/dt]/dT]/dt, d[d[d[dE(t,w,m)/dT]/dt]/dT]/dt, d[d[d[dE(t,a,i)/dT]/dt]/dT]/dt, d[d[d[dE(t,a,m)/dT]/dt]/dT]/dt,  d[d[d[dE(t,i,m)/dT]/dt]/dT]/dt, d[d[d[dE(w,a,i)/dT]/dt]/dT]/dt, d[d[d[dE(w,a,m)/dT]/dt]/dT]/dt, d[d[d[dE(w,i,m)/dT]/dt]/dT]/dt, d[d[d[dE(a,i,m)/dT]/dt]/dT]/dt, d[d[d[dE(t,w,a,i)/dT]/dt]/dT]/dt, d[d[d[dE(t,w,a,m)/dt/dt, d[d[d[dE(t,w,i,m)/dT]/dt]/dT]/dt, d[d[d[dE(t,a,i,m)/dT]/dt]/dT]/dt, d[d[d[dE(w,a,i,m)/dT]/dt]/dT]/dt, d[d[d[dE(t,w,a,i,m)/dT]/dt]/dT]/dt..

 

or as:

 

d[d[d[dE(t)/dT]/dT]/dt]/dt, d[d[d[dE(w)/dT]/dT]/dt]/dt, d[d[d[dE(a)/dT]/dT]/dt]/dt, d[d[d[dE(i)/dT]/dT]/dt]/dt, d[d[d[dE(m)/dT]/dT]/dt]/dt, d[d[d[dE(t,w)/dT]/dT]/dt]/dt, d[d[d[dE(t,a)/dT]/dT]/dt]/dt, d[d[d[dE(t,i)/dT]/dT]/dt]/dt, d[d[d[dE(t,m)/dT]/dT]/dt]/dt, d[d[d[dE(w,a)/dT]/dT]/dt]/dt, d[d[d[dE(w,i)/dT]/dT]/dt]/dt, d[d[d[dE(w,m)/dT]/dT]/dt]/dt, d[d[d[dE(a,i)/dT]/dT]/dt]/dt, d[d[d[dE(a,m)/ dT]/dT]/dt]/dt, d[d[d[dE(i,m)/ dT]/dT]/dt]/dt, d[d[d[dE(t,w,a)/dT]/dT]/dt]/dt, d[d[d[dE(t,w,i)/dT]/dT]/dt]/dt, d[d[d[dE(t,w,m)/dT]/dT]/dt]/dt, d[d[d[dE(t,a,i)/dT]/dT]/dt]/dt, d[d[d[dE(t,a,m)/dT]/dT]/dt]/dt,  d[d[d[dE(t,i,m)/dT]/dT]/dt]/dt, d[d[d[dE(w,a,i)/dT]/dT]/dt]/dt, d[d[d[dE(w,a,m)/dT]/dT]/dt]/dt, d[d[d[dE(w,i,m)/dT]/dT]/dt]/dt, d[d[d[dE(a,i,m)/dT]/dT]/dt]/dt, d[d[d[dE(t,w,a,i)/dT]/dT]/dt]/dt, d[d[d[dE(t,w,a,m)/dt/dt, d[d[d[dE(t,w,i,m)/dT]/dT]/dt]/dt, d[d[d[dE(t,a,i,m)/dT]/dT]/dt]/dt, d[d[d[dE(w,a,i,m)/dT]/dT]/dt]/dt, d[d[d[dE(t,w,a,i,m)/dT]/dT]/dt]/dt..

 

 

We can also take higher order duel dimensional derivatives of emotion as a function of thought and time but the symbolic expression of the set of such derivatives very soon becomes excessively lengthly to write and so these higher order derivatives as such are not mentioned here except to say that they would be computed in an analogous manner to the second order duel dimensional derivatives described above.

 

.

 

 

 

 

 

We can also express emotion qualitatively, statistically, and perhaps with the use of some forms of real analyses as a derivative with respect to will or with respect to  w.

 

Given that E(w) =  E(t and/or w and/or a and/or i and/or m), the following first order derivatives of emotion with respect to will are possible.

 

 

dE(t)/dw, dE(w)/dw, dE(a)/dw, dE(i)/dw, dE(m)/dw, dE(t,w)/dw, dE(t,a)/dw, dE(t,i)/dw, dE(t,m)/dw, dE(w,a)/dw, dE(w,i)/dw, dE(w,m)/dw, dE(a,i)/dw, dE(a,m)/dw, dE(i,m)/dw, dE(t,w,a)/dw, dE(t,w,i)/dw, dE(t,w,m)/dw, dE(t,a,i)/dw, dE(t,a,m)/dw, dE(t,i,m)/dw, dE(w,a,i)/dw, dE(w,a,m)/dw, dE(w,i,m)/dw, dE(a,i,m)/dw, dE(t,w,a,i)/dw, dE(t,w,a,m)/dw, dE(t,w,i,m)/dw, dE(t,a,i,m)/dw, dE(w,a,i,m)/dw, dE(t,w,a,i,m)/dw.

 

 

Or more succinctly,  dE/dw = dE(t and/or w and/or a and/or i and/or m)/dw

 

 

Or perhaps dE(w)/dw =d E{[t(w)] and/or [w(w)] and/or [a(w)] and/or [i(w)] and/or [m(w)]}/dw.

 

 

Likewise, we can take the second will derivatives of  E as follows:

 

 

 

d[dE(t)/dw]/dw, d[dE(w)/dw]/dw, d[dE(a)/dw]/dw, d[dE(i)/dw]/dw, d[dE(m)/dw]/dw, d[dE(t,w)/dw]/dw, d[dE(t,a)/dw]/dw, d[dE(t,i)/dw]/dw, d[dE(t,m)/dw]/dw, d[dE(w,a)/dw]/dw, d[dE(w,i)/dw]/dw, d[dE(w,m)/dw]/dw, d[dE(a,i)/dw]/dw, d[dE(a,m)/dw]/dw, d[dE(i,m)/dw/dw, d[dE(t,w,a)/dw]/dw, d[dE(t,w,i)/dw]/dw, d[dE(t,w,m)/dw]/dw, d[dE(t,a,i)/dw]/dw, d[dE(t,a,m)/dw]/dw,  d[dE(t,i,m)/dw]/dw, d[dE(w,a,i)/dw]/dw, d[dE(w,a,m)/dw]/dw, d[dE(w,i,m)/dw]/dw, d[dE(a,i,m)/dw]/dw, d[dE(t,w,a,i)/dw]/dw, d[dE(t,w,a,m)/dw/dw, d[dE(t,w,i,m)/dw]/dw, d[dE(t,a,i,m)/dw]/dw, d[dE(w,a,i,m)/dw]/dw, d[dE(t,w,a,i,m)/dw]/dw..

 

 

or more succinctly, as d(dE/dw)/dw = d[d E(t and/or w and/or a and/or i and/or m)/dw]/dw = Ew2

 

 

or as

 

 

d[dE(w)/dw]/dw  = d[d E{[t(w)] and/or [w(w)] and/or [a(w)] and/or [i(w)] and/or [m(w)]}/dw]/dw = Ew2.

 

 

 

Likewise, we can take the third will derivatives of  E as follows:

 

 

 

d[d[dE(t)/dw]/dw]/dw, d[d[dE(w)/dw]/dw]/dw, d[d[dE(a)/dw]/dw]/dw, d[d[dE(i)/dw]/dw]/dw, d[d[dE(m)/dw]/dw]/dw, d[d[dE(t,w)/dw]/dw]/dw, d[d[dE(t,a)/dw]/dw]/dw, d[d[dE(t,i)/dw]/dw]/dw, d[d[dE(t,m)/dw]/dw]/dw, d[d[dE(w,a)/dw]/dw]/dw, d[d[dE(w,i)/dw]/dw]/dw, d[d[dE(w,m)/dw]/dw]/dw, d[d[dE(a,i)/dw]/dw]/dw, d[d[dE(a,m)/dw]/dw]/dw, d[d[dE(i,m)/dw/dw]/dw, d[d[dE(t,w,a)/dw]/dw]/dw, d[d[dE(t,w,i)/dw]/dw]/dw, d[d[dE(t,w,m)/dw]/dw]/dw, d[d[dE(t,a,i)/dw]/dw]/dw, d[d[dE(t,a,m)/dw]/dw]/dw,  d[d[dE(t,i,m)/dw]/dw]/dw, d[d[dE(w,a,i)/dw]/dw]/dw, d[d[dE(w,a,m)/dw]/dw]/dw, d[d[dE(w,i,m)/dw]/dw]/dw, d[d[dE(a,i,m)/dw]/dw]/dw, d[d[dE(t,w,a,i)/dw]/dw]/dw, d[d[dE(t,w,a,m)/dw/dw]/dw, d[d[dE(t,w,i,m)/dw]/dw]/dw, d[d[dE(t,a,i,m)/dw]/dw]/dw, d[d[dE(w,a,i,m)/dw]/dw]/dw, d[d[dE(t,w,a,i,m)/dw]/dw]/dw.

 

 

or more succinctly, as d[d(dE/dw)/dw]/dw = d[d[d E(t and/or w and/or a and/or i and/or m)/dw]/dw]/dw = Ew3

 

 

or as

 

 

d[d[dE(w)/dw]/dw]/dw  = d[d[d E{[t(w)] and/or [w(w)] and/or [a(w)] and/or [i(w)] and/or [m(w)]}/dw]/dw]/dw = Ew3.

 

 

We can also form the expressions;

 

 

d[d[f(E)]/dw]/dw = d{d [E[t(w)]]/dw and/or d[E[w(w)]]/dw and/or d[E[a(w)]]/dw and/or d[E[i(w)]]/dw and/or d[E[m(w)]]/dw}/dw  = f(Ew)2

 

 

and

 

 

d[d[d[f(E)]/dw]/dw]/dw = d{d{ d [E[t(w)]]/dw and/or d[E[w(w)]]/dw and/or d[E[a(w)]]/dw and/or d[E[i(w)]]/dw and/or d[E[m(w)]]/dw}/dw}/dw  = f(Ew)3A, where A stands for type A differentiation which is not to be confused with the meaning of so-called Type A personality as A is used as an ordinal in a totally different context here.

 

 

and

 

 

d[d[d[f(E)]/dw]/dw]/dw = d{d[d [E[t(w)]]/dw]/dw  and/or d[d [E[w(w)]]/dw]/dw  and/or d[d [E[a(w)]]/dw]/dw  and/or d[d [E[i(w)]]/dw]/dw  and/or d[d [E[m(w)]]/dw]/dw }/dw = f(Ew)3B, where B stands for type B differentiation which is not to be confused with the meaning of so-called Type  B personality as B is used as an ordinal in a totally different context here .

 

 

In fact, one can form yet higher order derivatives of emotions with respect to will as follows.

 

 

Ew5 = d Ew4/dw = d[dEw3/dw]/dw

 

 

 

Ew5 = dEw4/dw =  d[d[d[d[d E{[t(w)] and/or [w(w)] and/or [a(w)] and/or [i(w)] and/or [m(w)]}/dw]/dw]/dw]/dw]/dw.

 

 

 

f(Ew)5A = d[f(Ew)4A]/dw = d[d [f(Ew)3A]/dw]/dw =  d{d{d{d{ d [E[t(w)]]/dw and/or d[E[w(w)]]/dw and/or d[E[a(w)]]/dw and/or d[E[i(w)]]/dw and/or d[E[m(w)]]/dw}/dw}/dw]/dw]/dw

 

 

 

 

Ew6 = d Ew5/dw = d[d Ew4/dw]/dw = d[d[dEw3/dw]/dw]/dw

 

 

 

Ew6 = dEw5/dw = d[d[d[d[d[d E{[t(w)] and/or [w(w)] and/or [a(w)] and/or [i(w)] and/or [m(w)]}/dw]/dw]/dw]/dw]/dw]/dw

 

 

 

f(Ew)6A = d[f(Ew)5A]/dw = d{ d{d{d{d{ d [E[t(w)]]/dw and/or d[E[w(w)]]/dw and/or d[E[a(w)]]/dw and/or d[E[i(w)]]/dw and/or d[E[m(w)]]/dw}/dw}/dw]/dw]/dw]/dw

 

 

 

 

Ew7 = dEw6/dw

 

f(Ew)7A = d[f(Ew)6A]/dw

 

 

Ew8 = d Ew7/dw

 

f(Ew)8A = d[f(Ew)7A]/dw

 

 

 

Ew9 = d Ew8/dw

 

f(Ew)9A = d[f(Ew)8A]/dw

 

 

Ew10…, Ew11…, Ew12 … etc.

 

 

Anyone for Ew ensemble, or Ew infinity scrapper, or Ew (Aleph 0), or Ew(Aleph 1), or Ew (Aleph 2), or how about Ew Aleph (Aleph 0), or Ew Aleph (Aleph 1) , or Ew Aleph (Aleph 2), or even Ew Aleph (Aleph (Aleph 0)), or Ew Aleph (Aleph (Aleph 1)), or Ew Aleph (Aleph (Aleph 2)), and so on?

 

 

 

 

Thus, for the set of the sets of derivatives of Ew1 through Ew(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ew1 through Ew(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)},…, {П(0,31)[R]}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ew1 through Ew(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ew1 through Ew(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the derivative states in the set of the sets of derivatives of Ew1 through Ew(Aleph 0) is plausible equal to:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ew1 through Ew(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ew1 through Ew(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}}}.

 

For the set of the sets of derivatives of Ew1 through Ew(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Ew(Aleph 0) derivative space at the level of 0/(Aleph 0), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Ew1 through Ew(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ew1 through Ew (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ew1 through Ew(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ew1 through Ew(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Ew1 through Ew(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ew1 through Ew(Aleph 1), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Ew1 through  Ew(Aleph 2), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Ew1 through Ew(Aleph 3), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Ew(Aleph 0) derivative space at the level of 0/(Aleph 1), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Ew1 through Ew(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ew1 through Ew(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ew1 through Ew(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ew1 through  Ew(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations  for the set of the sets of derivatives of Ew1 through Ew(Aleph 0) is plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ew1 through Ew(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Ew1 through Ew(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Ew1 through Ew(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

 

For super-continuous Ew(Aleph 0) derivative space at the level of 0/(Aleph 2), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Ew1 through Ew(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ew1 through Ew(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ew1 through Ew(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ew1 through Ew(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Ew1 through Ew(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ew1 through Ew(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Ew1 through Ew(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Ew1 through Ew(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}}}

 

An so-on ad infinitum.

 

 

Similar series can be developed for super-continuity at any applicable level such as 0/(Aleph 3), 0/(Aleph 4), 0/(Aleph 5),…, 0/(Aleph Ω), 0/(Aleph (Aleph 0)), …, 0/(Aleph (Aleph 1)), …, 0/(Aleph (Aleph 2)), …, 0/(Aleph (Aleph 3)),…, 0/(Aleph (Aleph Ω)),…, 0/(Aleph (Aleph (Aleph 0))), …, 0/(Aleph (Aleph (Aleph 1))),…, 0/(Aleph (Aleph (Aleph 2))),…, 0/(Aleph (Aleph (Aleph 3))),…, 0/(Aleph (Aleph  (Aleph Ω))), …

 

An so-on ad infinitum.

In addition to these numerical functions of Ew as functions of summation series of product series functions, in order to really appreciate the enourmous complexity of the human soul in terms of its potential to evolve and be differentiated from all other souls in its characteristics, we would need to consider how every single category and even every single species of emotions of the form Ew can very. Since there may exist an arbitrarily high infinite number species of Ew, the number of numerical functions of Ew is utterly beyond recogning. I will cover such notions in terms of mathematical notation in yet another series of articles I will write on this general concept.

 

 

 

Perhaps these numbers are applicable when one considers that the human soul, in its accidental form and perhaps even in its substantial form stores all experience and other psychodynamics based phenomenon. Every experience adds to the accidental form of the human soul and this includes the souls of all those still alive on Earth, all those in Purgatory, all those in Heaven, all those in Hell, and all those in any Limbo.

Since the human soul can grow without limit in terms of its psychodynamic time –flow world line, such a consideration offers another mechanism where the number of derivative states, combinations of derivative states, and even super-continuity of the derivative state space can grow forever.

 

Folks, for those of you who might balk at me for including literally all souls in the above consideration, including the souls in Hell, as well as bodily extraterrestrial souls and the souls of so-called bodily ultraterrestials sometimes referred to as etherians in the new age UFO buff culture, my reply is that we simply do not understand the full scope of GOD’s Divine Economy. We may never fully comprehend the scope of the Divine Economy because such an utterly eternal scheme, is, well, eternal and never ending.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The general meaning of will derivatives of emotion can be viewed as the manner in which the qualitative and/or quantitative aspects of emotion as a function of will very with will. The manner in which emotions very with will may be multi- will-aspect dimensional wherein the dimensions of derivations can be multiple, and wherein the derivations can be taken in parallel, series parallel or in serial manner. The differentials can be partial or non-partial derivatives, or both partial and non-partial for a given computation.

 

In fact, since there is in theory, no limit to the numbers of qualitatively and quantitatively different acts of will or volitional states, and perhaps no limit to the number of possible different types or classes of acts of will or volitional states, wherein each person has his or her own unique acts or will or volitional states, the number of volitional state dimensions that can effect emotions is literally infinite, given the entirety of the set of created persons, and perhaps also literally infinite for each person as an individual, although we can not intellectually and intuitively understand this infinite number.

 

 

It is interesting to consider the ramifactions of being able to perform realistic calculations involving will derivatives of emotion from a mathematical, theoretical, scientific,  and philosophical perspective.

 

Persons for which one or more nth order derivatives of emotion with respect to will that have large absolute values would tend to have their emotions highly influenced by will, or at least for the emotions under consideration with respect to the dimension of the specific will act type(s) or class(es) for which the differentiation(s) are being performed. Perhaps a strong coupling between emotion and will indicates a well integrated personality and commensurately, a high degree of emotional capacity and a high degree of emotional intelligence as well as perhaps very strong will power.

 

We would expect that disembodied human souls, ETI souls, and/or UTI souls in Heaven, Limbo, highly evolved bodily ETI persons, highly evolved UTI persons, and angels to have emotions of all kinds and intensities which are highly subject to will.

 

 

We can also consider two dimensional ith ordered derivatives of emotion with respect to will and time, or with respect to w and T, respectively.

 

Given that E[(w)(T)] =  E[(t and/or w and/or a and/or i and/or m)(w)(T)], the following first order two dimensional derivatives of emotion with respect to will and Time are possible.

 

 

d[dE[(t)(T)]/dw]/dT, d[dE[(w)(T)]/dw]/dT, d[dE[(a)(T)]/dw]/dT, d[dE[(i)(T)]/dw]/dT, d[dE[(m)(T)]/dw]/dT, d[dE[(t,w)(T)]/dw]/dT, d[dE[(t,a)(T)]/dw]/dT, d[dE[(t,i)(T)]/dw]/dT, d[dE[(t,m)(T)]/dw]/dT, d[dE[(w,a)(T)]/dw]/dT, d[dE[(w,i)(T)]/dw]/dT, d[dE[(w,m)(T)]/dw]/dT, d[dE[(a,i)(T)]/dw]/dT, d[dE[(a,m)(T)]/dw]/dT, d[dE[(i,m)(T)]/dw]/dT, d[dE[(t,w,a)(T)]/dw]/dT, d[dE[(t,w,i)(T)]/dw]/dT, d[dE[(t,w,m)(T)]/dw]/dT, d[dE[(t,a,i)(T)]/dw]/dT, d[dE[(t,a,m)(T)]/dw]/dT, d[dE[(t,i,m)(T)]/dw]/dT, d[dE[(w,a,i)(T)]/dw]/dT, d[dE[(w,a,m)(T)]/dw]/dT, d[dE[(w,i,m)(T)]/dw]/dT, d[dE[(a,i,m)(T)]/dw]/dT, d[dE[(t,w,a,i)(T)]/dw]/dT, d[dE[(t,w,a,m)(T)]/dw]/dT, d[dE[(t,w,i,m)(T)]/dw]/dT, d[dE[(t,a,i,m)(T)]/dw]/dT, d[dE[(w,a,i,m)(T)]/dw]/dT, d[dE[(t,w,a,i,m)(T)]/dw]/dT.

 

 

Or more succinctly,  d[dE(T)/dw]/dT = d[dE[(T)(t and/or w and/or a and/or i and/or m)]/dw]/dT

 

or

 

d[dE(T)/dT]/dw = d[dE[(T)(t and/or w and/or a and/or i and/or m)]/dT]/dw

 

 

 

 

 

Or perhaps d[d E[(w)(T)]/dw]/dT  = d[d E [{[t(w)] and/or [w(w)] and/or [a(w)] and/or [i(w)] and/or [m(w)]}(T)]/dw]/dT

 

or

 

Or perhaps d[d E[(w)(T)]/dT]/dw  = d[d E [{[t(w)] and/or [w(w)] and/or [a(w)] and/or [i(w)] and/or [m(w)]}(T)]/dT]/dw

 

 

 

Likewise, we can take the second dual dimension will -time derivatives of  E as follows:

 

d[d[d[dE[(t)(T)]/dw]/dT]/dw]/dT, d[d[d[dE[(w)(T)]/dw]/dT]/dw]/dT, d[d[d[dE[(a)(T)]/dw]/dT]/dw]/dT, d[d[d[dE[(i)(T)]/dw]/dT]/dw]/dT, d[d[d[dE[(m)(T)]/dw]/dT]/dw]/dT, d[d[d[dE[(t,w)(T)]/dw]/dT]/dw]/dT, d[d[d[dE[(t,a)(T)]/dw]/dT]/dw]/dT, d[d[d[dE[(t,i)(T)]/dw]/dT]/dw]/dT, d[d[d[dE[(t,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dE[(w,a)(T)]/dw]/dT]/dw]/dT, d[d[d[dE[(w,i)(T)]/dw]/dT]/dw]/dT, d[d[d[dE[(w,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dE[(a,i)(T)]/dw]/dT]/dw]/dT, d[d[d[dE[(a,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dE[(i,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dE[(t,w,a)(T)]/dw]/dT]/dw]/dT, d[d[d[dE[(t,w,i)(T)]/dw]/dT]/dw]/dT, d[d[d[dE[(t,w,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dE[(t,a,i)(T)]/dw]/dT]/dw]/dT, d[d[d[dE[(t,a,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dE[(t,i,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dE[(w,a,i)(T)]/dw]/dT]/dw]/dT, d[d[d[dE[(w,a,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dE[(w,i,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dE[(a,i,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dE[(t,w,a,i)(T)]/dw]/dT]/dw]/dT, d[d[d[dE[(t,w,a,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dE[(t,w,i,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dE[(t,a,i,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dE[(w,a,i,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dE[(t,w,a,i,m)(T)]/dw]/dT]/dw]/dT.

 

or as:

 

 

 

d[d[d[dE[(t)(T)]/dw]/dT]/dT]/dw, d[d[d[dE[(w)(T)]/dw]/dT]/dT]/dw, d[d[d[dE[(a)(T)]/dw]/dT]/dT]/dw, d[d[d[dE[(i)(T)]/dw]/dT]/dT]/dw, d[d[d[dE[(m)(T)]/dw]/dT]/dT]/dw, d[d[d[dE[(t,w)(T)]/dw]/dT]/dT]/dw, d[d[d[dE[(t,a)(T)]/dw]/dT]/dT]/dw, d[d[d[dE[(t,i)(T)]/dw]/dT]/dT]/dw, d[d[d[dE[(t,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dE[(w,a)(T)]/dw]/dT]/dT]/dw, d[d[d[dE[(w,i)(T)]/dw]/dT]/dT]/dw, d[d[d[dE[(w,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dE[(a,i)(T)]/dw]/dT]/dT]/dw, d[d[d[dE[(a,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dE[(i,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dE[(t,w,a)(T)]/dw]/dT]/dT]/dw, d[d[d[dE[(t,w,i)(T)]/dw]/dT]/dT]/dw, d[d[d[dE[(t,w,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dE[(t,a,i)(T)]/dw]/dT]/dT]/dw, d[d[d[dE[(t,a,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dE[(t,i,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dE[(w,a,i)(T)]/dw]/dT]/dT]/dw, d[d[d[dE[(w,a,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dE[(w,i,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dE[(a,i,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dE[(t,w,a,i)(T)]/dw]/dT]/dT]/dw, d[d[d[dE[(t,w,a,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dE[(t,w,i,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dE[(t,a,i,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dE[(w,a,i,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dE[(t,w,a,i,m)(T)]/dw]/dT]/dT]/dw.

 

or as:

 

d[d[d[dE[(t)(T)]/dT]/dw]/dw]/dT, d[d[d[dE[(w)(T)]/dT]/dw]/dw]/dT, d[d[d[dE[(a)(T)]/dT]/dw]/dw]/dT, d[d[d[dE[(i)(T)]/dT]/dw]/dw]/dT, d[d[d[dE[(m)(T)]/dT]/dw]/dw]/dT, d[d[d[dE[(t,w)(T)]/dT]/dw]/dw]/dT, d[d[d[dE[(t,a)(T)]/dT]/dw]/dw]/dT, d[d[d[dE[(t,i)(T)]/dT]/dw]/dw]/dT, d[d[d[dE[(t,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dE[(w,a)(T)]/dT]/dw]/dw]/dT, d[d[d[dE[(w,i)(T)]/dT]/dw]/dw]/dT, d[d[d[dE[(w,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dE[(a,i)(T)]/dT]/dw]/dw]/dT, d[d[d[dE[(a,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dE[(i,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dE[(t,w,a)(T)]/dT]/dw]/dw]/dT, d[d[d[dE[(t,w,i)(T)]/dT]/dw]/dw]/dT, d[d[d[dE[(t,w,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dE[(t,a,i)(T)]/dT]/dw]/dw]/dT, d[d[d[dE[(t,a,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dE[(t,i,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dE[(w,a,i)(T)]/dT]/dw]/dw]/dT, d[d[d[dE[(w,a,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dE[(w,i,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dE[(a,i,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dE[(t,w,a,i)(T)]/dT]/dw]/dw]/dT, d[d[d[dE[(t,w,a,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dE[(t,w,i,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dE[(t,a,i,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dE[(w,a,i,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dE[(t,w,a,i,m)(T)]/dT]/dw]/dw]/dT.

 

 

or as;

 

 

 

 

d[d[d[dE(t)/dw]/dw]/dT]/dT, d[d[d[dE(w)/dw]/dw]/dT]/dT, d[d[d[dE(a)/dw]/dw]/dT]/dT, d[d[d[dE(i)/dw]/dw]/dT]/dT, d[d[d[dE(m)/dw]/dw]/dT]/dT, d[d[d[dE(t,w)/dw]/dw]/dT]/dT, d[d[d[dE(t,a)/dw]/dw]/dT]/dT, d[d[d[dE(t,i)/dw]/dw]/dT]/dT, d[d[d[dE(t,m)/dw]/dw]/dT]/dT, d[d[d[dE(w,a)/dw]/dw]/dT]/dT, d[d[d[dE(w,i)/dw]/dw]/dT]/dT, d[d[d[dE(w,m)/dw]/dw]/dT]/dT, d[d[d[dE(a,i)/dw]/dw]/dT]/dT, d[d[d[dE(a,m)/dw]/dw]/dT]/dT, d[d[d[dE(i,m)/dw]/dw]/dT]/dT, d[d[d[dE(t,w,a)/dw]/dw]/dT]/dT, d[d[d[dE(t,w,i)/dw]/dw]/dT]/dT, d[d[d[dE(t,w,m)/dw]/dw]/dT]/dT, d[d[d[dE(t,a,i)/dw]/dw]/dT]/dT, d[d[d[dE(t,a,m)/dw]/dw]/dT]/dT,  d[d[d[dE(t,i,m)/dw]/dw]/dT]/dT, d[d[d[dE(w,a,i)/dw]/dw]/dT]/dT, d[d[d[dE(w,a,m)/dw]/dw]/dT]/dT, d[d[d[dE(w,i,m)/dw]/dw]/dT]/dT, d[d[d[dE(a,i,m)/dw]/dw]/dT]/dT, d[d[d[dE(t,w,a,i)/dw]/dw]/dT]/dT, d[d[d[dE(t,w,a,m)/dw/dw, d[d[d[dE(t,w,i,m)/dw]/dw]/dT]/dT, d[d[d[dE(t,a,i,m)/dw]/dw]/dT]/dT, d[d[d[dE(w,a,i,m)/dw]/dw]/dT]/dT, d[d[d[dE(t,w,a,i,m)/dw]/dw]/dT]/dT..

 

or as:

 

d[d[d[dE(t)/dT]/dw]/dT]/dw, d[d[d[dE(w)/dT]/dw]/dT]/dw, d[d[d[dE(a)/dT]/dw]/dT]/dw, d[d[d[dE(i)/dT]/dw]/dT]/dw, d[d[d[dE(m)/dT]/dw]/dT]/dw, d[d[d[dE(t,w)/dT]/dw]/dT]/dw, d[d[d[dE(t,a)/dT]/dw]/dT]/dw, d[d[d[dE(t,i)/dT]/dw]/dT]/dw, d[d[d[dE(t,m)/dT]/dw]/dT]/dw, d[d[d[dE(w,a)/dT]/dw]/dT]/dw, d[d[d[dE(w,i)/dT]/dw]/dT]/dw, d[d[d[dE(w,m)/dT]/dw]/dT]/dw, d[d[d[dE(a,i)/dT]/dw]/dT]/dw, d[d[d[dE(a,m)/dT]/dw]/dT]/dw, d[d[d[dE(i,m)/ dT]/dw]/dT]/dw, d[d[d[dE(t,w,a)/dT]/dw]/dT]/dw, d[d[d[dE(t,w,i)/dT]/dw]/dT]/dw, d[d[d[dE(t,w,m)/dT]/dw]/dT]/dw, d[d[d[dE(t,a,i)/dT]/dw]/dT]/dw, d[d[d[dE(t,a,m)/dT]/dw]/dT]/dw,  d[d[d[dE(t,i,m)/dT]/dw]/dT]/dw, d[d[d[dE(w,a,i)/dT]/dw]/dT]/dw, d[d[d[dE(w,a,m)/dT]/dw]/dT]/dw, d[d[d[dE(w,i,m)/dT]/dw]/dT]/dw, d[d[d[dE(a,i,m)/dT]/dw]/dT]/dw, d[d[d[dE(t,w,a,i)/dT]/dw]/dT]/dw, d[d[d[dE(t,w,a,m)/dw/dw, d[d[d[dE(t,w,i,m)/dT]/dw]/dT]/dw, d[d[d[dE(t,a,i,m)/dT]/dw]/dT]/dw, d[d[d[dE(w,a,i,m)/dT]/dw]/dT]/dw, d[d[d[dE(t,w,a,i,m)/dT]/dw]/dT]/dw..

 

or as:

 

d[d[d[dE(t)/dT]/dT]/dw]/dw, d[d[d[dE(w)/dT]/dT]/dw]/dw, d[d[d[dE(a)/dT]/dT]/dw]/dw, d[d[d[dE(i)/dT]/dT]/dw]/dw, d[d[d[dE(m)/dT]/dT]/dw]/dw, d[d[d[dE(t,w)/dT]/dT]/dw]/dw, d[d[d[dE(t,a)/dT]/dT]/dw]/dw, d[d[d[dE(t,i)/dT]/dT]/dw]/dw, d[d[d[dE(t,m)/dT]/dT]/dw]/dw, d[d[d[dE(w,a)/dT]/dT]/dw]/dw, d[d[d[dE(w,i)/dT]/dT]/dw]/dw, d[d[d[dE(w,m)/dT]/dT]/dw]/dw, d[d[d[dE(a,i)/dT]/dT]/dw]/dw, d[d[d[dE(a,m)/ dT]/dT]/dw]/dw, d[d[d[dE(i,m)/ dT]/dT]/dw]/dw, d[d[d[dE(t,w,a)/dT]/dT]/dw]/dw, d[d[d[dE(t,w,i)/dT]/dT]/dw]/dw, d[d[d[dE(t,w,m)/dT]/dT]/dw]/dw, d[d[d[dE(t,a,i)/dT]/dT]/dw]/dw, d[d[d[dE(t,a,m)/dT]/dT]/dw]/dw,  d[d[d[dE(t,i,m)/dT]/dT]/dw]/dw, d[d[d[dE(w,a,i)/dT]/dT]/dw]/dw, d[d[d[dE(w,a,m)/dT]/dT]/dw]/dw, d[d[d[dE(w,i,m)/dT]/dT]/dw]/dw, d[d[d[dE(a,i,m)/dT]/dT]/dw]/dw, d[d[d[dE(t,w,a,i)/dT]/dT]/dw]/dw, d[d[d[dE(t,w,a,m)/dw/dw, d[d[d[dE(t,w,i,m)/dT]/dT]/dw]/dw, d[d[d[dE(t,a,i,m)/dT]/dT]/dw]/dw, d[d[d[dE(w,a,i,m)/dT]/dT]/dw]/dw, d[d[d[dE(t,w,a,i,m)/dT]/dT]/dw]/dw..

 

We can also take higher order duel dimensional derivatives of emotion as a function of will and time but the symbolic expression of the set of such derivatives very soon becomes excessively lengthly to write and so these higher order derivatives as such are not mentioned here except to say that they would be computed in an analogous manner to the second order duel dimensional derivatives described above.

 

 

We can also express emotion qualitatively, statistically, and perhaps with the use of some forms of real analysis as a derivative with respect to  affect or with respect to a.

 

Given that E(a) =  E(t and/or w and/or a and/or i and/or m), the following first order derivatives of emotion with respect to affect are possible.

 

 

dE(t)/da, dE(w)/da, dE(a)/da, dE(i)/da, dE(m)/da, dE(t,w)/da, dE(t,a)/da, dE(t,i)/da, dE(t,m)/da, dE(w,a)/da, dE(w,i)/da, dE(w,m)/da, dE(a,i)/da, dE(a,m)/da, dE(i,m)/da, dE(t,w,a)/da, dE(t,w,i)/da, dE(t,w,m)/da, dE(t,a,i)/da, dE(t,a,m)/da, dE(t,i,m)/da, dE(w,a,i)/da, dE(w,a,m)/da, dE(w,i,m)/da, dE(a,i,m)/da, dE(t,w,a,i)/da, dE(t,w,a,m)/da, dE(t,w,i,m)/da, dE(t,a,i,m)/da, dE(w,a,i,m)/da, dE(t,w,a,i,m)/da.

 

 

Or more succinctly, dE/da = dE(t and/or w and/or a and/or i and/or m)/da

 

 

Or perhaps dE(a)/da =d E{[t(a)] and/or [w(a)] and/or [a(a)] and/or [i(a)] and/or [m(a)]}/da.

 

 

Likewise, we can take the second affect derivatives of  E as follows:

 

 

 

d[dE(t)/da]/da, d[dE(w)/da]/da, d[dE(a)/da]/da, d[dE(i)/da]/da, d[dE(m)/da]/da, d[dE(t,w)/da]/da, d[dE(t,a)/da]/da, d[dE(t,i)/da]/da, d[dE(t,m)/da]/da, d[dE(w,a)/da]/da, d[dE(w,i)/da]/da, d[dE(w,m)/da]/da, d[dE(a,i)/da]/da, d[dE(a,m)/da]/da, d[dE(i,m)/da/da, d[dE(t,w,a)/da]/da, d[dE(t,w,i)/da]/da, d[dE(t,w,m)/da]/da, d[dE(t,a,i)/da]/da, d[dE(t,a,m)/da]/da,  d[dE(t,i,m)/da]/da, d[dE(w,a,i)/da]/da, d[dE(w,a,m)/da]/da, d[dE(w,i,m)/da]/da, d[dE(a,i,m)/da]/da, d[dE(t,w,a,i)/da]/da, d[dE(t,w,a,m)/da/da, d[dE(t,w,i,m)/da]/da, d[dE(t,a,i,m)/da]/da, d[dE(w,a,i,m)/da]/da, d[dE(t,w,a,i,m)/da]/da..

 

 

or more succinctly, as d(dE/da)/da = d[d E(t and/or w and/or a and/or i and/or m)/da]/da = Ea2

 

 

or as

 

 

d[dE(a)/da]/da  = d[d E{[t(a)] and/or [w(a)] and/or [a(a)] and/or [i(a)] and/or [m(a)]}/da]/da = Ea2.

 

 

 

Likewise, we can take the third affect derivatives of  E as follows:

 

 

 

d[d[dE(t)/da]/da]/da, d[d[dE(w)/da]/da]/da, d[d[dE(a)/da]/da]/da, d[d[dE(i)/da]/da]/da, d[d[dE(m)/da]/da]/da, d[d[dE(t,w)/da]/da]/da, d[d[dE(t,a)/da]/da]/da, d[d[dE(t,i)/da]/da]/da, d[d[dE(t,m)/da]/da]/da, d[d[dE(w,a)/da]/da]/da, d[d[dE(w,i)/da]/da]/da, d[d[dE(w,m)/da]/da]/da, d[d[dE(a,i)/da]/da]/da, d[d[dE(a,m)/da]/da]/da, d[d[dE(i,m)/da/da]/da, d[d[dE(t,w,a)/da]/da]/da, d[d[dE(t,w,i)/da]/da]/da, d[d[dE(t,w,m)/da]/da]/da, d[d[dE(t,a,i)/da]/da]/da, d[d[dE(t,a,m)/da]/da]/da,  d[d[dE(t,i,m)/da]/da]/da, d[d[dE(w,a,i)/da]/da]/da, d[d[dE(w,a,m)/da]/da]/da, d[d[dE(w,i,m)/da]/da]/da, d[d[dE(a,i,m)/da]/da]/da, d[d[dE(t,w,a,i)/da]/da]/da, d[d[dE(t,w,a,m)/da/da]/da, d[d[dE(t,w,i,m)/da]/da]/da, d[d[dE(t,a,i,m)/da]/da]/da, d[d[dE(w,a,i,m)/da]/da]/da, d[d[dE(t,w,a,i,m)/da]/da]/da.

 

 

or more succinctly, as d[d(dE/da)/da]/da = d[d[d E(t and/or w and/or a and/or i and/or m)/da]/da]/da = Ea3

 

 

or as

 

 

d[d[dE(a)/da]/da]/da  = d[d[d E{[t(a)] and/or [w(a)] and/or [a(a)] and/or [i(a)] and/or [m(a)]}/da]/da]/da = Ea3.

 

 

We can also form the expressions;

 

 

d[d[f(E)]/da]/da = d{d [E[t(a)]]/da and/or d[E[w(a)]]/da and/or d[E[a(a)]]/da and/or d[E[i(a)]]/da and/or d[E[m(a)]]/da}/da  = f(Ea)2

 

 

and

 

 

d[d[d[f(E)]/da]/da]/da = d{d{ d [E[t(a)]]/da and/or d[E[w(a)]]/da and/or d[E[a(a)]]/da and/or d[E[i(a)]]/da and/or d[E[m(a)]]/da}/da}/da  = f(Ea)3A, where A stands for type A differentiation which is not to be confused with the meaning of so-called Type A personality as A is used as an ordinal in a totally different context here.

 

 

and

 

 

d[d[d[f(E)]/da]/da]/da = d{d[d [E[t(a)]]/da]/da  and/or d[d [E[w(a)]]/da]/da  and/or d[d [E[a(a)]]/da]/da  and/or d[d [E[i(a)]]/da]/da  and/or d[d [E[m(a)]]/da]/da }/da = f(Ea)3B, where B stands for type B differentiation which is not to be confused with the meaning of so-called Type  B personality as B is used as an ordinal in a totally different context here. .

 

 

In fact, one can form yet higher order derivatives of emotions with respect to affect as follows.

 

 

Ea5 = d Ea4/da = d[dEa3/da]/da

 

 

 

Ea5 = dEa4/da =  d[d[d[d[d E{[t(a)] and/or [w(a)] and/or [a(a)] and/or [i(a)] and/or [m(a)]}/da]/da]/da]/da]/da.

 

 

 

f(Ea)5A = d[f(Ea)4A]/da = d[d [f(Ea)3A]/da]/da =  d{d{d{d{ d [E[t(a)]]/da and/or d[E[w(a)]]/da and/or d[E[a(a)]]/da and/or d[E[i(a)]]/da and/or d[E[m(a)]]/da}/da}/da]/da]/da

 

 

 

 

Ea6 = d Ea5/da = d[d Ea4/da]/da = d[d[dEa3/da]/da]/da

 

 

 

Ea6 = dEa5/da = d[d[d[d[d[d E{[t(a)] and/or [w(a)] and/or [a(a)] and/or [i(a)] and/or [m(a)]}/da]/da]/da]/da]/da]/da

 

 

 

f(Ea)6A = d[f(Ea)5A]/da = d{ d{d{d{d{ d [E[t(a)]]/da and/or d[E[w(a)]]/da and/or d[E[a(a)]]/da and/or d[E[i(a)]]/da and/or d[E[m(a)]]/da}/da}/da]/da]/da]/da

 

 

 

 

Ea7 = dEa6/da

 

f(Ea)7A = d[f(Ea)6A]/da

 

 

Ea8 = d Ea7/da

 

f(Ea)8A = d[f(Ea)7A]/da

 

 

 

Ea9 = d Ea8/da

 

f(Ea)9A = d[f(Ea)8A]/da

 

 

Ea10…, Ea11…, Ea12 … etc.

 

 

Anyone for Ea ensemble, or Ea infinity scrapper, or Ea (Aleph 0), or Ea(Aleph 1), or Ea (Aleph 2), or how about Ea Aleph (Aleph 0), or Ea Aleph (Aleph 1) , or Ea Aleph (Aleph 2), or even Ea Aleph (Aleph (Aleph 0)), or Ea Aleph (Aleph (Aleph 1)), or Ea Aleph (Aleph (Aleph 2)), and so on?

 

 

 

Thus, for the set of the sets of derivatives of Ea1 through Ea(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ea1 through Ea(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)},…, {П(0,31)[R]}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ea1 through Ea(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ea1 through Ea(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the derivative states in the set of the sets of derivatives of Ea1 through Ea(Aleph 0) is plausible equal to:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ea1 through Ea(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ea1 through Ea(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}}}.

 

For the set of the sets of derivatives of Ea1 through Ea(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Ea(Aleph 0) derivative space at the level of 0/(Aleph 0), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Ea1 through Ea(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ea1 through Ea(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ea1 through Ea(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ea1 through Ea(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Ea1 through Ea(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ea1 through Ea(Aleph 1), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Ea1 through  Ea(Aleph 2), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Ea1 through Ea(Aleph 3), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Ea(Aleph 0) derivative space at the level of 0/(Aleph 1), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Ea1 through Ea(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ea1 through Ea(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ea1 through Ea(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ea1 through  Ea(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations  for the set of the sets of derivatives of Ea1 through Ea(Aleph 0) is plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ea1 through Ea(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Ea1 through Ea(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Ea1 through Ea(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

 

For super-continuous Ea(Aleph 0) derivative space at the level of 0/(Aleph 2), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Ea1 through Ea(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ea1 through Ea(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ea1 through Ea(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ea1 through Ea(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Ea1 through Ea(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ea1 through Ea(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Ea1 through Ea(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Ea1 through Ea(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}}}

 

 

and so on, ad infinitum.

 

Similar series can be developed for super-continuity at any applicable level such as 0/(Aleph 3), 0/(Aleph 4), 0/(Aleph 5),…, 0/(Aleph Ω), 0/(Aleph (Aleph 0)), …, 0/(Aleph (Aleph 1)), …, 0/(Aleph (Aleph 2)), …, 0/(Aleph (Aleph 3)),…, 0/(Aleph (Aleph Ω)),…, 0/(Aleph (Aleph (Aleph 0))), …, 0/(Aleph (Aleph (Aleph 1))),…, 0/(Aleph (Aleph (Aleph 2))),…, 0/(Aleph (Aleph (Aleph 3))),…, 0/(Aleph (Aleph  (Aleph Ω))), …

 

An so-on ad infinitum.

 

In addition to these numerical functions of Ea as functions of summation series of product series functions, in order to really appreciate the enourmous complexity of the human soul in terms of its potential to evolve and be differentiated from all other souls in its characteristics, we would need to consider how every single category and even every single species of emotions of the form Ea can very. Since there may exist an arbitrarily high infinite number species of Ea, the number of numerical functions of Ea is utterly beyond recogning. I will cover such notions in terms of mathematical notation in yet another series of articles I will write on this general concept.

 

 

 

Perhaps these numbers are applicable when one considers that the human soul, in its accidental form and perhaps even in its substantial form stores all experience and other psychodynamics based phenomenon. Every experience adds to the accidental form of the human soul and this includes the souls of all those still alive on Earth, all those in Purgatory, all those in Heaven, all those in Hell, and all those in any Limbo.

Since the human soul can grow without limit in terms of its psychodynamic time –flow world line, such a consideration offers another mechanism where the number of derivative states, combinations of derivative states, and even super-continuity of the derivative state space can grow forever.

 

Folks, for those of you who might balk at me for including literally all souls in the above consideration, including the souls in Hell, as well as bodily extraterrestrial souls and the souls of so-called bodily ultraterrestials sometimes referred to as etherians in the new age UFO buff culture, my reply is that we simply do not understand the full scope of GOD’s Divine Economy. We may never fully comprehend the scope of the Divine Economy because such an utterly eternal scheme, is, well, eternal and never ending.

 

 

 

 

 

 

 

 

 

The general meaning of affect derivatives of emotion can be viewed as the manner in which the qualitative and/or quantitative aspects of emotion as a function of affect very with affect. The manner in which emotions very with affect may be multi- affect-aspect dimensional wherein the dimensions of derivations can be multiple, and wherein the derivations can be taken in parallel, series parallel or in serial manner. The differentials can be partial or non-partial derivatives, or both partial and non-partial for a given computation.

 

In fact, since there is in theory, no limit to the numbers of qualitatively and quantitatively different affective states, and perhaps no limit to the number of possible different types or classes of affective states, wherein each person has his or her own unique affective rxperiences, the number of affect dimensions that can effect emotions is literally infinite, given the entirety of the set of created persons, and perhaps also literally infinite for each person as an individual, although we can not intellectually and intuitively understand this infinite number.

 

 

It is interesting to consider the ramifactions of being able to perform realistic calculations involving affect derivatives of emotion from a mathematical, theoretical, scientific,  and philosophical perspective.

 

Persons for which one or more nth order derivatives of emotion with respect to affect that have large absolute values would tend to have their emotions highly influenced by affect, or at least for the emotions under consideration with respect to the dimension of the specific affect type(s) or class(es) for which the differentiation(s) are being performed. Perhaps a strong coupling between emotion and affect indicates a well integrated personality and commensurately, a high degree of emotional capacity and a high degree of emotional intelligence as well as perhaps very strong affect power.

 

We would expect that disembodied human souls, ETI souls, and/or UTI souls in Heaven, Limbo, highly evolved bodily ETI persons, highly evolved UTI persons, and angels to have emotions of all kinds and intensities which are highly subject to affect.

 

 

We can also consider that two dimensional nth ordered derivatives of emotion with respect to affect and time, or with respect to a and T, respectively.

 

Given that E[(a)(T)] =  E[(t and/or w and/or a and/or i and/or m)(w)(T)], the following first order two dimensional derivatives of emotion with respect to affect and Time are possible.

 

 

d[dE[(t)(T)]/da]/dT, d[dE[(w)(T)]/da]/dT, d[dE[(a)(T)]/da]/dT, d[dE[(i)(T)]/da]/dT, d[dE[(m)(T)]/da]/dT, d[dE[(t,w)(T)]/da]/dT, d[dE[(t,a)(T)]/da]/dT, d[dE[(t,i)(T)]/da]/dT, d[dE[(t,m)(T)]/da]/dT, d[dE[(w,a)(T)]/da]/dT, d[dE[(w,i)(T)]/da]/dT, d[dE[(w,m)(T)]/da]/dT, d[dE[(a,i)(T)]/da]/dT, d[dE[(a,m)(T)]/da]/dT, d[dE[(i,m)(T)]/da]/dT, d[dE[(t,w,a)(T)]/da]/dT, d[dE[(t,w,i)(T)]/da]/dT, d[dE[(t,w,m)(T)]/da]/dT, d[dE[(t,a,i)(T)]/da]/dT, d[dE[(t,a,m)(T)]/da]/dT, d[dE[(t,i,m)(T)]/da]/dT, d[dE[(w,a,i)(T)]/da]/dT, d[dE[(w,a,m)(T)]/da]/dT, d[dE[(w,i,m)(T)]/da]/dT, d[dE[(a,i,m)(T)]/da]/dT, d[dE[(t,w,a,i)(T)]/da]/dT, d[dE[(t,w,a,m)(T)]/da]/dT, d[dE[(t,w,i,m)(T)]/da]/dT, d[dE[(t,a,i,m)(T)]/da]/dT, d[dE[(w,a,i,m)(T)]/da]/dT, d[dE[(t,w,a,i,m)(T)]/da]/dT.

 

 

Or more succinctly,  d[dE(T)/da]/dT = d[dE[(T)(t and/or w and/or a and/or i and/or m)]/da]/dT

 

or

 

d[dE(T)/dT]/da = d[dE[(T)(t and/or w and/or a and/or i and/or m)]/dT]/da

 

 

 

 

 

Or perhaps d[d E[(a)(T)]/da]/dT  = d[d E [{[t(t)] and/or [w(t)] and/or [a(t)] and/or [i(t)] and/or [m(t)]}(T)]/da]/dT

 

or

 

Or perhaps d[d E[(a)(T)]/dT]/da  = d[d E [{[t(t)] and/or [w(t)] and/or [a(t)] and/or [i(t)] and/or [m(t)]}(T)]/dT]/da

 

 

 

Likewise, we can take the second dual dimension affect -time derivatives of  E as follows:

 

d[d[d[dE[(t)(T)]/da]/dT]/da]/dT, d[d[d[dE[(w)(T)]/da]/dT]/da]/dT, d[d[d[dE[(a)(T)]/da]/dT]/da]/dT, d[d[d[dE[(i)(T)]/da]/dT]/da]/dT, d[d[d[dE[(m)(T)]/da]/dT]/da]/dT, d[d[d[dE[(t,w)(T)]/da]/dT]/da]/dT, d[d[d[dE[(t,a)(T)]/da]/dT]/da]/dT, d[d[d[dE[(t,i)(T)]/da]/dT]/da]/dT, d[d[d[dE[(t,m)(T)]/da]/dT]/da]/dT, d[d[d[dE[(w,a)(T)]/da]/dT]/da]/dT, d[d[d[dE[(w,i)(T)]/da]/dT]/da]/dT, d[d[d[dE[(w,m)(T)]/da]/dT]/da]/dT, d[d[d[dE[(a,i)(T)]/da]/dT]/da]/dT, d[d[d[dE[(a,m)(T)]/da]/dT]/da]/dT, d[d[d[dE[(i,m)(T)]/da]/dT]/da]/dT, d[d[d[dE[(t,w,a)(T)]/da]/dT]/da]/dT, d[d[d[dE[(t,w,i)(T)]/da]/dT]/da]/dT, d[d[d[dE[(t,w,m)(T)]/da]/dT]/da]/dT, d[d[d[dE[(t,a,i)(T)]/da]/dT]/da]/dT, d[d[d[dE[(t,a,m)(T)]/da]/dT]/da]/dT, d[d[d[dE[(t,i,m)(T)]/da]/dT]/da]/dT, d[d[d[dE[(w,a,i)(T)]/da]/dT]/da]/dT, d[d[d[dE[(w,a,m)(T)]/da]/dT]/da]/dT, d[d[d[dE[(w,i,m)(T)]/da]/dT]/da]/dT, d[d[d[dE[(a,i,m)(T)]/da]/dT]/da]/dT, d[d[d[dE[(t,w,a,i)(T)]/da]/dT]/da]/dT, d[d[d[dE[(t,w,a,m)(T)]/da]/dT]/da]/dT, d[d[d[dE[(t,w,i,m)(T)]/da]/dT]/da]/dT, d[d[d[dE[(t,a,i,m)(T)]/da]/dT]/da]/dT, d[d[d[dE[(w,a,i,m)(T)]/da]/dT]/da]/dT, d[d[d[dE[(t,w,a,i,m)(T)]/da]/dT]/da]/dT.

 

or as:

 

 

 

d[d[d[dE[(t)(T)]/da]/dT]/dT]/da, d[d[d[dE[(w)(T)]/da]/dT]/dT]/da, d[d[d[dE[(a)(T)]/da]/dT]/dT]/da, d[d[d[dE[(i)(T)]/da]/dT]/dT]/da, d[d[d[dE[(m)(T)]/da]/dT]/dT]/da, d[d[d[dE[(t,w)(T)]/da]/dT]/dT]/da, d[d[d[dE[(t,a)(T)]/da]/dT]/dT]/da, d[d[d[dE[(t,i)(T)]/da]/dT]/dT]/da, d[d[d[dE[(t,m)(T)]/da]/dT]/dT]/da, d[d[d[dE[(w,a)(T)]/da]/dT]/dT]/da, d[d[d[dE[(w,i)(T)]/da]/dT]/dT]/da, d[d[d[dE[(w,m)(T)]/da]/dT]/dT]/da, d[d[d[dE[(a,i)(T)]/da]/dT]/dT]/da, d[d[d[dE[(a,m)(T)]/da]/dT]/dT]/da, d[d[d[dE[(i,m)(T)]/da]/dT]/dT]/da, d[d[d[dE[(t,w,a)(T)]/da]/dT]/dT]/da, d[d[d[dE[(t,w,i)(T)]/da]/dT]/dT]/da, d[d[d[dE[(t,w,m)(T)]/da]/dT]/dT]/da, d[d[d[dE[(t,a,i)(T)]/da]/dT]/dT]/da, d[d[d[dE[(t,a,m)(T)]/da]/dT]/dT]/da, d[d[d[dE[(t,i,m)(T)]/da]/dT]/dT]/da, d[d[d[dE[(w,a,i)(T)]/da]/dT]/dT]/da, d[d[d[dE[(w,a,m)(T)]/da]/dT]/dT]/da, d[d[d[dE[(w,i,m)(T)]/da]/dT]/dT]/da, d[d[d[dE[(a,i,m)(T)]/da]/dT]/dT]/da, d[d[d[dE[(t,w,a,i)(T)]/da]/dT]/dT]/da, d[d[d[dE[(t,w,a,m)(T)]/da]/dT]/dT]/da, d[d[d[dE[(t,w,i,m)(T)]/da]/dT]/dT]/da, d[d[d[dE[(t,a,i,m)(T)]/da]/dT]/dT]/da, d[d[d[dE[(w,a,i,m)(T)]/da]/dT]/dT]/da, d[d[d[dE[(t,w,a,i,m)(T)]/da]/dT]/dT]/da.

 

or as:

 

d[d[d[dE[(t)(T)]/dT]/da]/da]/dT, d[d[d[dE[(w)(T)]/dT]/da]/da]/dT, d[d[d[dE[(a)(T)]/dT]/da]/da]/dT, d[d[d[dE[(i)(T)]/dT]/da]/da]/dT, d[d[d[dE[(m)(T)]/dT]/da]/da]/dT, d[d[d[dE[(t,w)(T)]/dT]/da]/da]/dT, d[d[d[dE[(t,a)(T)]/dT]/da]/da]/dT, d[d[d[dE[(t,i)(T)]/dT]/da]/da]/dT, d[d[d[dE[(t,m)(T)]/dT]/da]/da]/dT, d[d[d[dE[(w,a)(T)]/dT]/da]/da]/dT, d[d[d[dE[(w,i)(T)]/dT]/da]/da]/dT, d[d[d[dE[(w,m)(T)]/dT]/da]/da]/dT, d[d[d[dE[(a,i)(T)]/dT]/da]/da]/dT, d[d[d[dE[(a,m)(T)]/dT]/da]/da]/dT, d[d[d[dE[(i,m)(T)]/dT]/da]/da]/dT, d[d[d[dE[(t,w,a)(T)]/dT]/da]/da]/dT, d[d[d[dE[(t,w,i)(T)]/dT]/da]/da]/dT, d[d[d[dE[(t,w,m)(T)]/dT]/da]/da]/dT, d[d[d[dE[(t,a,i)(T)]/dT]/da]/da]/dT, d[d[d[dE[(t,a,m)(T)]/dT]/da]/da]/dT, d[d[d[dE[(t,i,m)(T)]/dT]/da]/da]/dT, d[d[d[dE[(w,a,i)(T)]/dT]/da]/da]/dT, d[d[d[dE[(w,a,m)(T)]/dT]/da]/da]/dT, d[d[d[dE[(w,i,m)(T)]/dT]/da]/da]/dT, d[d[d[dE[(a,i,m)(T)]/dT]/da]/da]/dT, d[d[d[dE[(t,w,a,i)(T)]/dT]/da]/da]/dT, d[d[d[dE[(t,w,a,m)(T)]/dT]/da]/da]/dT, d[d[d[dE[(t,w,i,m)(T)]/dT]/da]/da]/dT, d[d[d[dE[(t,a,i,m)(T)]/dT]/da]/da]/dT, d[d[d[dE[(w,a,i,m)(T)]/dT]/da]/da]/dT, d[d[d[dE[(t,w,a,i,m)(T)]/dT]/da]/da]/dT.

 

 

or as;

 

 

 

 

d[d[d[dE(t)/da]/da]/dT]/dT, d[d[d[dE(w)/da]/da]/dT]/dT, d[d[d[dE(a)/da]/da]/dT]/dT, d[d[d[dE(i)/da]/da]/dT]/dT, d[d[d[dE(m)/da]/da]/dT]/dT, d[d[d[dE(t,w)/da]/da]/dT]/dT, d[d[d[dE(t,a)/da]/da]/dT]/dT, d[d[d[dE(t,i)/da]/da]/dT]/dT, d[d[d[dE(t,m)/da]/da]/dT]/dT, d[d[d[dE(w,a)/da]/da]/dT]/dT, d[d[d[dE(w,i)/da]/da]/dT]/dT, d[d[d[dE(w,m)/da]/da]/dT]/dT, d[d[d[dE(a,i)/da]/da]/dT]/dT, d[d[d[dE(a,m)/da]/da]/dT]/dT, d[d[d[dE(i,m)/da]/da]/dT]/dT, d[d[d[dE(t,w,a)/da]/da]/dT]/dT, d[d[d[dE(t,w,i)/da]/da]/dT]/dT, d[d[d[dE(t,w,m)/da]/da]/dT]/dT, d[d[d[dE(t,a,i)/da]/da]/dT]/dT, d[d[d[dE(t,a,m)/da]/da]/dT]/dT,  d[d[d[dE(t,i,m)/da]/da]/dT]/dT, d[d[d[dE(w,a,i)/da]/da]/dT]/dT, d[d[d[dE(w,a,m)/da]/da]/dT]/dT, d[d[d[dE(w,i,m)/da]/da]/dT]/dT, d[d[d[dE(a,i,m)/da]/da]/dT]/dT, d[d[d[dE(t,w,a,i)/da]/da]/dT]/dT, d[d[d[dE(t,w,a,m)/da/da, d[d[d[dE(t,w,i,m)/da]/da]/dT]/dT, d[d[d[dE(t,a,i,m)/da]/da]/dT]/dT, d[d[d[dE(w,a,i,m)/da]/da]/dT]/dT, d[d[d[dE(t,w,a,i,m)/da]/da]/dT]/dT..

 

or as:

 

d[d[d[dE(t)/dT]/da]/dT]/da, d[d[d[dE(w)/dT]/da]/dT]/da, d[d[d[dE(a)/dT]/da]/dT]/da, d[d[d[dE(i)/dT]/da]/dT]/da, d[d[d[dE(m)/dT]/da]/dT]/da, d[d[d[dE(t,w)/dT]/da]/dT]/da, d[d[d[dE(t,a)/dT]/da]/dT]/da, d[d[d[dE(t,i)/dT]/da]/dT]/da, d[d[d[dE(t,m)/dT]/da]/dT]/da, d[d[d[dE(w,a)/dT]/da]/dT]/da, d[d[d[dE(w,i)/dT]/da]/dT]/da, d[d[d[dE(w,m)/dT]/da]/dT]/da, d[d[d[dE(a,i)/dT]/da]/dT]/da, d[d[d[dE(a,m)/dT]/da]/dT]/da, d[d[d[dE(i,m)/ dT]/da]/dT]/da, d[d[d[dE(t,w,a)/dT]/da]/dT]/da, d[d[d[dE(t,w,i)/dT]/da]/dT]/da, d[d[d[dE(t,w,m)/dT]/da]/dT]/da, d[d[d[dE(t,a,i)/dT]/da]/dT]/da, d[d[d[dE(t,a,m)/dT]/da]/dT]/da,  d[d[d[dE(t,i,m)/dT]/da]/dT]/da, d[d[d[dE(w,a,i)/dT]/da]/dT]/da, d[d[d[dE(w,a,m)/dT]/da]/dT]/da, d[d[d[dE(w,i,m)/dT]/da]/dT]/da, d[d[d[dE(a,i,m)/dT]/da]/dT]/da, d[d[d[dE(t,w,a,i)/dT]/da]/dT]/da, d[d[d[dE(t,w,a,m)/da/da, d[d[d[dE(t,w,i,m)/dT]/da]/dT]/da, d[d[d[dE(t,a,i,m)/dT]/da]/dT]/da, d[d[d[dE(w,a,i,m)/dT]/da]/dT]/da, d[d[d[dE(t,w,a,i,m)/dT]/da]/dT]/da..

 

or as:

 

d[d[d[dE(t)/dT]/dT]/da]/da, d[d[d[dE(w)/dT]/dT]/da]/da, d[d[d[dE(a)/dT]/dT]/da]/da, d[d[d[dE(i)/dT]/dT]/da]/da, d[d[d[dE(m)/dT]/dT]/da]/da, d[d[d[dE(t,w)/dT]/dT]/da]/da, d[d[d[dE(t,a)/dT]/dT]/da]/da, d[d[d[dE(t,i)/dT]/dT]/da]/da, d[d[d[dE(t,m)/dT]/dT]/da]/da, d[d[d[dE(w,a)/dT]/dT]/da]/da, d[d[d[dE(w,i)/dT]/dT]/da]/da, d[d[d[dE(w,m)/dT]/dT]/da]/da, d[d[d[dE(a,i)/dT]/dT]/da]/da, d[d[d[dE(a,m)/ dT]/dT]/da]/da, d[d[d[dE(i,m)/ dT]/dT]/da]/da, d[d[d[dE(t,w,a)/dT]/dT]/da]/da, d[d[d[dE(t,w,i)/dT]/dT]/da]/da, d[d[d[dE(t,w,m)/dT]/dT]/da]/da, d[d[d[dE(t,a,i)/dT]/dT]/da]/da, d[d[d[dE(t,a,m)/dT]/dT]/da]/da,  d[d[d[dE(t,i,m)/dT]/dT]/da]/da, d[d[d[dE(w,a,i)/dT]/dT]/da]/da, d[d[d[dE(w,a,m)/dT]/dT]/da]/da, d[d[d[dE(w,i,m)/dT]/dT]/da]/da, d[d[d[dE(a,i,m)/dT]/dT]/da]/da, d[d[d[dE(t,w,a,i)/dT]/dT]/da]/da, d[d[d[dE(t,w,a,m)/da/da, d[d[d[dE(t,w,i,m)/dT]/dT]/da]/da, d[d[d[dE(t,a,i,m)/dT]/dT]/da]/da, d[d[d[dE(w,a,i,m)/dT]/dT]/da]/da, d[d[d[dE(t,w,a,i,m)/dT]/dT]/da]/da..

 

We can also take higher order duel dimensional derivatives of emotion as a function of affect and time but the symbolic expression of the set of such derivatives very soon becomes excessively lengthly to write and so these higher order derivatives as such are not mentioned here except to say that they would be computed in an analogous manner to the second order duel dimensional derivatives described above.

 

.

 

 

We can also express emotion qualitatively, statistically, and perhaps with the use of some forms of real analyses as a derivative with respect to  instinct or with respect to i.

 

Given that E(i) =  E(t and/or w and/or a and/or i and/or m) or perhaps the following notation can be more appropriate in certain circumstances.

 

 

 

 

Thus the following first order derivatives of emotion with respect to instinct are possible.

 

 

dE(t)/di, dE(w)/di, dE(a)/di, dE(i)/di, dE(m)/di, dE(t,w)/di, dE(t,a)/di, dE(t,i)/di, dE(t,m)/di, dE(w,a)/di, dE(w,i)/di, dE(w,m)/di, dE(a,i)/di, dE(a,m)/di, dE(i,m)/di, dE(t,w,a)/di, dE(t,w,i)/di, dE(t,w,m)/di, dE(t,a,i)/di, dE(t,a,m)/di, dE(t,i,m)/di, dE(w,a,i)/di, dE(w,a,m)/di, dE(w,i,m)/di, dE(a,i,m)/di, dE(t,w,a,i)/di, dE(t,w,a,m)/di, dE(t,w,i,m)/di, dE(t,a,i,m)/di, dE(w,a,i,m)/di, dE(t,w,a,i,m)/di.

 

 

Or more succinctly,  dE/di = dE(t and/or w and/or a and/or i and/or m)/di

 

 

Or perhaps dE(i)/di =d E{[t(i)] and/or [w(i)] and/or [a(i)] and/or [i(i)] and/or [m(i)]}/di.

 

 

Likewise, we can take the second instinct derivatives of  E as follows:

 

 

 

d[dE(t)/di]/di, d[dE(w)/di]/di, d[dE(a)/di]/di, d[dE(i)/di]/di, d[dE(m)/di]/di, d[dE(t,w)/di]/di, d[dE(t,a)/di]/di, d[dE(t,i)/di]/di, d[dE(t,m)/di]/di, d[dE(w,a)/di]/di, d[dE(w,i)/di]/di, d[dE(w,m)/di]/di, d[dE(a,i)/di]/di, d[dE(a,m)/di]/di, d[dE(i,m)/di/di, d[dE(t,w,a)/di]/di, d[dE(t,w,i)/di]/di, d[dE(t,w,m)/di]/di, d[dE(t,a,i)/di]/di, d[dE(t,a,m)/di]/di,  d[dE(t,i,m)/di]/di, d[dE(w,a,i)/di]/di, d[dE(w,a,m)/di]/di, d[dE(w,i,m)/di]/di, d[dE(a,i,m)/di]/di, d[dE(t,w,a,i)/di]/di, d[dE(t,w,a,m)/di/di, d[dE(t,w,i,m)/di]/di, d[dE(t,a,i,m)/di]/di, d[dE(w,a,i,m)/di]/di, d[dE(t,w,a,i,m)/di]/di..

 

 

or more succinctly, as d(dE/di)/di = d[d E(t and/or w and/or a and/or i and/or m)/di]/di = Ei2

 

 

or as

 

 

d[dE(i)/di]/di  = d[d E{[t(i)] and/or [w(i)] and/or [a(i)] and/or [i(i)] and/or [m(i)]}/di]/di = Ei2.

 

 

 

Likewise, we can take the third instinct derivatives of  E as follows:

 

 

 

d[d[dE(t)/di]/di]/di, d[d[dE(w)/di]/di]/di, d[d[dE(a)/di]/di]/di, d[d[dE(i)/di]/di]/di, d[d[dE(m)/di]/di]/di, d[d[dE(t,w)/di]/di]/di, d[d[dE(t,a)/di]/di]/di, d[d[dE(t,i)/di]/di]/di, d[d[dE(t,m)/di]/di]/di, d[d[dE(w,a)/di]/di]/di, d[d[dE(w,i)/di]/di]/di, d[d[dE(w,m)/di]/di]/di, d[d[dE(a,i)/di]/di]/di, d[d[dE(a,m)/di]/di]/di, d[d[dE(i,m)/di/di]/di, d[d[dE(t,w,a)/di]/di]/di, d[d[dE(t,w,i)/di]/di]/di, d[d[dE(t,w,m)/di]/di]/di, d[d[dE(t,a,i)/di]/di]/di, d[d[dE(t,a,m)/di]/di]/di,  d[d[dE(t,i,m)/di]/di]/di, d[d[dE(w,a,i)/di]/di]/di, d[d[dE(w,a,m)/di]/di]/di, d[d[dE(w,i,m)/di]/di]/di, d[d[dE(a,i,m)/di]/di]/di, d[d[dE(t,w,a,i)/di]/di]/di, d[d[dE(t,w,a,m)/di/di]/di, d[d[dE(t,w,i,m)/di]/di]/di, d[d[dE(t,a,i,m)/di]/di]/di, d[d[dE(w,a,i,m)/di]/di]/di, d[d[dE(t,w,a,i,m)/di]/di]/di.

 

 

or more succinctly, as d[d(dE/di)/di]/di = d[d[d E(t and/or w and/or a and/or i and/or m)/di]/di]/di = Ei3

 

 

or as

 

 

d[d[dE(i)/di]/di]/di  = d[d[d E{[t(i)] and/or [w(i)] and/or [a(i)] and/or [i(i)] and/or [m(i)]}/di]/di]/di = Ei3.

 

 

We can also form the expressions;

 

 

d[d[f(E)]/di]/di = d{d [E[t(i)]]/di and/or d[E[w(i)]]/di and/or d[E[a(i)]]/di and/or d[E[i(i)]]/di and/or d[E[m(i)]]/di}/di  = f(Ei)2

 

 

and

 

 

d[d[d[f(E)]/di]/di]/di = d{d{ d [E[t(i)]]/di and/or d[E[w(i)]]/di and/or d[E[a(i)]]/di and/or d[E[i(i)]]/di and/or d[E[m(i)]]/di}/di}/di  = f(Ei)3A, where A stands for type A differentiation which is not to be confused with the meaning of so-called Type A personality as A is used as an ordinal in a totally different context here.

 

 

and

 

 

d[d[d[f(E)]/di]/di]/di = d{d[d [E[t(i)]]/di]/di  and/or d[d [E[w(i)]]/di]/di  and/or d[d [E[a(i)]]/di]/di  and/or d[d [E[i(i)]]/di]/di  and/or d[d [E[m(i)]]/di]/di }/di = f(Ei)3B, where B stands for type B differentiation which is not to be confused with the meaning of so-called Type  B personality as B is used as an ordinal in a totally different context here .

 

 

In fact, one can form yet higher order derivatives of emotions with respect to instinct as follows.

 

 

Ei5 = d Ei4/di = d[dEi3/di]/di

 

 

 

Ei5 = dEi4/di =  d[d[d[d[d E{[t(i)] and/or [w(i)] and/or [a(i)] and/or [i(i)] and/or [m(i)]}/di]/di]/di]/di]/di.

 

 

 

f(Ei)5A = d[f(Ei)4A]/di = d[d [f(Ei)3A]/di]/di =  d{d{d{d{ d [E[t(i)]]/di and/or d[E[w(i)]]/di and/or d[E[a(i)]]/di and/or d[E[i(i)]]/di and/or d[E[m(i)]]/di}/di}/di]/di]/di

 

 

 

 

Ei6 = d Ei5/di = d[d Ei4/di]/di = d[d[dEi3/di]/di]/di

 

 

 

Ei6 = dEi5/di = d[d[d[d[d[d E{[t(i)] and/or [w(i)] and/or [a(i)] and/or [i(i)] and/or [m(i)]}/di]/di]/di]/di]/di]/di

 

 

 

f(Ei)6A = d[f(Ei)5A]/di = d{ d{d{d{d{ d [E[t(i)]]/di and/or d[E[w(i)]]/di and/or d[E[a(i)]]/di and/or d[E[i(i)]]/di and/or d[E[m(i)]]/di}/di}/di]/di]/di]/di

 

 

 

 

Ei7 = dEi6/di

 

f(Ei)7A = d[f(Ei)6A]/di

 

 

Ei8 = d Ei7/di

 

f(Ei)8A = d[f(Ei)7A]/di

 

 

 

Ei9 = d Ei8/di

 

f(Ei)9A = d[f(Ei)8A]/di

 

 

Ei10…, Ei11…, Ei12 … etc.

 

 

Anyone for Ei ensemble, or Ei infinity scrapper, or Ei (Aleph 0), or Ei(Aleph 1), or Ei (Aleph 2), or how about Ei Aleph (Aleph 0), or Ei Aleph (Aleph 1) , or Ei Aleph (Aleph 2), or even Ei Aleph (Aleph (Aleph 0)), or Ei Aleph (Aleph (Aleph 1)), or Ei Aleph (Aleph (Aleph 2)), and so on?

 

Thus, for the set of the sets of derivatives of Ei1 through Ei(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ei1 through Ei(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)},…, {П(0,31)[R]}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ei1 through Ei(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ei1 through Ei(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the derivative states in the set of the sets of derivatives of Ei1 through Ei(Aleph 0) is plausible equal to:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ei1 through Ei(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ei1 through Ei(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}}}.

 

For the set of the sets of derivatives of Ei1 through Ei(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Ei(Aleph 0) derivative space at the level of 0/(Aleph 0), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Ei1 through Ei(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ei1 through Ei (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ei1 through Ei(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ei1 through Ei(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Ei1 through Ei(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ei1 through Ei(Aleph 1), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Ei1 through  Ei(Aleph 2), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Ei1 through Ei(Aleph 3), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Ei(Aleph 0) derivative space at the level of 0/(Aleph 1), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Ei1 through Ei(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ei1 through Ei(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ei1 through Ei(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ei1 through  Ei(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations  for the set of the sets of derivatives of Ei1 through Ei(Aleph 0) is plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ei1 through Ei(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Ei1 through Ei(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Ei1 through Ei(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

 

For super-continuous Ei(Aleph 0) derivative space at the level of 0/(Aleph 2), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Ei1 through Ei(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ei1 through Ei(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ei1 through Ei(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ei1 through Ei(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Ei1 through Ei(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ei1 through Ei(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Ei1 through Ei(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Ei1 through Ei(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

 

Similar series can be developed for super-continuity at any applicable level such as 0/(Aleph 3), 0/(Aleph 4), 0/(Aleph 5),…, 0/(Aleph Ω), 0/(Aleph (Aleph 0)), …, 0/(Aleph (Aleph 1)), …, 0/(Aleph (Aleph 2)), …, 0/(Aleph (Aleph 3)),…, 0/(Aleph (Aleph Ω)),…, 0/(Aleph (Aleph (Aleph 0))), …, 0/(Aleph (Aleph (Aleph 1))),…, 0/(Aleph (Aleph (Aleph 2))),…, 0/(Aleph (Aleph (Aleph 3))),…, 0/(Aleph (Aleph  (Aleph Ω))), …

 

An so-on ad infinitum.

 

In addition to these numerical functions of Ei as functions of summation series of product series functions, in order to really appreciate the enourmous complexity of the human soul in terms of its potential to evolve and be differentiated from all other souls in its characteristics, we would need to consider how every single category and even every single species of emotions of the form Ei can very. Since there may exist an arbitrarily high infinite number species of Ei, the number of numerical functions of Ei is utterly beyond recogning. I will cover such notions in terms of mathematical notation in yet another series of articles I will write on this general concept.

 

 

 

Perhaps these numbers are applicable when one considers that the human soul, in its accidental form and perhaps even in its substantial form stores all experience and other psychodynamics based phenomenon. Every experience adds to the accidental form of the human soul and this includes the souls of all those still alive on Earth, all those in Purgatory, all those in Heaven, all those in Hell, and all those in any Limbo.

Since the human soul can grow without limit in terms of its psychodynamic time –flow world line, such a consideration offers another mechanism where the number of derivative states, combinations of derivative states, and even super-continuity of the derivative state space can grow forever.

 

Folks, for those of you who might balk at me for including literally all souls in the above consideration, including the souls in Hell, as well as bodily extraterrestrial souls and the souls of so-called bodily ultraterrestials sometimes referred to as etherians in the new age UFO buff culture, my reply is that we simply do not understand the full scope of GOD’s Divine Economy. We may never fully comprehend the scope of the Divine Economy because such an utterly eternal scheme, is, well, eternal and never ending.

 

 

 

 

 

The general meaning of instinct derivatives of emotion can be viewed as the manner in which the qualitative and/or quantitative aspects of emotion as a function of instinct very with instinct. The manner in which emotions very with instinct may be multi- instinct-aspect dimensional wherein the dimensions of derivations can be multiple, and wherein the derivations can be taken in parallel, series parallel or in serial manner. The differentials can be partial or non-partial derivatives, or both partial and non-partial for a given computation.

 

In fact, since there is in theory, no limit to the numbers of qualitatively and quantitatively different instincts, and perhaps no limit to the number of possible different types or classes of instincts or potential instincts, wherein each person has his or her own unique instincts and instinctual experiences, the number of instinct dimensions that can effect emotions is literally infinite, given the entirety of the set of created persons, and perhaps also literally infinite for each person as an individual, although we can not intellectually and intuitively understand this infinite number.

 

 

It is interesting to consider the ramifactions of being able to perform realistic calculations involving instinct derivatives of emotion from a mathematical, theoretical, scientific,  and philosophical perspective.

 

Persons for which one or more nth order derivatives of emotion with respect to instinct that have large absolute values would tend to have their emotions highly influenced by instinct, or at least for the emotions under consideration with respect to the dimension of the specific instinct act type(s) or class(es) for which the differentiation(s) are being performed. Perhaps a strong coupling between emotion and instinct indicates a well integrated personality and commensurately, a high degree of emotional capacity and a high degree of emotional intelligence as well as perhaps very strong instinct power.

 

We would expect that disembodied human souls, ETI souls, and/or UTI souls in Heaven, Limbo, highly evolved bodily ETI persons, highly evolved UTI persons, and angels to have emotions of all kinds and intensities which are perhaps  highly subject to advanced instincts such as spiritual instincts, spiritual intuitions, and even perhaps, psychic powers.

 

 

We can also consider that two dimensional nth ordered derivatives of emotion with respect to instinct and time, or with respect to i and T, respectively.

 

Given that E[(i)(T)] =  E[(t and/or w and/or a and/or i and/or m)(i)(T)], the following first order two dimensional derivatives of emotion with respect to instinct and Time are possible.

 

 

d[dE[(t)(T)]/di]/dT, d[dE[(w)(T)]/di]/dT, d[dE[(a)(T)]/di]/dT, d[dE[(i)(T)]/di]/dT, d[dE[(m)(T)]/di]/dT, d[dE[(t,w)(T)]/di]/dT, d[dE[(t,a)(T)]/di]/dT, d[dE[(t,i)(T)]/di]/dT, d[dE[(t,m)(T)]/di]/dT, d[dE[(w,a)(T)]/di]/dT, d[dE[(w,i)(T)]/di]/dT, d[dE[(w,m)(T)]/di]/dT, d[dE[(a,i)(T)]/di]/dT, d[dE[(a,m)(T)]/di]/dT, d[dE[(i,m)(T)]/di]/dT, d[dE[(t,w,a)(T)]/di]/dT, d[dE[(t,w,i)(T)]/di]/dT, d[dE[(t,w,m)(T)]/di]/dT, d[dE[(t,a,i)(T)]/di]/dT, d[dE[(t,a,m)(T)]/di]/dT, d[dE[(t,i,m)(T)]/di]/dT, d[dE[(w,a,i)(T)]/di]/dT, d[dE[(w,a,m)(T)]/di]/dT, d[dE[(w,i,m)(T)]/di]/dT, d[dE[(a,i,m)(T)]/di]/dT, d[dE[(t,w,a,i)(T)]/di]/dT, d[dE[(t,w,a,m)(T)]/di]/dT, d[dE[(t,w,i,m)(T)]/di]/dT, d[dE[(t,a,i,m)(T)]/di]/dT, d[dE[(w,a,i,m)(T)]/di]/dT, d[dE[(t,w,a,i,m)(T)]/di]/dT.

 

 

Or more succinctly,  d[dE(T)/di]/dT = d[dE[(T)(t and/or w and/or a and/or i and/or m)]/di]/dT

 

or

 

d[dE(T)/dT]/di = d[dE[(T)(t and/or w and/or a and/or i and/or m)]/dT]/di

 

 

 

 

 

Or perhaps d[d E[(i)(T)]/di]/dT  = d[d E [{[t(i)] and/or [w(i)] and/or [a(i)] and/or [i(i)] and/or [m(i)]}(T)]/di]/dT

 

or

 

Or perhaps d[d E[(i)(T)]/dT]/di  = d[d E [{[t(i)] and/or [w(i)] and/or [a(i)] and/or [i(i)] and/or [m(i)]}(T)]/dT]/di

 

 

 

Likewise, we can take the second dual dimension instinct -time derivatives of  E as follows:

 

d[d[d[dE[(t)(T)]/di]/dT]/di]/dT, d[d[d[dE[(w)(T)]/di]/dT]/di]/dT, d[d[d[dE[(a)(T)]/di]/dT]/di]/dT, d[d[d[dE[(i)(T)]/di]/dT]/di]/dT, d[d[d[dE[(m)(T)]/di]/dT]/di]/dT, d[d[d[dE[(t,w)(T)]/di]/dT]/di]/dT, d[d[d[dE[(t,a)(T)]/di]/dT]/di]/dT, d[d[d[dE[(t,i)(T)]/di]/dT]/di]/dT, d[d[d[dE[(t,m)(T)]/di]/dT]/di]/dT, d[d[d[dE[(w,a)(T)]/di]/dT]/di]/dT, d[d[d[dE[(w,i)(T)]/di]/dT]/di]/dT, d[d[d[dE[(w,m)(T)]/di]/dT]/di]/dT, d[d[d[dE[(a,i)(T)]/di]/dT]/di]/dT, d[d[d[dE[(a,m)(T)]/di]/dT]/di]/dT, d[d[d[dE[(i,m)(T)]/di]/dT]/di]/dT, d[d[d[dE[(t,w,a)(T)]/di]/dT]/di]/dT, d[d[d[dE[(t,w,i)(T)]/di]/dT]/di]/dT, d[d[d[dE[(t,w,m)(T)]/di]/dT]/di]/dT, d[d[d[dE[(t,a,i)(T)]/di]/dT]/di]/dT, d[d[d[dE[(t,a,m)(T)]/di]/dT]/di]/dT, d[d[d[dE[(t,i,m)(T)]/di]/dT]/di]/dT, d[d[d[dE[(w,a,i)(T)]/di]/dT]/di]/dT, d[d[d[dE[(w,a,m)(T)]/di]/dT]/di]/dT, d[d[d[dE[(w,i,m)(T)]/di]/dT]/di]/dT, d[d[d[dE[(a,i,m)(T)]/di]/dT]/di]/dT, d[d[d[dE[(t,w,a,i)(T)]/di]/dT]/di]/dT, d[d[d[dE[(t,w,a,m)(T)]/di]/dT]/di]/dT, d[d[d[dE[(t,w,i,m)(T)]/di]/dT]/di]/dT, d[d[d[dE[(t,a,i,m)(T)]/di]/dT]/di]/dT, d[d[d[dE[(w,a,i,m)(T)]/di]/dT]/di]/dT, d[d[d[dE[(t,w,a,i,m)(T)]/di]/dT]/di]/dT.

 

or as:

 

 

 

d[d[d[dE[(t)(T)]/di]/dT]/dT]/di, d[d[d[dE[(w)(T)]/di]/dT]/dT]/di, d[d[d[dE[(a)(T)]/di]/dT]/dT]/di, d[d[d[dE[(i)(T)]/di]/dT]/dT]/di, d[d[d[dE[(m)(T)]/di]/dT]/dT]/di, d[d[d[dE[(t,w)(T)]/di]/dT]/dT]/di, d[d[d[dE[(t,a)(T)]/di]/dT]/dT]/di, d[d[d[dE[(t,i)(T)]/di]/dT]/dT]/di, d[d[d[dE[(t,m)(T)]/di]/dT]/dT]/di, d[d[d[dE[(w,a)(T)]/di]/dT]/dT]/di, d[d[d[dE[(w,i)(T)]/di]/dT]/dT]/di, d[d[d[dE[(w,m)(T)]/di]/dT]/dT]/di, d[d[d[dE[(a,i)(T)]/di]/dT]/dT]/di, d[d[d[dE[(a,m)(T)]/di]/dT]/dT]/di, d[d[d[dE[(i,m)(T)]/di]/dT]/dT]/di, d[d[d[dE[(t,w,a)(T)]/di]/dT]/dT]/di, d[d[d[dE[(t,w,i)(T)]/di]/dT]/dT]/di, d[d[d[dE[(t,w,m)(T)]/di]/dT]/dT]/di, d[d[d[dE[(t,a,i)(T)]/di]/dT]/dT]/di, d[d[d[dE[(t,a,m)(T)]/di]/dT]/dT]/di, d[d[d[dE[(t,i,m)(T)]/di]/dT]/dT]/di, d[d[d[dE[(w,a,i)(T)]/di]/dT]/dT]/di, d[d[d[dE[(w,a,m)(T)]/di]/dT]/dT]/di, d[d[d[dE[(w,i,m)(T)]/di]/dT]/dT]/di, d[d[d[dE[(a,i,m)(T)]/di]/dT]/dT]/di, d[d[d[dE[(t,w,a,i)(T)]/di]/dT]/dT]/di, d[d[d[dE[(t,w,a,m)(T)]/di]/dT]/dT]/di, d[d[d[dE[(t,w,i,m)(T)]/di]/dT]/dT]/di, d[d[d[dE[(t,a,i,m)(T)]/di]/dT]/dT]/di, d[d[d[dE[(w,a,i,m)(T)]/di]/dT]/dT]/di, d[d[d[dE[(t,w,a,i,m)(T)]/di]/dT]/dT]/di.

 

or as:

 

d[d[d[dE[(t)(T)]/dT]/di]/di]/dT, d[d[d[dE[(w)(T)]/dT]/di]/di]/dT, d[d[d[dE[(a)(T)]/dT]/di]/di]/dT, d[d[d[dE[(i)(T)]/dT]/di]/di]/dT, d[d[d[dE[(m)(T)]/dT]/di]/di]/dT, d[d[d[dE[(t,w)(T)]/dT]/di]/di]/dT, d[d[d[dE[(t,a)(T)]/dT]/di]/di]/dT, d[d[d[dE[(t,i)(T)]/dT]/di]/di]/dT, d[d[d[dE[(t,m)(T)]/dT]/di]/di]/dT, d[d[d[dE[(w,a)(T)]/dT]/di]/di]/dT, d[d[d[dE[(w,i)(T)]/dT]/di]/di]/dT, d[d[d[dE[(w,m)(T)]/dT]/di]/di]/dT, d[d[d[dE[(a,i)(T)]/dT]/di]/di]/dT, d[d[d[dE[(a,m)(T)]/dT]/di]/di]/dT, d[d[d[dE[(i,m)(T)]/dT]/di]/di]/dT, d[d[d[dE[(t,w,a)(T)]/dT]/di]/di]/dT, d[d[d[dE[(t,w,i)(T)]/dT]/di]/di]/dT, d[d[d[dE[(t,w,m)(T)]/dT]/di]/di]/dT, d[d[d[dE[(t,a,i)(T)]/dT]/di]/di]/dT, d[d[d[dE[(t,a,m)(T)]/dT]/di]/di]/dT, d[d[d[dE[(t,i,m)(T)]/dT]/di]/di]/dT, d[d[d[dE[(w,a,i)(T)]/dT]/di]/di]/dT, d[d[d[dE[(w,a,m)(T)]/dT]/di]/di]/dT, d[d[d[dE[(w,i,m)(T)]/dT]/di]/di]/dT, d[d[d[dE[(a,i,m)(T)]/dT]/di]/di]/dT, d[d[d[dE[(t,w,a,i)(T)]/dT]/di]/di]/dT, d[d[d[dE[(t,w,a,m)(T)]/dT]/di]/di]/dT, d[d[d[dE[(t,w,i,m)(T)]/dT]/di]/di]/dT, d[d[d[dE[(t,a,i,m)(T)]/dT]/di]/di]/dT, d[d[d[dE[(w,a,i,m)(T)]/dT]/di]/di]/dT, d[d[d[dE[(t,w,a,i,m)(T)]/dT]/di]/di]/dT.

 

 

or as;

 

 

 

 

d[d[d[dE(t)/di]/di]/dT]/dT, d[d[d[dE(w)/di]/di]/dT]/dT, d[d[d[dE(a)/di]/di]/dT]/dT, d[d[d[dE(i)/di]/di]/dT]/dT, d[d[d[dE(m)/di]/di]/dT]/dT, d[d[d[dE(t,w)/di]/di]/dT]/dT, d[d[d[dE(t,a)/di]/di]/dT]/dT, d[d[d[dE(t,i)/di]/di]/dT]/dT, d[d[d[dE(t,m)/di]/di]/dT]/dT, d[d[d[dE(w,a)/di]/di]/dT]/dT, d[d[d[dE(w,i)/di]/di]/dT]/dT, d[d[d[dE(w,m)/di]/di]/dT]/dT, d[d[d[dE(a,i)/di]/di]/dT]/dT, d[d[d[dE(a,m)/di]/di]/dT]/dT, d[d[d[dE(i,m)/di]/di]/dT]/dT, d[d[d[dE(t,w,a)/di]/di]/dT]/dT, d[d[d[dE(t,w,i)/di]/di]/dT]/dT, d[d[d[dE(t,w,m)/di]/di]/dT]/dT, d[d[d[dE(t,a,i)/di]/di]/dT]/dT, d[d[d[dE(t,a,m)/di]/di]/dT]/dT,  d[d[d[dE(t,i,m)/di]/di]/dT]/dT, d[d[d[dE(w,a,i)/di]/di]/dT]/dT, d[d[d[dE(w,a,m)/di]/di]/dT]/dT, d[d[d[dE(w,i,m)/di]/di]/dT]/dT, d[d[d[dE(a,i,m)/di]/di]/dT]/dT, d[d[d[dE(t,w,a,i)/di]/di]/dT]/dT, d[d[d[dE(t,w,a,m)/di/di, d[d[d[dE(t,w,i,m)/di]/di]/dT]/dT, d[d[d[dE(t,a,i,m)/di]/di]/dT]/dT, d[d[d[dE(w,a,i,m)/di]/di]/dT]/dT, d[d[d[dE(t,w,a,i,m)/di]/di]/dT]/dT..

 

or as:

 

d[d[d[dE(t)/dT]/di]/dT]/di, d[d[d[dE(w)/dT]/di]/dT]/di, d[d[d[dE(a)/dT]/di]/dT]/di, d[d[d[dE(i)/dT]/di]/dT]/di, d[d[d[dE(m)/dT]/di]/dT]/di, d[d[d[dE(t,w)/dT]/di]/dT]/di, d[d[d[dE(t,a)/dT]/di]/dT]/di, d[d[d[dE(t,i)/dT]/di]/dT]/di, d[d[d[dE(t,m)/dT]/di]/dT]/di, d[d[d[dE(w,a)/dT]/di]/dT]/di, d[d[d[dE(w,i)/dT]/di]/dT]/di, d[d[d[dE(w,m)/dT]/di]/dT]/di, d[d[d[dE(a,i)/dT]/di]/dT]/di, d[d[d[dE(a,m)/dT]/di]/dT]/di, d[d[d[dE(i,m)/ dT]/di]/dT]/di, d[d[d[dE(t,w,a)/dT]/di]/dT]/di, d[d[d[dE(t,w,i)/dT]/di]/dT]/di, d[d[d[dE(t,w,m)/dT]/di]/dT]/di, d[d[d[dE(t,a,i)/dT]/di]/dT]/di, d[d[d[dE(t,a,m)/dT]/di]/dT]/di,  d[d[d[dE(t,i,m)/dT]/di]/dT]/di, d[d[d[dE(w,a,i)/dT]/di]/dT]/di, d[d[d[dE(w,a,m)/dT]/di]/dT]/di, d[d[d[dE(w,i,m)/dT]/di]/dT]/di, d[d[d[dE(a,i,m)/dT]/di]/dT]/di, d[d[d[dE(t,w,a,i)/dT]/di]/dT]/di, d[d[d[dE(t,w,a,m)/di/di, d[d[d[dE(t,w,i,m)/dT]/di]/dT]/di, d[d[d[dE(t,a,i,m)/dT]/di]/dT]/di, d[d[d[dE(w,a,i,m)/dT]/di]/dT]/di, d[d[d[dE(t,w,a,i,m)/dT]/di]/dT]/di..

 

or as:

 

d[d[d[dE(t)/dT]/dT]/di]/di, d[d[d[dE(w)/dT]/dT]/di]/di, d[d[d[dE(a)/dT]/dT]/di]/di, d[d[d[dE(i)/dT]/dT]/di]/di, d[d[d[dE(m)/dT]/dT]/di]/di, d[d[d[dE(t,w)/dT]/dT]/di]/di, d[d[d[dE(t,a)/dT]/dT]/di]/di, d[d[d[dE(t,i)/dT]/dT]/di]/di, d[d[d[dE(t,m)/dT]/dT]/di]/di, d[d[d[dE(w,a)/dT]/dT]/di]/di, d[d[d[dE(w,i)/dT]/dT]/di]/di, d[d[d[dE(w,m)/dT]/dT]/di]/di, d[d[d[dE(a,i)/dT]/dT]/di]/di, d[d[d[dE(a,m)/ dT]/dT]/di]/di, d[d[d[dE(i,m)/ dT]/dT]/di]/di, d[d[d[dE(t,w,a)/dT]/dT]/di]/di, d[d[d[dE(t,w,i)/dT]/dT]/di]/di, d[d[d[dE(t,w,m)/dT]/dT]/di]/di, d[d[d[dE(t,a,i)/dT]/dT]/di]/di, d[d[d[dE(t,a,m)/dT]/dT]/di]/di,  d[d[d[dE(t,i,m)/dT]/dT]/di]/di, d[d[d[dE(w,a,i)/dT]/dT]/di]/di, d[d[d[dE(w,a,m)/dT]/dT]/di]/di, d[d[d[dE(w,i,m)/dT]/dT]/di]/di, d[d[d[dE(a,i,m)/dT]/dT]/di]/di, d[d[d[dE(t,w,a,i)/dT]/dT]/di]/di, d[d[d[dE(t,w,a,m)/di/di, d[d[d[dE(t,w,i,m)/dT]/dT]/di]/di, d[d[d[dE(t,a,i,m)/dT]/dT]/di]/di, d[d[d[dE(w,a,i,m)/dT]/dT]/di]/di, d[d[d[dE(t,w,a,i,m)/dT]/dT]/di]/di..

 

We can also take higher order duel dimensional derivatives of emotion as a function of instinct and time but the symbolic expression of the set of such derivatives very soon becomes excessively lengthly to write and so these higher order derivatives as such are not mentioned here except to say that they would be computed in an analogous manner to the second order duel dimensional derivatives described above.

 

 

 

These seemingly crazy differentials might have some use in extreme psychological states that can be experienced by souls who are departed and whose emotions, although perhaps spiritualized, are nonetheless, not limited by a body and its brain.

 

 

Another type of being that might experience such extreme emotional change capacities might be none other then some of our friends we believe to exist as pure body-less and brain-less spirits known as angels.

 

 

Since I have dared to speculate this far, perhaps we can speculate as to whether any intelligent extraterrestrials persons or any so-called ultra-terrestrials persons that are more emotionally evolved then we ordinary humans might be capable of experiencing large absolute valued terms of En. Some such ETI and UTI persons may  have evolved over billions of years, or perhaps have far greater powers of sensation, emotion, and intuition such as would seem plausible for any such persons and their civilizations who have not fallen from the state of innocence into the state of sin as we humans have, or perhaps such beings never had the option of  sanctifying grace opened to them but nonetheless may have been created at a naturally more perfect level then we humans, and who therefore might exhibit greater natural powers of emotion and sensation.

 

 

 

 

 

 

 

 

 

 

 

 

We can also express emotion qualitatively, statistically, and perhaps with the use of some forms of real analyses as a derivative with respect to memory of with respect to m.

 

Given that E(m) =  E(t and/or w and/or a and/or i and/or m) or perhaps the following notation can be more appropriate in certain circumstances.

 

 

 

 

Thus the following first order derivatives of emotion with respect to memory are possible.

 

 

dE(t)/dm, dE(w)/dm, dE(a)/dm, dE(i)/dm, dE(m)/dm, dE(t,w)/dm, dE(t,a)/dm, dE(t,i)/dm, dE(t,m)/dm, dE(w,a)/dm, dE(w,i)/dm, dE(w,m)/dm, dE(a,i)/dm, dE(a,m)/dm, dE(i,m)/dm, dE(t,w,a)/dm, dE(t,w,i)/dm, dE(t,w,m)/dm, dE(t,a,i)/dm, dE(t,a,m)/dm, dE(t,i,m)/dm, dE(w,a,i)/dm, dE(w,a,m)/dm, dE(w,i,m)/dm, dE(a,i,m)/dm, dE(t,w,a,i)/dm, dE(t,w,a,m)/dm, dE(t,w,i,m)/dm, dE(t,a,i,m)/dm, dE(w,a,i,m)/dm, dE(t,w,a,i,m)/dm.

 

 

Or more succinctly,  dE/dm = dE(t and/or w and/or a and/or i and/or m)/dm

 

 

Or perhaps dE(m)/dm =d E{[t(m)] and/or [w(m)] and/or [a(m)] and/or [i(m)] and/or [m(m)]}/dm.

 

 

Likewise, we can take the second memory derivatives of  E as follows:

 

 

 

d[dE(t)/dm]/dm, d[dE(w)/dm]/dm, d[dE(a)/dm]/dm, d[dE(i)/dm]/dm, d[dE(m)/dm]/dm, d[dE(t,w)/dm]/dm, d[dE(t,a)/dm]/dm, d[dE(t,i)/dm]/dm, d[dE(t,m)/dm]/dm, d[dE(w,a)/dm]/dm, d[dE(w,i)/dm]/dm, d[dE(w,m)/dm]/dm, d[dE(a,i)/dm]/dm, d[dE(a,m)/dm]/dm, d[dE(i,m)/dm/dm, d[dE(t,w,a)/dm]/dm, d[dE(t,w,i)/dm]/dm, d[dE(t,w,m)/dm]/dm, d[dE(t,a,i)/dm]/dm, d[dE(t,a,m)/dm]/dm,  d[dE(t,i,m)/dm]/dm, d[dE(w,a,i)/dm]/dm, d[dE(w,a,m)/dm]/dm, d[dE(w,i,m)/dm]/dm, d[dE(a,i,m)/dm]/dm, d[dE(t,w,a,i)/dm]/dm, d[dE(t,w,a,m)/dm/dm, d[dE(t,w,i,m)/dm]/dm, d[dE(t,a,i,m)/dm]/dm, d[dE(w,a,i,m)/dm]/dm, d[dE(t,w,a,i,m)/dm]/dm..

 

 

or more succinctly, as d(dE/dm)/dm = d[d E(t and/or w and/or a and/or i and/or m)/dm]/dm = Em2

 

 

or as

 

 

d[dE(m)/dm]/dm  = d[d E{[t(m)] and/or [w(m)] and/or [a(m)] and/or [i(m)] and/or [m(m)]}/dm]/dm = Em2.

 

 

 

Likewise, we can take the third memory derivatives of  E as follows:

 

 

 

d[d[dE(t)/dm]/dm]/dm, d[d[dE(w)/dm]/dm]/dm, d[d[dE(a)/dm]/dm]/dm, d[d[dE(i)/dm]/dm]/dm, d[d[dE(m)/dm]/dm]/dm, d[d[dE(t,w)/dm]/dm]/dm, d[d[dE(t,a)/dm]/dm]/dm, d[d[dE(t,i)/dm]/dm]/dm, d[d[dE(t,m)/dm]/dm]/dm, d[d[dE(w,a)/dm]/dm]/dm, d[d[dE(w,i)/dm]/dm]/dm, d[d[dE(w,m)/dm]/dm]/dm, d[d[dE(a,i)/dm]/dm]/dm, d[d[dE(a,m)/dm]/dm]/dm, d[d[dE(i,m)/dm/dm]/dm, d[d[dE(t,w,a)/dm]/dm]/dm, d[d[dE(t,w,i)/dm]/dm]/dm, d[d[dE(t,w,m)/dm]/dm]/dm, d[d[dE(t,a,i)/dm]/dm]/dm, d[d[dE(t,a,m)/dm]/dm]/dm,  d[d[dE(t,i,m)/dm]/dm]/dm, d[d[dE(w,a,i)/dm]/dm]/dm, d[d[dE(w,a,m)/dm]/dm]/dm, d[d[dE(w,i,m)/dm]/dm]/dm, d[d[dE(a,i,m)/dm]/dm]/dm, d[d[dE(t,w,a,i)/dm]/dm]/dm, d[d[dE(t,w,a,m)/dm/dm]/dm, d[d[dE(t,w,i,m)/dm]/dm]/dm, d[d[dE(t,a,i,m)/dm]/dm]/dm, d[d[dE(w,a,i,m)/dm]/dm]/dm, d[d[dE(t,w,a,i,m)/dm]/dm]/dm.

 

 

or more succinctly, as d[d(dE/dm)/dm]/dm = d[d[d E(t and/or w and/or a and/or i and/or m)/dm]/dm]/dm = Em3

 

 

or as

 

 

d[d[dE(m)/dm]/dm]/dm  = d[d[d E{[t(m)] and/or [w(m)] and/or [a(m)] and/or [i(m)] and/or [m(m)]}/dm]/dm]/dm = Em3.

 

 

We can also form the expressions;

 

 

d[d[f(E)]/dm]/dm = d{d [E[t(m)]]/dm and/or d[E[w(m)]]/dm and/or d[E[a(m)]]/dm and/or d[E[i(m)]]/dm and/or d[E[m(m)]]/dm}/dm  = f(Em)2

 

 

and

 

 

d[d[d[f(E)]/dm]/dm]/dm = d{d{ d [E[t(m)]]/dm and/or d[E[w(m)]]/dm and/or d[E[a(m)]]/dm and/or d[E[i(m)]]/dm and/or d[E[m(m)]]/dm}/dm}/dm  = f(Em)3A, where A stands for type A differentiation which is not to be confused with the meaning of so-called Type A personality as A is used as an ordinal in a totally different context here.

 

 

and

 

 

d[d[d[f(E)]/dm]/dm]/dm = d{d[d [E[t(m)]]/dm]/dm  and/or d[d [E[w(m)]]/dm]/dm  and/or d[d [E[a(m)]]/dm]/dm  and/or d[d [E[i(m)]]/dm]/dm  and/or d[d [E[m(m)]]/dm]/dm }/dm = f(Em)3B, where B stands for type B differentiation which is not to be confused with the meaning of so-called Type  B personality as B is used as an ordinal in a totally different context here .

 

 

In fact, one can form yet higher order derivatives of emotions with respect to memory as follows.

 

 

Em5 = d Em4/dm = d[dEm3/dm]/dm

 

 

 

Em5 = dEm4/dm =  d[d[d[d[d E{[t(m)] and/or [w(m)] and/or [a(m)] and/or [i(m)] and/or [m(m)]}/dm]/dm]/dm]/dm]/dm.

 

 

 

f(Em)5A = d[f(Em)4A]/dm = d[d [f(Em)3A]/dm]/dm =  d{d{d{d{ d [E[t(m)]]/dm and/or d[E[w(m)]]/dm and/or d[E[a(m)]]/dm and/or d[E[i(m)]]/dm and/or d[E[m(m)]]/dm}/dm}/dm]/dm]/dm

 

 

 

 

Em6 = d Em5/dm = d[d Em4/dm]/dm = d[d[dEm3/dm]/dm]/dm

 

 

 

Em6 = dEm5/dm = d[d[d[d[d[d E{[t(m)] and/or [w(m)] and/or [a(m)] and/or [i(m)] and/or [m(m)]}/dm]/dm]/dm]/dm]/dm]/dm

 

 

 

f(Em)6A = d[f(Em)5A]/dm = d{ d{d{d{d{ d [E[t(m)]]/dm and/or d[E[w(m)]]/dm and/or d[E[a(m)]]/dm and/or d[E[i(m)]]/dm and/or d[E[m(m)]]/dm}/dm}/dm]/dm]/dm]/dm

 

 

 

 

Em7 = dEm6/dm

 

f(Em)7A = d[f(Em)6A]/dm

 

 

Em8 = d Em7/dm

 

f(Em)8A = d[f(Em)7A]/dm

 

 

 

Em9 = d Em8/dm

 

f(Em)9A = d[f(Em)8A]/dm

 

 

Em10…, Em11…, Em12 … etc.

 

 

Anyone for Em ensemble, or Em infinity scrapper, or Em (Aleph 0), or Em(Aleph 1), or Em (Aleph 2), or how about Em Aleph (Aleph 0), or Em Aleph (Aleph 1) , or Em Aleph (Aleph 2), or even Em Aleph (Aleph (Aleph 0)), or Em Aleph (Aleph (Aleph 1)), or Em Aleph (Aleph (Aleph 2)), and so on?

 

 

Thus, for the set of the sets of derivatives of Em1 through Em(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Em1 through Em(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)},…, {П(0,31)[R]}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Em1 through Em(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Em1 through Em(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the derivative states in the set of the sets of derivatives of Em1 through Em(Aleph 0) is plausible equal to:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Em1 through Em(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Em1 through Em(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}}}.

 

For the set of the sets of derivatives of Em1 through Em(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Em(Aleph 0) derivative space at the level of 0/(Aleph 0), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Em1 through Em(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Em1 through Em (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Em1 through Em(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Em1 through Em(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Em1 through Em(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Em1 through Em(Aleph 1), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Em1 through  Em(Aleph 2), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Em1 through Em(Aleph 3), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Em(Aleph 0) derivative space at the level of 0/(Aleph 1), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Em1 through Em(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Em1 through Em(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Em1 through Em(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Em1 through  Em(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations  for the set of the sets of derivatives of Em1 through Em(Aleph 0) is plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Em1 through Em(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Em1 through Em(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Em1 through Em(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

 

For super-continuous Em(Aleph 0) derivative space at the level of 0/(Aleph 2), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Em1 through Em(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Em1 through Em(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Em1 through Em(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Em1 through Em(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Em1 through Em(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Em1 through Em(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Em1 through Em(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Em1 through Em(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}}}

 

 

and so on, ad infinitum.

 

Similar series can be developed for super-continuity at any applicable level such as 0/(Aleph 3), 0/(Aleph 4), 0/(Aleph 5),…, 0/(Aleph Ω), 0/(Aleph (Aleph 0)), …, 0/(Aleph (Aleph 1)), …, 0/(Aleph (Aleph 2)), …, 0/(Aleph (Aleph 3)),…, 0/(Aleph (Aleph Ω)),…, 0/(Aleph (Aleph (Aleph 0))), …, 0/(Aleph (Aleph (Aleph 1))),…, 0/(Aleph (Aleph (Aleph 2))),…, 0/(Aleph (Aleph (Aleph 3))),…, 0/(Aleph (Aleph  (Aleph Ω))), …

 

An so-on ad infinitum.

 

Perhaps these numbers are applicable when one considers that the human soul, in its accidental form and perhaps even in its substantial form stores all experience and other psychodynamics based phenomenon. Every experience adds to the accidental form of the human soul and this includes the souls of all those still alive on Earth, all those in Purgatory, all those in Heaven, all those in Hell, and all those in any Limbo.

Since the human soul can grow without limit in terms of its psychodynamic time –flow world line, such a consideration offers another mechanism where the number of derivative states, combinations of derivative states, and even super-continuity of the derivative state space can grow forever.

 

Folks, for those of you who might balk at me for including literally all souls in the above consideration, including the souls in Hell, as well as bodily extraterrestrial souls and the souls of so-called bodily ultraterrestials sometimes referred to as etherians in the new age UFO buff culture, my reply is that we simply do not understand the full scope of GOD’s Divine Economy. We may never fully comprehend the scope of the Divine Economy because such an utterly eternal scheme, is, well, eternal and never ending.

 

In addition to these numerical functions of Em as functions of summation series of product series functions, in order to really appreciate the enourmous complexity of the human soul in terms of its potential to evolve and be differentiated from all other souls in its characteristics, we would need to consider how every single category and even every single species of emotions of the form Em can very. Since there may exist an arbitrarily high infinite number species of Em, the number of numerical functions of Em is utterly beyond recogning. I will cover such notions in terms of mathematical notation in yet another series of articles I will write on this general concept.

 

 

 

 

 

The general meaning of memory derivatives of emotion can be viewed as the manner in which the qualitative and/or quantitative aspects of emotion as a function of memory very with memory. The manner in which emotions very with memory may be multi- memory-aspect dimensional wherein the dimensions of derivations can be multiple, and wherein the derivations can be taken in parallel, series parallel or in serial manner. The differentials can be partial or non-partial derivatives, or both partial and non-partial for a given computation.

 

In fact, since there is in theory, no limit to the numbers of qualitatively and quantitatively different memories, and perhaps no limit to the number of possible different types or classes of memories, wherein each person has his or her own unique memories, the number of memory dimensions that can effect emotions is literally infinite, given the entirety of the set of created persons, and perhaps also literally infinite for each person as an individual, although we can not intellectually and intuitively understand this infinite number.

 

 

It is interesting to consider the ramifactions of being able to perform realistic calculations involving memory derivatives of emotion from a mathematical, theoretical, scientific,  and philosophical perspective.

 

Persons for which one or more nth order derivatives of emotion with respect to memory that have large absolute values would tend to have their emotions highly influenced by memory, or at least for the emotions under consideration with respect to the dimension of the specific memory act type(s) or class(es) for which the differentiation(s) are being performed. Perhaps a strong coupling between emotion and memory indicates a well integrated personality and commensurately, a high degree of emotional capacity and a high degree of emotional intelligence as well as perhaps very strong memory power.

 

We would expect that disembodied human souls, ETI souls, and/or UTI souls in Heaven, Limbo, highly evolved bodily ETI persons, highly evolved UTI persons, and angels to have emotions of all kinds and intensities which are perhaps  highly subject to powereful memorys such as spiritual memorys, psychological memories, emotional memories, intellectual memories, interpersonal memories, auto-biographical memories, and even perhaps, memories facilitated by advanced psychic powers.

 

 

We can also consider that two dimensional nth ordered derivatives of emotion with respect to memory and time, or with respect to i and T, respectively.

 

Given that E[(m)(T)] =  E[(t and/or w and/or a and/or i and/or m)(m)(T)], the following first order two dimensional derivatives of emotion with respect to memory and Time are possible.

 

 

d[dE[(t)(T)]/dm]/dT, d[dE[(w)(T)]/dm]/dT, d[dE[(a)(T)]/dm]/dT, d[dE[(i)(T)]/dm]/dT, d[dE[(m)(T)]/dm]/dT, d[dE[(t,w)(T)]/dm]/dT, d[dE[(t,a)(T)]/dm]/dT, d[dE[(t,i)(T)]/dm]/dT, d[dE[(t,m)(T)]/dm]/dT, d[dE[(w,a)(T)]/dm]/dT, d[dE[(w,i)(T)]/dm]/dT, d[dE[(w,m)(T)]/dm]/dT, d[dE[(a,i)(T)]/dm]/dT, d[dE[(a,m)(T)]/dm]/dT, d[dE[(i,m)(T)]/dm]/dT, d[dE[(t,w,a)(T)]/dm]/dT, d[dE[(t,w,i)(T)]/dm]/dT, d[dE[(t,w,m)(T)]/dm]/dT, d[dE[(t,a,i)(T)]/dm]/dT, d[dE[(t,a,m)(T)]/dm]/dT, d[dE[(t,i,m)(T)]/dm]/dT, d[dE[(w,a,i)(T)]/dm]/dT, d[dE[(w,a,m)(T)]/dm]/dT, d[dE[(w,i,m)(T)]/dm]/dT, d[dE[(a,i,m)(T)]/dm]/dT, d[dE[(t,w,a,i)(T)]/dm]/dT, d[dE[(t,w,a,m)(T)]/dm]/dT, d[dE[(t,w,i,m)(T)]/dm]/dT, d[dE[(t,a,i,m)(T)]/dm]/dT, d[dE[(w,a,i,m)(T)]/dm]/dT, d[dE[(t,w,a,i,m)(T)]/dm]/dT.

 

 

Or more succinctly,  d[dE(T)/dm]/dT = d[dE[(T)(t and/or w and/or a and/or m and/or m)]/dm]/dT

 

or

 

d[dE(T)/dT]/dm = d[dE[(T)(t and/or w and/or a and/or i and/or m)]/dT]/dm

 

 

 

 

 

Or perhaps d[d E[(m)(T)]/dm]/dT  = d[d E [{[t(m)] and/or [w(m)] and/or [a(m)] and/or [i(m)] and/or [m(m)]}(T)]/dm]/dT

 

or

 

Or perhaps d[d E[(m)(T)]/dT]/dm  = d[d E [{[t(m)] and/or [w(m)] and/or [a(i)] and/or [i(m)] and/or [m(m)]}(T)]/dT]/dm

 

 

 

Likewise, we can take the second dual dimension memory -time derivatives of  E as follows:

 

d[d[d[dE[(t)(T)]/dm]/dT]/dm]/dT, d[d[d[dE[(w)(T)]/dm]/dT]/dm]/dT, d[d[d[dE[(a)(T)]/dm]/dT]/dm]/dT, d[d[d[dE[(i)(T)]/dm]/dT]/dm]/dT, d[d[d[dE[(m)(T)]/dm]/dT]/dm]/dT, d[d[d[dE[(t,w)(T)]/dm]/dT]/dm]/dT, d[d[d[dE[(t,a)(T)]/dm]/dT]/dm]/dT, d[d[d[dE[(t,i)(T)]/dm]/dT]/dm]/dT, d[d[d[dE[(t,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dE[(w,a)(T)]/dm]/dT]/dm]/dT, d[d[d[dE[(w,i)(T)]/dm]/dT]/dm]/dT, d[d[d[dE[(w,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dE[(a,i)(T)]/dm]/dT]/dm]/dT, d[d[d[dE[(a,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dE[(i,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dE[(t,w,a)(T)]/dm]/dT]/dm]/dT, d[d[d[dE[(t,w,i)(T)]/dm]/dT]/dm]/dT, d[d[d[dE[(t,w,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dE[(t,a,i)(T)]/dm]/dT]/dm]/dT, d[d[d[dE[(t,a,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dE[(t,i,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dE[(w,a,i)(T)]/dm]/dT]/dm]/dT, d[d[d[dE[(w,a,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dE[(w,i,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dE[(a,i,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dE[(t,w,a,i)(T)]/dm]/dT]/dm]/dT, d[d[d[dE[(t,w,a,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dE[(t,w,i,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dE[(t,a,i,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dE[(w,a,i,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dE[(t,w,a,i,m)(T)]/dm]/dT]/dm]/dT.

 

or as:

 

 

 

d[d[d[dE[(t)(T)]/dm]/dT]/dT]/dm, d[d[d[dE[(w)(T)]/dm]/dT]/dT]/dm, d[d[d[dE[(a)(T)]/dm]/dT]/dT]/dm, d[d[d[dE[(i)(T)]/dm]/dT]/dT]/dm, d[d[d[dE[(m)(T)]/dm]/dT]/dT]/dm, d[d[d[dE[(t,w)(T)]/dm]/dT]/dT]/dm, d[d[d[dE[(t,a)(T)]/dm]/dT]/dT]/dm, d[d[d[dE[(t,i)(T)]/dm]/dT]/dT]/dm, d[d[d[dE[(t,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dE[(w,a)(T)]/dm]/dT]/dT]/dm, d[d[d[dE[(w,i)(T)]/dm]/dT]/dT]/dm, d[d[d[dE[(w,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dE[(a,i)(T)]/dm]/dT]/dT]/dm, d[d[d[dE[(a,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dE[(i,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dE[(t,w,a)(T)]/dm]/dT]/dT]/dm, d[d[d[dE[(t,w,i)(T)]/dm]/dT]/dT]/dm, d[d[d[dE[(t,w,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dE[(t,a,i)(T)]/dm]/dT]/dT]/dm, d[d[d[dE[(t,a,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dE[(t,i,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dE[(w,a,i)(T)]/dm]/dT]/dT]/dm, d[d[d[dE[(w,a,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dE[(w,i,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dE[(a,i,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dE[(t,w,a,i)(T)]/dm]/dT]/dT]/dm, d[d[d[dE[(t,w,a,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dE[(t,w,i,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dE[(t,a,i,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dE[(w,a,i,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dE[(t,w,a,i,m)(T)]/dm]/dT]/dT]/dm.

 

or as:

 

d[d[d[dE[(t)(T)]/dT]/dm]/dm]/dT, d[d[d[dE[(w)(T)]/dT]/dm]/dm]/dT, d[d[d[dE[(a)(T)]/dT]/dm]/dm]/dT, d[d[d[dE[(i)(T)]/dT]/dm]/dm]/dT, d[d[d[dE[(m)(T)]/dT]/dm]/dm]/dT, d[d[d[dE[(t,w)(T)]/dT]/dm]/dm]/dT, d[d[d[dE[(t,a)(T)]/dT]/dm]/dm]/dT, d[d[d[dE[(t,i)(T)]/dT]/dm]/dm]/dT, d[d[d[dE[(t,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dE[(w,a)(T)]/dT]/dm]/dm]/dT, d[d[d[dE[(w,i)(T)]/dT]/dm]/dm]/dT, d[d[d[dE[(w,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dE[(a,i)(T)]/dT]/dm]/dm]/dT, d[d[d[dE[(a,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dE[(i,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dE[(t,w,a)(T)]/dT]/dm]/dm]/dT, d[d[d[dE[(t,w,i)(T)]/dT]/dm]/dm]/dT, d[d[d[dE[(t,w,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dE[(t,a,i)(T)]/dT]/dm]/dm]/dT, d[d[d[dE[(t,a,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dE[(t,i,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dE[(w,a,i)(T)]/dT]/dm]/dm]/dT, d[d[d[dE[(w,a,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dE[(w,i,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dE[(a,i,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dE[(t,w,a,i)(T)]/dT]/dm]/dm]/dT, d[d[d[dE[(t,w,a,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dE[(t,w,i,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dE[(t,a,i,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dE[(w,a,i,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dE[(t,w,a,i,m)(T)]/dT]/dm]/dm]/dT.

 

 

or as;

 

 

 

 

d[d[d[dE(t)/dm]/dm]/dT]/dT, d[d[d[dE(w)/dm]/dm]/dT]/dT, d[d[d[dE(a)/dm]/dm]/dT]/dT, d[d[d[dE(i)/dm]/dm]/dT]/dT, d[d[d[dE(m)/dm]/dm]/dT]/dT, d[d[d[dE(t,w)/dm]/dm]/dT]/dT, d[d[d[dE(t,a)/dm]/dm]/dT]/dT, d[d[d[dE(t,i)/dm]/dm]/dT]/dT, d[d[d[dE(t,m)/dm]/dm]/dT]/dT, d[d[d[dE(w,a)/dm]/dm]/dT]/dT, d[d[d[dE(w,i)/dm]/dm]/dT]/dT, d[d[d[dE(w,m)/dm]/dm]/dT]/dT, d[d[d[dE(a,i)/dm]/dm]/dT]/dT, d[d[d[dE(a,m)/dm]/dm]/dT]/dT, d[d[d[dE(i,m)/dm]/dm]/dT]/dT, d[d[d[dE(t,w,a)/dm]/dm]/dT]/dT, d[d[d[dE(t,w,i)/dm]/dm]/dT]/dT, d[d[d[dE(t,w,m)/dm]/dm]/dT]/dT, d[d[d[dE(t,a,i)/dm]/dm]/dT]/dT, d[d[d[dE(t,a,m)/dm]/dm]/dT]/dT,  d[d[d[dE(t,i,m)/dm]/dm]/dT]/dT, d[d[d[dE(w,a,i)/dm]/dm]/dT]/dT, d[d[d[dE(w,a,m)/dm]/dm]/dT]/dT, d[d[d[dE(w,i,m)/dm]/dm]/dT]/dT, d[d[d[dE(a,i,m)/dm]/dm]/dT]/dT, d[d[d[dE(t,w,a,i)/dm]/dm]/dT]/dT, d[d[d[dE(t,w,a,m)/dm/dm, d[d[d[dE(t,w,i,m)/dm]/dm]/dT]/dT, d[d[d[dE(t,a,i,m)/dm]/dm]/dT]/dT, d[d[d[dE(w,a,i,m)/dm]/dm]/dT]/dT, d[d[d[dE(t,w,a,i,m)/dm]/dm]/dT]/dT..

 

or as:

 

d[d[d[dE(t)/dT]/dm]/dT]/dm, d[d[d[dE(w)/dT]/dm]/dT]/dm, d[d[d[dE(a)/dT]/dm]/dT]/dm, d[d[d[dE(i)/dT]/dm]/dT]/dm, d[d[d[dE(m)/dT]/dm]/dT]/dm, d[d[d[dE(t,w)/dT]/dm]/dT]/dm, d[d[d[dE(t,a)/dT]/dm]/dT]/dm, d[d[d[dE(t,i)/dT]/dm]/dT]/dm, d[d[d[dE(t,m)/dT]/dm]/dT]/dm, d[d[d[dE(w,a)/dT]/dm]/dT]/dm, d[d[d[dE(w,i)/dT]/dm]/dT]/dm, d[d[d[dE(w,m)/dT]/dm]/dT]/dm, d[d[d[dE(a,i)/dT]/dm]/dT]/dm, d[d[d[dE(a,m)/dT]/dm]/dT]/dm, d[d[d[dE(i,m)/ dT]/dm]/dT]/dm, d[d[d[dE(t,w,a)/dT]/dm]/dT]/dm, d[d[d[dE(t,w,i)/dT]/dm]/dT]/dm, d[d[d[dE(t,w,m)/dT]/dm]/dT]/dm, d[d[d[dE(t,a,i)/dT]/dm]/dT]/dm, d[d[d[dE(t,a,m)/dT]/dm]/dT]/dm,  d[d[d[dE(t,i,m)/dT]/dm]/dT]/dm, d[d[d[dE(w,a,i)/dT]/dm]/dT]/dm, d[d[d[dE(w,a,m)/dT]/dm]/dT]/dm, d[d[d[dE(w,i,m)/dT]/dm]/dT]/dm, d[d[d[dE(a,i,m)/dT]/dm]/dT]/dm, d[d[d[dE(t,w,a,i)/dT]/dm]/dT]/dm, d[d[d[dE(t,w,a,m)/dm/dm, d[d[d[dE(t,w,i,m)/dT]/dm]/dT]/dm, d[d[d[dE(t,a,i,m)/dT]/dm]/dT]/dm, d[d[d[dE(w,a,i,m)/dT]/dm]/dT]/dm, d[d[d[dE(t,w,a,i,m)/dT]/dm]/dT]/dm..

 

or as:

 

d[d[d[dE(t)/dT]/dT]/dm]/dm, d[d[d[dE(w)/dT]/dT]/dm]/dm, d[d[d[dE(a)/dT]/dT]/dm]/dm, d[d[d[dE(i)/dT]/dT]/dm]/dm, d[d[d[dE(m)/dT]/dT]/dm]/dm, d[d[d[dE(t,w)/dT]/dT]/dm]/dm, d[d[d[dE(t,a)/dT]/dT]/dm]/dm, d[d[d[dE(t,i)/dT]/dT]/dm]/dm, d[d[d[dE(t,m)/dT]/dT]/dm]/dm, d[d[d[dE(w,a)/dT]/dT]/dm]/dm, d[d[d[dE(w,i)/dT]/dT]/dm]/dm, d[d[d[dE(w,m)/dT]/dT]/dm]/dm, d[d[d[dE(a,i)/dT]/dT]/dm]/dm, d[d[d[dE(a,m)/ dT]/dT]/dm]/dm, d[d[d[dE(i,m)/ dT]/dT]/dm]/dm, d[d[d[dE(t,w,a)/dT]/dT]/dm]/dm, d[d[d[dE(t,w,i)/dT]/dT]/dm]/dm, d[d[d[dE(t,w,m)/dT]/dT]/dm]/dm, d[d[d[dE(t,a,i)/dT]/dT]/dm]/dm, d[d[d[dE(t,a,m)/dT]/dT]/dm]/dm,  d[d[d[dE(t,i,m)/dT]/dT]/dm]/dm, d[d[d[dE(w,a,i)/dT]/dT]/dm]/dm, d[d[d[dE(w,a,m)/dT]/dT]/dm]/dm, d[d[d[dE(w,i,m)/dT]/dT]/dm]/dm, d[d[d[dE(a,i,m)/dT]/dT]/dm]/dm, d[d[d[dE(t,w,a,i)/dT]/dT]/dm]/dm, d[d[d[dE(t,w,a,m)/dm/dm, d[d[d[dE(t,w,i,m)/dT]/dT]/dm]/dm, d[d[d[dE(t,a,i,m)/dT]/dT]/dm]/dm, d[d[d[dE(w,a,i,m)/dT]/dT]/dm]/dm, d[d[d[dE(t,w,a,i,m)/dT]/dT]/dm]/dm..

 

We can also take higher order duel dimensional derivatives of emotion as a function of memory and time but the symbolic expression of the set of such derivatives very soon becomes excessively lengthly to write and so these higher order derivatives as such are not mentioned here except to say that they would be computed in an analogous manner to the second order duel dimensional derivatives described above.

 

 

 

We can also express emotion qualitatively, statistically, and perhaps with the use of some forms of real analyses as a derivative with respect to  emotion or of E.

 

Given that E(e) =  E(t and/or w and/or a and/or i and/or m) or perhaps the following notation can be more appropriate in certain circumstances.

 

 

 

 

Thus the following first order derivatives of emotion with respect to emotion are possible.

 

 

dE(t)/dE, dE(w)/dE, dE(a)/dE, dE(i)/dE, dE(m)/dE, dE(t,w)/dE, dE(t,a)/dE, dE(t,i)/dE, dE(t,m)/dE, dE(w,a)/dE, dE(w,i)/dE, dE(w,m)/dE, dE(a,i)/dE, dE(a,m)/dE, dE(i,m)/dE, dE(t,w,a)/dE, dE(t,w,i)/dE, dE(t,w,m)/dE, dE(t,a,i)/dE, dE(t,a,m)/dE, dE(t,i,m)/dE, dE(w,a,i)/dE, dE(w,a,m)/dE, dE(w,i,m)/dE, dE(a,i,m)/dE, dE(t,w,a,i)/dE, dE(t,w,a,m)/dE, dE(t,w,i,m)/dE, dE(t,a,i,m)/dE, dE(w,a,i,m)/dE, dE(t,w,a,i,m)/dE.

 

 

Or more succinctly,  dE/dE = dE(t and/or w and/or a and/or i and/or m)/dE

 

 

Or perhaps dE(e)/dE =d E{[t(e)] and/or [w(e)] and/or [a(e)] and/or [i(e)] and/or [m(e)]}/dE.

 

 

Likewise, we can take the second emotion derivatives of  E as follows:

 

 

 

d[dE(t)/dE]/dE, d[dE(w)/dE]/dE, d[dE(a)/dE]/dE, d[dE(i)/dE]/dE, d[dE(m)/dE]/dE, d[dE(t,w)/dE]/dE, d[dE(t,a)/dE]/dE, d[dE(t,i)/dE]/dE, d[dE(t,m)/dE]/dE, d[dE(w,a)/dE]/dE, d[dE(w,i)/dE]/dE, d[dE(w,m)/dE]/dE, d[dE(a,i)/dE]/dE, d[dE(a,m)/dE]/dE, d[dE(i,m)/dE/dE, d[dE(t,w,a)/dE]/dE, d[dE(t,w,i)/dE]/dE, d[dE(t,w,m)/dE]/dE, d[dE(t,a,i)/dE]/dE, d[dE(t,a,m)/dE]/dE,  d[dE(t,i,m)/dE]/dE, d[dE(w,a,i)/dE]/dE, d[dE(w,a,m)/dE]/dE, d[dE(w,i,m)/dE]/dE, d[dE(a,i,m)/dE]/dE, d[dE(t,w,a,i)/dE]/dE, d[dE(t,w,a,m)/dE/dE, d[dE(t,w,i,m)/dE]/dE, d[dE(t,a,i,m)/dE]/dE, d[dE(w,a,i,m)/dE]/dE, d[dE(t,w,a,i,m)/dE]/dE..

 

 

or more succinctly, as d(dE/dE)/dE = d[d E(t and/or w and/or a and/or i and/or m)/dE]/dE = Ee2

 

 

or as

 

 

d[dE(e)/dE]/dE  = d[d E{[t(e)] and/or [w(e)] and/or [a(e)] and/or [i(e)] and/or [m(e)]}/dE]/dE = Ee2.

 

 

 

Likewise, we can take the third emotion derivatives of  E as follows:

 

 

 

d[d[dE(t)/dE]/dE]/dE, d[d[dE(w)/dE]/dE]/dE, d[d[dE(a)/dE]/dE]/dE, d[d[dE(i)/dE]/dE]/dE, d[d[dE(m)/dE]/dE]/dE, d[d[dE(t,w)/dE]/dE]/dE, d[d[dE(t,a)/dE]/dE]/dE, d[d[dE(t,i)/dE]/dE]/dE, d[d[dE(t,m)/dE]/dE]/dE, d[d[dE(w,a)/dE]/dE]/dE, d[d[dE(w,i)/dE]/dE]/dE, d[d[dE(w,m)/dE]/dE]/dE, d[d[dE(a,i)/dE]/dE]/dE, d[d[dE(a,m)/dE]/dE]/dE, d[d[dE(i,m)/dE/dE]/dE, d[d[dE(t,w,a)/dE]/dE]/dE, d[d[dE(t,w,i)/dE]/dE]/dE, d[d[dE(t,w,m)/dE]/dE]/dE, d[d[dE(t,a,i)/dE]/dE]/dE, d[d[dE(t,a,m)/dE]/dE]/dE,  d[d[dE(t,i,m)/dE]/dE]/dE, d[d[dE(w,a,i)/dE]/dE]/dE, d[d[dE(w,a,m)/dE]/dE]/dE, d[d[dE(w,i,m)/dE]/dE]/dE, d[d[dE(a,i,m)/dE]/dE]/dE, d[d[dE(t,w,a,i)/dE]/dE]/dE, d[d[dE(t,w,a,m)/dE/dE]/dE, d[d[dE(t,w,i,m)/dE]/dE]/dE, d[d[dE(t,a,i,m)/dE]/dE]/dE, d[d[dE(w,a,i,m)/dE]/dE]/dE, d[d[dE(t,w,a,i,m)/dE]/dE]/dE.

 

 

or more succinctly, as d[d(dE/dE)/dE]/dE = d[d[d E(t and/or w and/or a and/or i and/or m)/dE]/dE]/dE = Ee3

 

 

or as

 

 

d[d[dE(e)/dE]/dE]/dE  = d[d[d E{[t(e)] and/or [w(e)] and/or [a(e)] and/or [i(e)] and/or [m(e)]}/dE]/dE]/dE = Ee3.

 

 

We can also form the expressions;

 

 

d[d[f(E)]/dE]/dE = d{d [E[t(e)]]/dE and/or d[E[w(e)]]/dE and/or d[E[a(e)]]/dE and/or d[E[i(e)]]/dE and/or d[E[m(e)]]/dE}/dE  = f(Ee)2

 

 

and

 

 

d[d[d[f(E)]/dE]/dE]/dE = d{d{ d [E[t(e)]]/dE and/or d[E[w(e)]]/dE and/or d[E[a(e)]]/dE and/or d[E[i(e)]]/dE and/or d[E[m(e)]]/dE}/dE}/dE  = f(Ee)3A, where A stands for type A differentiation which is not to be confused with the meaning of so-called Type A personality as A is used as an ordinal in a totally different context here.

 

 

and

 

 

d[d[d[f(E)]/dE]/dE]/dE = d{d[d [E[t(e)]]/dE]/dE  and/or d[d [E[w(e)]]/dE]/dE  and/or d[d [E[a(e)]]/dE]/dE  and/or d[d [E[i(e)]]/dE]/dE  and/or d[d [E[m(e)]]/dE]/dE }/dE = f(Ee)3B, where B stands for type B differentiation which is not to be confused with the meaning of so-called Type  B personality as B is used as an ordinal in a totally different context here .

 

 

In fact, one can form yet higher order derivatives of emotions with respect to emotion as follows.

 

 

Ee5 = d Ee4/dE = d[dEe3/dE]/dE

 

 

 

Ee5 = dEe4/dE =  d[d[d[d[d E{[t(e)] and/or [w(e)] and/or [a(e)] and/or [i(e)] and/or [m(e)]}/dE]/dE]/dE]/dE]/dE.

 

 

 

f(Ee)5A = d[f(Ee)4A]/dE = d[d [f(Ee)3A]/dE]/dE =  d{d{d{d{ d [E[t(e)]]/dE and/or d[E[w(e)]]/dE and/or d[E[a(e)]]/dE and/or d[E[i(e)]]/dE and/or d[E[m(e)]]/dE}/dE}/dE]/dE]/dE

 

 

 

 

Ee6 = d Ee5/dE = d[d Ee4/dE]/dE = d[d[dEe3/dE]/dE]/dE

 

 

 

Ee6 = dEe5/dE = d[d[d[d[d[d E{[t(e)] and/or [w(e)] and/or [a(e)] and/or [i(e)] and/or [m(e)]}/dE]/dE]/dE]/dE]/dE]/dE

 

 

 

f(Ee)6A = d[f(Ee)5A]/dE = d{ d{d{d{d{ d [E[t(e)]]/dE and/or d[E[w(e)]]/dE and/or d[E[a(e)]]/dE and/or d[E[i(e)]]/dE and/or d[E[m(e)]]/dE}/dE}/dE]/dE]/dE]/dE

 

 

 

 

Ee7 = dEe6/dE

 

f(Ee)7A = d[f(Ee)6A]/dE

 

 

Ee8 = d Ee7/dE

 

f(Ee)8A = d[f(Ee)7A]/dE

 

 

 

Ee9 = d Ee8/dE

 

f(Ee)9A = d[f(Ee)8A]/dE

 

 

Ee10…, Ee11…, Ee12 … etc.

 

 

Anyone for Ee ensemble, or Ee infinity scrapper, or Ee (Aleph 0), or Ee(Aleph 1), or Ee (Aleph 2), or how about Ee Aleph (Aleph 0), or Ee Aleph (Aleph 1) , or Ee Aleph (Aleph 2), or even Ee Aleph (Aleph (Aleph 0)), or Ee Aleph (Aleph (Aleph 1)), or Ee Aleph (Aleph (Aleph 2)), and so on?

 

 

Thus, for the set of the sets of derivatives of Ee1 through Ee(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ee1 through Ee(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)},…, {П(0,31)[R]}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ee1 through Ee(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ee1 through Ee(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the derivative states in the set of the sets of derivatives of Ee1 through Ee(Aleph 0) is plausible equal to:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ee1 through Ee(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ee1 through Ee(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}}}.

 

For the set of the sets of derivatives of Ee1 through Ee(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Ee(Aleph 0) derivative space at the level of 0/(Aleph 0), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Ee1 through Ee(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ee1 through Ee(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ee1 through Ee(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ee1 through Ee(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Ee1 through Ee(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ee1 through Ee(Aleph 1), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Ee1 through  Ee(Aleph 2), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Ee1 through Ee(Aleph 3), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Ee(Aleph 0) derivative space at the level of 0/(Aleph 1), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Ee1 through Ee(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ee1 through Ee(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ee1 through Ee(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ee1 through  Ee(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations  for the set of the sets of derivatives of Ee1 through Ee(Aleph 0) is plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ee1 through Ee(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Ee1 through Ee(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Ee1 through Ee(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

 

For super-continuous Ee(Aleph 0) derivative space at the level of 0/(Aleph 2), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Ee1 through Ee(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ee1 through Ee(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ee1 through Ee(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ee1 through Ee(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Ee1 through Ee(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ee1 through Ee(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Ee1 through Ee(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Ee1 through Ee(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

Similar series can be developed for super-continuity at any applicable level such as 0/(Aleph 3), 0/(Aleph 4), 0/(Aleph 5),…, 0/(Aleph Ω), 0/(Aleph (Aleph 0)), …, 0/(Aleph (Aleph 1)), …, 0/(Aleph (Aleph 2)), …, 0/(Aleph (Aleph 3)),…, 0/(Aleph (Aleph Ω)),…, 0/(Aleph (Aleph (Aleph 0))), …, 0/(Aleph (Aleph (Aleph 1))),…, 0/(Aleph (Aleph (Aleph 2))),…, 0/(Aleph (Aleph (Aleph 3))),…, 0/(Aleph (Aleph  (Aleph Ω))), …

 

An so-on ad infinitum.

 

In addition to these numerical functions of Ee as functions of summation series of product series functions, in order to really appreciate the enourmous complexity of the human soul in terms of its potential to evolve and be differentiated from all other souls in its characteristics, we would need to consider how every single category and even every single species of emotions of the form Ee can very. Since there may exist an arbitrarily high infinite number species of Ee, the number of numerical functions of Ee is utterly beyond recogning. I will cover such notions in terms of mathematical notation in yet another series of articles I will write on this general concept.

 

Perhaps these numbers are applicable when one considers that the human soul, in its accidental form and perhaps even in its substantial form stores all experience and other psychodynamics based phenomenon. Every experience adds to the accidental form of the human soul and this includes the souls of all those still alive on Earth, all those in Purgatory, all those in Heaven, all those in Hell, and all those in any Limbo.

Since the human soul can grow without limit in terms of its psychodynamic time –flow world line, such a consideration offers another mechanism where the number of derivative states, combinations of derivative states, and even super-continuity of the derivative state space can grow forever.

 

Folks, for those of you who might balk at me for including literally all souls in the above consideration, including the souls in Hell, as well as bodily extraterrestrial souls and the souls of so-called bodily ultraterrestials sometimes referred to as etherians in the new age UFO buff culture, my reply is that we simply do not understand the full scope of GOD’s Divine Economy. We may never fully comprehend the scope of the Divine Economy because such an utterly eternal scheme is, well, eternal and never ending.

 

 

 

 

 

 

The general meaning of emotion derivatives of emotion can be viewed as the manner in which the qualitative and/or quantitative aspects of emotion as a function of emotion  very with emotion. The manner in which emotions very with emotion may be multi- emotion-aspect dimensional wherein the dimensions of derivations can be multiple, and wherein the derivations can be taken in parallel, series parallel or in serial manner. The differentials can be partial or non-partial derivatives, or both partial and non-partial for a given computation.

 

In fact, since there is in theory, no limit to the numbers of qualitatively and quantitatively different memories, and perhaps no limit to the number of possible different types or classes of memories, wherein each person has his or her own unique memories, the number of emotion dimensions that can effect emotions is literally infinite, given the entirety of the set of created persons, and perhaps also literally infinite for each person as an individual, although we cannot intellectually and intuitively understand this infinite number.

 

 

It is interesting to consider the ramifactions of being able to perform realistic calculations involving emotion derivatives of emotion from a mathematical, theoretical, scientific,  and philosophical perspective.

 

Persons for which one or more nth order derivatives of emotion with respect to emotion that have large absolute values would tend to have their emotions highly influenced by emotion, or at least for the emotions under consideration with respect to the dimension of the specific emotion act type(s) or class(es) for which the differentiation(s) are being performed. Perhaps a strong coupling between emotion and emotion indicates a well integrated personality and commensurately, a high degree of emotional capacity and a high degree of emotional intelligence as well as perhaps very strong emotion power.

 

We would expect that disembodied human souls, ETI souls, and/or UTI souls in Heaven, Limbo, highly evolved bodily ETI persons, highly evolved UTI persons, and angels to have emotions of all kinds and intensities which are perhaps  highly subject to powereful emotions such as spiritual emotions, psychological memories, emotional memories, intellectual memories, interpersonal memories, auto-biographical memories, and even perhaps, memories facilitated by advanced psychic powers.

 

 

We can also consider that two dimensional nth ordered derivatives of emotion with respect to emotion and time, or with respect to i and T, respectively.

 

Given that E[(e)(T)] =  E[(t and/or w and/or a and/or i and/or m)(e)(T)], the following first order two dimensional derivatives of emotion with respect to emotion and Time are possible.

 

 

d[dE[(t)(T)]/dE]/dT, d[dE[(w)(T)]/dE]/dT, d[dE[(a)(T)]/dE]/dT, d[dE[(i)(T)]/dE]/dT, d[dE[(m)(T)]/dE]/dT, d[dE[(t,w)(T)]/dE]/dT, d[dE[(t,a)(T)]/dE]/dT, d[dE[(t,i)(T)]/dE]/dT, d[dE[(t,m)(T)]/dE]/dT, d[dE[(w,a)(T)]/dE]/dT, d[dE[(w,i)(T)]/dE]/dT, d[dE[(w,m)(T)]/dE]/dT, d[dE[(a,i)(T)]/dE]/dT, d[dE[(a,m)(T)]/dE]/dT, d[dE[(i,m)(T)]/dE]/dT, d[dE[(t,w,a)(T)]/dE]/dT, d[dE[(t,w,i)(T)]/dE]/dT, d[dE[(t,w,m)(T)]/dE]/dT, d[dE[(t,a,i)(T)]/dE]/dT, d[dE[(t,a,m)(T)]/dE]/dT, d[dE[(t,i,m)(T)]/dE]/dT, d[dE[(w,a,i)(T)]/dE]/dT, d[dE[(w,a,m)(T)]/dE]/dT, d[dE[(w,i,m)(T)]/dE]/dT, d[dE[(a,i,m)(T)]/dE]/dT, d[dE[(t,w,a,i)(T)]/dE]/dT, d[dE[(t,w,a,m)(T)]/dE]/dT, d[dE[(t,w,i,m)(T)]/dE]/dT, d[dE[(t,a,i,m)(T)]/dE]/dT, d[dE[(w,a,i,m)(T)]/dE]/dT, d[dE[(t,w,a,i,m)(T)]/dE]/dT.

 

 

Or more succinctly,  d[dE(T)/dE]/dT = d[dE[(T)(t and/or w and/or a and/or m and/or m)]/dE]/dT

 

or

 

d[dE(T)/dT]/dE = d[dE[(T)(t and/or w and/or a and/or i and/or m)]/dT]/dE

 

 

 

 

 

Or perhaps d[d E[(e)(T)]/dE]/dT  = d[d E [{[t(e)] and/or [w(e)] and/or [a(e)] and/or [i(e)] and/or [m(e)]}(T)]/dE]/dT

 

or

 

Or perhaps d[d E[(e)(T)]/dT]/dE  = d[d E [{[t(e)] and/or [w(e)] and/or [a(e)] and/or [i(e)] and/or [m(e)]}(T)]/dT]/dE

 

 

 

Likewise, we can take the second dual dimension emotion -time derivatives of  E as follows:

 

d[d[d[dE[(t)(T)]/dE]/dT]/dE]/dT, d[d[d[dE[(w)(T)]/dE]/dT]/dE]/dT, d[d[d[dE[(a)(T)]/dE]/dT]/dE]/dT, d[d[d[dE[(i)(T)]/dE]/dT]/dE]/dT, d[d[d[dE[(m)(T)]/dE]/dT]/dE]/dT, d[d[d[dE[(t,w)(T)]/dE]/dT]/dE]/dT, d[d[d[dE[(t,a)(T)]/dE]/dT]/dE]/dT, d[d[d[dE[(t,i)(T)]/dE]/dT]/dE]/dT, d[d[d[dE[(t,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dE[(w,a)(T)]/dE]/dT]/dE]/dT, d[d[d[dE[(w,i)(T)]/dE]/dT]/dE]/dT, d[d[d[dE[(w,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dE[(a,i)(T)]/dE]/dT]/dE]/dT, d[d[d[dE[(a,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dE[(i,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dE[(t,w,a)(T)]/dE]/dT]/dE]/dT, d[d[d[dE[(t,w,i)(T)]/dE]/dT]/dE]/dT, d[d[d[dE[(t,w,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dE[(t,a,i)(T)]/dE]/dT]/dE]/dT, d[d[d[dE[(t,a,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dE[(t,i,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dE[(w,a,i)(T)]/dE]/dT]/dE]/dT, d[d[d[dE[(w,a,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dE[(w,i,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dE[(a,i,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dE[(t,w,a,i)(T)]/dE]/dT]/dE]/dT, d[d[d[dE[(t,w,a,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dE[(t,w,i,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dE[(t,a,i,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dE[(w,a,i,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dE[(t,w,a,i,m)(T)]/dE]/dT]/dE]/dT.

 

or as:

 

 

 

d[d[d[dE[(t)(T)]/dE]/dT]/dT]/dE, d[d[d[dE[(w)(T)]/dE]/dT]/dT]/dE, d[d[d[dE[(a)(T)]/dE]/dT]/dT]/dE, d[d[d[dE[(i)(T)]/dE]/dT]/dT]/dE, d[d[d[dE[(m)(T)]/dE]/dT]/dT]/dE, d[d[d[dE[(t,w)(T)]/dE]/dT]/dT]/dE, d[d[d[dE[(t,a)(T)]/dE]/dT]/dT]/dE, d[d[d[dE[(t,i)(T)]/dE]/dT]/dT]/dE, d[d[d[dE[(t,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dE[(w,a)(T)]/dE]/dT]/dT]/dE, d[d[d[dE[(w,i)(T)]/dE]/dT]/dT]/dE, d[d[d[dE[(w,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dE[(a,i)(T)]/dE]/dT]/dT]/dE, d[d[d[dE[(a,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dE[(i,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dE[(t,w,a)(T)]/dE]/dT]/dT]/dE, d[d[d[dE[(t,w,i)(T)]/dE]/dT]/dT]/dE, d[d[d[dE[(t,w,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dE[(t,a,i)(T)]/dE]/dT]/dT]/dE, d[d[d[dE[(t,a,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dE[(t,i,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dE[(w,a,i)(T)]/dE]/dT]/dT]/dE, d[d[d[dE[(w,a,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dE[(w,i,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dE[(a,i,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dE[(t,w,a,i)(T)]/dE]/dT]/dT]/dE, d[d[d[dE[(t,w,a,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dE[(t,w,i,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dE[(t,a,i,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dE[(w,a,i,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dE[(t,w,a,i,m)(T)]/dE]/dT]/dT]/dE.

 

or as:

 

d[d[d[dE[(t)(T)]/dT]/dE]/dE]/dT, d[d[d[dE[(w)(T)]/dT]/dE]/dE]/dT, d[d[d[dE[(a)(T)]/dT]/dE]/dE]/dT, d[d[d[dE[(i)(T)]/dT]/dE]/dE]/dT, d[d[d[dE[(m)(T)]/dT]/dE]/dE]/dT, d[d[d[dE[(t,w)(T)]/dT]/dE]/dE]/dT, d[d[d[dE[(t,a)(T)]/dT]/dE]/dE]/dT, d[d[d[dE[(t,i)(T)]/dT]/dE]/dE]/dT, d[d[d[dE[(t,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dE[(w,a)(T)]/dT]/dE]/dE]/dT, d[d[d[dE[(w,i)(T)]/dT]/dE]/dE]/dT, d[d[d[dE[(w,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dE[(a,i)(T)]/dT]/dE]/dE]/dT, d[d[d[dE[(a,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dE[(i,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dE[(t,w,a)(T)]/dT]/dE]/dE]/dT, d[d[d[dE[(t,w,i)(T)]/dT]/dE]/dE]/dT, d[d[d[dE[(t,w,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dE[(t,a,i)(T)]/dT]/dE]/dE]/dT, d[d[d[dE[(t,a,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dE[(t,i,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dE[(w,a,i)(T)]/dT]/dE]/dE]/dT, d[d[d[dE[(w,a,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dE[(w,i,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dE[(a,i,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dE[(t,w,a,i)(T)]/dT]/dE]/dE]/dT, d[d[d[dE[(t,w,a,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dE[(t,w,i,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dE[(t,a,i,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dE[(w,a,i,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dE[(t,w,a,i,m)(T)]/dT]/dE]/dE]/dT.

 

 

or as;

 

 

 

 

d[d[d[dE(t)/dE]/dE]/dT]/dT, d[d[d[dE(w)/dE]/dE]/dT]/dT, d[d[d[dE(a)/dE]/dE]/dT]/dT, d[d[d[dE(i)/dE]/dE]/dT]/dT, d[d[d[dE(m)/dE]/dE]/dT]/dT, d[d[d[dE(t,w)/dE]/dE]/dT]/dT, d[d[d[dE(t,a)/dE]/dE]/dT]/dT, d[d[d[dE(t,i)/dE]/dE]/dT]/dT, d[d[d[dE(t,m)/dE]/dE]/dT]/dT, d[d[d[dE(w,a)/dE]/dE]/dT]/dT, d[d[d[dE(w,i)/dE]/dE]/dT]/dT, d[d[d[dE(w,m)/dE]/dE]/dT]/dT, d[d[d[dE(a,i)/dE]/dE]/dT]/dT, d[d[d[dE(a,m)/dE]/dE]/dT]/dT, d[d[d[dE(i,m)/dE]/dE]/dT]/dT, d[d[d[dE(t,w,a)/dE]/dE]/dT]/dT, d[d[d[dE(t,w,i)/dE]/dE]/dT]/dT, d[d[d[dE(t,w,m)/dE]/dE]/dT]/dT, d[d[d[dE(t,a,i)/dE]/dE]/dT]/dT, d[d[d[dE(t,a,m)/dE]/dE]/dT]/dT,  d[d[d[dE(t,i,m)/dE]/dE]/dT]/dT, d[d[d[dE(w,a,i)/dE]/dE]/dT]/dT, d[d[d[dE(w,a,m)/dE]/dE]/dT]/dT, d[d[d[dE(w,i,m)/dE]/dE]/dT]/dT, d[d[d[dE(a,i,m)/dE]/dE]/dT]/dT, d[d[d[dE(t,w,a,i)/dE]/dE]/dT]/dT, d[d[d[dE(t,w,a,m)/dE/dE, d[d[d[dE(t,w,i,m)/dE]/dE]/dT]/dT, d[d[d[dE(t,a,i,m)/dE]/dE]/dT]/dT, d[d[d[dE(w,a,i,m)/dE]/dE]/dT]/dT, d[d[d[dE(t,w,a,i,m)/dE]/dE]/dT]/dT..

 

or as:

 

d[d[d[dE(t)/dT]/dE]/dT]/dE, d[d[d[dE(w)/dT]/dE]/dT]/dE, d[d[d[dE(a)/dT]/dE]/dT]/dE, d[d[d[dE(i)/dT]/dE]/dT]/dE, d[d[d[dE(m)/dT]/dE]/dT]/dE, d[d[d[dE(t,w)/dT]/dE]/dT]/dE, d[d[d[dE(t,a)/dT]/dE]/dT]/dE, d[d[d[dE(t,i)/dT]/dE]/dT]/dE, d[d[d[dE(t,m)/dT]/dE]/dT]/dE, d[d[d[dE(w,a)/dT]/dE]/dT]/dE, d[d[d[dE(w,i)/dT]/dE]/dT]/dE, d[d[d[dE(w,m)/dT]/dE]/dT]/dE, d[d[d[dE(a,i)/dT]/dE]/dT]/dE, d[d[d[dE(a,m)/dT]/dE]/dT]/dE, d[d[d[dE(i,m)/ dT]/dE]/dT]/dE, d[d[d[dE(t,w,a)/dT]/dE]/dT]/dE, d[d[d[dE(t,w,i)/dT]/dE]/dT]/dE, d[d[d[dE(t,w,m)/dT]/dE]/dT]/dE, d[d[d[dE(t,a,i)/dT]/dE]/dT]/dE, d[d[d[dE(t,a,m)/dT]/dE]/dT]/dE,  d[d[d[dE(t,i,m)/dT]/dE]/dT]/dE, d[d[d[dE(w,a,i)/dT]/dE]/dT]/dE, d[d[d[dE(w,a,m)/dT]/dE]/dT]/dE, d[d[d[dE(w,i,m)/dT]/dE]/dT]/dE, d[d[d[dE(a,i,m)/dT]/dE]/dT]/dE, d[d[d[dE(t,w,a,i)/dT]/dE]/dT]/dE, d[d[d[dE(t,w,a,m)/dE/dE, d[d[d[dE(t,w,i,m)/dT]/dE]/dT]/dE, d[d[d[dE(t,a,i,m)/dT]/dE]/dT]/dE, d[d[d[dE(w,a,i,m)/dT]/dE]/dT]/dE, d[d[d[dE(t,w,a,i,m)/dT]/dE]/dT]/dE..

 

or as:

 

d[d[d[dE(t)/dT]/dT]/dE]/dE, d[d[d[dE(w)/dT]/dT]/dE]/dE, d[d[d[dE(a)/dT]/dT]/dE]/dE, d[d[d[dE(i)/dT]/dT]/dE]/dE, d[d[d[dE(m)/dT]/dT]/dE]/dE, d[d[d[dE(t,w)/dT]/dT]/dE]/dE, d[d[d[dE(t,a)/dT]/dT]/dE]/dE, d[d[d[dE(t,i)/dT]/dT]/dE]/dE, d[d[d[dE(t,m)/dT]/dT]/dE]/dE, d[d[d[dE(w,a)/dT]/dT]/dE]/dE, d[d[d[dE(w,i)/dT]/dT]/dE]/dE, d[d[d[dE(w,m)/dT]/dT]/dE]/dE, d[d[d[dE(a,i)/dT]/dT]/dE]/dE, d[d[d[dE(a,m)/ dT]/dT]/dE]/dE, d[d[d[dE(i,m)/ dT]/dT]/dE]/dE, d[d[d[dE(t,w,a)/dT]/dT]/dE]/dE, d[d[d[dE(t,w,i)/dT]/dT]/dE]/dE, d[d[d[dE(t,w,m)/dT]/dT]/dE]/dE, d[d[d[dE(t,a,i)/dT]/dT]/dE]/dE, d[d[d[dE(t,a,m)/dT]/dT]/dE]/dE,  d[d[d[dE(t,i,m)/dT]/dT]/dE]/dE, d[d[d[dE(w,a,i)/dT]/dT]/dE]/dE, d[d[d[dE(w,a,m)/dT]/dT]/dE]/dE, d[d[d[dE(w,i,m)/dT]/dT]/dE]/dE, d[d[d[dE(a,i,m)/dT]/dT]/dE]/dE, d[d[d[dE(t,w,a,i)/dT]/dT]/dE]/dE, d[d[d[dE(t,w,a,m)/dE/dE, d[d[d[dE(t,w,i,m)/dT]/dT]/dE]/dE, d[d[d[dE(t,a,i,m)/dT]/dT]/dE]/dE, d[d[d[dE(w,a,i,m)/dT]/dT]/dE]/dE, d[d[d[dE(t,w,a,i,m)/dT]/dT]/dE]/dE..

 

We can also take higher order duel dimensional derivatives of emotion as a function of emotion and time but the symbolic expression of the set of such derivatives very soon becomes excessively lengthly to write and so these higher order derivatives as such are not mentioned here except to say that they would be computed in an analogous manner to the second order duel dimensional derivatives described above.

 

 

 

 

 

These seemingly crazy differentials might have some use in extreme psychological states that can be experienced by souls who are departed and whose emotions, although perhaps spiritualized, are nonetheless, not limited by a body and its brain.

 

 

Another type of being that might experience such extreme emotional change capacities might be none other then some of our friends we believe to exist as pure body-less and brain-less spirits known as angels.

 

 

Since I have dared to speculate this far, perhaps we can speculate as to whether any intelligent extraterrestrials persons or any so-called ultra-terrestrials persons that are more emotionally evolved then we ordinary humans might be capable of experiencing large absolute valued terms of En. Some such ETI and UTI persons may  have evolved over billions of years, or perhaps have far greater powers of sensation, emotion, and intuition such as would seem plausible for any such persons and their civilizations who have not fallen from the state of innocence into the state of sin as we humans have, or perhaps such beings never had the option of  sanctifying grace opened to them but nonetheless may have been created at a naturally more perfect level then we humans, and who therefore might exhibit greater natural powers of emotion and sensation.

 

 

 

 

Now, the above variable of time, T,  can have multiple meanings or aspects. One such meaning is objective time and in such a case for large non-zero values of En, where n = 1,2,3,…, the person experiencing such an emotion or complex of emotions  might not subjectively experience the emotion(s) as occurring any faster than we ordinary humans do.

 

 

However, another interpretation of the variable of Time is subjective time. In such a case for large non-zero absolute values of En, where n = 1,2,3,…, the person experiencing such an emotion or complex of emotions  would subjectively experience the emotion(s) as occurring or changing faster than we ordinary humans experience, in fact the higher the absolute value of non-zero En, especially for large n, the rate of change of emotion with respect to time would progress at an incredible rate. We ordinary humans would likely be completely overwhelmed by subjective psychic experiences of such En phenomenon.

 

 

Could there be other objective temporal dimensions beside the one objective temporal dimension that we know of, and the seemingly one subjective dimension of time that we experience? As someone who normally writes on the topic of exotic space craft propulsion systems such as proposed interstellar space craft propulsion systems, I am familiar with the theoretical paradigms that there may exist higher dimensions of space and perhaps more than one dimension of time, and so I say, never say never.

 

The above notation of derivatives and differential equations is just an infinitesimal glimpse of the number of possible equations as such and related constructs. Trust me, I can reasonably in good confidence re-assure you of such.

 

 

29) Just A Shadow Of A Glimpse Of The Utterly Limitless Number Derivatives of Human Affect With Respect To Time, Thought, Volition, Affect, Memory, Instinct, And Emotion  Where These Latter 6 Psychodynamic Parameter Are Likely Just An Infinitesimal Fraction Of The Number Of Possible Psychodynamic Parameters, Of Which In This Life, We Have  A Glimpse Of Relatively Few.

 

 

 

 

Affect  can be a function or partially a function of emotion, will, affect, instinct, emotion and/or memory; and thought as such can be expressed as follows:

 

 

A(t), A(w), A(a), A(i), A(m), A(t,w), A(t,a), A(t,i), A(t,m), A(w,a), A(w,i), A(w,m), A(a,i), A(a,m), A(i,m), A(t,w,a), A(t,w,i), A(t,w,m), A(t,a,i), A(t,a,m), A(t,i,m), A(w,a,i), A(w,a,m), A(w,i,m), A(a,i,m), A(t,w,a,i), A(t,w,a,m), A(t,w,i,m), A(t,a,i,m), A(w,a,i,m), A(t,w,a,i,m)

 

A(t,e), A(w,e), A(a,e), A(i,e), A(m,e), A(t,w,e), A(t,a,e), A(t,i,e), A(t,m,e), A(w,a,e), A(w,i,e), A(w,m,e), A(a,i,e), A(a,m,e), A(i,m,e), A(t,w,a,e), A(t,w,i,e), A(t,w,m,e), A(t,a,i,e), A(t,a,m,e), A(t,i,m,e), A(w,a,i,e), A(w,a,m,e), A(w,i,m,e), A(a,i,m,e), A(t,w,a,i,e), A(t,w,a,m,e), A(t,w,i,m,e), A(t,a,i,m,e), A(w,a,i,m,e), A(t,w,a,i,m,e).

 

Note that some differential expressions involving  the form of functions of will, or A,  as a function of emotion, e, by itself, or in conjunction with any sub-set of the parameters of t,w,a,i,m, are not included to the same extent as many similar expressions including A, and these other parameters denoted by the small letters, t,w,a,i, and/or m in this section. A more comphrensive post will include the currently omitted explicit formulas incorporating the parameter, e. Note that capital e, or E, is a parameter that is often included in the differential equations herein, but then so in a slightly different context than e would have be included. The difference between e and E will become clear from the context of the specific formulas.

 

In all, there are (2 EXP n) – 1 = (2 EXP 6) – 1 = 63 expressions as such if one assumes the previous five dimensions of will.

 

 

In all, there are (2 EXP n) – 1 = (2 EXP 6) – 1 = 63 expressions as such if one assumes the previous five dimensions of will.

 

Assuming that each of the above function f(A is perfectly continuous, the number of forms that the general emotion function, f(A), can have is plausibly equal to П(1,62)R where R is the number of real numbers.

 

Assuming that each of the above functions f(A) is super-continuous at the level of 0/(Aleph 0) where Aleph 0 is the number of integers, the number of forms that the general emotion function, f(A), can have is plausibly equal to П(1,62)[R x (Aleph 0)] where R is the number of real numbers.

 

Assuming that each of the above functions f(A) is super-continuous at the level of 0/(Aleph 1) where Aleph 1 is the number of real numbers according to the Continuum Hypotheses, the number of forms that the general affect function, f(A), can have is plausibly equal to П(1,62)[R x (Aleph 1)] where R is the number of real numbers.

 

Assuming that each of the above functions f(A) is super-continuous at the level of 0/(Aleph 2) where Aleph 2 is is greater than Aleph 1 by a factor of infinity (the exact details of this infinity of which are a little more involve than the latter simple statement), the number of forms that the general affect function, f(A), can have is plausibly equal to П(1,62)[R x (Aleph 2)] where R is the number of real numbers.

 

Assuming that each of the above functions f(A) is super-continuous at the level of 0/(Aleph 3) where Aleph 3 is is greater than Aleph 2 by a factor of infinity (the exact details of this infinity of which are a little more involve than the latter simple statement), the number of forms that the general affect function, f(A), can have is plausibly equal to П(1,62)[R x (Aleph 3)] where R is the number of real numbers.

 

… and so on ad infinitum to, through, and beyond the following product series, П(1,62)[R x (Aleph 4)],   П(1,62)[R x (Aleph 5)],  П(1,62)[R x (Aleph 6)],…,  П(1,62)[R x (Aleph Ω)], …,  П(1,62)[R x (Aleph (Aleph 0))], …, П(1,62)[R x (Aleph (Aleph 1))], …, П(1,62)[R x (Aleph (Aleph 2))], … , П(1,62)[R x (Aleph (Aleph Ω))], …, П(1,62)[R x (Aleph (Aleph (Aleph 0)))] and so on perhaps in an ever lasting series even a  the latter level of abstraction.

 

 

We can summarize all of these combinations as follows in compact symbolism that is intuitively clear to follow:

 

 

A = A(t and/or w and/or a and/or i and/or m)

 

 

We can express A as a function of time as follows: A(T) =  A[(t and/or w and/or a and/or i and/or m),(T)] or perhaps the following notation can be more appropriate in certain circumstances.

 

 

A(T) = A{[t(T)] and/or [w(T)] and/or [a(T)] and/or [i(T)] and/or [m(T)]}.

 

 

Thus, the following first order derivatives of affect with respect to time are possible.

 

 

dA(t)/dT, dA(w)/dT, dA(a)/dT, dA(i)/dT, dA(m)/dT, dA(t,w)/dT, dA(t,a)/dT, dA(t,i)/dT, dA(t,m)/dT, dA(w,a)/dT, dA(w,i)/dT, dA(w,m)/dT, dA(a,i)/dT, dA(a,m)/dT, dA(i,m)/dT, dA(t,w,a)/dT, dA(t,w,i)/dT, dA(t,w,m)/dT, dA(t,a,i)/dT, dA(t,a,m)/dT, dA(t,i,m)/dT, dA(w,a,i)/dT, dA(w,a,m)/dT, dA(w,i,m)/dT, dA(a,i,m)/dT, dA(t,w,a,i)/dT, dA(t,w,a,m)/dT, dA(t,w,i,m)/dT, dA(t,a,i,m)/dT, dA(w,a,i,m)/dT, dA(t,w,a,i,m)/dT.

 

 

Or more succinctly,  dA/dT = dA(t and/or w and/or a and/or i and/or m)/dT

 

 

Or perhaps dA(T)/dT =d A{[t(T)] and/or [w(T)] and/or [a(T)] and/or [i(T)] and/or [m(T)]}/dT.

 

 

Likewise, we can take the second time derivatives of  A as follows:

 

 

 

d[dA(t)/dT]/dT, d[dA(w)/dT]/dT, d[dA(a)/dT]/dT, d[dA(i)/dT]/dT, d[dA(m)/dT]/dT, d[dA(t,w)/dT]/dT, d[dA(t,a)/dT]/dT, d[dA(t,i)/dT]/dT, d[dA(t,m)/dT]/dT, d[dA(w,a)/dT]/dT, d[dA(w,i)/dT]/dT, d[dA(w,m)/dT]/dT, d[dA(a,i)/dT]/dT, d[dA(a,m)/dT]/dT, d[dA(i,m)/dT/dT, d[dA(t,w,a)/dT]/dT, d[dA(t,w,i)/dT]/dT, d[dA(t,w,m)/dT]/dT, d[dA(t,a,i)/dT]/dT, d[dA(t,a,m)/dT]/dT,  d[dA(t,i,m)/dT]/dT, d[dA(w,a,i)/dT]/dT, d[dA(w,a,m)/dT]/dT, d[dA(w,i,m)/dT]/dT, d[dA(a,i,m)/dT]/dT, d[dA(t,w,a,i)/dT]/dT, d[dA(t,w,a,m)/dT/dT, d[dA(t,w,i,m)/dT]/dT, d[dA(t,a,i,m)/dT]/dT, d[dA(w,a,i,m)/dT]/dT, d[dA(t,w,a,i,m)/dT]/dT..

 

 

or more succinctly, as d(dA/dT)/dT = d[d A(t and/or w and/or a and/or i and/or m)/dT]/dT = A2

 

 

or as

 

 

d[dA(T)/dT]/dT  = d[d A{[t(T)] and/or [w(T)] and/or [a(T)] and/or [i(T)] and/or [m(T)]}/dT]/dT = A2.

 

 

 

Likewise, we can take the third time derivatives of  A as follows:

 

 

 

d[d[dA(t)/dT]/dT]/dT, d[d[dA(w)/dT]/dT]/dT, d[d[dA(a)/dT]/dT]/dT, d[d[dA(i)/dT]/dT]/dT, d[d[dA(m)/dT]/dT]/dT, d[d[dA(t,w)/dT]/dT]/dT, d[d[dA(t,a)/dT]/dT]/dT, d[d[dA(t,i)/dT]/dT]/dT, d[d[dA(t,m)/dT]/dT]/dT, d[d[dA(w,a)/dT]/dT]/dT, d[d[dA(w,i)/dT]/dT]/dT, d[d[dA(w,m)/dT]/dT]/dT, d[d[dA(a,i)/dT]/dT]/dT, d[d[dA(a,m)/dT]/dT]/dT, d[d[dA(i,m)/dT/dT]/dT, d[d[dA(t,w,a)/dT]/dT]/dT, d[d[dA(t,w,i)/dT]/dT]/dT, d[d[dA(t,w,m)/dT]/dT]/dT, d[d[dA(t,a,i)/dT]/dT]/dT, d[d[dA(t,a,m)/dT]/dT]/dT,  d[d[dA(t,i,m)/dT]/dT]/dT, d[d[dA(w,a,i)/dT]/dT]/dT, d[d[dA(w,a,m)/dT]/dT]/dT, d[d[dA(w,i,m)/dT]/dT]/dT, d[d[dA(a,i,m)/dT]/dT]/dT, d[d[dA(t,w,a,i)/dT]/dT]/dT, d[d[dA(t,w,a,m)/dT/dT]/dT, d[d[dA(t,w,i,m)/dT]/dT]/dT, d[d[dA(t,a,i,m)/dT]/dT]/dT, d[d[dA(w,a,i,m)/dT]/dT]/dT, d[d[dA(t,w,a,i,m)/dT]/dT]/dT.

 

 

or more succinctly, as d[d(dA/dT)/dT]/dT = d[d[d A(t and/or w and/or a and/or i and/or m)/dT]/dT]/dT = A3

 

 

or as

 

 

d[d[dA(T)/dT]/dT]/dT  = d[d[d A{[t(T)] and/or [w(T)] and/or [a(T)] and/or [i(T)] and/or [m(T)]}/dT]/dT]/dT = A3.

 

 

We can also form the expressions;

 

 

d[d[f(A)]/dT]/dT = d{d [A[t(T)]]/dT and/or d[A[w(T)]]/dT and/or d[A[a(T)]]/dT and/or d[A[i(T)]]/dT and/or d[A[m(T)]]/dT}/dT  = f(A)2

 

 

and

 

 

d[d[d[f(A)]/dT]/dT]/dT = d{d{ d [A[t(T)]]/dT and/or d[A[w(T)]]/dT and/or d[A[a(T)]]/dT and/or d[A[i(T)]]/dT and/or d[A[m(T)]]/dT}/dT}/dT  = f(A)3A, where A stands for type A differentiation which is not to be confused with the meaning of so-called Type A personality as A is used as an ordinal in a totally different context here.

 

 

and

 

 

d[d[d[f(A)]/dT]/dT]/dT = d{d[d [A[t(T)]]/dT]/dT  and/or d[d [A[w(T)]]/dT]/dT  and/or d[d [A[a(T)]]/dT]/dT  and/or d[d [A[i(T)]]/dT]/dT  and/or d[d [A[m(T)]]/dT]/dT }/dT = f(A)3B, where B stands for type B differentiation which is not to be confused with the meaning of a  so-called Type  B personality as B is used as an ordinal in a totally different context here .

 

 

In fact, one can form yet higher order derivatives of affects with respect to time as follows.

 

 

A5 = d A4/dT = d[dA3/dT]/dT

 

 

 

A5 = d A4/dT =  d[d[d[d[d A{[t(T)] and/or [w(T)] and/or [a(T)] and/or [i(T)] and/or [m(T)]}/dT]/dT]/dT]/dT]/dT.

 

 

 

f(A)5A = d[f(A)4A]/dT = d[d [f(A)3A]/dT]/dT =  d{d{d{d{ d [A[t(T)]]/dT and/or d[A[w(T)]]/dT and/or d[A[a(T)]]/dT and/or d[A[i(T)]]/dT and/or d[A[m(T)]]/dT}/dT}/dT]/dT]/dT

 

 

 

 

A6 = d A5/dT = d[d A4/dT]/dT = d[d[dA3/dT]/dT]/dT

 

 

 

A6 = dA5/dT = d[d[d[d[d[d A{[t(T)] and/or [w(T)] and/or [a(T)] and/or [i(T)] and/or [m(T)]}/dT]/dT]/dT]/dT]/dT]/dT

 

 

 

f(A)6A = d[f(A)5A]/dT = d{ d{d{d{d{ d [A[t(T)]]/dT and/or d[A[w(T)]]/dT and/or d[A[a(T)]]/dT and/or d[A[i(T)]]/dT and/or d[A[m(T)]]/dT}/dT}/dT]/dT]/dT]/dT

 

 

 

 

A7 = dA6/dT

 

f(A)7A = d[f(A)6A]/dT

 

 

A8 = d A7/dT

 

f(A)8A = d[f(A)7A]/dT

 

 

 

A9 = d A8/dT

 

f(A)9A = d[f(A)8A]/dT

 

 

A10…, A11…, A12 … etc.

 

 

Anyone for A ensemble, or A infinity scrapper, or A (Aleph 0), or A(Aleph 1), or A(Aleph 2), or how about A Aleph (Aleph 0), or A Aleph (Aleph 1) , or A Aleph (Aleph 2), or even A Aleph (Aleph (Aleph 0)), or A Aleph (Aleph (Aleph 1)), or A Aleph (Aleph (Aleph 2)), and so on?

 

Thus, for the set of the sets of derivatives of A1 through A(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}.

 

For the set of the sets of derivatives of A1 through A(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)},…, {П(0,31)[R]}_{(Aleph 1)}.

 

For the set of the sets of derivatives of A1 through A(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}.

 

For the set of the sets of derivatives of A1 through A(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the derivative states in the set of the sets of derivatives of A1 through A(Aleph 0) is plausible equal to:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of A1 through A(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of A1 through A(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}}}.

 

For the set of the sets of derivatives of A1 through A(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous A(Aleph 0) derivative space at the level of 0/(Aleph 0), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of A1 through A(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of A1 through A(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of A1 through A(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of A1 through A(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of A1 through A(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of A1 through A(Aleph 1), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of A1 through  A(Aleph 2), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of A1 through A(Aleph 3), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous A(Aleph 0) derivative space at the level of 0/(Aleph 1), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of A1 through A(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of A1 through A(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of A1 through A(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of A1 through  A(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations  for the set of the sets of derivatives of A1 through A(Aleph 0) is plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of A1 through A(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of A1 through A(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of A1 through A(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

 

For super-continuous A(Aleph 0) derivative space at the level of 0/(Aleph 2), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of A1 through A(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of A1 through A(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of A1 through A(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of A1 through A(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of A1 through A(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of A1 through A(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of A1 through A(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of A1 through A(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

Similar series can be developed for super-continuity at any applicable level such as 0/(Aleph 3), 0/(Aleph 4), 0/(Aleph 5),…, 0/(Aleph Ω), 0/(Aleph (Aleph 0)), …, 0/(Aleph (Aleph 1)), …, 0/(Aleph (Aleph 2)), …, 0/(Aleph (Aleph 3)),…, 0/(Aleph (Aleph Ω)),…, 0/(Aleph (Aleph (Aleph 0))), …, 0/(Aleph (Aleph (Aleph 1))),…, 0/(Aleph (Aleph (Aleph 2))),…, 0/(Aleph (Aleph (Aleph 3))),…, 0/(Aleph (Aleph  (Aleph Ω))), …

 

An so-on ad infinitum.

 

 

In addition to these numerical functions of A as functions of summation series of product series functions, in order to really appreciate the enourmous complexity of the human soul in terms of its potential to evolve and be differentiated from all other souls in its characteristics, we would need to consider how every single category and even every single species of affect of the form A can very. Since there may exist an arbitrarily high infinite number species of A, the number of numerical functions of A  is utterly beyond recogning. I will cover such notions in terms of mathematical notation in yet another series of articles I will write on this general concept.

 

 

Perhaps these numbers are applicable when one considers that the human soul, in its accidental form and perhaps even in its substantial form stores all experience and other psychodynamics based phenomenon. Every experience adds to the accidental form of the human soul and this includes the souls of all those still alive on Earth, all those in Purgatory, all those in Heaven, all those in Hell, and all those in any Limbo.

Since the human soul can grow without limit in terms of its psychodynamic time –flow world line, such a consideration offers another mechanism where the number of derivative states, combinations of derivative states, and even super-continuity of the derivative state space can grow forever.

 

Folks, for those of you who might balk at me for including literally all souls in the above consideration, including the souls in Hell, as well as bodily extraterrestrial souls and the souls of so-called bodily ultraterrestials sometimes referred to as etherians in the new age UFO buff culture, my reply is that we simply do not understand the full scope of GOD’s Divine Economy. We may never fully comprehend the scope of the Divine Economy because such an utterly eternal scheme, is, well, eternal and never ending.

 

 

We can also express affect qualitatively, statistically, and perhaps with the use of some forms of real analyses as a derivative with respect to emotion or with respect to E.

 

Given that A(E) =  A(t and/or w and/or a and/or i and/or m), the following first order derivatives of affect  with respect to emotion are possible.

 

 

dA(t)/dE, dA(w)/dE, dA(a)/dE, dA(i)/dE, dA(m)/dE, dA(t,w)/dE, dA(t,a)/dE, dA(t,i)/dE, dA(t,m)/dE, dA(w,a)/dE, dA(w,i)/dE, dA(w,m)/dE, dA(a,i)/dE, dA(a,m)/dE, dA(i,m)/dE, dA(t,w,a)/dE, dA(t,w,i)/dE, dA(t,w,m)/dE, dA(t,a,i)/dE, dA(t,a,m)/dE, dA(t,i,m)/dE, dA(w,a,i)/dE, dA(w,a,m)/dE, dA(w,i,m)/dE, dA(a,i,m)/dE, dA(t,w,a,i)/dE, dA(t,w,a,m)/dE, dA(t,w,i,m)/dE, dA(t,a,i,m)/dE, dA(w,a,i,m)/dE, dA(t,w,a,i,m)/dE.

 

 

Or more succinctly,  dA/dE = dA(t and/or w and/or a and/or i and/or m)/dE

 

 

Or perhaps dA(e)/dE =d A{[t(e)] and/or [w(e)] and/or [a(e)] and/or [i(e)] and/or [m(e)]}/dE.

 

 

Likewise, we can take the second emotion derivatives of  A as follows:

 

 

 

d[dA(t)/dE]/dE, d[dA(w)/dE]/dE, d[dA(a)/dE]/dE, d[dA(i)/dE]/dE, d[dA(m)/dE]/dE, d[dA(t,w)/dE]/dE, d[dA(t,a)/dE]/dE, d[dA(t,i)/dE]/dE, d[dA(t,m)/dE]/dE, d[dA(w,a)/dE]/dE, d[dA(w,i)/dE]/dE, d[dA(w,m)/dE]/dE, d[dA(a,i)/dE]/dE, d[dA(a,m)/dE]/dE, d[dA(i,m)/dE/dE, d[dA(t,w,a)/dE]/dE, d[dA(t,w,i)/dE]/dE, d[dA(t,w,m)/dE]/dE, d[dA(t,a,i)/dE]/dE, d[dA(t,a,m)/dE]/dE,  d[dA(t,i,m)/dE]/dE, d[dA(w,a,i)/dE]/dE, d[dA(w,a,m)/dE]/dE, d[dA(w,i,m)/dE]/dE, d[dA(a,i,m)/dE]/dE, d[dA(t,w,a,i)/dE]/dE, d[dA(t,w,a,m)/dE/dE, d[dA(t,w,i,m)/dE]/dE, d[dA(t,a,i,m)/dE]/dE, d[dA(w,a,i,m)/dE]/dE, d[dA(t,w,a,i,m)/dE]/dE..

 

 

or more succinctly, as d(dA/dE)/dE = d[d A(t and/or w and/or a and/or i and/or m)/dE]/dE = Ae2

 

 

or as

 

 

d[dA(e)/dE]/dE  = d[d A{[t(e)] and/or [w(e)] and/or [a(e)] and/or [i(e)] and/or [m(e)]}/dE]/dE = Ae2.

 

 

 

Likewise, we can take the third emotion derivatives of  A as follows:

 

 

 

d[d[dA(t)/dE]/dE]/dE, d[d[dA(w)/dE]/dE]/dE, d[d[dA(a)/dE]/dE]/dE, d[d[dA(i)/dE]/dE]/dE, d[d[dA(m)/dE]/dE]/dE, d[d[dA(t,w)/dE]/dE]/dE, d[d[dA(t,a)/dE]/dE]/dE, d[d[dA(t,i)/dE]/dE]/dE, d[d[dA(t,m)/dE]/dE]/dE, d[d[dA(w,a)/dE]/dE]/dE, d[d[dA(w,i)/dE]/dE]/dE, d[d[dA(w,m)/dE]/dE]/dE, d[d[dA(a,i)/dE]/dE]/dE, d[d[dA(a,m)/dE]/dE]/dE, d[d[dA(i,m)/dE/dE]/dE, d[d[dA(t,w,a)/dE]/dE]/dE, d[d[dA(t,w,i)/dE]/dE]/dE, d[d[dA(t,w,m)/dE]/dE]/dE, d[d[dA(t,a,i)/dE]/dE]/dE, d[d[dA(t,a,m)/dE]/dE]/dE,  d[d[dA(t,i,m)/dE]/dE]/dE, d[d[dA(w,a,i)/dE]/dE]/dE, d[d[dA(w,a,m)/dE]/dE]/dE, d[d[dA(w,i,m)/dE]/dE]/dE, d[d[dA(a,i,m)/dE]/dE]/dE, d[d[dA(t,w,a,i)/dE]/dE]/dE, d[d[dA(t,w,a,m)/dE/dE]/dE, d[d[dA(t,w,i,m)/dE]/dE]/dE, d[d[dA(t,a,i,m)/dE]/dE]/dE, d[d[dA(w,a,i,m)/dE]/dE]/dE, d[d[dA(t,w,a,i,m)/dE]/dE]/dE.

 

 

or more succinctly, as d[d(dA/dE)/dE]/dE = d[d[d A(t and/or w and/or a and/or i and/or m)/dE]/dE]/dE = Ae3

 

 

or as

 

 

d[d[dA(e)/dE]/dE]/dE  = d[d[d A{[t(e)] and/or [w(e)] and/or [a(e)] and/or [i(e)] and/or [m(e)]}/dE]/dE]/dE = Ae3.

 

 

We can also form the expressions;

 

 

d[d[f(A)]/dE]/dE = d{d [A[t(e)]]/dE and/or d[A[w(e)]]/dE and/or d[A[a(e)]]/dE and/or d[A[i(e)]]/dE and/or d[A[m(e)]]/dE}/dE  = f(Ae)2

 

 

and

 

 

d[d[d[f(A)]/dE]/dE]/dE = d{d{ d [A[t(e)]]/dE and/or d[A[w(e)]]/dE and/or d[A[a(e)]]/dE and/or d[A[i(e)]]/dE and/or d[A[m(e)]]/dE}/dE}/dE  = f(Ae)3A, where A stands for type A differentiation which is not to be confused with the meaning of so-called Type A personality as A is used as an ordinal in a totally different context here.

 

 

and

 

 

d[d[d[f(A)]/dE]/dE]/dE = d{d[d [A[t(e)]]/dE]/dE  and/or d[d [A[w(e)]]/dE]/dE  and/or d[d [A[a(e)]]/dE]/dE  and/or d[d [A[i(e)]]/dE]/dE  and/or d[d [A[m(e)]]/dE]/dE }/dE = f(At)3B, where B stands for type B differentiation which is not to be confused with the meaning of so-called Type  B personality as B is used as an ordinal in a totally different context here .

 

 

In fact, one can form yet higher order derivatives of affects with respect to emotion as follows.

 

 

Ae5 = d Ae4/dE = d[dAe3/dE]/dE

 

 

 

Ae5 = dAe4/dE =  d[d[d[d[d A{[t(e)] and/or [w(e)] and/or [a(e)] and/or [i(e)] and/or [m(e)]}/dE]/dE]/dE]/dE]/dE.

 

 

 

f(Ae)5A = d[f(Ae)4A]/dE = d[d [f(Ae)3A]/dE]/dE =  d{d{d{d{ d [A[t(e)]]/dE and/or d[A[w(e)]]/dE and/or d[A[a(e)]]/dE and/or d[A[i(e)]]/dE and/or d[A[m(e)]]/dE}/dE}/dE]/dE]/dE

 

 

 

 

Ae6 = d Ae5/dE = d[d Ae4/dE]/dE = d[d[dAe3/dE]/dE]/dE

 

 

 

Ae6 = dAe5/dE = d[d[d[d[d[d A{[t(e)] and/or [w(e)] and/or [a(e)] and/or [i(e)] and/or [m(e)]}/dE]/dE]/dE]/dE]/dE]/dE

 

 

 

f(Ae)6A = d[f(Ae)5A]/dE = d{ d{d{d{d{ d [A[t(e)]]/dE and/or d[A[w(e)]]/dE and/or d[A[a(e)]]/dE and/or d[A[i(e)]]/dE and/or d[A[m(e)]]/dE}/dE}/dE]/dE]/dE]/dE

 

 

 

 

Ae7 = dAe6/dE

 

f(Ae)7A = d[f(Ae)6A]/dE

 

 

Ae8 = d Ae7/dE

 

f(Ae)8A = d[f(Ae)7A]/dE

 

 

 

Ae9 = d Ae8/dE

 

f(Ae)9A = d[f(Ae)8A]/dE

 

 

Ae10…, Ae11…, Ae12 … etc.

 

 

Anyone for Ae ensemble, or Ae infinity scrapper, or Ae (Aleph 0), or Ae(Aleph 1), or Ae(Aleph 2), or how about Ae Aleph (Aleph 0), or Ae Aleph (Aleph 1) , or Ae Aleph (Aleph 2), or even Ae Aleph (Aleph (Aleph 0)), or Ae Aleph (Aleph (Aleph 1)), or Ae Aleph (Aleph (Aleph 2)), and so on?

 

 

Thus, for the set of the sets of derivatives of Ae1 through Ae(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ae1 through Ae(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)},…, {П(0,31)[R]}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ae1 through Ae(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ae1 through Ae(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the derivative states in the set of the sets of derivatives of Ae1 through Ae(Aleph 0) is plausible equal to:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ae1 through Ae(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ae1 through Ae(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}}}.

 

For the set of the sets of derivatives of Ae1 through Ae(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Ae(Aleph 0) derivative space at the level of 0/(Aleph 0), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Ae1 through Ae(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ae1 through Ae(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ae1 through Ae(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ae1 through Ae(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Ae1 through Ae(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ae1 through Ae(Aleph 1), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Ae1 through  Ae(Aleph 2), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Ae1 through Ae(Aleph 3), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Ae(Aleph 0) derivative space at the level of 0/(Aleph 1), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Ae1 through Ae(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ae1 through Ae(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ae1 through Ae(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ae1 through  Ae(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations  for the set of the sets of derivatives of Ae1 through Ae(Aleph 0) is plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ae1 through Ae(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Ae1 through Ae(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Ae1 through Ae(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

 

For super-continuous Ae(Aleph 0) derivative space at the level of 0/(Aleph 2), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Ae1 through Ae(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ae1 through Ae(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ae1 through Ae(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ae1 through Ae(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Ae1 through Ae(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ae1 through Ae(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Ae1 through Ae(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Ae1 through Ae(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

Similar series can be developed for super-continuity at any applicable level such as 0/(Aleph 3), 0/(Aleph 4), 0/(Aleph 5),…, 0/(Aleph Ω), 0/(Aleph (Aleph 0)), …, 0/(Aleph (Aleph 1)), …, 0/(Aleph (Aleph 2)), …, 0/(Aleph (Aleph 3)),…, 0/(Aleph (Aleph Ω)),…, 0/(Aleph (Aleph (Aleph 0))), …, 0/(Aleph (Aleph (Aleph 1))),…, 0/(Aleph (Aleph (Aleph 2))),…, 0/(Aleph (Aleph (Aleph 3))),…, 0/(Aleph (Aleph  (Aleph Ω))), …

 

An so-on ad infinitum.

 

 

In addition to these numerical functions of Ae as functions of summation series of product series functions, in order to really appreciate the enourmous complexity of the human soul in terms of its potential to evolve and be differentiated from all other souls in its characteristics, we would need to consider how every single category and even every single species of affect  of the form Ae can very. Since there may exist an arbitrarily high infinite number species of Ae, the number numerical functions of Ae is utterly beyond recogning. I will cover such notions in terms of mathematical notation in yet another series of articles I will write on this general concept.

 

 

Perhaps these numbers are applicable when one considers that the human soul, in its accidental form and perhaps even in its substantial form stores all experience and other psychodynamics based phenomenon. Every experience adds to the accidental form of the human soul and this includes the souls of all those still alive on Earth, all those in Purgatory, all those in Heaven, all those in Hell, and all those in any Limbo.

Since the human soul can grow without limit in terms of its psychodynamic time –flow world line, such a consideration offers another mechanism where the number of derivative states, combinations of derivative states, and even super-continuity of the derivative state space can grow forever.

 

Folks, for those of you who might balk at me for including literally all souls in the above consideration, including the souls in Hell, as well as bodily extraterrestrial souls and the souls of so-called bodily ultraterrestials sometimes referred to as etherians in the new age UFO buff culture, my reply is that we simply do not understand the full scope of GOD’s Divine Economy. We may never fully comprehend the scope of the Divine Economy because such an utterly eternal scheme, is, well, eternal and never ending.

 

 

 

 

The general meaning of emotion derivatives of affect can be viewed as the manner in which the qualitative and/or quantitative aspects of affect as a function of affect very with emotion(s). The manner in which affects very with affect may be multi-affect dimensional wherein the dimensions of derivations can be multiple, and wherein the derivations can be taken in parallel, series parallel or serial manner The differentials can be partial or non-partial derivatives, or both partial and non-partial for a given computation.

 

In fact, since there is in theory, no limit to the numbers of qualitatively and quantitatively different affects, and perhaps no limit to the number of possible different types or classes of affects, wherein each person has his or her own unique affects, the number of affect dimensions that can effect affects is literally infinite, given the entirety of the set of created persons, and perhaps also literally infinite for each person as an individual, although we can not intellectually and intuitively understand this specific infinite number.

 

It is interesting to consider the ramifactions of being able to perform realistic calculations involving emotion derivatives of affect from a mathematical, theoretical, scientific,  and philosophical perspective.

 

Persons for which one or more nth order derivatives of affect with respect to emotion that have large absolute values would tend to have their affects highly influenced by affect, or at least for the affect under consideration with respect to the dimension of the specific affect type(s) or class(es) for which the differentiation(s) are performed. Perhaps a strong coupling between affect and emotion indicates a well integrated personality and commensurately, a high degree of affect capacity and a high degree of affect intelligence.

 

We would expect that disembodied human souls, ETI souls, and/or UTI souls in Heaven, Limbo, highly evolved bodily ETI persons, highly evolved UTI persons, and angels to have affect of all kinds and intensities which are highly subject to affect.

 

 

We can also consider two dimensional nth ordered derivatives of affect with respect to emotion and time, or with respect to t and T, respectively.

 

Given that A[(e)(T)] =  A[(t and/or w and/or a and/or i and/or m)(e)(T)], the following first order two dimensional derivatives of affect with respect to emotion and Time are possible.

 

 

d[dA[(t)(T)]/dE]/dT, d[dA[(w)(T)]/dE]/dT, d[dA[(a)(T)]/dE]/dT, d[dA[(i)(T)]/dE]/dT, d[dA[(m)(T)]/dE]/dT, d[dA[(t,w)(T)]/dE]/dT, d[dA[(t,a)(T)]/dE]/dT, d[dA[(t,i)(T)]/dE]/dT, d[dA[(t,m)(T)]/dE]/dT, d[dA[(w,a)(T)]/dE]/dT, d[dA[(w,i)(T)]/dE]/dT, d[dA[(w,m)(T)]/dE]/dT, d[dA[(a,i)(T)]/dE]/dT, d[dA[(a,m)(T)]/dE]/dT, d[dA[(i,m)(T)]/dE]/dT, d[dA[(t,w,a)(T)]/dE]/dT, d[dA[(t,w,i)(T)]/dE]/dT, d[dA[(t,w,m)(T)]/dE]/dT, d[dA[(t,a,i)(T)]/dE]/dT, d[dA[(t,a,m)(T)]/dE]/dT, d[dA[(t,i,m)(T)]/dE]/dT, d[dA[(w,a,i)(T)]/dE]/dT, d[dA[(w,a,m)(T)]/dE]/dT, d[dA[(w,i,m)(T)]/dE]/dT, d[dA[(a,i,m)(T)]/dE]/dT, d[dA[(t,w,a,i)(T)]/dE]/dT, d[dA[(t,w,a,m)(T)]/dE]/dT, d[dA[(t,w,i,m)(T)]/dE]/dT, d[dA[(t,a,i,m)(T)]/dE]/dT, d[dA[(w,a,i,m)(T)]/dE]/dT, d[dA[(t,w,a,i,m)(T)]/dE]/dT.

 

 

Or more succinctly,  d[dA(T)/dE]/dT = d[dA[(T)(t and/or w and/or a and/or i and/or m)]/dE]/dT

 

or

 

d[dA(T)/dT]/dE = d[dA[(T)(t and/or w and/or a and/or i and/or m)]/dT]/dE

 

 

 

 

 

Or perhaps d[d A[(e)(T)]/dE]/dT  = d[d A [{[t(e)] and/or [w(e)] and/or [a(e)] and/or [i(e)] and/or [m(e)]}(T)]/dE]/dT

 

or

 

Or perhaps d[d A[(e)(T)]/dT]/dE  = d[d A [{[t(e)] and/or [w(e)] and/or [a(e)] and/or [i(e)] and/or [m(e)]}(T)]/dT]/dE

 

 

 

Likewise, we can take the second dual dimensioned affect-time derivatives of  A as follows:

 

d[d[d[dA[(e)(T)]/dE]/dT]/dE]/dT, d[d[d[dA[(w)(T)]/dE]/dT]/dE]/dT, d[d[d[dA[(a)(T)]/dE]/dT]/dE]/dT, d[d[d[dA[(i)(T)]/dE]/dT]/dE]/dT, d[d[d[dA[(m)(T)]/dE]/dT]/dE]/dT, d[d[d[dA[(t,w)(T)]/dE]/dT]/dE]/dT, d[d[d[dA[(t,a)(T)]/dE]/dT]/dE]/dT, d[d[d[dA[(t,i)(T)]/dE]/dT]/dE]/dT, d[d[d[dA[(t,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dA[(w,a)(T)]/dE]/dT]/dE]/dT, d[d[d[dA[(w,i)(T)]/dE]/dT]/dE]/dT, d[d[d[dA[(w,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dA[(a,i)(T)]/dE]/dT]/dE]/dT, d[d[d[dA[(a,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dA[(i,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dA[(t,w,a)(T)]/dE]/dT]/dE]/dT, d[d[d[dA[(t,w,i)(T)]/dE]/dT]/dE]/dT, d[d[d[dA[(t,w,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dA[(t,a,i)(T)]/dE]/dT]/dE]/dT, d[d[d[dA[(t,a,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dA[(t,i,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dA[(w,a,i)(T)]/dE]/dT]/dE]/dT, d[d[d[dA[(w,a,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dA[(w,i,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dA[(a,i,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dA[(t,w,a,i)(T)]/dE]/dT]/dE]/dT, d[d[d[dA[(t,w,a,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dA[(t,w,i,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dA[(t,a,i,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dA[(w,a,i,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dA[(t,w,a,i,m)(T)]/dE]/dT]/dE]/dT.

 

or as:

 

 

 

d[d[d[dA[(t)(T)]/dE]/dT]/dT]/dE, d[d[d[dA[(w)(T)]/dE]/dT]/dT]/dE, d[d[d[dA[(a)(T)]/dE]/dT]/dT]/dE, d[d[d[dA[(i)(T)]/dE]/dT]/dT]/dE, d[d[d[dA[(m)(T)]/dE]/dT]/dT]/dE, d[d[d[dA[(t,w)(T)]/dE]/dT]/dT]/dE, d[d[d[dA[(t,a)(T)]/dE]/dT]/dT]/dE, d[d[d[dA[(t,i)(T)]/dE]/dT]/dT]/dE, d[d[d[dA[(t,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dA[(w,a)(T)]/dE]/dT]/dT]/dE, d[d[d[dA[(w,i)(T)]/dE]/dT]/dT]/dE, d[d[d[dA[(w,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dA[(a,i)(T)]/dE]/dT]/dT]/dE, d[d[d[dA[(a,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dA[(i,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dA[(t,w,a)(T)]/dE]/dT]/dT]/dE, d[d[d[dA[(t,w,i)(T)]/dE]/dT]/dT]/dE, d[d[d[dA[(t,w,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dA[(t,a,i)(T)]/dE]/dT]/dT]/dE, d[d[d[dA[(t,a,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dA[(t,i,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dA[(w,a,i)(T)]/dE]/dT]/dT]/dE, d[d[d[dA[(w,a,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dA[(w,i,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dA[(a,i,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dA[(t,w,a,i)(T)]/dE]/dT]/dT]/dE, d[d[d[dA[(t,w,a,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dA[(t,w,i,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dA[(t,a,i,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dA[(w,a,i,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dA[(t,w,a,i,m)(T)]/dE]/dT]/dT]/dE.

 

or as:

 

d[d[d[dA[(t)(T)]/dT]/dE]/dE]/dT, d[d[d[dA[(w)(T)]/dT]/dE]/dE]/dT, d[d[d[dA[(a)(T)]/dT]/dE]/dE]/dT, d[d[d[dA[(i)(T)]/dT]/dE]/dE]/dT, d[d[d[dA[(m)(T)]/dT]/dE]/dE]/dT, d[d[d[dA[(t,w)(T)]/dT]/dE]/dE]/dT, d[d[d[dA[(t,a)(T)]/dT]/dE]/dE]/dT, d[d[d[dA[(t,i)(T)]/dT]/dE]/dE]/dT, d[d[d[dA[(t,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dA[(w,a)(T)]/dT]/dE]/dE]/dT, d[d[d[dA[(w,i)(T)]/dT]/dE]/dE]/dT, d[d[d[dA[(w,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dA[(a,i)(T)]/dT]/dE]/dE]/dT, d[d[d[dA[(a,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dA[(i,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dA[(t,w,a)(T)]/dT]/dE]/dE]/dT, d[d[d[dA[(t,w,i)(T)]/dT]/dE]/dE]/dT, d[d[d[dA[(t,w,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dA[(t,a,i)(T)]/dT]/dE]/dE]/dT, d[d[d[dA[(t,a,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dA[(t,i,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dA[(w,a,i)(T)]/dT]/dE]/dE]/dT, d[d[d[dA[(w,a,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dA[(w,i,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dA[(a,i,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dA[(t,w,a,i)(T)]/dT]/dE]/dE]/dT, d[d[d[dA[(t,w,a,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dA[(t,w,i,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dA[(t,a,i,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dA[(w,a,i,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dA[(t,w,a,i,m)(T)]/dT]/dE]/dE]/dT.

 

 

or as;

 

 

 

 

d[d[d[dA(t)/dE]/dE]/dT]/dT, d[d[d[dA(w)/dE]/dE]/dT]/dT, d[d[d[dA(a)/dE]/dE]/dT]/dT, d[d[d[dA(i)/dE]/dE]/dT]/dT, d[d[d[dA(m)/dE]/dE]/dT]/dT, d[d[d[dA(t,w)/dE]/dE]/dT]/dT, d[d[d[dA(t,a)/dE]/dE]/dT]/dT, d[d[d[dA(t,i)/dE]/dE]/dT]/dT, d[d[d[dA(t,m)/dE]/dE]/dT]/dT, d[d[d[dA(w,a)/dE]/dE]/dT]/dT, d[d[d[dA(w,i)/dE]/dE]/dT]/dT, d[d[d[dA(w,m)/dE]/dE]/dT]/dT, d[d[d[dA(a,i)/dE]/dE]/dT]/dT, d[d[d[dA(a,m)/dE]/dE]/dT]/dT, d[d[d[dA(i,m)/dE]/dE]/dT]/dT, d[d[d[dA(t,w,a)/dE]/dE]/dT]/dT, d[d[d[dA(t,w,i)/dE]/dE]/dT]/dT, d[d[d[dA(t,w,m)/dE]/dE]/dT]/dT, d[d[d[dA(t,a,i)/dE]/dE]/dT]/dT, d[d[d[dA(t,a,m)/dE]/dE]/dT]/dT,  d[d[d[dA(t,i,m)/dE]/dE]/dT]/dT, d[d[d[dA(w,a,i)/dE]/dE]/dT]/dT, d[d[d[dA(w,a,m)/dE]/dE]/dT]/dT, d[d[d[dA(w,i,m)/dE]/dE]/dT]/dT, d[d[d[dA(a,i,m)/dE]/dE]/dT]/dT, d[d[d[dA(t,w,a,i)/dE]/dE]/dT]/dT, d[d[d[dA(t,w,a,m)/dE/dE, d[d[d[dA(t,w,i,m)/dE]/dE]/dT]/dT, d[d[d[dA(t,a,i,m)/dE]/dE]/dT]/dT, d[d[d[dA(w,a,i,m)/dE]/dE]/dT]/dT, d[d[d[dA(t,w,a,i,m)/dE]/dE]/dT]/dT..

 

or as:

 

d[d[d[dA(t)/dT]/dE]/dT]/dE, d[d[d[dA(w)/dT]/dE]/dT]/dE, d[d[d[dA(a)/dT]/dE]/dT]/dE, d[d[d[dA(i)/dT]/dE]/dT]/dE, d[d[d[dA(m)/dT]/dE]/dT]/dE, d[d[d[dA(t,w)/dT]/dE]/dT]/dE, d[d[d[dA(t,a)/dT]/dE]/dT]/dE, d[d[d[dA(t,i)/dT]/dE]/dT]/dE, d[d[d[dA(t,m)/dT]/dE]/dT]/dE, d[d[d[dA(w,a)/dT]/dE]/dT]/dE, d[d[d[dA(w,i)/dT]/dE]/dT]/dE, d[d[d[dA(w,m)/dT]/dE]/dT]/dE, d[d[d[dA(a,i)/dT]/dE]/dT]/dE, d[d[d[dA(a,m)/dT]/dE]/dT]/dE, d[d[d[dA(i,m)/ dT]/dE]/dT]/dE, d[d[d[dA(t,w,a)/dT]/dE]/dT]/dE, d[d[d[dA(t,w,i)/dT]/dE]/dT]/dE, d[d[d[dA(t,w,m)/dT]/dE]/dT]/dE, d[d[d[dA(t,a,i)/dT]/dE]/dT]/dE, d[d[d[dA(t,a,m)/dT]/dE]/dT]/dE,  d[d[d[dA(t,i,m)/dT]/dE]/dT]/dE, d[d[d[dA(w,a,i)/dT]/dE]/dT]/dE, d[d[d[dA(w,a,m)/dT]/dE]/dT]/dE, d[d[d[dA(w,i,m)/dT]/dE]/dT]/dE, d[d[d[dA(a,i,m)/dT]/dE]/dT]/dE, d[d[d[dA(t,w,a,i)/dT]/dE]/dT]/dE, d[d[d[dA(t,w,a,m)/dE/dE, d[d[d[dA(t,w,i,m)/dT]/dE]/dT]/dE, d[d[d[dA(t,a,i,m)/dT]/dE]/dT]/dE, d[d[d[dA(w,a,i,m)/dT]/dE]/dT]/dE, d[d[d[dA(t,w,a,i,m)/dT]/dE]/dT]/dE..

 

or as:

 

d[d[d[dA(t)/dT]/dT]/dE]/dE, d[d[d[dA(w)/dT]/dT]/dE]/dE, d[d[d[dA(a)/dT]/dT]/dE]/dE, d[d[d[dA(i)/dT]/dT]/dE]/dE, d[d[d[dA(m)/dT]/dT]/dE]/dE, d[d[d[dA(t,w)/dT]/dT]/dE]/dE, d[d[d[dA(t,a)/dT]/dT]/dE]/dE, d[d[d[dA(t,i)/dT]/dT]/dE]/dE, d[d[d[dA(t,m)/dT]/dT]/dE]/dE, d[d[d[dA(w,a)/dT]/dT]/dE]/dE, d[d[d[dA(w,i)/dT]/dT]/dE]/dE, d[d[d[dA(w,m)/dT]/dT]/dE]/dE, d[d[d[dA(a,i)/dT]/dT]/dE]/dE, d[d[d[dA(a,m)/ dT]/dT]/dE]/dE, d[d[d[dA(i,m)/ dT]/dT]/dE]/dE, d[d[d[dA(t,w,a)/dT]/dT]/dE]/dE, d[d[d[dA(t,w,i)/dT]/dT]/dE]/dE, d[d[d[dA(t,w,m)/dT]/dT]/dE]/dE, d[d[d[dA(t,a,i)/dT]/dT]/dE]/dE, d[d[d[dA(t,a,m)/dT]/dT]/dE]/dE,  d[d[d[dA(t,i,m)/dT]/dT]/dE]/dE, d[d[d[dA(w,a,i)/dT]/dT]/dE]/dE, d[d[d[dA(w,a,m)/dT]/dT]/dE]/dE, d[d[d[dA(w,i,m)/dT]/dT]/dE]/dE, d[d[d[dA(a,i,m)/dT]/dT]/dE]/dE, d[d[d[dA(t,w,a,i)/dT]/dT]/dE]/dE, d[d[d[dA(t,w,a,m)/dE/dE, d[d[d[dA(t,w,i,m)/dT]/dT]/dE]/dE, d[d[d[dA(t,a,i,m)/dT]/dT]/dE]/dE, d[d[d[dA(w,a,i,m)/dT]/dT]/dE]/dE, d[d[d[dA(t,w,a,i,m)/dT]/dT]/dE]/dE..

 

 

We can also take higher order duel dimensional derivatives of affect as a function of emotion and time but the symbolic expression of the set of such derivatives very soon becomes excessively lengthly to write and so these higher order derivatives as such are not mentioned here except to say that they would be computed in an analogous manner to the second order duel dimensional derivatives described above.

 

.

 

 

 

 

 

We can also express affect qualitatively, statistically, and perhaps with the use of some forms of real analyses as a derivative with respect to will or with respect to  w.

 

Given that A(w) =  A(t and/or w and/or a and/or i and/or m), the following first order derivatives of affect with respect to will are possible.

 

 

dA(t)/dw, dA(w)/dw, dA(a)/dw, dA(i)/dw, dA(m)/dw, dA(t,w)/dw, dA(t,a)/dw, dA(t,i)/dw, dA(t,m)/dw, dA(w,a)/dw, dA(w,i)/dw, dA(w,m)/dw, dA(a,i)/dw, dA(a,m)/dw, dA(i,m)/dw, dA(t,w,a)/dw, dA(t,w,i)/dw, dA(t,w,m)/dw, dA(t,a,i)/dw, dA(t,a,m)/dw, dA(t,i,m)/dw, dA(w,a,i)/dw, dA(w,a,m)/dw, dA(w,i,m)/dw, dA(a,i,m)/dw, dA(t,w,a,i)/dw, dA(t,w,a,m)/dw, dA(t,w,i,m)/dw, dA(t,a,i,m)/dw, dA(w,a,i,m)/dw, dA(t,w,a,i,m)/dw.

 

 

Or more succinctly,  dA/dw = dA(t and/or w and/or a and/or i and/or m)/dw

 

 

Or perhaps dA(w)/dw =d A{[t(w)] and/or [w(w)] and/or [a(w)] and/or [i(w)] and/or [m(w)]}/dw.

 

 

Likewise, we can take the second will derivatives of  A as follows:

 

 

 

d[dA(t)/dw]/dw, d[dA(w)/dw]/dw, d[dA(a)/dw]/dw, d[dA(i)/dw]/dw, d[dA(m)/dw]/dw, d[dA(t,w)/dw]/dw, d[dA(t,a)/dw]/dw, d[dA(t,i)/dw]/dw, d[dA(t,m)/dw]/dw, d[dA(w,a)/dw]/dw, d[dA(w,i)/dw]/dw, d[dA(w,m)/dw]/dw, d[dA(a,i)/dw]/dw, d[dA(a,m)/dw]/dw, d[dA(i,m)/dw/dw, d[dA(t,w,a)/dw]/dw, d[dA(t,w,i)/dw]/dw, d[dA(t,w,m)/dw]/dw, d[dA(t,a,i)/dw]/dw, d[dA(t,a,m)/dw]/dw,  d[dA(t,i,m)/dw]/dw, d[dA(w,a,i)/dw]/dw, d[dA(w,a,m)/dw]/dw, d[dA(w,i,m)/dw]/dw, d[dA(a,i,m)/dw]/dw, d[dA(t,w,a,i)/dw]/dw, d[dA(t,w,a,m)/dw/dw, d[dA(t,w,i,m)/dw]/dw, d[dA(t,a,i,m)/dw]/dw, d[dA(w,a,i,m)/dw]/dw, d[dA(t,w,a,i,m)/dw]/dw..

 

 

or more succinctly, as d(dA/dw)/dw = d[d A(t and/or w and/or a and/or i and/or m)/dw]/dw = Aw2

 

 

or as

 

 

d[dA(w)/dw]/dw  = d[d A{[t(w)] and/or [w(w)] and/or [a(w)] and/or [i(w)] and/or [m(w)]}/dw]/dw = Aw2.

 

 

 

Likewise, we can take the third will derivatives of  A as follows:

 

 

 

d[d[dA(t)/dw]/dw]/dw, d[d[dA(w)/dw]/dw]/dw, d[d[dA(a)/dw]/dw]/dw, d[d[dA(i)/dw]/dw]/dw, d[d[dA(m)/dw]/dw]/dw, d[d[dA(t,w)/dw]/dw]/dw, d[d[dA(t,a)/dw]/dw]/dw, d[d[dA(t,i)/dw]/dw]/dw, d[d[dA(t,m)/dw]/dw]/dw, d[d[dA(w,a)/dw]/dw]/dw, d[d[dA(w,i)/dw]/dw]/dw, d[d[dA(w,m)/dw]/dw]/dw, d[d[dA(a,i)/dw]/dw]/dw, d[d[dA(a,m)/dw]/dw]/dw, d[d[dA(i,m)/dw/dw]/dw, d[d[dA(t,w,a)/dw]/dw]/dw, d[d[dA(t,w,i)/dw]/dw]/dw, d[d[dA(t,w,m)/dw]/dw]/dw, d[d[dA(t,a,i)/dw]/dw]/dw, d[d[dA(t,a,m)/dw]/dw]/dw,  d[d[dA(t,i,m)/dw]/dw]/dw, d[d[dA(w,a,i)/dw]/dw]/dw, d[d[dA(w,a,m)/dw]/dw]/dw, d[d[dA(w,i,m)/dw]/dw]/dw, d[d[dA(a,i,m)/dw]/dw]/dw, d[d[dA(t,w,a,i)/dw]/dw]/dw, d[d[dA(t,w,a,m)/dw/dw]/dw, d[d[dA(t,w,i,m)/dw]/dw]/dw, d[d[dA(t,a,i,m)/dw]/dw]/dw, d[d[dA(w,a,i,m)/dw]/dw]/dw, d[d[dA(t,w,a,i,m)/dw]/dw]/dw.

 

 

or more succinctly, as d[d(dA/dw)/dw]/dw = d[d[d A(t and/or w and/or a and/or i and/or m)/dw]/dw]/dw = Aw3

 

 

or as

 

 

d[d[dA(w)/dw]/dw]/dw  = d[d[d A{[t(w)] and/or [w(w)] and/or [a(w)] and/or [i(w)] and/or [m(w)]}/dw]/dw]/dw = Aw3.

 

 

We can also form the expressions;

 

 

d[d[f(A)]/dw]/dw = d{d [A[t(w)]]/dw and/or d[A[w(w)]]/dw and/or d[A[a(w)]]/dw and/or d[A[i(w)]]/dw and/or d[A[m(w)]]/dw}/dw  = f(Aw)2

 

 

and

 

 

d[d[d[f(A)]/dw]/dw]/dw = d{d{ d [A[t(w)]]/dw and/or d[A[w(w)]]/dw and/or d[A[a(w)]]/dw and/or d[A[i(w)]]/dw and/or d[A[m(w)]]/dw}/dw}/dw  = f(Aw)3A, where A stands for type A differentiation which is not to be confused with the meaning of so-called Type A personality as A is used as an ordinal in a totally different context here.

 

 

and

 

 

d[d[d[f(A)]/dw]/dw]/dw = d{d[d [A[t(w)]]/dw]/dw  and/or d[d [A[w(w)]]/dw]/dw  and/or d[d [A[a(w)]]/dw]/dw  and/or d[d [A[i(w)]]/dw]/dw  and/or d[d [A[m(w)]]/dw]/dw }/dw = f(Aw)3B, where B stands for type B differentiation which is not to be confused with the meaning of so-called Type  B personality as B is used as an ordinal in a totally different context here .

 

 

In fact, one can form yet higher order derivatives of affect with respect to will as follows.

 

 

Aw5 = d Aw4/dw = d[dAw3/dw]/dw

 

 

 

Aw5 = dAw4/dw =  d[d[d[d[d A{[t(w)] and/or [w(w)] and/or [a(w)] and/or [i(w)] and/or [m(w)]}/dw]/dw]/dw]/dw]/dw.

 

 

 

f(Aw)5A = d[f(Aw)4A]/dw = d[d [f(Aw)3A]/dw]/dw =  d{d{d{d{ d [A[t(w)]]/dw and/or d[A[w(w)]]/dw and/or d[A[a(w)]]/dw and/or d[A[i(w)]]/dw and/or d[A[m(w)]]/dw}/dw}/dw]/dw]/dw

 

 

 

 

Aw6 = d Aw5/dw = d[d Aw4/dw]/dw = d[d[dAw3/dw]/dw]/dw

 

 

 

Aw6 = dAw5/dw = d[d[d[d[d[d A{[t(w)] and/or [w(w)] and/or [a(w)] and/or [i(w)] and/or [m(w)]}/dw]/dw]/dw]/dw]/dw]/dw

 

 

 

f(Aw)6A = d[f(Aw)5A]/dw = d{ d{d{d{d{ d [A[t(w)]]/dw and/or d[A[w(w)]]/dw and/or d[A[a(w)]]/dw and/or d[A[i(w)]]/dw and/or d[A[m(w)]]/dw}/dw}/dw]/dw]/dw]/dw

 

 

 

 

Aw7 = dAw6/dw

 

f(Aw)7A = d[f(Aw)6A]/dw

 

 

Aw8 = d Aw7/dw

 

f(Aw)8A = d[f(Aw)7A]/dw

 

 

 

Aw9 = d Aw8/dw

 

f(Aw)9A = d[f(Aw)8A]/dw

 

 

Aw10…, Aw11…, Aw12 … etc.

 

 

Anyone for Aw ensemble, or Aw infinity scrapper, or Aw (Aleph 0), or Aw(Aleph 1), or Aw (Aleph 2), or how about Aw Aleph (Aleph 0), or Aw Aleph (Aleph 1) , or Aw Aleph (Aleph 2), or even Aw Aleph (Aleph (Aleph 0)), or Aw Aleph (Aleph (Aleph 1)), or Aw Aleph (Aleph (Aleph 2)), and so on?

 

 

Thus, for the set of the sets of derivatives of Aw1 through Aw(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Aw1 through Aw(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)},…, {П(0,31)[R]}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Aw1 through Aw(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Aw1 through Aw(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the derivative states in the set of the sets of derivatives of Aw1 through Aw(Aleph 0) is plausible equal to:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Aw1 through Aw(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Aw1 through Aw(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}}}.

 

For the set of the sets of derivatives of Aw1 through Aw(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Aw(Aleph 0) derivative space at the level of 0/(Aleph 0), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Aw1 through Aw(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Aw1 through Aw(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Aw1 through Aw(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Aw1 through Aw(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Aw1 through Aw(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Aw1 through Aw(Aleph 1), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Aw1 through  Aw(Aleph 2), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Aw1 through Aw(Aleph 3), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Aw(Aleph 0) derivative space at the level of 0/(Aleph 1), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Aw1 through Aw(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Aw1 through Aw(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Aw1 through Aw(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Aw1 through  Aw(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations  for the set of the sets of derivatives of Aw1 through Aw(Aleph 0) is plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Aw1 through Aw(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Aw1 through Aw(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Aw1 through Aw(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

 

For super-continuous Aw(Aleph 0) derivative space at the level of 0/(Aleph 2), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Aw1 through Aw(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Aw1 through Aw(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Aw1 through Aw(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Aw1 through Aw(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Aw1 through Aw(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Aw1 through Aw(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Aw1 through Aw(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Aw1 through Aw(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

Similar series can be developed for super-continuity at any applicable level such as 0/(Aleph 3), 0/(Aleph 4), 0/(Aleph 5),…, 0/(Aleph Ω), 0/(Aleph (Aleph 0)), …, 0/(Aleph (Aleph 1)), …, 0/(Aleph (Aleph 2)), …, 0/(Aleph (Aleph 3)),…, 0/(Aleph (Aleph Ω)),…, 0/(Aleph (Aleph (Aleph 0))), …, 0/(Aleph (Aleph (Aleph 1))),…, 0/(Aleph (Aleph (Aleph 2))),…, 0/(Aleph (Aleph (Aleph 3))),…, 0/(Aleph (Aleph  (Aleph Ω))), …

 

An so-on ad infinitum.

 

 

In addition to these numerical functions of Aw as functions of summation series of product series functions, in order to really appreciate the enourmous complexity of the human soul in terms of its potential to evolve and be differentiated from all other souls in its characteristics, we would need to consider how every single category and even every single species of affect of the form Aw can very. Since there may exist an arbitrarily high infinite number species of Aw, the number of numerical functions of Aw is utterly beyond recogning. I will cover such notions in terms of mathematical notation in yet another series of articles I will write on this general concept.

 

 

Perhaps these numbers are applicable when one considers that the human soul, in its accidental form and perhaps even in its substantial form stores all experience and other psychodynamics based phenomenon. Every experience adds to the accidental form of the human soul and this includes the souls of all those still alive on Earth, all those in Purgatory, all those in Heaven, all those in Hell, and all those in any Limbo.

Since the human soul can grow without limit in terms of its psychodynamic time –flow world line, such a consideration offers another mechanism where the number of derivative states, combinations of derivative states, and even super-continuity of the derivative state space can grow forever.

 

Folks, for those of you who might balk at me for including literally all souls in the above consideration, including the souls in Hell, as well as bodily extraterrestrial souls and the souls of so-called bodily ultraterrestials sometimes referred to as etherians in the new age UFO buff culture, my reply is that we simply do not understand the full scope of GOD’s Divine Economy. We may never fully comprehend the scope of the Divine Economy because such an utterly eternal scheme, is, well, eternal and never ending.

 

 

The general meaning of will derivatives of affect can be viewed as the manner in which the qualitative and/or quantitative aspects of affect as a function of will very with will. The manner in which affects very with will may be multi- will-aspect dimensional wherein the dimensions of derivations can be multiple, and wherein the derivations can be taken in parallel, series parallel or in serial manner. The differentials can be partial or non-partial derivatives, or both partial and non-partial for a given computation.

 

In fact, since there is in theory, no limit to the numbers of qualitatively and quantitatively different acts of will or volitional states, and perhaps no limit to the number of possible different types or classes of acts of will or volitional states, wherein each person has his or her own unique acts or will or volitional states, the number of volitional state dimensions that can effect affects is literally infinite, given the entirety of the set of created persons, and perhaps also literally infinite for each person as an individual, although we can not intellectually and intuitively understand this infinite number.

 

 

It is interesting to consider the ramifactions of being able to perform realistic calculations involving will derivatives of affect from a mathematical, theoretical, scientific,  and philosophical perspective.

 

Persons for which one or more nth order derivatives of affect with respect to will that have large absolute values would tend to have their affect highly influenced by will, or at least for the affects under consideration with respect to the dimension of the specific will act type(s) or class(es) for which the differentiation(s) are being performed. Perhaps a strong coupling between affect and will indicates a well integrated personality and commensurately, a high degree of affect capacity and a high degree of affect intelligence as well as perhaps very strong will power.

 

We would expect that disembodied human souls, ATI souls, and/or UTI souls in Heaven, Limbo, highly evolved bodily ATI persons, highly evolved UTI persons, and angels to have affects of all kinds and intensities which are highly subject to will.

 

 

We can also consider two dimensional ith ordered derivatives of affect with respect to will and time, or with respect to w and T, respectively.

 

Given that A[(w)(T)] =  A[(t and/or w and/or a and/or i and/or m)(w)(T)], the following first order two dimensional derivatives of affect with respect to will and Time are possible.

 

 

d[dA[(t)(T)]/dw]/dT, d[dA[(w)(T)]/dw]/dT, d[dA[(a)(T)]/dw]/dT, d[dA[(i)(T)]/dw]/dT, d[dA[(m)(T)]/dw]/dT, d[dA[(t,w)(T)]/dw]/dT, d[dA[(t,a)(T)]/dw]/dT, d[dA[(t,i)(T)]/dw]/dT, d[dA[(t,m)(T)]/dw]/dT, d[dA[(w,a)(T)]/dw]/dT, d[dA[(w,i)(T)]/dw]/dT, d[dA[(w,m)(T)]/dw]/dT, d[dA[(a,i)(T)]/dw]/dT, d[dA[(a,m)(T)]/dw]/dT, d[dA[(i,m)(T)]/dw]/dT, d[dA[(t,w,a)(T)]/dw]/dT, d[dA[(t,w,i)(T)]/dw]/dT, d[dA[(t,w,m)(T)]/dw]/dT, d[dA[(t,a,i)(T)]/dw]/dT, d[dA[(t,a,m)(T)]/dw]/dT, d[dA[(t,i,m)(T)]/dw]/dT, d[dA[(w,a,i)(T)]/dw]/dT, d[dA[(w,a,m)(T)]/dw]/dT, d[dA[(w,i,m)(T)]/dw]/dT, d[dA[(a,i,m)(T)]/dw]/dT, d[dA[(t,w,a,i)(T)]/dw]/dT, d[dA[(t,w,a,m)(T)]/dw]/dT, d[dA[(t,w,i,m)(T)]/dw]/dT, d[dA[(t,a,i,m)(T)]/dw]/dT, d[dA[(w,a,i,m)(T)]/dw]/dT, d[dA[(t,w,a,i,m)(T)]/dw]/dT.

 

 

Or more succinctly,  d[dA(T)/dw]/dT = d[dA[(T)(t and/or w and/or a and/or i and/or m)]/dw]/dT

 

or

 

d[dA(T)/dT]/dw = d[dA[(T)(t and/or w and/or a and/or i and/or m)]/dT]/dw

 

 

 

 

 

Or perhaps d[d A[(w)(T)]/dw]/dT  = d[d A [{[t(w)] and/or [w(w)] and/or [a(w)] and/or [i(w)] and/or [m(w)]}(T)]/dw]/dT

 

or

 

Or perhaps d[d A[(w)(T)]/dT]/dw  = d[d A [{[t(w)] and/or [w(w)] and/or [a(w)] and/or [i(w)] and/or [m(w)]}(T)]/dT]/dw

 

 

 

Likewise, we can take the second dual dimension will -time derivatives of  A as follows:

 

d[d[d[dA[(t)(T)]/dw]/dT]/dw]/dT, d[d[d[dA[(w)(T)]/dw]/dT]/dw]/dT, d[d[d[dA[(a)(T)]/dw]/dT]/dw]/dT, d[d[d[dA[(i)(T)]/dw]/dT]/dw]/dT, d[d[d[dA[(m)(T)]/dw]/dT]/dw]/dT, d[d[d[dA[(t,w)(T)]/dw]/dT]/dw]/dT, d[d[d[dA[(t,a)(T)]/dw]/dT]/dw]/dT, d[d[d[dA[(t,i)(T)]/dw]/dT]/dw]/dT, d[d[d[dA[(t,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dA[(w,a)(T)]/dw]/dT]/dw]/dT, d[d[d[dA[(w,i)(T)]/dw]/dT]/dw]/dT, d[d[d[dA[(w,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dA[(a,i)(T)]/dw]/dT]/dw]/dT, d[d[d[dA[(a,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dA[(i,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dA[(t,w,a)(T)]/dw]/dT]/dw]/dT, d[d[d[dA[(t,w,i)(T)]/dw]/dT]/dw]/dT, d[d[d[dA[(t,w,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dA[(t,a,i)(T)]/dw]/dT]/dw]/dT, d[d[d[dA[(t,a,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dA[(t,i,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dA[(w,a,i)(T)]/dw]/dT]/dw]/dT, d[d[d[dA[(w,a,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dA[(w,i,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dA[(a,i,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dA[(t,w,a,i)(T)]/dw]/dT]/dw]/dT, d[d[d[dA[(t,w,a,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dA[(t,w,i,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dA[(t,a,i,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dA[(w,a,i,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dA[(t,w,a,i,m)(T)]/dw]/dT]/dw]/dT.

 

or as:

 

 

 

d[d[d[dA[(t)(T)]/dw]/dT]/dT]/dw, d[d[d[dA[(w)(T)]/dw]/dT]/dT]/dw, d[d[d[dA[(a)(T)]/dw]/dT]/dT]/dw, d[d[d[dA[(i)(T)]/dw]/dT]/dT]/dw, d[d[d[dA[(m)(T)]/dw]/dT]/dT]/dw, d[d[d[dA[(t,w)(T)]/dw]/dT]/dT]/dw, d[d[d[dA[(t,a)(T)]/dw]/dT]/dT]/dw, d[d[d[dA[(t,i)(T)]/dw]/dT]/dT]/dw, d[d[d[dA[(t,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dA[(w,a)(T)]/dw]/dT]/dT]/dw, d[d[d[dA[(w,i)(T)]/dw]/dT]/dT]/dw, d[d[d[dA[(w,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dA[(a,i)(T)]/dw]/dT]/dT]/dw, d[d[d[dA[(a,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dA[(i,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dA[(t,w,a)(T)]/dw]/dT]/dT]/dw, d[d[d[dA[(t,w,i)(T)]/dw]/dT]/dT]/dw, d[d[d[dA[(t,w,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dA[(t,a,i)(T)]/dw]/dT]/dT]/dw, d[d[d[dA[(t,a,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dA[(t,i,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dA[(w,a,i)(T)]/dw]/dT]/dT]/dw, d[d[d[dA[(w,a,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dA[(w,i,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dA[(a,i,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dA[(t,w,a,i)(T)]/dw]/dT]/dT]/dw, d[d[d[dA[(t,w,a,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dA[(t,w,i,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dA[(t,a,i,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dA[(w,a,i,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dA[(t,w,a,i,m)(T)]/dw]/dT]/dT]/dw.

 

or as:

 

d[d[d[dA[(t)(T)]/dT]/dw]/dw]/dT, d[d[d[dA[(w)(T)]/dT]/dw]/dw]/dT, d[d[d[dA[(a)(T)]/dT]/dw]/dw]/dT, d[d[d[dA[(i)(T)]/dT]/dw]/dw]/dT, d[d[d[dA[(m)(T)]/dT]/dw]/dw]/dT, d[d[d[dA[(t,w)(T)]/dT]/dw]/dw]/dT, d[d[d[dA[(t,a)(T)]/dT]/dw]/dw]/dT, d[d[d[dA[(t,i)(T)]/dT]/dw]/dw]/dT, d[d[d[dA[(t,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dA[(w,a)(T)]/dT]/dw]/dw]/dT, d[d[d[dA[(w,i)(T)]/dT]/dw]/dw]/dT, d[d[d[dA[(w,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dA[(a,i)(T)]/dT]/dw]/dw]/dT, d[d[d[dA[(a,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dA[(i,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dA[(t,w,a)(T)]/dT]/dw]/dw]/dT, d[d[d[dA[(t,w,i)(T)]/dT]/dw]/dw]/dT, d[d[d[dA[(t,w,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dA[(t,a,i)(T)]/dT]/dw]/dw]/dT, d[d[d[dA[(t,a,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dA[(t,i,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dA[(w,a,i)(T)]/dT]/dw]/dw]/dT, d[d[d[dA[(w,a,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dA[(w,i,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dA[(a,i,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dA[(t,w,a,i)(T)]/dT]/dw]/dw]/dT, d[d[d[dA[(t,w,a,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dA[(t,w,i,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dA[(t,a,i,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dA[(w,a,i,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dA[(t,w,a,i,m)(T)]/dT]/dw]/dw]/dT.

 

 

or as;

 

 

 

 

d[d[d[dA(t)/dw]/dw]/dT]/dT, d[d[d[dA(w)/dw]/dw]/dT]/dT, d[d[d[dA(a)/dw]/dw]/dT]/dT, d[d[d[dA(i)/dw]/dw]/dT]/dT, d[d[d[dA(m)/dw]/dw]/dT]/dT, d[d[d[dA(t,w)/dw]/dw]/dT]/dT, d[d[d[dA(t,a)/dw]/dw]/dT]/dT, d[d[d[dA(t,i)/dw]/dw]/dT]/dT, d[d[d[dA(t,m)/dw]/dw]/dT]/dT, d[d[d[dA(w,a)/dw]/dw]/dT]/dT, d[d[d[dA(w,i)/dw]/dw]/dT]/dT, d[d[d[dA(w,m)/dw]/dw]/dT]/dT, d[d[d[dA(a,i)/dw]/dw]/dT]/dT, d[d[d[dA(a,m)/dw]/dw]/dT]/dT, d[d[d[dA(i,m)/dw]/dw]/dT]/dT, d[d[d[dA(t,w,a)/dw]/dw]/dT]/dT, d[d[d[dA(t,w,i)/dw]/dw]/dT]/dT, d[d[d[dA(t,w,m)/dw]/dw]/dT]/dT, d[d[d[dA(t,a,i)/dw]/dw]/dT]/dT, d[d[d[dA(t,a,m)/dw]/dw]/dT]/dT,  d[d[d[dA(t,i,m)/dw]/dw]/dT]/dT, d[d[d[dA(w,a,i)/dw]/dw]/dT]/dT, d[d[d[dA(w,a,m)/dw]/dw]/dT]/dT, d[d[d[dA(w,i,m)/dw]/dw]/dT]/dT, d[d[d[dA(a,i,m)/dw]/dw]/dT]/dT, d[d[d[dA(t,w,a,i)/dw]/dw]/dT]/dT, d[d[d[dA(t,w,a,m)/dw/dw, d[d[d[dA(t,w,i,m)/dw]/dw]/dT]/dT, d[d[d[dA(t,a,i,m)/dw]/dw]/dT]/dT, d[d[d[dA(w,a,i,m)/dw]/dw]/dT]/dT, d[d[d[dA(t,w,a,i,m)/dw]/dw]/dT]/dT..

 

or as:

 

d[d[d[dA(t)/dT]/dw]/dT]/dw, d[d[d[dA(w)/dT]/dw]/dT]/dw, d[d[d[dA(a)/dT]/dw]/dT]/dw, d[d[d[dA(i)/dT]/dw]/dT]/dw, d[d[d[dA(m)/dT]/dw]/dT]/dw, d[d[d[dA(t,w)/dT]/dw]/dT]/dw, d[d[d[dA(t,a)/dT]/dw]/dT]/dw, d[d[d[dA(t,i)/dT]/dw]/dT]/dw, d[d[d[dA(t,m)/dT]/dw]/dT]/dw, d[d[d[dA(w,a)/dT]/dw]/dT]/dw, d[d[d[dA(w,i)/dT]/dw]/dT]/dw, d[d[d[dA(w,m)/dT]/dw]/dT]/dw, d[d[d[dA(a,i)/dT]/dw]/dT]/dw, d[d[d[dA(a,m)/dT]/dw]/dT]/dw, d[d[d[dA(i,m)/ dT]/dw]/dT]/dw, d[d[d[dA(t,w,a)/dT]/dw]/dT]/dw, d[d[d[dA(t,w,i)/dT]/dw]/dT]/dw, d[d[d[dA(t,w,m)/dT]/dw]/dT]/dw, d[d[d[dA(t,a,i)/dT]/dw]/dT]/dw, d[d[d[dA(t,a,m)/dT]/dw]/dT]/dw,  d[d[d[dA(t,i,m)/dT]/dw]/dT]/dw, d[d[d[dA(w,a,i)/dT]/dw]/dT]/dw, d[d[d[dA(w,a,m)/dT]/dw]/dT]/dw, d[d[d[dA(w,i,m)/dT]/dw]/dT]/dw, d[d[d[dA(a,i,m)/dT]/dw]/dT]/dw, d[d[d[dA(t,w,a,i)/dT]/dw]/dT]/dw, d[d[d[dA(t,w,a,m)/dw/dw, d[d[d[dA(t,w,i,m)/dT]/dw]/dT]/dw, d[d[d[dA(t,a,i,m)/dT]/dw]/dT]/dw, d[d[d[dA(w,a,i,m)/dT]/dw]/dT]/dw, d[d[d[dA(t,w,a,i,m)/dT]/dw]/dT]/dw..

 

or as:

 

d[d[d[dA(t)/dT]/dT]/dw]/dw, d[d[d[dA(w)/dT]/dT]/dw]/dw, d[d[d[dA(a)/dT]/dT]/dw]/dw, d[d[d[dA(i)/dT]/dT]/dw]/dw, d[d[d[dA(m)/dT]/dT]/dw]/dw, d[d[d[dA(t,w)/dT]/dT]/dw]/dw, d[d[d[dA(t,a)/dT]/dT]/dw]/dw, d[d[d[dA(t,i)/dT]/dT]/dw]/dw, d[d[d[dA(t,m)/dT]/dT]/dw]/dw, d[d[d[dA(w,a)/dT]/dT]/dw]/dw, d[d[d[dA(w,i)/dT]/dT]/dw]/dw, d[d[d[dA(w,m)/dT]/dT]/dw]/dw, d[d[d[dA(a,i)/dT]/dT]/dw]/dw, d[d[d[dA(a,m)/ dT]/dT]/dw]/dw, d[d[d[dA(i,m)/ dT]/dT]/dw]/dw, d[d[d[dA(t,w,a)/dT]/dT]/dw]/dw, d[d[d[dA(t,w,i)/dT]/dT]/dw]/dw, d[d[d[dA(t,w,m)/dT]/dT]/dw]/dw, d[d[d[dA(t,a,i)/dT]/dT]/dw]/dw, d[d[d[dA(t,a,m)/dT]/dT]/dw]/dw,  d[d[d[dA(t,i,m)/dT]/dT]/dw]/dw, d[d[d[dA(w,a,i)/dT]/dT]/dw]/dw, d[d[d[dA(w,a,m)/dT]/dT]/dw]/dw, d[d[d[dA(w,i,m)/dT]/dT]/dw]/dw, d[d[d[dA(a,i,m)/dT]/dT]/dw]/dw, d[d[d[dA(t,w,a,i)/dT]/dT]/dw]/dw, d[d[d[dA(t,w,a,m)/dw/dw, d[d[d[dA(t,w,i,m)/dT]/dT]/dw]/dw, d[d[d[dA(t,a,i,m)/dT]/dT]/dw]/dw, d[d[d[dA(w,a,i,m)/dT]/dT]/dw]/dw, d[d[d[dA(t,w,a,i,m)/dT]/dT]/dw]/dw..

 

We can also take higher order duel dimensional derivatives of affect as a function of will and time but the symbolic expression of the set of such derivatives very soon becomes excessively lengthly to write and so these higher order derivatives as such are not mentioned here except to say that they would be computed in an analogous manner to the second order duel dimensional derivatives described above.

 

 

We can also express affect  qualitatively, statistically, and perhaps with the use of some forms of real analysis as a thought derivative of affect.

 

Given that A(a) =  A(t and/or w and/or a and/or i and/or m), the following first order derivatives of affect with respect to thought are possible.

 

 

dA(t)/dt, dA(w)/dt, dA(a)/dt, dA(i)/dt, dA(m)/dt, dA(t,w)/dt, dA(t,a)/dt, dA(t,i)/dt, dA(t,m)/dt, dA(w,a)/dt, dA(w,i)/dt, dA(w,m)/dt, dA(a,i)/dt, dA(a,m)/dt, dA(i,m)/dt, dA(t,w,a)/dt, dA(t,w,i)/dt, dA(t,w,m)/dt, dA(t,a,i)/dt, dA(t,a,m)/dt, dA(t,i,m)/dt, dA(w,a,i)/dt, dA(w,a,m)/dt, dA(w,i,m)/dt, dA(a,i,m)/dt, dA(t,w,a,i)/dt, dA(t,w,a,m)/dt, dA(t,w,i,m)/dt, dA(t,a,i,m)/dt, dA(w,a,i,m)/dt, dA(t,w,a,i,m)/dt.

 

 

Or more succinctly, dA/dt = dA(t and/or w and/or a and/or i and/or m)/dt

 

 

Or perhaps dA(t)/dt =d A{[t(t)] and/or [w(t)] and/or [a(t)] and/or [i(t)] and/or [m(t)]}/dt.

 

 

Likewise, we can take the second thought derivatives of  A as follows:

 

 

 

d[dA(t)/dt]/dt, d[dA(w)/dt]/dt, d[dA(a)/dt]/dt, d[dA(i)/dt]/dt, d[dA(m)/dt]/dt, d[dA(t,w)/dt]/dt, d[dA(t,a)/dt]/dt, d[dA(t,i)/dt]/dt, d[dA(t,m)/dt]/dt, d[dA(w,a)/dt]/dt, d[dA(w,i)/dt]/dt, d[dA(w,m)/dt]/dt, d[dA(a,i)/dt]/dt, d[dA(a,m)/dt]/dt, d[dA(i,m)/dt/dt, d[dA(t,w,a)/dt]/dt, d[dA(t,w,i)/dt]/dt, d[dA(t,w,m)/dt]/dt, d[dA(t,a,i)/dt]/dt, d[dA(t,a,m)/dt]/dt,  d[dA(t,i,m)/dt]/dt, d[dA(w,a,i)/dt]/dt, d[dA(w,a,m)/dt]/dt, d[dA(w,i,m)/dt]/dt, d[dA(a,i,m)/dt]/dt, d[dA(t,w,a,i)/dt]/dt, d[dA(t,w,a,m)/dt/dt, d[dA(t,w,i,m)/dt]/dt, d[dA(t,a,i,m)/dt]/dt, d[dA(w,a,i,m)/dt]/dt, d[dA(t,w,a,i,m)/dt]/dt..

 

 

or more succinctly, as d(dA/dt)/dt = d[d A(t and/or w and/or a and/or i and/or m)/dt]/dt = At2

 

 

or as

 

 

d[dA(t)/dt]/dt  = d[d A{[t(t)] and/or [w(t)] and/or [a(w)] and/or [i(t)] and/or [m(t)]}/dt]/dt = At2.

 

 

 

Likewise, we can take the third thought derivatives of  A as follows:

 

 

 

d[d[dA(t)/dt]/dt]/dt, d[d[dA(w)/dt]/dt]/dt, d[d[dA(a)/dt]/dt]/dt, d[d[dA(i)/dt]/dt]/dt, d[d[dA(m)/dt]/dt]/dt, d[d[dA(t,w)/dt]/dt]/dt, d[d[dA(t,a)/dt]/dt]/dt, d[d[dA(t,i)/dt]/dt]/dt, d[d[dA(t,m)/dt]/dt]/dt, d[d[dA(w,a)/dt]/dt]/dt, d[d[dA(w,i)/dt]/dt]/dt, d[d[dA(w,m)/dt]/dt]/dt, d[d[dA(a,i)/dt]/dt]/dt, d[d[dA(a,m)/dt]/dt]/dt, d[d[dA(i,m)/dt/dt]/dt, d[d[dA(t,w,a)/dt]/dt]/dt, d[d[dA(t,w,i)/dt]/dt]/dt, d[d[dA(t,w,m)/dt]/dt]/dt, d[d[dA(t,a,i)/dt]/dt]/dt, d[d[dA(t,a,m)/dt]/dt]/dt,  d[d[dA(t,i,m)/dt]/dt]/dt, d[d[dA(w,a,i)/dt]/dt]/dt, d[d[dA(w,a,m)/dt]/dt]/dt, d[d[dA(w,i,m)/dt]/dt]/dt, d[d[dA(a,i,m)/dt]/dt]/dt, d[d[dA(t,w,a,i)/dt]/dt]/dt, d[d[dA(t,w,a,m)/dt/dt]/dt, d[d[dA(t,w,i,m)/dt]/dt]/dt, d[d[dA(t,a,i,m)/dt]/dt]/dt, d[d[dA(w,a,i,m)/dt]/dt]/dt, d[d[dA(t,w,a,i,m)/dt]/dt]/dt.

 

 

or more succinctly, as d[d(dA/dt)/dt]/dt = d[d[d A(t and/or w and/or a and/or i and/or m)/dt]/dt]/dt = At3

 

 

or as

 

 

d[d[dA(t)/dt]/dt]/dt  = d[d[d A{[t(t)] and/or [w(t)] and/or [a(t)] and/or [i(t)] and/or [m(t)]}/dt]/dt]/dt = At3.

 

 

We can also form the expressions;

 

 

d[d[f(A)]/dt]/dt = d{d [A[t(t)]]/dt and/or d[A[w(t)]]/dt and/or d[A[a(t)]]/dt and/or d[A[i(t)]]/dt and/or d[A[m(t)]]/dt}/dt  = f(At)2

 

 

and

 

 

d[d[d[f(A)]/dt]/dt]/dt = d{d{ d [A[t(t)]]/dt and/or d[A[w(t)]]/dt and/or d[A[a(t)]]/dt and/or d[A[i(t)]]/dt and/or d[A[m(t)]]/dt}/dt}/dt  = f(At)3A, where A stands for type A differentiation which is not to be confused with the meaning of so-called Type A personality as A is used as an ordinal in a totally different context here.

 

 

and

 

 

d[d[d[f(A)]/dt]/dt]/dt = d{d[d [A[t(t)]]/dt]/dt  and/or d[d [A[w(t)]]/dt]/dt  and/or d[d [A[a(t)]]/dt]/dt  and/or d[d [A[i(t)]]/dt]/dt  and/or d[d [A[m(t)]]/dt]/dt }/dt = f(At)3B, where B stands for type B differentiation which is not to be confused with the meaning of so-called Type  B personality as B is used as an ordinal in a totally different context here. .

 

 

In fact, one can form yet higher order derivatives of affects with respect to thought as follows.

 

 

At5 = d At4/dt = d[dAt3/dt]/dt

 

 

 

At5 = dAt4/dt =  d[d[d[d[d A{[t(t)] and/or [w(t)] and/or [a(t)] and/or [i(t)] and/or [m(t)]}/dt]/dt]/dt]/dt]/dt.

 

 

 

f(At)5A = d[f(Aa)4A]/dt = d[d [f(Aa)3A]/dt]/dt =  d{d{d{d{ d [A[t(t)]]/dt and/or d[A[w(t)]]/dt and/or d[A[a(t)]]/dt and/or d[A[i(t)]]/dt and/or d[A[m(t)]]/dt}/dt}/dt]/dt]/dt

 

 

 

 

At6 = d At5/dt = d[d At4/dt]/dt = d[d[dAt3/dt]/dt]/dt

 

 

 

At6 = dAt5/dt = d[d[d[d[d[d A{[t(t)] and/or [w(t)] and/or [a(t)] and/or [i(t)] and/or [m(t)]}/dt]/dt]/dt]/dt]/dt]/dt

 

 

 

f(At)6A = d[f(At)5A]/dt = d{ d{d{d{d{ d [A[t(t)]]/dt and/or d[A[w(t)]]/dt and/or d[A[a(t)]]/dt and/or d[A[i(t)]]/dt and/or d[A[m(t)]]/dt}/dt}/dt]/dt]/dt]/dt

 

 

 

 

At7 = dAt6/dt

 

f(At)7A = d[f(At)6A]/dt

 

 

At8 = d At7/dt

 

f(At)8A = d[f(At)7A]/dt

 

 

 

At9 = d At8/dt

 

f(At)9A = d[f(At)8A]/dt

 

 

At10…, At11…, At12 … etc.

 

 

Anyone for At ensemble, or At infinity scrapper, or At (Aleph 0), or At(Aleph 1), or At (Aleph 2), or how about At Aleph (Aleph 0), or At Aleph (Aleph 1) , or At Aleph (Aleph 2), or even At Aleph (Aleph (Aleph 0)), or At Aleph (Aleph (Aleph 1)), or At Aleph (Aleph (Aleph 2)), and so on?

 

 

Thus, for the set of the sets of derivatives of At1 through At(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}.

 

For the set of the sets of derivatives of At1 through At(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)},…, {П(0,31)[R]}_{(Aleph 1)}.

 

For the set of the sets of derivatives of At1 through At(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}.

 

For the set of the sets of derivatives of At1 through At(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the derivative states in the set of the sets of derivatives of At1 through At(Aleph 0) is plausible equal to:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of At1 through At(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of At1 through At(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}}}.

 

For the set of the sets of derivatives of At1 through At(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous At(Aleph 0) derivative space at the level of 0/(Aleph 0), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of At1 through At(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of At1 through At(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of At1 through At(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of At1 through At(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of At1 through At(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of At1 through At(Aleph 1), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of At1 through  At(Aleph 2), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of At1 through At(Aleph 3), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous At(Aleph 0) derivative space at the level of 0/(Aleph 1), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of At1 through At(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of At1 through At(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of At1 through At(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of At1 through  At(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations  for the set of the sets of derivatives of At1 through At(Aleph 0) is plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of At1 through At(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of At1 through At(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of At1 through At(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

 

For super-continuous At(Aleph 0) derivative space at the level of 0/(Aleph 2), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of At1 through At(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of At1 through At(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of At1 through At(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of At1 through At(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of At1 through At(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of At1 through At(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of At1 through At(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of At1 through At(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

Similar series can be developed for super-continuity at any applicable level such as 0/(Aleph 3), 0/(Aleph 4), 0/(Aleph 5),…, 0/(Aleph Ω), 0/(Aleph (Aleph 0)), …, 0/(Aleph (Aleph 1)), …, 0/(Aleph (Aleph 2)), …, 0/(Aleph (Aleph 3)),…, 0/(Aleph (Aleph Ω)),…, 0/(Aleph (Aleph (Aleph 0))), …, 0/(Aleph (Aleph (Aleph 1))),…, 0/(Aleph (Aleph (Aleph 2))),…, 0/(Aleph (Aleph (Aleph 3))),…, 0/(Aleph (Aleph  (Aleph Ω))), …

 

An so-on ad infinitum.

 

 

In addition to these numerical functions of At as functions of summation series of product series functions, in order to really appreciate the enourmous complexity of the human soul in terms of its potential to evolve and be differentiated from all other souls in its characteristics, we would need to consider how every single category and even every single species of affect of the form At can very. Since there may exist an arbitrarily high infinite number species of At, the number numerical functions of At  is utterly beyond recogning. I will cover such notions in terms of mathematical notation in yet another series of articles I will write on this general concept.

 

 

Perhaps these numbers are applicable when one considers that the human soul, in its accidental form and perhaps even in its substantial form stores all experience and other psychodynamics based phenomenon. Every experience adds to the accidental form of the human soul and this includes the souls of all those still alive on Earth, all those in Purgatory, all those in Heaven, all those in Hell, and all those in any Limbo.

Since the human soul can grow without limit in terms of its psychodynamic time –flow world line, such a consideration offers another mechanism where the number of derivative states, combinations of derivative states, and even super-continuity of the derivative state space can grow forever.

 

Folks, for those of you who might balk at me for including literally all souls in the above consideration, including the souls in Hell, as well as bodily extraterrestrial souls and the souls of so-called bodily ultraterrestials sometimes referred to as etherians in the new age UFO buff culture, my reply is that we simply do not understand the full scope of GOD’s Divine Economy. We may never fully comprehend the scope of the Divine Economy because such an utterly eternal scheme, is, well, eternal and never ending.

 

The general meaning of thought derivatives of affect can be viewed as the manner in which the qualitative and/or quantitative aspects of affect as a function of thought very with thought. The manner in which affects very with thought may be multi- thought-aspect dimensional wherein the dimensions of derivations can be multiple, and wherein the derivations can be taken in parallel, series parallel or in serial manner. The differentials can be partial or non-partial derivatives, or both partial and non-partial for a given computation.

 

In fact, since there is in theory, no limit to the numbers of qualitatively and quantitatively different affective states, and perhaps no limit to the number of possible different types or classes of affective states, wherein each person has his or her own unique affective experiences, the number of affect dimensions that can effect affects is literally infinite, given the entirety of the set of created persons, and perhaps also literally infinite for each person as an individual, although we can not intellectually and intuitively understand this infinite number.

 

 

It is interesting to consider the ramifactions of being able to perform realistic calculations involving thought derivatives of affect from a mathematical, theoretical, scientific,  and philosophical perspective.

 

Persons for which one or more nth order derivatives of affect with respect to thought that have large absolute values would tend to have their affects highly influenced by thought, or at least for the affects under consideration with respect to the dimension of the specific affect type(s) or class(es) for which the differentiation(s) are being performed. Perhaps a strong coupling between affect to thought indicates a well integrated personality and commensurately, a high degree of affect capacity and a high degree of affective intelligence as well as perhaps very strong affect power.

 

We would expect that disembodied human souls, ATI souls, and/or UTI souls in Heaven, Limbo, highly evolved bodily ATI persons, highly evolved UTI persons, and angels to have affects of all kinds and intensities which are highly subject to affect.

 

 

We can also consider that two dimensional nth ordered derivatives of affects with respect to thought and time, or with respect to a and T, respectively.

 

Given that A[(t)(T)] =  A[(t and/or w and/or a and/or i and/or m)(w)(T)], the following first order two dimensional derivatives of affect with respect to thought and Time are possible.

 

 

d[dA[(t)(T)]/dt]/dT, d[dA[(w)(T)]/dt]/dT, d[dA[(a)(T)]/dt]/dT, d[dA[(i)(T)]/dt]/dT, d[dA[(m)(T)]/dt]/dT, d[dA[(t,w)(T)]/dt]/dT, d[dA[(t,a)(T)]/dt]/dT, d[dA[(t,i)(T)]/dt]/dT, d[dA[(t,m)(T)]/dt]/dT, d[dA[(w,a)(T)]/dt]/dT, d[dA[(w,i)(T)]/dt]/dT, d[dA[(w,m)(T)]/dt]/dT, d[dA[(a,i)(T)]/dt]/dT, d[dA[(a,m)(T)]/dt]/dT, d[dA[(i,m)(T)]/dt]/dT, d[dA[(t,w,a)(T)]/dt]/dT, d[dA[(t,w,i)(T)]/dt]/dT, d[dA[(t,w,m)(T)]/dt]/dT, d[dA[(t,a,i)(T)]/dt]/dT, d[dA[(t,a,m)(T)]/dt]/dT, d[dA[(t,i,m)(T)]/dt]/dT, d[dA[(w,a,i)(T)]/dt]/dT, d[dA[(w,a,m)(T)]/dt]/dT, d[dA[(w,i,m)(T)]/dt]/dT, d[dA[(a,i,m)(T)]/dt]/dT, d[dA[(t,w,a,i)(T)]/dt]/dT, d[dA[(t,w,a,m)(T)]/dt]/dT, d[dA[(t,w,i,m)(T)]/dt]/dT, d[dA[(t,a,i,m)(T)]/dt]/dT, d[dA[(w,a,i,m)(T)]/dt]/dT, d[dA[(t,w,a,i,m)(T)]/dt]/dT.

 

 

Or more succinctly,  d[dA(T)/dt]/dT = d[dA[(T)(t and/or w and/or a and/or i and/or m)]/dt]/dT

 

or

 

d[dA(T)/dT]/dt = d[dA[(T)(t and/or w and/or a and/or i and/or m)]/dT]/dt

 

 

 

 

 

Or perhaps d[d A[(t)(T)]/dt]/dT  = d[d A [{[t(t)] and/or [w(t)] and/or [a(t)] and/or [i(t)] and/or [m(t)]}(T)]/dt]/dT

 

or

 

Or perhaps d[d A[(t)(T)]/dT]/dt  = d[d A [{[t(t)] and/or [w(t)] and/or [a(t)] and/or [i(t)] and/or [m(t)]}(T)]/dT]/dt

 

 

 

Likewise, we can take the second dual dimension thought -time derivatives of  A as follows:

 

d[d[d[dA[(t)(T)]/dt]/dT]/dt]/dT, d[d[d[dA[(w)(T)]/dt]/dT]/dt]/dT, d[d[d[dA[(a)(T)]/dt]/dT]/dt]/dT, d[d[d[dA[(i)(T)]/dt]/dT]/dt]/dT, d[d[d[dA[(m)(T)]/dt]/dT]/dt]/dT, d[d[d[dA[(t,w)(T)]/dt]/dT]/dt]/dT, d[d[d[dA[(t,a)(T)]/dt]/dT]/dt]/dT, d[d[d[dA[(t,i)(T)]/dt]/dT]/dt]/dT, d[d[d[dA[(t,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dA[(w,a)(T)]/dt]/dT]/dt]/dT, d[d[d[dA[(w,i)(T)]/dt]/dT]/dt]/dT, d[d[d[dA[(w,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dA[(a,i)(T)]/dt]/dT]/dt]/dT, d[d[d[dA[(a,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dA[(i,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dA[(t,w,a)(T)]/dt]/dT]/dt]/dT, d[d[d[dA[(t,w,i)(T)]/dt]/dT]/dt]/dT, d[d[d[dA[(t,w,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dA[(t,a,i)(T)]/dt]/dT]/dt]/dT, d[d[d[dA[(t,a,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dA[(t,i,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dA[(w,a,i)(T)]/dt]/dT]/dt]/dT, d[d[d[dA[(w,a,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dA[(w,i,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dA[(a,i,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dA[(t,w,a,i)(T)]/dt]/dT]/dt]/dT, d[d[d[dA[(t,w,a,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dA[(t,w,i,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dA[(t,a,i,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dA[(w,a,i,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dA[(t,w,a,i,m)(T)]/dt]/dT]/dt]/dT.

 

or as:

 

 

 

d[d[d[dA[(t)(T)]/dt]/dT]/dT]/dt, d[d[d[dA[(w)(T)]/dt]/dT]/dT]/dt, d[d[d[dA[(a)(T)]/dt]/dT]/dT]/dt, d[d[d[dA[(i)(T)]/dt]/dT]/dT]/dt, d[d[d[dA[(m)(T)]/dt]/dT]/dT]/dt, d[d[d[dA[(t,w)(T)]/dt]/dT]/dT]/dt, d[d[d[dA[(t,a)(T)]/dt]/dT]/dT]/dt, d[d[d[dA[(t,i)(T)]/dt]/dT]/dT]/dt, d[d[d[dA[(t,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dA[(w,a)(T)]/dt]/dT]/dT]/dt, d[d[d[dA[(w,i)(T)]/dt]/dT]/dT]/dt, d[d[d[dA[(w,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dA[(a,i)(T)]/dt]/dT]/dT]/dt, d[d[d[dA[(a,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dA[(i,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dA[(t,w,a)(T)]/dt]/dT]/dT]/dt, d[d[d[dA[(t,w,i)(T)]/dt]/dT]/dT]/dt, d[d[d[dA[(t,w,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dA[(t,a,i)(T)]/dt]/dT]/dT]/dt, d[d[d[dA[(t,a,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dA[(t,i,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dA[(w,a,i)(T)]/dt]/dT]/dT]/dt, d[d[d[dA[(w,a,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dA[(w,i,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dA[(a,i,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dA[(t,w,a,i)(T)]/dt]/dT]/dT]/dt, d[d[d[dA[(t,w,a,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dA[(t,w,i,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dA[(t,a,i,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dA[(w,a,i,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dA[(t,w,a,i,m)(T)]/dt]/dT]/dT]/dt.

 

or as:

 

d[d[d[dA[(t)(T)]/dT]/dt]/dt]/dT, d[d[d[dA[(w)(T)]/dT]/dt]/dt]/dT, d[d[d[dA[(a)(T)]/dT]/dt]/dt]/dT, d[d[d[dA[(i)(T)]/dT]/dt]/dt]/dT, d[d[d[dA[(m)(T)]/dT]/dt]/dt]/dT, d[d[d[dA[(t,w)(T)]/dT]/dt]/dt]/dT, d[d[d[dA[(t,a)(T)]/dT]/dt]/dt]/dT, d[d[d[dA[(t,i)(T)]/dT]/dt]/dt]/dT, d[d[d[dA[(t,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dA[(w,a)(T)]/dT]/dt]/dt]/dT, d[d[d[dA[(w,i)(T)]/dT]/dt]/dt]/dT, d[d[d[dA[(w,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dA[(a,i)(T)]/dT]/dt]/dt]/dT, d[d[d[dA[(a,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dA[(i,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dA[(t,w,a)(T)]/dT]/dt]/dt]/dT, d[d[d[dA[(t,w,i)(T)]/dT]/dt]/dt]/dT, d[d[d[dA[(t,w,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dA[(t,a,i)(T)]/dT]/dt]/dt]/dT, d[d[d[dA[(t,a,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dA[(t,i,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dA[(w,a,i)(T)]/dT]/dt]/dt]/dT, d[d[d[dA[(w,a,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dA[(w,i,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dA[(a,i,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dA[(t,w,a,i)(T)]/dT]/dt]/dt]/dT, d[d[d[dA[(t,w,a,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dA[(t,w,i,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dA[(t,a,i,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dA[(w,a,i,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dA[(t,w,a,i,m)(T)]/dT]/dt]/dt]/dT.

 

 

or as;

 

 

 

 

d[d[d[dA(t)/dt]/dt]/dT]/dT, d[d[d[dA(w)/dt]/dt]/dT]/dT, d[d[d[dA(a)/dt]/dt]/dT]/dT, d[d[d[dA(i)/dt]/dt]/dT]/dT, d[d[d[dA(m)/dt]/dt]/dT]/dT, d[d[d[dA(t,w)/dt]/dt]/dT]/dT, d[d[d[dA(t,a)/dt]/dt]/dT]/dT, d[d[d[dA(t,i)/dt]/dt]/dT]/dT, d[d[d[dA(t,m)/dt]/dt]/dT]/dT, d[d[d[dA(w,a)/dt]/dt]/dT]/dT, d[d[d[dA(w,i)/dt]/dt]/dT]/dT, d[d[d[dA(w,m)/dt]/dt]/dT]/dT, d[d[d[dA(a,i)/dt]/dt]/dT]/dT, d[d[d[dA(a,m)/dt]/dt]/dT]/dT, d[d[d[dA(i,m)/dt]/dt]/dT]/dT, d[d[d[dA(t,w,a)/dt]/dt]/dT]/dT, d[d[d[dA(t,w,i)/dt]/dt]/dT]/dT, d[d[d[dA(t,w,m)/dt]/dt]/dT]/dT, d[d[d[dA(t,a,i)/dt]/dt]/dT]/dT, d[d[d[dA(t,a,m)/dt]/dt]/dT]/dT,  d[d[d[dA(t,i,m)/dt]/dt]/dT]/dT, d[d[d[dA(w,a,i)/dt]/dt]/dT]/dT, d[d[d[dA(w,a,m)/dt]/dt]/dT]/dT, d[d[d[dA(w,i,m)/dt]/dt]/dT]/dT, d[d[d[dA(a,i,m)/dt]/dt]/dT]/dT, d[d[d[dA(t,w,a,i)/dt]/dt]/dT]/dT, d[d[d[dA(t,w,a,m)/dt/dt, d[d[d[dA(t,w,i,m)/dt]/dt]/dT]/dT, d[d[d[dA(t,a,i,m)/dt]/dt]/dT]/dT, d[d[d[dA(w,a,i,m)/dt]/dt]/dT]/dT, d[d[d[dA(t,w,a,i,m)/dt]/dt]/dT]/dT..

 

or as:

 

d[d[d[dA(t)/dT]/dt]/dT]/dt, d[d[d[dA(w)/dT]/dt]/dT]/dt, d[d[d[dA(a)/dT]/dt]/dT]/dt, d[d[d[dA(i)/dT]/dt]/dT]/dt, d[d[d[dA(m)/dT]/dt]/dT]/dt, d[d[d[dA(t,w)/dT]/dt]/dT]/dt, d[d[d[dA(t,a)/dT]/dt]/dT]/dt, d[d[d[dA(t,i)/dT]/dt]/dT]/dt, d[d[d[dA(t,m)/dT]/dt]/dT]/dt, d[d[d[dA(w,a)/dT]/dt]/dT]/dt, d[d[d[dA(w,i)/dT]/dt]/dT]/dt, d[d[d[dA(w,m)/dT]/dt]/dT]/dt, d[d[d[dA(a,i)/dT]/dt]/dT]/dt, d[d[d[dA(a,m)/dT]/dt]/dT]/dt, d[d[d[dA(i,m)/ dT]/dt]/dT]/dt, d[d[d[dA(t,w,a)/dT]/dt]/dT]/dt, d[d[d[dA(t,w,i)/dT]/dt]/dT]/dt, d[d[d[dA(t,w,m)/dT]/dt]/dT]/dt, d[d[d[dA(t,a,i)/dT]/dt]/dT]/dt, d[d[d[dA(t,a,m)/dT]/dt]/dT]/dt,  d[d[d[dA(t,i,m)/dT]/dt]/dT]/dt, d[d[d[dA(w,a,i)/dT]/dt]/dT]/dt, d[d[d[dA(w,a,m)/dT]/dt]/dT]/dt, d[d[d[dA(w,i,m)/dT]/dt]/dT]/dt, d[d[d[dA(a,i,m)/dT]/dt]/dT]/dt, d[d[d[dA(t,w,a,i)/dT]/dt]/dT]/dt, d[d[d[dA(t,w,a,m)/dt/dt, d[d[d[dA(t,w,i,m)/dT]/dt]/dT]/dt, d[d[d[dA(t,a,i,m)/dT]/dt]/dT]/dt, d[d[d[dA(w,a,i,m)/dT]/dt]/dT]/dt, d[d[d[dA(t,w,a,i,m)/dT]/dt]/dT]/dt..

 

or as:

 

d[d[d[dA(t)/dT]/dT]/dt]/dt, d[d[d[dA(w)/dT]/dT]/dt]/dt, d[d[d[dA(a)/dT]/dT]/dt]/dt, d[d[d[dA(i)/dT]/dT]/dt]/dt, d[d[d[dA(m)/dT]/dT]/dt]/dt, d[d[d[dA(t,w)/dT]/dT]/dt]/dt, d[d[d[dA(t,a)/dT]/dT]/dt]/dt, d[d[d[dA(t,i)/dT]/dT]/dt]/dt, d[d[d[dA(t,m)/dT]/dT]/dt]/dt, d[d[d[dA(w,a)/dT]/dT]/dt]/dt, d[d[d[dA(w,i)/dT]/dT]/dt]/dt, d[d[d[dA(w,m)/dT]/dT]/dt]/dt, d[d[d[dA(a,i)/dT]/dT]/dt]/dt, d[d[d[dA(a,m)/ dT]/dT]/dt]/dt, d[d[d[dA(i,m)/ dT]/dT]/dt]/dt, d[d[d[dA(t,w,a)/dT]/dT]/dt]/dt, d[d[d[dA(t,w,i)/dT]/dT]/dt]/dt, d[d[d[dA(t,w,m)/dT]/dT]/dt]/dt, d[d[d[dA(t,a,i)/dT]/dT]/dt]/dt, d[d[d[dA(t,a,m)/dT]/dT]/dt]/dt,  d[d[d[dA(t,i,m)/dT]/dT]/dt]/dt, d[d[d[dA(w,a,i)/dT]/dT]/dt]/dt, d[d[d[dA(w,a,m)/dT]/dT]/dt]/dt, d[d[d[dA(w,i,m)/dT]/dT]/dt]/dt, d[d[d[dA(a,i,m)/dT]/dT]/dt]/dt, d[d[d[dA(t,w,a,i)/dT]/dT]/dt]/dt, d[d[d[dA(t,w,a,m)/dt/dt, d[d[d[dA(t,w,i,m)/dT]/dT]/dt]/dt, d[d[d[dA(t,a,i,m)/dT]/dT]/dt]/dt, d[d[d[dA(w,a,i,m)/dT]/dT]/dt]/dt, d[d[d[dA(t,w,a,i,m)/dT]/dT]/dt]/dt..

 

We can also take higher order duel dimensional derivatives of affect as a function of thought and time but the symbolic expression of the set of such derivatives very soon becomes excessively lengthly to write and so these higher order derivatives as such are not mentioned here except to say that they would be computed in an analogous manner to the second order duel dimensional derivatives described above.

 

 

.

 

 

We can also express affect qualitatively, statistically, and perhaps with the use of some forms of real analyses as a derivative with respect to instinct or with respect to i.

 

Given that A(i) =  A(t and/or w and/or a and/or i and/or m) or perhaps the following notation can be more appropriate in certain circumstances.

 

 

 

 

Thus the following first order derivatives of affect with respect to instinct are possible.

 

 

dA(t)/di, dA(w)/di, dA(a)/di, dA(i)/di, dA(m)/di, dA(t,w)/di, dA(t,a)/di, dA(t,i)/di, dA(t,m)/di, dA(w,a)/di, dA(w,i)/di, dA(w,m)/di, dA(a,i)/di, dA(a,m)/di, dA(i,m)/di, dA(t,w,a)/di, dA(t,w,i)/di, dA(t,w,m)/di, dA(t,a,i)/di, dA(t,a,m)/di, dA(t,i,m)/di, dA(w,a,i)/di, dA(w,a,m)/di, dA(w,i,m)/di, dA(a,i,m)/di, dA(t,w,a,i)/di, dA(t,w,a,m)/di, dA(t,w,i,m)/di, dA(t,a,i,m)/di, dA(w,a,i,m)/di, dA(t,w,a,i,m)/di.

 

 

Or more succinctly,  dA/di = dA(t and/or w and/or a and/or i and/or m)/di

 

 

Or perhaps dA(i)/di =d A{[t(i)] and/or [w(i)] and/or [a(i)] and/or [i(i)] and/or [m(i)]}/di.

 

 

Likewise, we can take the second instinct derivatives of  A as follows:

 

 

 

d[dA(t)/di]/di, d[dA(w)/di]/di, d[dA(a)/di]/di, d[dA(i)/di]/di, d[dA(m)/di]/di, d[dA(t,w)/di]/di, d[dA(t,a)/di]/di, d[dA(t,i)/di]/di, d[dA(t,m)/di]/di, d[dA(w,a)/di]/di, d[dA(w,i)/di]/di, d[dA(w,m)/di]/di, d[dA(a,i)/di]/di, d[dA(a,m)/di]/di, d[dA(i,m)/di/di, d[dA(t,w,a)/di]/di, d[dA(t,w,i)/di]/di, d[dA(t,w,m)/di]/di, d[dA(t,a,i)/di]/di, d[dA(t,a,m)/di]/di,  d[dA(t,i,m)/di]/di, d[dA(w,a,i)/di]/di, d[dA(w,a,m)/di]/di, d[dA(w,i,m)/di]/di, d[dA(a,i,m)/di]/di, d[dA(t,w,a,i)/di]/di, d[dA(t,w,a,m)/di/di, d[dA(t,w,i,m)/di]/di, d[dA(t,a,i,m)/di]/di, d[dA(w,a,i,m)/di]/di, d[dA(t,w,a,i,m)/di]/di..

 

 

or more succinctly, as d(dA/di)/di = d[d A(t and/or w and/or a and/or i and/or m)/di]/di = Ai2

 

 

or as

 

 

d[dA(i)/di]/di  = d[d A{[t(i)] and/or [w(i)] and/or [a(i)] and/or [i(i)] and/or [m(i)]}/di]/di = Ai2.

 

 

 

Likewise, we can take the third instinct derivatives of  A as follows:

 

 

 

d[d[dA(t)/di]/di]/di, d[d[dA(w)/di]/di]/di, d[d[dA(a)/di]/di]/di, d[d[dA(i)/di]/di]/di, d[d[dA(m)/di]/di]/di, d[d[dA(t,w)/di]/di]/di, d[d[dA(t,a)/di]/di]/di, d[d[dA(t,i)/di]/di]/di, d[d[dA(t,m)/di]/di]/di, d[d[dA(w,a)/di]/di]/di, d[d[dA(w,i)/di]/di]/di, d[d[dA(w,m)/di]/di]/di, d[d[dA(a,i)/di]/di]/di, d[d[dA(a,m)/di]/di]/di, d[d[dA(i,m)/di/di]/di, d[d[dA(t,w,a)/di]/di]/di, d[d[dA(t,w,i)/di]/di]/di, d[d[dA(t,w,m)/di]/di]/di, d[d[dA(t,a,i)/di]/di]/di, d[d[dA(t,a,m)/di]/di]/di,  d[d[dA(t,i,m)/di]/di]/di, d[d[dA(w,a,i)/di]/di]/di, d[d[dA(w,a,m)/di]/di]/di, d[d[dA(w,i,m)/di]/di]/di, d[d[dA(a,i,m)/di]/di]/di, d[d[dA(t,w,a,i)/di]/di]/di, d[d[dA(t,w,a,m)/di/di]/di, d[d[dA(t,w,i,m)/di]/di]/di, d[d[dA(t,a,i,m)/di]/di]/di, d[d[dA(w,a,i,m)/di]/di]/di, d[d[dA(t,w,a,i,m)/di]/di]/di.

 

 

or more succinctly, as d[d(dA/di)/di]/di = d[d[d A(t and/or w and/or a and/or i and/or m)/di]/di]/di = Ai3

 

 

or as

 

 

d[d[dA(i)/di]/di]/di  = d[d[d A{[t(i)] and/or [w(i)] and/or [a(i)] and/or [i(i)] and/or [m(i)]}/di]/di]/di = Ai3.

 

 

We can also form the expressions;

 

 

d[d[f(A)]/di]/di = d{d [A[t(i)]]/di and/or d[A[w(i)]]/di and/or d[A[a(i)]]/di and/or d[A[i(i)]]/di and/or d[A[m(i)]]/di}/di  = f(Ai)2

 

 

and

 

 

d[d[d[f(A)]/di]/di]/di = d{d{ d [A[t(i)]]/di and/or d[A[w(i)]]/di and/or d[A[a(i)]]/di and/or d[A[i(i)]]/di and/or d[A[m(i)]]/di}/di}/di  = f(Ai)3A, where A stands for type A differentiation which is not to be confused with the meaning of so-called Type A personality as A is used as an ordinal in a totally different context here.

 

 

and

 

 

d[d[d[f(A)]/di]/di]/di = d{d[d [A[t(i)]]/di]/di  and/or d[d [A[w(i)]]/di]/di  and/or d[d [A[a(i)]]/di]/di  and/or d[d [A[i(i)]]/di]/di  and/or d[d [A[m(i)]]/di]/di }/di = f(Ai)3B, where B stands for type B differentiation which is not to be confused with the meaning of so-called Type  B personality as B is used as an ordinal in a totally different context here .

 

 

In fact, one can form yet higher order derivatives of affects with respect to instinct as follows.

 

 

Ai5 = d Ai4/di = d[dAi3/di]/di

 

 

 

Ai5 = dAi4/di =  d[d[d[d[d A{[t(i)] and/or [w(i)] and/or [a(i)] and/or [i(i)] and/or [m(i)]}/di]/di]/di]/di]/di.

 

 

 

f(Ai)5A = d[f(Ai)4A]/di = d[d [f(Ai)3A]/di]/di =  d{d{d{d{ d [A[t(i)]]/di and/or d[A[w(i)]]/di and/or d[A[a(i)]]/di and/or d[A[i(i)]]/di and/or d[A[m(i)]]/di}/di}/di]/di]/di

 

 

 

 

Ai6 = d Ai5/di = d[d Ai4/di]/di = d[d[dAi3/di]/di]/di

 

 

 

Ai6 = dAi5/di = d[d[d[d[d[d A{[t(i)] and/or [w(i)] and/or [a(i)] and/or [i(i)] and/or [m(i)]}/di]/di]/di]/di]/di]/di

 

 

 

f(Ai)6A = d[f(Ai)5A]/di = d{ d{d{d{d{ d [A[t(i)]]/di and/or d[A[w(i)]]/di and/or d[A[a(i)]]/di and/or d[A[i(i)]]/di and/or d[A[m(i)]]/di}/di}/di]/di]/di]/di

 

 

 

 

Ai7 = dAi6/di

 

f(Ai)7A = d[f(Ai)6A]/di

 

 

Ai8 = d Ai7/di

 

f(Ai)8A = d[f(Ai)7A]/di

 

 

 

Ai9 = d Ai8/di

 

f(Ai)9A = d[f(Ai)8A]/di

 

 

Ai10…, Ai11…, Ai12 … etc.

 

 

Anyone for Ai ensemble, or Ai infinity scrapper, or Ai (Aleph 0), or Ai(Aleph 1), or Ai (Aleph 2), or how about Ai Aleph (Aleph 0), or Ai Aleph (Aleph 1) , or Ai Aleph (Aleph 2), or even Ai Aleph (Aleph (Aleph 0)), or Ai Aleph (Aleph (Aleph 1)), or Ai Aleph (Aleph (Aleph 2)), and so on?

 

 

Thus, for the set of the sets of derivatives of Ai1 through Ai(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ai1 through Ai(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)},…, {П(0,31)[R]}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ai1 through Ai(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ai1 through Ai(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the derivative states in the set of the sets of derivatives of Ai1 through Ai(Aleph 0) is plausible equal to:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ai1 through Ai(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ai1 through Ai(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}}}.

 

For the set of the sets of derivatives of Ai1 through Ai(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Ai(Aleph 0) derivative space at the level of 0/(Aleph 0), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Ai1 through Ai(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ai1 through Ai(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ai1 through Ai(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ai1 through Ai(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Ai1 through Ai(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ai1 through Ai(Aleph 1), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Ai1 through  Ai(Aleph 2), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Ai1 through Ai(Aleph 3), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Ai(Aleph 0) derivative space at the level of 0/(Aleph 1), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Ai1 through Ai(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ai1 through Ai(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ai1 through Ai(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ai1 through  Ai(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations  for the set of the sets of derivatives of Ai1 through Ai(Aleph 0) is plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ai1 through Ai(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Ai1 through Ai(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Ai1 through Ai(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

 

For super-continuous Ai(Aleph 0) derivative space at the level of 0/(Aleph 2), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Ai1 through Ai(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ai1 through Ai(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ai1 through Ai(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ai1 through Ai(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Ai1 through Ai(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ai1 through Ai(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Ai1 through Ai(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Ai1 through Ai(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

Similar series can be developed for super-continuity at any applicable level such as 0/(Aleph 3), 0/(Aleph 4), 0/(Aleph 5),…, 0/(Aleph Ω), 0/(Aleph (Aleph 0)), …, 0/(Aleph (Aleph 1)), …, 0/(Aleph (Aleph 2)), …, 0/(Aleph (Aleph 3)),…, 0/(Aleph (Aleph Ω)),…, 0/(Aleph (Aleph (Aleph 0))), …, 0/(Aleph (Aleph (Aleph 1))),…, 0/(Aleph (Aleph (Aleph 2))),…, 0/(Aleph (Aleph (Aleph 3))),…, 0/(Aleph (Aleph  (Aleph Ω))), …

 

An so-on ad infinitum.

 

 

In addition to these numerical functions of Ai as functions of summation series of product series functions, in order to really appreciate the enourmous complexity of the human soul in terms of its potential to evolve and be differentiated from all other souls in its characteristics, we would need to consider how every single category and even every single species of affect of the form Ai can very. Since there may exist an arbitrarily high infinite number species of Ai, the number of numerical functions of Ai is utterly beyond recogning. I will cover such notions in terms of mathematical notation in yet another series of articles I will write on this general concept.

 

 

Perhaps these numbers are applicable when one considers that the human soul, in its accidental form and perhaps even in its substantial form stores all experience and other psychodynamics based phenomenon. Every experience adds to the accidental form of the human soul and this includes the souls of all those still alive on Earth, all those in Purgatory, all those in Heaven, all those in Hell, and all those in any Limbo.

Since the human soul can grow without limit in terms of its psychodynamic time –flow world line, such a consideration offers another mechanism where the number of derivative states, combinations of derivative states, and even super-continuity of the derivative state space can grow forever.

 

Folks, for those of you who might balk at me for including literally all souls in the above consideration, including the souls in Hell, as well as bodily extraterrestrial souls and the souls of so-called bodily ultraterrestials sometimes referred to as etherians in the new age UFO buff culture, my reply is that we simply do not understand the full scope of GOD’s Divine Economy. We may never fully comprehend the scope of the Divine Economy because such an utterly eternal scheme, is, well, eternal and never ending.

 

 

The general meaning of instinct derivatives of affect can be viewed as the manner in which the qualitative and/or quantitative aspects of affect as a function of instinct very with instinct. The manner in which affects very with instinct may be multi- instinct-aspect dimensional wherein the dimensions of derivations can be multiple, and wherein the derivations can be taken in parallel, series parallel or in serial manner. The differentials can be partial or non-partial derivatives, or both partial and non-partial for a given computation.

 

In fact, since there is in theory, no limit to the numbers of qualitatively and quantitatively different instincts, and perhaps no limit to the number of possible different types or classes of instincts or potential instincts, wherein each person has his or her own unique instincts and instinctual experiences, the number of instinct dimensions that can effect affects is literally infinite, given the entirety of the set of created persons, and perhaps also literally infinite for each person as an individual, although we can not intellectually and intuitively understand this infinite number.

 

 

It is interesting to consider the ramifactions of being able to perform realistic calculations involving instinct derivatives of affect from a mathematical, theoretical, scientific,  and philosophical perspective.

 

Persons for which one or more nth order derivatives of affect with respect to instinct that have large absolute values would tend to have their affects highly influenced by instinct, or at least for the affects under consideration with respect to the dimension of the specific instinct act type(s) or class(es) for which the differentiation(s) are being performed. Perhaps a strong coupling between affect and instinct indicates a well integrated personality and commensurately, a high degree of affect capacity and a high degree of affective intelligence as well as perhaps very strong instinct power.

 

We would expect that disembodied human souls, ETI souls, and/or UTI souls in Heaven, Limbo, highly evolved bodily ETI persons, highly evolved UTI persons, and angels to have affects of all kinds and intensities which are perhaps  highly subject to advanced instincts such as spiritual instincts, spiritual intuitions, and even perhaps, psychic powers.

 

 

We can also consider that two dimensional nth ordered derivatives of affect with respect to instinct and time, or with respect to i and T, respectively.

 

Given that A[(i)(T)] =  A[(t and/or w and/or a and/or i and/or m)(i)(T)], the following first order two dimensional derivatives of affect with respect to instinct and Time are possible.

 

 

d[dA[(t)(T)]/di]/dT, d[dA[(w)(T)]/di]/dT, d[dA[(a)(T)]/di]/dT, d[dA[(i)(T)]/di]/dT, d[dA[(m)(T)]/di]/dT, d[dA[(t,w)(T)]/di]/dT, d[dA[(t,a)(T)]/di]/dT, d[dA[(t,i)(T)]/di]/dT, d[dA[(t,m)(T)]/di]/dT, d[dA[(w,a)(T)]/di]/dT, d[dA[(w,i)(T)]/di]/dT, d[dA[(w,m)(T)]/di]/dT, d[dA[(a,i)(T)]/di]/dT, d[dA[(a,m)(T)]/di]/dT, d[dA[(i,m)(T)]/di]/dT, d[dA[(t,w,a)(T)]/di]/dT, d[dA[(t,w,i)(T)]/di]/dT, d[dA[(t,w,m)(T)]/di]/dT, d[dA[(t,a,i)(T)]/di]/dT, d[dA[(t,a,m)(T)]/di]/dT, d[dA[(t,i,m)(T)]/di]/dT, d[dA[(w,a,i)(T)]/di]/dT, d[dA[(w,a,m)(T)]/di]/dT, d[dA[(w,i,m)(T)]/di]/dT, d[dA[(a,i,m)(T)]/di]/dT, d[dA[(t,w,a,i)(T)]/di]/dT, d[dA[(t,w,a,m)(T)]/di]/dT, d[dA[(t,w,i,m)(T)]/di]/dT, d[dA[(t,a,i,m)(T)]/di]/dT, d[dA[(w,a,i,m)(T)]/di]/dT, d[dA[(t,w,a,i,m)(T)]/di]/dT.

 

 

Or more succinctly,  d[dA(T)/di]/dT = d[dA[(T)(t and/or w and/or a and/or i and/or m)]/di]/dT

 

or

 

d[dA(T)/dT]/di = d[dA[(T)(t and/or w and/or a and/or i and/or m)]/dT]/di

 

 

 

 

 

Or perhaps d[d A[(i)(T)]/di]/dT  = d[d A [{[t(i)] and/or [w(i)] and/or [a(i)] and/or [i(i)] and/or [m(i)]}(T)]/di]/dT

 

or

 

Or perhaps d[d A[(i)(T)]/dT]/di  = d[d A [{[t(i)] and/or [w(i)] and/or [a(i)] and/or [i(i)] and/or [m(i)]}(T)]/dT]/di

 

 

 

Likewise, we can take the second dual dimension instinct -time derivatives of  A as follows:

 

d[d[d[dA[(t)(T)]/di]/dT]/di]/dT, d[d[d[dA[(w)(T)]/di]/dT]/di]/dT, d[d[d[dA[(a)(T)]/di]/dT]/di]/dT, d[d[d[dA[(i)(T)]/di]/dT]/di]/dT, d[d[d[dA[(m)(T)]/di]/dT]/di]/dT, d[d[d[dA[(t,w)(T)]/di]/dT]/di]/dT, d[d[d[dA[(t,a)(T)]/di]/dT]/di]/dT, d[d[d[dA[(t,i)(T)]/di]/dT]/di]/dT, d[d[d[dA[(t,m)(T)]/di]/dT]/di]/dT, d[d[d[dA[(w,a)(T)]/di]/dT]/di]/dT, d[d[d[dA[(w,i)(T)]/di]/dT]/di]/dT, d[d[d[dA[(w,m)(T)]/di]/dT]/di]/dT, d[d[d[dA[(a,i)(T)]/di]/dT]/di]/dT, d[d[d[dA[(a,m)(T)]/di]/dT]/di]/dT, d[d[d[dA[(i,m)(T)]/di]/dT]/di]/dT, d[d[d[dA[(t,w,a)(T)]/di]/dT]/di]/dT, d[d[d[dA[(t,w,i)(T)]/di]/dT]/di]/dT, d[d[d[dA[(t,w,m)(T)]/di]/dT]/di]/dT, d[d[d[dA[(t,a,i)(T)]/di]/dT]/di]/dT, d[d[d[dA[(t,a,m)(T)]/di]/dT]/di]/dT, d[d[d[dA[(t,i,m)(T)]/di]/dT]/di]/dT, d[d[d[dA[(w,a,i)(T)]/di]/dT]/di]/dT, d[d[d[dA[(w,a,m)(T)]/di]/dT]/di]/dT, d[d[d[dA[(w,i,m)(T)]/di]/dT]/di]/dT, d[d[d[dA[(a,i,m)(T)]/di]/dT]/di]/dT, d[d[d[dA[(t,w,a,i)(T)]/di]/dT]/di]/dT, d[d[d[dA[(t,w,a,m)(T)]/di]/dT]/di]/dT, d[d[d[dA[(t,w,i,m)(T)]/di]/dT]/di]/dT, d[d[d[dA[(t,a,i,m)(T)]/di]/dT]/di]/dT, d[d[d[dA[(w,a,i,m)(T)]/di]/dT]/di]/dT, d[d[d[dA[(t,w,a,i,m)(T)]/di]/dT]/di]/dT.

 

or as:

 

 

 

d[d[d[dA[(t)(T)]/di]/dT]/dT]/di, d[d[d[dA[(w)(T)]/di]/dT]/dT]/di, d[d[d[dA[(a)(T)]/di]/dT]/dT]/di, d[d[d[dA[(i)(T)]/di]/dT]/dT]/di, d[d[d[dA[(m)(T)]/di]/dT]/dT]/di, d[d[d[dA[(t,w)(T)]/di]/dT]/dT]/di, d[d[d[dA[(t,a)(T)]/di]/dT]/dT]/di, d[d[d[dA[(t,i)(T)]/di]/dT]/dT]/di, d[d[d[dA[(t,m)(T)]/di]/dT]/dT]/di, d[d[d[dA[(w,a)(T)]/di]/dT]/dT]/di, d[d[d[dA[(w,i)(T)]/di]/dT]/dT]/di, d[d[d[dA[(w,m)(T)]/di]/dT]/dT]/di, d[d[d[dA[(a,i)(T)]/di]/dT]/dT]/di, d[d[d[dA[(a,m)(T)]/di]/dT]/dT]/di, d[d[d[dA[(i,m)(T)]/di]/dT]/dT]/di, d[d[d[dA[(t,w,a)(T)]/di]/dT]/dT]/di, d[d[d[dA[(t,w,i)(T)]/di]/dT]/dT]/di, d[d[d[dA[(t,w,m)(T)]/di]/dT]/dT]/di, d[d[d[dA[(t,a,i)(T)]/di]/dT]/dT]/di, d[d[d[dA[(t,a,m)(T)]/di]/dT]/dT]/di, d[d[d[dA[(t,i,m)(T)]/di]/dT]/dT]/di, d[d[d[dA[(w,a,i)(T)]/di]/dT]/dT]/di, d[d[d[dA[(w,a,m)(T)]/di]/dT]/dT]/di, d[d[d[dA[(w,i,m)(T)]/di]/dT]/dT]/di, d[d[d[dA[(a,i,m)(T)]/di]/dT]/dT]/di, d[d[d[dA[(t,w,a,i)(T)]/di]/dT]/dT]/di, d[d[d[dA[(t,w,a,m)(T)]/di]/dT]/dT]/di, d[d[d[dA[(t,w,i,m)(T)]/di]/dT]/dT]/di, d[d[d[dA[(t,a,i,m)(T)]/di]/dT]/dT]/di, d[d[d[dA[(w,a,i,m)(T)]/di]/dT]/dT]/di, d[d[d[dA[(t,w,a,i,m)(T)]/di]/dT]/dT]/di.

 

or as:

 

d[d[d[dA[(t)(T)]/dT]/di]/di]/dT, d[d[d[dA[(w)(T)]/dT]/di]/di]/dT, d[d[d[dA[(a)(T)]/dT]/di]/di]/dT, d[d[d[dA[(i)(T)]/dT]/di]/di]/dT, d[d[d[dA[(m)(T)]/dT]/di]/di]/dT, d[d[d[dA[(t,w)(T)]/dT]/di]/di]/dT, d[d[d[dA[(t,a)(T)]/dT]/di]/di]/dT, d[d[d[dA[(t,i)(T)]/dT]/di]/di]/dT, d[d[d[dA[(t,m)(T)]/dT]/di]/di]/dT, d[d[d[dA[(w,a)(T)]/dT]/di]/di]/dT, d[d[d[dA[(w,i)(T)]/dT]/di]/di]/dT, d[d[d[dA[(w,m)(T)]/dT]/di]/di]/dT, d[d[d[dA[(a,i)(T)]/dT]/di]/di]/dT, d[d[d[dA[(a,m)(T)]/dT]/di]/di]/dT, d[d[d[dA[(i,m)(T)]/dT]/di]/di]/dT, d[d[d[dA[(t,w,a)(T)]/dT]/di]/di]/dT, d[d[d[dA[(t,w,i)(T)]/dT]/di]/di]/dT, d[d[d[dA[(t,w,m)(T)]/dT]/di]/di]/dT, d[d[d[dA[(t,a,i)(T)]/dT]/di]/di]/dT, d[d[d[dA[(t,a,m)(T)]/dT]/di]/di]/dT, d[d[d[dA[(t,i,m)(T)]/dT]/di]/di]/dT, d[d[d[dA[(w,a,i)(T)]/dT]/di]/di]/dT, d[d[d[dA[(w,a,m)(T)]/dT]/di]/di]/dT, d[d[d[dA[(w,i,m)(T)]/dT]/di]/di]/dT, d[d[d[dA[(a,i,m)(T)]/dT]/di]/di]/dT, d[d[d[dA[(t,w,a,i)(T)]/dT]/di]/di]/dT, d[d[d[dA[(t,w,a,m)(T)]/dT]/di]/di]/dT, d[d[d[dA[(t,w,i,m)(T)]/dT]/di]/di]/dT, d[d[d[dA[(t,a,i,m)(T)]/dT]/di]/di]/dT, d[d[d[dA[(w,a,i,m)(T)]/dT]/di]/di]/dT, d[d[d[dA[(t,w,a,i,m)(T)]/dT]/di]/di]/dT.

 

 

or as;

 

 

 

 

d[d[d[dA(t)/di]/di]/dT]/dT, d[d[d[dA(w)/di]/di]/dT]/dT, d[d[d[dA(a)/di]/di]/dT]/dT, d[d[d[dA(i)/di]/di]/dT]/dT, d[d[d[dA(m)/di]/di]/dT]/dT, d[d[d[dA(t,w)/di]/di]/dT]/dT, d[d[d[dA(t,a)/di]/di]/dT]/dT, d[d[d[dA(t,i)/di]/di]/dT]/dT, d[d[d[dA(t,m)/di]/di]/dT]/dT, d[d[d[dA(w,a)/di]/di]/dT]/dT, d[d[d[dA(w,i)/di]/di]/dT]/dT, d[d[d[dA(w,m)/di]/di]/dT]/dT, d[d[d[dA(a,i)/di]/di]/dT]/dT, d[d[d[dA(a,m)/di]/di]/dT]/dT, d[d[d[dA(i,m)/di]/di]/dT]/dT, d[d[d[dA(t,w,a)/di]/di]/dT]/dT, d[d[d[dA(t,w,i)/di]/di]/dT]/dT, d[d[d[dA(t,w,m)/di]/di]/dT]/dT, d[d[d[dA(t,a,i)/di]/di]/dT]/dT, d[d[d[dA(t,a,m)/di]/di]/dT]/dT,  d[d[d[dA(t,i,m)/di]/di]/dT]/dT, d[d[d[dA(w,a,i)/di]/di]/dT]/dT, d[d[d[dA(w,a,m)/di]/di]/dT]/dT, d[d[d[dA(w,i,m)/di]/di]/dT]/dT, d[d[d[dA(a,i,m)/di]/di]/dT]/dT, d[d[d[dA(t,w,a,i)/di]/di]/dT]/dT, d[d[d[dA(t,w,a,m)/di/di, d[d[d[dA(t,w,i,m)/di]/di]/dT]/dT, d[d[d[dA(t,a,i,m)/di]/di]/dT]/dT, d[d[d[dA(w,a,i,m)/di]/di]/dT]/dT, d[d[d[dA(t,w,a,i,m)/di]/di]/dT]/dT..

 

or as:

 

d[d[d[dA(t)/dT]/di]/dT]/di, d[d[d[dA(w)/dT]/di]/dT]/di, d[d[d[dA(a)/dT]/di]/dT]/di, d[d[d[dA(i)/dT]/di]/dT]/di, d[d[d[dA(m)/dT]/di]/dT]/di, d[d[d[dA(t,w)/dT]/di]/dT]/di, d[d[d[dA(t,a)/dT]/di]/dT]/di, d[d[d[dA(t,i)/dT]/di]/dT]/di, d[d[d[dA(t,m)/dT]/di]/dT]/di, d[d[d[dA(w,a)/dT]/di]/dT]/di, d[d[d[dA(w,i)/dT]/di]/dT]/di, d[d[d[dA(w,m)/dT]/di]/dT]/di, d[d[d[dA(a,i)/dT]/di]/dT]/di, d[d[d[dA(a,m)/dT]/di]/dT]/di, d[d[d[dA(i,m)/ dT]/di]/dT]/di, d[d[d[dA(t,w,a)/dT]/di]/dT]/di, d[d[d[dA(t,w,i)/dT]/di]/dT]/di, d[d[d[dA(t,w,m)/dT]/di]/dT]/di, d[d[d[dA(t,a,i)/dT]/di]/dT]/di, d[d[d[dA(t,a,m)/dT]/di]/dT]/di,  d[d[d[dA(t,i,m)/dT]/di]/dT]/di, d[d[d[dA(w,a,i)/dT]/di]/dT]/di, d[d[d[dA(w,a,m)/dT]/di]/dT]/di, d[d[d[dA(w,i,m)/dT]/di]/dT]/di, d[d[d[dA(a,i,m)/dT]/di]/dT]/di, d[d[d[dA(t,w,a,i)/dT]/di]/dT]/di, d[d[d[dA(t,w,a,m)/di/di, d[d[d[dA(t,w,i,m)/dT]/di]/dT]/di, d[d[d[dA(t,a,i,m)/dT]/di]/dT]/di, d[d[d[dA(w,a,i,m)/dT]/di]/dT]/di, d[d[d[dA(t,w,a,i,m)/dT]/di]/dT]/di..

 

or as:

 

d[d[d[dA(t)/dT]/dT]/di]/di, d[d[d[dA(w)/dT]/dT]/di]/di, d[d[d[dA(a)/dT]/dT]/di]/di, d[d[d[dA(i)/dT]/dT]/di]/di, d[d[d[dA(m)/dT]/dT]/di]/di, d[d[d[dA(t,w)/dT]/dT]/di]/di, d[d[d[dA(t,a)/dT]/dT]/di]/di, d[d[d[dA(t,i)/dT]/dT]/di]/di, d[d[d[dA(t,m)/dT]/dT]/di]/di, d[d[d[dA(w,a)/dT]/dT]/di]/di, d[d[d[dA(w,i)/dT]/dT]/di]/di, d[d[d[dA(w,m)/dT]/dT]/di]/di, d[d[d[dA(a,i)/dT]/dT]/di]/di, d[d[d[dA(a,m)/ dT]/dT]/di]/di, d[d[d[dA(i,m)/ dT]/dT]/di]/di, d[d[d[dA(t,w,a)/dT]/dT]/di]/di, d[d[d[dA(t,w,i)/dT]/dT]/di]/di, d[d[d[dA(t,w,m)/dT]/dT]/di]/di, d[d[d[dA(t,a,i)/dT]/dT]/di]/di, d[d[d[dA(t,a,m)/dT]/dT]/di]/di,  d[d[d[dA(t,i,m)/dT]/dT]/di]/di, d[d[d[dA(w,a,i)/dT]/dT]/di]/di, d[d[d[dA(w,a,m)/dT]/dT]/di]/di, d[d[d[dA(w,i,m)/dT]/dT]/di]/di, d[d[d[dA(a,i,m)/dT]/dT]/di]/di, d[d[d[dA(t,w,a,i)/dT]/dT]/di]/di, d[d[d[dA(t,w,a,m)/di/di, d[d[d[dA(t,w,i,m)/dT]/dT]/di]/di, d[d[d[dA(t,a,i,m)/dT]/dT]/di]/di, d[d[d[dA(w,a,i,m)/dT]/dT]/di]/di, d[d[d[dA(t,w,a,i,m)/dT]/dT]/di]/di..

 

We can also take higher order duel dimensional derivatives of affect as a function of instinct and time but the symbolic expression of the set of such derivatives very soon becomes excessively lengthly to write and so these higher order derivatives as such are not mentioned here except to say that they would be computed in an analogous manner to the second order duel dimensional derivatives described above.

 

 

 

These seemingly crazy differentials might have some use in extreme psychological states that can be experienced by souls who are departed and whose affects, although perhaps spiritualized, are nonetheless, not limited by a body and its brain.

 

 

Another type of being that might experience such extreme affect change capacities might be none other then some of our friends we believe to exist as pure body-less and brain-less spirits known as angels.

 

 

Since I have dared to speculate this far, perhaps we can speculate as to whether any intelligent extraterrestrials persons or any so-called ultra-terrestrials persons that are more cognitively evolved then we ordinary humans might be capable of experiencing large absolute valued terms of An. Some such ETI and UTI persons may  have evolved over billions of years, or perhaps have far greater powers of sensation, thought, and intuition such as would seem plausible for any such persons and their civilizations who have not fallen from the state of innocence into the state of sin as we humans have, or perhaps such beings never had the option of  sanctifying grace opened to them but nonetheless may have been created at a naturally more perfect level then we humans, and who therefore might exhibit greater natural powers of affect and sensation.

 

 

 

 

 

 

 

 

 

 

 

 

We can also express affect qualitatively, statistically, and perhaps with the use of some forms of real analyses as a derivative with respect to  memory or with respect to  m.

 

Given that A(m) =  A(t and/or w and/or a and/or i and/or m) or perhaps the following notation can be more appropriate in certain circumstances.

 

 

 

 

Thus the following first order derivatives of affect with respect to memory are possible.

 

 

dA(t)/dm, dA(w)/dm, dA(a)/dm, dA(i)/dm, dA(m)/dm, dA(t,w)/dm, dA(t,a)/dm, dA(t,i)/dm, dA(t,m)/dm, dA(w,a)/dm, dA(w,i)/dm, dA(w,m)/dm, dA(a,i)/dm, dA(a,m)/dm, dA(i,m)/dm, dA(t,w,a)/dm, dA(t,w,i)/dm, dA(t,w,m)/dm, dA(t,a,i)/dm, dA(t,a,m)/dm, dA(t,i,m)/dm, dA(w,a,i)/dm, dA(w,a,m)/dm, dA(w,i,m)/dm, dA(a,i,m)/dm, dA(t,w,a,i)/dm, dA(t,w,a,m)/dm, dA(t,w,i,m)/dm, dA(t,a,i,m)/dm, dA(w,a,i,m)/dm, dA(t,w,a,i,m)/dm.

 

 

Or more succinctly,  dA/dm = dA(t and/or w and/or a and/or i and/or m)/dm

 

 

Or perhaps dA(m)/dm =d A{[t(m)] and/or [w(m)] and/or [a(m)] and/or [i(m)] and/or [m(m)]}/dm.

 

 

Likewise, we can take the second memory derivatives of  A as follows:

 

 

 

d[dA(t)/dm]/dm, d[dA(w)/dm]/dm, d[dA(a)/dm]/dm, d[dA(i)/dm]/dm, d[dA(m)/dm]/dm, d[dA(t,w)/dm]/dm, d[dA(t,a)/dm]/dm, d[dA(t,i)/dm]/dm, d[dA(t,m)/dm]/dm, d[dA(w,a)/dm]/dm, d[dA(w,i)/dm]/dm, d[dA(w,m)/dm]/dm, d[dA(a,i)/dm]/dm, d[dA(a,m)/dm]/dm, d[dA(i,m)/dm/dm, d[dA(t,w,a)/dm]/dm, d[dA(t,w,i)/dm]/dm, d[dA(t,w,m)/dm]/dm, d[dA(t,a,i)/dm]/dm, d[dA(t,a,m)/dm]/dm,  d[dA(t,i,m)/dm]/dm, d[dA(w,a,i)/dm]/dm, d[dA(w,a,m)/dm]/dm, d[dA(w,i,m)/dm]/dm, d[dA(a,i,m)/dm]/dm, d[dA(t,w,a,i)/dm]/dm, d[dA(t,w,a,m)/dm/dm, d[dA(t,w,i,m)/dm]/dm, d[dA(t,a,i,m)/dm]/dm, d[dA(w,a,i,m)/dm]/dm, d[dA(t,w,a,i,m)/dm]/dm..

 

 

or more succinctly, as d(dA/dm)/dm = d[d A(t and/or w and/or a and/or i and/or m)/dm]/dm = Am2

 

 

or as

 

 

d[dA(m)/dm]/dm  = d[d A{[t(m)] and/or [w(m)] and/or [a(m)] and/or [i(m)] and/or [m(m)]}/dm]/dm = Am2.

 

 

 

Likewise, we can take the third memory derivatives of  A as follows:

 

 

 

d[d[dA(t)/dm]/dm]/dm, d[d[dA(w)/dm]/dm]/dm, d[d[dA(a)/dm]/dm]/dm, d[d[dA(i)/dm]/dm]/dm, d[d[dA(m)/dm]/dm]/dm, d[d[dA(t,w)/dm]/dm]/dm, d[d[dA(t,a)/dm]/dm]/dm, d[d[dA(t,i)/dm]/dm]/dm, d[d[dA(t,m)/dm]/dm]/dm, d[d[dA(w,a)/dm]/dm]/dm, d[d[dA(w,i)/dm]/dm]/dm, d[d[dA(w,m)/dm]/dm]/dm, d[d[dA(a,i)/dm]/dm]/dm, d[d[dA(a,m)/dm]/dm]/dm, d[d[dA(i,m)/dm/dm]/dm, d[d[dA(t,w,a)/dm]/dm]/dm, d[d[dA(t,w,i)/dm]/dm]/dm, d[d[dA(t,w,m)/dm]/dm]/dm, d[d[dA(t,a,i)/dm]/dm]/dm, d[d[dA(t,a,m)/dm]/dm]/dm,  d[d[dA(t,i,m)/dm]/dm]/dm, d[d[dA(w,a,i)/dm]/dm]/dm, d[d[dA(w,a,m)/dm]/dm]/dm, d[d[dA(w,i,m)/dm]/dm]/dm, d[d[dA(a,i,m)/dm]/dm]/dm, d[d[dA(t,w,a,i)/dm]/dm]/dm, d[d[dA(t,w,a,m)/dm/dm]/dm, d[d[dA(t,w,i,m)/dm]/dm]/dm, d[d[dA(t,a,i,m)/dm]/dm]/dm, d[d[dA(w,a,i,m)/dm]/dm]/dm, d[d[dA(t,w,a,i,m)/dm]/dm]/dm.

 

 

or more succinctly, as d[d(dA/dm)/dm]/dm = d[d[d A(t and/or w and/or a and/or i and/or m)/dm]/dm]/dm = Am3

 

 

or as

 

 

d[d[dA(m)/dm]/dm]/dm  = d[d[d A{[t(m)] and/or [w(m)] and/or [a(m)] and/or [i(m)] and/or [m(m)]}/dm]/dm]/dm = Am3.

 

 

We can also form the expressions;

 

 

d[d[f(A)]/dm]/dm = d{d [A[t(m)]]/dm and/or d[A[w(m)]]/dm and/or d[A[a(m)]]/dm and/or d[A[i(m)]]/dm and/or d[A[m(m)]]/dm}/dm  = f(Am)2

 

 

and

 

 

d[d[d[f(A)]/dm]/dm]/dm = d{d{ d [A[t(m)]]/dm and/or d[A[w(m)]]/dm and/or d[A[a(m)]]/dm and/or d[A[i(m)]]/dm and/or d[A[m(m)]]/dm}/dm}/dm  = f(Am)3A, where A stands for type A differentiation which is not to be confused with the meaning of so-called Type A personality as A is used as an ordinal in a totally different context here.

 

 

and

 

 

d[d[d[f(A)]/dm]/dm]/dm = d{d[d [A[t(m)]]/dm]/dm  and/or d[d [A[w(m)]]/dm]/dm  and/or d[d [A[a(m)]]/dm]/dm  and/or d[d [A[i(m)]]/dm]/dm  and/or d[d [A[m(m)]]/dm]/dm }/dm = f(Am)3B, where B stands for type B differentiation which is not to be confused with the meaning of so-called Type  B personality as B is used as an ordinal in a totally different context here .

 

 

In fact, one can form yet higher order derivatives of affects with respect to memory as follows.

 

 

Am5 = d Am4/dm = d[dAm3/dm]/dm

 

 

 

Am5 = dAm4/dm =  d[d[d[d[d A{[t(m)] and/or [w(m)] and/or [a(m)] and/or [i(m)] and/or [m(m)]}/dm]/dm]/dm]/dm]/dm.

 

 

 

f(Am)5A = d[f(Am)4A]/dm = d[d [f(Am)3A]/dm]/dm =  d{d{d{d{ d [A[t(m)]]/dm and/or d[A[w(m)]]/dm and/or d[A[a(m)]]/dm and/or d[A[i(m)]]/dm and/or d[A[m(m)]]/dm}/dm}/dm]/dm]/dm

 

 

 

 

Am6 = d Am5/dm = d[d Am4/dm]/dm = d[d[dAm3/dm]/dm]/dm

 

 

 

Am6 = dAm5/dm = d[d[d[d[d[d A{[t(m)] and/or [w(m)] and/or [a(m)] and/or [i(m)] and/or [m(m)]}/dm]/dm]/dm]/dm]/dm]/dm

 

 

 

f(Am)6A = d[f(Am)5A]/dm = d{ d{d{d{d{ d [A[t(m)]]/dm and/or d[A[w(m)]]/dm and/or d[A[a(m)]]/dm and/or d[A[i(m)]]/dm and/or d[A[m(m)]]/dm}/dm}/dm]/dm]/dm]/dm

 

 

 

 

Am7 = dAm6/dm

 

f(Am)7A = d[f(Am)6A]/dm

 

 

Am8 = d Am7/dm

 

f(Am)8A = d[f(Am)7A]/dm

 

 

 

Am9 = d Am8/dm

 

f(Am)9A = d[f(Am)8A]/dm

 

 

Am10…, Am11…, Am12 … etc.

 

 

Anyone for Am ensemble, or Am infinity scrapper, or Am (Aleph 0), or Am(Aleph 1), or Am (Aleph 2), or how about Am Aleph (Aleph 0), or Am Aleph (Aleph 1) , or Am Aleph (Aleph 2), or even Am Aleph (Aleph (Aleph 0)), or Am Aleph (Aleph (Aleph 1)), or Am Aleph (Aleph (Aleph 2)), and so on?

 

Thus, for the set of the sets of derivatives of Am1 through Am(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Am1 through Am(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)},…, {П(0,31)[R]}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Am1 through Am(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Am1 through Am(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the derivative states in the set of the sets of derivatives of Am1 through Am(Aleph 0) is plausible equal to:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Am1 through Am(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Am1 through Am(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}}}.

 

For the set of the sets of derivatives of Am1 through Am(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Am(Aleph 0) derivative space at the level of 0/(Aleph 0), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Am1 through Am(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Am1 through Am(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Am1 through Am(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Am1 through Am(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Am1 through Am(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Am1 through Am(Aleph 1), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Am1 through  Am(Aleph 2), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Am1 through Am(Aleph 3), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Am(Aleph 0) derivative space at the level of 0/(Aleph 1), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Am1 through Am(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Am1 through Am(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Am1 through Am(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Am1 through  Am(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations  for the set of the sets of derivatives of Am1 through Am(Aleph 0) is plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Am1 through Am(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Am1 through Am(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Am1 through Am(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

 

For super-continuous Am(Aleph 0) derivative space at the level of 0/(Aleph 2), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Am1 through Am(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Am1 through Am(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Am1 through Am(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Am1 through Am(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Am1 through Am(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Am1 through Am(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Am1 through Am(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Am1 through Am(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

Similar series can be developed for super-continuity at any applicable level such as 0/(Aleph 3), 0/(Aleph 4), 0/(Aleph 5),…, 0/(Aleph Ω), 0/(Aleph (Aleph 0)), …, 0/(Aleph (Aleph 1)), …, 0/(Aleph (Aleph 2)), …, 0/(Aleph (Aleph 3)),…, 0/(Aleph (Aleph Ω)),…, 0/(Aleph (Aleph (Aleph 0))), …, 0/(Aleph (Aleph (Aleph 1))),…, 0/(Aleph (Aleph (Aleph 2))),…, 0/(Aleph (Aleph (Aleph 3))),…, 0/(Aleph (Aleph  (Aleph Ω))), …

 

An so-on ad infinitum.

 

 

In addition to these numerical functions of Am as functions of summation series of product series functions, in order to really appreciate the enourmous complexity of the human soul in terms of its potential to evolve and be differentiated from all other souls in its characteristics, we would need to consider how every single category and even every single species of affect of the form Am can very. Since there may exist an arbitrarily high infinite number species of Am, the number of numerical functions of Am is utterly beyond recogning. I will cover such notions in terms of mathematical notation in yet another series of articles I will write on this general concept.

 

 

Perhaps these numbers are applicable when one considers that the human soul, in its accidental form and perhaps even in its substantial form stores all experience and other psychodynamics based phenomenon. Every experience adds to the accidental form of the human soul and this includes the souls of all those still alive on Earth, all those in Purgatory, all those in Heaven, all those in Hell, and all those in any Limbo.

Since the human soul can grow without limit in terms of its psychodynamic time –flow world line, such a consideration offers another mechanism where the number of derivative states, combinations of derivative states, and even super-continuity of the derivative state space can grow forever.

 

Folks, for those of you who might balk at me for including literally all souls in the above consideration, including the souls in Hell, as well as bodily extraterrestrial souls and the souls of so-called bodily ultraterrestials sometimes referred to as etherians in the new age UFO buff culture, my reply is that we simply do not understand the full scope of GOD’s Divine Economy. We may never fully comprehend the scope of the Divine Economy because such an utterly eternal scheme, is, well, eternal and never ending.

 

 

The general meaning of memory derivatives of affect can be viewed as the manner in which the qualitative and/or quantitative aspects of affect as a function of memory very with memory. The manner in which affects very with memory may be multi- memory-aspect dimensional wherein the dimensions of derivations can be multiple, and wherein the derivations can be taken in parallel, series parallel or in serial manner. The differentials can be partial or non-partial derivatives, or both partial and non-partial for a given computation.

 

In fact, since there is in theory, no limit to the numbers of qualitatively and quantitatively different memories, and perhaps no limit to the number of possible different types or classes of memories, wherein each person has his or her own unique memories, the number of memory dimensions that can effect affects is literally infinite, given the entirety of the set of created persons, and perhaps also literally infinite for each person as an individual, although we can not intellectually and intuitively understand this infinite number.

 

 

It is interesting to consider the ramifactions of being able to perform realistic calculations involving memory derivatives of affect from a mathematical, theoretical, scientific,  and philosophical perspective.

 

Persons for which one or more nth order derivatives of affect with respect to memory that have large absolute values would tend to have their affects highly influenced by memory, or at least for the affects under consideration with respect to the dimension of the specific memory act type(s) or class(es) for which the differentiation(s) are being performed. Perhaps a strong coupling between affect and memory indicates a well integrated personality and commensurately, a high degree of affect capacity and a high degree of affect intelligence as well as perhaps very strong memory power.

 

We would expect that disembodied human souls, ATI souls, and/or UTI souls in Heaven, Limbo, highly evolved bodily ATI persons, highly evolved UTI persons, and angels to have affects of all kinds and intensities which are perhaps  highly subject to powereful memorys such as spiritual memorys, psychological memories, emotional memories, intellectual memories, interpersonal memories, auto-biographical memories, and even perhaps, memories facilitated by advanced psychic powers.

 

 

We can also consider that two dimensional nth ordered derivatives of affect with respect to memory and time, or with respect to i and T, respectively.

 

Given that A[(m)(T)] =  A[(t and/or w and/or a and/or i and/or m)(m)(T)], the following first order two dimensional derivatives of affect with respect to memory and Time are possible.

 

 

d[dA[(t)(T)]/dm]/dT, d[dA[(w)(T)]/dm]/dT, d[dA[(a)(T)]/dm]/dT, d[dA[(i)(T)]/dm]/dT, d[dA[(m)(T)]/dm]/dT, d[dA[(t,w)(T)]/dm]/dT, d[dA[(t,a)(T)]/dm]/dT, d[dA[(t,i)(T)]/dm]/dT, d[dA[(t,m)(T)]/dm]/dT, d[dA[(w,a)(T)]/dm]/dT, d[dA[(w,i)(T)]/dm]/dT, d[dA[(w,m)(T)]/dm]/dT, d[dA[(a,i)(T)]/dm]/dT, d[dA[(a,m)(T)]/dm]/dT, d[dA[(i,m)(T)]/dm]/dT, d[dA[(t,w,a)(T)]/dm]/dT, d[dA[(t,w,i)(T)]/dm]/dT, d[dA[(t,w,m)(T)]/dm]/dT, d[dA[(t,a,i)(T)]/dm]/dT, d[dA[(t,a,m)(T)]/dm]/dT, d[dA[(t,i,m)(T)]/dm]/dT, d[dA[(w,a,i)(T)]/dm]/dT, d[dA[(w,a,m)(T)]/dm]/dT, d[dA[(w,i,m)(T)]/dm]/dT, d[dA[(a,i,m)(T)]/dm]/dT, d[dA[(t,w,a,i)(T)]/dm]/dT, d[dA[(t,w,a,m)(T)]/dm]/dT, d[dA[(t,w,i,m)(T)]/dm]/dT, d[dA[(t,a,i,m)(T)]/dm]/dT, d[dA[(w,a,i,m)(T)]/dm]/dT, d[dA[(t,w,a,i,m)(T)]/dm]/dT.

 

 

Or more succinctly,  d[dA(T)/dm]/dT = d[dA[(T)(t and/or w and/or a and/or m and/or m)]/dm]/dT

 

or

 

d[dA(T)/dT]/dm = d[dA[(T)(t and/or w and/or a and/or i and/or m)]/dT]/dm

 

 

 

 

 

Or perhaps d[d A[(m)(T)]/dm]/dT  = d[d A [{[t(m)] and/or [w(m)] and/or [a(m)] and/or [i(m)] and/or [m(m)]}(T)]/dm]/dT

 

or

 

Or perhaps d[d A[(m)(T)]/dT]/dm  = d[d A [{[t(m)] and/or [w(m)] and/or [a(i)] and/or [i(m)] and/or [m(m)]}(T)]/dT]/dm

 

 

 

Likewise, we can take the second dual dimension memory -time derivatives of  A as follows:

 

d[d[d[dA[(t)(T)]/dm]/dT]/dm]/dT, d[d[d[dA[(w)(T)]/dm]/dT]/dm]/dT, d[d[d[dA[(a)(T)]/dm]/dT]/dm]/dT, d[d[d[dA[(i)(T)]/dm]/dT]/dm]/dT, d[d[d[dA[(m)(T)]/dm]/dT]/dm]/dT, d[d[d[dA[(t,w)(T)]/dm]/dT]/dm]/dT, d[d[d[dA[(t,a)(T)]/dm]/dT]/dm]/dT, d[d[d[dA[(t,i)(T)]/dm]/dT]/dm]/dT, d[d[d[dA[(t,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dA[(w,a)(T)]/dm]/dT]/dm]/dT, d[d[d[dA[(w,i)(T)]/dm]/dT]/dm]/dT, d[d[d[dA[(w,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dA[(a,i)(T)]/dm]/dT]/dm]/dT, d[d[d[dA[(a,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dA[(i,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dA[(t,w,a)(T)]/dm]/dT]/dm]/dT, d[d[d[dA[(t,w,i)(T)]/dm]/dT]/dm]/dT, d[d[d[dA[(t,w,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dA[(t,a,i)(T)]/dm]/dT]/dm]/dT, d[d[d[dA[(t,a,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dA[(t,i,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dA[(w,a,i)(T)]/dm]/dT]/dm]/dT, d[d[d[dA[(w,a,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dA[(w,i,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dA[(a,i,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dA[(t,w,a,i)(T)]/dm]/dT]/dm]/dT, d[d[d[dA[(t,w,a,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dA[(t,w,i,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dA[(t,a,i,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dA[(w,a,i,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dA[(t,w,a,i,m)(T)]/dm]/dT]/dm]/dT.

 

or as:

 

 

 

d[d[d[dA[(t)(T)]/dm]/dT]/dT]/dm, d[d[d[dA[(w)(T)]/dm]/dT]/dT]/dm, d[d[d[dA[(a)(T)]/dm]/dT]/dT]/dm, d[d[d[dA[(i)(T)]/dm]/dT]/dT]/dm, d[d[d[dA[(m)(T)]/dm]/dT]/dT]/dm, d[d[d[dA[(t,w)(T)]/dm]/dT]/dT]/dm, d[d[d[dA[(t,a)(T)]/dm]/dT]/dT]/dm, d[d[d[dA[(t,i)(T)]/dm]/dT]/dT]/dm, d[d[d[dA[(t,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dA[(w,a)(T)]/dm]/dT]/dT]/dm, d[d[d[dA[(w,i)(T)]/dm]/dT]/dT]/dm, d[d[d[dA[(w,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dA[(a,i)(T)]/dm]/dT]/dT]/dm, d[d[d[dA[(a,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dA[(i,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dA[(t,w,a)(T)]/dm]/dT]/dT]/dm, d[d[d[dA[(t,w,i)(T)]/dm]/dT]/dT]/dm, d[d[d[dA[(t,w,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dA[(t,a,i)(T)]/dm]/dT]/dT]/dm, d[d[d[dA[(t,a,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dA[(t,i,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dA[(w,a,i)(T)]/dm]/dT]/dT]/dm, d[d[d[dA[(w,a,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dA[(w,i,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dA[(a,i,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dA[(t,w,a,i)(T)]/dm]/dT]/dT]/dm, d[d[d[dA[(t,w,a,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dA[(t,w,i,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dA[(t,a,i,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dA[(w,a,i,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dA[(t,w,a,i,m)(T)]/dm]/dT]/dT]/dm.

 

or as:

 

d[d[d[dA[(t)(T)]/dT]/dm]/dm]/dT, d[d[d[dA[(w)(T)]/dT]/dm]/dm]/dT, d[d[d[dA[(a)(T)]/dT]/dm]/dm]/dT, d[d[d[dA[(i)(T)]/dT]/dm]/dm]/dT, d[d[d[dA[(m)(T)]/dT]/dm]/dm]/dT, d[d[d[dA[(t,w)(T)]/dT]/dm]/dm]/dT, d[d[d[dA[(t,a)(T)]/dT]/dm]/dm]/dT, d[d[d[dA[(t,i)(T)]/dT]/dm]/dm]/dT, d[d[d[dA[(t,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dA[(w,a)(T)]/dT]/dm]/dm]/dT, d[d[d[dA[(w,i)(T)]/dT]/dm]/dm]/dT, d[d[d[dA[(w,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dA[(a,i)(T)]/dT]/dm]/dm]/dT, d[d[d[dA[(a,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dA[(i,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dA[(t,w,a)(T)]/dT]/dm]/dm]/dT, d[d[d[dA[(t,w,i)(T)]/dT]/dm]/dm]/dT, d[d[d[dA[(t,w,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dA[(t,a,i)(T)]/dT]/dm]/dm]/dT, d[d[d[dA[(t,a,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dA[(t,i,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dA[(w,a,i)(T)]/dT]/dm]/dm]/dT, d[d[d[dA[(w,a,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dA[(w,i,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dA[(a,i,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dA[(t,w,a,i)(T)]/dT]/dm]/dm]/dT, d[d[d[dA[(t,w,a,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dA[(t,w,i,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dA[(t,a,i,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dA[(w,a,i,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dA[(t,w,a,i,m)(T)]/dT]/dm]/dm]/dT.

 

 

or as;

 

 

 

 

d[d[d[dA(t)/dm]/dm]/dT]/dT, d[d[d[dA(w)/dm]/dm]/dT]/dT, d[d[d[dA(a)/dm]/dm]/dT]/dT, d[d[d[dA(i)/dm]/dm]/dT]/dT, d[d[d[dA(m)/dm]/dm]/dT]/dT, d[d[d[dA(t,w)/dm]/dm]/dT]/dT, d[d[d[dA(t,a)/dm]/dm]/dT]/dT, d[d[d[dA(t,i)/dm]/dm]/dT]/dT, d[d[d[dA(t,m)/dm]/dm]/dT]/dT, d[d[d[dA(w,a)/dm]/dm]/dT]/dT, d[d[d[dA(w,i)/dm]/dm]/dT]/dT, d[d[d[dA(w,m)/dm]/dm]/dT]/dT, d[d[d[dA(a,i)/dm]/dm]/dT]/dT, d[d[d[dA(a,m)/dm]/dm]/dT]/dT, d[d[d[dA(i,m)/dm]/dm]/dT]/dT, d[d[d[dA(t,w,a)/dm]/dm]/dT]/dT, d[d[d[dA(t,w,i)/dm]/dm]/dT]/dT, d[d[d[dA(t,w,m)/dm]/dm]/dT]/dT, d[d[d[dA(t,a,i)/dm]/dm]/dT]/dT, d[d[d[dA(t,a,m)/dm]/dm]/dT]/dT,  d[d[d[dA(t,i,m)/dm]/dm]/dT]/dT, d[d[d[dA(w,a,i)/dm]/dm]/dT]/dT, d[d[d[dA(w,a,m)/dm]/dm]/dT]/dT, d[d[d[dA(w,i,m)/dm]/dm]/dT]/dT, d[d[d[dA(a,i,m)/dm]/dm]/dT]/dT, d[d[d[dA(t,w,a,i)/dm]/dm]/dT]/dT, d[d[d[dA(t,w,a,m)/dm/dm, d[d[d[dA(t,w,i,m)/dm]/dm]/dT]/dT, d[d[d[dA(t,a,i,m)/dm]/dm]/dT]/dT, d[d[d[dA(w,a,i,m)/dm]/dm]/dT]/dT, d[d[d[dA(t,w,a,i,m)/dm]/dm]/dT]/dT..

 

or as:

 

d[d[d[dA(t)/dT]/dm]/dT]/dm, d[d[d[dA(w)/dT]/dm]/dT]/dm, d[d[d[dA(a)/dT]/dm]/dT]/dm, d[d[d[dA(i)/dT]/dm]/dT]/dm, d[d[d[dA(m)/dT]/dm]/dT]/dm, d[d[d[dA(t,w)/dT]/dm]/dT]/dm, d[d[d[dA(t,a)/dT]/dm]/dT]/dm, d[d[d[dA(t,i)/dT]/dm]/dT]/dm, d[d[d[dA(t,m)/dT]/dm]/dT]/dm, d[d[d[dA(w,a)/dT]/dm]/dT]/dm, d[d[d[dA(w,i)/dT]/dm]/dT]/dm, d[d[d[dA(w,m)/dT]/dm]/dT]/dm, d[d[d[dA(a,i)/dT]/dm]/dT]/dm, d[d[d[dA(a,m)/dT]/dm]/dT]/dm, d[d[d[dA(i,m)/ dT]/dm]/dT]/dm, d[d[d[dA(t,w,a)/dT]/dm]/dT]/dm, d[d[d[dA(t,w,i)/dT]/dm]/dT]/dm, d[d[d[dA(t,w,m)/dT]/dm]/dT]/dm, d[d[d[dA(t,a,i)/dT]/dm]/dT]/dm, d[d[d[dA(t,a,m)/dT]/dm]/dT]/dm,  d[d[d[dA(t,i,m)/dT]/dm]/dT]/dm, d[d[d[dA(w,a,i)/dT]/dm]/dT]/dm, d[d[d[dA(w,a,m)/dT]/dm]/dT]/dm, d[d[d[dA(w,i,m)/dT]/dm]/dT]/dm, d[d[d[dA(a,i,m)/dT]/dm]/dT]/dm, d[d[d[dA(t,w,a,i)/dT]/dm]/dT]/dm, d[d[d[dA(t,w,a,m)/dm/dm, d[d[d[dA(t,w,i,m)/dT]/dm]/dT]/dm, d[d[d[dA(t,a,i,m)/dT]/dm]/dT]/dm, d[d[d[dA(w,a,i,m)/dT]/dm]/dT]/dm, d[d[d[dA(t,w,a,i,m)/dT]/dm]/dT]/dm..

 

or as:

 

d[d[d[dA(t)/dT]/dT]/dm]/dm, d[d[d[dA(w)/dT]/dT]/dm]/dm, d[d[d[dA(a)/dT]/dT]/dm]/dm, d[d[d[dA(i)/dT]/dT]/dm]/dm, d[d[d[dA(m)/dT]/dT]/dm]/dm, d[d[d[dA(t,w)/dT]/dT]/dm]/dm, d[d[d[dA(t,a)/dT]/dT]/dm]/dm, d[d[d[dA(t,i)/dT]/dT]/dm]/dm, d[d[d[dA(t,m)/dT]/dT]/dm]/dm, d[d[d[dA(w,a)/dT]/dT]/dm]/dm, d[d[d[dA(w,i)/dT]/dT]/dm]/dm, d[d[d[dA(w,m)/dT]/dT]/dm]/dm, d[d[d[dA(a,i)/dT]/dT]/dm]/dm, d[d[d[dA(a,m)/ dT]/dT]/dm]/dm, d[d[d[dA(i,m)/ dT]/dT]/dm]/dm, d[d[d[dA(t,w,a)/dT]/dT]/dm]/dm, d[d[d[dA(t,w,i)/dT]/dT]/dm]/dm, d[d[d[dA(t,w,m)/dT]/dT]/dm]/dm, d[d[d[dA(t,a,i)/dT]/dT]/dm]/dm, d[d[d[dA(t,a,m)/dT]/dT]/dm]/dm,  d[d[d[dA(t,i,m)/dT]/dT]/dm]/dm, d[d[d[dA(w,a,i)/dT]/dT]/dm]/dm, d[d[d[dA(w,a,m)/dT]/dT]/dm]/dm, d[d[d[dA(w,i,m)/dT]/dT]/dm]/dm, d[d[d[dA(a,i,m)/dT]/dT]/dm]/dm, d[d[d[dA(t,w,a,i)/dT]/dT]/dm]/dm, d[d[d[dA(t,w,a,m)/dm/dm, d[d[d[dA(t,w,i,m)/dT]/dT]/dm]/dm, d[d[d[dA(t,a,i,m)/dT]/dT]/dm]/dm, d[d[d[dA(w,a,i,m)/dT]/dT]/dm]/dm, d[d[d[dA(t,w,a,i,m)/dT]/dT]/dm]/dm..

 

We can also take higher order duel dimensional derivatives of affect as a function of memory and time but the symbolic expression of the set of such derivatives very soon becomes excessively lengthly to write and so these higher order derivatives as such are not mentioned here except to say that they would be computed in an analogous manner to the second order duel dimensional derivatives described above.

 

 

 

These seemingly crazy differentials might have some use in extreme psychological states that can be experienced by souls who are departed and whose affects, although perhaps spiritualized, are nonetheless, not limited by a body and its brain.

 

 

Another type of being that might experience such extreme affects change capacities might be none other then some of our friends we believe to exist as pure body-less and brain-less spirits known as angels.

 

 

Since I have dared to speculate this far, perhaps we can speculate as to whether any intelligent extraterrestrials persons or any so-called ultra-terrestrials persons that are more cognitively evolved then we ordinary humans might be capable of experiencing large absolute valued terms of An. Some such ETI and UTI persons may  have evolved over billions of years, or perhaps have far greater powers of sensation, thought, and intuition such as would seem plausible for any such persons and their civilizations who have not fallen from the state of innocence into the state of sin as we humans have, or perhaps such beings never had the option of  sanctifying grace opened to them but nonetheless may have been created at a naturally more perfect level then we humans, and who therefore might exhibit greater natural powers of thought and sensation.

 

Given that A(a) =  A(t and/or w and/or a and/or i and/or m), the following first order derivatives of affect  with respect to affect are possible.

 

 

dA(t)/dA, dA(w)/dA, dA(a)/dA, dA(i)/dA, dA(m)/dA, dA(t,w)/dA, dA(t,a)/dA, dA(t,i)/dA, dA(t,m)/dA, dA(w,a)/dA, dA(w,i)/dA, dA(w,m)/dA, dA(a,i)/dA, dA(a,m)/dA, dA(i,m)/dA, dA(t,w,a)/dA, dA(t,w,i)/dA, dA(t,w,m)/dA, dA(t,a,i)/dA, dA(t,a,m)/dA, dA(t,i,m)/dA, dA(w,a,i)/dA, dA(w,a,m)/dA, dA(w,i,m)/dA, dA(a,i,m)/dA, dA(t,w,a,i)/dA, dA(t,w,a,m)/dA, dA(t,w,i,m)/dA, dA(t,a,i,m)/dA, dA(w,a,i,m)/dA, dA(t,w,a,i,m)/dA.

 

 

Or more succinctly,  dA/dA = dA(t and/or w and/or a and/or i and/or m)/dA

 

 

Or perhaps dA(a)/dA =d A{[t(a)] and/or [w(a)] and/or [a(a)] and/or [i(a)] and/or [m(a)]}/dA.

 

 

Likewise, we can take the second affect derivatives of  A as follows:

 

 

 

d[dA(t)/dA]/dA, d[dA(w)/dA]/dA, d[dA(a)/dA]/dA, d[dA(i)/dA]/dA, d[dA(m)/dA]/dA, d[dA(t,w)/dA]/dA, d[dA(t,a)/dA]/dA, d[dA(t,i)/dA]/dA, d[dA(t,m)/dA]/dA, d[dA(w,a)/dA]/dA, d[dA(w,i)/dA]/dA, d[dA(w,m)/dA]/dA, d[dA(a,i)/dA]/dA, d[dA(a,m)/dA]/dA, d[dA(i,m)/dA/dA, d[dA(t,w,a)/dA]/dA, d[dA(t,w,i)/dA]/dA, d[dA(t,w,m)/dA]/dA, d[dA(t,a,i)/dA]/dA, d[dA(t,a,m)/dA]/dA,  d[dA(t,i,m)/dA]/dA, d[dA(w,a,i)/dA]/dA, d[dA(w,a,m)/dA]/dA, d[dA(w,i,m)/dA]/dA, d[dA(a,i,m)/dA]/dA, d[dA(t,w,a,i)/dA]/dA, d[dA(t,w,a,m)/dA/dA, d[dA(t,w,i,m)/dA]/dA, d[dA(t,a,i,m)/dA]/dA, d[dA(w,a,i,m)/dA]/dA, d[dA(t,w,a,i,m)/dA]/dA..

 

 

or more succinctly, as d(dA/dA)/dA = d[d A(t and/or w and/or a and/or i and/or m)/dA]/dA = Aa2

 

 

or as

 

 

d[dA(a)/dA]/dA  = d[d A{[t(a)] and/or [w(a)] and/or [a(a)] and/or [i(a)] and/or [m(a)]}/dA]/dA = Aa2.

 

 

 

Likewise, we can take the third affect derivatives of  A as follows:

 

 

 

d[d[dA(t)/dA]/dA]/dA, d[d[dA(w)/dA]/dA]/dA, d[d[dA(a)/dA]/dA]/dA, d[d[dA(i)/dA]/dA]/dA, d[d[dA(m)/dA]/dA]/dA, d[d[dA(t,w)/dA]/dA]/dA, d[d[dA(t,a)/dA]/dA]/dA, d[d[dA(t,i)/dA]/dA]/dA, d[d[dA(t,m)/dA]/dA]/dA, d[d[dA(w,a)/dA]/dA]/dA, d[d[dA(w,i)/dA]/dA]/dA, d[d[dA(w,m)/dA]/dA]/dA, d[d[dA(a,i)/dA]/dA]/dA, d[d[dA(a,m)/dA]/dA]/dA, d[d[dA(i,m)/dA/dA]/dA, d[d[dA(t,w,a)/dA]/dA]/dA, d[d[dA(t,w,i)/dA]/dA]/dA, d[d[dA(t,w,m)/dA]/dA]/dA, d[d[dA(t,a,i)/dA]/dA]/dA, d[d[dA(t,a,m)/dA]/dA]/dA,  d[d[dA(t,i,m)/dA]/dA]/dA, d[d[dA(w,a,i)/dA]/dA]/dA, d[d[dA(w,a,m)/dA]/dA]/dA, d[d[dA(w,i,m)/dA]/dA]/dA, d[d[dA(a,i,m)/dA]/dA]/dA, d[d[dA(t,w,a,i)/dA]/dA]/dA, d[d[dA(t,w,a,m)/dA/dA]/dA, d[d[dA(t,w,i,m)/dA]/dA]/dA, d[d[dA(t,a,i,m)/dA]/dA]/dA, d[d[dA(w,a,i,m)/dA]/dA]/dA, d[d[dA(t,w,a,i,m)/dA]/dA]/dA.

 

 

or more succinctly, as d[d(dA/dA)/dA]/dA = d[d[d A(t and/or w and/or a and/or i and/or m)/dA]/dA]/dA = Aa3

 

 

or as

 

 

d[d[dA(a)/dA]/dA]/dA  = d[d[d A{[t(a)] and/or [w(a)] and/or [a(a)] and/or [i(a)] and/or [m(a)]}/dA]/dA]/dA = Aa3.

 

 

We can also form the expressions;

 

 

d[d[f(A)]/dA]/dA = d{d [A[t(a)]]/dA and/or d[A[w(a)]]/dA and/or d[A[a(a)]]/dA and/or d[A[i(a)]]/dA and/or d[A[m(a)]]/dA}/dA  = f(Aa)2

 

 

and

 

 

d[d[d[f(A)]/dA]/dA]/dA = d{d{ d [A[t(a)]]/dA and/or d[A[w(a)]]/dA and/or d[A[a(a)]]/dA and/or d[A[i(a)]]/dA and/or d[A[m(a)]]/dA}/dA}/dA  = f(Aa)3A, where A stands for type A differentiation which is not to be confused with the meaning of so-called Type A personality as A is used as an ordinal in a totally different context here.

 

 

and

 

 

d[d[d[f(A)]/dA]/dA]/dA = d{d[d [A[t(a)]]/dA]/dA  and/or d[d [A[w(a)]]/dA]/dA  and/or d[d [A[a(a)]]/dA]/dA  and/or d[d [A[i(a)]]/dA]/dA  and/or d[d [A[m(a)]]/dA]/dA }/dA = f(Aa)3B, where B stands for type B differentiation which is not to be confused with the meaning of so-called Type  B personality as B is used as an ordinal in a totally different context here .

 

 

In fact, one can form yet higher order derivatives of affects with respect to affect as follows.

 

 

Aa5 = d Aa4/dA = d[dAa3/dA]/dA

 

 

 

Aa5 = dAa4/dA =  d[d[d[d[d A{[t(a)] and/or [w(a)] and/or [a(a)] and/or [i(a)] and/or [m(a)]}/dA]/dA]/dA]/dA]/dA.

 

 

 

f(Aa)5A = d[f(Aa)4A]/dA = d[d [f(At)3A]/dA]/dA =  d{d{d{d{ d [A[t(a)]]/dA and/or d[A[w(a)]]/dA and/or d[A[a(a)]]/dA and/or d[A[i(a)]]/dA and/or d[A[m(a)]]/dA}/dA}/dA]/dA]/dA

 

 

 

 

Aa6 = d Aa5/dA = d[d Aa4/dA]/dA = d[d[dAa3/dA]/dA]/dA

 

 

 

Aa6 = dAa5/dA = d[d[d[d[d[d A{[t(a)] and/or [w(a)] and/or [a(a)] and/or [i(a)] and/or [m(a)]}/dA]/dA]/dA]/dA]/dA]/dA

 

 

 

f(Aa)6A = d[f(Aa)5A]/dA = d{ d{d{d{d{ d [A[t(a)]]/dA and/or d[A[w(a)]]/dA and/or d[A[a(a)]]/dA and/or d[A[i(a)]]/dA and/or d[A[m(a)]]/dA}/dA}/dA]/dA]/dA]/dA

 

 

 

 

Aa7 = dAa6/dA

 

f(Aa)7A = d[f(Aa)6A]/dA

 

 

Aa8 = d Aa7/dA

 

f(Aa)8A = d[f(Aa)7A]/dA

 

 

 

Aa9 = d Aa8/dA

 

f(Aa)9A = d[f(Aa)8A]/dA

 

 

Aa10…, Aa11…, Aa12 … etc.

 

 

Anyone for Aa ensemble, or Aa infinity scrapper, or Aa (Aleph 0), or Aa(Aleph 1), or Aa(Aleph 2), or how about Aa Aleph (Aleph 0), or Aa Aleph (Aleph 1) , or Aa Aleph (Aleph 2), or even Aa Aleph (Aleph (Aleph 0)), or Aa Aleph (Aleph (Aleph 1)), or Aa Aleph (Aleph (Aleph 2)), and so on?

 

Thus, for the set of the sets of derivatives of Aa1 through Aa(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Aa1 through Aa(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)},…, {П(0,31)[R]}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Aa1 through Aa(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Aa1 through Aa(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the derivative states in the set of the sets of derivatives of Aa1 through Aa(Aleph 0) is plausible equal to:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Aa1 through Aa(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Aa1 through Aa(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}}}.

 

For the set of the sets of derivatives of Aa1 through Aa(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Aa(Aleph 0) derivative space at the level of 0/(Aleph 0), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Aa1 through Aa(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Aa1 through Aa(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Aa1 through Aa(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Aa1 through Aa(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Aa1 through Aa(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Aa1 through Aa(Aleph 1), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Aa1 through  Aa(Aleph 2), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Aa1 through Aa(Aleph 3), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Aa(Aleph 0) derivative space at the level of 0/(Aleph 1), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Aa1 through Aa(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Aa1 through Aa(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Aa1 through Aa(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Aa1 through  Aa(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations  for the set of the sets of derivatives of Aa1 through Aa(Aleph 0) is plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Aa1 through Aa(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Aa1 through Aa(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Aa1 through Aa(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

 

For super-continuous Aa(Aleph 0) derivative space at the level of 0/(Aleph 2), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Aa1 through Aa(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Aa1 through Aa(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Aa1 through Aa(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Aa1 through Aa(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Aa1 through Aa(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Aa1 through Aa(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Aa1 through Aa(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Aa1 through Aa(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

Similar series can be developed for super-continuity at any applicable level such as 0/(Aleph 3), 0/(Aleph 4), 0/(Aleph 5),…, 0/(Aleph Ω), 0/(Aleph (Aleph 0)), …, 0/(Aleph (Aleph 1)), …, 0/(Aleph (Aleph 2)), …, 0/(Aleph (Aleph 3)),…, 0/(Aleph (Aleph Ω)),…, 0/(Aleph (Aleph (Aleph 0))), …, 0/(Aleph (Aleph (Aleph 1))),…, 0/(Aleph (Aleph (Aleph 2))),…, 0/(Aleph (Aleph (Aleph 3))),…, 0/(Aleph (Aleph  (Aleph Ω))), …

 

An so-on ad infinitum.

 

 

In addition to these numerical functions of Aa as functions of summation series of product series functions, in order to really appreciate the enourmous complexity of the human soul in terms of its potential to evolve and be differentiated from all other souls in its characteristics, we would need to consider how every single category and even every single species of affect of the form Aa can very. Since there may exist an arbitrarily high infinite number species of Aa, the number numerical functions of Aa is utterly beyond recogning. I will cover such notions in terms of mathematical notation in yet another series of articles I will write on this general concept.

 

 

Perhaps these numbers are applicable when one considers that the human soul, in its accidental form and perhaps even in its substantial form stores all experience and other psychodynamics based phenomenon. Every experience adds to the accidental form of the human soul and this includes the souls of all those still alive on Earth, all those in Purgatory, all those in Heaven, all those in Hell, and all those in any Limbo.

Since the human soul can grow without limit in terms of its psychodynamic time –flow world line, such a consideration offers another mechanism where the number of derivative states, combinations of derivative states, and even super-continuity of the derivative state space can grow forever.

 

Folks, for those of you who might balk at me for including literally all souls in the above consideration, including the souls in Hell, as well as bodily extraterrestrial souls and the souls of so-called bodily ultraterrestials sometimes referred to as etherians in the new age UFO buff culture, my reply is that we simply do not understand the full scope of GOD’s Divine Economy. We may never fully comprehend the scope of the Divine Economy because such an utterly eternal scheme, is, well, eternal and never ending.

 

 

 

 

The general meaning of affect derivatives of affect can be viewed as the manner in which the qualitative and/or quantitative aspects of affect as a function of affect very with affect(s). The manner in which affects very with affect may be multi-affect dimensional wherein the dimensions of derivations can be multiple, and wherein the derivations can be taken in parallel, series parallel or serial manner The differentials can be partial or non-partial derivatives, or both partial and non-partial for a given computation.

 

In fact, since there is in theory, no limit to the numbers of qualitatively and quantitatively different affects, and perhaps no limit to the number of possible different types or classes of affects, wherein each person has his or her own unique affects, the number of affect dimensions that can effect affects is literally infinite, given the entirety of the set of created persons, and perhaps also literally infinite for each person as an individual, although we can not intellectually and intuitively understand this specific infinite number.

 

It is interesting to consider the ramifactions of being able to perform realistic calculations involving affect derivatives of affect from a mathematical, theoretical, scientific,  and philosophical perspective.

 

Persons for which one or more nth order derivatives of affect with respect to affect that have large absolute values would tend to have their affects highly influenced by affect, or at least for the affect under consideration with respect to the dimension of the specific affect type(s) or class(es) for which the differentiation(s) are performed. Perhaps a strong coupling between affect and affect indicates a well integrated personality and commensurately, a high degree of affect capacity and a high degree of affect intelligence.

 

We would expect that disembodied human souls, ETI souls, and/or UTI souls in Heaven, Limbo, highly evolved bodily ETI persons, highly evolved UTI persons, and angels to have affect of all kinds and intensities which are highly subject to affect.

 

 

We can also consider two dimensional nth ordered derivatives of affect with respect to affect and time, or with respect to t and T, respectively.

 

Given that A[(a)(T)] =  A[(t and/or w and/or a and/or i and/or m)(a)(T)], the following first order two dimensional derivatives of affect with respect to affect and Time are possible.

 

 

d[dA[(t)(T)]/dA]/dT, d[dA[(w)(T)]/dA]/dT, d[dA[(a)(T)]/dA]/dT, d[dA[(i)(T)]/dA]/dT, d[dA[(m)(T)]/dA]/dT, d[dA[(t,w)(T)]/dA]/dT, d[dA[(t,a)(T)]/dA]/dT, d[dA[(t,i)(T)]/dA]/dT, d[dA[(t,m)(T)]/dA]/dT, d[dA[(w,a)(T)]/dA]/dT, d[dA[(w,i)(T)]/dA]/dT, d[dA[(w,m)(T)]/dA]/dT, d[dA[(a,i)(T)]/dA]/dT, d[dA[(a,m)(T)]/dA]/dT, d[dA[(i,m)(T)]/dA]/dT, d[dA[(t,w,a)(T)]/dA]/dT, d[dA[(t,w,i)(T)]/dA]/dT, d[dA[(t,w,m)(T)]/dA]/dT, d[dA[(t,a,i)(T)]/dA]/dT, d[dA[(t,a,m)(T)]/dA]/dT, d[dA[(t,i,m)(T)]/dA]/dT, d[dA[(w,a,i)(T)]/dA]/dT, d[dA[(w,a,m)(T)]/dA]/dT, d[dA[(w,i,m)(T)]/dA]/dT, d[dA[(a,i,m)(T)]/dA]/dT, d[dA[(t,w,a,i)(T)]/dA]/dT, d[dA[(t,w,a,m)(T)]/dA]/dT, d[dA[(t,w,i,m)(T)]/dA]/dT, d[dA[(t,a,i,m)(T)]/dA]/dT, d[dA[(w,a,i,m)(T)]/dA]/dT, d[dA[(t,w,a,i,m)(T)]/dA]/dT.

 

 

Or more succinctly,  d[dA(T)/dA]/dT = d[dA[(T)(t and/or w and/or a and/or i and/or m)]/dA]/dT

 

or

 

d[dA(T)/dT]/dA = d[dA[(T)(t and/or w and/or a and/or i and/or m)]/dT]/dA

 

 

 

 

 

Or perhaps d[d A[(a)(T)]/dA]/dT  = d[d A [{[t(a)] and/or [w(a)] and/or [a(a)] and/or [i(a)] and/or [m(a)]}(T)]/dA]/dT

 

or

 

Or perhaps d[d A[(a)(T)]/dT]/dA  = d[d A [{[t(a)] and/or [w(a)] and/or [a(a)] and/or [i(a)] and/or [m(a)]}(T)]/dT]/dA

 

 

 

Likewise, we can take the second dual dimensioned affect-time derivatives of  A as follows:

 

d[d[d[dA[(t)(T)]/dA]/dT]/dA]/dT, d[d[d[dA[(w)(T)]/dA]/dT]/dA]/dT, d[d[d[dA[(a)(T)]/dA]/dT]/dA]/dT, d[d[d[dA[(i)(T)]/dA]/dT]/dA]/dT, d[d[d[dA[(m)(T)]/dA]/dT]/dA]/dT, d[d[d[dA[(t,w)(T)]/dA]/dT]/dA]/dT, d[d[d[dA[(t,a)(T)]/dA]/dT]/dA]/dT, d[d[d[dA[(t,i)(T)]/dA]/dT]/dA]/dT, d[d[d[dA[(t,m)(T)]/dA]/dT]/dA]/dT, d[d[d[dA[(w,a)(T)]/dA]/dT]/dA]/dT, d[d[d[dA[(w,i)(T)]/dA]/dT]/dA]/dT, d[d[d[dA[(w,m)(T)]/dA]/dT]/dA]/dT, d[d[d[dA[(a,i)(T)]/dA]/dT]/dA]/dT, d[d[d[dA[(a,m)(T)]/dA]/dT]/dA]/dT, d[d[d[dA[(i,m)(T)]/dA]/dT]/dA]/dT, d[d[d[dA[(t,w,a)(T)]/dA]/dT]/dA]/dT, d[d[d[dA[(t,w,i)(T)]/dA]/dT]/dA]/dT, d[d[d[dA[(t,w,m)(T)]/dA]/dT]/dA]/dT, d[d[d[dA[(t,a,i)(T)]/dA]/dT]/dA]/dT, d[d[d[dA[(t,a,m)(T)]/dA]/dT]/dA]/dT, d[d[d[dA[(t,i,m)(T)]/dA]/dT]/dA]/dT, d[d[d[dA[(w,a,i)(T)]/dA]/dT]/dA]/dT, d[d[d[dA[(w,a,m)(T)]/dA]/dT]/dA]/dT, d[d[d[dA[(w,i,m)(T)]/dA]/dT]/dA]/dT, d[d[d[dA[(a,i,m)(T)]/dA]/dT]/dA]/dT, d[d[d[dA[(t,w,a,i)(T)]/dA]/dT]/dA]/dT, d[d[d[dA[(t,w,a,m)(T)]/dA]/dT]/dA]/dT, d[d[d[dA[(t,w,i,m)(T)]/dA]/dT]/dA]/dT, d[d[d[dA[(t,a,i,m)(T)]/dA]/dT]/dA]/dT, d[d[d[dA[(w,a,i,m)(T)]/dA]/dT]/dA]/dT, d[d[d[dA[(t,w,a,i,m)(T)]/dA]/dT]/dA]/dT.

 

or as:

 

 

 

d[d[d[dA[(t)(T)]/dA]/dT]/dT]/dA, d[d[d[dA[(w)(T)]/dA]/dT]/dT]/dA, d[d[d[dA[(a)(T)]/dA]/dT]/dT]/dA, d[d[d[dA[(i)(T)]/dA]/dT]/dT]/dA, d[d[d[dA[(m)(T)]/dA]/dT]/dT]/dA, d[d[d[dA[(t,w)(T)]/dA]/dT]/dT]/dA, d[d[d[dA[(t,a)(T)]/dA]/dT]/dT]/dA, d[d[d[dA[(t,i)(T)]/dA]/dT]/dT]/dA, d[d[d[dA[(t,m)(T)]/dA]/dT]/dT]/dA, d[d[d[dA[(w,a)(T)]/dA]/dT]/dT]/dA, d[d[d[dA[(w,i)(T)]/dA]/dT]/dT]/dA, d[d[d[dA[(w,m)(T)]/dA]/dT]/dT]/dA, d[d[d[dA[(a,i)(T)]/dA]/dT]/dT]/dA, d[d[d[dA[(a,m)(T)]/dA]/dT]/dT]/dA, d[d[d[dA[(i,m)(T)]/dA]/dT]/dT]/dA, d[d[d[dA[(t,w,a)(T)]/dA]/dT]/dT]/dA, d[d[d[dA[(t,w,i)(T)]/dA]/dT]/dT]/dA, d[d[d[dA[(t,w,m)(T)]/dA]/dT]/dT]/dA, d[d[d[dA[(t,a,i)(T)]/dA]/dT]/dT]/dA, d[d[d[dA[(t,a,m)(T)]/dA]/dT]/dT]/dA, d[d[d[dA[(t,i,m)(T)]/dA]/dT]/dT]/dA, d[d[d[dA[(w,a,i)(T)]/dA]/dT]/dT]/dA, d[d[d[dA[(w,a,m)(T)]/dA]/dT]/dT]/dA, d[d[d[dA[(w,i,m)(T)]/dA]/dT]/dT]/dA, d[d[d[dA[(a,i,m)(T)]/dA]/dT]/dT]/dA, d[d[d[dA[(t,w,a,i)(T)]/dA]/dT]/dT]/dA, d[d[d[dA[(t,w,a,m)(T)]/dA]/dT]/dT]/dA, d[d[d[dA[(t,w,i,m)(T)]/dA]/dT]/dT]/dA, d[d[d[dA[(t,a,i,m)(T)]/dA]/dT]/dT]/dA, d[d[d[dA[(w,a,i,m)(T)]/dA]/dT]/dT]/dA, d[d[d[dA[(t,w,a,i,m)(T)]/dA]/dT]/dT]/dA.

 

or as:

 

d[d[d[dA[(t)(T)]/dT]/dA]/dA]/dT, d[d[d[dA[(w)(T)]/dT]/dA]/dA]/dT, d[d[d[dA[(a)(T)]/dT]/dA]/dA]/dT, d[d[d[dA[(i)(T)]/dT]/dA]/dA]/dT, d[d[d[dA[(m)(T)]/dT]/dA]/dA]/dT, d[d[d[dA[(t,w)(T)]/dT]/dA]/dA]/dT, d[d[d[dA[(t,a)(T)]/dT]/dA]/dA]/dT, d[d[d[dA[(t,i)(T)]/dT]/dA]/dA]/dT, d[d[d[dA[(t,m)(T)]/dT]/dA]/dA]/dT, d[d[d[dA[(w,a)(T)]/dT]/dA]/dA]/dT, d[d[d[dA[(w,i)(T)]/dT]/dA]/dA]/dT, d[d[d[dA[(w,m)(T)]/dT]/dA]/dA]/dT, d[d[d[dA[(a,i)(T)]/dT]/dA]/dA]/dT, d[d[d[dA[(a,m)(T)]/dT]/dA]/dA]/dT, d[d[d[dA[(i,m)(T)]/dT]/dA]/dA]/dT, d[d[d[dA[(t,w,a)(T)]/dT]/dA]/dA]/dT, d[d[d[dA[(t,w,i)(T)]/dT]/dA]/dA]/dT, d[d[d[dA[(t,w,m)(T)]/dT]/dA]/dA]/dT, d[d[d[dA[(t,a,i)(T)]/dT]/dA]/dA]/dT, d[d[d[dA[(t,a,m)(T)]/dT]/dA]/dA]/dT, d[d[d[dA[(t,i,m)(T)]/dT]/dA]/dA]/dT, d[d[d[dA[(w,a,i)(T)]/dT]/dA]/dA]/dT, d[d[d[dA[(w,a,m)(T)]/dT]/dA]/dA]/dT, d[d[d[dA[(w,i,m)(T)]/dT]/dA]/dA]/dT, d[d[d[dA[(a,i,m)(T)]/dT]/dA]/dA]/dT, d[d[d[dA[(t,w,a,i)(T)]/dT]/dA]/dA]/dT, d[d[d[dA[(t,w,a,m)(T)]/dT]/dA]/dA]/dT, d[d[d[dA[(t,w,i,m)(T)]/dT]/dA]/dA]/dT, d[d[d[dA[(t,a,i,m)(T)]/dT]/dA]/dA]/dT, d[d[d[dA[(w,a,i,m)(T)]/dT]/dA]/dA]/dT, d[d[d[dA[(t,w,a,i,m)(T)]/dT]/dA]/dA]/dT.

 

 

or as;

 

 

 

 

d[d[d[dA(t)/dA]/dA]/dT]/dT, d[d[d[dA(w)/dA]/dA]/dT]/dT, d[d[d[dA(a)/dA]/dA]/dT]/dT, d[d[d[dA(i)/dA]/dA]/dT]/dT, d[d[d[dA(m)/dA]/dA]/dT]/dT, d[d[d[dA(t,w)/dA]/dA]/dT]/dT, d[d[d[dA(t,a)/dA]/dA]/dT]/dT, d[d[d[dA(t,i)/dA]/dA]/dT]/dT, d[d[d[dA(t,m)/dA]/dA]/dT]/dT, d[d[d[dA(w,a)/dA]/dA]/dT]/dT, d[d[d[dA(w,i)/dA]/dA]/dT]/dT, d[d[d[dA(w,m)/dA]/dA]/dT]/dT, d[d[d[dA(a,i)/dA]/dA]/dT]/dT, d[d[d[dA(a,m)/dA]/dA]/dT]/dT, d[d[d[dA(i,m)/dA]/dA]/dT]/dT, d[d[d[dA(t,w,a)/dA]/dA]/dT]/dT, d[d[d[dA(t,w,i)/dA]/dA]/dT]/dT, d[d[d[dA(t,w,m)/dA]/dA]/dT]/dT, d[d[d[dA(t,a,i)/dA]/dA]/dT]/dT, d[d[d[dA(t,a,m)/dA]/dA]/dT]/dT,  d[d[d[dA(t,i,m)/dA]/dA]/dT]/dT, d[d[d[dA(w,a,i)/dA]/dA]/dT]/dT, d[d[d[dA(w,a,m)/dA]/dA]/dT]/dT, d[d[d[dA(w,i,m)/dA]/dA]/dT]/dT, d[d[d[dA(a,i,m)/dA]/dA]/dT]/dT, d[d[d[dA(t,w,a,i)/dA]/dA]/dT]/dT, d[d[d[dA(t,w,a,m)/dA/dA, d[d[d[dA(t,w,i,m)/dA]/dA]/dT]/dT, d[d[d[dA(t,a,i,m)/dA]/dA]/dT]/dT, d[d[d[dA(w,a,i,m)/dA]/dA]/dT]/dT, d[d[d[dA(t,w,a,i,m)/dA]/dA]/dT]/dT..

 

or as:

 

d[d[d[dA(t)/dT]/dA]/dT]/dA, d[d[d[dA(w)/dT]/dA]/dT]/dA, d[d[d[dA(a)/dT]/dA]/dT]/dA, d[d[d[dA(i)/dT]/dA]/dT]/dA, d[d[d[dA(m)/dT]/dA]/dT]/dA, d[d[d[dA(t,w)/dT]/dA]/dT]/dA, d[d[d[dA(t,a)/dT]/dA]/dT]/dA, d[d[d[dA(t,i)/dT]/dA]/dT]/dA, d[d[d[dA(t,m)/dT]/dA]/dT]/dA, d[d[d[dA(w,a)/dT]/dA]/dT]/dA, d[d[d[dA(w,i)/dT]/dA]/dT]/dA, d[d[d[dA(w,m)/dT]/dA]/dT]/dA, d[d[d[dA(a,i)/dT]/dA]/dT]/dA, d[d[d[dA(a,m)/dT]/dA]/dT]/dA, d[d[d[dA(i,m)/ dT]/dA]/dT]/dA, d[d[d[dA(t,w,a)/dT]/dA]/dT]/dA, d[d[d[dA(t,w,i)/dT]/dA]/dT]/dA, d[d[d[dA(t,w,m)/dT]/dA]/dT]/dA, d[d[d[dA(t,a,i)/dT]/dA]/dT]/dA, d[d[d[dA(t,a,m)/dT]/dA]/dT]/dA,  d[d[d[dA(t,i,m)/dT]/dA]/dT]/dA, d[d[d[dA(w,a,i)/dT]/dA]/dT]/dA, d[d[d[dA(w,a,m)/dT]/dA]/dT]/dA, d[d[d[dA(w,i,m)/dT]/dA]/dT]/dA, d[d[d[dA(a,i,m)/dT]/dA]/dT]/dA, d[d[d[dA(t,w,a,i)/dT]/dA]/dT]/dA, d[d[d[dA(t,w,a,m)/dA/dA, d[d[d[dA(t,w,i,m)/dT]/dA]/dT]/dA, d[d[d[dA(t,a,i,m)/dT]/dA]/dT]/dA, d[d[d[dA(w,a,i,m)/dT]/dA]/dT]/dA, d[d[d[dA(t,w,a,i,m)/dT]/dA]/dT]/dA..

 

or as:

 

d[d[d[dA(t)/dT]/dT]/dA]/dA, d[d[d[dA(w)/dT]/dT]/dA]/dA, d[d[d[dA(a)/dT]/dT]/dA]/dA, d[d[d[dA(i)/dT]/dT]/dA]/dA, d[d[d[dA(m)/dT]/dT]/dA]/dA, d[d[d[dA(t,w)/dT]/dT]/dA]/dA, d[d[d[dA(t,a)/dT]/dT]/dA]/dA, d[d[d[dA(t,i)/dT]/dT]/dA]/dA, d[d[d[dA(t,m)/dT]/dT]/dA]/dA, d[d[d[dA(w,a)/dT]/dT]/dA]/dA, d[d[d[dA(w,i)/dT]/dT]/dA]/dA, d[d[d[dA(w,m)/dT]/dT]/dA]/dA, d[d[d[dA(a,i)/dT]/dT]/dA]/dA, d[d[d[dA(a,m)/ dT]/dT]/dA]/dA, d[d[d[dA(i,m)/ dT]/dT]/dA]/dA, d[d[d[dA(t,w,a)/dT]/dT]/dA]/dA, d[d[d[dA(t,w,i)/dT]/dT]/dA]/dA, d[d[d[dA(t,w,m)/dT]/dT]/dA]/dA, d[d[d[dA(t,a,i)/dT]/dT]/dA]/dA, d[d[d[dA(t,a,m)/dT]/dT]/dA]/dA,  d[d[d[dA(t,i,m)/dT]/dT]/dA]/dA, d[d[d[dA(w,a,i)/dT]/dT]/dA]/dA, d[d[d[dA(w,a,m)/dT]/dT]/dA]/dA, d[d[d[dA(w,i,m)/dT]/dT]/dA]/dA, d[d[d[dA(a,i,m)/dT]/dT]/dA]/dA, d[d[d[dA(t,w,a,i)/dT]/dT]/dA]/dA, d[d[d[dA(t,w,a,m)/dA/dA, d[d[d[dA(t,w,i,m)/dT]/dT]/dA]/dA, d[d[d[dA(t,a,i,m)/dT]/dT]/dA]/dA, d[d[d[dA(w,a,i,m)/dT]/dT]/dA]/dA, d[d[d[dA(t,w,a,i,m)/dT]/dT]/dA]/dA..

 

 

We can also take higher order duel dimensional derivatives of affect as a function of affect and time but the symbolic expression of the set of such derivatives very soon becomes excessively lengthly to write and so these higher order derivatives as such are not mentioned here except to say that they would be computed in an analogous manner to the second order duel dimensional derivatives described above.

 

 

 

 

Now, the above variable of time, T,  can have multiple meanings or aspects. One such meaning is objective time and in such a case for large non-zero values of An, where n = 1,2,3,…, the person experiencing such an affect or complex of affects  might not subjectively experience the affect(s) as occurring any faster than we ordinary humans do.

 

 

However, another interpretation of the variable of Time is subjective time. In such a case for large non-zero absolute values of An, where n = 1,2,3,…, the person experiencing such an affect or complex of affects  would subjectively experience the affect(s) as occurring or changing faster than we ordinary humans experience, in fact the higher the absolute value of non-zero An, especially for large n, the rate of change of affect with respect to time would progress at an incredible rate. We ordinary humans would likely be completely overwhelmed by subjective psychic experiences of such An phenomenon.

 

 

Could there be other objective temporal dimensions beside the one objective temporal dimension that we know of, and the seemingly one subjective dimension of time that we experience? As someone who normally writes on the topic of exotic space craft propulsion systems such as proposed interstellar space craft propulsion systems, I am familiar with the theoretical paradigms that there may exist higher dimensions of space and perhaps more than one dimension of time, and so I say, never say never.

 

The above notation of derivatives and differential equations is just an infinitesimal glimpse of the number of possible equations as such and related constructs. Trust me, I can reasonably in good confidence re-assure you of such.

 

 

 

30) Just A Shadow Of A Glimpse Of The Utterly Limitless Number Derivatives of Human Instinct  With Respect To Time, Thought, Volition, Affect, Memory, Instinct, And Emotion  Where These Latter 6 Psychodynamic Parameter Are Likely Just An Infinitesimal Fraction Of The Number Of Possible Psychodynamic Parameters, Of Which In This Life, We Have  A Glimpse Of Relatively Few.

 

Human instinct in its advanced forms is the stuff of intellectual and spiritual intuitions. In its romantic forms, instinct is the stuff of marriage and family.

 

In  this post, I make the conjecture that psychodynamic derivatives of instinct of various infinite orders are non-zero. In this life, we only notice a miniscule aspect of our souls and so we likely will never I this life have an intuitive glimpse of these derivatives of order 3 or greater. This does not mean that such infinite derivatives cannot exist, and perhaps at some levels extreme order derivatives exist for us in this life, except where the experienced aspects of such derivatives cancel out in some sort of renormalizations mechanism, provided perhaps by GOD, so that we can cope with our extreme unlimited potentials in a toned down manner so as to not be overwhelmed. After all, there is great joy in opening the small Christmas presents before the large ones just as there is great joy in driving our first few miles on a senic cross-continent road trip. Please join me on a quest to understand the human soul.

 

The possibility of non-zero various infinity ordered derivatives, or even extremely large order non-zero psychodynamic derivatives perhaps points to a super-stability and super-simplicity, or at the very least extreme simplicity, of the human soul amidst the complex spiritual and psychodynamic processes that occur in the temporal evolution of the human soul. After all, since the human soul is unchangeably the soul that it is, giving the spiritual, psychological, accidental, falcultative,  thermodynamic processes that occur within the human soul, the soul continues to be the soul that it precisely is and no other soul. This is true even for the souls of those who go to Hell.

 

Now we should all have hope in a life in Heaven upon bodily death, but to paraphrase the words of Blessed Pope John Paul II, the extent to which everlasting life is lived out in a life beyond the grave for the souls who go to Hell is a complete mystery to us at present. However, we must trust GODs providence and HIS Divine Economy regarding HIS currently vieled utmost altimate plans for HIS creatures. Thus, I implore the readership of my blog, and of this post in general, to Be Not Afraid! Coming from a sometimes grumpy older middle-aged adult male, I say Don’t Worry! Be Happy! Just being able to write articles and share with you some of my ideas gives me great enthusiasm.

 

Instinct  can be a function or partially a function of emotion, will, affect, instinct, emotion and/or memory; and thought as such can be expressed as follows:

 

 

I(t), I(w), I(a), I(i), I(m), I(t,w), I(t,a), I(t,i), I(t,m), I(w,a), I(w,i), I(w,m), I(a,i), I(a,m), I(i,m), I(t,w,a), I(t,w,i), I(t,w,m), I(t,a,i), I(t,a,m), I(t,i,m), I(w,a,i), I(w,a,m), I(w,i,m), I(a,i,m), I(t,w,a,i), I(t,w,a,m), I(t,w,i,m), I(t,a,i,m), I(w,a,i,m), I(t,w,a,i,m)

 

I(t,e), I(w,e), I(a,e), I(i,e), I(m,e), I(t,w,e), I(t,a,e), I(t,i,e), I(t,m,e), I(w,a,e), I(w,i,e), I(w,m,e), I(a,i,e), I(a,m,e), I(i,m,e), I(t,w,a,e), I(t,w,i,e), I(t,w,m,e), I(t,a,i,e), I(t,a,m,e), I(t,i,m,e), I(w,a,i,e), I(w,a,m,e), I(w,i,m,e), I(a,i,m,e), I(t,w,a,i,e), I(t,w,a,m,e), I(t,w,i,m,e), I(t,a,i,m,e), I(w,a,i,m,e), I(t,w,a,i,m,e).

 

Note that some differential expressions involving  the form of functions of instinct, or I,  as a function of emotion, e, by itself, or in conjunction with any sub-set of the parameters of t,w,a,i,m, are not included to the same extent as many similar expressions including I, and these other parameters denoted by the small letters, t,w,a,i, and/or m in this section. A more comphrensive post will include the currently omitted explicit formulas incorporating the parameter, e. Note that capital e, or E, is a parameter that is often included in the differential equations herein, but then so in a slightly different context than e would have be included. The difference between e and E will become clear from the context of the specific formulas.

 

In all, there are (2 EXP n) – 1 = (2 EXP 6) – 1 = 63 expressions as such if one assumes the previous five dimensions of will.

 

Assuming that each of the above function f(I)  is perfectly continuous, the number of forms that the general emotion function, f(I), can have is plausibly equal to П(1,62)R where R is the number of real numbers.

 

Assuming that each of the above functions f(I) is super-continuous at the level of 0/(Aleph 0) where Aleph 0 is the number of integers, the number of forms that the general emotion function, f(I), can have is plausibly equal to П(1,62)[R x (Aleph 0)] where R is the number of real numbers.

 

Assuming that each of the above functions f(I) is super-continuous at the level of 0/(Aleph 1) where Aleph 1 is the number of real numbers according to the Continuum Hypotheses, the number of forms that the general instinct function, f(I), can have is plausibly equal to П(1,62)[R x (Aleph 1)] where R is the number of real numbers.

 

Assuming that each of the above functions f(I) is super-continuous at the level of 0/(Aleph 2) where Aleph 2 is is greater than Aleph 1 by a factor of infinity (the exact details of this infinity of which are a little more involve than the latter simple statement), the number of forms that the general instinct function, f(I), can have is plausibly equal to П(1,62)[R x (Aleph 2)] where R is the number of real numbers.

 

Assuming that each of the above functions f(I) is super-continuous at the level of 0/(Aleph 3) where Aleph 3 is is greater than Aleph 2 by a factor of infinity (the exact details of this infinity of which are a little more involve than the latter simple statement), the number of forms that the general instinct function, f(I), can have is plausibly equal to П(1,62)[R x (Aleph 3)] where R is the number of real numbers.

 

… and so on ad infinitum to, through, and beyond the following product series, П(1,62)[R x (Aleph 4)],   П(1,62)[R x (Aleph 5)],  П(1,62)[R x (Aleph 6)],…,  П(1,62)[R x (Aleph Ω)], …,  П(1,62)[R x (Aleph (Aleph 0))], …, П(1,62)[R x (Aleph (Aleph 1))], …, П(1,62)[R x (Aleph (Aleph 2))], … , П(1,62)[R x (Aleph (Aleph Ω))], …, П(1,62)[R x (Aleph (Aleph (Aleph 0)))] and so on perhaps in an ever lasting series even a  the latter level of abstraction.

 

Assuming that each of the above functions f(I) is super-continuous at the level of 0/(Aleph 2) where Aleph 2 is is greater than Aleph 1 by a factor of infinity (the exact details of this infinity of which are a little more involve than the latter simple statement), the number of forms that the general instinct function, f(I), can have is plausibly equal to П(1,62)[R x (Aleph 2)] where R is the number of real numbers.

 

We can summarize all of these combinations as follows in compact symbolism that is intuitively clear to follow:

 

 

I = I(t and/or w and/or a and/or i and/or m)

 

 

We can express I as a function of time as follows: I(T) =  I[(t and/or w and/or a and/or i and/or m),(T)] or perhaps the following notation can be more appropriate in certain circumstances.

 

 

I(T) = I{[t(T)] and/or [w(T)] and/or [a(T)] and/or [i(T)] and/or [m(T)]}.

 

 

Thus, the following first order derivatives of instinct with respect to time are possible.

 

 

dI(t)/dT, dI(w)/dT, dI(a)/dT, dI(i)/dT, dI(m)/dT, dI(t,w)/dT, dI(t,a)/dT, dI(t,i)/dT, dI(t,m)/dT, dI(w,a)/dT, dI(w,i)/dT, dI(w,m)/dT, dI(a,i)/dT, dI(a,m)/dT, dI(i,m)/dT, dI(t,w,a)/dT, dI(t,w,i)/dT, dI(t,w,m)/dT, dI(t,a,i)/dT, dI(t,a,m)/dT, dI(t,i,m)/dT, dI(w,a,i)/dT, dI(w,a,m)/dT, dI(w,i,m)/dT, dI(a,i,m)/dT, dI(t,w,a,i)/dT, dI(t,w,a,m)/dT, dI(t,w,i,m)/dT, dI(t,a,i,m)/dT, dI(w,a,i,m)/dT, dI(t,w,a,i,m)/dT.

 

 

Or more succinctly,  dI/dT = dI(t and/or w and/or a and/or i and/or m)/dT

 

 

Or perhaps dI(T)/dT =d I{[t(T)] and/or [w(T)] and/or [a(T)] and/or [i(T)] and/or [m(T)]}/dT.

 

 

Likewise, we can take the second time derivatives of  I as follows:

 

 

 

d[dI(t)/dT]/dT, d[dI(w)/dT]/dT, d[dI(a)/dT]/dT, d[dI(i)/dT]/dT, d[dI(m)/dT]/dT, d[dI(t,w)/dT]/dT, d[dI(t,a)/dT]/dT, d[dI(t,i)/dT]/dT, d[dI(t,m)/dT]/dT, d[dI(w,a)/dT]/dT, d[dI(w,i)/dT]/dT, d[dI(w,m)/dT]/dT, d[dI(a,i)/dT]/dT, d[dI(a,m)/dT]/dT, d[dI(i,m)/dT/dT, d[dI(t,w,a)/dT]/dT, d[dI(t,w,i)/dT]/dT, d[dI(t,w,m)/dT]/dT, d[dI(t,a,i)/dT]/dT, d[dI(t,a,m)/dT]/dT,  d[dI(t,i,m)/dT]/dT, d[dI(w,a,i)/dT]/dT, d[dI(w,a,m)/dT]/dT, d[dI(w,i,m)/dT]/dT, d[dI(a,i,m)/dT]/dT, d[dI(t,w,a,i)/dT]/dT, d[dI(t,w,a,m)/dT/dT, d[dI(t,w,i,m)/dT]/dT, d[dI(t,a,i,m)/dT]/dT, d[dI(w,a,i,m)/dT]/dT, d[dI(t,w,a,i,m)/dT]/dT..

 

 

or more succinctly, as d(dI/dT)/dT = d[d I(t and/or w and/or a and/or i and/or m)/dT]/dT = I2

 

 

or as

 

 

d[dI(T)/dT]/dT  = d[d I{[t(T)] and/or [w(T)] and/or [a(T)] and/or [i(T)] and/or [m(T)]}/dT]/dT = I2.

 

 

 

Likewise, we can take the third time derivatives of  I as follows:

 

 

 

d[d[dI(t)/dT]/dT]/dT, d[d[dI(w)/dT]/dT]/dT, d[d[dI(a)/dT]/dT]/dT, d[d[dI(i)/dT]/dT]/dT, d[d[dI(m)/dT]/dT]/dT, d[d[dI(t,w)/dT]/dT]/dT, d[d[dI(t,a)/dT]/dT]/dT, d[d[dI(t,i)/dT]/dT]/dT, d[d[dI(t,m)/dT]/dT]/dT, d[d[dI(w,a)/dT]/dT]/dT, d[d[dI(w,i)/dT]/dT]/dT, d[d[dI(w,m)/dT]/dT]/dT, d[d[dI(a,i)/dT]/dT]/dT, d[d[dI(a,m)/dT]/dT]/dT, d[d[dI(i,m)/dT/dT]/dT, d[d[dI(t,w,a)/dT]/dT]/dT, d[d[dI(t,w,i)/dT]/dT]/dT, d[d[dI(t,w,m)/dT]/dT]/dT, d[d[dI(t,a,i)/dT]/dT]/dT, d[d[dI(t,a,m)/dT]/dT]/dT,  d[d[dI(t,i,m)/dT]/dT]/dT, d[d[dI(w,a,i)/dT]/dT]/dT, d[d[dI(w,a,m)/dT]/dT]/dT, d[d[dI(w,i,m)/dT]/dT]/dT, d[d[dI(a,i,m)/dT]/dT]/dT, d[d[dI(t,w,a,i)/dT]/dT]/dT, d[d[dI(t,w,a,m)/dT/dT]/dT, d[d[dI(t,w,i,m)/dT]/dT]/dT, d[d[dI(t,a,i,m)/dT]/dT]/dT, d[d[dI(w,a,i,m)/dT]/dT]/dT, d[d[dI(t,w,a,i,m)/dT]/dT]/dT.

 

 

or more succinctly, as d[d(dI/dT)/dT]/dT = d[d[d I(t and/or w and/or a and/or i and/or m)/dT]/dT]/dT = I3

 

 

or as

 

 

d[d[dI(T)/dT]/dT]/dT  = d[d[d I{[t(T)] and/or [w(T)] and/or [a(T)] and/or [i(T)] and/or [m(T)]}/dT]/dT]/dT = I3.

 

 

We can also form the expressions;

 

 

d[d[f(I)]/dT]/dT = d{d [I[t(T)]]/dT and/or d[I[w(T)]]/dT and/or d[I[a(T)]]/dT and/or d[I[i(T)]]/dT and/or d[I[m(T)]]/dT}/dT  = f(I)2

 

 

and

 

 

d[d[d[f(I)]/dT]/dT]/dT = d{d{ d [I[t(T)]]/dT and/or d[I[w(T)]]/dT and/or d[I[a(T)]]/dT and/or d[I[i(T)]]/dT and/or d[I[m(T)]]/dT}/dT}/dT  = f(I)3A, where A stands for type A differentiation which is not to be confused with the meaning of so-called Type A personality as A is used as an ordinal in a totally different context here.

 

 

and

 

 

d[d[d[f(I)]/dT]/dT]/dT = d{d[d [I[t(T)]]/dT]/dT  and/or d[d [I[w(T)]]/dT]/dT  and/or d[d [I[a(T)]]/dT]/dT  and/or d[d [I[i(T)]]/dT]/dT  and/or d[d [I[m(T)]]/dT]/dT }/dT = f(I)3B, where B stands for type B differentiation which is not to be confused with the meaning of a  so-called Type  B personality as B is used as an ordinal in a totally different context here .

 

 

In fact, one can form yet higher order derivatives of instincts with respect to time as follows.

 

 

I5 = d I4/dT = d[dI3/dT]/dT

 

 

 

I5 = d I4/dT =  d[d[d[d[d I{[t(T)] and/or [w(T)] and/or [a(T)] and/or [i(T)] and/or [m(T)]}/dT]/dT]/dT]/dT]/dT.

 

 

 

f(I)5A = d[f(I)4A]/dT = d[d [f(I)3A]/dT]/dT =  d{d{d{d{ d [I[t(T)]]/dT and/or d[I[w(T)]]/dT and/or d[I[a(T)]]/dT and/or d[I[i(T)]]/dT and/or d[I[m(T)]]/dT}/dT}/dT]/dT]/dT

 

 

 

 

I6 = d I5/dT = d[d I4/dT]/dT = d[d[dI3/dT]/dT]/dT

 

 

 

I6 = dI5/dT = d[d[d[d[d[d I{[t(T)] and/or [w(T)] and/or [a(T)] and/or [i(T)] and/or [m(T)]}/dT]/dT]/dT]/dT]/dT]/dT

 

 

 

f(I)6A = d[f(I)5A]/dT = d{ d{d{d{d{ d [I[t(T)]]/dT and/or d[I[w(T)]]/dT and/or d[I[a(T)]]/dT and/or d[I[i(T)]]/dT and/or d[I[m(T)]]/dT}/dT}/dT]/dT]/dT]/dT

 

 

 

 

I7 = dI6/dT

 

f(I)7A = d[f(I)6A]/dT

 

 

I8 = d I7/dT

 

f(I)8A = d[f(I)7A]/dT

 

 

 

I9 = d I8/dT

 

f(I)9A = d[f(I)8A]/dT

 

 

I10…, I11…, I12 … etc.

 

 

Anyone for I ensemble, or I infinity scrapper, or I (Aleph 0), or I(Aleph 1), or I(Aleph 2), or how about I Aleph (Aleph 0), or I Aleph (Aleph 1) , or I Aleph (Aleph 2), or even I Aleph (Aleph (Aleph 0)), or I Aleph (Aleph (Aleph 1)), or I Aleph (Aleph (Aleph 2)), and so on?

 

Thus, for the set of the sets of derivatives of I1 through I(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}.

 

For the set of the sets of derivatives of I1 through I(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)},…, {П(0,31)[R]}_{(Aleph 1)}.

 

For the set of the sets of derivatives of I1 through I(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}.

 

For the set of the sets of derivatives of I1 through I(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the derivative states in the set of the sets of derivatives of I1 through I(Aleph 0) is plausible equal to:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of I1 through I(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of I1 through I(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}}}.

 

For the set of the sets of derivatives of I1 through I(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous I(Aleph 0) derivative space at the level of 0/(Aleph 0), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of I1 through I(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of I1 through I(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of I1 through I(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of I1 through I(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of I1 through I(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of I1 through I(Aleph 1), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of I1 through  I(Aleph 2), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of I1 through I(Aleph 3), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous I(Aleph 0) derivative space at the level of 0/(Aleph 1), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of I1 through I(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of I1 through I(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of I1 through I(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of I1 through  I(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations  for the set of the sets of derivatives of I1 through I(Aleph 0) is plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of I1 through I(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of I1 through I(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of I1 through I(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

 

For super-continuous I(Aleph 0) derivative space at the level of 0/(Aleph 2), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of I1 through I(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of I1 through I(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of I1 through I(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of I1 through I(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of I1 through I(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of I1 through I(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of I1 through I(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of I1 through I(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

Similar series can be developed for super-continuity at any applicable level such as 0/(Aleph 3), 0/(Aleph 4), 0/(Aleph 5),…, 0/(Aleph Ω), 0/(Aleph (Aleph 0)), …, 0/(Aleph (Aleph 1)), …, 0/(Aleph (Aleph 2)), …, 0/(Aleph (Aleph 3)),…, 0/(Aleph (Aleph Ω)),…, 0/(Aleph (Aleph (Aleph 0))), …, 0/(Aleph (Aleph (Aleph 1))),…, 0/(Aleph (Aleph (Aleph 2))),…, 0/(Aleph (Aleph (Aleph 3))),…, 0/(Aleph (Aleph  (Aleph Ω))), …

 

An so-on ad infinitum.

 

 

In addition to these numerical functions of I as functions of summation series of product series functions, in order to really appreciate the enourmous complexity of the human soul in terms of its potential to evolve and be differentiated from all other souls in its characteristics, we would need to consider how every single category and even every single species of affect of the form I can very. Since there may exist an arbitrarily high infinite number species of I, the number of numerical functions of I is utterly beyond recogning. I will cover such notions in terms of mathematical notation in yet another series of articles I will write on this general concept.

 

 

Perhaps these numbers are applicable when one considers that the human soul, in its accidental form and perhaps even in its substantial form stores all experience and other psychodynamics based phenomenon. Every experience adds to the accidental form of the human soul and this includes the souls of all those still alive on Earth, all those in Purgatory, all those in Heaven, all those in Hell, and all those in any Limbo.

Since the human soul can grow without limit in terms of its psychodynamic time –flow world line, such a consideration offers another mechanism where the number of derivative states, combinations of derivative states, and even super-continuity of the derivative state space can grow forever.

 

Folks, for those of you who might balk at me for including literally all souls in the above consideration, including the souls in Hell, as well as bodily extraterrestrial souls and the souls of so-called bodily ultraterrestials sometimes referred to as etherians in the new age UFO buff culture, my reply is that we simply do not understand the full scope of GOD’s Divine Economy. We may never fully comprehend the scope of the Divine Economy because such an utterly eternal scheme, is, well, eternal and never ending.

 

 

 

 

We can also express instinct qualitatively, statistically, and perhaps with the use of some forms of real analyses as a derivative with respect to emotion or with respect to e.

 

Given that I(e) =  I(t and/or w and/or a and/or i and/or m), the following first order derivatives of instinct  with respect to emotion are possible.

 

 

dI(t)/dE, dI(w)/dE, dI(a)/dE, dI(i)/dE, dI(m)/dE, dI(t,w)/dE, dI(t,a)/dE, dI(t,i)/dE, dI(t,m)/dE, dI(w,a)/dE, dI(w,i)/dE, dI(w,m)/dE, dI(a,i)/dE, dI(a,m)/dE, dI(i,m)/dE, dI(t,w,a)/dE, dI(t,w,i)/dE, dI(t,w,m)/dE, dI(t,a,i)/dE, dI(t,a,m)/dE, dI(t,i,m)/dE, dI(w,a,i)/dE, dI(w,a,m)/dE, dI(w,i,m)/dE, dI(a,i,m)/dE, dI(t,w,a,i)/dE, dI(t,w,a,m)/dE, dI(t,w,i,m)/dE, dI(t,a,i,m)/dE, dI(w,a,i,m)/dE, dI(t,w,a,i,m)/dE.

 

 

Or more succinctly,  dI/dE = dI(t and/or w and/or a and/or i and/or m)/dE

 

 

Or perhaps dI(e)/dE =d I{[t(e)] and/or [w(e)] and/or [a(e)] and/or [i(e)] and/or [m(e)]}/dE.

 

 

Likewise, we can take the second emotion derivatives of  I as follows:

 

 

 

d[dI(t)/dE]/dE, d[dI(w)/dE]/dE, d[dI(a)/dE]/dE, d[dI(i)/dE]/dE, d[dI(m)/dE]/dE, d[dI(t,w)/dE]/dE, d[dI(t,a)/dE]/dE, d[dI(t,i)/dE]/dE, d[dI(t,m)/dE]/dE, d[dI(w,a)/dE]/dE, d[dI(w,i)/dE]/dE, d[dI(w,m)/dE]/dE, d[dI(a,i)/dE]/dE, d[dI(a,m)/dE]/dE, d[dI(i,m)/dE/dE, d[dI(t,w,a)/dE]/dE, d[dI(t,w,i)/dE]/dE, d[dI(t,w,m)/dE]/dE, d[dI(t,a,i)/dE]/dE, d[dI(t,a,m)/dE]/dE,  d[dI(t,i,m)/dE]/dE, d[dI(w,a,i)/dE]/dE, d[dI(w,a,m)/dE]/dE, d[dI(w,i,m)/dE]/dE, d[dI(a,i,m)/dE]/dE, d[dI(t,w,a,i)/dE]/dE, d[dI(t,w,a,m)/dE/dE, d[dI(t,w,i,m)/dE]/dE, d[dI(t,a,i,m)/dE]/dE, d[dI(w,a,i,m)/dE]/dE, d[dI(t,w,a,i,m)/dE]/dE..

 

 

or more succinctly, as d(dI/dE)/dE = d[d I(t and/or w and/or a and/or i and/or m)/dE]/dE = It2

 

 

or as

 

 

d[dI(e)/dE]/dE  = d[d I{[t(e)] and/or [w(e)] and/or [a(e)] and/or [i(e)] and/or [m(e)]}/dE]/dE = Ie2.

 

 

 

Likewise, we can take the third emotion derivatives of  I as follows:

 

 

 

d[d[dI(t)/dE]/dE]/dE, d[d[dI(w)/dE]/dE]/dE, d[d[dI(a)/dE]/dE]/dE, d[d[dI(i)/dE]/dE]/dE, d[d[dI(m)/dE]/dE]/dE, d[d[dI(t,w)/dE]/dE]/dE, d[d[dI(t,a)/dE]/dE]/dE, d[d[dI(t,i)/dE]/dE]/dE, d[d[dI(t,m)/dE]/dE]/dE, d[d[dI(w,a)/dE]/dE]/dE, d[d[dI(w,i)/dE]/dE]/dE, d[d[dI(w,m)/dE]/dE]/dE, d[d[dI(a,i)/dE]/dE]/dE, d[d[dI(a,m)/dE]/dE]/dE, d[d[dI(i,m)/dE/dE]/dE, d[d[dI(t,w,a)/dE]/dE]/dE, d[d[dI(t,w,i)/dE]/dE]/dE, d[d[dI(t,w,m)/dE]/dE]/dE, d[d[dI(t,a,i)/dE]/dE]/dE, d[d[dI(t,a,m)/dE]/dE]/dE,  d[d[dI(t,i,m)/dE]/dE]/dE, d[d[dI(w,a,i)/dE]/dE]/dE, d[d[dI(w,a,m)/dE]/dE]/dE, d[d[dI(w,i,m)/dE]/dE]/dE, d[d[dI(a,i,m)/dE]/dE]/dE, d[d[dI(t,w,a,i)/dE]/dE]/dE, d[d[dI(t,w,a,m)/dE/dE]/dE, d[d[dI(t,w,i,m)/dE]/dE]/dE, d[d[dI(t,a,i,m)/dE]/dE]/dE, d[d[dI(w,a,i,m)/dE]/dE]/dE, d[d[dI(t,w,a,i,m)/dE]/dE]/dE.

 

 

or more succinctly, as d[d(dI/dE)/dE]/dE = d[d[d I(t and/or w and/or a and/or i and/or m)/dE]/dE]/dE = Ie3

 

 

or as

 

 

d[d[dI(e)/dE]/dE]/dE  = d[d[d I{[t(e)] and/or [w(e)] and/or [a(e)] and/or [i(e)] and/or [m(e)]}/dE]/dE]/dE = Ie3.

 

 

We can also form the expressions;

 

 

d[d[f(I)]/dE]/dE = d{d [I[t(e)]]/dE and/or d[I[w(e)]]/dE and/or d[I[a(e)]]/dE and/or d[I[i(e)]]/dE and/or d[I[m(e)]]/dE}/dE  = f(Ie)2

 

 

and

 

 

d[d[d[f(I)]/dE]/dE]/dE = d{d{ d [I[t(e)]]/dE and/or d[I[w(e)]]/dE and/or d[I[a(e)]]/dE and/or d[I[i(e)]]/dE and/or d[I[m(e)]]/dE}/dE}/dE  = f(Ie)3A, where A stands for type A differentiation which is not to be confused with the meaning of so-called Type A personality as A is used as an ordinal in a totally different context here.

 

 

and

 

 

d[d[d[f(I)]/dE]/dE]/dE = d{d[d [I[t(e)]]/dE]/dE  and/or d[d [I[w(e)]]/dE]/dE  and/or d[d [I[a(e)]]/dE]/dE  and/or d[d [I[i(e)]]/dE]/dE  and/or d[d [I[m(e)]]/dE]/dE }/dE = f(Ie)3B, where B stands for type B differentiation which is not to be confused with the meaning of so-called Type  B personality as B is used as an ordinal in a totally different context here .

 

 

In fact, one can form yet higher order derivatives of instincts with respect to emotion as follows.

 

 

Ie5 = d Ie4/dE = d[dIe3/dE]/dE

 

 

 

Ie5 = dIe4/dE =  d[d[d[d[d I{[t(e)] and/or [w(e)] and/or [a(e)] and/or [i(e)] and/or [m(e)]}/dE]/dE]/dE]/dE]/dE.

 

 

 

f(Ie)5A = d[f(Ie)4A]/dE = d[d [f(Ie)3A]/dE]/dE =  d{d{d{d{ d [I[t(e)]]/dE and/or d[I[w(e)]]/dE and/or d[I[a(e)]]/dE and/or d[I[i(e)]]/dE and/or d[I[m(e)]]/dE}/dE}/dE]/dE]/dE

 

 

 

 

Ie6 = d Ie5/dE = d[d Ie4/dE]/dE = d[d[dIe3/dE]/dE]/dE

 

 

 

Ie6 = dIe5/dE = d[d[d[d[d[d I{[t(e)] and/or [w(e)] and/or [a(e)] and/or [i(e)] and/or [m(e)]}/dE]/dE]/dE]/dE]/dE]/dE

 

 

 

f(Ie)6A = d[f(Ie)5A]/dE = d{ d{d{d{d{ d [I[t(e)]]/dE and/or d[I[w(e)]]/dE and/or d[I[a(e)]]/dE and/or d[I[i(e)]]/dE and/or d[I[m(e)]]/dE}/dE}/dE]/dE]/dE]/dE

 

 

 

 

Ie7 = dIe6/dE

 

f(Ie)7A = d[f(Ie)6A]/dE

 

 

Ie8 = d Ie7/dE

 

f(Ie)8A = d[f(Ie)7A]/dE

 

 

 

Ie9 = d Ie8/dE

 

f(Ie)9A = d[f(Ie)8A]/dE

 

 

Ie10…, Ie11…, Ie12 … etc.

 

 

Anyone for Ie ensemble, or Ie infinity scrapper, or Ie (Aleph 0), or Ie(Aleph 1), or Ie(Aleph 2), or how about Ie Aleph (Aleph 0), or Ie Aleph (Aleph 1) , or Ie Aleph (Aleph 2), or even Ie Aleph (Aleph (Aleph 0)), or Ie Aleph (Aleph (Aleph 1)), or Ie Aleph (Aleph (Aleph 2)), and so on?

 

Thus, for the set of the sets of derivatives of Ie1 through Ie(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ie1 through Ie(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)},…, {П(0,31)[R]}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ie1 through Ie(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ie1 through Ie(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the derivative states in the set of the sets of derivatives of Ie1 through Ie(Aleph 0) is plausible equal to:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ie1 through Ie(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ie1 through Ie(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}}}.

 

For the set of the sets of derivatives of Ie1 through Ie(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Ie(Aleph 0) derivative space at the level of 0/(Aleph 0), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Ie1 through Ie(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ie1 through Ie(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ie1 through Ie(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ie1 through Ie(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Ie1 through Ie(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ie1 through Ie(Aleph 1), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Ie1 through  Ie(Aleph 2), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Ie1 through Ie(Aleph 3), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Ie(Aleph 0) derivative space at the level of 0/(Aleph 1), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Ie1 through Ie(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ie1 through Ie(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ie1 through Ie(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ie1 through  Ie(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations  for the set of the sets of derivatives of Ie1 through Ie(Aleph 0) is plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ie1 through Ie(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Ie1 through Ie(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Ie1 through Ie(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

 

For super-continuous Ie(Aleph 0) derivative space at the level of 0/(Aleph 2), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Ie1 through Ie(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ie1 through Ie(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ie1 through Ie(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ie1 through Ie(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Ie1 through Ie(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ie1 through Ie(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Ie1 through Ie(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Ie1 through Ie(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

Similar series can be developed for super-continuity at any applicable level such as 0/(Aleph 3), 0/(Aleph 4), 0/(Aleph 5),…, 0/(Aleph Ω), 0/(Aleph (Aleph 0)), …, 0/(Aleph (Aleph 1)), …, 0/(Aleph (Aleph 2)), …, 0/(Aleph (Aleph 3)),…, 0/(Aleph (Aleph Ω)),…, 0/(Aleph (Aleph (Aleph 0))), …, 0/(Aleph (Aleph (Aleph 1))),…, 0/(Aleph (Aleph (Aleph 2))),…, 0/(Aleph (Aleph (Aleph 3))),…, 0/(Aleph (Aleph  (Aleph Ω))), …

 

An so-on ad infinitum.

 

 

In addition to these numerical functions of Ie as functions of summation series of product series functions, in order to really appreciate the enourmous complexity of the human soul in terms of its potential to evolve and be differentiated from all other souls in its characteristics, we would need to consider how every single category and even every single species of affect of the form Ie can very. Since there may exist an arbitrarily high infinite number species of Ie, the number of numerical functions of Ie is utterly beyond recogning. I will cover such notions in terms of mathematical notation in yet another series of articles I will write on this general concept.

 

 

 

Perhaps these numbers are applicable when one considers that the human soul, in its accidental form and perhaps even in its substantial form stores all experience and other psychodynamics based phenomenon. Every experience adds to the accidental form of the human soul and this includes the souls of all those still alive on Earth, all those in Purgatory, all those in Heaven, all those in Hell, and all those in any Limbo.

Since the human soul can grow without limit in terms of its psychodynamic time –flow world line, such a consideration offers another mechanism where the number of derivative states, combinations of derivative states, and even super-continuity of the derivative state space can grow forever.

 

Folks, for those of you who might balk at me for including literally all souls in the above consideration, including the souls in Hell, as well as bodily extraterrestrial souls and the souls of so-called bodily ultraterrestials sometimes referred to as etherians in the new age UFO buff culture, my reply is that we simply do not understand the full scope of GOD’s Divine Economy. We may never fully comprehend the scope of the Divine Economy because such an utterly eternal scheme, is, well, eternal and never ending.

 

 

The general meaning of emotion derivatives of instinct can be viewed as the manner in which the qualitative and/or quantitative aspects of instinct as a function of instinct varies with emotion(s). The manner in which instincts very with emotion may be multi-emotion dimensional wherein the dimensions of derivations can be multiple, and wherein the derivations can be taken in parallel, series parallel or serial manner The differentials can be partial or non-partial derivatives, or both partial and non-partial for a given computation.

 

In fact, since there is in theory, no limit to the numbers of qualitatively and quantitatively different instincts, and perhaps no limit to the number of possible different types or classes of instincts, wherein each person has his or her own unique instincts, the number of instinct dimensions that can effect instincts is literally infinite, given the entirety of the set of created persons, and perhaps also literally infinite for each person as an individual, although we can not intellectually and intuitively understand this specific infinite number.

 

It is interesting to consider the ramifactions of being able to perform realistic calculations involving emotion derivatives of instinct from a mathematical, theoretical, scientific,  and philosophical perspective.

 

Persons for which one or more nth order derivatives of instinct with respect to emotion that have large absolute values would tend to have their instincts highly influenced by emotion, or at least for the instinct under consideration with respect to the dimension of the specific instinct type(s) or class(es) for which the differentiation(s) are performed. Perhaps a strong coupling between instinct and emotion indicates a well integrated personality and commensurately, a high degree of instinct capacity and a high degree of instinctual intelligence.

 

We would expect that disembodied human souls, ETI souls, and/or UTI souls in Heaven, Limbo, highly evolved bodily ETI persons, highly evolved UTI persons, and angels to have instinct of all kinds and intensities which are highly subject to instinct.

 

 

We can also consider two dimensional nth ordered derivatives of instinct with respect to emotion and time, or with respect to E and T, respectively.

 

Given that I[(E)(T)] =  I[(t and/or w and/or a and/or i and/or m)(e)(T)], the following first order two dimensional derivatives of instinct with respect to emotion and Time are possible.

 

 

d[dI[(t)(T)]/dE]/dT, d[dI[(w)(T)]/dE]/dT, d[dI[(a)(T)]/dE]/dT, d[dI[(i)(T)]/dE]/dT, d[dI[(m)(T)]/dE]/dT, d[dI[(t,w)(T)]/dE]/dT, d[dI[(t,a)(T)]/dE]/dT, d[dI[(t,i)(T)]/dE]/dT, d[dI[(t,m)(T)]/dE]/dT, d[dI[(w,a)(T)]/dE]/dT, d[dI[(w,i)(T)]/dE]/dT, d[dI[(w,m)(T)]/dE]/dT, d[dI[(a,i)(T)]/dE]/dT, d[dI[(a,m)(T)]/dE]/dT, d[dI[(i,m)(T)]/dE]/dT, d[dI[(t,w,a)(T)]/dE]/dT, d[dI[(t,w,i)(T)]/dE]/dT, d[dI[(t,w,m)(T)]/dE]/dT, d[dI[(t,a,i)(T)]/dE]/dT, d[dI[(t,a,m)(T)]/dE]/dT, d[dI[(t,i,m)(T)]/dE]/dT, d[dI[(w,a,i)(T)]/dE]/dT, d[dI[(w,a,m)(T)]/dE]/dT, d[dI[(w,i,m)(T)]/dE]/dT, d[dI[(a,i,m)(T)]/dE]/dT, d[dI[(t,w,a,i)(T)]/dE]/dT, d[dI[(t,w,a,m)(T)]/dE]/dT, d[dI[(t,w,i,m)(T)]/dE]/dT, d[dI[(t,a,i,m)(T)]/dE]/dT, d[dI[(w,a,i,m)(T)]/dE]/dT, d[dI[(t,w,a,i,m)(T)]/dE]/dT.

 

 

Or more succinctly,  d[dI(T)/dE]/dT = d[dI[(T)(t and/or w and/or a and/or i and/or m)]/dE]/dT

 

or

 

d[dI(T)/dT]/dE = d[dI[(T)(t and/or w and/or a and/or i and/or m)]/dT]/dE

 

 

 

 

 

Or perhaps d[d I[(E)(T)]/dE]/dT  = d[d I [{[t(e)] and/or [w(e)] and/or [a(e)] and/or [i(e)] and/or [m(e)]}(T)]/dE]/dT

 

or

 

Or perhaps d[d I[(E)(T)]/dT]/dE  = d[d I [{[t(e)] and/or [w(e)] and/or [a(e)] and/or [i(e)] and/or [m(e)]}(T)]/dT]/dE

 

 

 

Likewise, we can take the second dual dimensioned emotion-time derivatives of  I as follows:

 

d[d[d[dI[(t)(T)]/dE]/dT]/dE]/dT, d[d[d[dI[(w)(T)]/dE]/dT]/dE]/dT, d[d[d[dI[(a)(T)]/dE]/dT]/dE]/dT, d[d[d[dI[(i)(T)]/dE]/dT]/dE]/dT, d[d[d[dI[(m)(T)]/dE]/dT]/dE]/dT, d[d[d[dI[(t,w)(T)]/dE]/dT]/dE]/dT, d[d[d[dI[(t,a)(T)]/dE]/dT]/dE]/dT, d[d[d[dI[(t,i)(T)]/dE]/dT]/dE]/dT, d[d[d[dI[(t,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dI[(w,a)(T)]/dE]/dT]/dE]/dT, d[d[d[dI[(w,i)(T)]/dE]/dT]/dE]/dT, d[d[d[dI[(w,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dI[(a,i)(T)]/dE]/dT]/dE]/dT, d[d[d[dI[(a,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dI[(i,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dI[(t,w,a)(T)]/dE]/dT]/dE]/dT, d[d[d[dI[(t,w,i)(T)]/dE]/dT]/dE]/dT, d[d[d[dI[(t,w,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dI[(t,a,i)(T)]/dE]/dT]/dE]/dT, d[d[d[dI[(t,a,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dI[(t,i,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dI[(w,a,i)(T)]/dE]/dT]/dE]/dT, d[d[d[dI[(w,a,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dI[(w,i,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dI[(a,i,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dI[(t,w,a,i)(T)]/dE]/dT]/dE]/dT, d[d[d[dI[(t,w,a,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dI[(t,w,i,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dI[(t,a,i,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dI[(w,a,i,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dI[(t,w,a,i,m)(T)]/dE]/dT]/dE]/dT.

 

or as:

 

 

 

d[d[d[dI[(t)(T)]/dE]/dT]/dT]/dE, d[d[d[dI[(w)(T)]/dE]/dT]/dT]/dE, d[d[d[dI[(a)(T)]/dE]/dT]/dT]/dE, d[d[d[dI[(i)(T)]/dE]/dT]/dT]/dE, d[d[d[dI[(m)(T)]/dE]/dT]/dT]/dE, d[d[d[dI[(t,w)(T)]/dE]/dT]/dT]/dE, d[d[d[dI[(t,a)(T)]/dE]/dT]/dT]/dE, d[d[d[dI[(t,i)(T)]/dE]/dT]/dT]/dE, d[d[d[dI[(t,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dI[(w,a)(T)]/dE]/dT]/dT]/dE, d[d[d[dI[(w,i)(T)]/dE]/dT]/dT]/dE, d[d[d[dI[(w,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dI[(a,i)(T)]/dE]/dT]/dT]/dE, d[d[d[dI[(a,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dI[(i,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dI[(t,w,a)(T)]/dE]/dT]/dT]/dE, d[d[d[dI[(t,w,i)(T)]/dE]/dT]/dT]/dE, d[d[d[dI[(t,w,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dI[(t,a,i)(T)]/dE]/dT]/dT]/dE, d[d[d[dI[(t,a,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dI[(t,i,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dI[(w,a,i)(T)]/dE]/dT]/dT]/dE, d[d[d[dI[(w,a,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dI[(w,i,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dI[(a,i,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dI[(t,w,a,i)(T)]/dE]/dT]/dT]/dE, d[d[d[dI[(t,w,a,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dI[(t,w,i,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dI[(t,a,i,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dI[(w,a,i,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dI[(t,w,a,i,m)(T)]/dE]/dT]/dT]/dE.

 

or as:

 

d[d[d[dI[(t)(T)]/dT]/dE]/dE]/dT, d[d[d[dI[(w)(T)]/dT]/dE]/dE]/dT, d[d[d[dI[(a)(T)]/dT]/dE]/dE]/dT, d[d[d[dI[(i)(T)]/dT]/dE]/dE]/dT, d[d[d[dI[(m)(T)]/dT]/dE]/dE]/dT, d[d[d[dI[(t,w)(T)]/dT]/dE]/dE]/dT, d[d[d[dI[(t,a)(T)]/dT]/dE]/dE]/dT, d[d[d[dI[(t,i)(T)]/dT]/dE]/dE]/dT, d[d[d[dI[(t,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dI[(w,a)(T)]/dT]/dE]/dE]/dT, d[d[d[dI[(w,i)(T)]/dT]/dE]/dE]/dT, d[d[d[dI[(w,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dI[(a,i)(T)]/dT]/dE]/dE]/dT, d[d[d[dI[(a,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dI[(i,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dI[(t,w,a)(T)]/dT]/dE]/dE]/dT, d[d[d[dI[(t,w,i)(T)]/dT]/dE]/dE]/dT, d[d[d[dI[(t,w,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dI[(t,a,i)(T)]/dT]/dE]/dE]/dT, d[d[d[dI[(t,a,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dI[(t,i,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dI[(w,a,i)(T)]/dT]/dE]/dE]/dT, d[d[d[dI[(w,a,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dI[(w,i,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dI[(a,i,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dI[(t,w,a,i)(T)]/dT]/dE]/dE]/dT, d[d[d[dI[(t,w,a,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dI[(t,w,i,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dI[(t,a,i,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dI[(w,a,i,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dI[(t,w,a,i,m)(T)]/dT]/dE]/dE]/dT.

 

 

or as;

 

 

 

 

d[d[d[dI(t)/dE]/dE]/dT]/dT, d[d[d[dI(w)/dE]/dE]/dT]/dT, d[d[d[dI(a)/dE]/dE]/dT]/dT, d[d[d[dI(i)/dE]/dE]/dT]/dT, d[d[d[dI(m)/dE]/dE]/dT]/dT, d[d[d[dI(t,w)/dE]/dE]/dT]/dT, d[d[d[dI(t,a)/dE]/dE]/dT]/dT, d[d[d[dI(t,i)/dE]/dE]/dT]/dT, d[d[d[dI(t,m)/dE]/dE]/dT]/dT, d[d[d[dI(w,a)/dE]/dE]/dT]/dT, d[d[d[dI(w,i)/dE]/dE]/dT]/dT, d[d[d[dI(w,m)/dE]/dE]/dT]/dT, d[d[d[dI(a,i)/dE]/dE]/dT]/dT, d[d[d[dI(a,m)/dE]/dE]/dT]/dT, d[d[d[dI(i,m)/dE]/dE]/dT]/dT, d[d[d[dI(t,w,a)/dE]/dE]/dT]/dT, d[d[d[dI(t,w,i)/dE]/dE]/dT]/dT, d[d[d[dI(t,w,m)/dE]/dE]/dT]/dT, d[d[d[dI(t,a,i)/dE]/dE]/dT]/dT, d[d[d[dI(t,a,m)/dE]/dE]/dT]/dT,  d[d[d[dI(t,i,m)/dE]/dE]/dT]/dT, d[d[d[dI(w,a,i)/dE]/dE]/dT]/dT, d[d[d[dI(w,a,m)/dE]/dE]/dT]/dT, d[d[d[dI(w,i,m)/dE]/dE]/dT]/dT, d[d[d[dI(a,i,m)/dE]/dE]/dT]/dT, d[d[d[dI(t,w,a,i)/dE]/dE]/dT]/dT, d[d[d[dI(t,w,a,m)/dE/dE, d[d[d[dI(t,w,i,m)/dE]/dE]/dT]/dT, d[d[d[dI(t,a,i,m)/dE]/dE]/dT]/dT, d[d[d[dI(w,a,i,m)/dE]/dE]/dT]/dT, d[d[d[dI(t,w,a,i,m)/dE]/dE]/dT]/dT..

 

or as:

 

d[d[d[dI(t)/dT]/dE]/dT]/dE, d[d[d[dI(w)/dT]/dE]/dT]/dE, d[d[d[dI(a)/dT]/dE]/dT]/dE, d[d[d[dI(i)/dT]/dE]/dT]/dE, d[d[d[dI(m)/dT]/dE]/dT]/dE, d[d[d[dI(t,w)/dT]/dE]/dT]/dE, d[d[d[dI(t,a)/dT]/dE]/dT]/dE, d[d[d[dI(t,i)/dT]/dE]/dT]/dE, d[d[d[dI(t,m)/dT]/dE]/dT]/dE, d[d[d[dI(w,a)/dT]/dE]/dT]/dE, d[d[d[dI(w,i)/dT]/dE]/dT]/dE, d[d[d[dI(w,m)/dT]/dE]/dT]/dE, d[d[d[dI(a,i)/dT]/dE]/dT]/dE, d[d[d[dI(a,m)/dT]/dE]/dT]/dE, d[d[d[dI(i,m)/ dT]/dE]/dT]/dE, d[d[d[dI(t,w,a)/dT]/dE]/dT]/dE, d[d[d[dI(t,w,i)/dT]/dE]/dT]/dE, d[d[d[dI(t,w,m)/dT]/dE]/dT]/dE, d[d[d[dI(t,a,i)/dT]/dE]/dT]/dE, d[d[d[dI(t,a,m)/dT]/dE]/dT]/dE,  d[d[d[dI(t,i,m)/dT]/dE]/dT]/dE, d[d[d[dI(w,a,i)/dT]/dE]/dT]/dE, d[d[d[dI(w,a,m)/dT]/dE]/dT]/dE, d[d[d[dI(w,i,m)/dT]/dE]/dT]/dE, d[d[d[dI(a,i,m)/dT]/dE]/dT]/dE, d[d[d[dI(t,w,a,i)/dT]/dE]/dT]/dE, d[d[d[dI(t,w,a,m)/dE/dE, d[d[d[dI(t,w,i,m)/dT]/dE]/dT]/dE, d[d[d[dI(t,a,i,m)/dT]/dE]/dT]/dE, d[d[d[dI(w,a,i,m)/dT]/dE]/dT]/dE, d[d[d[dI(t,w,a,i,m)/dT]/dE]/dT]/dE..

 

or as:

 

d[d[d[dI(t)/dT]/dT]/dE]/dE, d[d[d[dI(w)/dT]/dT]/dE]/dE, d[d[d[dI(a)/dT]/dT]/dE]/dE, d[d[d[dI(i)/dT]/dT]/dE]/dE, d[d[d[dI(m)/dT]/dT]/dE]/dE, d[d[d[dI(t,w)/dT]/dT]/dE]/dE, d[d[d[dI(t,a)/dT]/dT]/dE]/dE, d[d[d[dI(t,i)/dT]/dT]/dE]/dE, d[d[d[dI(t,m)/dT]/dT]/dE]/dE, d[d[d[dI(w,a)/dT]/dT]/dE]/dE, d[d[d[dI(w,i)/dT]/dT]/dE]/dE, d[d[d[dI(w,m)/dT]/dT]/dE]/dE, d[d[d[dI(a,i)/dT]/dT]/dE]/dE, d[d[d[dI(a,m)/ dT]/dT]/dE]/dE, d[d[d[dI(i,m)/ dT]/dT]/dE]/dE, d[d[d[dI(t,w,a)/dT]/dT]/dE]/dE, d[d[d[dI(t,w,i)/dT]/dT]/dE]/dE, d[d[d[dI(t,w,m)/dT]/dT]/dE]/dE, d[d[d[dI(t,a,i)/dT]/dT]/dE]/dE, d[d[d[dI(t,a,m)/dT]/dT]/dE]/dE,  d[d[d[dI(t,i,m)/dT]/dT]/dE]/dE, d[d[d[dI(w,a,i)/dT]/dT]/dE]/dE, d[d[d[dI(w,a,m)/dT]/dT]/dE]/dE, d[d[d[dI(w,i,m)/dT]/dT]/dE]/dE, d[d[d[dI(a,i,m)/dT]/dT]/dE]/dE, d[d[d[dI(t,w,a,i)/dT]/dT]/dE]/dE, d[d[d[dI(t,w,a,m)/dE/dE, d[d[d[dI(t,w,i,m)/dT]/dT]/dE]/dE, d[d[d[dI(t,a,i,m)/dT]/dT]/dE]/dE, d[d[d[dI(w,a,i,m)/dT]/dT]/dE]/dE, d[d[d[dI(t,w,a,i,m)/dT]/dT]/dE]/dE..

 

 

We can also take higher order duel dimensional derivatives of instinct as a function of emotion and time but the symbolic expression of the set of such derivatives very soon becomes excessively lengthly to write and so these higher order derivatives as such are not mentioned here except to say that they would be computed in an analogous manner to the second order duel dimensional derivatives described above.

 

.

 

 

 

 

 

We can also express instinct qualitatively, statistically, and perhaps with the use of some forms of real analyses as a derivative  with respect to will or of w.

 

Given that I(w) =  I(t and/or w and/or a and/or i and/or m), the following first order derivatives of instinct with respect to will are possible.

 

 

dI(t)/dw, dI(w)/dw, dI(a)/dw, dI(i)/dw, dI(m)/dw, dI(t,w)/dw, dI(t,a)/dw, dI(t,i)/dw, dI(t,m)/dw, dI(w,a)/dw, dI(w,i)/dw, dI(w,m)/dw, dI(a,i)/dw, dI(a,m)/dw, dI(i,m)/dw, dI(t,w,a)/dw, dI(t,w,i)/dw, dI(t,w,m)/dw, dI(t,a,i)/dw, dI(t,a,m)/dw, dI(t,i,m)/dw, dI(w,a,i)/dw, dI(w,a,m)/dw, dI(w,i,m)/dw, dI(a,i,m)/dw, dI(t,w,a,i)/dw, dI(t,w,a,m)/dw, dI(t,w,i,m)/dw, dI(t,a,i,m)/dw, dI(w,a,i,m)/dw, dI(t,w,a,i,m)/dw.

 

 

Or more succinctly,  dI/dw = dI(t and/or w and/or a and/or i and/or m)/dw

 

 

Or perhaps dI(w)/dw =d I{[t(w)] and/or [w(w)] and/or [a(w)] and/or [i(w)] and/or [m(w)]}/dw.

 

 

Likewise, we can take the second will derivatives of  I as follows:

 

 

 

d[dI(t)/dw]/dw, d[dI(w)/dw]/dw, d[dI(a)/dw]/dw, d[dI(i)/dw]/dw, d[dI(m)/dw]/dw, d[dI(t,w)/dw]/dw, d[dI(t,a)/dw]/dw, d[dI(t,i)/dw]/dw, d[dI(t,m)/dw]/dw, d[dI(w,a)/dw]/dw, d[dI(w,i)/dw]/dw, d[dI(w,m)/dw]/dw, d[dI(a,i)/dw]/dw, d[dI(a,m)/dw]/dw, d[dI(i,m)/dw/dw, d[dI(t,w,a)/dw]/dw, d[dI(t,w,i)/dw]/dw, d[dI(t,w,m)/dw]/dw, d[dI(t,a,i)/dw]/dw, d[dI(t,a,m)/dw]/dw,  d[dI(t,i,m)/dw]/dw, d[dI(w,a,i)/dw]/dw, d[dI(w,a,m)/dw]/dw, d[dI(w,i,m)/dw]/dw, d[dI(a,i,m)/dw]/dw, d[dI(t,w,a,i)/dw]/dw, d[dI(t,w,a,m)/dw/dw, d[dI(t,w,i,m)/dw]/dw, d[dI(t,a,i,m)/dw]/dw, d[dI(w,a,i,m)/dw]/dw, d[dI(t,w,a,i,m)/dw]/dw..

 

 

or more succinctly, as d(dI/dw)/dw = d[d I(t and/or w and/or a and/or i and/or m)/dw]/dw = Iw2

 

 

or as

 

 

d[dI(w)/dw]/dw  = d[d I{[t(w)] and/or [w(w)] and/or [a(w)] and/or [i(w)] and/or [m(w)]}/dw]/dw = Iw2.

 

 

 

Likewise, we can take the third will derivatives of  I as follows:

 

 

 

d[d[dI(t)/dw]/dw]/dw, d[d[dI(w)/dw]/dw]/dw, d[d[dI(a)/dw]/dw]/dw, d[d[dI(i)/dw]/dw]/dw, d[d[dI(m)/dw]/dw]/dw, d[d[dI(t,w)/dw]/dw]/dw, d[d[dI(t,a)/dw]/dw]/dw, d[d[dI(t,i)/dw]/dw]/dw, d[d[dI(t,m)/dw]/dw]/dw, d[d[dI(w,a)/dw]/dw]/dw, d[d[dI(w,i)/dw]/dw]/dw, d[d[dI(w,m)/dw]/dw]/dw, d[d[dI(a,i)/dw]/dw]/dw, d[d[dI(a,m)/dw]/dw]/dw, d[d[dI(i,m)/dw/dw]/dw, d[d[dI(t,w,a)/dw]/dw]/dw, d[d[dI(t,w,i)/dw]/dw]/dw, d[d[dI(t,w,m)/dw]/dw]/dw, d[d[dI(t,a,i)/dw]/dw]/dw, d[d[dI(t,a,m)/dw]/dw]/dw,  d[d[dI(t,i,m)/dw]/dw]/dw, d[d[dI(w,a,i)/dw]/dw]/dw, d[d[dI(w,a,m)/dw]/dw]/dw, d[d[dI(w,i,m)/dw]/dw]/dw, d[d[dI(a,i,m)/dw]/dw]/dw, d[d[dI(t,w,a,i)/dw]/dw]/dw, d[d[dI(t,w,a,m)/dw/dw]/dw, d[d[dI(t,w,i,m)/dw]/dw]/dw, d[d[dI(t,a,i,m)/dw]/dw]/dw, d[d[dI(w,a,i,m)/dw]/dw]/dw, d[d[dI(t,w,a,i,m)/dw]/dw]/dw.

 

 

or more succinctly, as d[d(dI/dw)/dw]/dw = d[d[d I(t and/or w and/or a and/or i and/or m)/dw]/dw]/dw = Iw3

 

 

or as

 

 

d[d[dI(w)/dw]/dw]/dw  = d[d[d I{[t(w)] and/or [w(w)] and/or [a(w)] and/or [i(w)] and/or [m(w)]}/dw]/dw]/dw = Iw3.

 

 

We can also form the expressions;

 

 

d[d[f(I)]/dw]/dw = d{d [I[t(w)]]/dw and/or d[I[w(w)]]/dw and/or d[I[a(w)]]/dw and/or d[I[i(w)]]/dw and/or d[I[m(w)]]/dw}/dw  = f(Iw)2

 

 

and

 

 

d[d[d[f(I)]/dw]/dw]/dw = d{d{ d [I[t(w)]]/dw and/or d[I[w(w)]]/dw and/or d[I[a(w)]]/dw and/or d[I[i(w)]]/dw and/or d[I[m(w)]]/dw}/dw}/dw  = f(Iw)3A, where A stands for type A differentiation which is not to be confused with the meaning of so-called Type A personality as A is used as an ordinal in a totally different context here.

 

 

and

 

 

d[d[d[f(I)]/dw]/dw]/dw = d{d[d [I[t(w)]]/dw]/dw  and/or d[d [I[w(w)]]/dw]/dw  and/or d[d [I[a(w)]]/dw]/dw  and/or d[d [I[i(w)]]/dw]/dw  and/or d[d [I[m(w)]]/dw]/dw }/dw = f(Iw)3B, where B stands for type B differentiation which is not to be confused with the meaning of so-called Type  B personality as B is used as an ordinal in a totally different context here .

 

 

In fact, one can form yet higher order derivatives of instinct with respect to will as follows.

 

 

Iw5 = d Iw4/dw = d[dIw3/dw]/dw

 

 

 

Iw5 = dIw4/dw =  d[d[d[d[d I{[t(w)] and/or [w(w)] and/or [a(w)] and/or [i(w)] and/or [m(w)]}/dw]/dw]/dw]/dw]/dw.

 

 

 

f(Iw)5A = d[f(Iw)4A]/dw = d[d [f(Iw)3A]/dw]/dw =  d{d{d{d{ d [I[t(w)]]/dw and/or d[I[w(w)]]/dw and/or d[I[a(w)]]/dw and/or d[I[i(w)]]/dw and/or d[I[m(w)]]/dw}/dw}/dw]/dw]/dw

 

 

 

 

Iw6 = d Iw5/dw = d[d Iw4/dw]/dw = d[d[dIw3/dw]/dw]/dw

 

 

 

Iw6 = dIw5/dw = d[d[d[d[d[d I{[t(w)] and/or [w(w)] and/or [a(w)] and/or [i(w)] and/or [m(w)]}/dw]/dw]/dw]/dw]/dw]/dw

 

 

 

f(Iw)6A = d[f(Iw)5A]/dw = d{ d{d{d{d{ d [I[t(w)]]/dw and/or d[I[w(w)]]/dw and/or d[I[a(w)]]/dw and/or d[I[i(w)]]/dw and/or d[I[m(w)]]/dw}/dw}/dw]/dw]/dw]/dw

 

 

 

 

Iw7 = dIw6/dw

 

f(Iw)7A = d[f(Iw)6A]/dw

 

 

Iw8 = d Iw7/dw

 

f(Iw)8A = d[f(Iw)7A]/dw

 

 

 

Iw9 = d Iw8/dw

 

f(Iw)9A = d[f(Iw)8A]/dw

 

 

Iw10…, Iw11…, Iw12 … etc.

 

 

Anyone for Iw ensemble, or Iw infinity scrapper, or Iw (Aleph 0), or Iw(Aleph 1), or Iw (Aleph 2), or how about Iw Aleph (Aleph 0), or Iw Aleph (Aleph 1) , or Iw Aleph (Aleph 2), or even Iw Aleph (Aleph (Aleph 0)), or Iw Aleph (Aleph (Aleph 1)), or Iw Aleph (Aleph (Aleph 2)), and so on?

 

Thus, for the set of the sets of derivatives of Iw1 through Iw(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Iw1 through Iw(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)},…, {П(0,31)[R]}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Iw1 through Iw(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Iw1 through Iw(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the derivative states in the set of the sets of derivatives of Iw1 through Iw(Aleph 0) is plausible equal to:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Iw1 through Iw(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Iw1 through Iw(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}}}.

 

For the set of the sets of derivatives of Iw1 through Iw(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Iw(Aleph 0) derivative space at the level of 0/(Aleph 0), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Iw1 through Iw(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Iw1 through Iw(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Iw1 through Iw(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Iw1 through Iw(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Iw1 through Iw(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Iw1 through Iw(Aleph 1), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Iw1 through  Iw(Aleph 2), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Iw1 through Iw(Aleph 3), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Iw(Aleph 0) derivative space at the level of 0/(Aleph 1), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Iw1 through Iw(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Iw1 through Iw(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Iw1 through Iw(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Iw1 through  Iw(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations  for the set of the sets of derivatives of Iw1 through Iw(Aleph 0) is plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Iw1 through Iw(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Iw1 through Iw(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Iw1 through Iw(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

 

For super-continuous Iw(Aleph 0) derivative space at the level of 0/(Aleph 2), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Iw1 through Iw(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Iw1 through Iw(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Iw1 through Iw(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Iw1 through Iw(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Iw1 through Iw(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Iw1 through Iw(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Iw1 through Iw(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Iw1 through Iw(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

Similar series can be developed for super-continuity at any applicable level such as 0/(Aleph 3), 0/(Aleph 4), 0/(Aleph 5),…, 0/(Aleph Ω), 0/(Aleph (Aleph 0)), …, 0/(Aleph (Aleph 1)), …, 0/(Aleph (Aleph 2)), …, 0/(Aleph (Aleph 3)),…, 0/(Aleph (Aleph Ω)),…, 0/(Aleph (Aleph (Aleph 0))), …, 0/(Aleph (Aleph (Aleph 1))),…, 0/(Aleph (Aleph (Aleph 2))),…, 0/(Aleph (Aleph (Aleph 3))),…, 0/(Aleph (Aleph  (Aleph Ω))), …

 

An so-on ad infinitum.

 

In addition to these numerical functions of Iw as functions of summation series of product series functions, in order to really appreciate the enourmous complexity of the human soul in terms of its potential to evolve and be differentiated from all other souls in its characteristics, we would need to consider how every single category and even every single species of affect of the form Iw can very. Since there may exist an arbitrarily high infinite number species of Iw, the number of numerical functions of Iw is utterly beyond recogning. I will cover such notions in terms of mathematical notation in yet another series of articles I will write on this general concept.

 

 

 

Perhaps these numbers are applicable when one considers that the human soul, in its accidental form and perhaps even in its substantial form stores all experience and other psychodynamics based phenomenon. Every experience adds to the accidental form of the human soul and this includes the souls of all those still alive on Earth, all those in Purgatory, all those in Heaven, all those in Hell, and all those in any Limbo.

Since the human soul can grow without limit in terms of its psychodynamic time –flow world line, such a consideration offers another mechanism where the number of derivative states, combinations of derivative states, and even super-continuity of the derivative state space can grow forever.

 

Folks, for those of you who might balk at me for including literally all souls in the above consideration, including the souls in Hell, as well as bodily extraterrestrial souls and the souls of so-called bodily ultraterrestials sometimes referred to as etherians in the new age UFO buff culture, my reply is that we simply do not understand the full scope of GOD’s Divine Economy. We may never fully comprehend the scope of the Divine Economy because such an utterly eternal scheme, is, well, eternal and never ending.

 

 

The general meaning of will derivatives of instinct can be viewed as the manner in which the qualitative and/or quantitative aspects of instinct as a function of will very with will. The manner in which instincts very with will may be multi- will-aspect dimensional wherein the dimensions of derivations can be multiple, and wherein the derivations can be taken in parallel, series parallel or in serial manner. The differentials can be partial or non-partial derivatives, or both partial and non-partial for a given computation.

 

In fact, since there is in theory, no limit to the numbers of qualitatively and quantitatively different acts of will or volitional states, and perhaps no limit to the number of possible different types or classes of acts of will or volitional states, wherein each person has his or her own unique acts or will or volitional states, the number of volitional state dimensions that can effect instincts is literally infinite, given the entirety of the set of created persons, and perhaps also literally infinite for each person as an individual, although we can not intellectually and intuitively understand this infinite number.

 

 

It is interesting to consider the ramifactions of being able to perform realistic calculations involving will derivatives of instinct from a mathematical, theoretical, scientific,  and philosophical perspective.

 

Persons for which one or more nth order derivatives of instinct with respect to will that have large absolute values would tend to have their instincts highly influenced by will, or at least for the instincts under consideration with respect to the dimension of the specific will act type(s) or class(es) for which the differentiation(s) are being performed. Perhaps a strong coupling between instinct and will indicates a well integrated personality and commensurately, a high degree of instinct capacity and a high degree of instinct intelligence as well as perhaps very strong will power.

 

We would expect that disembodied human souls, ETI souls, and/or UTI souls in Heaven, Limbo, highly evolved bodily ETI persons, highly evolved UTI persons, and angels to have instincts of all kinds and intensities which are highly subject to will.

 

 

We can also consider two dimensional ith ordered derivatives of instinct with respect to will and time, or with respect to w and T, respectively.

 

Given that I[(w)(T)] =  I[(t and/or w and/or a and/or i and/or m)(w)(T)], the following first order two dimensional derivatives of instinct with respect to will and Time are possible.

 

 

d[dI[(t)(T)]/dw]/dT, d[dI[(w)(T)]/dw]/dT, d[dI[(a)(T)]/dw]/dT, d[dI[(i)(T)]/dw]/dT, d[dI[(m)(T)]/dw]/dT, d[dI[(t,w)(T)]/dw]/dT, d[dI[(t,a)(T)]/dw]/dT, d[dI[(t,i)(T)]/dw]/dT, d[dI[(t,m)(T)]/dw]/dT, d[dI[(w,a)(T)]/dw]/dT, d[dI[(w,i)(T)]/dw]/dT, d[dI[(w,m)(T)]/dw]/dT, d[dI[(a,i)(T)]/dw]/dT, d[dI[(a,m)(T)]/dw]/dT, d[dI[(i,m)(T)]/dw]/dT, d[dI[(t,w,a)(T)]/dw]/dT, d[dI[(t,w,i)(T)]/dw]/dT, d[dI[(t,w,m)(T)]/dw]/dT, d[dI[(t,a,i)(T)]/dw]/dT, d[dI[(t,a,m)(T)]/dw]/dT, d[dI[(t,i,m)(T)]/dw]/dT, d[dI[(w,a,i)(T)]/dw]/dT, d[dI[(w,a,m)(T)]/dw]/dT, d[dI[(w,i,m)(T)]/dw]/dT, d[dI[(a,i,m)(T)]/dw]/dT, d[dI[(t,w,a,i)(T)]/dw]/dT, d[dI[(t,w,a,m)(T)]/dw]/dT, d[dI[(t,w,i,m)(T)]/dw]/dT, d[dI[(t,a,i,m)(T)]/dw]/dT, d[dI[(w,a,i,m)(T)]/dw]/dT, d[dI[(t,w,a,i,m)(T)]/dw]/dT.

 

 

Or more succinctly,  d[dI(T)/dw]/dT = d[dI[(T)(t and/or w and/or a and/or i and/or m)]/dw]/dT

 

or

 

d[dI(T)/dT]/dw = d[dI[(T)(t and/or w and/or a and/or i and/or m)]/dT]/dw

 

 

 

 

 

Or perhaps d[d I[(w)(T)]/dw]/dT  = d[d I [{[t(w)] and/or [w(w)] and/or [a(w)] and/or [i(w)] and/or [m(w)]}(T)]/dw]/dT

 

or

 

Or perhaps d[d I[(w)(T)]/dT]/dw  = d[d I [{[t(w)] and/or [w(w)] and/or [a(w)] and/or [i(w)] and/or [m(w)]}(T)]/dT]/dw

 

 

 

Likewise, we can take the second dual dimension will -time derivatives of  I as follows:

 

d[d[d[dI[(t)(T)]/dw]/dT]/dw]/dT, d[d[d[dI[(w)(T)]/dw]/dT]/dw]/dT, d[d[d[dI[(a)(T)]/dw]/dT]/dw]/dT, d[d[d[dI[(i)(T)]/dw]/dT]/dw]/dT, d[d[d[dI[(m)(T)]/dw]/dT]/dw]/dT, d[d[d[dI[(t,w)(T)]/dw]/dT]/dw]/dT, d[d[d[dI[(t,a)(T)]/dw]/dT]/dw]/dT, d[d[d[dI[(t,i)(T)]/dw]/dT]/dw]/dT, d[d[d[dI[(t,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dI[(w,a)(T)]/dw]/dT]/dw]/dT, d[d[d[dI[(w,i)(T)]/dw]/dT]/dw]/dT, d[d[d[dI[(w,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dI[(a,i)(T)]/dw]/dT]/dw]/dT, d[d[d[dI[(a,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dI[(i,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dI[(t,w,a)(T)]/dw]/dT]/dw]/dT, d[d[d[dI[(t,w,i)(T)]/dw]/dT]/dw]/dT, d[d[d[dI[(t,w,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dI[(t,a,i)(T)]/dw]/dT]/dw]/dT, d[d[d[dI[(t,a,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dI[(t,i,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dI[(w,a,i)(T)]/dw]/dT]/dw]/dT, d[d[d[dI[(w,a,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dI[(w,i,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dI[(a,i,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dI[(t,w,a,i)(T)]/dw]/dT]/dw]/dT, d[d[d[dI[(t,w,a,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dI[(t,w,i,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dI[(t,a,i,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dI[(w,a,i,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dI[(t,w,a,i,m)(T)]/dw]/dT]/dw]/dT.

 

or as:

 

 

 

d[d[d[dI[(t)(T)]/dw]/dT]/dT]/dw, d[d[d[dI[(w)(T)]/dw]/dT]/dT]/dw, d[d[d[dI[(a)(T)]/dw]/dT]/dT]/dw, d[d[d[dI[(i)(T)]/dw]/dT]/dT]/dw, d[d[d[dI[(m)(T)]/dw]/dT]/dT]/dw, d[d[d[dI[(t,w)(T)]/dw]/dT]/dT]/dw, d[d[d[dI[(t,a)(T)]/dw]/dT]/dT]/dw, d[d[d[dI[(t,i)(T)]/dw]/dT]/dT]/dw, d[d[d[dI[(t,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dI[(w,a)(T)]/dw]/dT]/dT]/dw, d[d[d[dI[(w,i)(T)]/dw]/dT]/dT]/dw, d[d[d[dI[(w,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dI[(a,i)(T)]/dw]/dT]/dT]/dw, d[d[d[dI[(a,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dI[(i,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dI[(t,w,a)(T)]/dw]/dT]/dT]/dw, d[d[d[dI[(t,w,i)(T)]/dw]/dT]/dT]/dw, d[d[d[dI[(t,w,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dI[(t,a,i)(T)]/dw]/dT]/dT]/dw, d[d[d[dI[(t,a,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dI[(t,i,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dI[(w,a,i)(T)]/dw]/dT]/dT]/dw, d[d[d[dI[(w,a,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dI[(w,i,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dI[(a,i,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dI[(t,w,a,i)(T)]/dw]/dT]/dT]/dw, d[d[d[dI[(t,w,a,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dI[(t,w,i,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dI[(t,a,i,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dI[(w,a,i,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dI[(t,w,a,i,m)(T)]/dw]/dT]/dT]/dw.

 

or as:

 

d[d[d[dI[(t)(T)]/dT]/dw]/dw]/dT, d[d[d[dI[(w)(T)]/dT]/dw]/dw]/dT, d[d[d[dI[(a)(T)]/dT]/dw]/dw]/dT, d[d[d[dI[(i)(T)]/dT]/dw]/dw]/dT, d[d[d[dI[(m)(T)]/dT]/dw]/dw]/dT, d[d[d[dI[(t,w)(T)]/dT]/dw]/dw]/dT, d[d[d[dI[(t,a)(T)]/dT]/dw]/dw]/dT, d[d[d[dI[(t,i)(T)]/dT]/dw]/dw]/dT, d[d[d[dI[(t,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dI[(w,a)(T)]/dT]/dw]/dw]/dT, d[d[d[dI[(w,i)(T)]/dT]/dw]/dw]/dT, d[d[d[dI[(w,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dI[(a,i)(T)]/dT]/dw]/dw]/dT, d[d[d[dI[(a,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dI[(i,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dI[(t,w,a)(T)]/dT]/dw]/dw]/dT, d[d[d[dI[(t,w,i)(T)]/dT]/dw]/dw]/dT, d[d[d[dI[(t,w,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dI[(t,a,i)(T)]/dT]/dw]/dw]/dT, d[d[d[dI[(t,a,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dI[(t,i,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dI[(w,a,i)(T)]/dT]/dw]/dw]/dT, d[d[d[dI[(w,a,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dI[(w,i,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dI[(a,i,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dI[(t,w,a,i)(T)]/dT]/dw]/dw]/dT, d[d[d[dI[(t,w,a,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dI[(t,w,i,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dI[(t,a,i,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dI[(w,a,i,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dI[(t,w,a,i,m)(T)]/dT]/dw]/dw]/dT.

 

 

or as;

 

 

 

 

d[d[d[dI(t)/dw]/dw]/dT]/dT, d[d[d[dI(w)/dw]/dw]/dT]/dT, d[d[d[dI(a)/dw]/dw]/dT]/dT, d[d[d[dI(i)/dw]/dw]/dT]/dT, d[d[d[dI(m)/dw]/dw]/dT]/dT, d[d[d[dI(t,w)/dw]/dw]/dT]/dT, d[d[d[dI(t,a)/dw]/dw]/dT]/dT, d[d[d[dI(t,i)/dw]/dw]/dT]/dT, d[d[d[dI(t,m)/dw]/dw]/dT]/dT, d[d[d[dI(w,a)/dw]/dw]/dT]/dT, d[d[d[dI(w,i)/dw]/dw]/dT]/dT, d[d[d[dI(w,m)/dw]/dw]/dT]/dT, d[d[d[dI(a,i)/dw]/dw]/dT]/dT, d[d[d[dI(a,m)/dw]/dw]/dT]/dT, d[d[d[dI(i,m)/dw]/dw]/dT]/dT, d[d[d[dI(t,w,a)/dw]/dw]/dT]/dT, d[d[d[dI(t,w,i)/dw]/dw]/dT]/dT, d[d[d[dI(t,w,m)/dw]/dw]/dT]/dT, d[d[d[dI(t,a,i)/dw]/dw]/dT]/dT, d[d[d[dI(t,a,m)/dw]/dw]/dT]/dT,  d[d[d[dI(t,i,m)/dw]/dw]/dT]/dT, d[d[d[dI(w,a,i)/dw]/dw]/dT]/dT, d[d[d[dI(w,a,m)/dw]/dw]/dT]/dT, d[d[d[dI(w,i,m)/dw]/dw]/dT]/dT, d[d[d[dI(a,i,m)/dw]/dw]/dT]/dT, d[d[d[dI(t,w,a,i)/dw]/dw]/dT]/dT, d[d[d[dI(t,w,a,m)/dw/dw, d[d[d[dI(t,w,i,m)/dw]/dw]/dT]/dT, d[d[d[dI(t,a,i,m)/dw]/dw]/dT]/dT, d[d[d[dI(w,a,i,m)/dw]/dw]/dT]/dT, d[d[d[dI(t,w,a,i,m)/dw]/dw]/dT]/dT..

 

or as:

 

d[d[d[dI(t)/dT]/dw]/dT]/dw, d[d[d[dI(w)/dT]/dw]/dT]/dw, d[d[d[dI(a)/dT]/dw]/dT]/dw, d[d[d[dI(i)/dT]/dw]/dT]/dw, d[d[d[dI(m)/dT]/dw]/dT]/dw, d[d[d[dI(t,w)/dT]/dw]/dT]/dw, d[d[d[dI(t,a)/dT]/dw]/dT]/dw, d[d[d[dI(t,i)/dT]/dw]/dT]/dw, d[d[d[dI(t,m)/dT]/dw]/dT]/dw, d[d[d[dI(w,a)/dT]/dw]/dT]/dw, d[d[d[dI(w,i)/dT]/dw]/dT]/dw, d[d[d[dI(w,m)/dT]/dw]/dT]/dw, d[d[d[dI(a,i)/dT]/dw]/dT]/dw, d[d[d[dI(a,m)/dT]/dw]/dT]/dw, d[d[d[dI(i,m)/ dT]/dw]/dT]/dw, d[d[d[dI(t,w,a)/dT]/dw]/dT]/dw, d[d[d[dI(t,w,i)/dT]/dw]/dT]/dw, d[d[d[dI(t,w,m)/dT]/dw]/dT]/dw, d[d[d[dI(t,a,i)/dT]/dw]/dT]/dw, d[d[d[dI(t,a,m)/dT]/dw]/dT]/dw,  d[d[d[dI(t,i,m)/dT]/dw]/dT]/dw, d[d[d[dI(w,a,i)/dT]/dw]/dT]/dw, d[d[d[dI(w,a,m)/dT]/dw]/dT]/dw, d[d[d[dI(w,i,m)/dT]/dw]/dT]/dw, d[d[d[dI(a,i,m)/dT]/dw]/dT]/dw, d[d[d[dI(t,w,a,i)/dT]/dw]/dT]/dw, d[d[d[dI(t,w,a,m)/dw/dw, d[d[d[dI(t,w,i,m)/dT]/dw]/dT]/dw, d[d[d[dI(t,a,i,m)/dT]/dw]/dT]/dw, d[d[d[dI(w,a,i,m)/dT]/dw]/dT]/dw, d[d[d[dI(t,w,a,i,m)/dT]/dw]/dT]/dw..

 

or as:

 

d[d[d[dI(t)/dT]/dT]/dw]/dw, d[d[d[dI(w)/dT]/dT]/dw]/dw, d[d[d[dI(a)/dT]/dT]/dw]/dw, d[d[d[dI(i)/dT]/dT]/dw]/dw, d[d[d[dI(m)/dT]/dT]/dw]/dw, d[d[d[dI(t,w)/dT]/dT]/dw]/dw, d[d[d[dI(t,a)/dT]/dT]/dw]/dw, d[d[d[dI(t,i)/dT]/dT]/dw]/dw, d[d[d[dI(t,m)/dT]/dT]/dw]/dw, d[d[d[dI(w,a)/dT]/dT]/dw]/dw, d[d[d[dI(w,i)/dT]/dT]/dw]/dw, d[d[d[dI(w,m)/dT]/dT]/dw]/dw, d[d[d[dI(a,i)/dT]/dT]/dw]/dw, d[d[d[dI(a,m)/ dT]/dT]/dw]/dw, d[d[d[dI(i,m)/ dT]/dT]/dw]/dw, d[d[d[dI(t,w,a)/dT]/dT]/dw]/dw, d[d[d[dI(t,w,i)/dT]/dT]/dw]/dw, d[d[d[dI(t,w,m)/dT]/dT]/dw]/dw, d[d[d[dI(t,a,i)/dT]/dT]/dw]/dw, d[d[d[dI(t,a,m)/dT]/dT]/dw]/dw,  d[d[d[dI(t,i,m)/dT]/dT]/dw]/dw, d[d[d[dI(w,a,i)/dT]/dT]/dw]/dw, d[d[d[dI(w,a,m)/dT]/dT]/dw]/dw, d[d[d[dI(w,i,m)/dT]/dT]/dw]/dw, d[d[d[dI(a,i,m)/dT]/dT]/dw]/dw, d[d[d[dI(t,w,a,i)/dT]/dT]/dw]/dw, d[d[d[dI(t,w,a,m)/dw/dw, d[d[d[dI(t,w,i,m)/dT]/dT]/dw]/dw, d[d[d[dI(t,a,i,m)/dT]/dT]/dw]/dw, d[d[d[dI(w,a,i,m)/dT]/dT]/dw]/dw, d[d[d[dI(t,w,a,i,m)/dT]/dT]/dw]/dw..

 

We can also take higher order duel dimensional derivatives of instinct as a function of will and time but the symbolic expression of the set of such derivatives very soon becomes excessively lengthly to write and so these higher order derivatives as such are not mentioned here except to say that they would be computed in an analogous manner to the second order duel dimensional derivatives described above.

 

 

We can also express instinct  qualitatively, statistically, and perhaps with the use of some forms of real analysis as a derivative in terms of  affect or of a.

 

Given that I(a) =  I(t and/or w and/or a and/or i and/or m), the following first order derivatives of instinct with respect to affect are possible.

 

 

dI(t)/da, dI(w)/da, dI(a)/da, dI(i)/da, dI(m)/da, dI(t,w)/da, dI(t,a)/da, dI(t,i)/da, dI(t,m)/da, dI(w,a)/da, dI(w,i)/da, dI(w,m)/da, dI(a,i)/da, dI(a,m)/da, dI(i,m)/da, dI(t,w,a)/da, dI(t,w,i)/da, dI(t,w,m)/da, dI(t,a,i)/da, dI(t,a,m)/da, dI(t,i,m)/da, dI(w,a,i)/da, dI(w,a,m)/da, dI(w,i,m)/da, dI(a,i,m)/da, dI(t,w,a,i)/da, dI(t,w,a,m)/da, dI(t,w,i,m)/da, dI(t,a,i,m)/da, dI(w,a,i,m)/da, dI(t,w,a,i,m)/da.

 

 

Or more succinctly, dI/da = dI(t and/or w and/or a and/or i and/or m)/da

 

 

Or perhaps dI(a)/da =d I{[t(a)] and/or [w(a)] and/or [a(a)] and/or [i(a)] and/or [m(a)]}/da.

 

 

Likewise, we can take the second affect derivatives of  I as follows:

 

 

 

d[dI(t)/da]/da, d[dI(w)/da]/da, d[dI(a)/da]/da, d[dI(i)/da]/da, d[dI(m)/da]/da, d[dI(t,w)/da]/da, d[dI(t,a)/da]/da, d[dI(t,i)/da]/da, d[dI(t,m)/da]/da, d[dI(w,a)/da]/da, d[dI(w,i)/da]/da, d[dI(w,m)/da]/da, d[dI(a,i)/da]/da, d[dI(a,m)/da]/da, d[dI(i,m)/da/da, d[dI(t,w,a)/da]/da, d[dI(t,w,i)/da]/da, d[dI(t,w,m)/da]/da, d[dI(t,a,i)/da]/da, d[dI(t,a,m)/da]/da,  d[dI(t,i,m)/da]/da, d[dI(w,a,i)/da]/da, d[dI(w,a,m)/da]/da, d[dI(w,i,m)/da]/da, d[dI(a,i,m)/da]/da, d[dI(t,w,a,i)/da]/da, d[dI(t,w,a,m)/da/da, d[dI(t,w,i,m)/da]/da, d[dI(t,a,i,m)/da]/da, d[dI(w,a,i,m)/da]/da, d[dI(t,w,a,i,m)/da]/da..

 

 

or more succinctly, as d(dI/da)/da = d[d I(t and/or w and/or a and/or i and/or m)/da]/da = Ia2

 

 

or as

 

 

d[dI(a)/da]/da  = d[d I{[t(a)] and/or [w(a)] and/or [a(a)] and/or [i(a)] and/or [m(a)]}/da]/da = Ia2.

 

 

 

Likewise, we can take the third affect derivatives of  I as follows:

 

 

 

d[d[dI(t)/da]/da]/da, d[d[dI(w)/da]/da]/da, d[d[dI(a)/da]/da]/da, d[d[dI(i)/da]/da]/da, d[d[dI(m)/da]/da]/da, d[d[dI(t,w)/da]/da]/da, d[d[dI(t,a)/da]/da]/da, d[d[dI(t,i)/da]/da]/da, d[d[dI(t,m)/da]/da]/da, d[d[dI(w,a)/da]/da]/da, d[d[dI(w,i)/da]/da]/da, d[d[dI(w,m)/da]/da]/da, d[d[dI(a,i)/da]/da]/da, d[d[dI(a,m)/da]/da]/da, d[d[dI(i,m)/da/da]/da, d[d[dI(t,w,a)/da]/da]/da, d[d[dI(t,w,i)/da]/da]/da, d[d[dI(t,w,m)/da]/da]/da, d[d[dI(t,a,i)/da]/da]/da, d[d[dI(t,a,m)/da]/da]/da,  d[d[dI(t,i,m)/da]/da]/da, d[d[dI(w,a,i)/da]/da]/da, d[d[dI(w,a,m)/da]/da]/da, d[d[dI(w,i,m)/da]/da]/da, d[d[dI(a,i,m)/da]/da]/da, d[d[dI(t,w,a,i)/da]/da]/da, d[d[dI(t,w,a,m)/da/da]/da, d[d[dI(t,w,i,m)/da]/da]/da, d[d[dI(t,a,i,m)/da]/da]/da, d[d[dI(w,a,i,m)/da]/da]/da, d[d[dI(t,w,a,i,m)/da]/da]/da.

 

 

or more succinctly, as d[d(dI/da)/da]/da = d[d[d I(t and/or w and/or a and/or i and/or m)/da]/da]/da = Ia3

 

 

or as

 

 

d[d[dI(a)/da]/da]/da  = d[d[d I{[t(a)] and/or [w(a)] and/or [a(a)] and/or [i(a)] and/or [m(a)]}/da]/da]/da = Ia3.

 

 

We can also form the expressions;

 

 

d[d[f(I)]/da]/da = d{d [I[t(a)]]/da and/or d[I[w(a)]]/da and/or d[I[a(a)]]/da and/or d[I[i(a)]]/da and/or d[I[m(a)]]/da}/da  = f(Ia)2

 

 

and

 

 

d[d[d[f(I)]/da]/da]/da = d{d{ d [I[t(a)]]/da and/or d[I[w(a)]]/da and/or d[I[a(a)]]/da and/or d[I[i(a)]]/da and/or d[I[m(a)]]/da}/da}/da  = f(Ia)3A, where A stands for type A differentiation which is not to be confused with the meaning of so-called Type A personality as A is used as an ordinal in a totally different context here.

 

 

and

 

 

d[d[d[f(I)]/da]/da]/da = d{d[d [I[t(a)]]/da]/da  and/or d[d [I[w(a)]]/da]/da  and/or d[d [I[a(a)]]/da]/da  and/or d[d [I[i(a)]]/da]/da  and/or d[d [I[m(a)]]/da]/da }/da = f(Ia)3B, where B stands for type B differentiation which is not to be confused with the meaning of so-called Type  B personality as B is used as an ordinal in a totally different context here. .

 

 

In fact, one can form yet higher order derivatives of instincts with respect to affect as follows.

 

 

Ia5 = d Ia4/da = d[dIa3/da]/da

 

 

 

Ia5 = dIa4/da =  d[d[d[d[d I{[t(a)] and/or [w(a)] and/or [a(a)] and/or [i(a)] and/or [m(a)]}/da]/da]/da]/da]/da.

 

 

 

f(Ia)5A = d[f(Ia)4A]/da = d[d [f(Ia)3A]/da]/da =  d{d{d{d{ d [I[t(a)]]/da and/or d[I[w(a)]]/da and/or d[I[a(a)]]/da and/or d[I[i(a)]]/da and/or d[I[m(a)]]/da}/da}/da]/da]/da

 

 

 

 

Ia6 = d Ia5/da = d[d Ia4/da]/da = d[d[dIa3/da]/da]/da

 

 

 

Ia6 = dIa5/da = d[d[d[d[d[d I{[t(a)] and/or [w(a)] and/or [a(a)] and/or [i(a)] and/or [m(a)]}/da]/da]/da]/da]/da]/da

 

 

 

f(Ia)6A = d[f(Ia)5A]/da = d{ d{d{d{d{ d [I[t(a)]]/da and/or d[I[w(a)]]/da and/or d[I[a(a)]]/da and/or d[I[i(a)]]/da and/or d[I[m(a)]]/da}/da}/da]/da]/da]/da

 

 

 

 

Ia7 = dIa6/da

 

f(Ia)7A = d[f(Ia)6A]/da

 

 

Ia8 = d Ia7/da

 

f(Ia)8A = d[f(Ia)7A]/da

 

 

 

Ia9 = d Ia8/da

 

f(Ia)9A = d[f(Ia)8A]/da

 

 

Ia10…, Ia11…, Ia12 … etc.

 

 

Anyone for Ia ensemble, or Ia infinity scrapper, or Ia (Aleph 0), or Ia(Aleph 1), or Ia (Aleph 2), or how about Ia Aleph (Aleph 0), or Ia Aleph (Aleph 1) , or Ia Aleph (Aleph 2), or even Ia Aleph (Aleph (Aleph 0)), or Ia Aleph (Aleph (Aleph 1)), or Ia Aleph (Aleph (Aleph 2)), and so on?

 

Thus, for the set of the sets of derivatives of Ia1 through Ia(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ia1 through Ia(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)},…, {П(0,31)[R]}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ia1 through Ia(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ia1 through Ia(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the derivative states in the set of the sets of derivatives of Ia1 through Ia(Aleph 0) is plausible equal to:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ia1 through Ia(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ia1 through Ia(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}}}.

 

For the set of the sets of derivatives of Ia1 through Ia(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Ia(Aleph 0) derivative space at the level of 0/(Aleph 0), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Ia1 through Ia(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ia1 through Ia(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ia1 through Ia(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ia1 through Ia(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Ia1 through Ia(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ia1 through Ia(Aleph 1), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Ia1 through  Ia(Aleph 2), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Ia1 through Ia(Aleph 3), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Ia(Aleph 0) derivative space at the level of 0/(Aleph 1), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Ia1 through Ia(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ia1 through Ia(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ia1 through Ia(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ia1 through  Ia(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations  for the set of the sets of derivatives of Ia1 through Ia(Aleph 0) is plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ia1 through Ia(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Ia1 through Ia(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Ia1 through Ia(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

 

For super-continuous Ia(Aleph 0) derivative space at the level of 0/(Aleph 2), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Ia1 through Ia(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ia1 through Ia(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ia1 through Ia(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ia1 through Ia(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Ia1 through Ia(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ia1 through Ia(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Ia1 through Ia(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Ia1 through Ia(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

Similar series can be developed for super-continuity at any applicable level such as 0/(Aleph 3), 0/(Aleph 4), 0/(Aleph 5),…, 0/(Aleph Ω), 0/(Aleph (Aleph 0)), …, 0/(Aleph (Aleph 1)), …, 0/(Aleph (Aleph 2)), …, 0/(Aleph (Aleph 3)),…, 0/(Aleph (Aleph Ω)),…, 0/(Aleph (Aleph (Aleph 0))), …, 0/(Aleph (Aleph (Aleph 1))),…, 0/(Aleph (Aleph (Aleph 2))),…, 0/(Aleph (Aleph (Aleph 3))),…, 0/(Aleph (Aleph  (Aleph Ω))), …

 

An so-on ad infinitum.

 

In addition to these numerical functions of Ia as functions of summation series of product series functions, in order to really appreciate the enourmous complexity of the human soul in terms of its potential to evolve and be differentiated from all other souls in its characteristics, we would need to consider how every single category and even every single species of affect of the form Ia can very. Since there may exist an arbitrarily high infinite number species of Ia, the number of numerical functions of Ia is utterly beyond recogning. I will cover such notions in terms of mathematical notation in yet another series of articles I will write on this general concept.

 

 

 

Perhaps these numbers are applicable when one considers that the human soul, in its accidental form and perhaps even in its substantial form stores all experience and other psychodynamics based phenomenon. Every experience adds to the accidental form of the human soul and this includes the souls of all those still alive on Earth, all those in Purgatory, all those in Heaven, all those in Hell, and all those in any Limbo.

Since the human soul can grow without limit in terms of its psychodynamic time –flow world line, such a consideration offers another mechanism where the number of derivative states, combinations of derivative states, and even super-continuity of the derivative state space can grow forever.

 

Folks, for those of you who might balk at me for including literally all souls in the above consideration, including the souls in Hell, as well as bodily extraterrestrial souls and the souls of so-called bodily ultraterrestials sometimes referred to as etherians in the new age UFO buff culture, my reply is that we simply do not understand the full scope of GOD’s Divine Economy. We may never fully comprehend the scope of the Divine Economy because such an utterly eternal scheme, is, well, eternal and never ending.

 

 

 

The general meaning of affect derivatives of instinct can be viewed as the manner in which the qualitative and/or quantitative aspects of instinct as a function of affect very with affect. The manner in which instincts very with affect may be multi- affect-aspect dimensional wherein the dimensions of derivations can be multiple, and wherein the derivations can be taken in parallel, series parallel or in serial manner. The differentials can be partial or non-partial derivatives, or both partial and non-partial for a given computation.

 

In fact, since there is in theory, no limit to the numbers of qualitatively and quantitatively different affective states, and perhaps no limit to the number of possible different types or classes of affective states, wherein each person has his or her own unique affective rxperiences, the number of affect dimensions that can effect instincts is literally infinite, given the entirety of the set of created persons, and perhaps also literally infinite for each person as an individual, although we can not intellectually and intuitively understand this infinite number.

 

 

It is interesting to consider the ramifactions of being able to perform realistic calculations involving affect derivatives of instinct from a mathematical, theoretical, scientific,  and philosophical perspective.

 

Persons for which one or more nth order derivatives of instinct with respect to affect that have large absolute values would tend to have their instincts highly influenced by affect, or at least for the instincts under consideration with respect to the dimension of the specific affect type(s) or class(es) for which the differentiation(s) are being performed. Perhaps a strong coupling between instinct and affect indicates a well integrated personality and commensurately, a high degree of instinct capacity and a high degree of instinct intelligence as well as perhaps very strong affect power.

 

We would expect that disembodied human souls, ETI souls, and/or UTI souls in Heaven, Limbo, highly evolved bodily ETI persons, highly evolved UTI persons, and angels to have spiritual instincts of all kinds and intensities which are highly subject to affect.

 

 

We can also consider that two dimensional nth ordered derivatives of instinct with respect to affect and time, or with respect to a and T, respectively.

 

Given that I[(a)(T)] =  I[(t and/or w and/or a and/or i and/or m)(w)(T)], the following first order two dimensional derivatives of instinct with respect to affect and Time are possible.

 

 

d[dI[(t)(T)]/da]/dT, d[dI[(w)(T)]/da]/dT, d[dI[(a)(T)]/da]/dT, d[dI[(i)(T)]/da]/dT, d[dI[(m)(T)]/da]/dT, d[dI[(t,w)(T)]/da]/dT, d[dI[(t,a)(T)]/da]/dT, d[dI[(t,i)(T)]/da]/dT, d[dI[(t,m)(T)]/da]/dT, d[dI[(w,a)(T)]/da]/dT, d[dI[(w,i)(T)]/da]/dT, d[dI[(w,m)(T)]/da]/dT, d[dI[(a,i)(T)]/da]/dT, d[dI[(a,m)(T)]/da]/dT, d[dI[(i,m)(T)]/da]/dT, d[dI[(t,w,a)(T)]/da]/dT, d[dI[(t,w,i)(T)]/da]/dT, d[dI[(t,w,m)(T)]/da]/dT, d[dI[(t,a,i)(T)]/da]/dT, d[dI[(t,a,m)(T)]/da]/dT, d[dI[(t,i,m)(T)]/da]/dT, d[dI[(w,a,i)(T)]/da]/dT, d[dI[(w,a,m)(T)]/da]/dT, d[dI[(w,i,m)(T)]/da]/dT, d[dI[(a,i,m)(T)]/da]/dT, d[dI[(t,w,a,i)(T)]/da]/dT, d[dI[(t,w,a,m)(T)]/da]/dT, d[dI[(t,w,i,m)(T)]/da]/dT, d[dI[(t,a,i,m)(T)]/da]/dT, d[dI[(w,a,i,m)(T)]/da]/dT, d[dI[(t,w,a,i,m)(T)]/da]/dT.

 

 

Or more succinctly,  d[dI(T)/da]/dT = d[dI[(T)(t and/or w and/or a and/or i and/or m)]/da]/dT

 

or

 

d[dI(T)/dT]/da = d[dI[(T)(t and/or w and/or a and/or i and/or m)]/dT]/da

 

 

 

 

 

Or perhaps d[d I[(a)(T)]/da]/dT  = d[d I [{[t(a)] and/or [w(a)] and/or [a(a)] and/or [i(a)] and/or [m(a)]}(T)]/da]/dT

 

or

 

Or perhaps d[d I[(a)(T)]/dT]/da  = d[d I [{[t(a)] and/or [w(a)] and/or [a(a)] and/or [i(a)] and/or [m(a)]}(T)]/dT]/da

 

 

 

Likewise, we can take the second dual dimension affect -time derivatives of  I as follows:

 

d[d[d[dI[(t)(T)]/da]/dT]/da]/dT, d[d[d[dI[(w)(T)]/da]/dT]/da]/dT, d[d[d[dI[(a)(T)]/da]/dT]/da]/dT, d[d[d[dI[(i)(T)]/da]/dT]/da]/dT, d[d[d[dI[(m)(T)]/da]/dT]/da]/dT, d[d[d[dI[(t,w)(T)]/da]/dT]/da]/dT, d[d[d[dI[(t,a)(T)]/da]/dT]/da]/dT, d[d[d[dI[(t,i)(T)]/da]/dT]/da]/dT, d[d[d[dI[(t,m)(T)]/da]/dT]/da]/dT, d[d[d[dI[(w,a)(T)]/da]/dT]/da]/dT, d[d[d[dI[(w,i)(T)]/da]/dT]/da]/dT, d[d[d[dI[(w,m)(T)]/da]/dT]/da]/dT, d[d[d[dI[(a,i)(T)]/da]/dT]/da]/dT, d[d[d[dI[(a,m)(T)]/da]/dT]/da]/dT, d[d[d[dI[(i,m)(T)]/da]/dT]/da]/dT, d[d[d[dI[(t,w,a)(T)]/da]/dT]/da]/dT, d[d[d[dI[(t,w,i)(T)]/da]/dT]/da]/dT, d[d[d[dI[(t,w,m)(T)]/da]/dT]/da]/dT, d[d[d[dI[(t,a,i)(T)]/da]/dT]/da]/dT, d[d[d[dI[(t,a,m)(T)]/da]/dT]/da]/dT, d[d[d[dI[(t,i,m)(T)]/da]/dT]/da]/dT, d[d[d[dI[(w,a,i)(T)]/da]/dT]/da]/dT, d[d[d[dI[(w,a,m)(T)]/da]/dT]/da]/dT, d[d[d[dI[(w,i,m)(T)]/da]/dT]/da]/dT, d[d[d[dI[(a,i,m)(T)]/da]/dT]/da]/dT, d[d[d[dI[(t,w,a,i)(T)]/da]/dT]/da]/dT, d[d[d[dI[(t,w,a,m)(T)]/da]/dT]/da]/dT, d[d[d[dI[(t,w,i,m)(T)]/da]/dT]/da]/dT, d[d[d[dI[(t,a,i,m)(T)]/da]/dT]/da]/dT, d[d[d[dI[(w,a,i,m)(T)]/da]/dT]/da]/dT, d[d[d[dI[(t,w,a,i,m)(T)]/da]/dT]/da]/dT.

 

or as:

 

 

 

d[d[d[dI[(t)(T)]/da]/dT]/dT]/da, d[d[d[dI[(w)(T)]/da]/dT]/dT]/da, d[d[d[dI[(a)(T)]/da]/dT]/dT]/da, d[d[d[dI[(i)(T)]/da]/dT]/dT]/da, d[d[d[dI[(m)(T)]/da]/dT]/dT]/da, d[d[d[dI[(t,w)(T)]/da]/dT]/dT]/da, d[d[d[dI[(t,a)(T)]/da]/dT]/dT]/da, d[d[d[dI[(t,i)(T)]/da]/dT]/dT]/da, d[d[d[dI[(t,m)(T)]/da]/dT]/dT]/da, d[d[d[dI[(w,a)(T)]/da]/dT]/dT]/da, d[d[d[dI[(w,i)(T)]/da]/dT]/dT]/da, d[d[d[dI[(w,m)(T)]/da]/dT]/dT]/da, d[d[d[dI[(a,i)(T)]/da]/dT]/dT]/da, d[d[d[dI[(a,m)(T)]/da]/dT]/dT]/da, d[d[d[dI[(i,m)(T)]/da]/dT]/dT]/da, d[d[d[dI[(t,w,a)(T)]/da]/dT]/dT]/da, d[d[d[dI[(t,w,i)(T)]/da]/dT]/dT]/da, d[d[d[dI[(t,w,m)(T)]/da]/dT]/dT]/da, d[d[d[dI[(t,a,i)(T)]/da]/dT]/dT]/da, d[d[d[dI[(t,a,m)(T)]/da]/dT]/dT]/da, d[d[d[dI[(t,i,m)(T)]/da]/dT]/dT]/da, d[d[d[dI[(w,a,i)(T)]/da]/dT]/dT]/da, d[d[d[dI[(w,a,m)(T)]/da]/dT]/dT]/da, d[d[d[dI[(w,i,m)(T)]/da]/dT]/dT]/da, d[d[d[dI[(a,i,m)(T)]/da]/dT]/dT]/da, d[d[d[dI[(t,w,a,i)(T)]/da]/dT]/dT]/da, d[d[d[dI[(t,w,a,m)(T)]/da]/dT]/dT]/da, d[d[d[dI[(t,w,i,m)(T)]/da]/dT]/dT]/da, d[d[d[dI[(t,a,i,m)(T)]/da]/dT]/dT]/da, d[d[d[dI[(w,a,i,m)(T)]/da]/dT]/dT]/da, d[d[d[dI[(t,w,a,i,m)(T)]/da]/dT]/dT]/da.

 

or as:

 

d[d[d[dI[(t)(T)]/dT]/da]/da]/dT, d[d[d[dI[(w)(T)]/dT]/da]/da]/dT, d[d[d[dI[(a)(T)]/dT]/da]/da]/dT, d[d[d[dI[(i)(T)]/dT]/da]/da]/dT, d[d[d[dI[(m)(T)]/dT]/da]/da]/dT, d[d[d[dI[(t,w)(T)]/dT]/da]/da]/dT, d[d[d[dI[(t,a)(T)]/dT]/da]/da]/dT, d[d[d[dI[(t,i)(T)]/dT]/da]/da]/dT, d[d[d[dI[(t,m)(T)]/dT]/da]/da]/dT, d[d[d[dI[(w,a)(T)]/dT]/da]/da]/dT, d[d[d[dI[(w,i)(T)]/dT]/da]/da]/dT, d[d[d[dI[(w,m)(T)]/dT]/da]/da]/dT, d[d[d[dI[(a,i)(T)]/dT]/da]/da]/dT, d[d[d[dI[(a,m)(T)]/dT]/da]/da]/dT, d[d[d[dI[(i,m)(T)]/dT]/da]/da]/dT, d[d[d[dI[(t,w,a)(T)]/dT]/da]/da]/dT, d[d[d[dI[(t,w,i)(T)]/dT]/da]/da]/dT, d[d[d[dI[(t,w,m)(T)]/dT]/da]/da]/dT, d[d[d[dI[(t,a,i)(T)]/dT]/da]/da]/dT, d[d[d[dI[(t,a,m)(T)]/dT]/da]/da]/dT, d[d[d[dI[(t,i,m)(T)]/dT]/da]/da]/dT, d[d[d[dI[(w,a,i)(T)]/dT]/da]/da]/dT, d[d[d[dI[(w,a,m)(T)]/dT]/da]/da]/dT, d[d[d[dI[(w,i,m)(T)]/dT]/da]/da]/dT, d[d[d[dI[(a,i,m)(T)]/dT]/da]/da]/dT, d[d[d[dI[(t,w,a,i)(T)]/dT]/da]/da]/dT, d[d[d[dI[(t,w,a,m)(T)]/dT]/da]/da]/dT, d[d[d[dI[(t,w,i,m)(T)]/dT]/da]/da]/dT, d[d[d[dI[(t,a,i,m)(T)]/dT]/da]/da]/dT, d[d[d[dI[(w,a,i,m)(T)]/dT]/da]/da]/dT, d[d[d[dI[(t,w,a,i,m)(T)]/dT]/da]/da]/dT.

 

 

or as;

 

 

 

 

d[d[d[dI(t)/da]/da]/dT]/dT, d[d[d[dI(w)/da]/da]/dT]/dT, d[d[d[dI(a)/da]/da]/dT]/dT, d[d[d[dI(i)/da]/da]/dT]/dT, d[d[d[dI(m)/da]/da]/dT]/dT, d[d[d[dI(t,w)/da]/da]/dT]/dT, d[d[d[dI(t,a)/da]/da]/dT]/dT, d[d[d[dI(t,i)/da]/da]/dT]/dT, d[d[d[dI(t,m)/da]/da]/dT]/dT, d[d[d[dI(w,a)/da]/da]/dT]/dT, d[d[d[dI(w,i)/da]/da]/dT]/dT, d[d[d[dI(w,m)/da]/da]/dT]/dT, d[d[d[dI(a,i)/da]/da]/dT]/dT, d[d[d[dI(a,m)/da]/da]/dT]/dT, d[d[d[dI(i,m)/da]/da]/dT]/dT, d[d[d[dI(t,w,a)/da]/da]/dT]/dT, d[d[d[dI(t,w,i)/da]/da]/dT]/dT, d[d[d[dI(t,w,m)/da]/da]/dT]/dT, d[d[d[dI(t,a,i)/da]/da]/dT]/dT, d[d[d[dI(t,a,m)/da]/da]/dT]/dT,  d[d[d[dI(t,i,m)/da]/da]/dT]/dT, d[d[d[dI(w,a,i)/da]/da]/dT]/dT, d[d[d[dI(w,a,m)/da]/da]/dT]/dT, d[d[d[dI(w,i,m)/da]/da]/dT]/dT, d[d[d[dI(a,i,m)/da]/da]/dT]/dT, d[d[d[dI(t,w,a,i)/da]/da]/dT]/dT, d[d[d[dI(t,w,a,m)/da/da, d[d[d[dI(t,w,i,m)/da]/da]/dT]/dT, d[d[d[dI(t,a,i,m)/da]/da]/dT]/dT, d[d[d[dI(w,a,i,m)/da]/da]/dT]/dT, d[d[d[dI(t,w,a,i,m)/da]/da]/dT]/dT..

 

or as:

 

d[d[d[dI(t)/dT]/da]/dT]/da, d[d[d[dI(w)/dT]/da]/dT]/da, d[d[d[dI(a)/dT]/da]/dT]/da, d[d[d[dI(i)/dT]/da]/dT]/da, d[d[d[dI(m)/dT]/da]/dT]/da, d[d[d[dI(t,w)/dT]/da]/dT]/da, d[d[d[dI(t,a)/dT]/da]/dT]/da, d[d[d[dI(t,i)/dT]/da]/dT]/da, d[d[d[dI(t,m)/dT]/da]/dT]/da, d[d[d[dI(w,a)/dT]/da]/dT]/da, d[d[d[dI(w,i)/dT]/da]/dT]/da, d[d[d[dI(w,m)/dT]/da]/dT]/da, d[d[d[dI(a,i)/dT]/da]/dT]/da, d[d[d[dI(a,m)/dT]/da]/dT]/da, d[d[d[dI(i,m)/ dT]/da]/dT]/da, d[d[d[dI(t,w,a)/dT]/da]/dT]/da, d[d[d[dI(t,w,i)/dT]/da]/dT]/da, d[d[d[dI(t,w,m)/dT]/da]/dT]/da, d[d[d[dI(t,a,i)/dT]/da]/dT]/da, d[d[d[dI(t,a,m)/dT]/da]/dT]/da,  d[d[d[dI(t,i,m)/dT]/da]/dT]/da, d[d[d[dI(w,a,i)/dT]/da]/dT]/da, d[d[d[dI(w,a,m)/dT]/da]/dT]/da, d[d[d[dI(w,i,m)/dT]/da]/dT]/da, d[d[d[dI(a,i,m)/dT]/da]/dT]/da, d[d[d[dI(t,w,a,i)/dT]/da]/dT]/da, d[d[d[dI(t,w,a,m)/da/da, d[d[d[dI(t,w,i,m)/dT]/da]/dT]/da, d[d[d[dI(t,a,i,m)/dT]/da]/dT]/da, d[d[d[dI(w,a,i,m)/dT]/da]/dT]/da, d[d[d[dI(t,w,a,i,m)/dT]/da]/dT]/da..

 

or as:

 

d[d[d[dI(t)/dT]/dT]/da]/da, d[d[d[dI(w)/dT]/dT]/da]/da, d[d[d[dI(a)/dT]/dT]/da]/da, d[d[d[dI(i)/dT]/dT]/da]/da, d[d[d[dI(m)/dT]/dT]/da]/da, d[d[d[dI(t,w)/dT]/dT]/da]/da, d[d[d[dI(t,a)/dT]/dT]/da]/da, d[d[d[dI(t,i)/dT]/dT]/da]/da, d[d[d[dI(t,m)/dT]/dT]/da]/da, d[d[d[dI(w,a)/dT]/dT]/da]/da, d[d[d[dI(w,i)/dT]/dT]/da]/da, d[d[d[dI(w,m)/dT]/dT]/da]/da, d[d[d[dI(a,i)/dT]/dT]/da]/da, d[d[d[dI(a,m)/ dT]/dT]/da]/da, d[d[d[dI(i,m)/ dT]/dT]/da]/da, d[d[d[dI(t,w,a)/dT]/dT]/da]/da, d[d[d[dI(t,w,i)/dT]/dT]/da]/da, d[d[d[dI(t,w,m)/dT]/dT]/da]/da, d[d[d[dI(t,a,i)/dT]/dT]/da]/da, d[d[d[dI(t,a,m)/dT]/dT]/da]/da,  d[d[d[dI(t,i,m)/dT]/dT]/da]/da, d[d[d[dI(w,a,i)/dT]/dT]/da]/da, d[d[d[dI(w,a,m)/dT]/dT]/da]/da, d[d[d[dI(w,i,m)/dT]/dT]/da]/da, d[d[d[dI(a,i,m)/dT]/dT]/da]/da, d[d[d[dI(t,w,a,i)/dT]/dT]/da]/da, d[d[d[dI(t,w,a,m)/da/da, d[d[d[dI(t,w,i,m)/dT]/dT]/da]/da, d[d[d[dI(t,a,i,m)/dT]/dT]/da]/da, d[d[d[dI(w,a,i,m)/dT]/dT]/da]/da, d[d[d[dI(t,w,a,i,m)/dT]/dT]/da]/da..

 

We can also take higher order duel dimensional derivatives of instinct as a function of affect and time but the symbolic expression of the set of such derivatives very soon becomes excessively lengthly to write and so these higher order derivatives as such are not mentioned here except to say that they would be computed in an analogous manner to the second order duel dimensional derivatives described above.

 

.

 

 

We can also express instinct qualitatively, statistically, and perhaps with the use of some forms of real analyses as a derivative in terms of  instinct or of i.

 

Given that I(i) =  I(t and/or w and/or a and/or i and/or m) or perhaps the following notation can be more appropriate in certain circumstances.

 

 

 

 

Thus the following first order derivatives of instinct with respect to instinct are possible.

 

 

dI(t)/di, dI(w)/di, dI(a)/di, dI(i)/di, dI(m)/di, dI(t,w)/di, dI(t,a)/di, dI(t,i)/di, dI(t,m)/di, dI(w,a)/di, dI(w,i)/di, dI(w,m)/di, dI(a,i)/di, dI(a,m)/di, dI(i,m)/di, dI(t,w,a)/di, dI(t,w,i)/di, dI(t,w,m)/di, dI(t,a,i)/di, dI(t,a,m)/di, dI(t,i,m)/di, dI(w,a,i)/di, dI(w,a,m)/di, dI(w,i,m)/di, dI(a,i,m)/di, dI(t,w,a,i)/di, dI(t,w,a,m)/di, dI(t,w,i,m)/di, dI(t,a,i,m)/di, dI(w,a,i,m)/di, dI(t,w,a,i,m)/di.

 

 

Or more succinctly,  dI/di = dI(t and/or w and/or a and/or i and/or m)/di

 

 

Or perhaps dI(i)/di =d I{[t(i)] and/or [w(i)] and/or [a(i)] and/or [i(i)] and/or [m(i)]}/di.

 

 

Likewise, we can take the second instinct derivatives of  I as follows:

 

 

 

d[dI(t)/di]/di, d[dI(w)/di]/di, d[dI(a)/di]/di, d[dI(i)/di]/di, d[dI(m)/di]/di, d[dI(t,w)/di]/di, d[dI(t,a)/di]/di, d[dI(t,i)/di]/di, d[dI(t,m)/di]/di, d[dI(w,a)/di]/di, d[dI(w,i)/di]/di, d[dI(w,m)/di]/di, d[dI(a,i)/di]/di, d[dI(a,m)/di]/di, d[dI(i,m)/di/di, d[dI(t,w,a)/di]/di, d[dI(t,w,i)/di]/di, d[dI(t,w,m)/di]/di, d[dI(t,a,i)/di]/di, d[dI(t,a,m)/di]/di,  d[dI(t,i,m)/di]/di, d[dI(w,a,i)/di]/di, d[dI(w,a,m)/di]/di, d[dI(w,i,m)/di]/di, d[dI(a,i,m)/di]/di, d[dI(t,w,a,i)/di]/di, d[dI(t,w,a,m)/di/di, d[dI(t,w,i,m)/di]/di, d[dI(t,a,i,m)/di]/di, d[dI(w,a,i,m)/di]/di, d[dI(t,w,a,i,m)/di]/di..

 

 

or more succinctly, as d(dI/di)/di = d[d I(t and/or w and/or a and/or i and/or m)/di]/di = Ii2

 

 

or as

 

 

d[dI(i)/di]/di  = d[d I{[t(i)] and/or [w(i)] and/or [a(i)] and/or [i(i)] and/or [m(i)]}/di]/di = Ii2.

 

 

 

Likewise, we can take the third instinct derivatives of  I as follows:

 

 

 

d[d[dI(t)/di]/di]/di, d[d[dI(w)/di]/di]/di, d[d[dI(a)/di]/di]/di, d[d[dI(i)/di]/di]/di, d[d[dI(m)/di]/di]/di, d[d[dI(t,w)/di]/di]/di, d[d[dI(t,a)/di]/di]/di, d[d[dI(t,i)/di]/di]/di, d[d[dI(t,m)/di]/di]/di, d[d[dI(w,a)/di]/di]/di, d[d[dI(w,i)/di]/di]/di, d[d[dI(w,m)/di]/di]/di, d[d[dI(a,i)/di]/di]/di, d[d[dI(a,m)/di]/di]/di, d[d[dI(i,m)/di/di]/di, d[d[dI(t,w,a)/di]/di]/di, d[d[dI(t,w,i)/di]/di]/di, d[d[dI(t,w,m)/di]/di]/di, d[d[dI(t,a,i)/di]/di]/di, d[d[dI(t,a,m)/di]/di]/di,  d[d[dI(t,i,m)/di]/di]/di, d[d[dI(w,a,i)/di]/di]/di, d[d[dI(w,a,m)/di]/di]/di, d[d[dI(w,i,m)/di]/di]/di, d[d[dI(a,i,m)/di]/di]/di, d[d[dI(t,w,a,i)/di]/di]/di, d[d[dI(t,w,a,m)/di/di]/di, d[d[dI(t,w,i,m)/di]/di]/di, d[d[dI(t,a,i,m)/di]/di]/di, d[d[dI(w,a,i,m)/di]/di]/di, d[d[dI(t,w,a,i,m)/di]/di]/di.

 

 

or more succinctly, as d[d(dI/di)/di]/di = d[d[d I(t and/or w and/or a and/or i and/or m)/di]/di]/di = Ii3

 

 

or as

 

 

d[d[dI(i)/di]/di]/di  = d[d[d I{[t(i)] and/or [w(i)] and/or [a(i)] and/or [i(i)] and/or [m(i)]}/di]/di]/di = Ii3.

 

 

We can also form the expressions;

 

 

d[d[f(I)]/di]/di = d{d [I[t(i)]]/di and/or d[I[w(i)]]/di and/or d[I[a(i)]]/di and/or d[I[i(i)]]/di and/or d[I[m(i)]]/di}/di  = f(Ii)2

 

 

and

 

 

d[d[d[f(I)]/di]/di]/di = d{d{ d [I[t(i)]]/di and/or d[I[w(i)]]/di and/or d[I[a(i)]]/di and/or d[I[i(i)]]/di and/or d[I[m(i)]]/di}/di}/di  = f(Ii)3A, where A stands for type A differentiation which is not to be confused with the meaning of so-called Type A personality as A is used as an ordinal in a totally different context here.

 

 

and

 

 

d[d[d[f(I)]/di]/di]/di = d{d[d [I[t(i)]]/di]/di  and/or d[d [I[w(i)]]/di]/di  and/or d[d [I[a(i)]]/di]/di  and/or d[d [I[i(i)]]/di]/di  and/or d[d [I[m(i)]]/di]/di }/di = f(Ii)3B, where B stands for type B differentiation which is not to be confused with the meaning of so-called Type  B personality as B is used as an ordinal in a totally different context here .

 

 

In fact, one can form yet higher order derivatives of instincts with respect to instinct as follows.

 

 

Ii5 = d Ii4/di = d[dIi3/di]/di

 

 

 

Ii5 = dIi4/di =  d[d[d[d[d I{[t(i)] and/or [w(i)] and/or [a(i)] and/or [i(i)] and/or [m(i)]}/di]/di]/di]/di]/di.

 

 

 

f(Ii)5A = d[f(Ii)4A]/di = d[d [f(Ii)3A]/di]/di =  d{d{d{d{ d [I[t(i)]]/di and/or d[I[w(i)]]/di and/or d[I[a(i)]]/di and/or d[I[i(i)]]/di and/or d[I[m(i)]]/di}/di}/di]/di]/di

 

 

 

 

Ii6 = d Ii5/di = d[d Ii4/di]/di = d[d[dIi3/di]/di]/di

 

 

 

Ii6 = dIi5/di = d[d[d[d[d[d I{[t(i)] and/or [w(i)] and/or [a(i)] and/or [i(i)] and/or [m(i)]}/di]/di]/di]/di]/di]/di

 

 

 

f(Ii)6A = d[f(Ii)5A]/di = d{ d{d{d{d{ d [I[t(i)]]/di and/or d[I[w(i)]]/di and/or d[I[a(i)]]/di and/or d[I[i(i)]]/di and/or d[I[m(i)]]/di}/di}/di]/di]/di]/di

 

 

 

 

Ii7 = dIi6/di

 

f(Ii)7A = d[f(Ii)6A]/di

 

 

Ii8 = d Ii7/di

 

f(Ii)8A = d[f(Ii)7A]/di

 

 

 

Ii9 = d Ii8/di

 

f(Ii)9A = d[f(Ii)8A]/di

 

 

Ii10…, Ii11…, Ii12 … etc.

 

 

Thus, for the set of the sets of derivatives of Ii1 through Ii(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ii1 through Ii(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)},…, {П(0,31)[R]}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ii1 through Ii(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ii1 through Ii(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the derivative states in the set of the sets of derivatives of Ii1 through Ii(Aleph 0) is plausible equal to:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ii1 through Ii(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ii1 through Ii(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}}}.

 

For the set of the sets of derivatives of Ii1 through Ii(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Ii(Aleph 0) derivative space at the level of 0/(Aleph 0), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Ii1 through Ii(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ii1 through Ii(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ii1 through Ii(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ii1 through Ii(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Ii1 through Ii(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ii1 through Ii(Aleph 1), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Ii1 through  Ii(Aleph 2), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Ii1 through Ii(Aleph 3), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Ii(Aleph 0) derivative space at the level of 0/(Aleph 1), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Ii1 through Ii(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ii1 through Ii(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ii1 through Ii(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ii1 through  Ii(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations  for the set of the sets of derivatives of Ii1 through Ii(Aleph 0) is plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ii1 through Ii(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Ii1 through Ii(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Ii1 through Ii(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

 

For super-continuous Ii(Aleph 0) derivative space at the level of 0/(Aleph 2), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Ii1 through Ii(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ii1 through Ii(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ii1 through Ii(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ii1 through Ii(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Ii1 through Ii(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ii1 through Ii(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Ii1 through Ii(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Ii1 through Ii(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

Similar series can be developed for super-continuity at any applicable level such as 0/(Aleph 3), 0/(Aleph 4), 0/(Aleph 5),…, 0/(Aleph Ω), 0/(Aleph (Aleph 0)), …, 0/(Aleph (Aleph 1)), …, 0/(Aleph (Aleph 2)), …, 0/(Aleph (Aleph 3)),…, 0/(Aleph (Aleph Ω)),…, 0/(Aleph (Aleph (Aleph 0))), …, 0/(Aleph (Aleph (Aleph 1))),…, 0/(Aleph (Aleph (Aleph 2))),…, 0/(Aleph (Aleph (Aleph 3))),…, 0/(Aleph (Aleph  (Aleph Ω))), …

 

An so-on ad infinitum.

 

In addition to these numerical functions of Ii as functions of summation series of product series functions, in order to really appreciate the enourmous complexity of the human soul in terms of its potential to evolve and be differentiated from all other souls in its characteristics, we would need to consider how every single category and even every single species of affect of the form Ii can very. Since there may exist an arbitrarily high infinite number species of Ii, the number of numerical functions of Ii is utterly beyond recogning. I will cover such notions in terms of mathematical notation in yet another series of articles I will write on this general concept.

 

 

 

Perhaps these numbers are applicable when one considers that the human soul, in its accidental form and perhaps even in its substantial form stores all experience and other psychodynamics based phenomenon. Every experience adds to the accidental form of the human soul and this includes the souls of all those still alive on Earth, all those in Purgatory, all those in Heaven, all those in Hell, and all those in any Limbo.

Since the human soul can grow without limit in terms of its psychodynamic time –flow world line, such a consideration offers another mechanism where the number of derivative states, combinations of derivative states, and even super-continuity of the derivative state space can grow forever.

 

Folks, for those of you who might balk at me for including literally all souls in the above consideration, including the souls in Hell, as well as bodily extraterrestrial souls and the souls of so-called bodily ultraterrestials sometimes referred to as etherians in the new age UFO buff culture, my reply is that we simply do not understand the full scope of GOD’s Divine Economy. We may never fully comprehend the scope of the Divine Economy because such an utterly eternal scheme, is, well, eternal and never ending.

 

 

The general meaning of instinct derivatives of instinct can be viewed as the manner in which the qualitative and/or quantitative aspects of instinct  as a function of instinct very with instinct. The manner in which instincts very with instinct  may be multi- instinct-aspect dimensional wherein the dimensions of derivations can be multiple, and wherein the derivations can be taken in parallel, series parallel or in serial manner. The differentials can be partial or non-partial derivatives, or both partial and non-partial for a given computation.

 

In fact, since there is in theory, no limit to the numbers of qualitatively and quantitatively different instincts, and perhaps no limit to the number of possible different types or classes of instincts or potential instincts, wherein each person has his or her own unique instincts and instinctual experiences, the number of instinct dimensions that can effect instinct is literally infinite, given the entirety of the set of created persons, and perhaps also literally infinite for each person as an individual, although we can not intellectually and intuitively understand this infinite number.

 

 

It is interesting to consider the ramifactions of being able to perform realistic calculations involving instinct derivatives of instinct from a mathematical, theoretical, scientific,  and philosophical perspective.

 

Persons for which one or more nth order derivatives of instinct with respect to instinct that have large absolute values would tend to have their instinct highly influenced by instinct, or at least for the instinct under consideration with respect to the dimension of the specific instinct type(s) or class(es) for which the differentiation(s) are being performed. Perhaps a strong coupling between instinct and instinct indicates a well integrated personality and commensurately, a high degree of instinct capacity and a high degree of instinctive intelligence as well as perhaps very strong instinct power.

 

We would expect that disembodied human souls, ETI souls, and/or UTI souls in Heaven, Limbo, highly evolved bodily ETI persons, highly evolved UTI persons, and angels to have spiritual instincts of all kinds and intensities which are perhaps  highly subject to advanced instincts such as spiritual instinct, spiritual intuitions, and even perhaps, psychic powers.

 

 

We can also consider that two dimensional nth ordered derivatives of instinct with respect to instinct and time, or with respect to i and T, respectively.

 

Given that I[(i)(T)] =  I[(t and/or w and/or a and/or i and/or m)(i)(T)], the following first order two dimensional derivatives of instincts  with respect to instinct and Time are possible.

 

 

d[dI[(t)(T)]/di]/dT, d[dI[(w)(T)]/di]/dT, d[dI[(a)(T)]/di]/dT, d[dI[(i)(T)]/di]/dT, d[dI[(m)(T)]/di]/dT, d[dI[(t,w)(T)]/di]/dT, d[dI[(t,a)(T)]/di]/dT, d[dI[(t,i)(T)]/di]/dT, d[dI[(t,m)(T)]/di]/dT, d[dI[(w,a)(T)]/di]/dT, d[dI[(w,i)(T)]/di]/dT, d[dI[(w,m)(T)]/di]/dT, d[dI[(a,i)(T)]/di]/dT, d[dI[(a,m)(T)]/di]/dT, d[dI[(i,m)(T)]/di]/dT, d[dI[(t,w,a)(T)]/di]/dT, d[dI[(t,w,i)(T)]/di]/dT, d[dI[(t,w,m)(T)]/di]/dT, d[dI[(t,a,i)(T)]/di]/dT, d[dI[(t,a,m)(T)]/di]/dT, d[dI[(t,i,m)(T)]/di]/dT, d[dI[(w,a,i)(T)]/di]/dT, d[dI[(w,a,m)(T)]/di]/dT, d[dI[(w,i,m)(T)]/di]/dT, d[dI[(a,i,m)(T)]/di]/dT, d[dI[(t,w,a,i)(T)]/di]/dT, d[dI[(t,w,a,m)(T)]/di]/dT, d[dI[(t,w,i,m)(T)]/di]/dT, d[dI[(t,a,i,m)(T)]/di]/dT, d[dI[(w,a,i,m)(T)]/di]/dT, d[dI[(t,w,a,i,m)(T)]/di]/dT.

 

 

Or more succinctly,  d[dI(T)/di]/dT = d[dI[(T)(t and/or w and/or a and/or i and/or m)]/di]/dT

 

or

 

d[dI(T)/dT]/di = d[dI[(T)(t and/or w and/or a and/or i and/or m)]/dT]/di

 

 

 

 

 

Or perhaps d[d I[(i)(T)]/di]/dT  = d[d I [{[t(i)] and/or [w(i)] and/or [a(i)] and/or [i(i)] and/or [m(i)]}(T)]/di]/dT

 

or

 

Or perhaps d[d I[(i)(T)]/dT]/di  = d[d I [{[t(i)] and/or [w(i)] and/or [a(i)] and/or [i(i)] and/or [m(i)]}(T)]/dT]/di

 

 

 

Likewise, we can take the second dual dimension instinct -time derivatives of  I as follows:

 

d[d[d[dI[(t)(T)]/di]/dT]/di]/dT, d[d[d[dI[(w)(T)]/di]/dT]/di]/dT, d[d[d[dI[(a)(T)]/di]/dT]/di]/dT, d[d[d[dI[(i)(T)]/di]/dT]/di]/dT, d[d[d[dI[(m)(T)]/di]/dT]/di]/dT, d[d[d[dI[(t,w)(T)]/di]/dT]/di]/dT, d[d[d[dI[(t,a)(T)]/di]/dT]/di]/dT, d[d[d[dI[(t,i)(T)]/di]/dT]/di]/dT, d[d[d[dI[(t,m)(T)]/di]/dT]/di]/dT, d[d[d[dI[(w,a)(T)]/di]/dT]/di]/dT, d[d[d[dI[(w,i)(T)]/di]/dT]/di]/dT, d[d[d[dI[(w,m)(T)]/di]/dT]/di]/dT, d[d[d[dI[(a,i)(T)]/di]/dT]/di]/dT, d[d[d[dI[(a,m)(T)]/di]/dT]/di]/dT, d[d[d[dI[(i,m)(T)]/di]/dT]/di]/dT, d[d[d[dI[(t,w,a)(T)]/di]/dT]/di]/dT, d[d[d[dI[(t,w,i)(T)]/di]/dT]/di]/dT, d[d[d[dI[(t,w,m)(T)]/di]/dT]/di]/dT, d[d[d[dI[(t,a,i)(T)]/di]/dT]/di]/dT, d[d[d[dI[(t,a,m)(T)]/di]/dT]/di]/dT, d[d[d[dI[(t,i,m)(T)]/di]/dT]/di]/dT, d[d[d[dI[(w,a,i)(T)]/di]/dT]/di]/dT, d[d[d[dI[(w,a,m)(T)]/di]/dT]/di]/dT, d[d[d[dI[(w,i,m)(T)]/di]/dT]/di]/dT, d[d[d[dI[(a,i,m)(T)]/di]/dT]/di]/dT, d[d[d[dI[(t,w,a,i)(T)]/di]/dT]/di]/dT, d[d[d[dI[(t,w,a,m)(T)]/di]/dT]/di]/dT, d[d[d[dI[(t,w,i,m)(T)]/di]/dT]/di]/dT, d[d[d[dI[(t,a,i,m)(T)]/di]/dT]/di]/dT, d[d[d[dI[(w,a,i,m)(T)]/di]/dT]/di]/dT, d[d[d[dI[(t,w,a,i,m)(T)]/di]/dT]/di]/dT.

 

or as:

 

 

 

d[d[d[dI[(t)(T)]/di]/dT]/dT]/di, d[d[d[dI[(w)(T)]/di]/dT]/dT]/di, d[d[d[dI[(a)(T)]/di]/dT]/dT]/di, d[d[d[dI[(i)(T)]/di]/dT]/dT]/di, d[d[d[dI[(m)(T)]/di]/dT]/dT]/di, d[d[d[dI[(t,w)(T)]/di]/dT]/dT]/di, d[d[d[dI[(t,a)(T)]/di]/dT]/dT]/di, d[d[d[dI[(t,i)(T)]/di]/dT]/dT]/di, d[d[d[dI[(t,m)(T)]/di]/dT]/dT]/di, d[d[d[dI[(w,a)(T)]/di]/dT]/dT]/di, d[d[d[dI[(w,i)(T)]/di]/dT]/dT]/di, d[d[d[dI[(w,m)(T)]/di]/dT]/dT]/di, d[d[d[dI[(a,i)(T)]/di]/dT]/dT]/di, d[d[d[dI[(a,m)(T)]/di]/dT]/dT]/di, d[d[d[dI[(i,m)(T)]/di]/dT]/dT]/di, d[d[d[dI[(t,w,a)(T)]/di]/dT]/dT]/di, d[d[d[dI[(t,w,i)(T)]/di]/dT]/dT]/di, d[d[d[dI[(t,w,m)(T)]/di]/dT]/dT]/di, d[d[d[dI[(t,a,i)(T)]/di]/dT]/dT]/di, d[d[d[dI[(t,a,m)(T)]/di]/dT]/dT]/di, d[d[d[dI[(t,i,m)(T)]/di]/dT]/dT]/di, d[d[d[dI[(w,a,i)(T)]/di]/dT]/dT]/di, d[d[d[dI[(w,a,m)(T)]/di]/dT]/dT]/di, d[d[d[dI[(w,i,m)(T)]/di]/dT]/dT]/di, d[d[d[dI[(a,i,m)(T)]/di]/dT]/dT]/di, d[d[d[dI[(t,w,a,i)(T)]/di]/dT]/dT]/di, d[d[d[dI[(t,w,a,m)(T)]/di]/dT]/dT]/di, d[d[d[dI[(t,w,i,m)(T)]/di]/dT]/dT]/di, d[d[d[dI[(t,a,i,m)(T)]/di]/dT]/dT]/di, d[d[d[dI[(w,a,i,m)(T)]/di]/dT]/dT]/di, d[d[d[dI[(t,w,a,i,m)(T)]/di]/dT]/dT]/di.

 

or as:

 

d[d[d[dI[(t)(T)]/dT]/di]/di]/dT, d[d[d[dI[(w)(T)]/dT]/di]/di]/dT, d[d[d[dI[(a)(T)]/dT]/di]/di]/dT, d[d[d[dI[(i)(T)]/dT]/di]/di]/dT, d[d[d[dI[(m)(T)]/dT]/di]/di]/dT, d[d[d[dI[(t,w)(T)]/dT]/di]/di]/dT, d[d[d[dI[(t,a)(T)]/dT]/di]/di]/dT, d[d[d[dI[(t,i)(T)]/dT]/di]/di]/dT, d[d[d[dI[(t,m)(T)]/dT]/di]/di]/dT, d[d[d[dI[(w,a)(T)]/dT]/di]/di]/dT, d[d[d[dI[(w,i)(T)]/dT]/di]/di]/dT, d[d[d[dI[(w,m)(T)]/dT]/di]/di]/dT, d[d[d[dI[(a,i)(T)]/dT]/di]/di]/dT, d[d[d[dI[(a,m)(T)]/dT]/di]/di]/dT, d[d[d[dI[(i,m)(T)]/dT]/di]/di]/dT, d[d[d[dI[(t,w,a)(T)]/dT]/di]/di]/dT, d[d[d[dI[(t,w,i)(T)]/dT]/di]/di]/dT, d[d[d[dI[(t,w,m)(T)]/dT]/di]/di]/dT, d[d[d[dI[(t,a,i)(T)]/dT]/di]/di]/dT, d[d[d[dI[(t,a,m)(T)]/dT]/di]/di]/dT, d[d[d[dI[(t,i,m)(T)]/dT]/di]/di]/dT, d[d[d[dI[(w,a,i)(T)]/dT]/di]/di]/dT, d[d[d[dI[(w,a,m)(T)]/dT]/di]/di]/dT, d[d[d[dI[(w,i,m)(T)]/dT]/di]/di]/dT, d[d[d[dI[(a,i,m)(T)]/dT]/di]/di]/dT, d[d[d[dI[(t,w,a,i)(T)]/dT]/di]/di]/dT, d[d[d[dI[(t,w,a,m)(T)]/dT]/di]/di]/dT, d[d[d[dI[(t,w,i,m)(T)]/dT]/di]/di]/dT, d[d[d[dI[(t,a,i,m)(T)]/dT]/di]/di]/dT, d[d[d[dI[(w,a,i,m)(T)]/dT]/di]/di]/dT, d[d[d[dI[(t,w,a,i,m)(T)]/dT]/di]/di]/dT.

 

 

or as;

 

 

 

 

d[d[d[dI(t)/di]/di]/dT]/dT, d[d[d[dI(w)/di]/di]/dT]/dT, d[d[d[dI(a)/di]/di]/dT]/dT, d[d[d[dI(i)/di]/di]/dT]/dT, d[d[d[dI(m)/di]/di]/dT]/dT, d[d[d[dI(t,w)/di]/di]/dT]/dT, d[d[d[dI(t,a)/di]/di]/dT]/dT, d[d[d[dI(t,i)/di]/di]/dT]/dT, d[d[d[dI(t,m)/di]/di]/dT]/dT, d[d[d[dI(w,a)/di]/di]/dT]/dT, d[d[d[dI(w,i)/di]/di]/dT]/dT, d[d[d[dI(w,m)/di]/di]/dT]/dT, d[d[d[dI(a,i)/di]/di]/dT]/dT, d[d[d[dI(a,m)/di]/di]/dT]/dT, d[d[d[dI(i,m)/di]/di]/dT]/dT, d[d[d[dI(t,w,a)/di]/di]/dT]/dT, d[d[d[dI(t,w,i)/di]/di]/dT]/dT, d[d[d[dI(t,w,m)/di]/di]/dT]/dT, d[d[d[dI(t,a,i)/di]/di]/dT]/dT, d[d[d[dI(t,a,m)/di]/di]/dT]/dT,  d[d[d[dI(t,i,m)/di]/di]/dT]/dT, d[d[d[dI(w,a,i)/di]/di]/dT]/dT, d[d[d[dI(w,a,m)/di]/di]/dT]/dT, d[d[d[dI(w,i,m)/di]/di]/dT]/dT, d[d[d[dI(a,i,m)/di]/di]/dT]/dT, d[d[d[dI(t,w,a,i)/di]/di]/dT]/dT, d[d[d[dI(t,w,a,m)/di/di, d[d[d[dI(t,w,i,m)/di]/di]/dT]/dT, d[d[d[dI(t,a,i,m)/di]/di]/dT]/dT, d[d[d[dI(w,a,i,m)/di]/di]/dT]/dT, d[d[d[dI(t,w,a,i,m)/di]/di]/dT]/dT..

 

or as:

 

d[d[d[dI(t)/dT]/di]/dT]/di, d[d[d[dI(w)/dT]/di]/dT]/di, d[d[d[dI(a)/dT]/di]/dT]/di, d[d[d[dI(i)/dT]/di]/dT]/di, d[d[d[dI(m)/dT]/di]/dT]/di, d[d[d[dI(t,w)/dT]/di]/dT]/di, d[d[d[dI(t,a)/dT]/di]/dT]/di, d[d[d[dI(t,i)/dT]/di]/dT]/di, d[d[d[dI(t,m)/dT]/di]/dT]/di, d[d[d[dI(w,a)/dT]/di]/dT]/di, d[d[d[dI(w,i)/dT]/di]/dT]/di, d[d[d[dI(w,m)/dT]/di]/dT]/di, d[d[d[dI(a,i)/dT]/di]/dT]/di, d[d[d[dI(a,m)/dT]/di]/dT]/di, d[d[d[dI(i,m)/ dT]/di]/dT]/di, d[d[d[dI(t,w,a)/dT]/di]/dT]/di, d[d[d[dI(t,w,i)/dT]/di]/dT]/di, d[d[d[dI(t,w,m)/dT]/di]/dT]/di, d[d[d[dI(t,a,i)/dT]/di]/dT]/di, d[d[d[dI(t,a,m)/dT]/di]/dT]/di,  d[d[d[dI(t,i,m)/dT]/di]/dT]/di, d[d[d[dI(w,a,i)/dT]/di]/dT]/di, d[d[d[dI(w,a,m)/dT]/di]/dT]/di, d[d[d[dI(w,i,m)/dT]/di]/dT]/di, d[d[d[dI(a,i,m)/dT]/di]/dT]/di, d[d[d[dI(t,w,a,i)/dT]/di]/dT]/di, d[d[d[dI(t,w,a,m)/di/di, d[d[d[dI(t,w,i,m)/dT]/di]/dT]/di, d[d[d[dI(t,a,i,m)/dT]/di]/dT]/di, d[d[d[dI(w,a,i,m)/dT]/di]/dT]/di, d[d[d[dI(t,w,a,i,m)/dT]/di]/dT]/di..

 

or as:

 

d[d[d[dI(t)/dT]/dT]/di]/di, d[d[d[dI(w)/dT]/dT]/di]/di, d[d[d[dI(a)/dT]/dT]/di]/di, d[d[d[dI(i)/dT]/dT]/di]/di, d[d[d[dI(m)/dT]/dT]/di]/di, d[d[d[dI(t,w)/dT]/dT]/di]/di, d[d[d[dI(t,a)/dT]/dT]/di]/di, d[d[d[dI(t,i)/dT]/dT]/di]/di, d[d[d[dI(t,m)/dT]/dT]/di]/di, d[d[d[dI(w,a)/dT]/dT]/di]/di, d[d[d[dI(w,i)/dT]/dT]/di]/di, d[d[d[dI(w,m)/dT]/dT]/di]/di, d[d[d[dI(a,i)/dT]/dT]/di]/di, d[d[d[dI(a,m)/ dT]/dT]/di]/di, d[d[d[dI(i,m)/ dT]/dT]/di]/di, d[d[d[dI(t,w,a)/dT]/dT]/di]/di, d[d[d[dI(t,w,i)/dT]/dT]/di]/di, d[d[d[dI(t,w,m)/dT]/dT]/di]/di, d[d[d[dI(t,a,i)/dT]/dT]/di]/di, d[d[d[dI(t,a,m)/dT]/dT]/di]/di,  d[d[d[dI(t,i,m)/dT]/dT]/di]/di, d[d[d[dI(w,a,i)/dT]/dT]/di]/di, d[d[d[dI(w,a,m)/dT]/dT]/di]/di, d[d[d[dI(w,i,m)/dT]/dT]/di]/di, d[d[d[dI(a,i,m)/dT]/dT]/di]/di, d[d[d[dI(t,w,a,i)/dT]/dT]/di]/di, d[d[d[dI(t,w,a,m)/di/di, d[d[d[dI(t,w,i,m)/dT]/dT]/di]/di, d[d[d[dI(t,a,i,m)/dT]/dT]/di]/di, d[d[d[dI(w,a,i,m)/dT]/dT]/di]/di, d[d[d[dI(t,w,a,i,m)/dT]/dT]/di]/di..

 

We can also take higher order duel dimensional derivatives of instinct as a function of instinct  and time but the symbolic expression of the set of such derivatives very soon becomes excessively lengthly to write and so these higher order derivatives as such are not mentioned here except to say that they would be computed in an analogous manner to the second order duel dimensional derivatives described above.

 

 

 

These seemingly crazy differentials might have some application in the study of extreme psychological states that can be experienced by souls who are departed and whose instincts, although perhaps spiritualized, are limited by a body and its brain.

 

 

Another type of being that might experience such extreme instinct change capacities might be none other then some of our friends we believe to exist as pure body-less and brain-less spirits known as angels.

 

 

Since I have dared to speculate this far, perhaps we can speculate as to whether any intelligent extraterrestrials persons or any so-called ultra-terrestrials persons that are more instinctualy evolved then we ordinary humans might be capable of experiencing large absolute valued terms of In. Some such ETI and UTI persons may  have evolved over billions of years, or perhaps have far greater powers of sensation, instinct, and intuition such as would seem plausible for any such persons and their civilizations who have not fallen from the state of innocence into the state of sin as we humans have, or perhaps such beings never had the option of  sanctifying grace opened to them but nonetheless may have been created at a naturally more perfect level then we humans, and who therefore might exhibit greater natural powers of instinct and sensation.

 

 

 

 

 

 

 

 

 

 

 

 

We can also express instinct qualitatively, statistically, and perhaps with the use of some forms of real analyses as a derivative with respect to  memory or of m.

 

Given that I(m) =  I(t and/or w and/or a and/or i and/or m) or perhaps the following notation can be more appropriate in certain circumstances.

 

 

 

 

Thus the following first order derivatives of instinct with respect to memory are possible.

 

 

dI(t)/dm, dI(w)/dm, dI(a)/dm, dI(i)/dm, dI(m)/dm, dI(t,w)/dm, dI(t,a)/dm, dI(t,i)/dm, dI(t,m)/dm, dI(w,a)/dm, dI(w,i)/dm, dI(w,m)/dm, dI(a,i)/dm, dI(a,m)/dm, dI(i,m)/dm, dI(t,w,a)/dm, dI(t,w,i)/dm, dI(t,w,m)/dm, dI(t,a,i)/dm, dI(t,a,m)/dm, dI(t,i,m)/dm, dI(w,a,i)/dm, dI(w,a,m)/dm, dI(w,i,m)/dm, dI(a,i,m)/dm, dI(t,w,a,i)/dm, dI(t,w,a,m)/dm, dI(t,w,i,m)/dm, dI(t,a,i,m)/dm, dI(w,a,i,m)/dm, dI(t,w,a,i,m)/dm.

 

 

Or more succinctly,  dI/dm = dI(t and/or w and/or a and/or i and/or m)/dm

 

 

Or perhaps dI(m)/dm =d I{[t(m)] and/or [w(m)] and/or [a(m)] and/or [i(m)] and/or [m(m)]}/dm.

 

 

Likewise, we can take the second memory derivatives of  I as follows:

 

 

 

d[dI(t)/dm]/dm, d[dI(w)/dm]/dm, d[dI(a)/dm]/dm, d[dI(i)/dm]/dm, d[dI(m)/dm]/dm, d[dI(t,w)/dm]/dm, d[dI(t,a)/dm]/dm, d[dI(t,i)/dm]/dm, d[dI(t,m)/dm]/dm, d[dI(w,a)/dm]/dm, d[dI(w,i)/dm]/dm, d[dI(w,m)/dm]/dm, d[dI(a,i)/dm]/dm, d[dI(a,m)/dm]/dm, d[dI(i,m)/dm/dm, d[dI(t,w,a)/dm]/dm, d[dI(t,w,i)/dm]/dm, d[dI(t,w,m)/dm]/dm, d[dI(t,a,i)/dm]/dm, d[dI(t,a,m)/dm]/dm,  d[dI(t,i,m)/dm]/dm, d[dI(w,a,i)/dm]/dm, d[dI(w,a,m)/dm]/dm, d[dI(w,i,m)/dm]/dm, d[dI(a,i,m)/dm]/dm, d[dI(t,w,a,i)/dm]/dm, d[dI(t,w,a,m)/dm/dm, d[dI(t,w,i,m)/dm]/dm, d[dI(t,a,i,m)/dm]/dm, d[dI(w,a,i,m)/dm]/dm, d[dI(t,w,a,i,m)/dm]/dm..

 

 

or more succinctly, as d(dI/dm)/dm = d[d I(t and/or w and/or a and/or i and/or m)/dm]/dm = Im2

 

 

or as

 

 

d[dI(m)/dm]/dm  = d[d I{[t(m)] and/or [w(m)] and/or [a(m)] and/or [i(m)] and/or [m(m)]}/dm]/dm = Im2.

 

 

 

Likewise, we can take the third memory derivatives of  I as follows:

 

 

 

d[d[dI(t)/dm]/dm]/dm, d[d[dI(w)/dm]/dm]/dm, d[d[dI(a)/dm]/dm]/dm, d[d[dI(i)/dm]/dm]/dm, d[d[dI(m)/dm]/dm]/dm, d[d[dI(t,w)/dm]/dm]/dm, d[d[dI(t,a)/dm]/dm]/dm, d[d[dI(t,i)/dm]/dm]/dm, d[d[dI(t,m)/dm]/dm]/dm, d[d[dI(w,a)/dm]/dm]/dm, d[d[dI(w,i)/dm]/dm]/dm, d[d[dI(w,m)/dm]/dm]/dm, d[d[dI(a,i)/dm]/dm]/dm, d[d[dI(a,m)/dm]/dm]/dm, d[d[dI(i,m)/dm/dm]/dm, d[d[dI(t,w,a)/dm]/dm]/dm, d[d[dI(t,w,i)/dm]/dm]/dm, d[d[dI(t,w,m)/dm]/dm]/dm, d[d[dI(t,a,i)/dm]/dm]/dm, d[d[dI(t,a,m)/dm]/dm]/dm,  d[d[dI(t,i,m)/dm]/dm]/dm, d[d[dI(w,a,i)/dm]/dm]/dm, d[d[dI(w,a,m)/dm]/dm]/dm, d[d[dI(w,i,m)/dm]/dm]/dm, d[d[dI(a,i,m)/dm]/dm]/dm, d[d[dI(t,w,a,i)/dm]/dm]/dm, d[d[dI(t,w,a,m)/dm/dm]/dm, d[d[dI(t,w,i,m)/dm]/dm]/dm, d[d[dI(t,a,i,m)/dm]/dm]/dm, d[d[dI(w,a,i,m)/dm]/dm]/dm, d[d[dI(t,w,a,i,m)/dm]/dm]/dm.

 

 

or more succinctly, as d[d(dI/dm)/dm]/dm = d[d[d I(t and/or w and/or a and/or i and/or m)/dm]/dm]/dm = Im3

 

 

or as

 

 

d[d[dI(m)/dm]/dm]/dm  = d[d[d I{[t(m)] and/or [w(m)] and/or [a(m)] and/or [i(m)] and/or [m(m)]}/dm]/dm]/dm = Im3.

 

 

We can also form the expressions;

 

 

d[d[f(I)]/dm]/dm = d{d [I[t(m)]]/dm and/or d[I[w(m)]]/dm and/or d[I[a(m)]]/dm and/or d[I[i(m)]]/dm and/or d[I[m(m)]]/dm}/dm  = f(Im)2

 

 

and

 

 

d[d[d[f(I)]/dm]/dm]/dm = d{d{ d [I[t(m)]]/dm and/or d[I[w(m)]]/dm and/or d[I[a(m)]]/dm and/or d[I[i(m)]]/dm and/or d[I[m(m)]]/dm}/dm}/dm  = f(Im)3A, where A stands for type A differentiation which is not to be confused with the meaning of so-called Type A personality as A is used as an ordinal in a totally different context here.

 

 

and

 

 

d[d[d[f(I)]/dm]/dm]/dm = d{d[d [I[t(m)]]/dm]/dm  and/or d[d [I[w(m)]]/dm]/dm  and/or d[d [I[a(m)]]/dm]/dm  and/or d[d [I[i(m)]]/dm]/dm  and/or d[d [I[m(m)]]/dm]/dm }/dm = f(Im)3B, where B stands for type B differentiation which is not to be confused with the meaning of so-called Type  B personality as B is used as an ordinal in a totally different context here .

 

 

In fact, one can form yet higher order derivatives of instincts with respect to memory as follows.

 

 

Im5 = d Im4/dm = d[dIm3/dm]/dm

 

 

 

Im5 = dIm4/dm =  d[d[d[d[d I{[t(m)] and/or [w(m)] and/or [a(m)] and/or [i(m)] and/or [m(m)]}/dm]/dm]/dm]/dm]/dm.

 

 

 

f(Im)5A = d[f(Im)4A]/dm = d[d [f(Im)3A]/dm]/dm =  d{d{d{d{ d [I[t(m)]]/dm and/or d[I[w(m)]]/dm and/or d[I[a(m)]]/dm and/or d[I[i(m)]]/dm and/or d[I[m(m)]]/dm}/dm}/dm]/dm]/dm

 

 

 

 

Im6 = d Im5/dm = d[d Im4/dm]/dm = d[d[dIm3/dm]/dm]/dm

 

 

 

Im6 = dIm5/dm = d[d[d[d[d[d I{[t(m)] and/or [w(m)] and/or [a(m)] and/or [i(m)] and/or [m(m)]}/dm]/dm]/dm]/dm]/dm]/dm

 

 

 

f(Im)6A = d[f(Im)5A]/dm = d{ d{d{d{d{ d [I[t(m)]]/dm and/or d[I[w(m)]]/dm and/or d[I[a(m)]]/dm and/or d[I[i(m)]]/dm and/or d[I[m(m)]]/dm}/dm}/dm]/dm]/dm]/dm

 

 

 

 

Im7 = dIm6/dm

 

f(Im)7A = d[f(Im)6A]/dm

 

 

Im8 = d Im7/dm

 

f(Im)8A = d[f(Im)7A]/dm

 

 

 

Im9 = d Im8/dm

 

f(Im)9A = d[f(Im)8A]/dm

 

 

Im10…, Im11…, Im12 … etc.

 

 

Anyone for Im ensemble, or Im infinity scrapper, or Im (Aleph 0), or Im(Aleph 1), or Im (Aleph 2), or how about Im Aleph (Aleph 0), or Im Aleph (Aleph 1) , or Im Aleph (Aleph 2), or even Im Aleph (Aleph (Aleph 0)), or Im Aleph (Aleph (Aleph 1)), or Im Aleph (Aleph (Aleph 2)), and so on?

 

 

Thus, for the set of the sets of derivatives of Im1 through Im(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Im1 through Im(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)},…, {П(0,31)[R]}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Im1 through Im(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Im1 through Im(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the derivative states in the set of the sets of derivatives of Im1 through Im(Aleph 0) is plausible equal to:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Im1 through Im(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Im1 through Im(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}}}.

 

For the set of the sets of derivatives of Im1 through Im(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Im(Aleph 0) derivative space at the level of 0/(Aleph 0), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Im1 through Im(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Im1 through Im(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Im1 through Im(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Im1 through Im(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Im1 through Im(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Im1 through Im(Aleph 1), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Im1 through  Im(Aleph 2), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Im1 through Im(Aleph 3), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Im(Aleph 0) derivative space at the level of 0/(Aleph 1), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Im1 through Im(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Im1 through Im(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Im1 through Im(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Im1 through  Im(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations  for the set of the sets of derivatives of Im1 through Im(Aleph 0) is plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Im1 through Im(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Im1 through Im(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Im1 through Im(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

 

For super-continuous Im(Aleph 0) derivative space at the level of 0/(Aleph 2), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Im1 through Im(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Im1 through Im(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Im1 through Im(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Im1 through Im(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Im1 through Im(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Im1 through Im(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Im1 through Im(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Im1 through Im(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

 

The general meaning of memory derivatives of instinct can be viewed as the manner in which the qualitative and/or quantitative aspects of instinct as a function of memory very with memory. The manner in which instincts very with memory may be multi- memory-aspect dimensional wherein the dimensions of derivations can be multiple, and wherein the derivations can be taken in parallel, series parallel or in serial manner. The differentials can be partial or non-partial derivatives, or both partial and non-partial for a given computation.

 

In fact, since there is in theory, no limit to the numbers of qualitatively and quantitatively different memories, and perhaps no limit to the number of possible different types or classes of memories, wherein each person has his or her own unique memories, the number of memory dimensions that can effect instincts is literally infinite, given the entirety of the set of created persons, and perhaps also literally infinite for each person as an individual, although we can not intellectually and intuitively understand this infinite number.

 

 

It is interesting to consider the ramifactions of being able to perform realistic calculations involving memory derivatives of instinct from a mathematical, theoretical, scientific,  and philosophical perspective.

 

Persons for which one or more nth order derivatives of instinct with respect to memory that have large absolute values would tend to have their instincts highly influenced by memory, or at least for the instincts under consideration with respect to the dimension of the specific memory act type(s) or class(es) for which the differentiation(s) are being performed. Perhaps a strong coupling between instinct and memory indicates a well integrated personality and commensurately, a high degree of instinct capacity and a high degree of instinct intelligence as well as perhaps very strong memory power.

 

We would expect that disembodied human souls, ETI souls, and/or UTI souls in Heaven, Limbo, highly evolved bodily ETI persons, highly evolved UTI persons, and angels to have instincts of all kinds and intensities which are perhaps  highly subject to powereful memorys such as spiritual memorys, psychological memories, emotional memories, intellectual memories, interpersonal memories, auto-biographical memories, and even perhaps, memories facilitated by advanced psychic powers.

 

 

We can also consider that two dimensional nth ordered derivatives of instinct with respect to memory and time, or with respect to i and T, respectively.

 

Given that I[(m)(T)] =  I[(t and/or w and/or a and/or i and/or m)(m)(T)], the following first order two dimensional derivatives of instinct with respect to memory and Time are possible.

 

 

d[dI[(t)(T)]/dm]/dT, d[dI[(w)(T)]/dm]/dT, d[dI[(a)(T)]/dm]/dT, d[dI[(i)(T)]/dm]/dT, d[dI[(m)(T)]/dm]/dT, d[dI[(t,w)(T)]/dm]/dT, d[dI[(t,a)(T)]/dm]/dT, d[dI[(t,i)(T)]/dm]/dT, d[dI[(t,m)(T)]/dm]/dT, d[dI[(w,a)(T)]/dm]/dT, d[dI[(w,i)(T)]/dm]/dT, d[dI[(w,m)(T)]/dm]/dT, d[dI[(a,i)(T)]/dm]/dT, d[dI[(a,m)(T)]/dm]/dT, d[dI[(i,m)(T)]/dm]/dT, d[dI[(t,w,a)(T)]/dm]/dT, d[dI[(t,w,i)(T)]/dm]/dT, d[dI[(t,w,m)(T)]/dm]/dT, d[dI[(t,a,i)(T)]/dm]/dT, d[dI[(t,a,m)(T)]/dm]/dT, d[dI[(t,i,m)(T)]/dm]/dT, d[dI[(w,a,i)(T)]/dm]/dT, d[dI[(w,a,m)(T)]/dm]/dT, d[dI[(w,i,m)(T)]/dm]/dT, d[dI[(a,i,m)(T)]/dm]/dT, d[dI[(t,w,a,i)(T)]/dm]/dT, d[dI[(t,w,a,m)(T)]/dm]/dT, d[dI[(t,w,i,m)(T)]/dm]/dT, d[dI[(t,a,i,m)(T)]/dm]/dT, d[dI[(w,a,i,m)(T)]/dm]/dT, d[dI[(t,w,a,i,m)(T)]/dm]/dT.

 

 

Or more succinctly,  d[dI(T)/dm]/dT = d[dI[(T)(t and/or w and/or a and/or m and/or m)]/dm]/dT

 

or

 

d[dI(T)/dT]/dm = d[dI[(T)(t and/or w and/or a and/or i and/or m)]/dT]/dm

 

 

 

 

 

Or perhaps d[d I[(m)(T)]/dm]/dT  = d[d I [{[t(m)] and/or [w(m)] and/or [a(m)] and/or [i(m)] and/or [m(m)]}(T)]/dm]/dT

 

or

 

Or perhaps d[d I[(m)(T)]/dT]/dm  = d[d I [{[t(m)] and/or [w(m)] and/or [a(i)] and/or [i(m)] and/or [m(m)]}(T)]/dT]/dm

 

 

 

Likewise, we can take the second dual dimension memory -time derivatives of  I as follows:

 

d[d[d[dI[(t)(T)]/dm]/dT]/dm]/dT, d[d[d[dI[(w)(T)]/dm]/dT]/dm]/dT, d[d[d[dI[(a)(T)]/dm]/dT]/dm]/dT, d[d[d[dI[(i)(T)]/dm]/dT]/dm]/dT, d[d[d[dI[(m)(T)]/dm]/dT]/dm]/dT, d[d[d[dI[(t,w)(T)]/dm]/dT]/dm]/dT, d[d[d[dI[(t,a)(T)]/dm]/dT]/dm]/dT, d[d[d[dI[(t,i)(T)]/dm]/dT]/dm]/dT, d[d[d[dI[(t,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dI[(w,a)(T)]/dm]/dT]/dm]/dT, d[d[d[dI[(w,i)(T)]/dm]/dT]/dm]/dT, d[d[d[dI[(w,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dI[(a,i)(T)]/dm]/dT]/dm]/dT, d[d[d[dI[(a,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dI[(i,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dI[(t,w,a)(T)]/dm]/dT]/dm]/dT, d[d[d[dI[(t,w,i)(T)]/dm]/dT]/dm]/dT, d[d[d[dI[(t,w,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dI[(t,a,i)(T)]/dm]/dT]/dm]/dT, d[d[d[dI[(t,a,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dI[(t,i,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dI[(w,a,i)(T)]/dm]/dT]/dm]/dT, d[d[d[dI[(w,a,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dI[(w,i,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dI[(a,i,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dI[(t,w,a,i)(T)]/dm]/dT]/dm]/dT, d[d[d[dI[(t,w,a,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dI[(t,w,i,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dI[(t,a,i,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dI[(w,a,i,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dI[(t,w,a,i,m)(T)]/dm]/dT]/dm]/dT.

 

or as:

 

 

 

d[d[d[dI[(t)(T)]/dm]/dT]/dT]/dm, d[d[d[dI[(w)(T)]/dm]/dT]/dT]/dm, d[d[d[dI[(a)(T)]/dm]/dT]/dT]/dm, d[d[d[dI[(i)(T)]/dm]/dT]/dT]/dm, d[d[d[dI[(m)(T)]/dm]/dT]/dT]/dm, d[d[d[dI[(t,w)(T)]/dm]/dT]/dT]/dm, d[d[d[dI[(t,a)(T)]/dm]/dT]/dT]/dm, d[d[d[dI[(t,i)(T)]/dm]/dT]/dT]/dm, d[d[d[dI[(t,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dI[(w,a)(T)]/dm]/dT]/dT]/dm, d[d[d[dI[(w,i)(T)]/dm]/dT]/dT]/dm, d[d[d[dI[(w,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dI[(a,i)(T)]/dm]/dT]/dT]/dm, d[d[d[dI[(a,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dI[(i,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dI[(t,w,a)(T)]/dm]/dT]/dT]/dm, d[d[d[dI[(t,w,i)(T)]/dm]/dT]/dT]/dm, d[d[d[dI[(t,w,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dI[(t,a,i)(T)]/dm]/dT]/dT]/dm, d[d[d[dI[(t,a,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dI[(t,i,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dI[(w,a,i)(T)]/dm]/dT]/dT]/dm, d[d[d[dI[(w,a,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dI[(w,i,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dI[(a,i,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dI[(t,w,a,i)(T)]/dm]/dT]/dT]/dm, d[d[d[dI[(t,w,a,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dI[(t,w,i,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dI[(t,a,i,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dI[(w,a,i,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dI[(t,w,a,i,m)(T)]/dm]/dT]/dT]/dm.

 

or as:

 

d[d[d[dI[(t)(T)]/dT]/dm]/dm]/dT, d[d[d[dI[(w)(T)]/dT]/dm]/dm]/dT, d[d[d[dI[(a)(T)]/dT]/dm]/dm]/dT, d[d[d[dI[(i)(T)]/dT]/dm]/dm]/dT, d[d[d[dI[(m)(T)]/dT]/dm]/dm]/dT, d[d[d[dI[(t,w)(T)]/dT]/dm]/dm]/dT, d[d[d[dI[(t,a)(T)]/dT]/dm]/dm]/dT, d[d[d[dI[(t,i)(T)]/dT]/dm]/dm]/dT, d[d[d[dI[(t,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dI[(w,a)(T)]/dT]/dm]/dm]/dT, d[d[d[dI[(w,i)(T)]/dT]/dm]/dm]/dT, d[d[d[dI[(w,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dI[(a,i)(T)]/dT]/dm]/dm]/dT, d[d[d[dI[(a,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dI[(i,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dI[(t,w,a)(T)]/dT]/dm]/dm]/dT, d[d[d[dI[(t,w,i)(T)]/dT]/dm]/dm]/dT, d[d[d[dI[(t,w,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dI[(t,a,i)(T)]/dT]/dm]/dm]/dT, d[d[d[dI[(t,a,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dI[(t,i,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dI[(w,a,i)(T)]/dT]/dm]/dm]/dT, d[d[d[dI[(w,a,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dI[(w,i,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dI[(a,i,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dI[(t,w,a,i)(T)]/dT]/dm]/dm]/dT, d[d[d[dI[(t,w,a,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dI[(t,w,i,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dI[(t,a,i,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dI[(w,a,i,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dI[(t,w,a,i,m)(T)]/dT]/dm]/dm]/dT.

 

 

or as;

 

 

 

 

d[d[d[dI(t)/dm]/dm]/dT]/dT, d[d[d[dI(w)/dm]/dm]/dT]/dT, d[d[d[dI(a)/dm]/dm]/dT]/dT, d[d[d[dI(i)/dm]/dm]/dT]/dT, d[d[d[dI(m)/dm]/dm]/dT]/dT, d[d[d[dI(t,w)/dm]/dm]/dT]/dT, d[d[d[dI(t,a)/dm]/dm]/dT]/dT, d[d[d[dI(t,i)/dm]/dm]/dT]/dT, d[d[d[dI(t,m)/dm]/dm]/dT]/dT, d[d[d[dI(w,a)/dm]/dm]/dT]/dT, d[d[d[dI(w,i)/dm]/dm]/dT]/dT, d[d[d[dI(w,m)/dm]/dm]/dT]/dT, d[d[d[dI(a,i)/dm]/dm]/dT]/dT, d[d[d[dI(a,m)/dm]/dm]/dT]/dT, d[d[d[dI(i,m)/dm]/dm]/dT]/dT, d[d[d[dI(t,w,a)/dm]/dm]/dT]/dT, d[d[d[dI(t,w,i)/dm]/dm]/dT]/dT, d[d[d[dI(t,w,m)/dm]/dm]/dT]/dT, d[d[d[dI(t,a,i)/dm]/dm]/dT]/dT, d[d[d[dI(t,a,m)/dm]/dm]/dT]/dT,  d[d[d[dI(t,i,m)/dm]/dm]/dT]/dT, d[d[d[dI(w,a,i)/dm]/dm]/dT]/dT, d[d[d[dI(w,a,m)/dm]/dm]/dT]/dT, d[d[d[dI(w,i,m)/dm]/dm]/dT]/dT, d[d[d[dI(a,i,m)/dm]/dm]/dT]/dT, d[d[d[dI(t,w,a,i)/dm]/dm]/dT]/dT, d[d[d[dI(t,w,a,m)/dm/dm, d[d[d[dI(t,w,i,m)/dm]/dm]/dT]/dT, d[d[d[dI(t,a,i,m)/dm]/dm]/dT]/dT, d[d[d[dI(w,a,i,m)/dm]/dm]/dT]/dT, d[d[d[dI(t,w,a,i,m)/dm]/dm]/dT]/dT..

 

or as:

 

d[d[d[dI(t)/dT]/dm]/dT]/dm, d[d[d[dI(w)/dT]/dm]/dT]/dm, d[d[d[dI(a)/dT]/dm]/dT]/dm, d[d[d[dI(i)/dT]/dm]/dT]/dm, d[d[d[dI(m)/dT]/dm]/dT]/dm, d[d[d[dI(t,w)/dT]/dm]/dT]/dm, d[d[d[dI(t,a)/dT]/dm]/dT]/dm, d[d[d[dI(t,i)/dT]/dm]/dT]/dm, d[d[d[dI(t,m)/dT]/dm]/dT]/dm, d[d[d[dI(w,a)/dT]/dm]/dT]/dm, d[d[d[dI(w,i)/dT]/dm]/dT]/dm, d[d[d[dI(w,m)/dT]/dm]/dT]/dm, d[d[d[dI(a,i)/dT]/dm]/dT]/dm, d[d[d[dI(a,m)/dT]/dm]/dT]/dm, d[d[d[dI(i,m)/ dT]/dm]/dT]/dm, d[d[d[dI(t,w,a)/dT]/dm]/dT]/dm, d[d[d[dI(t,w,i)/dT]/dm]/dT]/dm, d[d[d[dI(t,w,m)/dT]/dm]/dT]/dm, d[d[d[dI(t,a,i)/dT]/dm]/dT]/dm, d[d[d[dI(t,a,m)/dT]/dm]/dT]/dm,  d[d[d[dI(t,i,m)/dT]/dm]/dT]/dm, d[d[d[dI(w,a,i)/dT]/dm]/dT]/dm, d[d[d[dI(w,a,m)/dT]/dm]/dT]/dm, d[d[d[dI(w,i,m)/dT]/dm]/dT]/dm, d[d[d[dI(a,i,m)/dT]/dm]/dT]/dm, d[d[d[dI(t,w,a,i)/dT]/dm]/dT]/dm, d[d[d[dI(t,w,a,m)/dm/dm, d[d[d[dI(t,w,i,m)/dT]/dm]/dT]/dm, d[d[d[dI(t,a,i,m)/dT]/dm]/dT]/dm, d[d[d[dI(w,a,i,m)/dT]/dm]/dT]/dm, d[d[d[dI(t,w,a,i,m)/dT]/dm]/dT]/dm..

 

or as:

 

d[d[d[dI(t)/dT]/dT]/dm]/dm, d[d[d[dI(w)/dT]/dT]/dm]/dm, d[d[d[dI(a)/dT]/dT]/dm]/dm, d[d[d[dI(i)/dT]/dT]/dm]/dm, d[d[d[dI(m)/dT]/dT]/dm]/dm, d[d[d[dI(t,w)/dT]/dT]/dm]/dm, d[d[d[dI(t,a)/dT]/dT]/dm]/dm, d[d[d[dI(t,i)/dT]/dT]/dm]/dm, d[d[d[dI(t,m)/dT]/dT]/dm]/dm, d[d[d[dI(w,a)/dT]/dT]/dm]/dm, d[d[d[dI(w,i)/dT]/dT]/dm]/dm, d[d[d[dI(w,m)/dT]/dT]/dm]/dm, d[d[d[dI(a,i)/dT]/dT]/dm]/dm, d[d[d[dI(a,m)/ dT]/dT]/dm]/dm, d[d[d[dI(i,m)/ dT]/dT]/dm]/dm, d[d[d[dI(t,w,a)/dT]/dT]/dm]/dm, d[d[d[dI(t,w,i)/dT]/dT]/dm]/dm, d[d[d[dI(t,w,m)/dT]/dT]/dm]/dm, d[d[d[dI(t,a,i)/dT]/dT]/dm]/dm, d[d[d[dI(t,a,m)/dT]/dT]/dm]/dm,  d[d[d[dI(t,i,m)/dT]/dT]/dm]/dm, d[d[d[dI(w,a,i)/dT]/dT]/dm]/dm, d[d[d[dI(w,a,m)/dT]/dT]/dm]/dm, d[d[d[dI(w,i,m)/dT]/dT]/dm]/dm, d[d[d[dI(a,i,m)/dT]/dT]/dm]/dm, d[d[d[dI(t,w,a,i)/dT]/dT]/dm]/dm, d[d[d[dI(t,w,a,m)/dm/dm, d[d[d[dI(t,w,i,m)/dT]/dT]/dm]/dm, d[d[d[dI(t,a,i,m)/dT]/dT]/dm]/dm, d[d[d[dI(w,a,i,m)/dT]/dT]/dm]/dm, d[d[d[dI(t,w,a,i,m)/dT]/dT]/dm]/dm..

 

We can also take higher order duel dimensional derivatives of instinct as a function of memory and time but the symbolic expression of the set of such derivatives very soon becomes excessively lengthly to write and so these higher order derivatives as such are not mentioned here except to say that they would be computed in an analogous manner to the second order duel dimensional derivatives described above.

 

 

 

These seemingly crazy differentials might have some use in extreme psychological states that can be experienced by souls who are departed and whose instincts, although perhaps spiritualized, are nonetheless, not limited by a body and its brain.

 

 

Another type of being that might experience such extreme instincts change capacities might be none other then some of our friends we believe to exist as pure body-less and brain-less spirits known as angels.

 

 

Since I have dared to speculate this far, perhaps we can speculate as to whether any intelligent extraterrestrials persons or any so-called ultra-terrestrials persons that are more cognitively evolved then we ordinary humans might be capable of experiencing large absolute valued terms of In. Some such ETI and UTI persons may  have evolved over billions of years, or perhaps have far greater powers of sensation, instinct, and intuition such as would seem plausible for any such persons and their civilizations who have not fallen from the state of innocence into the state of sin as we humans have, or perhaps such beings never had the option of  sanctifying grace opened to them but nonetheless may have been created at a naturally more perfect level then we humans, and who therefore might exhibit greater natural powers of instinct and sensation.

 

 

We can also express instinct qualitatively, statistically, and perhaps with the use of some forms of real analyses as a thought derivative.

 

Given that I(i) =  I(t and/or w and/or a and/or i and/or m),perhaps the following notation can be more appropriate in certain circumstances.

 

 

 

 

Thus the following first order derivatives of instinct with respect to thought are possible.

 

 

dt(t)/dt, dt(w)/dt, dt(a)/dt, dt(i)/dt, dt(m)/dt, dt(t,w)/dt, dt(t,a)/dt, dt(t,i)/dt, dt(t,m)/dt, dt(w,a)/dt, dt(w,i)/dt, dt(w,m)/dt, dt(a,i)/dt, dt(a,m)/dt, dt(i,m)/dt, dt(t,w,a)/dt, dt(t,w,i)/dt, dt(t,w,m)/dt, dt(t,a,i)/dt, dt(t,a,m)/dt, dt(t,i,m)/dt, dt(w,a,i)/dt, dt(w,a,m)/dt, dt(w,i,m)/dt, dt(a,i,m)/dt, dt(t,w,a,i)/dt, dt(t,w,a,m)/dt, dt(t,w,i,m)/dt, dt(t,a,i,m)/dt, dt(w,a,i,m)/dt, dt(t,w,a,i,m)/dt.

 

 

Or more succinctly,  dt/dt = dt(t and/or w and/or a and/or i and/or m)/dt

 

 

Or perhaps dt(t)/dt =d I{[t(t)] and/or [w(t)] and/or [a(t)] and/or [i(t)] and/or [m(t)]}/dt.

 

 

Likewise, we can take the second thought derivatives of  I as follows:

 

 

 

d[dt(t)/dt]/dt, d[dt(w)/dt]/dt, d[dt(a)/dt]/dt, d[dt(i)/dt]/dt, d[dt(m)/dt]/dt, d[dt(t,w)/dt]/dt, d[dt(t,a)/dt]/dt, d[dt(t,i)/dt]/dt, d[dt(t,m)/dt]/dt, d[dt(w,a)/dt]/dt, d[dt(w,i)/dt]/dt, d[dt(w,m)/dt]/dt, d[dt(a,i)/dt]/dt, d[dt(a,m)/dt]/dt, d[dt(i,m)/dt/dt, d[dt(t,w,a)/dt]/dt, d[dt(t,w,i)/dt]/dt, d[dt(t,w,m)/dt]/dt, d[dt(t,a,i)/dt]/dt, d[dt(t,a,m)/dt]/dt,  d[dt(t,i,m)/dt]/dt, d[dt(w,a,i)/dt]/dt, d[dt(w,a,m)/dt]/dt, d[dt(w,i,m)/dt]/dt, d[dt(a,i,m)/dt]/dt, d[dt(t,w,a,i)/dt]/dt, d[dt(t,w,a,m)/dt/dt, d[dt(t,w,i,m)/dt]/dt, d[dt(t,a,i,m)/dt]/dt, d[dt(w,a,i,m)/dt]/dt, d[dt(t,w,a,i,m)/dt]/dt..

 

 

or more succinctly, as d(dt/dt)/dt = d[d I(t and/or w and/or a and/or i and/or m)/dt]/dt = It2

 

 

or as

 

 

d[dt(t)/dt]/dt  = d[d I{[t(t)] and/or [w(t)] and/or [a(t)] and/or [i(t)] and/or [m(t)]}/dt]/dt = It2.

 

 

 

Likewise, we can take the third thought derivatives of  I as follows:

 

 

 

d[d[dt(t)/dt]/dt]/dt, d[d[dt(w)/dt]/dt]/dt, d[d[dt(a)/dt]/dt]/dt, d[d[dt(i)/dt]/dt]/dt, d[d[dt(m)/dt]/dt]/dt, d[d[dt(t,w)/dt]/dt]/dt, d[d[dt(t,a)/dt]/dt]/dt, d[d[dt(t,i)/dt]/dt]/dt, d[d[dt(t,m)/dt]/dt]/dt, d[d[dt(w,a)/dt]/dt]/dt, d[d[dt(w,i)/dt]/dt]/dt, d[d[dt(w,m)/dt]/dt]/dt, d[d[dt(a,i)/dt]/dt]/dt, d[d[dt(a,m)/dt]/dt]/dt, d[d[dt(i,m)/dt/dt]/dt, d[d[dt(t,w,a)/dt]/dt]/dt, d[d[dt(t,w,i)/dt]/dt]/dt, d[d[dt(t,w,m)/dt]/dt]/dt, d[d[dt(t,a,i)/dt]/dt]/dt, d[d[dt(t,a,m)/dt]/dt]/dt,  d[d[dt(t,i,m)/dt]/dt]/dt, d[d[dt(w,a,i)/dt]/dt]/dt, d[d[dt(w,a,m)/dt]/dt]/dt, d[d[dt(w,i,m)/dt]/dt]/dt, d[d[dt(a,i,m)/dt]/dt]/dt, d[d[dt(t,w,a,i)/dt]/dt]/dt, d[d[dt(t,w,a,m)/dt/dt]/dt, d[d[dt(t,w,i,m)/dt]/dt]/dt, d[d[dt(t,a,i,m)/dt]/dt]/dt, d[d[dt(w,a,i,m)/dt]/dt]/dt, d[d[dt(t,w,a,i,m)/dt]/dt]/dt.

 

 

or more succinctly, as d[d(dt/dt)/dt]/dt = d[d[d I(t and/or w and/or a and/or i and/or m)/dt]/dt]/dt = It3

 

 

or as

 

 

d[d[dt(t)/dt]/dt]/dt  = d[d[d I{[t(t)] and/or [w(t)] and/or [a(t)] and/or [i(t)] and/or [m(t)]}/dt]/dt]/dt = It3.

 

 

We can also form the expressions;

 

 

d[d[f(I)]/dt]/dt = d{d [I[t(t)]]/dt and/or d[I[w(t)]]/dt and/or d[I[a(t)]]/dt and/or d[I[i(t)]]/dt and/or d[I[m(t)]]/dt}/dt  = f(It)2

 

 

and

 

 

d[d[d[f(I)]/dt]/dt]/dt = d{d{ d [I[t(t)]]/dt and/or d[I[w(t)]]/dt and/or d[I[a(t)]]/dt and/or d[I[i(t)]]/dt and/or d[I[m(t)]]/dt}/dt}/dt  = f(It)3A, where A stands for type A dtfferentiation which is not to be confused with the meaning of so-called Type A personality as A is used as an ordinal in a totally different context here.

 

 

and

 

 

d[d[d[f(I)]/dt]/dt]/dt = d{d[d [I[t(t)]]/dt]/dt  and/or d[d [I[w(t)]]/dt]/dt  and/or d[d [I[a(t)]]/dt]/dt  and/or d[d [I[i(t)]]/dt]/dt  and/or d[d [I[m(t)]]/dt]/dt }/dt = f(It)3B, where B stands for type B dtfferentiation which is not to be confused with the meaning of so-called Type  B personality as B is used as an ordtnal in a totally dtfferent context here .

 

 

In fact, one can form yet higher order derivatives of instincts with respect to thought as follows.

 

 

It5 = d It4/dt = d[dIt3/dt]/dt

 

 

 

It5 = dIt4/dt =  d[d[d[d[d I{[t(t)] and/or [w(t)] and/or [a(t)] and/or [i(t)] and/or [m(t)]}/dt]/dt]/dt]/dt]/dt.

 

 

 

f(It)5A = d[f(It)4A]/dt = d[d [f(It)3A]/dt]/dt =  d{d{d{d{ d [I[t(t)]]/dt and/or d[I[w(t)]]/dt and/or d[I[a(t)]]/dt and/or d[I[i(t)]]/dt and/or d[I[m(t)]]/dt}/dt}/dt]/dt]/dt

 

 

 

 

It6 = d It5/dt = d[d It4/dt]/dt = d[d[dIt3/dt]/dt]/dt

 

 

 

It6 = dIt5/dt = d[d[d[d[d[d I{[t(t)] and/or [w(t)] and/or [a(t)] and/or [i(t)] and/or [m(t)]}/dt]/dt]/dt]/dt]/dt]/dt

 

 

 

f(It)6A = d[f(It)5A]/dt = d{ d{d{d{d{ d [I[t(t)]]/dt and/or d[I[w(t)]]/dt and/or d[I[a(t)]]/dt and/or d[I[i(t)]]/dt and/or d[I[m(t)]]/dt}/dt}/dt]/dt]/dt]/dt

 

 

 

 

It7 = dIt6/dt

 

f(It)7A = d[f(It)6A]/dt

 

 

It8 = d It7/dt

 

f(It)8A = d[f(It)7A]/dt

 

 

 

It9 = d It8/dt

 

f(It)9A = d[f(It)8A]/dt

 

 

It10…, It11…, It12 … etc.

 

 

Anyone for It ensemble, or It infinity scrapper, or It (Aleph 0), or It(Aleph 1), or It (Aleph 2), or how about It Aleph (Aleph 0), or It Aleph (Aleph 1) , or It Aleph (Aleph 2), or even It Aleph (Aleph (Aleph 0)), or It Aleph (Aleph (Aleph 1)), or It Aleph (Aleph (Aleph 2)), and so on?

 

Thus, for the set of the sets of derivatives of It1 through It(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}.

 

For the set of the sets of derivatives of It1 through It(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)},…, {П(0,31)[R]}_{(Aleph 1)}.

 

For the set of the sets of derivatives of It1 through It(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}.

 

For the set of the sets of derivatives of It1 through It(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the derivative states in the set of the sets of derivatives of It1 through It(Aleph 0) is plausible equal to:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of It1 through It(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of It1 through It(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}}}.

 

For the set of the sets of derivatives of It1 through It(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous It(Aleph 0) derivative space at the level of 0/(Aleph 0), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of It1 through It(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of It1 through It(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of It1 through It(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of It1 through It(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of It1 through It(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of It1 through It(Aleph 1), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of It1 through  It(Aleph 2), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of It1 through It(Aleph 3), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous It(Aleph 0) derivative space at the level of 0/(Aleph 1), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of It1 through It(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of It1 through It(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of It1 through It(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of It1 through  It(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations  for the set of the sets of derivatives of It1 through It(Aleph 0) is plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of It1 through It(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of It1 through It(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of It1 through It(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

 

For super-continuous It(Aleph 0) derivative space at the level of 0/(Aleph 2), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of It1 through It(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of It1 through It(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of It1 through It(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of It1 through It(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of It1 through It(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of It1 through It(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of It1 through It(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of It1 through It(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

The general meaning of thought derivatives of instinct can be viewed as the manner in which the qualitative and/or quantitative aspects of instinct  as a function of thought very with thought. The manner in which instincts very with thought  may be multi- thought-aspect dimensional wherein the dimensions of derivations can be multiple, and wherein the derivations can be taken in parallel, series parallel or in serial manner. The differentials can be partial or non-partial derivatives, or both partial and non-partial for a given computation.

 

In fact, since there is in theory, no limit to the numbers of qualitatively and quantitatively different instincts, and perhaps no limit to the number of possible different types or classes of instincts or potential instincts, wherein each person has his or her own unique instincts and instinctual experiences, the number of thought dimensions that can effect instinct is literally infinite, given the entirety of the set of created persons, and perhaps also literally infinite for each person as an individual, although we can not intellectually and intuitively understand this infinite number.

 

 

It is interesting to consider the ramifactions of being able to perform realistic calculations involving thought derivatives of instinct from a mathematical, theoretical, scientific,  and philosophical perspective.

 

Persons for which one or more nth order derivatives of instinct with respect to thought that have large absolute values would tend to have their instinct highly influenced by thought, or at least for the instinct under consideration with respect to the dimension of the specific thought type(s) or class(es) for which the differentiation(s) are being performed. Perhaps a strong coupling between thought and instinct indicates a well integrated personality and commensurately, a high degree of thought capacity and a high degree of instinctive intelligence as well as perhaps very strong instinct power.

 

We would expect that disembodted human souls, ETI souls, and/or UTI souls in Heaven, Limbo, highly evolved bodily ETI persons, highly evolved UTI persons, and angels to have spiritual instincts of all kinds and intensities which are perhaps  highly subject to advanced thoughts such as spiritual thoughts, spiritual intuitions, and even perhaps, psychic powers.

 

 

We can also consider that two dimensional nth ordered derivatives of instinct with respect to thought and time, or with respect to i and T, respectively.

 

Given that I[(t)(T)] =  I[(t and/or w and/or a and/or i and/or m)(t)(T)], the following first order two dimensional derivatives of instincts  with respect to thought and Time are possible.

 

 

d[dt[(t)(T)]/dt]/dT, d[dt[(w)(T)]/dt]/dT, d[dt[(a)(T)]/dt]/dT, d[dt[(i)(T)]/dt]/dT, d[dt[(m)(T)]/dt]/dT, d[dt[(t,w)(T)]/dt]/dT, d[dt[(t,a)(T)]/dt]/dT, d[dt[(t,i)(T)]/dt]/dT, d[dt[(t,m)(T)]/dt]/dT, d[dt[(w,a)(T)]/dt]/dT, d[dt[(w,i)(T)]/dt]/dT, d[dt[(w,m)(T)]/dt]/dT, d[dt[(a,i)(T)]/dt]/dT, d[dt[(a,m)(T)]/dt]/dT, d[dt[(i,m)(T)]/dt]/dT, d[dt[(t,w,a)(T)]/dt]/dT, d[dt[(t,w,i)(T)]/dt]/dT, d[dt[(t,w,m)(T)]/dt]/dT, d[dt[(t,a,i)(T)]/dt]/dT, d[dt[(t,a,m)(T)]/dt]/dT, d[dt[(t,i,m)(T)]/dt]/dT, d[dt[(w,a,i)(T)]/dt]/dT, d[dt[(w,a,m)(T)]/dt]/dT, d[dt[(w,i,m)(T)]/dt]/dT, d[dt[(a,i,m)(T)]/dt]/dT, d[dt[(t,w,a,i)(T)]/dt]/dT, d[dt[(t,w,a,m)(T)]/dt]/dT, d[dt[(t,w,i,m)(T)]/dt]/dT, d[dt[(t,a,i,m)(T)]/dt]/dT, d[dt[(w,a,i,m)(T)]/dt]/dT, d[dt[(t,w,a,i,m)(T)]/dt]/dT.

 

 

Or more succinctly,  d[dt(T)/dt]/dT = d[dt[(T)(t and/or w and/or a and/or i and/or m)]/dt]/dT

 

or

 

d[dt(T)/dT]/dt = d[dt[(T)(t and/or w and/or a and/or i and/or m)]/dT]/dt

 

 

 

 

 

Or perhaps d[d I[(t)(T)]/dt]/dT  = d[d I [{[t(t)] and/or [w(t)] and/or [a(t)] and/or [i(t)] and/or [m(t)]}(T)]/dt]/dT

 

or

 

Or perhaps d[d I[(t)(T)]/dT]/dt  = d[d I [{[t(t)] and/or [w(t)] and/or [a(t)] and/or [i(t)] and/or [m(t)]}(T)]/dT]/dt

 

 

 

Likewise, we can take the second dual dimension thought -time derivatives of  I as follows:

 

d[d[d[dt[(t)(T)]/dt]/dT]/dt]/dT, d[d[d[dt[(w)(T)]/dt]/dT]/dt]/dT, d[d[d[dt[(a)(T)]/dt]/dT]/dt]/dT, d[d[d[dt[(i)(T)]/dt]/dT]/dt]/dT, d[d[d[dt[(m)(T)]/dt]/dT]/dt]/dT, d[d[d[dt[(t,w)(T)]/dt]/dT]/dt]/dT, d[d[d[dt[(t,a)(T)]/dt]/dT]/dt]/dT, d[d[d[dt[(t,i)(T)]/dt]/dT]/dt]/dT, d[d[d[dt[(t,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dt[(w,a)(T)]/dt]/dT]/dt]/dT, d[d[d[dt[(w,i)(T)]/dt]/dT]/dt]/dT, d[d[d[dt[(w,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dt[(a,i)(T)]/dt]/dT]/dt]/dT, d[d[d[dt[(a,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dt[(i,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dt[(t,w,a)(T)]/dt]/dT]/dt]/dT, d[d[d[dt[(t,w,i)(T)]/dt]/dT]/dt]/dT, d[d[d[dt[(t,w,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dt[(t,a,i)(T)]/dt]/dT]/dt]/dT, d[d[d[dt[(t,a,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dt[(t,i,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dt[(w,a,i)(T)]/dt]/dT]/dt]/dT, d[d[d[dt[(w,a,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dt[(w,i,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dt[(a,i,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dt[(t,w,a,i)(T)]/dt]/dT]/dt]/dT, d[d[d[dt[(t,w,a,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dt[(t,w,i,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dt[(t,a,i,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dt[(w,a,i,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dt[(t,w,a,i,m)(T)]/dt]/dT]/dt]/dT.

 

or as:

 

 

 

d[d[d[dt[(t)(T)]/dt]/dT]/dT]/dt, d[d[d[dt[(w)(T)]/dt]/dT]/dT]/dt, d[d[d[dt[(a)(T)]/dt]/dT]/dT]/dt, d[d[d[dt[(i)(T)]/dt]/dT]/dT]/dt, d[d[d[dt[(m)(T)]/dt]/dT]/dT]/dt, d[d[d[dt[(t,w)(T)]/dt]/dT]/dT]/dt, d[d[d[dt[(t,a)(T)]/dt]/dT]/dT]/dt, d[d[d[dt[(t,i)(T)]/dt]/dT]/dT]/dt, d[d[d[dt[(t,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dt[(w,a)(T)]/dt]/dT]/dT]/dt, d[d[d[dt[(w,i)(T)]/dt]/dT]/dT]/dt, d[d[d[dt[(w,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dt[(a,i)(T)]/dt]/dT]/dT]/dt, d[d[d[dt[(a,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dt[(i,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dt[(t,w,a)(T)]/dt]/dT]/dT]/dt, d[d[d[dt[(t,w,i)(T)]/dt]/dT]/dT]/dt, d[d[d[dt[(t,w,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dt[(t,a,i)(T)]/dt]/dT]/dT]/dt, d[d[d[dt[(t,a,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dt[(t,i,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dt[(w,a,i)(T)]/dt]/dT]/dT]/dt, d[d[d[dt[(w,a,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dt[(w,i,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dt[(a,i,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dt[(t,w,a,i)(T)]/dt]/dT]/dT]/dt, d[d[d[dt[(t,w,a,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dt[(t,w,i,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dt[(t,a,i,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dt[(w,a,i,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dt[(t,w,a,i,m)(T)]/dt]/dT]/dT]/dt.

 

or as:

 

d[d[d[dt[(t)(T)]/dT]/dt]/dt]/dT, d[d[d[dt[(w)(T)]/dT]/dt]/dt]/dT, d[d[d[dt[(a)(T)]/dT]/dt]/dt]/dT, d[d[d[dt[(i)(T)]/dT]/dt]/dt]/dT, d[d[d[dt[(m)(T)]/dT]/dt]/dt]/dT, d[d[d[dt[(t,w)(T)]/dT]/dt]/dt]/dT, d[d[d[dt[(t,a)(T)]/dT]/dt]/dt]/dT, d[d[d[dt[(t,i)(T)]/dT]/dt]/dt]/dT, d[d[d[dt[(t,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dt[(w,a)(T)]/dT]/dt]/dt]/dT, d[d[d[dt[(w,i)(T)]/dT]/dt]/dt]/dT, d[d[d[dt[(w,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dt[(a,i)(T)]/dT]/dt]/dt]/dT, d[d[d[dt[(a,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dt[(i,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dt[(t,w,a)(T)]/dT]/dt]/dt]/dT, d[d[d[dt[(t,w,i)(T)]/dT]/dt]/dt]/dT, d[d[d[dt[(t,w,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dt[(t,a,i)(T)]/dT]/dt]/dt]/dT, d[d[d[dt[(t,a,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dt[(t,i,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dt[(w,a,i)(T)]/dT]/dt]/dt]/dT, d[d[d[dt[(w,a,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dt[(w,i,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dt[(a,i,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dt[(t,w,a,i)(T)]/dT]/dt]/dt]/dT, d[d[d[dt[(t,w,a,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dt[(t,w,i,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dt[(t,a,i,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dt[(w,a,i,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dt[(t,w,a,i,m)(T)]/dT]/dt]/dt]/dT.

 

 

or as;

 

 

 

 

d[d[d[dt(t)/dt]/dt]/dT]/dT, d[d[d[dt(w)/dt]/dt]/dT]/dT, d[d[d[dt(a)/dt]/dt]/dT]/dT, d[d[d[dt(i)/dt]/dt]/dT]/dT, d[d[d[dt(m)/dt]/dt]/dT]/dT, d[d[d[dt(t,w)/dt]/dt]/dT]/dT, d[d[d[dt(t,a)/dt]/dt]/dT]/dT, d[d[d[dt(t,i)/dt]/dt]/dT]/dT, d[d[d[dt(t,m)/dt]/dt]/dT]/dT, d[d[d[dt(w,a)/dt]/dt]/dT]/dT, d[d[d[dt(w,i)/dt]/dt]/dT]/dT, d[d[d[dt(w,m)/dt]/dt]/dT]/dT, d[d[d[dt(a,i)/dt]/dt]/dT]/dT, d[d[d[dt(a,m)/dt]/dt]/dT]/dT, d[d[d[dt(i,m)/dt]/dt]/dT]/dT, d[d[d[dt(t,w,a)/dt]/dt]/dT]/dT, d[d[d[dt(t,w,i)/dt]/dt]/dT]/dT, d[d[d[dt(t,w,m)/dt]/dt]/dT]/dT, d[d[d[dt(t,a,i)/dt]/dt]/dT]/dT, d[d[d[dt(t,a,m)/dt]/dt]/dT]/dT,  d[d[d[dt(t,i,m)/dt]/dt]/dT]/dT, d[d[d[dt(w,a,i)/dt]/dt]/dT]/dT, d[d[d[dt(w,a,m)/dt]/dt]/dT]/dT, d[d[d[dt(w,i,m)/dt]/dt]/dT]/dT, d[d[d[dt(a,i,m)/dt]/dt]/dT]/dT, d[d[d[dt(t,w,a,i)/dt]/dt]/dT]/dT, d[d[d[dt(t,w,a,m)/dt/dt, d[d[d[dt(t,w,i,m)/dt]/dt]/dT]/dT, d[d[d[dt(t,a,i,m)/dt]/dt]/dT]/dT, d[d[d[dt(w,a,i,m)/dt]/dt]/dT]/dT, d[d[d[dt(t,w,a,i,m)/dt]/dt]/dT]/dT..

 

or as:

 

d[d[d[dt(t)/dT]/dt]/dT]/dt, d[d[d[dt(w)/dT]/dt]/dT]/dt, d[d[d[dt(a)/dT]/dt]/dT]/dt, d[d[d[dt(i)/dT]/dt]/dT]/dt, d[d[d[dt(m)/dT]/dt]/dT]/dt, d[d[d[dt(t,w)/dT]/dt]/dT]/dt, d[d[d[dt(t,a)/dT]/dt]/dT]/dt, d[d[d[dt(t,i)/dT]/dt]/dT]/dt, d[d[d[dt(t,m)/dT]/dt]/dT]/dt, d[d[d[dt(w,a)/dT]/dt]/dT]/dt, d[d[d[dt(w,i)/dT]/dt]/dT]/dt, d[d[d[dt(w,m)/dT]/dt]/dT]/dt, d[d[d[dt(a,i)/dT]/dt]/dT]/dt, d[d[d[dt(a,m)/dT]/dt]/dT]/dt, d[d[d[dt(i,m)/ dT]/dt]/dT]/dt, d[d[d[dt(t,w,a)/dT]/dt]/dT]/dt, d[d[d[dt(t,w,i)/dT]/dt]/dT]/dt, d[d[d[dt(t,w,m)/dT]/dt]/dT]/dt, d[d[d[dt(t,a,i)/dT]/dt]/dT]/dt, d[d[d[dt(t,a,m)/dT]/dt]/dT]/dt,  d[d[d[dt(t,i,m)/dT]/dt]/dT]/dt, d[d[d[dt(w,a,i)/dT]/dt]/dT]/dt, d[d[d[dt(w,a,m)/dT]/dt]/dT]/dt, d[d[d[dt(w,i,m)/dT]/dt]/dT]/dt, d[d[d[dt(a,i,m)/dT]/dt]/dT]/dt, d[d[d[dt(t,w,a,i)/dT]/dt]/dT]/dt, d[d[d[dt(t,w,a,m)/dt/dt, d[d[d[dt(t,w,i,m)/dT]/dt]/dT]/dt, d[d[d[dt(t,a,i,m)/dT]/dt]/dT]/dt, d[d[d[dt(w,a,i,m)/dT]/dt]/dT]/dt, d[d[d[dt(t,w,a,i,m)/dT]/dt]/dT]/dt..

 

or as:

 

d[d[d[dt(t)/dT]/dT]/dt]/dt, d[d[d[dt(w)/dT]/dT]/dt]/dt, d[d[d[dt(a)/dT]/dT]/dt]/dt, d[d[d[dt(i)/dT]/dT]/dt]/dt, d[d[d[dt(m)/dT]/dT]/dt]/dt, d[d[d[dt(t,w)/dT]/dT]/dt]/dt, d[d[d[dt(t,a)/dT]/dT]/dt]/dt, d[d[d[dt(t,i)/dT]/dT]/dt]/dt, d[d[d[dt(t,m)/dT]/dT]/dt]/dt, d[d[d[dt(w,a)/dT]/dT]/dt]/dt, d[d[d[dt(w,i)/dT]/dT]/dt]/dt, d[d[d[dt(w,m)/dT]/dT]/dt]/dt, d[d[d[dt(a,i)/dT]/dT]/dt]/dt, d[d[d[dt(a,m)/ dT]/dT]/dt]/dt, d[d[d[dt(i,m)/ dT]/dT]/dt]/dt, d[d[d[dt(t,w,a)/dT]/dT]/dt]/dt, d[d[d[dt(t,w,i)/dT]/dT]/dt]/dt, d[d[d[dt(t,w,m)/dT]/dT]/dt]/dt, d[d[d[dt(t,a,i)/dT]/dT]/dt]/dt, d[d[d[dt(t,a,m)/dT]/dT]/dt]/dt,  d[d[d[dt(t,i,m)/dT]/dT]/dt]/dt, d[d[d[dt(w,a,i)/dT]/dT]/dt]/dt, d[d[d[dt(w,a,m)/dT]/dT]/dt]/dt, d[d[d[dt(w,i,m)/dT]/dT]/dt]/dt, d[d[d[dt(a,i,m)/dT]/dT]/dt]/dt, d[d[d[dt(t,w,a,i)/dT]/dT]/dt]/dt, d[d[d[dt(t,w,a,m)/dt/dt, d[d[d[dt(t,w,i,m)/dT]/dT]/dt]/dt, d[d[d[dt(t,a,i,m)/dT]/dT]/dt]/dt, d[d[d[dt(w,a,i,m)/dT]/dT]/dt]/dt, d[d[d[dt(t,w,a,i,m)/dT]/dT]/dt]/dt..

 

We can also take higher order duel dimensional derivatives of instinct as a function of thought and time but the symbolic expression of the set of such derivatives very soon becomes excessively lengthly to write and so these higher order derivatives as such are not mentioned here except to say that they would be computed in an analogous manner to the second order duel dtmensional derivatives described above.

 

 

 

These seemingly crazy dtfferentials might have some application in the study of extreme psychological states that can be experienced by souls who are departed and whose instincts, although perhaps spiritualized, are limited by a body and its brain.

 

 

Another type of being that might experience such extreme instinct change capacities might be none other then some of our friends we believe to exist as pure body-less and brain-less spirits known as angels.

 

 

Since I have dared to speculate this far, perhaps we can speculate as to whether any intelligent extraterrestrials persons or any so-called ultra-terrestrials persons that are more instinctualy evolved then we ordinary humans might be capable of experiencing large absolute valued terms of In. Some such ETI and UTI persons may  have evolved over billions of years, or perhaps have far greater powers of sensation, thought, and intuition such as would seem plausible for any such persons and their civilizations who have not fallen from the state of innocence into the state of sin as we humans have, or perhaps such beings never had the option of  sanctifying grace opened to them but nonetheless may have been created at a naturally more perfect level then we humans, and who therefore might exhibit greater natural powers of thought and sensation.

 

 

 

These seemingly crazy differentials might have some application in the study of extreme psychological states that can be experienced by souls who are departed and whose instincts, although perhaps spiritualized, are limited by a body and its brain.

 

 

Another type of being that might experience such extreme instinct change capacities might be none other then some of our friends we believe to exist as pure body-less and brain-less spirits known as angels.

 

 

 

Now, the above variable of time, T,  can have multiple meanings or aspects. One such meaning is objective time and in such a case for large non-zero values of In, where n = 1,2,3,…, the person experiencing such an instinct or complex of instincts  might not subjectively experience the instinct(s) as occurring any faster than we ordinary humans do.

 

 

However, another interpretation of the variable of Time is subjective time. In such a case for large non-zero absolute values of In, where n = 1,2,3,…, the person experiencing such an instinct or complex of instincts  would subjectively experience the instinct(s) as occurring or changing faster than we ordinary humans experience, in fact the higher the absolute value of non-zero In, especially for large n, the rate of change of instinct with respect to time would progress at an incredible rate. We ordinary humans would likely be completely overwhelmed by subjective psychic experiences of such In phenomenon.

 

 

Could there be other objective temporal dimensions beside the one objective temporal dimension that we know of, and the seemingly one subjective dimension of time that we experience? As someone who normally writes on the topic of exotic space craft propulsion systems such as proposed interstellar space craft propulsion systems, I am familiar with the theoretical paradigms that there may exist higher dimensions of space and perhaps more than one dimension of time, and so I say, never say never.

 

 

The above notation of derivatives and differential equations is just an infinitesimal glimpse of the number of possible equations as such and related constructs. Trust me, I can reasonably in good confidence re-assure you of such.

 

 

32) Just A Shadow Of A Glimpse Of The Utterly Limitless Number Derivatives of Human Memory  With Respect To Time, Thought, Volition, Affect, Memory, Instinct, And Emotion  Where These Latter 6 Psychodynamic Parameter Are Likely Just An Infinitesimal Fraction Of The Number Of Possible Psychodynamic Parameters, Of Which In This Life, We Have  A Glimpse Of Relatively Few.

 

In this article, we will cover the notion of arbitrary finite and more or less arbitrarily infinity ordered derivatives of human, ETI, and UTI memory with respect to time, thought, will, affect, memory, instinct, and emotion.

 

Even in the case where the first order derivatives as such are small in magnitude, this does not preclude non-zero first order derivatives of more or less arbitrary infinity orders with respect to the same psychodynamic variables. This is plausibly true since the derivatives described herein are not totally quantitative and in many respect are not quantitative. Also, for the quantitative aspects of such infinity ordered derivatives of  memory, the complexity of the precise mathematical expressions may be such that there are an arbitrarily infinite number of  various infinite ordered derivatives such that the numerical infinities cancel out.

 

Another argument for the plausibility of  non-zero infinite order derivatives of memory is that each aspect of human psychodynamic activity or states are immeadiately present to themselves in the sense that each such activity or change of state occurs within the complete and total simultaneous unity of the associated human person, more specifically within the associated human soul.

 

Yet another argument is that the difference in the various derivatives as such may be small even in the midst of a range of derivatives that spans infinite numbers of orders. Such small differences may be the result of infinities that cancel out, but may also be the result of non-numerically quantifiable aspects of the sets of such derivatives.

 

The Human Heart is so complex that I am not sure how the concepts described herein can be not valid even amidst the generally non violent or at least not too violent or not too over whelmingly strong effects of one psychodynamic parameter state on another.

 

So despite the fact that we do not notice infinitely rapid or infinite intra-reactive changes within our psychodynamic states, the arguments for the plausibility of non-zero infinite ordered derivatives of memory with respect to other basic psychodynamic parameters or aspects is argued as above and mathematically categorized herein below.

 

 

 

 

Memory  as such can be a function or partially a function of emotion, will, affect, instinct, emotion and/or memory; and thought as such can be expressed as follows:

 

 

M(t), M(w), M(a), M(i), M(m), M(t,w), M(t,a), M(t,i), M(t,m), M(w,a), M(w,i), M(w,m), M(a,i), M(a,m), M(i,m), M(t,w,a), M(t,w,i), M(t,w,m), M(t,a,i), M(t,a,m), M(t,i,m), M(w,a,i), M(w,a,m), M(w,i,m), M(a,i,m), M(t,w,a,i), M(t,w,a,m), M(t,w,i,m), M(t,a,i,m), M(w,a,i,m), M(t,w,a,i,m)

 

M(t,e), M(w,e), M(a,e), M(i,e), M(m,e), M(t,w,e), M(t,a,e), M(t,i,e), M(t,m,e), M(w,a,e), M(w,i,e), M(w,m,e), M(a,i,e), M(a,m,e), M(i,m,e), M(t,w,a,e), M(t,w,i,e), M(t,w,m,e), M(t,a,i,e), M(t,a,m,e), M(t,i,m,e), M(w,a,i,e), M(w,a,m,e), M(w,i,m,e), M(a,i,m,e), M(t,w,a,i,e), M(t,w,a,m,e), M(t,w,i,m,e), M(t,a,i,m,e), M(w,a,i,m,e), M(t,w,a,i,m,e).

 

Note that some differential expressions involving  the form of functions of memory, or M,  as a function of emotion, e, by itself, or in conjunction with any sub-set of the parameters of t,w,a,i,m, are not included to the same extent as many similar expressions including M, and these other parameters denoted by the small letters, t,w,a,i, and/or m in this section. A more comphrensive post will include the currently omitted explicit formulas incorporating the parameter, e. Note that capital e, or E, is a parameter that is often included in the differential equations herein, but then so in a slightly different context than e would have be included. The difference between e and E will become clear from the context of the specific formulas.

 

In all, there are (2 EXP n) – 1 = (2 EXP 6) – 1 = 63 expressions as such if one assumes the previous five dimensions of will.

 

Assuming that each of the above function f(M)  is perfectly continuous, the number of forms that the general emotion function, f(M), can have is plausibly equal to П(1,62)R where R is the number of real numbers.

 

Assuming that each of the above functions f(M) is super-continuous at the level of 0/(Aleph 0) where Aleph 0 is the number of integers, the number of forms that the general emotion function, f(M), can have is plausibly equal to П(1,62)[R x (Aleph 0)] where R is the number of real numbers.

 

Assuming that each of the above functions f(M) is super-continuous at the level of 0/(Aleph 1) where Aleph 1 is the number of real numbers according to the Continuum Hypotheses, the number of forms that the general memory function, f(M), can have is plausibly equal to П(1,62)[R x (Aleph 1)] where R is the number of real numbers.

 

Assuming that each of the above functions f(M) is super-continuous at the level of 0/(Aleph 2) where Aleph 2 is is greater than Aleph 1 by a factor of infinity (the exact details of this infinity of which are a little more involve than the latter simple statement), the number of forms that the general memory function, f(M), can have is plausibly equal to П(1,62)[R x (Aleph 2)] where R is the number of real numbers.

 

Assuming that each of the above functions f(M) is super-continuous at the level of 0/(Aleph 3) where Aleph 3 is is greater than Aleph 2 by a factor of infinity (the exact details of this infinity of which are a little more involve than the latter simple statement), the number of forms that the general memory function, f(M), can have is plausibly equal to П(1,62)[R x (Aleph 3)] where R is the number of real numbers.

 

… and so on ad infinitum to, through, and beyond the following product series, П(1,62)[R x (Aleph 4)],   П(1,62)[R x (Aleph 5)],  П(1,62)[R x (Aleph 6)],…,  П(1,62)[R x (Aleph Ω)], …,  П(1,62)[R x (Aleph (Aleph 0))], …, П(1,62)[R x (Aleph (Aleph 1))], …, П(1,62)[R x (Aleph (Aleph 2))], … , П(1,62)[R x (Aleph (Aleph Ω))], …, П(1,62)[R x (Aleph (Aleph (Aleph 0)))] and so on perhaps in an ever lasting series even a  the latter level of abstraction.

 

Assuming that each of the above functions f(M) is super-continuous at the level of 0/(Aleph 2) where Aleph 2 is is greater than Aleph 1 by a factor of infinity (the exact details of this infinity of which are a little more involve than the latter simple statement), the number of forms that the general memory function, f(M), can have is plausibly equal to П(1,62)[R x (Aleph 2)] where R is the number of real numbers.

 

 

 

We can summarize all of these combinations as follows in compact symbolism that is intuitively clear to follow:

 

 

M = M(t and/or w and/or a and/or i and/or m)

 

 

We can express M as a function of time as follows: M(T) =  M[(t and/or w and/or a and/or i and/or m),(T)] or perhaps the following notation can be more appropriate in certain circumstances.

 

 

M(T) = M{[t(T)] and/or [w(T)] and/or [a(T)] and/or [i(T)] and/or [m(T)]}.

 

 

Thus, the following first order derivatives of memory with respect to time are possible.

 

 

dM(t)/dT, dM(w)/dT, dM(a)/dT, dM(i)/dT, dM(m)/dT, dM(t,w)/dT, dM(t,a)/dT, dM(t,i)/dT, dM(t,m)/dT, dM(w,a)/dT, dM(w,i)/dT, dM(w,m)/dT, dM(a,i)/dT, dM(a,m)/dT, dM(i,m)/dT, dM(t,w,a)/dT, dM(t,w,i)/dT, dM(t,w,m)/dT, dM(t,a,i)/dT, dM(t,a,m)/dT, dM(t,i,m)/dT, dM(w,a,i)/dT, dM(w,a,m)/dT, dM(w,i,m)/dT, dM(a,i,m)/dT, dM(t,w,a,i)/dT, dM(t,w,a,m)/dT, dM(t,w,i,m)/dT, dM(t,a,i,m)/dT, dM(w,a,i,m)/dT, dM(t,w,a,i,m)/dT.

 

 

Or more succinctly,  dM/dT = dM(t and/or w and/or a and/or i and/or m)/dT

 

 

Or perhaps dM(T)/dT =d M{[t(T)] and/or [w(T)] and/or [a(T)] and/or [i(T)] and/or [m(T)]}/dT.

 

 

Likewise, we can take the second time derivatives of  M as follows:

 

 

 

d[dM(t)/dT]/dT, d[dM(w)/dT]/dT, d[dM(a)/dT]/dT, d[dM(i)/dT]/dT, d[dM(m)/dT]/dT, d[dM(t,w)/dT]/dT, d[dM(t,a)/dT]/dT, d[dM(t,i)/dT]/dT, d[dM(t,m)/dT]/dT, d[dM(w,a)/dT]/dT, d[dM(w,i)/dT]/dT, d[dM(w,m)/dT]/dT, d[dM(a,i)/dT]/dT, d[dM(a,m)/dT]/dT, d[dM(i,m)/dT/dT, d[dM(t,w,a)/dT]/dT, d[dM(t,w,i)/dT]/dT, d[dM(t,w,m)/dT]/dT, d[dM(t,a,i)/dT]/dT, d[dM(t,a,m)/dT]/dT,  d[dM(t,i,m)/dT]/dT, d[dM(w,a,i)/dT]/dT, d[dM(w,a,m)/dT]/dT, d[dM(w,i,m)/dT]/dT, d[dM(a,i,m)/dT]/dT, d[dM(t,w,a,i)/dT]/dT, d[dM(t,w,a,m)/dT/dT, d[dM(t,w,i,m)/dT]/dT, d[dM(t,a,i,m)/dT]/dT, d[dM(w,a,i,m)/dT]/dT, d[dM(t,w,a,i,m)/dT]/dT..

 

 

or more succinctly, as d(dM/dT)/dT = d[d M(t and/or w and/or a and/or i and/or m)/dT]/dT = M2

 

 

or as

 

 

d[dM(T)/dT]/dT  = d[d M{[t(T)] and/or [w(T)] and/or [a(T)] and/or [i(T)] and/or [m(T)]}/dT]/dT = M2.

 

 

 

Likewise, we can take the third time derivatives of  M as follows:

 

 

 

d[d[dM(t)/dT]/dT]/dT, d[d[dM(w)/dT]/dT]/dT, d[d[dM(a)/dT]/dT]/dT, d[d[dM(i)/dT]/dT]/dT, d[d[dM(m)/dT]/dT]/dT, d[d[dM(t,w)/dT]/dT]/dT, d[d[dM(t,a)/dT]/dT]/dT, d[d[dM(t,i)/dT]/dT]/dT, d[d[dM(t,m)/dT]/dT]/dT, d[d[dM(w,a)/dT]/dT]/dT, d[d[dM(w,i)/dT]/dT]/dT, d[d[dM(w,m)/dT]/dT]/dT, d[d[dM(a,i)/dT]/dT]/dT, d[d[dM(a,m)/dT]/dT]/dT, d[d[dM(i,m)/dT/dT]/dT, d[d[dM(t,w,a)/dT]/dT]/dT, d[d[dM(t,w,i)/dT]/dT]/dT, d[d[dM(t,w,m)/dT]/dT]/dT, d[d[dM(t,a,i)/dT]/dT]/dT, d[d[dM(t,a,m)/dT]/dT]/dT,  d[d[dM(t,i,m)/dT]/dT]/dT, d[d[dM(w,a,i)/dT]/dT]/dT, d[d[dM(w,a,m)/dT]/dT]/dT, d[d[dM(w,i,m)/dT]/dT]/dT, d[d[dM(a,i,m)/dT]/dT]/dT, d[d[dM(t,w,a,i)/dT]/dT]/dT, d[d[dM(t,w,a,m)/dT/dT]/dT, d[d[dM(t,w,i,m)/dT]/dT]/dT, d[d[dM(t,a,i,m)/dT]/dT]/dT, d[d[dM(w,a,i,m)/dT]/dT]/dT, d[d[dM(t,w,a,i,m)/dT]/dT]/dT.

 

 

or more succinctly, as d[d(dM/dT)/dT]/dT = d[d[d M(t and/or w and/or a and/or i and/or m)/dT]/dT]/dT = M3

 

 

or as

 

 

d[d[dM(T)/dT]/dT]/dT  = d[d[d M{[t(T)] and/or [w(T)] and/or [a(T)] and/or [i(T)] and/or [m(T)]}/dT]/dT]/dT = M3.

 

 

We can also form the expressions;

 

 

d[d[f(M)]/dT]/dT = d{d [M[t(T)]]/dT and/or d[M[w(T)]]/dT and/or d[M[a(T)]]/dT and/or d[M[i(T)]]/dT and/or d[M[m(T)]]/dT}/dT  = f(M)2

 

 

and

 

 

d[d[d[f(M)]/dT]/dT]/dT = d{d{ d [M[t(T)]]/dT and/or d[M[w(T)]]/dT and/or d[M[a(T)]]/dT and/or d[M[i(T)]]/dT and/or d[M[m(T)]]/dT}/dT}/dT  = f(M)3A, where A stands for type A differentiation which is not to be confused with the meaning of so-called Type A personality as A is used as an ordinal in a totally different context here.

 

 

and

 

 

d[d[d[f(M)]/dT]/dT]/dT = d{d[d [M[t(T)]]/dT]/dT  and/or d[d [M[w(T)]]/dT]/dT  and/or d[d [M[a(T)]]/dT]/dT  and/or d[d [M[i(T)]]/dT]/dT  and/or d[d [M[m(T)]]/dT]/dT }/dT = f(M)3B, where B stands for type B differentiation which is not to be confused with the meaning of a  so-called Type  B personality as B is used as an ordinal in a totally different context here .

 

 

In fact, one can form yet higher order derivatives of memories with respect to time as follows.

 

 

M5 = d M4/dT = d[dM3/dT]/dT

 

 

 

M5 = d M4/dT =  d[d[d[d[d M{[t(T)] and/or [w(T)] and/or [a(T)] and/or [i(T)] and/or [m(T)]}/dT]/dT]/dT]/dT]/dT.

 

 

 

f(M)5A = d[f(M)4A]/dT = d[d [f(M)3A]/dT]/dT =  d{d{d{d{ d [M[t(T)]]/dT and/or d[M[w(T)]]/dT and/or d[M[a(T)]]/dT and/or d[M[i(T)]]/dT and/or d[M[m(T)]]/dT}/dT}/dT]/dT]/dT

 

 

 

 

M6 = d M5/dT = d[d M4/dT]/dT = d[d[dM3/dT]/dT]/dT

 

 

 

M6 = dM5/dT = d[d[d[d[d[d M{[t(T)] and/or [w(T)] and/or [a(T)] and/or [i(T)] and/or [m(T)]}/dT]/dT]/dT]/dT]/dT]/dT

 

 

 

f(M)6A = d[f(M)5A]/dT = d{ d{d{d{d{ d [M[t(T)]]/dT and/or d[M[w(T)]]/dT and/or d[M[a(T)]]/dT and/or d[M[i(T)]]/dT and/or d[M[m(T)]]/dT}/dT}/dT]/dT]/dT]/dT

 

 

 

 

M7 = dM6/dT

 

f(M)7A = d[f(M)6A]/dT

 

 

M8 = d M7/dT

 

f(M)8A = d[f(M)7A]/dT

 

 

 

M9 = d M8/dT

 

f(M)9A = d[f(M)8A]/dT

 

 

M10…, M11…, M12 … etc.

 

 

Anyone for M ensemble, or M infinity scrapper, or M (Aleph 0), or M(Aleph 1), or M(Aleph 2), or how about M Aleph (Aleph 0), or M Aleph (Aleph 1) , or M Aleph (Aleph 2), or even M Aleph (Aleph (Aleph 0)), or M Aleph (Aleph (Aleph 1)), or M Aleph (Aleph (Aleph 2)), and so on?

 

We can also express memory qualitatively, statistically, and perhaps with the use of some forms of real analyses as a derivative of with respect to emotion or with respect to E.

 

Given that M(e) =  M(t and/or w and/or a and/or i and/or m), the following first order derivatives of memory  with respect to emotion are possible.

 

 

dM(t)/dE, dM(w)/dE, dM(a)/dE, dM(i)/dE, dM(m)/dE, dM(t,w)/dE, dM(t,a)/dE, dM(t,i)/dE, dM(t,m)/dE, dM(w,a)/dE, dM(w,i)/dE, dM(w,m)/dE, dM(a,i)/dE, dM(a,m)/dE, dM(i,m)/dE, dM(t,w,a)/dE, dM(t,w,i)/dE, dM(t,w,m)/dE, dM(t,a,i)/dE, dM(t,a,m)/dE, dM(t,i,m)/dE, dM(w,a,i)/dE, dM(w,a,m)/dE, dM(w,i,m)/dE, dM(a,i,m)/dE, dM(t,w,a,i)/dE, dM(t,w,a,m)/dE, dM(t,w,i,m)/dE, dM(t,a,i,m)/dE, dM(w,a,i,m)/dE, dM(t,w,a,i,m)/dE.

 

 

Or more succinctly,  dM/dE = dM(t and/or w and/or a and/or i and/or m)/dE

 

 

Or perhaps dM(e)/dE =d M{[t(e)] and/or [w(e)] and/or [a(e)] and/or [i(e)] and/or [m(e)]}/dE.

 

 

Likewise, we can take the second emotion derivatives of  M as follows:

 

 

 

d[dM(t)/dE]/dE, d[dM(w)/dE]/dE, d[dM(a)/dE]/dE, d[dM(i)/dE]/dE, d[dM(m)/dE]/dE, d[dM(t,w)/dE]/dE, d[dM(t,a)/dE]/dE, d[dM(t,i)/dE]/dE, d[dM(t,m)/dE]/dE, d[dM(w,a)/dE]/dE, d[dM(w,i)/dE]/dE, d[dM(w,m)/dE]/dE, d[dM(a,i)/dE]/dE, d[dM(a,m)/dE]/dE, d[dM(i,m)/dE/dE, d[dM(t,w,a)/dE]/dE, d[dM(t,w,i)/dE]/dE, d[dM(t,w,m)/dE]/dE, d[dM(t,a,i)/dE]/dE, d[dM(t,a,m)/dE]/dE,  d[dM(t,i,m)/dE]/dE, d[dM(w,a,i)/dE]/dE, d[dM(w,a,m)/dE]/dE, d[dM(w,i,m)/dE]/dE, d[dM(a,i,m)/dE]/dE, d[dM(t,w,a,i)/dE]/dE, d[dM(t,w,a,m)/dE/dE, d[dM(t,w,i,m)/dE]/dE, d[dM(t,a,i,m)/dE]/dE, d[dM(w,a,i,m)/dE]/dE, d[dM(t,w,a,i,m)/dE]/dE..

 

 

or more succinctly, as d(dM/dE)/dE = d[d M(t and/or w and/or a and/or i and/or m)/dE]/dE = Me2

 

 

or as

 

 

d[dM(e)/dE]/dE  = d[d M{[t(e)] and/or [w(e)] and/or [a(e)] and/or [i(e)] and/or [m(e)]}/dE]/dE = Me2.

 

 

 

Likewise, we can take the third emotion derivatives of  M as follows:

 

 

 

d[d[dM(t)/dE]/dE]/dE, d[d[dM(w)/dE]/dE]/dE, d[d[dM(a)/dE]/dE]/dE, d[d[dM(i)/dE]/dE]/dE, d[d[dM(m)/dE]/dE]/dE, d[d[dM(t,w)/dE]/dE]/dE, d[d[dM(t,a)/dE]/dE]/dE, d[d[dM(t,i)/dE]/dE]/dE, d[d[dM(t,m)/dE]/dE]/dE, d[d[dM(w,a)/dE]/dE]/dE, d[d[dM(w,i)/dE]/dE]/dE, d[d[dM(w,m)/dE]/dE]/dE, d[d[dM(a,i)/dE]/dE]/dE, d[d[dM(a,m)/dE]/dE]/dE, d[d[dM(i,m)/dE/dE]/dE, d[d[dM(t,w,a)/dE]/dE]/dE, d[d[dM(t,w,i)/dE]/dE]/dE, d[d[dM(t,w,m)/dE]/dE]/dE, d[d[dM(t,a,i)/dE]/dE]/dE, d[d[dM(t,a,m)/dE]/dE]/dE,  d[d[dM(t,i,m)/dE]/dE]/dE, d[d[dM(w,a,i)/dE]/dE]/dE, d[d[dM(w,a,m)/dE]/dE]/dE, d[d[dM(w,i,m)/dE]/dE]/dE, d[d[dM(a,i,m)/dE]/dE]/dE, d[d[dM(t,w,a,i)/dE]/dE]/dE, d[d[dM(t,w,a,m)/dE/dE]/dE, d[d[dM(t,w,i,m)/dE]/dE]/dE, d[d[dM(t,a,i,m)/dE]/dE]/dE, d[d[dM(w,a,i,m)/dE]/dE]/dE, d[d[dM(t,w,a,i,m)/dE]/dE]/dE.

 

 

or more succinctly, as d[d(dM/dE)/dE]/dE = d[d[d M(t and/or w and/or a and/or i and/or m)/dE]/dE]/dE = Me3

 

 

or as

 

 

d[d[dM(e)/dE]/dE]/dE  = d[d[d M{[t(e)] and/or [w(e)] and/or [a(e)] and/or [i(e)] and/or [m(e)]}/dE]/dE]/dE = Me3.

 

 

We can also form the expressions;

 

 

d[d[f(M)]/dE]/dE = d{d [M[t(e)]]/dE and/or d[M[w(e)]]/dE and/or d[M[a(e)]]/dE and/or d[M[i(e)]]/dE and/or d[M[m(e)]]/dE}/dE  = f(Me)2

 

 

and

 

 

d[d[d[f(M)]/dE]/dE]/dE = d{d{ d [M[t(e)]]/dE and/or d[M[w(e)]]/dE and/or d[M[a(e)]]/dE and/or d[M[i(e)]]/dE and/or d[M[m(e)]]/dE}/dE}/dE  = f(ME)3A, where A stands for type A differentiation which is not to be confused with the meaning of so-called Type A personality as A is used as an ordinal in a totally different context here.

 

 

and

 

 

d[d[d[f(M)]/dE]/dE]/dE = d{d[d [M[t(e)]]/dE]/dE  and/or d[d [M[w(e)]]/dE]/dE  and/or d[d [M[a(e)]]/dE]/dE  and/or d[d [M[i(e)]]/dE]/dE  and/or d[d [M[m(e)]]/dE]/dE }/dE = f(ME)3B, where B stands for type B differentiation which is not to be confused with the meaning of so-called Type  B personality as B is used as an ordinal in a totally different context here .

 

 

In fact, one can form yet higher order derivatives of memorys with respect to emotion as follows.

 

 

Me5 = d Me4/dE = d[dMe3/dE]/dE

 

 

 

Me5 = dMe4/dE =  d[d[d[d[d M{[t(e)] and/or [w(e)] and/or [a(e)] and/or [i(e)] and/or [m(e)]}/dE]/dE]/dE]/dE]/dE.

 

 

 

f(Me)5A = d[f(Me)4A]/dE = d[d [f(Me)3A]/dE]/dE =  d{d{d{d{ d [M[t(e)]]/dE and/or d[M[w(e)]]/dE and/or d[M[a(e)]]/dE and/or d[M[i(e)]]/dE and/or d[M[m(e)]]/dE}/dE}/dE]/dE]/dE

 

 

 

 

Me6 = d Me5/dE = d[d Me4/dE]/dE = d[d[dMe3/dE]/dE]/dE

 

 

 

Me6 = dMe5/dE = d[d[d[d[d[d M{[t(e)] and/or [w(e)] and/or [a(e)] and/or [i(e)] and/or [m(e)]}/dE]/dE]/dE]/dE]/dE]/dE

 

 

 

f(Me)6A = d[f(Me)5A]/dE = d{ d{d{d{d{ d [M[t(e)]]/dE and/or d[M[w(e)]]/dE and/or d[M[a(e)]]/dE and/or d[M[i(e)]]/dE and/or d[M[m(e)]]/dE}/dE}/dE]/dE]/dE]/dE

 

 

 

 

Me7 = dMe6/dE

 

f(Me)7A = d[f(Me)6A]/dE

 

 

Me8 = d Me7/dE

 

f(Me)8A = d[f(Me)7A]/dE

 

 

 

Me9 = d Me8/dE

 

f(Me)9A = d[f(Me)8A]/dE

 

 

Me10…, Me11…, Me12 … Mec.

 

 

Anyone for Me ensemble, or Me infiniEy scrapper, or Me (Aleph 0), or Me(Aleph 1), or Me(Aleph 2), or how about Me Aleph (Aleph 0), or Me Aleph (Aleph 1) , or Me Aleph (Aleph 2), or even Me Aleph (Aleph (Aleph 0)), or ME Aleph (Aleph (Aleph 1)), or ME Aleph (Aleph (Aleph 2)), and so on?

 

Thus, for the set of the sets of derivatives of ME1 through ME(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}.

 

For the set of the sets of derivatives of ME1 through ME (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)},…, {П(0,31)[R]}_{(Aleph 1)}.

 

For the set of the sets of derivatives of ME 1 through ME (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}.

 

For the set of the sets of derivatives of ME 1 through ME (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the derivative states in the set of the sets of derivatives of ME 1 through I(Aleph 0) is plausible equal to:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of ME 1 through ME (Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of ME 1 through ME (Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}}}.

 

For the set of the sets of derivatives of ME 1 through ME (Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous ME I(Aleph 0) derivative space at the level of 0/(Aleph 0), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of ME 1 through ME (Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of ME 1 through ME (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of ME 1 through ME (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of ME 1 through ME (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of ME 1 through ME (Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of ME 1 through ME (Aleph 1), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of ME 1 through  ME (Aleph 2), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of ME I1 through ME (Aleph 3), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous ME (Aleph 0) derivative space at the level of 0/(Aleph 1), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of ME 1 through ME (Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of ME 1 through ME (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of ME 1 through ME (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of ME 1 through  ME (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations  for the set of the sets of derivatives of ME 1 through ME (Aleph 0) is plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of ME 1 through ME (Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of ME 1 through ME (Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of ME 1 through ME (Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

 

For super-continuous ME (Aleph 0) derivative space at the level of 0/(Aleph 2), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of ME 1 through ME (Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of ME 1 through ME (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of ME 1 through ME (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of ME I1 through ME (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of ME 1 through ME (Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of ME I1 through ME (Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of ME 1 through ME (Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of ME I1 through ME (Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

Similar series can be developed for super-continuity at any applicable level such as 0/(Aleph 3), 0/(Aleph 4), 0/(Aleph 5),…, 0/(Aleph Ω), 0/(Aleph (Aleph 0)), …, 0/(Aleph (Aleph 1)), …, 0/(Aleph (Aleph 2)), …, 0/(Aleph (Aleph 3)),…, 0/(Aleph (Aleph Ω)),…, 0/(Aleph (Aleph (Aleph 0))), …, 0/(Aleph (Aleph (Aleph 1))),…, 0/(Aleph (Aleph (Aleph 2))),…, 0/(Aleph (Aleph (Aleph 3))),…, 0/(Aleph (Aleph  (Aleph Ω))), …

 

An so-on ad infinitum.

 

 

In addition to these numerical functions of ME as functions of summation series of product series functions, in order to really appreciate the enourmous complexity of the human soul in terms of its potential to evolve and be differentiated from all other souls in its characteristics, we would need to consider how every single category and even every single species of memory of the form ME can very. Since there may exist an arbitrarily high infinite number species of ME, the number of numerical functions of ME is utterly beyond recogning. I will cover such notions in terms of mathematical notation in yet another series of articles I will write on this general concept.

 

 

Perhaps these numbers are applicable when one considers that the human soul, in its accidental form and perhaps even in its substantial form stores all experience and other psychodynamics based phenomenon. Every experience adds to the accidental form of the human soul and this includes the souls of all those still alive on Earth, all those in Purgatory, all those in Heaven, all those in Hell, and all those in any Limbo.

Since the human soul can grow without limit in terms of its psychodynamic time –flow world line, such a consideration offers another mechanism where the number of derivative states, combinations of derivative states, and even super-continuity of the derivative state space can grow forever.

 

Folks, for those of you who might balk at me for including literally all souls in the above consideration, including the souls in Hell, as well as bodily extraterrestrial souls and the souls of so-called bodily ultraterrestials sometimes referred to as etherians in the new age UFO buff culture, my reply is that we simply do not understand the full scope of GOD’s Divine Economy. We may never fully comprehend the scope of the Divine Economy because such an utterly eternal scheme, is, well, eternal and never ending.

 

 

The general meaning of emotion derivatives of memory can be viewed as the manner in which the qualitative and/or quantitative aspects of memory as a function of memory very with emotion(s). The manner in which memories very with emotion may be multi-emotion dimensional wherein the dimensions of derivations can be multiple, and wherein the derivations can be taken in parallel, series parallel or serial manner The differentials can be partial or non-partial derivatives, or both partial and non-partial for a given computation.

 

In fact, since there is in theory, no limit to the numbers of qualitatively and quantitatively different memorys, and perhaps no limit to the number of possible different types or classes of memorys, wherein each person has his or her own unique memories, the number of memory dimensions that can effect memories is literally infinite, given the entirety of the set of created persons, and perhaps also literally infinite for each person as an individual, although we can not intellectually and intuitively understand this specific infinite number.

 

It is interesting to consider the ramifactions of being able to perform realistic calculations involving emotion derivatives of memory from a mathematical, theoretical, scientific,  and philosophical perspective.

 

Persons for which one or more nth order derivatives of memory with respect to emotion that have large absolute values would tend to have their memories highly influenced by emotion, or at least for the memory under consideration with respect to the dimension of the specific memory type(s) or class(es) for which the differentiation(s) are performed. Perhaps a strong coupling between memory and emotion indicates a well integrated personality and commensurately, a high degree of memory capacity and a high degree of memory intelligence.

 

We would expect that disembodied human souls, ETI souls, and/or UTI souls in Heaven, Limbo, highly evolved bodily ETI persons, highly evolved UTI persons, and angels to have memory of all kinds and intensities which are highly subject to memory.

 

 

We can also consider two dimensional nth ordered derivatives of memory with respect to emotion and time, or with respect to t and T, respectively.

 

Given that M[(e)(T)] =  M[(t and/or w and/or a and/or i and/or m)(e)(T)], the following first order two dimensional derivatives of memory with respect to emotion and Time are possible.

 

 

d[dM[(t)(T)]/dE]/dT, d[dM[(w)(T)]/dE]/dT, d[dM[(a)(T)]/dE]/dT, d[dM[(i)(T)]/dE]/dT, d[dM[(m)(T)]/dE]/dT, d[dM[(t,w)(T)]/dE]/dT, d[dM[(t,a)(T)]/dE]/dT, d[dM[(t,i)(T)]/dE]/dT, d[dM[(t,m)(T)]/dE]/dT, d[dM[(w,a)(T)]/dE]/dT, d[dM[(w,i)(T)]/dE]/dT, d[dM[(w,m)(T)]/dE]/dT, d[dM[(a,i)(T)]/dE]/dT, d[dM[(a,m)(T)]/dE]/dT, d[dM[(i,m)(T)]/dE]/dT, d[dM[(t,w,a)(T)]/dE]/dT, d[dM[(t,w,i)(T)]/dE]/dT, d[dM[(t,w,m)(T)]/dE]/dT, d[dM[(t,a,i)(T)]/dE]/dT, d[dM[(t,a,m)(T)]/dE]/dT, d[dM[(t,i,m)(T)]/dE]/dT, d[dM[(w,a,i)(T)]/dE]/dT, d[dM[(w,a,m)(T)]/dE]/dT, d[dM[(w,i,m)(T)]/dE]/dT, d[dM[(a,i,m)(T)]/dE]/dT, d[dM[(t,w,a,i)(T)]/dE]/dT, d[dM[(t,w,a,m)(T)]/dE]/dT, d[dM[(t,w,i,m)(T)]/dE]/dT, d[dM[(t,a,i,m)(T)]/dE]/dT, d[dM[(w,a,i,m)(T)]/dE]/dT, d[dM[(t,w,a,i,m)(T)]/dE]/dT.

 

 

Or more succinctly,  d[dM(T)/dE]/dT = d[dM[(T)(t and/or w and/or a and/or i and/or m)]/dE]/dT

 

or

 

d[dM(T)/dT]/dE = d[dM[(T)(t and/or w and/or a and/or i and/or m)]/dT]/dE

 

 

 

 

 

Or perhaps d[d M[(e)(T)]/dE]/dT  = d[d M [{[t(e)] and/or [w(e)] and/or [a(e)] and/or [i(e)] and/or [m(e)]}(T)]/dE]/dT

 

or

 

Or perhaps d[d M[(e)(T)]/dT]/dE  = d[d M [{[t(e)] and/or [w(e)] and/or [a(e)] and/or [i(e)] and/or [m(e)]}(T)]/dT]/dE

 

 

 

Likewise, we can take the second dual dimensioned memory-time derivatives of  M as follows:

 

d[d[d[dM[(t)(T)]/dE]/dT]/dE]/dT, d[d[d[dM[(w)(T)]/dE]/dT]/dE]/dT, d[d[d[dM[(a)(T)]/dE]/dT]/dE]/dT, d[d[d[dM[(i)(T)]/dE]/dT]/dE]/dT, d[d[d[dM[(m)(T)]/dE]/dT]/dE]/dT, d[d[d[dM[(t,w)(T)]/dE]/dT]/dE]/dT, d[d[d[dM[(t,a)(T)]/dE]/dT]/dE]/dT, d[d[d[dM[(t,i)(T)]/dE]/dT]/dE]/dT, d[d[d[dM[(t,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dM[(w,a)(T)]/dE]/dT]/dE]/dT, d[d[d[dM[(w,i)(T)]/dE]/dT]/dE]/dT, d[d[d[dM[(w,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dM[(a,i)(T)]/dE]/dT]/dE]/dT, d[d[d[dM[(a,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dM[(i,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dM[(t,w,a)(T)]/dE]/dT]/dE]/dT, d[d[d[dM[(t,w,i)(T)]/dE]/dT]/dE]/dT, d[d[d[dM[(t,w,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dM[(t,a,i)(T)]/dE]/dT]/dE]/dT, d[d[d[dM[(t,a,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dM[(t,i,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dM[(w,a,i)(T)]/dE]/dT]/dE]/dT, d[d[d[dM[(w,a,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dM[(w,i,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dM[(a,i,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dM[(t,w,a,i)(T)]/dE]/dT]/dE]/dT, d[d[d[dM[(t,w,a,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dM[(t,w,i,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dM[(t,a,i,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dM[(w,a,i,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dM[(t,w,a,i,m)(T)]/dE]/dT]/dE]/dT.

 

or as:

 

 

 

d[d[d[dM[(t)(T)]/dE]/dT]/dT]/dE, d[d[d[dM[(w)(T)]/dE]/dT]/dT]/dE, d[d[d[dM[(a)(T)]/dE]/dT]/dT]/dE, d[d[d[dM[(i)(T)]/dE]/dT]/dT]/dE, d[d[d[dM[(m)(T)]/dE]/dT]/dT]/dE, d[d[d[dM[(t,w)(T)]/dE]/dT]/dT]/dE, d[d[d[dM[(t,a)(T)]/dE]/dT]/dT]/dE, d[d[d[dM[(t,i)(T)]/dE]/dT]/dT]/dE, d[d[d[dM[(t,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dM[(w,a)(T)]/dE]/dT]/dT]/dE, d[d[d[dM[(w,i)(T)]/dE]/dT]/dT]/dE, d[d[d[dM[(w,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dM[(a,i)(T)]/dE]/dT]/dT]/dE, d[d[d[dM[(a,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dM[(i,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dM[(t,w,a)(T)]/dE]/dT]/dT]/dE, d[d[d[dM[(t,w,i)(T)]/dE]/dT]/dT]/dE, d[d[d[dM[(t,w,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dM[(t,a,i)(T)]/dE]/dT]/dT]/dE, d[d[d[dM[(t,a,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dM[(t,i,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dM[(w,a,i)(T)]/dE]/dT]/dT]/dE, d[d[d[dM[(w,a,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dM[(w,i,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dM[(a,i,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dM[(t,w,a,i)(T)]/dE]/dT]/dT]/dE, d[d[d[dM[(t,w,a,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dM[(t,w,i,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dM[(t,a,i,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dM[(w,a,i,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dM[(t,w,a,i,m)(T)]/dE]/dT]/dT]/dE.

 

or as:

 

d[d[d[dM[(t)(T)]/dT]/dE]/dE]/dT, d[d[d[dM[(w)(T)]/dT]/dE]/dE]/dT, d[d[d[dM[(a)(T)]/dT]/dE]/dE]/dT, d[d[d[dM[(i)(T)]/dT]/dE]/dE]/dT, d[d[d[dM[(m)(T)]/dT]/dE]/dE]/dT, d[d[d[dM[(t,w)(T)]/dT]/dE]/dE]/dT, d[d[d[dM[(t,a)(T)]/dT]/dE]/dE]/dT, d[d[d[dM[(t,i)(T)]/dT]/dE]/dE]/dT, d[d[d[dM[(t,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dM[(w,a)(T)]/dT]/dE]/dE]/dT, d[d[d[dM[(w,i)(T)]/dT]/dE]/dE]/dT, d[d[d[dM[(w,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dM[(a,i)(T)]/dT]/dE]/dE]/dT, d[d[d[dM[(a,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dM[(i,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dM[(t,w,a)(T)]/dT]/dE]/dE]/dT, d[d[d[dM[(t,w,i)(T)]/dT]/dE]/dE]/dT, d[d[d[dM[(t,w,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dM[(t,a,i)(T)]/dT]/dE]/dE]/dT, d[d[d[dM[(t,a,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dM[(t,i,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dM[(w,a,i)(T)]/dT]/dE]/dE]/dT, d[d[d[dM[(w,a,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dM[(w,i,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dM[(a,i,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dM[(t,w,a,i)(T)]/dT]/dE]/dE]/dT, d[d[d[dM[(t,w,a,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dM[(t,w,i,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dM[(t,a,i,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dM[(w,a,i,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dM[(t,w,a,i,m)(T)]/dT]/dE]/dE]/dT.

 

 

or as;

 

 

 

 

d[d[d[dM(t)/dE]/dE]/dT]/dT, d[d[d[dM(w)/dE]/dE]/dT]/dT, d[d[d[dM(a)/dE]/dE]/dT]/dT, d[d[d[dM(i)/dE]/dE]/dT]/dT, d[d[d[dM(m)/dE]/dE]/dT]/dT, d[d[d[dM(t,w)/dE]/dE]/dT]/dT, d[d[d[dM(t,a)/dE]/dE]/dT]/dT, d[d[d[dM(t,i)/dE]/dE]/dT]/dT, d[d[d[dM(t,m)/dE]/dE]/dT]/dT, d[d[d[dM(w,a)/dE]/dE]/dT]/dT, d[d[d[dM(w,i)/dE]/dE]/dT]/dT, d[d[d[dM(w,m)/dE]/dE]/dT]/dT, d[d[d[dM(a,i)/dE]/dE]/dT]/dT, d[d[d[dM(a,m)/dE]/dE]/dT]/dT, d[d[d[dM(i,m)/dE]/dE]/dT]/dT, d[d[d[dM(t,w,a)/dE]/dE]/dT]/dT, d[d[d[dM(t,w,i)/dE]/dE]/dT]/dT, d[d[d[dM(t,w,m)/dE]/dE]/dT]/dT, d[d[d[dM(t,a,i)/dE]/dE]/dT]/dT, d[d[d[dM(t,a,m)/dE]/dE]/dT]/dT,  d[d[d[dM(t,i,m)/dE]/dE]/dT]/dT, d[d[d[dM(w,a,i)/dE]/dE]/dT]/dT, d[d[d[dM(w,a,m)/dE]/dE]/dT]/dT, d[d[d[dM(w,i,m)/dE]/dE]/dT]/dT, d[d[d[dM(a,i,m)/dE]/dE]/dT]/dT, d[d[d[dM(t,w,a,i)/dE]/dE]/dT]/dT, d[d[d[dM(t,w,a,m)/dE/dE, d[d[d[dM(t,w,i,m)/dE]/dE]/dT]/dT, d[d[d[dM(t,a,i,m)/dE]/dE]/dT]/dT, d[d[d[dM(w,a,i,m)/dE]/dE]/dT]/dT, d[d[d[dM(t,w,a,i,m)/dE]/dE]/dT]/dT..

 

or as:

 

d[d[d[dM(t)/dT]/dE]/dT]/dE, d[d[d[dM(w)/dT]/dE]/dT]/dE, d[d[d[dM(a)/dT]/dE]/dT]/dE, d[d[d[dM(i)/dT]/dE]/dT]/dE, d[d[d[dM(m)/dT]/dE]/dT]/dE, d[d[d[dM(t,w)/dT]/dE]/dT]/dE, d[d[d[dM(t,a)/dT]/dE]/dT]/dE, d[d[d[dM(t,i)/dT]/dE]/dT]/dE, d[d[d[dM(t,m)/dT]/dE]/dT]/dE, d[d[d[dM(w,a)/dT]/dE]/dT]/dE, d[d[d[dM(w,i)/dT]/dE]/dT]/dE, d[d[d[dM(w,m)/dT]/dE]/dT]/dE, d[d[d[dM(a,i)/dT]/dE]/dT]/dE, d[d[d[dM(a,m)/dT]/dE]/dT]/dE, d[d[d[dM(i,m)/ dT]/dE]/dT]/dE, d[d[d[dM(t,w,a)/dT]/dE]/dT]/dE, d[d[d[dM(t,w,i)/dT]/dE]/dT]/dE, d[d[d[dM(t,w,m)/dT]/dE]/dT]/dE, d[d[d[dM(t,a,i)/dT]/dE]/dT]/dE, d[d[d[dM(t,a,m)/dT]/dE]/dT]/dE,  d[d[d[dM(t,i,m)/dT]/dE]/dT]/dE, d[d[d[dM(w,a,i)/dT]/dE]/dT]/dE, d[d[d[dM(w,a,m)/dT]/dE]/dT]/dE, d[d[d[dM(w,i,m)/dT]/dE]/dT]/dE, d[d[d[dM(a,i,m)/dT]/dE]/dT]/dE, d[d[d[dM(t,w,a,i)/dT]/dE]/dT]/dE, d[d[d[dM(t,w,a,m)/dE/dE, d[d[d[dM(t,w,i,m)/dT]/dE]/dT]/dE, d[d[d[dM(t,a,i,m)/dT]/dE]/dT]/dE, d[d[d[dM(w,a,i,m)/dT]/dE]/dT]/dE, d[d[d[dM(t,w,a,i,m)/dT]/dE]/dT]/dE..

 

or as:

 

d[d[d[dM(t)/dT]/dT]/dE]/dE, d[d[d[dM(w)/dT]/dT]/dE]/dE, d[d[d[dM(a)/dT]/dT]/dE]/dE, d[d[d[dM(i)/dT]/dT]/dE]/dE, d[d[d[dM(m)/dT]/dT]/dE]/dE, d[d[d[dM(t,w)/dT]/dT]/dE]/dE, d[d[d[dM(t,a)/dT]/dT]/dE]/dE, d[d[d[dM(t,i)/dT]/dT]/dE]/dE, d[d[d[dM(t,m)/dT]/dT]/dE]/dE, d[d[d[dM(w,a)/dT]/dT]/dE]/dE, d[d[d[dM(w,i)/dT]/dT]/dE]/dE, d[d[d[dM(w,m)/dT]/dT]/dE]/dE, d[d[d[dM(a,i)/dT]/dT]/dE]/dE, d[d[d[dM(a,m)/ dT]/dT]/dE]/dE, d[d[d[dM(i,m)/ dT]/dT]/dE]/dE, d[d[d[dM(t,w,a)/dT]/dT]/dE]/dE, d[d[d[dM(t,w,i)/dT]/dT]/dE]/dE, d[d[d[dM(t,w,m)/dT]/dT]/dE]/dE, d[d[d[dM(t,a,i)/dT]/dT]/dE]/dE, d[d[d[dM(t,a,m)/dT]/dT]/dE]/dE,  d[d[d[dM(t,i,m)/dT]/dT]/dE]/dE, d[d[d[dM(w,a,i)/dT]/dT]/dE]/dE, d[d[d[dM(w,a,m)/dT]/dT]/dE]/dE, d[d[d[dM(w,i,m)/dT]/dT]/dE]/dE, d[d[d[dM(a,i,m)/dT]/dT]/dE]/dE, d[d[d[dM(t,w,a,i)/dT]/dT]/dE]/dE, d[d[d[dM(t,w,a,m)/dE/dE, d[d[d[dM(t,w,i,m)/dT]/dT]/dE]/dE, d[d[d[dM(t,a,i,m)/dT]/dT]/dE]/dE, d[d[d[dM(w,a,i,m)/dT]/dT]/dE]/dE, d[d[d[dM(t,w,a,i,m)/dT]/dT]/dE]/dE..

 

 

We can also take higher order duel dimensional derivatives of memory as a function of emotion and time but the symbolic expression of the set of such derivatives very soon becomes excessively lengthly to write and so these higher order derivatives as such are not mentioned here except to say that they would be computed in an analogous manner to the second order duel dimensional derivatives described above.

 

.

 

 

 

 

 

We can also express memory qualitatively, statistically, and perhaps with the use of some forms of real analyses as a derivative with respect to will or of w.

 

Given that M(w) =  M(t and/or w and/or a and/or i and/or m), the following first order derivatives of memory with respect to will are possible.

 

 

dM(t)/dw, dM(w)/dw, dM(a)/dw, dM(i)/dw, dM(m)/dw, dM(t,w)/dw, dM(t,a)/dw, dM(t,i)/dw, dM(t,m)/dw, dM(w,a)/dw, dM(w,i)/dw, dM(w,m)/dw, dM(a,i)/dw, dM(a,m)/dw, dM(i,m)/dw, dM(t,w,a)/dw, dM(t,w,i)/dw, dM(t,w,m)/dw, dM(t,a,i)/dw, dM(t,a,m)/dw, dM(t,i,m)/dw, dM(w,a,i)/dw, dM(w,a,m)/dw, dM(w,i,m)/dw, dM(a,i,m)/dw, dM(t,w,a,i)/dw, dM(t,w,a,m)/dw, dM(t,w,i,m)/dw, dM(t,a,i,m)/dw, dM(w,a,i,m)/dw, dM(t,w,a,i,m)/dw.

 

 

Or more succinctly,  dM/dw = dM(t and/or w and/or a and/or i and/or m)/dw

 

 

Or perhaps dM(w)/dw =d M{[t(w)] and/or [w(w)] and/or [a(w)] and/or [i(w)] and/or [m(w)]}/dw.

 

 

Likewise, we can take the second will derivatives of  M as follows:

 

 

 

d[dM(t)/dw]/dw, d[dM(w)/dw]/dw, d[dM(a)/dw]/dw, d[dM(i)/dw]/dw, d[dM(m)/dw]/dw, d[dM(t,w)/dw]/dw, d[dM(t,a)/dw]/dw, d[dM(t,i)/dw]/dw, d[dM(t,m)/dw]/dw, d[dM(w,a)/dw]/dw, d[dM(w,i)/dw]/dw, d[dM(w,m)/dw]/dw, d[dM(a,i)/dw]/dw, d[dM(a,m)/dw]/dw, d[dM(i,m)/dw/dw, d[dM(t,w,a)/dw]/dw, d[dM(t,w,i)/dw]/dw, d[dM(t,w,m)/dw]/dw, d[dM(t,a,i)/dw]/dw, d[dM(t,a,m)/dw]/dw,  d[dM(t,i,m)/dw]/dw, d[dM(w,a,i)/dw]/dw, d[dM(w,a,m)/dw]/dw, d[dM(w,i,m)/dw]/dw, d[dM(a,i,m)/dw]/dw, d[dM(t,w,a,i)/dw]/dw, d[dM(t,w,a,m)/dw/dw, d[dM(t,w,i,m)/dw]/dw, d[dM(t,a,i,m)/dw]/dw, d[dM(w,a,i,m)/dw]/dw, d[dM(t,w,a,i,m)/dw]/dw..

 

 

or more succinctly, as d(dM/dw)/dw = d[d M(t and/or w and/or a and/or i and/or m)/dw]/dw = Mw2

 

 

or as

 

 

d[dM(w)/dw]/dw  = d[d M{[t(w)] and/or [w(w)] and/or [a(w)] and/or [i(w)] and/or [m(w)]}/dw]/dw = Mw2.

 

 

 

Likewise, we can take the third will derivatives of  M as follows:

 

 

 

d[d[dM(t)/dw]/dw]/dw, d[d[dM(w)/dw]/dw]/dw, d[d[dM(a)/dw]/dw]/dw, d[d[dM(i)/dw]/dw]/dw, d[d[dM(m)/dw]/dw]/dw, d[d[dM(t,w)/dw]/dw]/dw, d[d[dM(t,a)/dw]/dw]/dw, d[d[dM(t,i)/dw]/dw]/dw, d[d[dM(t,m)/dw]/dw]/dw, d[d[dM(w,a)/dw]/dw]/dw, d[d[dM(w,i)/dw]/dw]/dw, d[d[dM(w,m)/dw]/dw]/dw, d[d[dM(a,i)/dw]/dw]/dw, d[d[dM(a,m)/dw]/dw]/dw, d[d[dM(i,m)/dw/dw]/dw, d[d[dM(t,w,a)/dw]/dw]/dw, d[d[dM(t,w,i)/dw]/dw]/dw, d[d[dM(t,w,m)/dw]/dw]/dw, d[d[dM(t,a,i)/dw]/dw]/dw, d[d[dM(t,a,m)/dw]/dw]/dw,  d[d[dM(t,i,m)/dw]/dw]/dw, d[d[dM(w,a,i)/dw]/dw]/dw, d[d[dM(w,a,m)/dw]/dw]/dw, d[d[dM(w,i,m)/dw]/dw]/dw, d[d[dM(a,i,m)/dw]/dw]/dw, d[d[dM(t,w,a,i)/dw]/dw]/dw, d[d[dM(t,w,a,m)/dw/dw]/dw, d[d[dM(t,w,i,m)/dw]/dw]/dw, d[d[dM(t,a,i,m)/dw]/dw]/dw, d[d[dM(w,a,i,m)/dw]/dw]/dw, d[d[dM(t,w,a,i,m)/dw]/dw]/dw.

 

 

or more succinctly, as d[d(dM/dw)/dw]/dw = d[d[d M(t and/or w and/or a and/or i and/or m)/dw]/dw]/dw = Mw3

 

 

or as

 

 

d[d[dM(w)/dw]/dw]/dw  = d[d[d M{[t(w)] and/or [w(w)] and/or [a(w)] and/or [i(w)] and/or [m(w)]}/dw]/dw]/dw = Mw3.

 

 

We can also form the expressions;

 

 

d[d[f(M)]/dw]/dw = d{d [M[t(w)]]/dw and/or d[M[w(w)]]/dw and/or d[M[a(w)]]/dw and/or d[M[i(w)]]/dw and/or d[M[m(w)]]/dw}/dw  = f(Mw)2

 

 

and

 

 

d[d[d[f(M)]/dw]/dw]/dw = d{d{ d [M[t(w)]]/dw and/or d[M[w(w)]]/dw and/or d[M[a(w)]]/dw and/or d[M[i(w)]]/dw and/or d[M[m(w)]]/dw}/dw}/dw  = f(Mw)3A, where A stands for type A differentiation which is not to be confused with the meaning of so-called Type A personality as A is used as an ordinal in a totally different context here.

 

 

and

 

 

d[d[d[f(M)]/dw]/dw]/dw = d{d[d [M[t(w)]]/dw]/dw  and/or d[d [M[w(w)]]/dw]/dw  and/or d[d [M[a(w)]]/dw]/dw  and/or d[d [M[i(w)]]/dw]/dw  and/or d[d [M[m(w)]]/dw]/dw }/dw = f(Mw)3B, where B stands for type B differentiation which is not to be confused with the meaning of so-called Type  B personality as B is used as an ordinal in a totally different context here .

 

 

In fact, one can form yet higher order derivatives of memory with respect to will as follows.

 

 

Mw5 = d Mw4/dw = d[dMw3/dw]/dw

 

 

 

Mw5 = dMw4/dw =  d[d[d[d[d M{[t(w)] and/or [w(w)] and/or [a(w)] and/or [i(w)] and/or [m(w)]}/dw]/dw]/dw]/dw]/dw.

 

 

 

f(Mw)5A = d[f(Mw)4A]/dw = d[d [f(Mw)3A]/dw]/dw =  d{d{d{d{ d [M[t(w)]]/dw and/or d[M[w(w)]]/dw and/or d[M[a(w)]]/dw and/or d[M[i(w)]]/dw and/or d[M[m(w)]]/dw}/dw}/dw]/dw]/dw

 

 

 

 

Mw6 = d Mw5/dw = d[d Mw4/dw]/dw = d[d[dMw3/dw]/dw]/dw

 

 

 

Mw6 = dMw5/dw = d[d[d[d[d[d M{[t(w)] and/or [w(w)] and/or [a(w)] and/or [i(w)] and/or [m(w)]}/dw]/dw]/dw]/dw]/dw]/dw

 

 

 

f(Mw)6A = d[f(Mw)5A]/dw = d{ d{d{d{d{ d [M[t(w)]]/dw and/or d[M[w(w)]]/dw and/or d[M[a(w)]]/dw and/or d[M[i(w)]]/dw and/or d[M[m(w)]]/dw}/dw}/dw]/dw]/dw]/dw

 

 

 

 

Mw7 = dMw6/dw

 

f(Mw)7A = d[f(Mw)6A]/dw

 

 

Mw8 = d Mw7/dw

 

f(Mw)8A = d[f(Mw)7A]/dw

 

 

 

Mw9 = d Mw8/dw

 

f(Mw)9A = d[f(Mw)8A]/dw

 

 

Mw10…, Mw11…, Mw12 … etc.

 

 

Anyone for Mw ensemble, or Mw infinity scrapper, or Mw (Aleph 0), or Mw(Aleph 1), or Mw (Aleph 2), or how about Mw Aleph (Aleph 0), or Mw Aleph (Aleph 1) , or Mw Aleph (Aleph 2), or even Mw Aleph (Aleph (Aleph 0)), or Mw Aleph (Aleph (Aleph 1)), or Mw Aleph (Aleph (Aleph 2)), and so on?

 

Thus, for the set of the sets of derivatives of Mw1 through Mw(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Mw1 through Mw(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)},…, {П(0,31)[R]}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Mw1 through Mw(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Mw1 through Mw(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the derivative states in the set of the sets of derivatives of Mw1 through Mw(Aleph 0) is plausible equal to:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Mw1 through Mw(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Mw1 through Mw(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}}}.

 

For the set of the sets of derivatives of Mw1 through Mw(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Mw(Aleph 0) derivative space at the level of 0/(Aleph 0), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Mw1 through Mw(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Mw1 through Mw(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Mw1 through Mw(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Mw1 through Mw(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Mw1 through Iw(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Mw1 through Mw(Aleph 1), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Mw1 through  Mw(Aleph 2), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Mw1 through Mw(Aleph 3), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Mw(Aleph 0) derivative space at the level of 0/(Aleph 1), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Mw1 through Mw(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Mw1 through Mw(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Mw1 through Mw(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Mw1 through  Mw(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations  for the set of the sets of derivatives of Mw1 through Mw(Aleph 0) is plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Mw1 through Mw(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Mw1 through Mw(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Mw1 through Mw(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

 

For super-continuous Mw(Aleph 0) derivative space at the level of 0/(Aleph 2), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Mw1 through Mw(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Mw1 through Mw(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Mw1 through Mw(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Mw1 through Mw(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Mw1 through Mw(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Mw1 through Mw(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Mw1 through Mw(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Mw1 through Mw(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

Similar series can be developed for super-continuity at any applicable level such as 0/(Aleph 3), 0/(Aleph 4), 0/(Aleph 5),…, 0/(Aleph Ω), 0/(Aleph (Aleph 0)), …, 0/(Aleph (Aleph 1)), …, 0/(Aleph (Aleph 2)), …, 0/(Aleph (Aleph 3)),…, 0/(Aleph (Aleph Ω)),…, 0/(Aleph (Aleph (Aleph 0))), …, 0/(Aleph (Aleph (Aleph 1))),…, 0/(Aleph (Aleph (Aleph 2))),…, 0/(Aleph (Aleph (Aleph 3))),…, 0/(Aleph (Aleph  (Aleph Ω))), …

 

An so-on ad infinitum.

 

In addition to these numerical functions of Mw as functions of summation series of product series functions, in order to really appreciate the enourmous complexity of the human soul in terms of its potential to evolve and be differentiated from all other souls in its characteristics, we would need to consider how every single category and even every single species of memory of the form Mw can very. Since there may exist an arbitrarily high infinite number species of Mw, the number of numerical functions of Mw is utterly beyond recogning. I will cover such notions in terms of mathematical notation in yet another series of articles I will write on this general concept.

 

 

 

Perhaps these numbers are applicable when one considers that the human soul, in its accidental form and perhaps even in its substantial form stores all experience and other psychodynamics based phenomenon. Every experience adds to the accidental form of the human soul and this includes the souls of all those still alive on Earth, all those in Purgatory, all those in Heaven, all those in Hell, and all those in any Limbo.

Since the human soul can grow without limit in terms of its psychodynamic time –flow world line, such a consideration offers another mechanism where the number of derivative states, combinations of derivative states, and even super-continuity of the derivative state space can grow forever.

 

Folks, for those of you who might balk at me for including literally all souls in the above consideration, including the souls in Hell, as well as bodily extraterrestrial souls and the souls of so-called bodily ultraterrestials sometimes referred to as etherians in the new age UFO buff culture, my reply is that we simply do not understand the full scope of GOD’s Divine Economy. We may never fully comprehend the scope of the Divine Economy because such an utterly eternal scheme, is, well, eternal and never ending.

 

 

The general meaning of will derivatives of memory can be viewed as the manner in which the qualitative and/or quantitative aspects of memory as a function of will very with will. The manner in which memories very with will may be multi- will-aspect dimensional wherein the dimensions of derivations can be multiple, and wherein the derivations can be taken in parallel, series parallel or in serial manner. The differentials can be partial or non-partial derivatives, or both partial and non-partial for a given computation.

 

In fact, since there is in theory, no limit to the numbers of qualitatively and quantitatively different acts of will or volitional states, and perhaps no limit to the number of possible different types or classes of acts of will or volitional states, wherein each person has his or her own unique acts or will or volitional states, the number of volitional state dimensions that can effect memories is literally infinite, given the entirety of the set of created persons, and perhaps also literally infinite for each person as an individual, although we can not intellectually and intuitively understand this infinite number.

 

 

It is interesting to consider the ramifactions of being able to perform realistic calculations involving will derivatives of memory from a mathematical, theoretical, scientific,  and philosophical perspective.

 

Persons for which one or more nth order derivatives of memory with respect to will that have large absolute values would tend to have their memories highly influenced by will, or at least for the memories under consideration with respect to the dimension of the specific will act type(s) or class(es) for which the differentiation(s) are being performed. Perhaps a strong coupling between memory and will indicates a well integrated personality and commensurately, a high degree of memory capacity and a high degree of memory intelligence as well as perhaps very strong will power.

 

 

 

We can also consider two dimensional ith ordered derivatives of memory with respect to will and time, or with respect to w and T, respectively.

 

Given that M[(w)(T)] =  M[(t and/or w and/or a and/or i and/or m)(w)(T)], the following first order two dimensional derivatives of memory with respect to will and Time are possible.

 

 

d[dM[(t)(T)]/dw]/dT, d[dM[(w)(T)]/dw]/dT, d[dM[(a)(T)]/dw]/dT, d[dM[(i)(T)]/dw]/dT, d[dM[(m)(T)]/dw]/dT, d[dM[(t,w)(T)]/dw]/dT, d[dM[(t,a)(T)]/dw]/dT, d[dM[(t,i)(T)]/dw]/dT, d[dM[(t,m)(T)]/dw]/dT, d[dM[(w,a)(T)]/dw]/dT, d[dM[(w,i)(T)]/dw]/dT, d[dM[(w,m)(T)]/dw]/dT, d[dM[(a,i)(T)]/dw]/dT, d[dM[(a,m)(T)]/dw]/dT, d[dM[(i,m)(T)]/dw]/dT, d[dM[(t,w,a)(T)]/dw]/dT, d[dM[(t,w,i)(T)]/dw]/dT, d[dM[(t,w,m)(T)]/dw]/dT, d[dM[(t,a,i)(T)]/dw]/dT, d[dM[(t,a,m)(T)]/dw]/dT, d[dM[(t,i,m)(T)]/dw]/dT, d[dM[(w,a,i)(T)]/dw]/dT, d[dM[(w,a,m)(T)]/dw]/dT, d[dM[(w,i,m)(T)]/dw]/dT, d[dM[(a,i,m)(T)]/dw]/dT, d[dM[(t,w,a,i)(T)]/dw]/dT, d[dM[(t,w,a,m)(T)]/dw]/dT, d[dM[(t,w,i,m)(T)]/dw]/dT, d[dM[(t,a,i,m)(T)]/dw]/dT, d[dM[(w,a,i,m)(T)]/dw]/dT, d[dM[(t,w,a,i,m)(T)]/dw]/dT.

 

 

Or more succinctly,  d[dM(T)/dw]/dT = d[dM[(T)(t and/or w and/or a and/or i and/or m)]/dw]/dT

 

or

 

d[dM(T)/dT]/dw = d[dM[(T)(t and/or w and/or a and/or i and/or m)]/dT]/dw

 

 

 

 

 

Or perhaps d[d M[(w)(T)]/dw]/dT  = d[d M [{[t(w)] and/or [w(w)] and/or [a(w)] and/or [i(w)] and/or [m(w)]}(T)]/dw]/dT

 

or

 

Or perhaps d[d M[(w)(T)]/dT]/dw  = d[d M [{[t(w)] and/or [w(w)] and/or [a(w)] and/or [i(w)] and/or [m(w)]}(T)]/dT]/dw

 

 

 

Likewise, we can take the second dual dimension will -time derivatives of  M as follows:

 

d[d[d[dM[(t)(T)]/dw]/dT]/dw]/dT, d[d[d[dM[(w)(T)]/dw]/dT]/dw]/dT, d[d[d[dM[(a)(T)]/dw]/dT]/dw]/dT, d[d[d[dM[(i)(T)]/dw]/dT]/dw]/dT, d[d[d[dM[(m)(T)]/dw]/dT]/dw]/dT, d[d[d[dM[(t,w)(T)]/dw]/dT]/dw]/dT, d[d[d[dM[(t,a)(T)]/dw]/dT]/dw]/dT, d[d[d[dM[(t,i)(T)]/dw]/dT]/dw]/dT, d[d[d[dM[(t,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dM[(w,a)(T)]/dw]/dT]/dw]/dT, d[d[d[dM[(w,i)(T)]/dw]/dT]/dw]/dT, d[d[d[dM[(w,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dM[(a,i)(T)]/dw]/dT]/dw]/dT, d[d[d[dM[(a,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dM[(i,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dM[(t,w,a)(T)]/dw]/dT]/dw]/dT, d[d[d[dM[(t,w,i)(T)]/dw]/dT]/dw]/dT, d[d[d[dM[(t,w,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dM[(t,a,i)(T)]/dw]/dT]/dw]/dT, d[d[d[dM[(t,a,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dM[(t,i,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dM[(w,a,i)(T)]/dw]/dT]/dw]/dT, d[d[d[dM[(w,a,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dM[(w,i,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dM[(a,i,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dM[(t,w,a,i)(T)]/dw]/dT]/dw]/dT, d[d[d[dM[(t,w,a,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dM[(t,w,i,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dM[(t,a,i,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dM[(w,a,i,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dM[(t,w,a,i,m)(T)]/dw]/dT]/dw]/dT.

 

or as:

 

 

 

d[d[d[dM[(t)(T)]/dw]/dT]/dT]/dw, d[d[d[dM[(w)(T)]/dw]/dT]/dT]/dw, d[d[d[dM[(a)(T)]/dw]/dT]/dT]/dw, d[d[d[dM[(i)(T)]/dw]/dT]/dT]/dw, d[d[d[dM[(m)(T)]/dw]/dT]/dT]/dw, d[d[d[dM[(t,w)(T)]/dw]/dT]/dT]/dw, d[d[d[dM[(t,a)(T)]/dw]/dT]/dT]/dw, d[d[d[dM[(t,i)(T)]/dw]/dT]/dT]/dw, d[d[d[dM[(t,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dM[(w,a)(T)]/dw]/dT]/dT]/dw, d[d[d[dM[(w,i)(T)]/dw]/dT]/dT]/dw, d[d[d[dM[(w,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dM[(a,i)(T)]/dw]/dT]/dT]/dw, d[d[d[dM[(a,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dM[(i,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dM[(t,w,a)(T)]/dw]/dT]/dT]/dw, d[d[d[dM[(t,w,i)(T)]/dw]/dT]/dT]/dw, d[d[d[dM[(t,w,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dM[(t,a,i)(T)]/dw]/dT]/dT]/dw, d[d[d[dM[(t,a,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dM[(t,i,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dM[(w,a,i)(T)]/dw]/dT]/dT]/dw, d[d[d[dM[(w,a,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dM[(w,i,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dM[(a,i,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dM[(t,w,a,i)(T)]/dw]/dT]/dT]/dw, d[d[d[dM[(t,w,a,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dM[(t,w,i,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dM[(t,a,i,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dM[(w,a,i,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dM[(t,w,a,i,m)(T)]/dw]/dT]/dT]/dw.

 

or as:

 

d[d[d[dM[(t)(T)]/dT]/dw]/dw]/dT, d[d[d[dM[(w)(T)]/dT]/dw]/dw]/dT, d[d[d[dM[(a)(T)]/dT]/dw]/dw]/dT, d[d[d[dM[(i)(T)]/dT]/dw]/dw]/dT, d[d[d[dM[(m)(T)]/dT]/dw]/dw]/dT, d[d[d[dM[(t,w)(T)]/dT]/dw]/dw]/dT, d[d[d[dM[(t,a)(T)]/dT]/dw]/dw]/dT, d[d[d[dM[(t,i)(T)]/dT]/dw]/dw]/dT, d[d[d[dM[(t,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dM[(w,a)(T)]/dT]/dw]/dw]/dT, d[d[d[dM[(w,i)(T)]/dT]/dw]/dw]/dT, d[d[d[dM[(w,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dM[(a,i)(T)]/dT]/dw]/dw]/dT, d[d[d[dM[(a,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dM[(i,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dM[(t,w,a)(T)]/dT]/dw]/dw]/dT, d[d[d[dM[(t,w,i)(T)]/dT]/dw]/dw]/dT, d[d[d[dM[(t,w,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dM[(t,a,i)(T)]/dT]/dw]/dw]/dT, d[d[d[dM[(t,a,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dM[(t,i,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dM[(w,a,i)(T)]/dT]/dw]/dw]/dT, d[d[d[dM[(w,a,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dM[(w,i,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dM[(a,i,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dM[(t,w,a,i)(T)]/dT]/dw]/dw]/dT, d[d[d[dM[(t,w,a,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dM[(t,w,i,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dM[(t,a,i,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dM[(w,a,i,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dM[(t,w,a,i,m)(T)]/dT]/dw]/dw]/dT.

 

 

or as;

 

 

 

 

d[d[d[dM(t)/dw]/dw]/dT]/dT, d[d[d[dM(w)/dw]/dw]/dT]/dT, d[d[d[dM(a)/dw]/dw]/dT]/dT, d[d[d[dM(i)/dw]/dw]/dT]/dT, d[d[d[dM(m)/dw]/dw]/dT]/dT, d[d[d[dM(t,w)/dw]/dw]/dT]/dT, d[d[d[dM(t,a)/dw]/dw]/dT]/dT, d[d[d[dM(t,i)/dw]/dw]/dT]/dT, d[d[d[dM(t,m)/dw]/dw]/dT]/dT, d[d[d[dM(w,a)/dw]/dw]/dT]/dT, d[d[d[dM(w,i)/dw]/dw]/dT]/dT, d[d[d[dM(w,m)/dw]/dw]/dT]/dT, d[d[d[dM(a,i)/dw]/dw]/dT]/dT, d[d[d[dM(a,m)/dw]/dw]/dT]/dT, d[d[d[dM(i,m)/dw]/dw]/dT]/dT, d[d[d[dM(t,w,a)/dw]/dw]/dT]/dT, d[d[d[dM(t,w,i)/dw]/dw]/dT]/dT, d[d[d[dM(t,w,m)/dw]/dw]/dT]/dT, d[d[d[dM(t,a,i)/dw]/dw]/dT]/dT, d[d[d[dM(t,a,m)/dw]/dw]/dT]/dT,  d[d[d[dM(t,i,m)/dw]/dw]/dT]/dT, d[d[d[dM(w,a,i)/dw]/dw]/dT]/dT, d[d[d[dM(w,a,m)/dw]/dw]/dT]/dT, d[d[d[dM(w,i,m)/dw]/dw]/dT]/dT, d[d[d[dM(a,i,m)/dw]/dw]/dT]/dT, d[d[d[dM(t,w,a,i)/dw]/dw]/dT]/dT, d[d[d[dM(t,w,a,m)/dw/dw, d[d[d[dM(t,w,i,m)/dw]/dw]/dT]/dT, d[d[d[dM(t,a,i,m)/dw]/dw]/dT]/dT, d[d[d[dM(w,a,i,m)/dw]/dw]/dT]/dT, d[d[d[dM(t,w,a,i,m)/dw]/dw]/dT]/dT..

 

or as:

 

d[d[d[dM(t)/dT]/dw]/dT]/dw, d[d[d[dM(w)/dT]/dw]/dT]/dw, d[d[d[dM(a)/dT]/dw]/dT]/dw, d[d[d[dM(i)/dT]/dw]/dT]/dw, d[d[d[dM(m)/dT]/dw]/dT]/dw, d[d[d[dM(t,w)/dT]/dw]/dT]/dw, d[d[d[dM(t,a)/dT]/dw]/dT]/dw, d[d[d[dM(t,i)/dT]/dw]/dT]/dw, d[d[d[dM(t,m)/dT]/dw]/dT]/dw, d[d[d[dM(w,a)/dT]/dw]/dT]/dw, d[d[d[dM(w,i)/dT]/dw]/dT]/dw, d[d[d[dM(w,m)/dT]/dw]/dT]/dw, d[d[d[dM(a,i)/dT]/dw]/dT]/dw, d[d[d[dM(a,m)/dT]/dw]/dT]/dw, d[d[d[dM(i,m)/ dT]/dw]/dT]/dw, d[d[d[dM(t,w,a)/dT]/dw]/dT]/dw, d[d[d[dM(t,w,i)/dT]/dw]/dT]/dw, d[d[d[dM(t,w,m)/dT]/dw]/dT]/dw, d[d[d[dM(t,a,i)/dT]/dw]/dT]/dw, d[d[d[dM(t,a,m)/dT]/dw]/dT]/dw,  d[d[d[dM(t,i,m)/dT]/dw]/dT]/dw, d[d[d[dM(w,a,i)/dT]/dw]/dT]/dw, d[d[d[dM(w,a,m)/dT]/dw]/dT]/dw, d[d[d[dM(w,i,m)/dT]/dw]/dT]/dw, d[d[d[dM(a,i,m)/dT]/dw]/dT]/dw, d[d[d[dM(t,w,a,i)/dT]/dw]/dT]/dw, d[d[d[dM(t,w,a,m)/dw/dw, d[d[d[dM(t,w,i,m)/dT]/dw]/dT]/dw, d[d[d[dM(t,a,i,m)/dT]/dw]/dT]/dw, d[d[d[dM(w,a,i,m)/dT]/dw]/dT]/dw, d[d[d[dM(t,w,a,i,m)/dT]/dw]/dT]/dw..

 

or as:

 

d[d[d[dM(t)/dT]/dT]/dw]/dw, d[d[d[dM(w)/dT]/dT]/dw]/dw, d[d[d[dM(a)/dT]/dT]/dw]/dw, d[d[d[dM(i)/dT]/dT]/dw]/dw, d[d[d[dM(m)/dT]/dT]/dw]/dw, d[d[d[dM(t,w)/dT]/dT]/dw]/dw, d[d[d[dM(t,a)/dT]/dT]/dw]/dw, d[d[d[dM(t,i)/dT]/dT]/dw]/dw, d[d[d[dM(t,m)/dT]/dT]/dw]/dw, d[d[d[dM(w,a)/dT]/dT]/dw]/dw, d[d[d[dM(w,i)/dT]/dT]/dw]/dw, d[d[d[dM(w,m)/dT]/dT]/dw]/dw, d[d[d[dM(a,i)/dT]/dT]/dw]/dw, d[d[d[dM(a,m)/ dT]/dT]/dw]/dw, d[d[d[dM(i,m)/ dT]/dT]/dw]/dw, d[d[d[dM(t,w,a)/dT]/dT]/dw]/dw, d[d[d[dM(t,w,i)/dT]/dT]/dw]/dw, d[d[d[dM(t,w,m)/dT]/dT]/dw]/dw, d[d[d[dM(t,a,i)/dT]/dT]/dw]/dw, d[d[d[dM(t,a,m)/dT]/dT]/dw]/dw,  d[d[d[dM(t,i,m)/dT]/dT]/dw]/dw, d[d[d[dM(w,a,i)/dT]/dT]/dw]/dw, d[d[d[dM(w,a,m)/dT]/dT]/dw]/dw, d[d[d[dM(w,i,m)/dT]/dT]/dw]/dw, d[d[d[dM(a,i,m)/dT]/dT]/dw]/dw, d[d[d[dM(t,w,a,i)/dT]/dT]/dw]/dw, d[d[d[dM(t,w,a,m)/dw/dw, d[d[d[dM(t,w,i,m)/dT]/dT]/dw]/dw, d[d[d[dM(t,a,i,m)/dT]/dT]/dw]/dw, d[d[d[dM(w,a,i,m)/dT]/dT]/dw]/dw, d[d[d[dM(t,w,a,i,m)/dT]/dT]/dw]/dw..

 

We can also take higher order duel dimensional derivatives of memory as a function of will and time but the symbolic expression of the set of such derivatives very soon becomes excessively lengthly to write and so these higher order derivatives as such are not mentioned here except to say that they would be computed in an analogous manner to the second order duel dimensional derivatives described above.

 

 

We can also express memory qualitatively, statistically, and perhaps with the use of some forms of real analysis as a derivative with respect to affect or of a.

 

Given that M(a) =  M(t and/or w and/or a and/or i and/or m), the following first order derivatives of memory with respect to affect are possible.

 

 

dM(t)/da, dM(w)/da, dM(a)/da, dM(i)/da, dM(m)/da, dM(t,w)/da, dM(t,a)/da, dM(t,i)/da, dM(t,m)/da, dM(w,a)/da, dM(w,i)/da, dM(w,m)/da, dM(a,i)/da, dM(a,m)/da, dM(i,m)/da, dM(t,w,a)/da, dM(t,w,i)/da, dM(t,w,m)/da, dM(t,a,i)/da, dM(t,a,m)/da, dM(t,i,m)/da, dM(w,a,i)/da, dM(w,a,m)/da, dM(w,i,m)/da, dM(a,i,m)/da, dM(t,w,a,i)/da, dM(t,w,a,m)/da, dM(t,w,i,m)/da, dM(t,a,i,m)/da, dM(w,a,i,m)/da, dM(t,w,a,i,m)/da.

 

 

Or more succinctly, dM/da = dM(t and/or w and/or a and/or i and/or m)/da

 

 

Or perhaps dM(a)/da =d M{[t(a)] and/or [w(a)] and/or [a(a)] and/or [i(a)] and/or [m(a)]}/da.

 

 

Likewise, we can take the second affect derivatives of  M as follows:

 

 

 

d[dM(t)/da]/da, d[dM(w)/da]/da, d[dM(a)/da]/da, d[dM(i)/da]/da, d[dM(m)/da]/da, d[dM(t,w)/da]/da, d[dM(t,a)/da]/da, d[dM(t,i)/da]/da, d[dM(t,m)/da]/da, d[dM(w,a)/da]/da, d[dM(w,i)/da]/da, d[dM(w,m)/da]/da, d[dM(a,i)/da]/da, d[dM(a,m)/da]/da, d[dM(i,m)/da/da, d[dM(t,w,a)/da]/da, d[dM(t,w,i)/da]/da, d[dM(t,w,m)/da]/da, d[dM(t,a,i)/da]/da, d[dM(t,a,m)/da]/da,  d[dM(t,i,m)/da]/da, d[dM(w,a,i)/da]/da, d[dM(w,a,m)/da]/da, d[dM(w,i,m)/da]/da, d[dM(a,i,m)/da]/da, d[dM(t,w,a,i)/da]/da, d[dM(t,w,a,m)/da/da, d[dM(t,w,i,m)/da]/da, d[dM(t,a,i,m)/da]/da, d[dM(w,a,i,m)/da]/da, d[dM(t,w,a,i,m)/da]/da..

 

 

or more succinctly, as d(dM/da)/da = d[d M(t and/or w and/or a and/or i and/or m)/da]/da = Ma2

 

 

or as

 

 

d[dM(a)/da]/da  = d[d M{[t(a)] and/or [w(a)] and/or [a(a)] and/or [i(a)] and/or [m(a)]}/da]/da = Ma2.

 

 

 

Likewise, we can take the third affect derivatives of  M as follows:

 

 

 

d[d[dM(t)/da]/da]/da, d[d[dM(w)/da]/da]/da, d[d[dM(a)/da]/da]/da, d[d[dM(i)/da]/da]/da, d[d[dM(m)/da]/da]/da, d[d[dM(t,w)/da]/da]/da, d[d[dM(t,a)/da]/da]/da, d[d[dM(t,i)/da]/da]/da, d[d[dM(t,m)/da]/da]/da, d[d[dM(w,a)/da]/da]/da, d[d[dM(w,i)/da]/da]/da, d[d[dM(w,m)/da]/da]/da, d[d[dM(a,i)/da]/da]/da, d[d[dM(a,m)/da]/da]/da, d[d[dM(i,m)/da/da]/da, d[d[dM(t,w,a)/da]/da]/da, d[d[dM(t,w,i)/da]/da]/da, d[d[dM(t,w,m)/da]/da]/da, d[d[dM(t,a,i)/da]/da]/da, d[d[dM(t,a,m)/da]/da]/da,  d[d[dM(t,i,m)/da]/da]/da, d[d[dM(w,a,i)/da]/da]/da, d[d[dM(w,a,m)/da]/da]/da, d[d[dM(w,i,m)/da]/da]/da, d[d[dM(a,i,m)/da]/da]/da, d[d[dM(t,w,a,i)/da]/da]/da, d[d[dM(t,w,a,m)/da/da]/da, d[d[dM(t,w,i,m)/da]/da]/da, d[d[dM(t,a,i,m)/da]/da]/da, d[d[dM(w,a,i,m)/da]/da]/da, d[d[dM(t,w,a,i,m)/da]/da]/da.

 

 

or more succinctly, as d[d(dM/da)/da]/da = d[d[d M(t and/or w and/or a and/or i and/or m)/da]/da]/da = Ma3

 

 

or as

 

 

d[d[dM(a)/da]/da]/da  = d[d[d M{[t(a)] and/or [w(a)] and/or [a(a)] and/or [i(a)] and/or [m(a)]}/da]/da]/da = Ma3.

 

 

We can also form the expressions;

 

 

d[d[f(M)]/da]/da = d{d [M[t(a)]]/da and/or d[M[w(a)]]/da and/or d[M[a(a)]]/da and/or d[M[i(a)]]/da and/or d[M[m(a)]]/da}/da  = f(Ma)2

 

 

and

 

 

d[d[d[f(M)]/da]/da]/da = d{d{ d [M[t(a)]]/da and/or d[M[w(a)]]/da and/or d[M[a(a)]]/da and/or d[M[i(a)]]/da and/or d[M[m(a)]]/da}/da}/da  = f(Ma)3A, where A stands for type A differentiation which is not to be confused with the meaning of so-called Type A personality as A is used as an ordinal in a totally different context here.

 

 

and

 

 

d[d[d[f(M)]/da]/da]/da = d{d[d [M[t(a)]]/da]/da  and/or d[d [M[w(a)]]/da]/da  and/or d[d [M[a(a)]]/da]/da  and/or d[d [M[i(a)]]/da]/da  and/or d[d [M[m(a)]]/da]/da }/da = f(Ma)3B, where B stands for type B differentiation which is not to be confused with the meaning of so-called Type  B personality as B is used as an ordinal in a totally different context here. .

 

 

In fact, one can form yet higher order derivatives of memories with respect to affect as follows.

 

 

Ma5 = d Ma4/da = d[dMa3/da]/da

 

 

 

Ma5 = dMa4/da =  d[d[d[d[d M{[t(a)] and/or [w(a)] and/or [a(a)] and/or [i(a)] and/or [m(a)]}/da]/da]/da]/da]/da.

 

 

 

f(Ma)5A = d[f(Ma)4A]/da = d[d [f(Ma)3A]/da]/da =  d{d{d{d{ d [M[t(a)]]/da and/or d[M[w(a)]]/da and/or d[M[a(a)]]/da and/or d[M[i(a)]]/da and/or d[M[m(a)]]/da}/da}/da]/da]/da

 

 

 

 

Ma6 = d Ma5/da = d[d Ma4/da]/da = d[d[dMa3/da]/da]/da

 

 

 

Ma6 = dMa5/da = d[d[d[d[d[d M{[t(a)] and/or [w(a)] and/or [a(a)] and/or [i(a)] and/or [m(a)]}/da]/da]/da]/da]/da]/da

 

 

 

f(Ma)6A = d[f(Ma)5A]/da = d{ d{d{d{d{ d [M[t(a)]]/da and/or d[M[w(a)]]/da and/or d[M[a(a)]]/da and/or d[M[i(a)]]/da and/or d[M[m(a)]]/da}/da}/da]/da]/da]/da

 

 

 

 

Ma7 = dMa6/da

 

f(Ma)7A = d[f(Ma)6A]/da

 

 

Ma8 = d Ma7/da

 

f(Ma)8A = d[f(Ma)7A]/da

 

 

 

Ma9 = d Ma8/da

 

f(Ma)9A = d[f(Ma)8A]/da

 

 

Ma10…, Ma11…, Ma12 … etc.

 

 

Anyone for Ma ensemble, or Ma infinity scrapper, or Ma (Aleph 0), or Ma(Aleph 1), or Ma (Aleph 2), or how about Ma Aleph (Aleph 0), or Ma Aleph (Aleph 1) , or Ma Aleph (Aleph 2), or even Ma Aleph (Aleph (Aleph 0)), or Ma Aleph (Aleph (Aleph 1)), or Ma Aleph (Aleph (Aleph 2)), and so on?

 

Thus, for the set of the sets of derivatives of Ma1 through Ma(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ma1 through Ma(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)},…, {П(0,31)[R]}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ma1 through Ma(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ma1 through Ma(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the derivative states in the set of the sets of derivatives of Ma1 through Ma(Aleph 0) is plausible equal to:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ma1 through Ma(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ma1 through Ma(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}}}.

 

For the set of the sets of derivatives of Ma1 through Ma(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Ma(Aleph 0) derivative space at the level of 0/(Aleph 0), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Ma1 through Ma(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ma1 through Ma(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ma1 through Ma(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ma1 through Ma(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Ma1 through Ma(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ma1 through Ma(Aleph 1), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Ma1 through  Ma(Aleph 2), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Ma1 through Ma(Aleph 3), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Ma(Aleph 0) derivative space at the level of 0/(Aleph 1), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Ma1 through Ma(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ma1 through Ma(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ma1 through Ma(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ma1 through  Ma(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations  for the set of the sets of derivatives of Ma1 through Ma(Aleph 0) is plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ma1 through Ma(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Ma1 through Ma(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Ma1 through Ma(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

 

For super-continuous Ia(Aleph 0) derivative space at the level of 0/(Aleph 2), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Ma1 through Ma(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ma1 through Ma(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ma1 through Ma(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ma1 through Ma(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Ma1 through Ma(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ma1 through Ma(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Ma1 through Ma(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Ma1 through Ma(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

Similar series can be developed for super-continuity at any applicable level such as 0/(Aleph 3), 0/(Aleph 4), 0/(Aleph 5),…, 0/(Aleph Ω), 0/(Aleph (Aleph 0)), …, 0/(Aleph (Aleph 1)), …, 0/(Aleph (Aleph 2)), …, 0/(Aleph (Aleph 3)),…, 0/(Aleph (Aleph Ω)),…, 0/(Aleph (Aleph (Aleph 0))), …, 0/(Aleph (Aleph (Aleph 1))),…, 0/(Aleph (Aleph (Aleph 2))),…, 0/(Aleph (Aleph (Aleph 3))),…, 0/(Aleph (Aleph  (Aleph Ω))), …

 

An so-on ad infinitum.

 

In addition to these numerical functions of Ma as functions of summation series of product series functions, in order to really appreciate the enourmous complexity of the human soul in terms of its potential to evolve and be differentiated from all other souls in its characteristics, we would need to consider how every single category and even every single species of memory of the form Ma can very. Since there may exist an arbitrarily high infinite number species of Ma, the number of numerical functions of Ma is utterly beyond recogning. I will cover such notions in terms of mathematical notation in yet another series of articles I will write on this general concept.

 

 

 

Perhaps these numbers are applicable when one considers that the human soul, in its accidental form and perhaps even in its substantial form stores all experience and other psychodynamics based phenomenon. Every experience adds to the accidental form of the human soul and this includes the souls of all those still alive on Earth, all those in Purgatory, all those in Heaven, all those in Hell, and all those in any Limbo.

Since the human soul can grow without limit in terms of its psychodynamic time –flow world line, such a consideration offers another mechanism where the number of derivative states, combinations of derivative states, and even super-continuity of the derivative state space can grow forever.

 

Folks, for those of you who might balk at me for including literally all souls in the above consideration, including the souls in Hell, as well as bodily extraterrestrial souls and the souls of so-called bodily ultraterrestials sometimes referred to as etherians in the new age UFO buff culture, my reply is that we simply do not understand the full scope of GOD’s Divine Economy. We may never fully comprehend the scope of the Divine Economy because such an utterly eternal scheme, is, well, eternal and never ending.

 

 

 

The general meaning of affect derivatives of memory can be viewed as the manner in which the qualitative and/or quantitative aspects of memory as a function of affect very with affect. The manner in which memories very with affect may be multi- affect-aspect dimensional wherein the dimensions of derivations can be multiple, and wherein the derivations can be taken in parallel, series parallel or in serial manner. The differentials can be partial or non-partial derivatives, or both partial and non-partial for a given computation.

 

In fact, since there is in theory, no limit to the numbers of qualitatively and quantitatively different affective states, and perhaps no limit to the number of possible different types or classes of affective states, wherein each person has his or her own unique affective experiences, the number of affect dimensions that can effect memories is literally infinite, given the entirety of the set of created persons, and perhaps also literally infinite for each person as an individual, although we can not intellectually and intuitively understand this infinite number.

 

 

It is interesting to consider the ramifactions of being able to perform realistic calculations involving affect derivatives of memory from a mathematical, theoretical, scientific,  and philosophical perspective.

 

Persons for which one or more nth order derivatives of memory with respect to affect that have large absolute values would tend to have their memories highly influenced by affect, or at least for the memories under consideration with respect to the dimension of the specific affect type(s) or class(es) for which the differentiation(s) are being performed. Perhaps a strong coupling between memory and affect indicates a well integrated personality and commensurately, a high degree of memory capacity and a high degree of memory intelligence as well as perhaps very strong affect power.

 

 

 

We can also consider that two dimensional nth ordered derivatives of memory with respect to affect and time, or with respect to a and T, respectively.

 

Given that M[(a)(T)] =  M[(t and/or w and/or a and/or i and/or m)(w)(T)], the following first order two dimensional derivatives of memory with respect to affect and Time are possible.

 

 

d[dM[(t)(T)]/da]/dT, d[dM[(w)(T)]/da]/dT, d[dM[(a)(T)]/da]/dT, d[dM[(i)(T)]/da]/dT, d[dM[(m)(T)]/da]/dT, d[dM[(t,w)(T)]/da]/dT, d[dM[(t,a)(T)]/da]/dT, d[dM[(t,i)(T)]/da]/dT, d[dM[(t,m)(T)]/da]/dT, d[dM[(w,a)(T)]/da]/dT, d[dM[(w,i)(T)]/da]/dT, d[dM[(w,m)(T)]/da]/dT, d[dM[(a,i)(T)]/da]/dT, d[dM[(a,m)(T)]/da]/dT, d[dM[(i,m)(T)]/da]/dT, d[dM[(t,w,a)(T)]/da]/dT, d[dM[(t,w,i)(T)]/da]/dT, d[dM[(t,w,m)(T)]/da]/dT, d[dM[(t,a,i)(T)]/da]/dT, d[dM[(t,a,m)(T)]/da]/dT, d[dM[(t,i,m)(T)]/da]/dT, d[dM[(w,a,i)(T)]/da]/dT, d[dM[(w,a,m)(T)]/da]/dT, d[dM[(w,i,m)(T)]/da]/dT, d[dM[(a,i,m)(T)]/da]/dT, d[dM[(t,w,a,i)(T)]/da]/dT, d[dM[(t,w,a,m)(T)]/da]/dT, d[dM[(t,w,i,m)(T)]/da]/dT, d[dM[(t,a,i,m)(T)]/da]/dT, d[dM[(w,a,i,m)(T)]/da]/dT, d[dM[(t,w,a,i,m)(T)]/da]/dT.

 

 

Or more succinctly,  d[dM(T)/da]/dT = d[dM[(T)(t and/or w and/or a and/or i and/or m)]/da]/dT

 

or

 

d[dM(T)/dT]/da = d[dM[(T)(t and/or w and/or a and/or i and/or m)]/dT]/da

 

 

 

 

 

Or perhaps d[d M[(a)(T)]/da]/dT  = d[d M [{[t(a)] and/or [w(a)] and/or [a(a)] and/or [i(a)] and/or [m(a)]}(T)]/da]/dT

 

or

 

Or perhaps d[d M[(a)(T)]/dT]/da  = d[d M [{[t(a)] and/or [w(a)] and/or [a(a)] and/or [i(a)] and/or [m(a)]}(T)]/dT]/da

 

 

 

Likewise, we can take the second dual dimension affect -time derivatives of  M as follows:

 

d[d[d[dM[(t)(T)]/da]/dT]/da]/dT, d[d[d[dM[(w)(T)]/da]/dT]/da]/dT, d[d[d[dM[(a)(T)]/da]/dT]/da]/dT, d[d[d[dM[(i)(T)]/da]/dT]/da]/dT, d[d[d[dM[(m)(T)]/da]/dT]/da]/dT, d[d[d[dM[(t,w)(T)]/da]/dT]/da]/dT, d[d[d[dM[(t,a)(T)]/da]/dT]/da]/dT, d[d[d[dM[(t,i)(T)]/da]/dT]/da]/dT, d[d[d[dM[(t,m)(T)]/da]/dT]/da]/dT, d[d[d[dM[(w,a)(T)]/da]/dT]/da]/dT, d[d[d[dM[(w,i)(T)]/da]/dT]/da]/dT, d[d[d[dM[(w,m)(T)]/da]/dT]/da]/dT, d[d[d[dM[(a,i)(T)]/da]/dT]/da]/dT, d[d[d[dM[(a,m)(T)]/da]/dT]/da]/dT, d[d[d[dM[(i,m)(T)]/da]/dT]/da]/dT, d[d[d[dM[(t,w,a)(T)]/da]/dT]/da]/dT, d[d[d[dM[(t,w,i)(T)]/da]/dT]/da]/dT, d[d[d[dM[(t,w,m)(T)]/da]/dT]/da]/dT, d[d[d[dM[(t,a,i)(T)]/da]/dT]/da]/dT, d[d[d[dM[(t,a,m)(T)]/da]/dT]/da]/dT, d[d[d[dM[(t,i,m)(T)]/da]/dT]/da]/dT, d[d[d[dM[(w,a,i)(T)]/da]/dT]/da]/dT, d[d[d[dM[(w,a,m)(T)]/da]/dT]/da]/dT, d[d[d[dM[(w,i,m)(T)]/da]/dT]/da]/dT, d[d[d[dM[(a,i,m)(T)]/da]/dT]/da]/dT, d[d[d[dM[(t,w,a,i)(T)]/da]/dT]/da]/dT, d[d[d[dM[(t,w,a,m)(T)]/da]/dT]/da]/dT, d[d[d[dM[(t,w,i,m)(T)]/da]/dT]/da]/dT, d[d[d[dM[(t,a,i,m)(T)]/da]/dT]/da]/dT, d[d[d[dM[(w,a,i,m)(T)]/da]/dT]/da]/dT, d[d[d[dM[(t,w,a,i,m)(T)]/da]/dT]/da]/dT.

 

or as:

 

 

 

d[d[d[dM[(t)(T)]/da]/dT]/dT]/da, d[d[d[dM[(w)(T)]/da]/dT]/dT]/da, d[d[d[dM[(a)(T)]/da]/dT]/dT]/da, d[d[d[dM[(i)(T)]/da]/dT]/dT]/da, d[d[d[dM[(m)(T)]/da]/dT]/dT]/da, d[d[d[dM[(t,w)(T)]/da]/dT]/dT]/da, d[d[d[dM[(t,a)(T)]/da]/dT]/dT]/da, d[d[d[dM[(t,i)(T)]/da]/dT]/dT]/da, d[d[d[dM[(t,m)(T)]/da]/dT]/dT]/da, d[d[d[dM[(w,a)(T)]/da]/dT]/dT]/da, d[d[d[dM[(w,i)(T)]/da]/dT]/dT]/da, d[d[d[dM[(w,m)(T)]/da]/dT]/dT]/da, d[d[d[dM[(a,i)(T)]/da]/dT]/dT]/da, d[d[d[dM[(a,m)(T)]/da]/dT]/dT]/da, d[d[d[dM[(i,m)(T)]/da]/dT]/dT]/da, d[d[d[dM[(t,w,a)(T)]/da]/dT]/dT]/da, d[d[d[dM[(t,w,i)(T)]/da]/dT]/dT]/da, d[d[d[dM[(t,w,m)(T)]/da]/dT]/dT]/da, d[d[d[dM[(t,a,i)(T)]/da]/dT]/dT]/da, d[d[d[dM[(t,a,m)(T)]/da]/dT]/dT]/da, d[d[d[dM[(t,i,m)(T)]/da]/dT]/dT]/da, d[d[d[dM[(w,a,i)(T)]/da]/dT]/dT]/da, d[d[d[dM[(w,a,m)(T)]/da]/dT]/dT]/da, d[d[d[dM[(w,i,m)(T)]/da]/dT]/dT]/da, d[d[d[dM[(a,i,m)(T)]/da]/dT]/dT]/da, d[d[d[dM[(t,w,a,i)(T)]/da]/dT]/dT]/da, d[d[d[dM[(t,w,a,m)(T)]/da]/dT]/dT]/da, d[d[d[dM[(t,w,i,m)(T)]/da]/dT]/dT]/da, d[d[d[dM[(t,a,i,m)(T)]/da]/dT]/dT]/da, d[d[d[dM[(w,a,i,m)(T)]/da]/dT]/dT]/da, d[d[d[dM[(t,w,a,i,m)(T)]/da]/dT]/dT]/da.

 

or as:

 

d[d[d[dM[(t)(T)]/dT]/da]/da]/dT, d[d[d[dM[(w)(T)]/dT]/da]/da]/dT, d[d[d[dM[(a)(T)]/dT]/da]/da]/dT, d[d[d[dM[(i)(T)]/dT]/da]/da]/dT, d[d[d[dM[(m)(T)]/dT]/da]/da]/dT, d[d[d[dM[(t,w)(T)]/dT]/da]/da]/dT, d[d[d[dM[(t,a)(T)]/dT]/da]/da]/dT, d[d[d[dM[(t,i)(T)]/dT]/da]/da]/dT, d[d[d[dM[(t,m)(T)]/dT]/da]/da]/dT, d[d[d[dM[(w,a)(T)]/dT]/da]/da]/dT, d[d[d[dM[(w,i)(T)]/dT]/da]/da]/dT, d[d[d[dM[(w,m)(T)]/dT]/da]/da]/dT, d[d[d[dM[(a,i)(T)]/dT]/da]/da]/dT, d[d[d[dM[(a,m)(T)]/dT]/da]/da]/dT, d[d[d[dM[(i,m)(T)]/dT]/da]/da]/dT, d[d[d[dM[(t,w,a)(T)]/dT]/da]/da]/dT, d[d[d[dM[(t,w,i)(T)]/dT]/da]/da]/dT, d[d[d[dM[(t,w,m)(T)]/dT]/da]/da]/dT, d[d[d[dM[(t,a,i)(T)]/dT]/da]/da]/dT, d[d[d[dM[(t,a,m)(T)]/dT]/da]/da]/dT, d[d[d[dM[(t,i,m)(T)]/dT]/da]/da]/dT, d[d[d[dM[(w,a,i)(T)]/dT]/da]/da]/dT, d[d[d[dM[(w,a,m)(T)]/dT]/da]/da]/dT, d[d[d[dM[(w,i,m)(T)]/dT]/da]/da]/dT, d[d[d[dM[(a,i,m)(T)]/dT]/da]/da]/dT, d[d[d[dM[(t,w,a,i)(T)]/dT]/da]/da]/dT, d[d[d[dM[(t,w,a,m)(T)]/dT]/da]/da]/dT, d[d[d[dM[(t,w,i,m)(T)]/dT]/da]/da]/dT, d[d[d[dM[(t,a,i,m)(T)]/dT]/da]/da]/dT, d[d[d[dM[(w,a,i,m)(T)]/dT]/da]/da]/dT, d[d[d[dM[(t,w,a,i,m)(T)]/dT]/da]/da]/dT.

 

 

or as;

 

 

 

 

d[d[d[dM(t)/da]/da]/dT]/dT, d[d[d[dM(w)/da]/da]/dT]/dT, d[d[d[dM(a)/da]/da]/dT]/dT, d[d[d[dM(i)/da]/da]/dT]/dT, d[d[d[dM(m)/da]/da]/dT]/dT, d[d[d[dM(t,w)/da]/da]/dT]/dT, d[d[d[dM(t,a)/da]/da]/dT]/dT, d[d[d[dM(t,i)/da]/da]/dT]/dT, d[d[d[dM(t,m)/da]/da]/dT]/dT, d[d[d[dM(w,a)/da]/da]/dT]/dT, d[d[d[dM(w,i)/da]/da]/dT]/dT, d[d[d[dM(w,m)/da]/da]/dT]/dT, d[d[d[dM(a,i)/da]/da]/dT]/dT, d[d[d[dM(a,m)/da]/da]/dT]/dT, d[d[d[dM(i,m)/da]/da]/dT]/dT, d[d[d[dM(t,w,a)/da]/da]/dT]/dT, d[d[d[dM(t,w,i)/da]/da]/dT]/dT, d[d[d[dM(t,w,m)/da]/da]/dT]/dT, d[d[d[dM(t,a,i)/da]/da]/dT]/dT, d[d[d[dM(t,a,m)/da]/da]/dT]/dT,  d[d[d[dM(t,i,m)/da]/da]/dT]/dT, d[d[d[dM(w,a,i)/da]/da]/dT]/dT, d[d[d[dM(w,a,m)/da]/da]/dT]/dT, d[d[d[dM(w,i,m)/da]/da]/dT]/dT, d[d[d[dM(a,i,m)/da]/da]/dT]/dT, d[d[d[dM(t,w,a,i)/da]/da]/dT]/dT, d[d[d[dM(t,w,a,m)/da/da, d[d[d[dM(t,w,i,m)/da]/da]/dT]/dT, d[d[d[dM(t,a,i,m)/da]/da]/dT]/dT, d[d[d[dM(w,a,i,m)/da]/da]/dT]/dT, d[d[d[dM(t,w,a,i,m)/da]/da]/dT]/dT..

 

or as:

 

d[d[d[dM(t)/dT]/da]/dT]/da, d[d[d[dM(w)/dT]/da]/dT]/da, d[d[d[dM(a)/dT]/da]/dT]/da, d[d[d[dM(i)/dT]/da]/dT]/da, d[d[d[dM(m)/dT]/da]/dT]/da, d[d[d[dM(t,w)/dT]/da]/dT]/da, d[d[d[dM(t,a)/dT]/da]/dT]/da, d[d[d[dM(t,i)/dT]/da]/dT]/da, d[d[d[dM(t,m)/dT]/da]/dT]/da, d[d[d[dM(w,a)/dT]/da]/dT]/da, d[d[d[dM(w,i)/dT]/da]/dT]/da, d[d[d[dM(w,m)/dT]/da]/dT]/da, d[d[d[dM(a,i)/dT]/da]/dT]/da, d[d[d[dM(a,m)/dT]/da]/dT]/da, d[d[d[dM(i,m)/ dT]/da]/dT]/da, d[d[d[dM(t,w,a)/dT]/da]/dT]/da, d[d[d[dM(t,w,i)/dT]/da]/dT]/da, d[d[d[dM(t,w,m)/dT]/da]/dT]/da, d[d[d[dM(t,a,i)/dT]/da]/dT]/da, d[d[d[dM(t,a,m)/dT]/da]/dT]/da,  d[d[d[dM(t,i,m)/dT]/da]/dT]/da, d[d[d[dM(w,a,i)/dT]/da]/dT]/da, d[d[d[dM(w,a,m)/dT]/da]/dT]/da, d[d[d[dM(w,i,m)/dT]/da]/dT]/da, d[d[d[dM(a,i,m)/dT]/da]/dT]/da, d[d[d[dM(t,w,a,i)/dT]/da]/dT]/da, d[d[d[dM(t,w,a,m)/da/da, d[d[d[dM(t,w,i,m)/dT]/da]/dT]/da, d[d[d[dM(t,a,i,m)/dT]/da]/dT]/da, d[d[d[dM(w,a,i,m)/dT]/da]/dT]/da, d[d[d[dM(t,w,a,i,m)/dT]/da]/dT]/da..

 

or as:

 

d[d[d[dM(t)/dT]/dT]/da]/da, d[d[d[dM(w)/dT]/dT]/da]/da, d[d[d[dM(a)/dT]/dT]/da]/da, d[d[d[dM(i)/dT]/dT]/da]/da, d[d[d[dM(m)/dT]/dT]/da]/da, d[d[d[dM(t,w)/dT]/dT]/da]/da, d[d[d[dM(t,a)/dT]/dT]/da]/da, d[d[d[dM(t,i)/dT]/dT]/da]/da, d[d[d[dM(t,m)/dT]/dT]/da]/da, d[d[d[dM(w,a)/dT]/dT]/da]/da, d[d[d[dM(w,i)/dT]/dT]/da]/da, d[d[d[dM(w,m)/dT]/dT]/da]/da, d[d[d[dM(a,i)/dT]/dT]/da]/da, d[d[d[dM(a,m)/ dT]/dT]/da]/da, d[d[d[dM(i,m)/ dT]/dT]/da]/da, d[d[d[dM(t,w,a)/dT]/dT]/da]/da, d[d[d[dM(t,w,i)/dT]/dT]/da]/da, d[d[d[dM(t,w,m)/dT]/dT]/da]/da, d[d[d[dM(t,a,i)/dT]/dT]/da]/da, d[d[d[dM(t,a,m)/dT]/dT]/da]/da,  d[d[d[dM(t,i,m)/dT]/dT]/da]/da, d[d[d[dM(w,a,i)/dT]/dT]/da]/da, d[d[d[dM(w,a,m)/dT]/dT]/da]/da, d[d[d[dM(w,i,m)/dT]/dT]/da]/da, d[d[d[dM(a,i,m)/dT]/dT]/da]/da, d[d[d[dM(t,w,a,i)/dT]/dT]/da]/da, d[d[d[dM(t,w,a,m)/da/da, d[d[d[dM(t,w,i,m)/dT]/dT]/da]/da, d[d[d[dM(t,a,i,m)/dT]/dT]/da]/da, d[d[d[dM(w,a,i,m)/dT]/dT]/da]/da, d[d[d[dM(t,w,a,i,m)/dT]/dT]/da]/da..

 

We can also take higher order duel dimensional derivatives of memory as a function of affect and time but the symbolic expression of the set of such derivatives very soon becomes excessively lengthly to write and so these higher order derivatives as such are not mentioned here except to say that they would be computed in an analogous manner to the second order duel dimensional derivatives described above.

 

.

 

 

We can also express memory qualitatively, statistically, and perhaps with the use of some forms of real analyses as a derivative with respect to instinct or of i.

 

Given that M(i) =  M(t and/or w and/or a and/or i and/or m) or perhaps the following notation can be more appropriate in certain circumstances.

 

 

 

 

Thus the following first order derivatives of memory with respect to instinct are possible.

 

 

dM(t)/di, dM(w)/di, dM(a)/di, dM(i)/di, dM(m)/di, dM(t,w)/di, dM(t,a)/di, dM(t,i)/di, dM(t,m)/di, dM(w,a)/di, dM(w,i)/di, dM(w,m)/di, dM(a,i)/di, dM(a,m)/di, dM(i,m)/di, dM(t,w,a)/di, dM(t,w,i)/di, dM(t,w,m)/di, dM(t,a,i)/di, dM(t,a,m)/di, dM(t,i,m)/di, dM(w,a,i)/di, dM(w,a,m)/di, dM(w,i,m)/di, dM(a,i,m)/di, dM(t,w,a,i)/di, dM(t,w,a,m)/di, dM(t,w,i,m)/di, dM(t,a,i,m)/di, dM(w,a,i,m)/di, dM(t,w,a,i,m)/di.

 

 

Or more succinctly,  dM/di = dM(t and/or w and/or a and/or i and/or m)/di

 

 

Or perhaps dM(i)/di =d M{[t(i)] and/or [w(i)] and/or [a(i)] and/or [i(i)] and/or [m(i)]}/di.

 

 

Likewise, we can take the second instinct derivatives of  M as follows:

 

 

 

d[dM(t)/di]/di, d[dM(w)/di]/di, d[dM(a)/di]/di, d[dM(i)/di]/di, d[dM(m)/di]/di, d[dM(t,w)/di]/di, d[dM(t,a)/di]/di, d[dM(t,i)/di]/di, d[dM(t,m)/di]/di, d[dM(w,a)/di]/di, d[dM(w,i)/di]/di, d[dM(w,m)/di]/di, d[dM(a,i)/di]/di, d[dM(a,m)/di]/di, d[dM(i,m)/di/di, d[dM(t,w,a)/di]/di, d[dM(t,w,i)/di]/di, d[dM(t,w,m)/di]/di, d[dM(t,a,i)/di]/di, d[dM(t,a,m)/di]/di,  d[dM(t,i,m)/di]/di, d[dM(w,a,i)/di]/di, d[dM(w,a,m)/di]/di, d[dM(w,i,m)/di]/di, d[dM(a,i,m)/di]/di, d[dM(t,w,a,i)/di]/di, d[dM(t,w,a,m)/di/di, d[dM(t,w,i,m)/di]/di, d[dM(t,a,i,m)/di]/di, d[dM(w,a,i,m)/di]/di, d[dM(t,w,a,i,m)/di]/di..

 

 

or more succinctly, as d(dM/di)/di = d[d M(t and/or w and/or a and/or i and/or m)/di]/di = Mi2

 

 

or as

 

 

d[dM(i)/di]/di  = d[d M{[t(i)] and/or [w(i)] and/or [a(i)] and/or [i(i)] and/or [m(i)]}/di]/di = Mi2.

 

 

 

Likewise, we can take the third instinct derivatives of  M as follows:

 

 

 

d[d[dM(t)/di]/di]/di, d[d[dM(w)/di]/di]/di, d[d[dM(a)/di]/di]/di, d[d[dM(i)/di]/di]/di, d[d[dM(m)/di]/di]/di, d[d[dM(t,w)/di]/di]/di, d[d[dM(t,a)/di]/di]/di, d[d[dM(t,i)/di]/di]/di, d[d[dM(t,m)/di]/di]/di, d[d[dM(w,a)/di]/di]/di, d[d[dM(w,i)/di]/di]/di, d[d[dM(w,m)/di]/di]/di, d[d[dM(a,i)/di]/di]/di, d[d[dM(a,m)/di]/di]/di, d[d[dM(i,m)/di/di]/di, d[d[dM(t,w,a)/di]/di]/di, d[d[dM(t,w,i)/di]/di]/di, d[d[dM(t,w,m)/di]/di]/di, d[d[dM(t,a,i)/di]/di]/di, d[d[dM(t,a,m)/di]/di]/di,  d[d[dM(t,i,m)/di]/di]/di, d[d[dM(w,a,i)/di]/di]/di, d[d[dM(w,a,m)/di]/di]/di, d[d[dM(w,i,m)/di]/di]/di, d[d[dM(a,i,m)/di]/di]/di, d[d[dM(t,w,a,i)/di]/di]/di, d[d[dM(t,w,a,m)/di/di]/di, d[d[dM(t,w,i,m)/di]/di]/di, d[d[dM(t,a,i,m)/di]/di]/di, d[d[dM(w,a,i,m)/di]/di]/di, d[d[dM(t,w,a,i,m)/di]/di]/di.

 

 

or more succinctly, as d[d(dM/di)/di]/di = d[d[d M(t and/or w and/or a and/or i and/or m)/di]/di]/di = Mi3

 

 

or as

 

 

d[d[dM(i)/di]/di]/di  = d[d[d M{[t(i)] and/or [w(i)] and/or [a(i)] and/or [i(i)] and/or [m(i)]}/di]/di]/di = Mi3.

 

 

We can also form the expressions;

 

 

d[d[f(M)]/di]/di = d{d [M[t(i)]]/di and/or d[M[w(i)]]/di and/or d[M[a(i)]]/di and/or d[M[i(i)]]/di and/or d[M[m(i)]]/di}/di  = f(Mi)2

 

 

and

 

 

d[d[d[f(M)]/di]/di]/di = d{d{ d [M[t(i)]]/di and/or d[M[w(i)]]/di and/or d[M[a(i)]]/di and/or d[M[i(i)]]/di and/or d[M[m(i)]]/di}/di}/di  = f(Mi)3A, where A stands for type A differentiation which is not to be confused with the meaning of so-called Type A personality as A is used as an ordinal in a totally different context here.

 

 

and

 

 

d[d[d[f(M)]/di]/di]/di = d{d[d [M[t(i)]]/di]/di  and/or d[d [M[w(i)]]/di]/di  and/or d[d [M[a(i)]]/di]/di  and/or d[d [M[i(i)]]/di]/di  and/or d[d [M[m(i)]]/di]/di }/di = f(Mi)3B, where B stands for type B differentiation which is not to be confused with the meaning of so-called Type  B personality as B is used as an ordinal in a totally different context here .

 

 

In fact, one can form yet higher order derivatives of memories with respect to instinct as follows.

 

 

Mi5 = d Mi4/di = d[dMi3/di]/di

 

 

 

Mi5 = dMi4/di =  d[d[d[d[d M{[t(i)] and/or [w(i)] and/or [a(i)] and/or [i(i)] and/or [m(i)]}/di]/di]/di]/di]/di.

 

 

 

f(Mi)5A = d[f(Mi)4A]/di = d[d [f(Mi)3A]/di]/di =  d{d{d{d{ d [M[t(i)]]/di and/or d[M[w(i)]]/di and/or d[M[a(i)]]/di and/or d[M[i(i)]]/di and/or d[M[m(i)]]/di}/di}/di]/di]/di

 

 

 

 

Mi6 = d Mi5/di = d[d Mi4/di]/di = d[d[dMi3/di]/di]/di

 

 

 

Mi6 = dMi5/di = d[d[d[d[d[d M{[t(i)] and/or [w(i)] and/or [a(i)] and/or [i(i)] and/or [m(i)]}/di]/di]/di]/di]/di]/di

 

 

 

f(Mi)6A = d[f(Mi)5A]/di = d{ d{d{d{d{ d [M[t(i)]]/di and/or d[M[w(i)]]/di and/or d[M[a(i)]]/di and/or d[M[i(i)]]/di and/or d[M[m(i)]]/di}/di}/di]/di]/di]/di

 

 

 

 

Mi7 = dMi6/di

 

f(Mi)7A = d[f(Mi)6A]/di

 

 

Mi8 = d Mi7/di

 

f(Mi)8A = d[f(Mi)7A]/di

 

 

 

Mi9 = d Mi8/di

 

f(Mi)9A = d[f(Mi)8A]/di

 

 

Mi10…, Mi11…, Mi12 … etc.

 

 

Anyone for Mi ensemble, or Mi infinity scrapper, or Mi (Aleph 0), or Mi(Aleph 1), or Mi (Aleph 2), or how about Mi Aleph (Aleph 0), or Mi Aleph (Aleph 1) , or Mi Aleph (Aleph 2), or even Mi Aleph (Aleph (Aleph 0)), or Mi Aleph (Aleph (Aleph 1)), or Mi Aleph (Aleph (Aleph 2)), and so on?

 

Thus, for the set of the sets of derivatives of Mi1 through Mi(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Mi1 through Mi(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)},…, {П(0,31)[R]}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Mi1 through Mi(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Mi1 through Mi(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the derivative states in the set of the sets of derivatives of Mi1 through Mi(Aleph 0) is plausible equal to:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Mi1 through Mi(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Mi1 through Mi(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}}}.

 

For the set of the sets of derivatives of Mi1 through Mi(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Mi(Aleph 0) derivative space at the level of 0/(Aleph 0), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Mi1 through Mi(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Mi1 through Mi(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Mi1 through Mi(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Mi1 through Mi(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Mi1 through Mi(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Mi1 through Mi(Aleph 1), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Mi1 through  Mi(Aleph 2), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Mi1 through Mi(Aleph 3), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Mi(Aleph 0) derivative space at the level of 0/(Aleph 1), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Mi1 through Mi(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Mi1 through Mi(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Mi1 through Mi(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Mi1 through  Mi(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations  for the set of the sets of derivatives of Mi1 through Mi(Aleph 0) is plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Mi1 through Mi(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Mi1 through Mi(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Mi1 through Mi(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

 

For super-continuous Mi(Aleph 0) derivative space at the level of 0/(Aleph 2), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Mi1 through Mi(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Mi1 through Mi(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Mi1 through Mi(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Mi1 through Mi(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Mi1 through Mi(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Mi1 through Mi(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Mi1 through Mi(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Mi1 through Mi(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

Similar series can be developed for super-continuity at any applicable level such as 0/(Aleph 3), 0/(Aleph 4), 0/(Aleph 5),…, 0/(Aleph Ω), 0/(Aleph (Aleph 0)), …, 0/(Aleph (Aleph 1)), …, 0/(Aleph (Aleph 2)), …, 0/(Aleph (Aleph 3)),…, 0/(Aleph (Aleph Ω)),…, 0/(Aleph (Aleph (Aleph 0))), …, 0/(Aleph (Aleph (Aleph 1))),…, 0/(Aleph (Aleph (Aleph 2))),…, 0/(Aleph (Aleph (Aleph 3))),…, 0/(Aleph (Aleph  (Aleph Ω))), …

 

An so-on ad infinitum.

 

In addition to these numerical functions of Mi as functions of summation series of product series functions, in order to really appreciate the enourmous complexity of the human soul in terms of its potential to evolve and be differentiated from all other souls in its characteristics, we would need to consider how every single category and even every single species of affect of the form Mi can very. Since there may exist an arbitrarily high infinite number species of Mi, the number of numerical functions of Mi is utterly beyond recogning. I will cover such notions in terms of mathematical notation in yet another series of articles I will write on this general concept.

 

 

 

Perhaps these numbers are applicable when one considers that the human soul, in its accidental form and perhaps even in its substantial form stores all experience and other psychodynamics based phenomenon. Every experience adds to the accidental form of the human soul and this includes the souls of all those still alive on Earth, all those in Purgatory, all those in Heaven, all those in Hell, and all those in any Limbo.

Since the human soul can grow without limit in terms of its psychodynamic time –flow world line, such a consideration offers another mechanism where the number of derivative states, combinations of derivative states, and even super-continuity of the derivative state space can grow forever.

 

Folks, for those of you who might balk at me for including literally all souls in the above consideration, including the souls in Hell, as well as bodily extraterrestrial souls and the souls of so-called bodily ultraterrestials sometimes referred to as etherians in the new age UFO buff culture, my reply is that we simply do not understand the full scope of GOD’s Divine Economy. We may never fully comprehend the scope of the Divine Economy because such an utterly eternal scheme, is, well, eternal and never ending.

 

 

The general meaning of instinct derivatives of memory can be viewed as the manner in which the qualitative and/or quantitative aspects of memory as a function of instinct very with instinct. The manner in which memories very with instinct may be multi- instinct-aspect dimensional wherein the dimensions of derivations can be multiple, and wherein the derivations can be taken in parallel, series parallel or in serial manner. The differentials can be partial or non-partial derivatives, or both partial and non-partial for a given computation.

 

In fact, since there is in theory, no limit to the numbers of qualitatively and quantitatively different instincts, and perhaps no limit to the number of possible different types or classes of instincts or potential instincts, wherein each person has his or her own unique instincts and instinctual experiences, the number of instinct dimensions that can effect memories is literally infinite, given the entirety of the set of created persons, and perhaps also literally infinite for each person as an individual, although we can not intellectually and intuitively understand this infinite number.

 

 

It is interesting to consider the ramifactions of being able to perform realistic calculations involving instinct derivatives of memory from a mathematical, theoretical, scientific,  and philosophical perspective.

 

Persons for which one or more nth order derivatives of memory with respect to instinct that have large absolute values would tend to have their memories highly influenced by instinct, or at least for the memories under consideration with respect to the dimension of the specific instinct act type(s) or class(es) for which the differentiation(s) are being performed. Perhaps a strong coupling between memory and instinct indicates a well integrated personality and commensurately, a high degree of memory capacity and a high degree of memory intelligence as well as perhaps very strong instinct power.

 

We would expect that disembodied human souls, (ETI souls, and/or UTI souls in Heaven, Limbo, highly evolved bodily (ETI persons, highly evolved UTI persons, and angels to have memories of all kinds and intensities which are perhaps  highly subject to advanced instincts such as spiritual instincts, spiritual intuitions, and even perhaps, psychic powers.

 

 

We can also consider that two dimensional nth ordered derivatives of memory with respect to instinct and time, or with respect to i and T, respectively.

 

Given that M[(i)(T)] =  M[(t and/or w and/or a and/or i and/or m)(i)(T)], the following first order two dimensional derivatives of memory with respect to instinct and Time are possible.

 

 

d[dM[(t)(T)]/di]/dT, d[dM[(w)(T)]/di]/dT, d[dM[(a)(T)]/di]/dT, d[dM[(i)(T)]/di]/dT, d[dM[(m)(T)]/di]/dT, d[dM[(t,w)(T)]/di]/dT, d[dM[(t,a)(T)]/di]/dT, d[dM[(t,i)(T)]/di]/dT, d[dM[(t,m)(T)]/di]/dT, d[dM[(w,a)(T)]/di]/dT, d[dM[(w,i)(T)]/di]/dT, d[dM[(w,m)(T)]/di]/dT, d[dM[(a,i)(T)]/di]/dT, d[dM[(a,m)(T)]/di]/dT, d[dM[(i,m)(T)]/di]/dT, d[dM[(t,w,a)(T)]/di]/dT, d[dM[(t,w,i)(T)]/di]/dT, d[dM[(t,w,m)(T)]/di]/dT, d[dM[(t,a,i)(T)]/di]/dT, d[dM[(t,a,m)(T)]/di]/dT, d[dM[(t,i,m)(T)]/di]/dT, d[dM[(w,a,i)(T)]/di]/dT, d[dM[(w,a,m)(T)]/di]/dT, d[dM[(w,i,m)(T)]/di]/dT, d[dM[(a,i,m)(T)]/di]/dT, d[dM[(t,w,a,i)(T)]/di]/dT, d[dM[(t,w,a,m)(T)]/di]/dT, d[dM[(t,w,i,m)(T)]/di]/dT, d[dM[(t,a,i,m)(T)]/di]/dT, d[dM[(w,a,i,m)(T)]/di]/dT, d[dM[(t,w,a,i,m)(T)]/di]/dT.

 

 

Or more succinctly,  d[dM(T)/di]/dT = d[dM[(T)(t and/or w and/or a and/or i and/or m)]/di]/dT

 

or

 

d[dM(T)/dT]/di = d[dM[(T)(t and/or w and/or a and/or i and/or m)]/dT]/di

 

 

 

 

 

Or perhaps d[d M[(i)(T)]/di]/dT  = d[d M [{[t(i)] and/or [w(i)] and/or [a(i)] and/or [i(i)] and/or [m(i)]}(T)]/di]/dT

 

or

 

Or perhaps d[d M[(i)(T)]/dT]/di  = d[d M [{[t(i)] and/or [w(i)] and/or [a(i)] and/or [i(i)] and/or [m(i)]}(T)]/dT]/di

 

 

 

Likewise, we can take the second dual dimension instinct -time derivatives of  M as follows:

 

d[d[d[dM[(t)(T)]/di]/dT]/di]/dT, d[d[d[dM[(w)(T)]/di]/dT]/di]/dT, d[d[d[dM[(a)(T)]/di]/dT]/di]/dT, d[d[d[dM[(i)(T)]/di]/dT]/di]/dT, d[d[d[dM[(m)(T)]/di]/dT]/di]/dT, d[d[d[dM[(t,w)(T)]/di]/dT]/di]/dT, d[d[d[dM[(t,a)(T)]/di]/dT]/di]/dT, d[d[d[dM[(t,i)(T)]/di]/dT]/di]/dT, d[d[d[dM[(t,m)(T)]/di]/dT]/di]/dT, d[d[d[dM[(w,a)(T)]/di]/dT]/di]/dT, d[d[d[dM[(w,i)(T)]/di]/dT]/di]/dT, d[d[d[dM[(w,m)(T)]/di]/dT]/di]/dT, d[d[d[dM[(a,i)(T)]/di]/dT]/di]/dT, d[d[d[dM[(a,m)(T)]/di]/dT]/di]/dT, d[d[d[dM[(i,m)(T)]/di]/dT]/di]/dT, d[d[d[dM[(t,w,a)(T)]/di]/dT]/di]/dT, d[d[d[dM[(t,w,i)(T)]/di]/dT]/di]/dT, d[d[d[dM[(t,w,m)(T)]/di]/dT]/di]/dT, d[d[d[dM[(t,a,i)(T)]/di]/dT]/di]/dT, d[d[d[dM[(t,a,m)(T)]/di]/dT]/di]/dT, d[d[d[dM[(t,i,m)(T)]/di]/dT]/di]/dT, d[d[d[dM[(w,a,i)(T)]/di]/dT]/di]/dT, d[d[d[dM[(w,a,m)(T)]/di]/dT]/di]/dT, d[d[d[dM[(w,i,m)(T)]/di]/dT]/di]/dT, d[d[d[dM[(a,i,m)(T)]/di]/dT]/di]/dT, d[d[d[dM[(t,w,a,i)(T)]/di]/dT]/di]/dT, d[d[d[dM[(t,w,a,m)(T)]/di]/dT]/di]/dT, d[d[d[dM[(t,w,i,m)(T)]/di]/dT]/di]/dT, d[d[d[dM[(t,a,i,m)(T)]/di]/dT]/di]/dT, d[d[d[dM[(w,a,i,m)(T)]/di]/dT]/di]/dT, d[d[d[dM[(t,w,a,i,m)(T)]/di]/dT]/di]/dT.

 

or as:

 

 

 

d[d[d[dM[(t)(T)]/di]/dT]/dT]/di, d[d[d[dM[(w)(T)]/di]/dT]/dT]/di, d[d[d[dM[(a)(T)]/di]/dT]/dT]/di, d[d[d[dM[(i)(T)]/di]/dT]/dT]/di, d[d[d[dM[(m)(T)]/di]/dT]/dT]/di, d[d[d[dM[(t,w)(T)]/di]/dT]/dT]/di, d[d[d[dM[(t,a)(T)]/di]/dT]/dT]/di, d[d[d[dM[(t,i)(T)]/di]/dT]/dT]/di, d[d[d[dM[(t,m)(T)]/di]/dT]/dT]/di, d[d[d[dM[(w,a)(T)]/di]/dT]/dT]/di, d[d[d[dM[(w,i)(T)]/di]/dT]/dT]/di, d[d[d[dM[(w,m)(T)]/di]/dT]/dT]/di, d[d[d[dM[(a,i)(T)]/di]/dT]/dT]/di, d[d[d[dM[(a,m)(T)]/di]/dT]/dT]/di, d[d[d[dM[(i,m)(T)]/di]/dT]/dT]/di, d[d[d[dM[(t,w,a)(T)]/di]/dT]/dT]/di, d[d[d[dM[(t,w,i)(T)]/di]/dT]/dT]/di, d[d[d[dM[(t,w,m)(T)]/di]/dT]/dT]/di, d[d[d[dM[(t,a,i)(T)]/di]/dT]/dT]/di, d[d[d[dM[(t,a,m)(T)]/di]/dT]/dT]/di, d[d[d[dM[(t,i,m)(T)]/di]/dT]/dT]/di, d[d[d[dM[(w,a,i)(T)]/di]/dT]/dT]/di, d[d[d[dM[(w,a,m)(T)]/di]/dT]/dT]/di, d[d[d[dM[(w,i,m)(T)]/di]/dT]/dT]/di, d[d[d[dM[(a,i,m)(T)]/di]/dT]/dT]/di, d[d[d[dM[(t,w,a,i)(T)]/di]/dT]/dT]/di, d[d[d[dM[(t,w,a,m)(T)]/di]/dT]/dT]/di, d[d[d[dM[(t,w,i,m)(T)]/di]/dT]/dT]/di, d[d[d[dM[(t,a,i,m)(T)]/di]/dT]/dT]/di, d[d[d[dM[(w,a,i,m)(T)]/di]/dT]/dT]/di, d[d[d[dM[(t,w,a,i,m)(T)]/di]/dT]/dT]/di.

 

or as:

 

d[d[d[dM[(t)(T)]/dT]/di]/di]/dT, d[d[d[dM[(w)(T)]/dT]/di]/di]/dT, d[d[d[dM[(a)(T)]/dT]/di]/di]/dT, d[d[d[dM[(i)(T)]/dT]/di]/di]/dT, d[d[d[dM[(m)(T)]/dT]/di]/di]/dT, d[d[d[dM[(t,w)(T)]/dT]/di]/di]/dT, d[d[d[dM[(t,a)(T)]/dT]/di]/di]/dT, d[d[d[dM[(t,i)(T)]/dT]/di]/di]/dT, d[d[d[dM[(t,m)(T)]/dT]/di]/di]/dT, d[d[d[dM[(w,a)(T)]/dT]/di]/di]/dT, d[d[d[dM[(w,i)(T)]/dT]/di]/di]/dT, d[d[d[dM[(w,m)(T)]/dT]/di]/di]/dT, d[d[d[dM[(a,i)(T)]/dT]/di]/di]/dT, d[d[d[dM[(a,m)(T)]/dT]/di]/di]/dT, d[d[d[dM[(i,m)(T)]/dT]/di]/di]/dT, d[d[d[dM[(t,w,a)(T)]/dT]/di]/di]/dT, d[d[d[dM[(t,w,i)(T)]/dT]/di]/di]/dT, d[d[d[dM[(t,w,m)(T)]/dT]/di]/di]/dT, d[d[d[dM[(t,a,i)(T)]/dT]/di]/di]/dT, d[d[d[dM[(t,a,m)(T)]/dT]/di]/di]/dT, d[d[d[dM[(t,i,m)(T)]/dT]/di]/di]/dT, d[d[d[dM[(w,a,i)(T)]/dT]/di]/di]/dT, d[d[d[dM[(w,a,m)(T)]/dT]/di]/di]/dT, d[d[d[dM[(w,i,m)(T)]/dT]/di]/di]/dT, d[d[d[dM[(a,i,m)(T)]/dT]/di]/di]/dT, d[d[d[dM[(t,w,a,i)(T)]/dT]/di]/di]/dT, d[d[d[dM[(t,w,a,m)(T)]/dT]/di]/di]/dT, d[d[d[dM[(t,w,i,m)(T)]/dT]/di]/di]/dT, d[d[d[dM[(t,a,i,m)(T)]/dT]/di]/di]/dT, d[d[d[dM[(w,a,i,m)(T)]/dT]/di]/di]/dT, d[d[d[dM[(t,w,a,i,m)(T)]/dT]/di]/di]/dT.

 

 

or as;

 

 

 

 

d[d[d[dM(t)/di]/di]/dT]/dT, d[d[d[dM(w)/di]/di]/dT]/dT, d[d[d[dM(a)/di]/di]/dT]/dT, d[d[d[dM(i)/di]/di]/dT]/dT, d[d[d[dM(m)/di]/di]/dT]/dT, d[d[d[dM(t,w)/di]/di]/dT]/dT, d[d[d[dM(t,a)/di]/di]/dT]/dT, d[d[d[dM(t,i)/di]/di]/dT]/dT, d[d[d[dM(t,m)/di]/di]/dT]/dT, d[d[d[dM(w,a)/di]/di]/dT]/dT, d[d[d[dM(w,i)/di]/di]/dT]/dT, d[d[d[dM(w,m)/di]/di]/dT]/dT, d[d[d[dM(a,i)/di]/di]/dT]/dT, d[d[d[dM(a,m)/di]/di]/dT]/dT, d[d[d[dM(i,m)/di]/di]/dT]/dT, d[d[d[dM(t,w,a)/di]/di]/dT]/dT, d[d[d[dM(t,w,i)/di]/di]/dT]/dT, d[d[d[dM(t,w,m)/di]/di]/dT]/dT, d[d[d[dM(t,a,i)/di]/di]/dT]/dT, d[d[d[dM(t,a,m)/di]/di]/dT]/dT,  d[d[d[dM(t,i,m)/di]/di]/dT]/dT, d[d[d[dM(w,a,i)/di]/di]/dT]/dT, d[d[d[dM(w,a,m)/di]/di]/dT]/dT, d[d[d[dM(w,i,m)/di]/di]/dT]/dT, d[d[d[dM(a,i,m)/di]/di]/dT]/dT, d[d[d[dM(t,w,a,i)/di]/di]/dT]/dT, d[d[d[dM(t,w,a,m)/di/di, d[d[d[dM(t,w,i,m)/di]/di]/dT]/dT, d[d[d[dM(t,a,i,m)/di]/di]/dT]/dT, d[d[d[dM(w,a,i,m)/di]/di]/dT]/dT, d[d[d[dM(t,w,a,i,m)/di]/di]/dT]/dT..

 

or as:

 

d[d[d[dM(t)/dT]/di]/dT]/di, d[d[d[dM(w)/dT]/di]/dT]/di, d[d[d[dM(a)/dT]/di]/dT]/di, d[d[d[dM(i)/dT]/di]/dT]/di, d[d[d[dM(m)/dT]/di]/dT]/di, d[d[d[dM(t,w)/dT]/di]/dT]/di, d[d[d[dM(t,a)/dT]/di]/dT]/di, d[d[d[dM(t,i)/dT]/di]/dT]/di, d[d[d[dM(t,m)/dT]/di]/dT]/di, d[d[d[dM(w,a)/dT]/di]/dT]/di, d[d[d[dM(w,i)/dT]/di]/dT]/di, d[d[d[dM(w,m)/dT]/di]/dT]/di, d[d[d[dM(a,i)/dT]/di]/dT]/di, d[d[d[dM(a,m)/dT]/di]/dT]/di, d[d[d[dM(i,m)/ dT]/di]/dT]/di, d[d[d[dM(t,w,a)/dT]/di]/dT]/di, d[d[d[dM(t,w,i)/dT]/di]/dT]/di, d[d[d[dM(t,w,m)/dT]/di]/dT]/di, d[d[d[dM(t,a,i)/dT]/di]/dT]/di, d[d[d[dM(t,a,m)/dT]/di]/dT]/di,  d[d[d[dM(t,i,m)/dT]/di]/dT]/di, d[d[d[dM(w,a,i)/dT]/di]/dT]/di, d[d[d[dM(w,a,m)/dT]/di]/dT]/di, d[d[d[dM(w,i,m)/dT]/di]/dT]/di, d[d[d[dM(a,i,m)/dT]/di]/dT]/di, d[d[d[dM(t,w,a,i)/dT]/di]/dT]/di, d[d[d[dM(t,w,a,m)/di/di, d[d[d[dM(t,w,i,m)/dT]/di]/dT]/di, d[d[d[dM(t,a,i,m)/dT]/di]/dT]/di, d[d[d[dM(w,a,i,m)/dT]/di]/dT]/di, d[d[d[dM(t,w,a,i,m)/dT]/di]/dT]/di..

 

or as:

 

d[d[d[dM(t)/dT]/dT]/di]/di, d[d[d[dM(w)/dT]/dT]/di]/di, d[d[d[dM(a)/dT]/dT]/di]/di, d[d[d[dM(i)/dT]/dT]/di]/di, d[d[d[dM(m)/dT]/dT]/di]/di, d[d[d[dM(t,w)/dT]/dT]/di]/di, d[d[d[dM(t,a)/dT]/dT]/di]/di, d[d[d[dM(t,i)/dT]/dT]/di]/di, d[d[d[dM(t,m)/dT]/dT]/di]/di, d[d[d[dM(w,a)/dT]/dT]/di]/di, d[d[d[dM(w,i)/dT]/dT]/di]/di, d[d[d[dM(w,m)/dT]/dT]/di]/di, d[d[d[dM(a,i)/dT]/dT]/di]/di, d[d[d[dM(a,m)/ dT]/dT]/di]/di, d[d[d[dM(i,m)/ dT]/dT]/di]/di, d[d[d[dM(t,w,a)/dT]/dT]/di]/di, d[d[d[dM(t,w,i)/dT]/dT]/di]/di, d[d[d[dM(t,w,m)/dT]/dT]/di]/di, d[d[d[dM(t,a,i)/dT]/dT]/di]/di, d[d[d[dM(t,a,m)/dT]/dT]/di]/di,  d[d[d[dM(t,i,m)/dT]/dT]/di]/di, d[d[d[dM(w,a,i)/dT]/dT]/di]/di, d[d[d[dM(w,a,m)/dT]/dT]/di]/di, d[d[d[dM(w,i,m)/dT]/dT]/di]/di, d[d[d[dM(a,i,m)/dT]/dT]/di]/di, d[d[d[dM(t,w,a,i)/dT]/dT]/di]/di, d[d[d[dM(t,w,a,m)/di/di, d[d[d[dM(t,w,i,m)/dT]/dT]/di]/di, d[d[d[dM(t,a,i,m)/dT]/dT]/di]/di, d[d[d[dM(w,a,i,m)/dT]/dT]/di]/di, d[d[d[dM(t,w,a,i,m)/dT]/dT]/di]/di..

 

We can also take higher order duel dimensional derivatives of memory as a function of instinct and time but the symbolic expression of the set of such derivatives very soon becomes excessively lengthly to write and so these higher order derivatives as such are not mentioned here except to say that they would be computed in an analogous manner to the second order duel dimensional derivatives described above.

 

 

 

These seemingly crazy differentials might have some use in extreme psychological states that can be experienced by souls who are departed and whose memories, although perhaps spiritualized, are nonetheless, not limited by a body and its brain.

 

 

Another type of being that might experience such extreme memory change capacities might be none other then some of our friends we believe to exist as pure body-less and brain-less spirits known as angels.

 

 

Since I have dared to speculate this far, perhaps we can speculate as to whether any intelligent extraterrestrials persons or any so-called ultra-terrestrials persons that are more cognitively evolved then we ordinary humans might be capable of experiencing large absolute valued terms of Mn. Some such ETI and UTI persons may  have evolved over billions of years, or perhaps have far greater powers of sensation, memory, and intuition such as would seem plausible for any such persons and their civilizations who have not fallen from the state of innocence into the state of sin as we humans have, or perhaps such beings never had the option of  sanctifying grace opened to them but nonetheless may have been created at a naturally more perfect level then we humans, and who therefore might exhibit greater natural powers of memory and sensation.

 

 

 

 

 

 

 

 

 

 

 

 

We can also express memory qualitatively, statistically, and perhaps with the use of some forms of real analyses as a derivative of memory or of m.

 

Given that M(m) =  M(t and/or w and/or a and/or i and/or m) or perhaps the following notation can be more appropriate in certain circumstances.

 

 

 

 

Thus the following first order derivatives of memory with respect to memory are possible.

 

 

dM(t)/dM, dM(w)/dM, dM(a)/dM, dM(i)/dM, dM(m)/dM, dM(t,w)/dM, dM(t,a)/dM, dM(t,i)/dM, dM(t,m)/dM, dM(w,a)/dM, dM(w,i)/dM, dM(w,m)/dM, dM(a,i)/dM, dM(a,m)/dM, dM(i,m)/dM, dM(t,w,a)/dM, dM(t,w,i)/dM, dM(t,w,m)/dM, dM(t,a,i)/dM, dM(t,a,m)/dM, dM(t,i,m)/dM, dM(w,a,i)/dM, dM(w,a,m)/dM, dM(w,i,m)/dM, dM(a,i,m)/dM, dM(t,w,a,i)/dM, dM(t,w,a,m)/dM, dM(t,w,i,m)/dM, dM(t,a,i,m)/dM, dM(w,a,i,m)/dM, dM(t,w,a,i,m)/dM.

 

 

Or more succinctly,  dM/dM = dM(t and/or w and/or a and/or i and/or m)/dM

 

 

Or perhaps dM(m)/dM =d M{[t(m)] and/or [w(m)] and/or [a(m)] and/or [i(m)] and/or [m(m)]}/dM.

 

 

Likewise, we can take the second memory derivatives of  M as follows:

 

 

 

d[dM(t)/dM]/dM, d[dM(w)/dM]/dM, d[dM(a)/dM]/dM, d[dM(i)/dM]/dM, d[dM(m)/dM]/dM, d[dM(t,w)/dM]/dM, d[dM(t,a)/dM]/dM, d[dM(t,i)/dM]/dM, d[dM(t,m)/dM]/dM, d[dM(w,a)/dM]/dM, d[dM(w,i)/dM]/dM, d[dM(w,m)/dM]/dM, d[dM(a,i)/dM]/dM, d[dM(a,m)/dM]/dM, d[dM(i,m)/dM/dM, d[dM(t,w,a)/dM]/dM, d[dM(t,w,i)/dM]/dM, d[dM(t,w,m)/dM]/dM, d[dM(t,a,i)/dM]/dM, d[dM(t,a,m)/dM]/dM,  d[dM(t,i,m)/dM]/dM, d[dM(w,a,i)/dM]/dM, d[dM(w,a,m)/dM]/dM, d[dM(w,i,m)/dM]/dM, d[dM(a,i,m)/dM]/dM, d[dM(t,w,a,i)/dM]/dM, d[dM(t,w,a,m)/dM/dM, d[dM(t,w,i,m)/dM]/dM, d[dM(t,a,i,m)/dM]/dM, d[dM(w,a,i,m)/dM]/dM, d[dM(t,w,a,i,m)/dM]/dM..

 

 

or more succinctly, as d(dM/dM)/dM = d[d M(t and/or w and/or a and/or i and/or m)/dM]/dM = Mm2

 

 

or as

 

 

d[dM(m)/dM]/dM  = d[d M{[t(m)] and/or [w(m)] and/or [a(m)] and/or [i(m)] and/or [m(m)]}/dM]/dM = Mm2.

 

 

 

Likewise, we can take the third memory derivatives of  M as follows:

 

 

 

d[d[dM(t)/dM]/dM]/dM, d[d[dM(w)/dM]/dM]/dM, d[d[dM(a)/dM]/dM]/dM, d[d[dM(i)/dM]/dM]/dM, d[d[dM(m)/dM]/dM]/dM, d[d[dM(t,w)/dM]/dM]/dM, d[d[dM(t,a)/dM]/dM]/dM, d[d[dM(t,i)/dM]/dM]/dM, d[d[dM(t,m)/dM]/dM]/dM, d[d[dM(w,a)/dM]/dM]/dM, d[d[dM(w,i)/dM]/dM]/dM, d[d[dM(w,m)/dM]/dM]/dM, d[d[dM(a,i)/dM]/dM]/dM, d[d[dM(a,m)/dM]/dM]/dM, d[d[dM(i,m)/dM/dM]/dM, d[d[dM(t,w,a)/dM]/dM]/dM, d[d[dM(t,w,i)/dM]/dM]/dM, d[d[dM(t,w,m)/dM]/dM]/dM, d[d[dM(t,a,i)/dM]/dM]/dM, d[d[dM(t,a,m)/dM]/dM]/dM,  d[d[dM(t,i,m)/dM]/dM]/dM, d[d[dM(w,a,i)/dM]/dM]/dM, d[d[dM(w,a,m)/dM]/dM]/dM, d[d[dM(w,i,m)/dM]/dM]/dM, d[d[dM(a,i,m)/dM]/dM]/dM, d[d[dM(t,w,a,i)/dM]/dM]/dM, d[d[dM(t,w,a,m)/dM/dM]/dM, d[d[dM(t,w,i,m)/dM]/dM]/dM, d[d[dM(t,a,i,m)/dM]/dM]/dM, d[d[dM(w,a,i,m)/dM]/dM]/dM, d[d[dM(t,w,a,i,m)/dM]/dM]/dM.

 

 

or more succinctly, as d[d(dM/dM)/dM]/dM = d[d[d M(t and/or w and/or a and/or i and/or m)/dM]/dM]/dM = Mm3

 

 

or as

 

 

d[d[dM(m)/dM]/dM]/dM  = d[d[d M{[t(m)] and/or [w(m)] and/or [a(m)] and/or [i(m)] and/or [m(m)]}/dM]/dM]/dM = Mm3.

 

 

We can also form the expressions;

 

 

d[d[f(M)]/dM]/dM = d{d [M[t(m)]]/dM and/or d[M[w(m)]]/dM and/or d[M[a(m)]]/dM and/or d[M[i(m)]]/dM and/or d[M[m(m)]]/dM}/dM  = f(Mm)2

 

 

and

 

 

d[d[d[f(M)]/dM]/dM]/dM = d{d{ d [M[t(m)]]/dM and/or d[M[w(m)]]/dM and/or d[M[a(m)]]/dM and/or d[M[i(m)]]/dM and/or d[M[m(m)]]/dM}/dM}/dM  = f(Mm)3A, where A stands for type A differentiation which is not to be confused with the meaning of so-called Type A personality as A is used as an ordinal in a totally different context here.

 

 

and

 

 

d[d[d[f(M)]/dM]/dM]/dM = d{d[d [M[t(m)]]/dM]/dM  and/or d[d [M[w(m)]]/dM]/dM  and/or d[d [M[a(m)]]/dM]/dM  and/or d[d [M[i(m)]]/dM]/dM  and/or d[d [M[m(m)]]/dM]/dM }/dM = f(Mm)3B, where B stands for type B differentiation which is not to be confused with the meaning of so-called Type  B personality as B is used as an ordinal in a totally different context here .

 

 

In fact, one can form yet higher order derivatives of memories with respect to memory as follows.

 

 

Mm5 = d Mm4/dM = d[dMm3/dM]/dM

 

 

 

Mm5 = dMm4/dM =  d[d[d[d[d M{[t(m)] and/or [w(m)] and/or [a(m)] and/or [i(m)] and/or [m(m)]}/dM]/dM]/dM]/dM]/dM.

 

 

 

f(Mm)5A = d[f(Mm)4A]/dM = d[d [f(Mm)3A]/dM]/dM =  d{d{d{d{ d [M[t(m)]]/dM and/or d[M[w(m)]]/dM and/or d[M[a(m)]]/dM and/or d[M[i(m)]]/dM and/or d[M[m(m)]]/dM}/dM}/dM]/dM]/dM

 

 

 

 

Mm6 = d Mm5/dM = d[d Mm4/dM]/dM = d[d[dMm3/dM]/dM]/dM

 

 

 

Mm6 = dMm5/dM = d[d[d[d[d[d M{[t(m)] and/or [w(m)] and/or [a(m)] and/or [i(m)] and/or [m(m)]}/dM]/dM]/dM]/dM]/dM]/dM

 

 

 

f(Mm)6A = d[f(Mm)5A]/dM = d{ d{d{d{d{ d [M[t(m)]]/dM and/or d[M[w(m)]]/dM and/or d[M[a(m)]]/dM and/or d[M[i(m)]]/dM and/or d[M[m(m)]]/dM}/dM}/dM]/dM]/dM]/dM

 

 

 

 

Mm7 = dMm6/dM

 

f(Mm)7A = d[f(Mm)6A]/dM

 

 

Mm8 = d Mm7/dM

 

f(Mm)8A = d[f(Mm)7A]/dM

 

 

 

Mm9 = d Mm8/dM

 

f(Mm)9A = d[f(Mm)8A]/dM

 

 

Mm10…, Mm11…, Mm12 … etc.

 

 

Anyone for Mm ensemble, or Mm infinity scrapper, or Mm (Aleph 0), or Mm(Aleph 1), or Mm (Aleph 2), or how about Mm Aleph (Aleph 0), or Mm Aleph (Aleph 1) , or Mm Aleph (Aleph 2), or even Mm Aleph (Aleph (Aleph 0)), or Mm Aleph (Aleph (Aleph 1)), or Mm Aleph (Aleph (Aleph 2)), and so on?

 

Thus, for the set of the sets of derivatives of Mm1 through Mm(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Mm1 through Mm(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)},…, {П(0,31)[R]}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Mm1 through Mm(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Mm1 through Mm(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the derivative states in the set of the sets of derivatives of Mm1 through Im(Aleph 0) is plausible equal to:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Mm1 through Mm(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Mm1 through Mm(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}}}.

 

For the set of the sets of derivatives of Mm1 through Mm(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Mm(Aleph 0) derivative space at the level of 0/(Aleph 0), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Mm1 through Mm(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Mm1 through Mm(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Mm1 through Mm(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Mm1 through Mm(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Mm1 through Mm(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Mm1 through Mm(Aleph 1), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Mm1 through  Mm(Aleph 2), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Mm1 through Mm(Aleph 3), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Mm(Aleph 0) derivative space at the level of 0/(Aleph 1), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Mm1 through Mm(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Mm1 through Mm(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Mm1 through Mm(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Mm1 through  Mm(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations  for the set of the sets of derivatives of Mm1 through Im(Aleph 0) is plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Mm1 through Mm(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Mm1 through Mm(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Mm1 through Mm(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

 

For super-continuous Mm(Aleph 0) derivative space at the level of 0/(Aleph 2), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Mm1 through Mm(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Mm1 through Mm(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Mm1 through Mm(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Mm1 through Mm(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Mm1 through Mm(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Mm1 through Mm(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Mm1 through Mm(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Mm1 through Mm(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

 

The general meaning of memory derivatives of memory can be viewed as the manner in which the qualitative and/or quantitative aspects of memories as a function of memory very with memory. The manner in which memories very with memory may be multi- memory-aspect dimensional wherein the dimensions of derivations can be multiple, and wherein the derivations can be taken in parallel, series parallel or in serial manner. The differentials can be partial or non-partial derivatives, or both partial and non-partial for a given computation.

 

In fact, since there is in theory, no limit to the numbers of qualitatively and quantitatively different memories, and perhaps no limit to the number of possible different types or classes of memories, wherein each person has his or her own unique memories, the number of memory dimensions that can effect memories is literally infinite, given the entirety of the set of created persons, and perhaps also literally infinite for each person as an individual, although we can not intellectually and intuitively understand this infinite number.

 

 

It is interesting to consider the ramifactions of being able to perform realistic calculations involving memory derivatives of memory from a mathematical, theoretical, scientific,  and philosophical perspective.

 

Persons for which one or more nth order derivatives of memory with respect to memory that have large absolute values would tend to have their memories highly influenced by memory, or at least for the memories under consideration with respect to the dimension of the specific memory act type(s) or class(es) for which the differentiation(s) are being performed. Perhaps a strong coupling between memory and memory indicates a well integrated personality and commensurately, a high degree of memory capacity and a high degree of memory intelligence as well as perhaps very strong memory power.

 

We would expect that disembodied human souls, ETI souls, and/or UTI souls in Heaven, Limbo, highly evolved bodily ETI persons, highly evolved UTI persons, and angels to have memories of all kinds and intensities which are perhaps  highly subject to powereful memorys such as spiritual memorys, psychological memories, emotional memories, intellectual memories, interpersonal memories, auto-biographical memories, and even perhaps, memories facilitated by advanced psychic powers.

 

 

We can also consider that two dimensional nth ordered derivatives of memory with respect to memory and time, or with respect to i and T, respectively.

 

Given that M[(m)(T)] =  M[(t and/or w and/or a and/or i and/or m)(m)(T)], the following first order two dimensional derivatives of memory with respect to memory and Time are possible.

 

 

d[dM[(t)(T)]/dM]/dT, d[dM[(w)(T)]/dM]/dT, d[dM[(a)(T)]/dM]/dT, d[dM[(i)(T)]/dM]/dT, d[dM[(m)(T)]/dM]/dT, d[dM[(t,w)(T)]/dM]/dT, d[dM[(t,a)(T)]/dM]/dT, d[dM[(t,i)(T)]/dM]/dT, d[dM[(t,m)(T)]/dM]/dT, d[dM[(w,a)(T)]/dM]/dT, d[dM[(w,i)(T)]/dM]/dT, d[dM[(w,m)(T)]/dM]/dT, d[dM[(a,i)(T)]/dM]/dT, d[dM[(a,m)(T)]/dM]/dT, d[dM[(i,m)(T)]/dM]/dT, d[dM[(t,w,a)(T)]/dM]/dT, d[dM[(t,w,i)(T)]/dM]/dT, d[dM[(t,w,m)(T)]/dM]/dT, d[dM[(t,a,i)(T)]/dM]/dT, d[dM[(t,a,m)(T)]/dM]/dT, d[dM[(t,i,m)(T)]/dM]/dT, d[dM[(w,a,i)(T)]/dM]/dT, d[dM[(w,a,m)(T)]/dM]/dT, d[dM[(w,i,m)(T)]/dM]/dT, d[dM[(a,i,m)(T)]/dM]/dT, d[dM[(t,w,a,i)(T)]/dM]/dT, d[dM[(t,w,a,m)(T)]/dM]/dT, d[dM[(t,w,i,m)(T)]/dM]/dT, d[dM[(t,a,i,m)(T)]/dM]/dT, d[dM[(w,a,i,m)(T)]/dM]/dT, d[dM[(t,w,a,i,m)(T)]/dM]/dT.

 

 

Or more succinctly,  d[dM(T)/dM]/dT = d[dM[(T)(t and/or w and/or a and/or m and/or m)]/dM]/dT

 

or

 

d[dM(T)/dT]/dM = d[dM[(T)(t and/or w and/or a and/or i and/or m)]/dT]/dM

 

 

 

 

 

Or perhaps d[d M[(m)(T)]/dM]/dT  = d[d M [{[t(m)] and/or [w(m)] and/or [a(m)] and/or [i(m)] and/or [m(m)]}(T)]/dM]/dT

 

or

 

Or perhaps d[d M[(m)(T)]/dT]/dM  = d[d M [{[t(m)] and/or [w(m)] and/or [a(i)] and/or [i(m)] and/or [m(m)]}(T)]/dT]/dM

 

 

 

Likewise, we can take the second dual dimension memory -time derivatives of  M as follows:

 

d[d[d[dM[(t)(T)]/dM]/dT]/dM]/dT, d[d[d[dM[(w)(T)]/dM]/dT]/dM]/dT, d[d[d[dM[(a)(T)]/dM]/dT]/dM]/dT, d[d[d[dM[(i)(T)]/dM]/dT]/dM]/dT, d[d[d[dM[(m)(T)]/dM]/dT]/dM]/dT, d[d[d[dM[(t,w)(T)]/dM]/dT]/dM]/dT, d[d[d[dM[(t,a)(T)]/dM]/dT]/dM]/dT, d[d[d[dM[(t,i)(T)]/dM]/dT]/dM]/dT, d[d[d[dM[(t,m)(T)]/dM]/dT]/dM]/dT, d[d[d[dM[(w,a)(T)]/dM]/dT]/dM]/dT, d[d[d[dM[(w,i)(T)]/dM]/dT]/dM]/dT, d[d[d[dM[(w,m)(T)]/dM]/dT]/dM]/dT, d[d[d[dM[(a,i)(T)]/dM]/dT]/dM]/dT, d[d[d[dM[(a,m)(T)]/dM]/dT]/dM]/dT, d[d[d[dM[(i,m)(T)]/dM]/dT]/dM]/dT, d[d[d[dM[(t,w,a)(T)]/dM]/dT]/dM]/dT, d[d[d[dM[(t,w,i)(T)]/dM]/dT]/dM]/dT, d[d[d[dM[(t,w,m)(T)]/dM]/dT]/dM]/dT, d[d[d[dM[(t,a,i)(T)]/dM]/dT]/dM]/dT, d[d[d[dM[(t,a,m)(T)]/dM]/dT]/dM]/dT, d[d[d[dM[(t,i,m)(T)]/dM]/dT]/dM]/dT, d[d[d[dM[(w,a,i)(T)]/dM]/dT]/dM]/dT, d[d[d[dM[(w,a,m)(T)]/dM]/dT]/dM]/dT, d[d[d[dM[(w,i,m)(T)]/dM]/dT]/dM]/dT, d[d[d[dM[(a,i,m)(T)]/dM]/dT]/dM]/dT, d[d[d[dM[(t,w,a,i)(T)]/dM]/dT]/dM]/dT, d[d[d[dM[(t,w,a,m)(T)]/dM]/dT]/dM]/dT, d[d[d[dM[(t,w,i,m)(T)]/dM]/dT]/dM]/dT, d[d[d[dM[(t,a,i,m)(T)]/dM]/dT]/dM]/dT, d[d[d[dM[(w,a,i,m)(T)]/dM]/dT]/dM]/dT, d[d[d[dM[(t,w,a,i,m)(T)]/dM]/dT]/dM]/dT.

 

or as:

 

 

 

d[d[d[dM[(t)(T)]/dM]/dT]/dT]/dM, d[d[d[dM[(w)(T)]/dM]/dT]/dT]/dM, d[d[d[dM[(a)(T)]/dM]/dT]/dT]/dM, d[d[d[dM[(i)(T)]/dM]/dT]/dT]/dM, d[d[d[dM[(m)(T)]/dM]/dT]/dT]/dM, d[d[d[dM[(t,w)(T)]/dM]/dT]/dT]/dM, d[d[d[dM[(t,a)(T)]/dM]/dT]/dT]/dM, d[d[d[dM[(t,i)(T)]/dM]/dT]/dT]/dM, d[d[d[dM[(t,m)(T)]/dM]/dT]/dT]/dM, d[d[d[dM[(w,a)(T)]/dM]/dT]/dT]/dM, d[d[d[dM[(w,i)(T)]/dM]/dT]/dT]/dM, d[d[d[dM[(w,m)(T)]/dM]/dT]/dT]/dM, d[d[d[dM[(a,i)(T)]/dM]/dT]/dT]/dM, d[d[d[dM[(a,m)(T)]/dM]/dT]/dT]/dM, d[d[d[dM[(i,m)(T)]/dM]/dT]/dT]/dM, d[d[d[dM[(t,w,a)(T)]/dM]/dT]/dT]/dM, d[d[d[dM[(t,w,i)(T)]/dM]/dT]/dT]/dM, d[d[d[dM[(t,w,m)(T)]/dM]/dT]/dT]/dM, d[d[d[dM[(t,a,i)(T)]/dM]/dT]/dT]/dM, d[d[d[dM[(t,a,m)(T)]/dM]/dT]/dT]/dM, d[d[d[dM[(t,i,m)(T)]/dM]/dT]/dT]/dM, d[d[d[dM[(w,a,i)(T)]/dM]/dT]/dT]/dM, d[d[d[dM[(w,a,m)(T)]/dM]/dT]/dT]/dM, d[d[d[dM[(w,i,m)(T)]/dM]/dT]/dT]/dM, d[d[d[dM[(a,i,m)(T)]/dM]/dT]/dT]/dM, d[d[d[dM[(t,w,a,i)(T)]/dM]/dT]/dT]/dM, d[d[d[dM[(t,w,a,m)(T)]/dM]/dT]/dT]/dM, d[d[d[dM[(t,w,i,m)(T)]/dM]/dT]/dT]/dM, d[d[d[dM[(t,a,i,m)(T)]/dM]/dT]/dT]/dM, d[d[d[dM[(w,a,i,m)(T)]/dM]/dT]/dT]/dM, d[d[d[dM[(t,w,a,i,m)(T)]/dM]/dT]/dT]/dM.

 

or as:

 

d[d[d[dM[(t)(T)]/dT]/dM]/dM]/dT, d[d[d[dM[(w)(T)]/dT]/dM]/dM]/dT, d[d[d[dM[(a)(T)]/dT]/dM]/dM]/dT, d[d[d[dM[(i)(T)]/dT]/dM]/dM]/dT, d[d[d[dM[(m)(T)]/dT]/dM]/dM]/dT, d[d[d[dM[(t,w)(T)]/dT]/dM]/dM]/dT, d[d[d[dM[(t,a)(T)]/dT]/dM]/dM]/dT, d[d[d[dM[(t,i)(T)]/dT]/dM]/dM]/dT, d[d[d[dM[(t,m)(T)]/dT]/dM]/dM]/dT, d[d[d[dM[(w,a)(T)]/dT]/dM]/dM]/dT, d[d[d[dM[(w,i)(T)]/dT]/dM]/dM]/dT, d[d[d[dM[(w,m)(T)]/dT]/dM]/dM]/dT, d[d[d[dM[(a,i)(T)]/dT]/dM]/dM]/dT, d[d[d[dM[(a,m)(T)]/dT]/dM]/dM]/dT, d[d[d[dM[(i,m)(T)]/dT]/dM]/dM]/dT, d[d[d[dM[(t,w,a)(T)]/dT]/dM]/dM]/dT, d[d[d[dM[(t,w,i)(T)]/dT]/dM]/dM]/dT, d[d[d[dM[(t,w,m)(T)]/dT]/dM]/dM]/dT, d[d[d[dM[(t,a,i)(T)]/dT]/dM]/dM]/dT, d[d[d[dM[(t,a,m)(T)]/dT]/dM]/dM]/dT, d[d[d[dM[(t,i,m)(T)]/dT]/dM]/dM]/dT, d[d[d[dM[(w,a,i)(T)]/dT]/dM]/dM]/dT, d[d[d[dM[(w,a,m)(T)]/dT]/dM]/dM]/dT, d[d[d[dM[(w,i,m)(T)]/dT]/dM]/dM]/dT, d[d[d[dM[(a,i,m)(T)]/dT]/dM]/dM]/dT, d[d[d[dM[(t,w,a,i)(T)]/dT]/dM]/dM]/dT, d[d[d[dM[(t,w,a,m)(T)]/dT]/dM]/dM]/dT, d[d[d[dM[(t,w,i,m)(T)]/dT]/dM]/dM]/dT, d[d[d[dM[(t,a,i,m)(T)]/dT]/dM]/dM]/dT, d[d[d[dM[(w,a,i,m)(T)]/dT]/dM]/dM]/dT, d[d[d[dM[(t,w,a,i,m)(T)]/dT]/dM]/dM]/dT.

 

 

or as;

 

 

 

 

d[d[d[dM(t)/dM]/dM]/dT]/dT, d[d[d[dM(w)/dM]/dM]/dT]/dT, d[d[d[dM(a)/dM]/dM]/dT]/dT, d[d[d[dM(i)/dM]/dM]/dT]/dT, d[d[d[dM(m)/dM]/dM]/dT]/dT, d[d[d[dM(t,w)/dM]/dM]/dT]/dT, d[d[d[dM(t,a)/dM]/dM]/dT]/dT, d[d[d[dM(t,i)/dM]/dM]/dT]/dT, d[d[d[dM(t,m)/dM]/dM]/dT]/dT, d[d[d[dM(w,a)/dM]/dM]/dT]/dT, d[d[d[dM(w,i)/dM]/dM]/dT]/dT, d[d[d[dM(w,m)/dM]/dM]/dT]/dT, d[d[d[dM(a,i)/dM]/dM]/dT]/dT, d[d[d[dM(a,m)/dM]/dM]/dT]/dT, d[d[d[dM(i,m)/dM]/dM]/dT]/dT, d[d[d[dM(t,w,a)/dM]/dM]/dT]/dT, d[d[d[dM(t,w,i)/dM]/dM]/dT]/dT, d[d[d[dM(t,w,m)/dM]/dM]/dT]/dT, d[d[d[dM(t,a,i)/dM]/dM]/dT]/dT, d[d[d[dM(t,a,m)/dM]/dM]/dT]/dT,  d[d[d[dM(t,i,m)/dM]/dM]/dT]/dT, d[d[d[dM(w,a,i)/dM]/dM]/dT]/dT, d[d[d[dM(w,a,m)/dM]/dM]/dT]/dT, d[d[d[dM(w,i,m)/dM]/dM]/dT]/dT, d[d[d[dM(a,i,m)/dM]/dM]/dT]/dT, d[d[d[dM(t,w,a,i)/dM]/dM]/dT]/dT, d[d[d[dM(t,w,a,m)/dM/dM, d[d[d[dM(t,w,i,m)/dM]/dM]/dT]/dT, d[d[d[dM(t,a,i,m)/dM]/dM]/dT]/dT, d[d[d[dM(w,a,i,m)/dM]/dM]/dT]/dT, d[d[d[dM(t,w,a,i,m)/dM]/dM]/dT]/dT..

 

or as:

 

d[d[d[dM(t)/dT]/dM]/dT]/dM, d[d[d[dM(w)/dT]/dM]/dT]/dM, d[d[d[dM(a)/dT]/dM]/dT]/dM, d[d[d[dM(i)/dT]/dM]/dT]/dM, d[d[d[dM(m)/dT]/dM]/dT]/dM, d[d[d[dM(t,w)/dT]/dM]/dT]/dM, d[d[d[dM(t,a)/dT]/dM]/dT]/dM, d[d[d[dM(t,i)/dT]/dM]/dT]/dM, d[d[d[dM(t,m)/dT]/dM]/dT]/dM, d[d[d[dM(w,a)/dT]/dM]/dT]/dM, d[d[d[dM(w,i)/dT]/dM]/dT]/dM, d[d[d[dM(w,m)/dT]/dM]/dT]/dM, d[d[d[dM(a,i)/dT]/dM]/dT]/dM, d[d[d[dM(a,m)/dT]/dM]/dT]/dM, d[d[d[dM(i,m)/ dT]/dM]/dT]/dM, d[d[d[dM(t,w,a)/dT]/dM]/dT]/dM, d[d[d[dM(t,w,i)/dT]/dM]/dT]/dM, d[d[d[dM(t,w,m)/dT]/dM]/dT]/dM, d[d[d[dM(t,a,i)/dT]/dM]/dT]/dM, d[d[d[dM(t,a,m)/dT]/dM]/dT]/dM,  d[d[d[dM(t,i,m)/dT]/dM]/dT]/dM, d[d[d[dM(w,a,i)/dT]/dM]/dT]/dM, d[d[d[dM(w,a,m)/dT]/dM]/dT]/dM, d[d[d[dM(w,i,m)/dT]/dM]/dT]/dM, d[d[d[dM(a,i,m)/dT]/dM]/dT]/dM, d[d[d[dM(t,w,a,i)/dT]/dM]/dT]/dM, d[d[d[dM(t,w,a,m)/dM/dM, d[d[d[dM(t,w,i,m)/dT]/dM]/dT]/dM, d[d[d[dM(t,a,i,m)/dT]/dM]/dT]/dM, d[d[d[dM(w,a,i,m)/dT]/dM]/dT]/dM, d[d[d[dM(t,w,a,i,m)/dT]/dM]/dT]/dM..

 

or as:

 

d[d[d[dM(t)/dT]/dT]/dM]/dM, d[d[d[dM(w)/dT]/dT]/dM]/dM, d[d[d[dM(a)/dT]/dT]/dM]/dM, d[d[d[dM(i)/dT]/dT]/dM]/dM, d[d[d[dM(m)/dT]/dT]/dM]/dM, d[d[d[dM(t,w)/dT]/dT]/dM]/dM, d[d[d[dM(t,a)/dT]/dT]/dM]/dM, d[d[d[dM(t,i)/dT]/dT]/dM]/dM, d[d[d[dM(t,m)/dT]/dT]/dM]/dM, d[d[d[dM(w,a)/dT]/dT]/dM]/dM, d[d[d[dM(w,i)/dT]/dT]/dM]/dM, d[d[d[dM(w,m)/dT]/dT]/dM]/dM, d[d[d[dM(a,i)/dT]/dT]/dM]/dM, d[d[d[dM(a,m)/ dT]/dT]/dM]/dM, d[d[d[dM(i,m)/ dT]/dT]/dM]/dM, d[d[d[dM(t,w,a)/dT]/dT]/dM]/dM, d[d[d[dM(t,w,i)/dT]/dT]/dM]/dM, d[d[d[dM(t,w,m)/dT]/dT]/dM]/dM, d[d[d[dM(t,a,i)/dT]/dT]/dM]/dM, d[d[d[dM(t,a,m)/dT]/dT]/dM]/dM,  d[d[d[dM(t,i,m)/dT]/dT]/dM]/dM, d[d[d[dM(w,a,i)/dT]/dT]/dM]/dM, d[d[d[dM(w,a,m)/dT]/dT]/dM]/dM, d[d[d[dM(w,i,m)/dT]/dT]/dM]/dM, d[d[d[dM(a,i,m)/dT]/dT]/dM]/dM, d[d[d[dM(t,w,a,i)/dT]/dT]/dM]/dM, d[d[d[dM(t,w,a,m)/dM/dM, d[d[d[dM(t,w,i,m)/dT]/dT]/dM]/dM, d[d[d[dM(t,a,i,m)/dT]/dT]/dM]/dM, d[d[d[dM(w,a,i,m)/dT]/dT]/dM]/dM, d[d[d[dM(t,w,a,i,m)/dT]/dT]/dM]/dM..

 

We can also take higher order duel dimensional derivatives of memory as a function of memory and time but the symbolic expression of the set of such derivatives very soon becomes excessively lengthly to write and so these higher order derivatives as such are not mentioned here except to say that they would be computed in an analogous manner to the second order duel dimensional derivatives described above.

 

 

 

These seemingly crazy differentials might have some use in extreme psychological states that can be experienced by souls who are departed and whose memories, although perhaps spiritualized, are nonetheless, not limited by a body and its brain.

 

 

Another type of being that might experience such extreme memories change capacities might be none other then some of our friends we believe to exist as pure body-less and brain-less spirits known as angels.

 

 

Since I have dared to speculate this far, perhaps we can speculate as to whether any intelligent extraterrestrials persons or any so-called ultra-terrestrials persons that are more cognitively evolved then we ordinary humans might be capable of experiencing large absolute valued terms of Mn. Some such ETI and UTI persons may  have evolved over billions of years, or perhaps have far greater powers of sensation, memory, and intuition such as would seem plausible for any such persons and their civilizations who have not fallen from the state of innocence into the state of sin as we humans have, or perhaps such beings never had the option of  sanctifying grace opened to them but nonetheless may have been created at a naturally more perfect level then we humans, and who therefore might exhibit greater natural powers of memory and sensation.

 

We can also express memory qualitatively, statistically, and perhaps with the use of some forms of real analyses as a derivative with  respect to  thought or of t

 

Given that M(t) =  M(t and/or w and/or a and/or i and/or m), the following first order derivatives of memory  with respect to thought are possible.

 

 

dM(t)/dt, dM(w)/dt, dM(a)/dt, dM(i)/dt, dM(m)/dt, dM(t,w)/dt, dM(t,a)/dt, dM(t,i)/dt, dM(t,m)/dt, dM(w,a)/dt, dM(w,i)/dt, dM(w,m)/dt, dM(a,i)/dt, dM(a,m)/dt, dM(i,m)/dt, dM(t,w,a)/dt, dM(t,w,i)/dt, dM(t,w,m)/dt, dM(t,a,i)/dt, dM(t,a,m)/dt, dM(t,i,m)/dt, dM(w,a,i)/dt, dM(w,a,m)/dt, dM(w,i,m)/dt, dM(a,i,m)/dt, dM(t,w,a,i)/dt, dM(t,w,a,m)/dt, dM(t,w,i,m)/dt, dM(t,a,i,m)/dt, dM(w,a,i,m)/dt, dM(t,w,a,i,m)/dt.

 

 

Or more succinctly,  dM/dt = dM(t and/or w and/or a and/or i and/or m)/dt

 

 

Or perhaps dM(t)/dt =d M{[t(t)] and/or [w(t)] and/or [a(t)] and/or [i(t)] and/or [m(t)]}/dt.

 

 

Likewise, we can take the second thought derivatives of  M as follows:

 

 

 

d[dM(t)/dt]/dt, d[dM(w)/dt]/dt, d[dM(a)/dt]/dt, d[dM(i)/dt]/dt, d[dM(m)/dt]/dt, d[dM(t,w)/dt]/dt, d[dM(t,a)/dt]/dt, d[dM(t,i)/dt]/dt, d[dM(t,m)/dt]/dt, d[dM(w,a)/dt]/dt, d[dM(w,i)/dt]/dt, d[dM(w,m)/dt]/dt, d[dM(a,i)/dt]/dt, d[dM(a,m)/dt]/dt, d[dM(i,m)/dt/dt, d[dM(t,w,a)/dt]/dt, d[dM(t,w,i)/dt]/dt, d[dM(t,w,m)/dt]/dt, d[dM(t,a,i)/dt]/dt, d[dM(t,a,m)/dt]/dt,  d[dM(t,i,m)/dt]/dt, d[dM(w,a,i)/dt]/dt, d[dM(w,a,m)/dt]/dt, d[dM(w,i,m)/dt]/dt, d[dM(a,i,m)/dt]/dt, d[dM(t,w,a,i)/dt]/dt, d[dM(t,w,a,m)/dt/dt, d[dM(t,w,i,m)/dt]/dt, d[dM(t,a,i,m)/dt]/dt, d[dM(w,a,i,m)/dt]/dt, d[dM(t,w,a,i,m)/dt]/dt..

 

 

or more succinctly, as d(dM/dt)/dt = d[d M(t and/or w and/or a and/or i and/or m)/dt]/dt = Mt2

 

 

or as

 

 

d[dM(t)/dt]/dt  = d[d M{[t(t)] and/or [w(t)] and/or [a(t)] and/or [i(t)] and/or [m(t)]}/dt]/dt = Mt2.

 

 

 

Likewise, we can take the third thought derivatives of  M as follows:

 

 

 

d[d[dM(t)/dt]/dt]/dt, d[d[dM(w)/dt]/dt]/dt, d[d[dM(a)/dt]/dt]/dt, d[d[dM(i)/dt]/dt]/dt, d[d[dM(m)/dt]/dt]/dt, d[d[dM(t,w)/dt]/dt]/dt, d[d[dM(t,a)/dt]/dt]/dt, d[d[dM(t,i)/dt]/dt]/dt, d[d[dM(t,m)/dt]/dt]/dt, d[d[dM(w,a)/dt]/dt]/dt, d[d[dM(w,i)/dt]/dt]/dt, d[d[dM(w,m)/dt]/dt]/dt, d[d[dM(a,i)/dt]/dt]/dt, d[d[dM(a,m)/dt]/dt]/dt, d[d[dM(i,m)/dt/dt]/dt, d[d[dM(t,w,a)/dt]/dt]/dt, d[d[dM(t,w,i)/dt]/dt]/dt, d[d[dM(t,w,m)/dt]/dt]/dt, d[d[dM(t,a,i)/dt]/dt]/dt, d[d[dM(t,a,m)/dt]/dt]/dt,  d[d[dM(t,i,m)/dt]/dt]/dt, d[d[dM(w,a,i)/dt]/dt]/dt, d[d[dM(w,a,m)/dt]/dt]/dt, d[d[dM(w,i,m)/dt]/dt]/dt, d[d[dM(a,i,m)/dt]/dt]/dt, d[d[dM(t,w,a,i)/dt]/dt]/dt, d[d[dM(t,w,a,m)/dt/dt]/dt, d[d[dM(t,w,i,m)/dt]/dt]/dt, d[d[dM(t,a,i,m)/dt]/dt]/dt, d[d[dM(w,a,i,m)/dt]/dt]/dt, d[d[dM(t,w,a,i,m)/dt]/dt]/dt.

 

 

or more succinctly, as d[d(dM/dt)/dt]/dt = d[d[d M(t and/or w and/or a and/or i and/or m)/dt]/dt]/dt = Mt3

 

 

or as

 

 

d[d[dM(t)/dt]/dt]/dt  = d[d[d M{[t(t)] and/or [w(t)] and/or [a(t)] and/or [i(t)] and/or [m(t)]}/dt]/dt]/dt = Mt3.

 

 

We can also form the expressions;

 

 

d[d[f(M)]/dt]/dt = d{d [M[t(t)]]/dt and/or d[M[w(t)]]/dt and/or d[M[a(t)]]/dt and/or d[M[i(t)]]/dt and/or d[M[m(t)]]/dt}/dt  = f(Mt)2

 

 

and

 

 

d[d[d[f(M)]/dt]/dt]/dt = d{d{ d [M[t(t)]]/dt and/or d[M[w(t)]]/dt and/or d[M[a(t)]]/dt and/or d[M[m(t)]]/dt and/or d[M[m(t)]]/dt}/dt}/dt  = f(Mt)3A, where A stands for type A differentiation which is not to be confused with the meaning of so-called Type A personality as A is used as an ordinal in a totally different context here.

 

 

and

 

 

d[d[d[f(M)]/dt]/dt]/dt = d{d[d [M[t(t)]]/dt]/dt  and/or d[d [M[w(t)]]/dt]/dt  and/or d[d [M[a(t)]]/dt]/dt  and/or d[d [M[i(t)]]/dt]/dt  and/or d[d [M[m(t)]]/dt]/dt }/dt = f(Mt)3B, where B stands for type B differentiation which is not to be confused with the meaning of so-called Type  B personality as B is used as an ordinal in a totally different context here .

 

 

In fact, one can form yet higher order derivatives of memorys with respect to thought as follows.

 

 

Mt5 = d Mt4/dt = d[dMt3/dt]/dt

 

 

 

Mt5 = dMt4/dt =  d[d[d[d[d M{[t(t)] and/or [w(t)] and/or [a(t)] and/or [i(t)] and/or [m(t)]}/dt]/dt]/dt]/dt]/dt.

 

 

 

f(Mt)5A = d[f(tM)4A]/dt = d[d [f(Mt)3A]/dt]/dt =  d{d{d{d{ d [M[t(t)]]/dt and/or d[M[w(t)]]/dt and/or d[M[a(t)]]/dt and/or d[M[i(t)]]/dt and/or d[M[m(t)]]/dt}/dt}/dt]/dt]/dt

 

 

 

 

Mt6 = d Mt5/dt = d[d Mt4/dt]/dt = d[d[dMt3/dt]/dt]/dt

 

 

 

Mt6 = dMt5/dt = d[d[d[d[d[d M{[t(t)] and/or [w(t)] and/or [a(t)] and/or [i(t)] and/or [m(t)]}/dt]/dt]/dt]/dt]/dt]/dt

 

 

 

f(Mt)6A = d[f(Mt)5A]/dt = d{ d{d{d{d{ d [M[t(t)]]/dt and/or d[M[w(t)]]/dt and/or d[M[a(t)]]/dt and/or d[M[i(t)]]/dt and/or d[M[m(t)]]/dt}/dt}/dt]/dt]/dt]/dt

 

 

 

 

Mt7 = dMt6/dt

 

f(Mt)7A = d[f(Mt)6A]/dt

 

 

Mt8 = d Mt7/dt

 

f(Mt)8A = d[f(Mt)7A]/dt

 

 

 

Mt9 = d Mt8/dt

 

f(Mt)9A = d[f(Mt)8A]/dt

 

 

Mt10…, Mt11…, Mt12 … etc.

 

 

Anyone for Mt ensemble, or Mt infinity scrapper, or Mt (Aleph 0), or Mt(Aleph 1), or Mt(Aleph 2), or how about Mt Aleph (Aleph 0), or Mt Aleph (Aleph 1) , or Mt Aleph (Aleph 2), or even Mt Aleph (Aleph (Aleph 0)), or Mt Aleph (Aleph (Aleph 1)), or Mt Aleph (Aleph (Aleph 2)), and so on?

 

Thus, for the set of the sets of derivatives of             Mt1 through Mt(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Mt1 through Mt(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)},…, {П(0,31)[R]}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Mt1 through Mt(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Mt1 through Mt(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the derivative states in the set of the sets of derivatives of Mt1 through Mt(Aleph 0) is plausible equal to:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Mt1 through Mt(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Mt1 through Mt(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}}}.

 

For the set of the sets of derivatives of Mt1 through Mt(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Mt(Aleph 0) derivative space at the level of 0/(Aleph 0), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Mt1 through Mt(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Mt1 through Mt(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Mt1 through Mt(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Mt1 through Mt(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Mt1 through Mt(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Mt1 through Mt(Aleph 1), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Mt1 through  Mt(Aleph 2), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Mt1 through Mt(Aleph 3), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Mt(Aleph 0) derivative space at the level of 0/(Aleph 1), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Mt1 through Mt(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Mt1 through Mt(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Mt1 through Mt(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Mt1 through  Mt(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations  for the set of the sets of derivatives of Mt1 through Mt(Aleph 0) is plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Mt1 through Mt(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Mt1 through Mt(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Mt1 through Mt(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

 

For super-continuous Mt(Aleph 0) derivative space at the level of 0/(Aleph 2), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Mt1 through Mt(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Mt1 through Mt(Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Mt1 through Mt(Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Mt1 through Mt(Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Mt1 through Mt(Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Mt1 through Mt(Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Mt1 through Mt(Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Mt1 through Mt(Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

The general meaning of thought derivatives of memory can be viewed as the manner in which the qualitative and/or quantitative aspects of memory  as a function of thought very with thought. The manner in which memories very with thought  may be multi- thought-aspect dimensional wherein the dimensions of derivations can be multiple, and wherein the derivations can be taken in parallel, series parallel or in serial manner. The differentials can be partial or non-partial derivatives, or both partial and non-partial for a given computation.

 

In fact, since there is in theory, no limit to the numbers of qualitatively and quantitatively different memories, and perhaps no limit to the number of possible different types or classes of memories or potential memories, wherein each person has his or her own unique memories, the number of thought dimensions that can effect memory is literally infinite, given the entirety of the set of created persons, and perhaps also literally infinite for each person as an individual, although we can not intellectually and intuitively understand this infinite number.

 

It is interesting to consider the ramifactions of being able to perform realistic calculations involving thought derivatives of memory from a mathematical, theoretical, scientific,  and philosophical perspective.

 

Persons for which one or more nth order derivatives of memory with respect to thought that have large absolute values would tend to have their memories highly influenced by thought, or at least for the memory under consideration with respect to the dimension of the specific memory type(s) or class(es) for which the differentiation(s) are performed. Perhaps a strong coupling between memory and thought indicates a well integrated personality and commensurately, a high degree of memory capacity and a high degree of memory intelligence.

 

We would expect that disembodied human souls, ETI souls, and/or UTI souls in Heaven, Limbo, highly evolved bodily ETI persons, highly evolved UTI persons, and angels to have memory of all kinds and intensities which are highly subject to memory.

 

 

We can also consider two dimensional nth ordered derivatives of memory with respect to thought and time, or with respect to t and T, respectively.

 

Given that M[(t)(T)] =  M[(t and/or w and/or a and/or i and/or m)(t)(T)], the following first order two dimensional derivatives of memory with respect to thought and Time are possible.

 

 

d[dM[(t)(T)]/dt]/dT, d[dM[(w)(T)]/dt]/dT, d[dM[(a)(T)]/dt]/dT, d[dM[(i)(T)]/dt]/dT, d[dM[(m)(T)]/dt]/dT, d[dM[(t,w)(T)]/dt]/dT, d[dM[(t,a)(T)]/dt]/dT, d[dM[(t,i)(T)]/dt]/dT, d[dM[(t,m)(T)]/dt]/dT, d[dM[(w,a)(T)]/dt]/dT, d[dM[(w,i)(T)]/dt]/dT, d[dM[(w,m)(T)]/dt]/dT, d[dM[(a,i)(T)]/dt]/dT, d[dM[(a,m)(T)]/dt]/dT, d[dM[(i,m)(T)]/dt]/dT, d[dM[(t,w,a)(T)]/dt]/dT, d[dM[(t,w,i)(T)]/dt]/dT, d[dM[(t,w,m)(T)]/dt]/dT, d[dM[(t,a,i)(T)]/dt]/dT, d[dM[(t,a,m)(T)]/dt]/dT, d[dM[(t,i,m)(T)]/dt]/dT, d[dM[(w,a,i)(T)]/dt]/dT, d[dM[(w,a,m)(T)]/dt]/dT, d[dM[(w,i,m)(T)]/dt]/dT, d[dM[(a,i,m)(T)]/dt]/dT, d[dM[(t,w,a,i)(T)]/dt]/dT, d[dM[(t,w,a,m)(T)]/dt]/dT, d[dM[(t,w,i,m)(T)]/dt]/dT, d[dM[(t,a,i,m)(T)]/dt]/dT, d[dM[(w,a,i,m)(T)]/dt]/dT, d[dM[(t,w,a,i,m)(T)]/dt]/dT.

 

 

Or more succinctly,  d[dM(T)/dt]/dT = d[dM[(T)(t and/or w and/or a and/or i and/or m)]/dt]/dT

 

or

 

d[dM(T)/dT]/dt = d[dM[(T)(t and/or w and/or a and/or i and/or m)]/dT]/dt

 

 

 

 

 

Or perhaps d[d M[(t)(T)]/dt]/dT  = d[d M [{[t(t)] and/or [w(t)] and/or [a(t)] and/or [i(t)] and/or [m(t)]}(T)]/dt]/dT

 

or

 

Or perhaps d[d M[(t)(T)]/dT]/dt  = d[d M [{[t(t)] and/or [w(t)] and/or [a(t)] and/or [i(t)] and/or [m(t)]}(T)]/dT]/dt

 

 

 

Likewise, we can take the second dual dimensioned memory-time derivatives of  M as follows:

 

d[d[d[dM[(t)(T)]/dt]/dT]/dt]/dT, d[d[d[dM[(w)(T)]/dt]/dT]/dt]/dT, d[d[d[dM[(a)(T)]/dt]/dT]/dt]/dT, d[d[d[dM[(i)(T)]/dt]/dT]/dt]/dT, d[d[d[dM[(m)(T)]/dt]/dT]/dt]/dT, d[d[d[dM[(t,w)(T)]/dt]/dT]/dt]/dT, d[d[d[dM[(t,a)(T)]/dt]/dT]/dt]/dT, d[d[d[dM[(t,i)(T)]/dt]/dT]/dt]/dT, d[d[d[dM[(t,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dM[(w,a)(T)]/dt]/dT]/dt]/dT, d[d[d[dM[(w,i)(T)]/dt]/dT]/dt]/dT, d[d[d[dM[(w,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dM[(a,i)(T)]/dt]/dT]/dt]/dT, d[d[d[dM[(a,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dM[(i,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dM[(t,w,a)(T)]/dt]/dT]/dt]/dT, d[d[d[dM[(t,w,i)(T)]/dt]/dT]/dt]/dT, d[d[d[dM[(t,w,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dM[(t,a,i)(T)]/dt]/dT]/dt]/dT, d[d[d[dM[(t,a,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dM[(t,i,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dM[(w,a,i)(T)]/dt]/dT]/dt]/dT, d[d[d[dM[(w,a,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dM[(w,i,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dM[(a,i,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dM[(t,w,a,i)(T)]/dt]/dT]/dt]/dT, d[d[d[dM[(t,w,a,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dM[(t,w,i,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dM[(t,a,i,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dM[(w,a,i,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dM[(t,w,a,i,m)(T)]/dt]/dT]/dt]/dT.

 

or as:

 

 

 

d[d[d[dM[(t)(T)]/dt]/dT]/dT]/dt, d[d[d[dM[(w)(T)]/dt]/dT]/dT]/dt, d[d[d[dM[(a)(T)]/dt]/dT]/dT]/dt, d[d[d[dM[(i)(T)]/dt]/dT]/dT]/dt, d[d[d[dM[(m)(T)]/dt]/dT]/dT]/dt, d[d[d[dM[(t,w)(T)]/dt]/dT]/dT]/dt, d[d[d[dM[(t,a)(T)]/dt]/dT]/dT]/dt, d[d[d[dM[(t,i)(T)]/dt]/dT]/dT]/dt, d[d[d[dM[(t,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dM[(w,a)(T)]/dt]/dT]/dT]/dt, d[d[d[dM[(w,i)(T)]/dt]/dT]/dT]/dt, d[d[d[dM[(w,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dM[(a,i)(T)]/dt]/dT]/dT]/dt, d[d[d[dM[(a,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dM[(i,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dM[(t,w,a)(T)]/dt]/dT]/dT]/dt, d[d[d[dM[(t,w,i)(T)]/dt]/dT]/dT]/dt, d[d[d[dM[(t,w,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dM[(t,a,i)(T)]/dt]/dT]/dT]/dt, d[d[d[dM[(t,a,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dM[(t,i,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dM[(w,a,i)(T)]/dt]/dT]/dT]/dt, d[d[d[dM[(w,a,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dM[(w,i,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dM[(a,i,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dM[(t,w,a,i)(T)]/dt]/dT]/dT]/dt, d[d[d[dM[(t,w,a,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dM[(t,w,i,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dM[(t,a,i,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dM[(w,a,i,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dM[(t,w,a,i,m)(T)]/dt]/dT]/dT]/dt.

 

or as:

 

d[d[d[dM[(t)(T)]/dT]/dt]/dt]/dT, d[d[d[dM[(w)(T)]/dT]/dt]/dt]/dT, d[d[d[dM[(a)(T)]/dT]/dt]/dt]/dT, d[d[d[dM[(i)(T)]/dT]/dt]/dt]/dT, d[d[d[dM[(m)(T)]/dT]/dt]/dt]/dT, d[d[d[dM[(t,w)(T)]/dT]/dt]/dt]/dT, d[d[d[dM[(t,a)(T)]/dT]/dt]/dt]/dT, d[d[d[dM[(t,i)(T)]/dT]/dt]/dt]/dT, d[d[d[dM[(t,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dM[(w,a)(T)]/dT]/dt]/dt]/dT, d[d[d[dM[(w,i)(T)]/dT]/dt]/dt]/dT, d[d[d[dM[(w,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dM[(a,i)(T)]/dT]/dt]/dt]/dT, d[d[d[dM[(a,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dM[(i,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dM[(t,w,a)(T)]/dT]/dt]/dt]/dT, d[d[d[dM[(t,w,i)(T)]/dT]/dt]/dt]/dT, d[d[d[dM[(t,w,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dM[(t,a,i)(T)]/dT]/dt]/dt]/dT, d[d[d[dM[(t,a,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dM[(t,i,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dM[(w,a,i)(T)]/dT]/dt]/dt]/dT, d[d[d[dM[(w,a,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dM[(w,i,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dM[(a,i,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dM[(t,w,a,i)(T)]/dT]/dt]/dt]/dT, d[d[d[dM[(t,w,a,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dM[(t,w,i,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dM[(t,a,i,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dM[(w,a,i,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dM[(t,w,a,i,m)(T)]/dT]/dt]/dt]/dT.

 

 

or as;

 

 

 

 

d[d[d[dM(t)/dt]/dt]/dT]/dT, d[d[d[dM(w)/dt]/dt]/dT]/dT, d[d[d[dM(a)/dt]/dt]/dT]/dT, d[d[d[dM(i)/dt]/dt]/dT]/dT, d[d[d[dM(m)/dt]/dt]/dT]/dT, d[d[d[dM(t,w)/dt]/dt]/dT]/dT, d[d[d[dM(t,a)/dt]/dt]/dT]/dT, d[d[d[dM(t,i)/dt]/dt]/dT]/dT, d[d[d[dM(t,m)/dt]/dt]/dT]/dT, d[d[d[dM(w,a)/dt]/dt]/dT]/dT, d[d[d[dM(w,i)/dt]/dt]/dT]/dT, d[d[d[dM(w,m)/dt]/dt]/dT]/dT, d[d[d[dM(a,i)/dt]/dt]/dT]/dT, d[d[d[dM(a,m)/dt]/dt]/dT]/dT, d[d[d[dM(i,m)/dt]/dt]/dT]/dT, d[d[d[dM(t,w,a)/dt]/dt]/dT]/dT, d[d[d[dM(t,w,i)/dt]/dt]/dT]/dT, d[d[d[dM(t,w,m)/dt]/dt]/dT]/dT, d[d[d[dM(t,a,i)/dt]/dt]/dT]/dT, d[d[d[dM(t,a,m)/dt]/dt]/dT]/dT,  d[d[d[dM(t,i,m)/dt]/dt]/dT]/dT, d[d[d[dM(w,a,i)/dt]/dt]/dT]/dT, d[d[d[dM(w,a,m)/dt]/dt]/dT]/dT, d[d[d[dM(w,i,m)/dt]/dt]/dT]/dT, d[d[d[dM(a,i,m)/dt]/dt]/dT]/dT, d[d[d[dM(t,w,a,i)/dt]/dt]/dT]/dT, d[d[d[dM(t,w,a,m)/dt/dt, d[d[d[dM(t,w,i,m)/dt]/dt]/dT]/dT, d[d[d[dM(t,a,i,m)/dt]/dt]/dT]/dT, d[d[d[dM(w,a,i,m)/dt]/dt]/dT]/dT, d[d[d[dM(t,w,a,i,m)/dt]/dt]/dT]/dT..

 

or as:

 

d[d[d[dM(t)/dT]/dt]/dT]/dt, d[d[d[dM(w)/dT]/dt]/dT]/dt, d[d[d[dM(a)/dT]/dt]/dT]/dt, d[d[d[dM(i)/dT]/dt]/dT]/dt, d[d[d[dM(m)/dT]/dt]/dT]/dt, d[d[d[dM(t,w)/dT]/dt]/dT]/dt, d[d[d[dM(t,a)/dT]/dt]/dT]/dt, d[d[d[dM(t,i)/dT]/dt]/dT]/dt, d[d[d[dM(t,m)/dT]/dt]/dT]/dt, d[d[d[dM(w,a)/dT]/dt]/dT]/dt, d[d[d[dM(w,i)/dT]/dt]/dT]/dt, d[d[d[dM(w,m)/dT]/dt]/dT]/dt, d[d[d[dM(a,i)/dT]/dt]/dT]/dt, d[d[d[dM(a,m)/dT]/dt]/dT]/dt, d[d[d[dM(i,m)/ dT]/dt]/dT]/dt, d[d[d[dM(t,w,a)/dT]/dt]/dT]/dt, d[d[d[dM(t,w,i)/dT]/dt]/dT]/dt, d[d[d[dM(t,w,m)/dT]/dt]/dT]/dt, d[d[d[dM(t,a,i)/dT]/dt]/dT]/dt, d[d[d[dM(t,a,m)/dT]/dt]/dT]/dt,  d[d[d[dM(t,i,m)/dT]/dt]/dT]/dt, d[d[d[dM(w,a,i)/dT]/dt]/dT]/dt, d[d[d[dM(w,a,m)/dT]/dt]/dT]/dt, d[d[d[dM(w,i,m)/dT]/dt]/dT]/dt, d[d[d[dM(a,i,m)/dT]/dt]/dT]/dt, d[d[d[dM(t,w,a,i)/dT]/dt]/dT]/dt, d[d[d[dM(t,w,a,m)/dt/dt, d[d[d[dM(t,w,i,m)/dT]/dt]/dT]/dt, d[d[d[dM(t,a,i,m)/dT]/dt]/dT]/dt, d[d[d[dM(w,a,i,m)/dT]/dt]/dT]/dt, d[d[d[dM(t,w,a,i,m)/dT]/dt]/dT]/dt..

 

or as:

 

d[d[d[dM(t)/dT]/dT]/dt]/dt, d[d[d[dM(w)/dT]/dT]/dt]/dt, d[d[d[dM(a)/dT]/dT]/dt]/dt, d[d[d[dM(i)/dT]/dT]/dt]/dt, d[d[d[dM(m)/dT]/dT]/dt]/dt, d[d[d[dM(t,w)/dT]/dT]/dt]/dt, d[d[d[dM(t,a)/dT]/dT]/dt]/dt, d[d[d[dM(t,i)/dT]/dT]/dt]/dt, d[d[d[dM(t,m)/dT]/dT]/dt]/dt, d[d[d[dM(w,a)/dT]/dT]/dt]/dt, d[d[d[dM(w,i)/dT]/dT]/dt]/dt, d[d[d[dM(w,m)/dT]/dT]/dt]/dt, d[d[d[dM(a,i)/dT]/dT]/dt]/dt, d[d[d[dM(a,m)/ dT]/dT]/dt]/dt, d[d[d[dM(i,m)/ dT]/dT]/dt]/dt, d[d[d[dM(t,w,a)/dT]/dT]/dt]/dt, d[d[d[dM(t,w,i)/dT]/dT]/dt]/dt, d[d[d[dM(t,w,m)/dT]/dT]/dt]/dt, d[d[d[dM(t,a,i)/dT]/dT]/dt]/dt, d[d[d[dM(t,a,m)/dT]/dT]/dt]/dt,  d[d[d[dM(t,i,m)/dT]/dT]/dt]/dt, d[d[d[dM(w,a,i)/dT]/dT]/dt]/dt, d[d[d[dM(w,a,m)/dT]/dT]/dt]/dt, d[d[d[dM(w,i,m)/dT]/dT]/dt]/dt, d[d[d[dM(a,i,m)/dT]/dT]/dt]/dt, d[d[d[dM(t,w,a,i)/dT]/dT]/dt]/dt, d[d[d[dM(t,w,a,m)/dt/dt, d[d[d[dM(t,w,i,m)/dT]/dT]/dt]/dt, d[d[d[dM(t,a,i,m)/dT]/dT]/dt]/dt, d[d[d[dM(w,a,i,m)/dT]/dT]/dt]/dt, d[d[d[dM(t,w,a,i,m)/dT]/dT]/dt]/dt..

 

 

We can also take higher order duel dimensional derivatives of memory as a function of thought and time but the symbolic expression of the set of such derivatives very soon becomes excessively lengthly to write and so these higher order derivatives as such are not mentioned here except to say that they would be computed in an analogous manner to the second order duel dimensional derivatives described above.

 

The above notation of derivatives and differential equations is just an infinitesimal glimpse of the number of possible equations as such and related constructs. Trust me, I can reasonably in good confidence re-assure you of such.

 

 

33) Just A Shadow Of A Glimpse Of The Utterly Limitless Number Derivatives of Human Thought  With Respect To Time, Thought, Volition, Affect, Memory, Instinct, And Emotion  Where These Latter 6 Psychodynamic Parameter Are Likely Just An Infinitesimal Fraction Of The Number Of Possible Psychodynamic Parameters, Of Which In This Life, We Have  A Glimpse Of Relatively Few.

 

 

 

 

Thought  as such can be a function or partially a function of emotion, will, affect, instinct, emotion and/or memory; and thought as such can be expressed as follows:

 

 

TH(t), TH(w), TH(a), TH(i), TH(m), TH(t,w), TH(t,a), TH(t,i), TH(t,m), TH(w,a), TH(w,i), TH(w,m), TH(a,i), TH(a,m), TH(i,m), TH(t,w,a), TH(t,w,i), TH(t,w,m), TH(t,a,i), TH(t,a,m), TH(t,i,m), TH(w,a,i), TH(w,a,m), TH(w,i,m), TH(a,i,m), TH(t,w,a,i), TH(t,w,a,m), TH(t,w,i,m), TH(t,a,i,m), TH(w,a,i,m), TH(t,w,a,i,m)

 

TH(t,e), TH(w,e), TH(a,e), TH(i,e), TH(m,e), TH(t,w,e), TH(t,a,e), TH(t,i,e), TH(t,m,e), TH(w,a,e), TH(w,i,e), TH(w,m,e), TH(a,i,e), TH(a,m,e), TH(i,m,e), TH(t,w,a,e), TH(t,w,i,e), TH(t,w,m,e), TH(t,a,i,e), TH(t,a,m,e), TH(t,i,m,e), TH(w,a,i,e), TH(w,a,m,e), TH(w,i,m,e), TH(a,i,m,e), TH(t,w,a,i,e), TH(t,w,a,m,e), TH(t,w,i,m,e), TH(t,a,i,m,e), TH(w,a,i,m,e), TH(t,w,a,i,m,e).

 

Note that some differential expressions involving  the form of functions of thought, or TH,  as a function of emotion, e, by itself, or in conjunction with any sub-set of the parameters of t,w,a,i,m, are not included to the same extent as many similar expressions including TH, and these other parameters denoted by the small letters, t,w,a,i, and/or m in this section. A more comphrensive post will include the currently omitted explicit formulas incorporating the parameter, e. Note that capital e, or E, is a parameter that is often included in the differential equations herein, but then so in a slightly different context than e would have be included. The difference between e and E will become clear from the context of the specific formulas.

 

In all, there are (2 EXP n) – 1 = (2 EXP 6) – 1 = 63 expressions as such if one assumes the previous five dimensions of thought.

 

In this article, we will cover the notion of arbitrary finite and more or less arbitrarily infinity ordered derivatives of human, ETI, and UTI thought with respect to time, thought, will, affect, memory, instinct, and emotion.

 

Even in the case where the first order derivatives as such are small in magnitude, this does not preclude non-zero first order derivatives of more or less arbitrary infinity orders with respect to the same psychodynamic variables. This is plausibly true since the derivatives described herein are not totally quantitative and in many respect are not quantitative. Also, for the quantitative aspects of such infinity ordered derivatives of  thought, the complexity of the precise mathematical expressions may be such that there are an arbitrarily infinite number of  various infinite ordered derivatives such that the numerical infinities cancel out.

 

Another argument for the plausibility of  non-zero infinite order derivatives of thought is that each aspect of human psychodynamic activity or states are immeadiately present to themselves in the sense that each such activity or change of state occurs within the complete and total simultaneous unity of the associated human person, more specifically within the associated human soul.

 

Yet another argument is that the difference in the various derivatives as such may be small even in the midst of a range of derivatives that spans infinite numbers of orders. Such small differences may be the result of infinities that cancel out, but may also be the result of non-numerically quantifiable aspects of the sets of such derivatives.

 

The Human Heart is so complex that I am not sure how the concepts described herein can be not valid even amidst the generally non violent or at least not too violent or not too over whelmingly strong effects of one psychodynamic parameter state on another.

 

So despite the fact that we do not notice infinitely rapid or infinite intra-reactive changes within our psychodynamic states, the arguments for the plausibility of non-zero infinite ordered derivatives of thought with respect to other basic psychodynamic parameters or aspects is argued as above and mathematically categorized herein below.

 

 

 

 

Thought  as such can be a function or partially a function of emotion, will, affect, instinct, emotion and/or memory; and thought as such can be expressed as follows:

 

 

TH(t), TH(w), TH(a), TH(i), TH(m), TH(t,w), TH(t,a), TH(t,i), TH(t,m), TH(w,a), TH(w,i), TH(w,m), TH(a,i), TH(a,m), TH(i,m), TH(t,w,a), TH(t,w,i), TH(t,w,m), TH(t,a,i), TH(t,a,m), TH(t,i,m), TH(w,a,i), TH(w,a,m), TH(w,i,m), TH(a,i,m), TH(t,w,a,i), TH(t,w,a,m), TH(t,w,i,m), TH(t,a,i,m), TH(w,a,i,m), TH(t,w,a,i,m)

 

TH(t,e), TH(w,e), TH(a,e), TH(i,e), TH(m,e), TH(t,w,e), TH(t,a,e), TH(t,i,e), TH(t,m,e), TH(w,a,e), TH(w,i,e), TH(w,m,e), TH(a,i,e), TH(a,m,e), TH(i,m,e), TH(t,w,a,e), TH(t,w,i,e), TH(t,w,m,e), TH(t,a,i,e), TH(t,a,m,e), TH(t,i,m,e), TH(w,a,i,e), TH(w,a,m,e), TH(w,i,m,e), TH(a,i,m,e), TH(t,w,a,i,e), TH(t,w,a,m,e), TH(t,w,i,m,e), TH(t,a,i,m,e), TH(w,a,i,m,e), TH(t,w,a,i,m,e).

 

 

Assuming that each of the above function f(TH)  is perfectly continuous, the number of forms that the general emotion function, f(TH), can have is plausibly equal to П(1,62)R where R is the number of real numbers.

 

Assuming that each of the above functions f(TH) is super-continuous at the level of 0/(Aleph 0) where Aleph 0 is the number of integers, the number of forms that the general emotion function, f(TH), can have is plausibly equal to П(1,62)[R x (Aleph 0)] where R is the number of real numbers.

 

Assuming that each of the above functions f(TH) is super-continuous at the level of 0/(Aleph 1) where Aleph 1 is the number of real numbers according to the Continuum Hypotheses, the number of forms that the general affect function, f(TH), can have is plausibly equal to П(1,62)[R x (Aleph 1)] where R is the number of real numbers.

 

Assuming that each of the above functions f(TH) is super-continuous at the level of 0/(Aleph 2) where Aleph 2 is is greater than Aleph 1 by a factor of infinity (the exact details of this infinity of which are a little more involve than the latter simple statement), the number of forms that the general thought function, f(TH), can have is plausibly equal to П(1,62)[R x (Aleph 2)] where R is the number of real numbers.

 

Assuming that each of the above functions f(TH) is super-continuous at the level of 0/(Aleph 3) where Aleph 3 is is greater than Aleph 2 by a factor of infinity (the exact details of this infinity of which are a little more involve than the latter simple statement), the number of forms that the general thought function, f(TH), can have is plausibly equal to П(1,62)[R x (Aleph 3)] where R is the number of real numbers.

 

… and so on ad infinitum to, through, and beyond the following product series, П(1,62)[R x (Aleph 4)],   П(1,62)[R x (Aleph 5)],  П(1,62)[R x (Aleph 6)],…,  П(1,62)[R x (Aleph Ω)], …,  П(1,62)[R x (Aleph (Aleph 0))], …, П(1,62)[R x (Aleph (Aleph 1))], …, П(1,62)[R x (Aleph (Aleph 2))], … , П(1,62)[R x (Aleph (Aleph Ω))], …, П(1,62)[R x (Aleph (Aleph (Aleph 0)))] and so on perhaps in an ever lasting series even a  the latter level of abstraction.

 

Assuming that each of the above functions f(TH) is super-continuous at the level of 0/(Aleph 2) where Aleph 2 is is greater than Aleph 1 by a factor of infinity (the exact details of this infinity of which are a little more involve than the latter simple statement), the number of forms that the general affect function, f(TH), can have is plausibly equal to П(1,62)[R x (Aleph 2)] where R is the number of real numbers.

 

 

 

We can summarize all of these combinations as follows in compact symbolism that is intuitively clear to follow:

 

 

TH = TH(t and/or w and/or a and/or i and/or m)

 

 

We can express TH as a function of time as follows: TH(T) =  TH[(t and/or w and/or a and/or i and/or m),(T)] or perhaps the following notation can be more appropriate in certain circumstances.

 

 

TH(T) = TH{[t(T)] and/or [w(T)] and/or [a(T)] and/or [i(T)] and/or [m(T)]}.

 

 

Thus, the following first order derivatives of thought with respect to time are possible.

 

 

dTH(t)/dT, dTH(w)/dT, dTH(a)/dT, dTH(i)/dT, dTH(m)/dT, dTH(t,w)/dT, dTH(t,a)/dT, dTH(t,i)/dT, dTH(t,m)/dT, dTH(w,a)/dT, dTH(w,i)/dT, dTH(w,m)/dT, dTH(a,i)/dT, dTH(a,m)/dT, dTH(i,m)/dT, dTH(t,w,a)/dT, dTH(t,w,i)/dT, dTH(t,w,m)/dT, dTH(t,a,i)/dT, dTH(t,a,m)/dT, dTH(t,i,m)/dT, dTH(w,a,i)/dT, dTH(w,a,m)/dT, dTH(w,i,m)/dT, dTH(a,i,m)/dT, dTH(t,w,a,i)/dT, dTH(t,w,a,m)/dT, dTH(t,w,i,m)/dT, dTH(t,a,i,m)/dT, dTH(w,a,i,m)/dT, dTH(t,w,a,i,m)/dT.

 

 

Or more succinctly,  dTH/dT = dTH(t and/or w and/or a and/or i and/or m)/dT

 

 

Or perhaps dTH(T)/dT =d TH{[t(T)] and/or [w(T)] and/or [a(T)] and/or [i(T)] and/or [m(T)]}/dT.

 

 

Likewise, we can take the second time derivatives of  TH as follows:

 

 

 

d[dTH(t)/dT]/dT, d[dTH(w)/dT]/dT, d[dTH(a)/dT]/dT, d[dTH(i)/dT]/dT, d[dTH(m)/dT]/dT, d[dTH(t,w)/dT]/dT, d[dTH(t,a)/dT]/dT, d[dTH(t,i)/dT]/dT, d[dTH(t,m)/dT]/dT, d[dTH(w,a)/dT]/dT, d[dTH(w,i)/dT]/dT, d[dTH(w,m)/dT]/dT, d[dTH(a,i)/dT]/dT, d[dTH(a,m)/dT]/dT, d[dTH(i,m)/dT/dT, d[dTH(t,w,a)/dT]/dT, d[dTH(t,w,i)/dT]/dT, d[dTH(t,w,m)/dT]/dT, d[dTH(t,a,i)/dT]/dT, d[dTH(t,a,m)/dT]/dT,  d[dTH(t,i,m)/dT]/dT, d[dTH(w,a,i)/dT]/dT, d[dTH(w,a,m)/dT]/dT, d[dTH(w,i,m)/dT]/dT, d[dTH(a,i,m)/dT]/dT, d[dTH(t,w,a,i)/dT]/dT, d[dTH(t,w,a,m)/dT/dT, d[dTH(t,w,i,m)/dT]/dT, d[dTH(t,a,i,m)/dT]/dT, d[dTH(w,a,i,m)/dT]/dT, d[dTH(t,w,a,i,m)/dT]/dT..

 

 

or more succinctly, as d(dTH/dT)/dT = d[d TH(t and/or w and/or a and/or i and/or m)/dT]/dT = TH2

 

 

or as

 

 

d[dTH(T)/dT]/dT  = d[d TH{[t(T)] and/or [w(T)] and/or [a(T)] and/or [i(T)] and/or [m(T)]}/dT]/dT = TH2.

 

 

 

Likewise, we can take the third time derivatives of  TH as follows:

 

 

 

d[d[dTH(t)/dT]/dT]/dT, d[d[dTH(w)/dT]/dT]/dT, d[d[dTH(a)/dT]/dT]/dT, d[d[dTH(i)/dT]/dT]/dT, d[d[dTH(m)/dT]/dT]/dT, d[d[dTH(t,w)/dT]/dT]/dT, d[d[dTH(t,a)/dT]/dT]/dT, d[d[dTH(t,i)/dT]/dT]/dT, d[d[dTH(t,m)/dT]/dT]/dT, d[d[dTH(w,a)/dT]/dT]/dT, d[d[dTH(w,i)/dT]/dT]/dT, d[d[dTH(w,m)/dT]/dT]/dT, d[d[dTH(a,i)/dT]/dT]/dT, d[d[dTH(a,m)/dT]/dT]/dT, d[d[dTH(i,m)/dT/dT]/dT, d[d[dTH(t,w,a)/dT]/dT]/dT, d[d[dTH(t,w,i)/dT]/dT]/dT, d[d[dTH(t,w,m)/dT]/dT]/dT, d[d[dTH(t,a,i)/dT]/dT]/dT, d[d[dTH(t,a,m)/dT]/dT]/dT,  d[d[dTH(t,i,m)/dT]/dT]/dT, d[d[dTH(w,a,i)/dT]/dT]/dT, d[d[dTH(w,a,m)/dT]/dT]/dT, d[d[dTH(w,i,m)/dT]/dT]/dT, d[d[dTH(a,i,m)/dT]/dT]/dT, d[d[dTH(t,w,a,i)/dT]/dT]/dT, d[d[dTH(t,w,a,m)/dT/dT]/dT, d[d[dTH(t,w,i,m)/dT]/dT]/dT, d[d[dTH(t,a,i,m)/dT]/dT]/dT, d[d[dTH(w,a,i,m)/dT]/dT]/dT, d[d[dTH(t,w,a,i,m)/dT]/dT]/dT.

 

 

or more succinctly, as d[d(dTH/dT)/dT]/dT = d[d[d TH(t and/or w and/or a and/or i and/or m)/dT]/dT]/dT = TH3

 

 

or as

 

 

d[d[dTH(T)/dT]/dT]/dT  = d[d[d TH{[t(T)] and/or [w(T)] and/or [a(T)] and/or [i(T)] and/or [m(T)]}/dT]/dT]/dT = TH3.

 

 

We can also form the expressions;

 

 

d[d[f(TH)]/dT]/dT = d{d [TH[t(T)]]/dT and/or d[TH[w(T)]]/dT and/or d[TH[a(T)]]/dT and/or d[TH[i(T)]]/dT and/or d[TH[m(T)]]/dT}/dT  = f(TH)2

 

 

and

 

 

d[d[d[f(TH)]/dT]/dT]/dT = d{d{ d [TH[t(T)]]/dT and/or d[TH[w(T)]]/dT and/or d[TH[a(T)]]/dT and/or d[TH[i(T)]]/dT and/or d[TH[m(T)]]/dT}/dT}/dT  = f(TH)3A, where A stands for type A differentiation which is not to be confused with the meaning of so-called Type A personality as A is used as an ordinal in a totally different context here.

 

 

and

 

 

d[d[d[f(TH)]/dT]/dT]/dT = d{d[d [TH[t(T)]]/dT]/dT  and/or d[d [TH[w(T)]]/dT]/dT  and/or d[d [TH[a(T)]]/dT]/dT  and/or d[d [TH[i(T)]]/dT]/dT  and/or d[d [TH[m(T)]]/dT]/dT }/dT = f(TH)3B, where B stands for type B differentiation which is not to be confused with the meaning of a  so-called Type  B personality as B is used as an ordinal in a totally different context here .

 

 

In fact, one can form yet higher order derivatives of thoughts with respect to time as follows.

 

 

TH5 = d TH4/dT = d[dTH3/dT]/dT

 

 

 

TH5 = d TH4/dT =  d[d[d[d[d TH{[t(T)] and/or [w(T)] and/or [a(T)] and/or [i(T)] and/or [m(T)]}/dT]/dT]/dT]/dT]/dT.

 

 

 

f(TH)5A = d[f(TH)4A]/dT = d[d [f(TH)3A]/dT]/dT =  d{d{d{d{ d [TH[t(T)]]/dT and/or d[TH[w(T)]]/dT and/or d[TH[a(T)]]/dT and/or d[TH[i(T)]]/dT and/or d[TH[m(T)]]/dT}/dT}/dT]/dT]/dT

 

 

 

 

TH6 = d TH5/dT = d[d TH4/dT]/dT = d[d[dTH3/dT]/dT]/dT

 

 

 

TH6 = dTH5/dT = d[d[d[d[d[d TH{[t(T)] and/or [w(T)] and/or [a(T)] and/or [i(T)] and/or [m(T)]}/dT]/dT]/dT]/dT]/dT]/dT

 

 

 

f(TH)6A = d[f(TH)5A]/dT = d{ d{d{d{d{ d [TH[t(T)]]/dT and/or d[TH[w(T)]]/dT and/or d[TH[a(T)]]/dT and/or d[TH[i(T)]]/dT and/or d[TH[m(T)]]/dT}/dT}/dT]/dT]/dT]/dT

 

 

 

 

TH7 = dTH6/dT

 

f(TH)7A = d[f(TH)6A]/dT

 

 

TH8 = d TH7/dT

 

f(TH)8A = d[f(TH)7A]/dT

 

 

 

TH9 = d TH8/dT

 

f(TH)9A = d[f(TH)8A]/dT

 

 

TH10…, TH11…, TH12 … etc.

 

 

Anyone for TH ensemble, or TH infinity scrapper, or TH (Aleph 0), or TH(Aleph 1), or TH(Aleph 2), or how about TH Aleph (Aleph 0), or TH Aleph (Aleph 1) , or TH Aleph (Aleph 2), or even TH Aleph (Aleph (Aleph 0)), or TH Aleph (Aleph (Aleph 1)), or TH Aleph (Aleph (Aleph 2)), and so on?

 

We can also express thought qualitatively, statistically, and perhaps with the use of some forms of real analyses as a derivative of emotion or of E

 

Given that TH(e) =  TH(t and/or w and/or a and/or i and/or m), the following first order derivatives of thought  with respect to emotion are possible.

 

 

dTH(t)/dE, dTH(w)/dE, dTH(a)/dE, dTH(i)/dE, dTH(m)/dE, dTH(t,w)/dE, dTH(t,a)/dE, dTH(t,i)/dE, dTH(t,m)/dE, dTH(w,a)/dE, dTH(w,i)/dE, dTH(w,m)/dE, dTH(a,i)/dE, dTH(a,m)/dE, dTH(i,m)/dE, dTH(t,w,a)/dE, dTH(t,w,i)/dE, dTH(t,w,m)/dE, dTH(t,a,i)/dE, dTH(t,a,m)/dE, dTH(t,i,m)/dE, dTH(w,a,i)/dE, dTH(w,a,m)/dE, dTH(w,i,m)/dE, dTH(a,i,m)/dE, dTH(t,w,a,i)/dE, dTH(t,w,a,m)/dE, dTH(t,w,i,m)/dE, dTH(t,a,i,m)/dE, dTH(w,a,i,m)/dE, dTH(t,w,a,i,m)/dE.

 

 

Or more succinctly,  dTH/dE = dTH(t and/or w and/or a and/or i and/or m)/dE

 

 

Or perhaps dTH(E)/dE =d TH{[t(e)] and/or [w(e)] and/or [a(e)] and/or [i(e)] and/or [m(e)]}/dE.

 

 

Likewise, we can take the second emotion derivatives of  TH as follows:

 

 

 

d[dTH(t)/dE]/dE, d[dTH(w)/dE]/dE, d[dTH(a)/dE]/dE, d[dTH(i)/dE]/dE, d[dTH(m)/dE]/dE, d[dTH(t,w)/dE]/dE, d[dTH(t,a)/dE]/dE, d[dTH(t,i)/dE]/dE, d[dTH(t,m)/dE]/dE, d[dTH(w,a)/dE]/dE, d[dTH(w,i)/dE]/dE, d[dTH(w,m)/dE]/dE, d[dTH(a,i)/dE]/dE, d[dTH(a,m)/dE]/dE, d[dTH(i,m)/dE/dE, d[dTH(t,w,a)/dE]/dE, d[dTH(t,w,i)/dE]/dE, d[dTH(t,w,m)/dE]/dE, d[dTH(t,a,i)/dE]/dE, d[dTH(t,a,m)/dE]/dE,  d[dTH(t,i,m)/dE]/dE, d[dTH(w,a,i)/dE]/dE, d[dTH(w,a,m)/dE]/dE, d[dTH(w,i,m)/dE]/dE, d[dTH(a,i,m)/dE]/dE, d[dTH(t,w,a,i)/dE]/dE, d[dTH(t,w,a,m)/dE/dE, d[dTH(t,w,i,m)/dE]/dE, d[dTH(t,a,i,m)/dE]/dE, d[dTH(w,a,i,m)/dE]/dE, d[dTH(t,w,a,i,m)/dE]/dE..

 

 

or more succinctly, as d(dTH/dE)/dE = d[d TH(t and/or w and/or a and/or i and/or m)/dE]/dE = THe2

 

 

or as

 

 

d[dTH(e)/dE]/dE  = d[d TH{[t(e)] and/or [w(e)] and/or [a(e)] and/or [i(e)] and/or [m(e)]}/dE]/dE = THe2.

 

 

 

Likewise, we can take the third emotion derivatives of  TH as follows:

 

 

 

d[d[dTH(t)/dE]/dE]/dE, d[d[dTH(w)/dE]/dE]/dE, d[d[dTH(a)/dE]/dE]/dE, d[d[dTH(i)/dE]/dE]/dE, d[d[dTH(m)/dE]/dE]/dE, d[d[dTH(t,w)/dE]/dE]/dE, d[d[dTH(t,a)/dE]/dE]/dE, d[d[dTH(t,i)/dE]/dE]/dE, d[d[dTH(t,m)/dE]/dE]/dE, d[d[dTH(w,a)/dE]/dE]/dE, d[d[dTH(w,i)/dE]/dE]/dE, d[d[dTH(w,m)/dE]/dE]/dE, d[d[dTH(a,i)/dE]/dE]/dE, d[d[dTH(a,m)/dE]/dE]/dE, d[d[dTH(i,m)/dE/dE]/dE, d[d[dTH(t,w,a)/dE]/dE]/dE, d[d[dTH(t,w,i)/dE]/dE]/dE, d[d[dTH(t,w,m)/dE]/dE]/dE, d[d[dTH(t,a,i)/dE]/dE]/dE, d[d[dTH(t,a,m)/dE]/dE]/dE,  d[d[dTH(t,i,m)/dE]/dE]/dE, d[d[dTH(w,a,i)/dE]/dE]/dE, d[d[dTH(w,a,m)/dE]/dE]/dE, d[d[dTH(w,i,m)/dE]/dE]/dE, d[d[dTH(a,i,m)/dE]/dE]/dE, d[d[dTH(t,w,a,i)/dE]/dE]/dE, d[d[dTH(t,w,a,m)/dE/dE]/dE, d[d[dTH(t,w,i,m)/dE]/dE]/dE, d[d[dTH(t,a,i,m)/dE]/dE]/dE, d[d[dTH(w,a,i,m)/dE]/dE]/dE, d[d[dTH(t,w,a,i,m)/dE]/dE]/dE.

 

 

or more succinctly, as d[d(dTH/dE)/dE]/dE = d[d[d TH(t and/or w and/or a and/or i and/or m)/dE]/dE]/dE = THe3

 

 

or as

 

 

d[d[dTH(e)/dE]/dE]/dE  = d[d[d TH{[t(e)] and/or [w(e)] and/or [a(e)] and/or [i(e)] and/or [m(e)]}/dE]/dE]/dE = THt3.

 

 

We can also form the expressions;

 

 

d[d[f(TH)]/dE]/dE = d{d [TH[t(e)]]/dE and/or d[TH[w(e)]]/dE and/or d[TH[a(e)]]/dE and/or d[TH[i(e)]]/dE and/or d[TH[m(e)]]/dE}/dE  = f(THe)2

 

 

and

 

 

d[d[d[f(TH)]/dE]/dE]/dE = d{d{ d [TH[t(e)]]/dE and/or d[TH[w(e)]]/dE and/or d[TH[a(e)]]/dE and/or d[TH[i(e)]]/dE and/or d[TH[m(e)]]/dE}/dE}/dE  = f(THe)3A, where A stands for type A differentiation which is not to be confused with the meaning of so-called Type A personality as A is used as an ordinal in a totally different context here.

 

 

and

 

 

d[d[d[f(TH)]/dE]/dE]/dE = d{d[d [TH[t(e)]]/dE]/dE  and/or d[d [TH[w(e)]]/dE]/dE  and/or d[d [TH[a(e)]]/dE]/dE  and/or d[d [TH[i(e)]]/dE]/dE  and/or d[d [TH[m(et)]]/dE]/dE }/dE = f(THe)3B, where B stands for type B differentiation which is not to be confused with the meaning of so-called Type  B personality as B is used as an ordinal in a totally different context here .

 

 

In fact, one can form yet higher order derivatives of thoughts with respect to emotion as follows.

 

 

THe5 = d THe4/dE = d[dTHe3/dE]/dE

 

 

 

THe5 = dTHe4/dE =  d[d[d[d[d TH{[t(e)] and/or [w(e)] and/or [a(e)] and/or [i(e)] and/or [m(e)]}/dE]/dE]/dE]/dE]/dE.

 

 

 

f(THe)5A = d[f(THe)4A]/dE = d[d [f(THe)3A]/dE]/dE =  d{d{d{d{ d [TH[t(e)]]/dE and/or d[TH[w(e)]]/dE and/or d[TH[a(e)]]/dE and/or d[TH[i(e)]]/dE and/or d[TH[m(e)]]/dE}/dE}/dE]/dE]/dE

 

 

 

 

THe6 = d THe5/dE = d[d THt4/dE]/dE = d[d[dTHt3/dE]/dE]/dE

 

 

 

THe6 = dTHe5/dE = d[d[d[d[d[d TH{[t(e)] and/or [w(e)] and/or [a(e)] and/or [i(e)] and/or [m(e)]}/dE]/dE]/dE]/dE]/dE]/dE

 

 

 

f(THe)6A = d[f(THe)5A]/dE = d{ d{d{d{d{ d [TH[t(e)]]/dE and/or d[TH[w(e)]]/dE and/or d[TH[a(e)]]/dE and/or d[TH[i(e)]]/dE and/or d[TH[m(e)]]/dE}/dE}/dE]/dE]/dE]/dE

 

 

 

 

THe7 = dTHe6/dE

 

f(THe)7A = d[f(THe)6A]/dE

 

 

THe8 = d THe7/dE

 

f(THe)8A = d[f(THe)7A]/dE

 

 

 

THe9 = d THe8/dE

 

f(THe)9A = d[f(THe)8A]/dE

 

 

THe10…, THe11…, THe12 … etc.

 

 

Anyone for THe ensemble, or THe infinity scrapper, or THe (Aleph 0), or THe(Aleph 1), or THe(Aleph 2), or how about THe Aleph (Aleph 0), or THe Aleph (Aleph 1) , or THe Aleph (Aleph 2), or even THe Aleph (Aleph (Aleph 0)), or THe Aleph (Aleph (Aleph 1)), or THe Aleph (Aleph (Aleph 2)), and so on?

 

Thus, for the set of the sets of derivatives of THe1 through THe(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}.

 

For the set of the sets of derivatives of THe1 through THe (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)},…, {П(0,31)[R]}_{(Aleph 1)}.

 

For the set of the sets of derivatives of THe 1 through THe (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}.

 

For the set of the sets of derivatives of THe 1 through THe (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the derivative states in the set of the sets of derivatives of THe 1 through The (Aleph 0) is plausible equal to:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of THe 1 through THe (Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of THe 1 through THe (Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}}}.

 

For the set of the sets of derivatives of THe 1 through THe (Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous THe I(Aleph 0) derivative space at the level of 0/(Aleph 0), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of THe 1 through THe (Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of THe 1 through THe (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of THe 1 through THe (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of THe 1 through THe (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of THe 1 through THe (Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of THe 1 through THe (Aleph 1), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of THe 1 through  THe (Aleph 2), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of THe I1 through THe (Aleph 3), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous The (Aleph 0) derivative space at the level of 0/(Aleph 1), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of THe 1 through THe (Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of THe 1 through THe (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of THe 1 through THe (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of THe 1 through  THe (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations  for the set of the sets of derivatives of THe 1 through THe (Aleph 0) is plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of THe 1 through THe (Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of THe 1 through THe (Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of THe 1 through THe (Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

 

For super-continuous THe (Aleph 0) derivative space at the level of 0/(Aleph 2), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of THe 1 through THe (Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of THe 1 through THe (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of THe 1 through THe (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of THe I1 through THe (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of THe 1 through THe (Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of THe I1 through THe (Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of THe 1 through THe (Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of THe I1 through THe (Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

Similar series can be developed for super-continuity at any applicable level such as 0/(Aleph 3), 0/(Aleph 4), 0/(Aleph 5),…, 0/(Aleph Ω), 0/(Aleph (Aleph 0)), …, 0/(Aleph (Aleph 1)), …, 0/(Aleph (Aleph 2)), …, 0/(Aleph (Aleph 3)),…, 0/(Aleph (Aleph Ω)),…, 0/(Aleph (Aleph (Aleph 0))), …, 0/(Aleph (Aleph (Aleph 1))),…, 0/(Aleph (Aleph (Aleph 2))),…, 0/(Aleph (Aleph (Aleph 3))),…, 0/(Aleph (Aleph  (Aleph Ω))), …

 

An so-on ad infinitum.

 

 

In addition to these numerical functions of THe as functions of summation series of product series functions, in order to really appreciate the enourmous complexity of the human soul in terms of its potential to evolve and be differentiated from all other souls in its characteristics, we would need to consider how every single category and even every single species of thought of the form THe can very. Since there may exist an arbitrarily high infinite number species of THe, the number of numerical functions of THe is utterly beyond recogning. I will cover such notions in terms of mathematical notation in yet another series of articles I will write on this general concept.

 

 

Perhaps these numbers are applicable when one considers that the human soul, in its accidental form and perhaps even in its substantial form stores all experience and other psychodynamics based phenomenon. Every experience adds to the accidental form of the human soul and this includes the souls of all those still alive on Earth, all those in Purgatory, all those in Heaven, all those in Hell, and all those in any Limbo.

Since the human soul can grow without limit in terms of its psychodynamic time –flow world line, such a consideration offers another mechanism where the number of derivative states, combinations of derivative states, and even super-continuity of the derivative state space can grow forever.

 

Folks, for those of you who might balk at me for including literally all souls in the above consideration, including the souls in Hell, as well as bodily extraterrestrial souls and the souls of so-called bodily ultraterrestials sometimes referred to as etherians in the new age UFO buff culture, my reply is that we simply do not understand the full scope of GOD’s Divine Economy. We may never fully comprehend the scope of the Divine Economy because such an utterly eternal scheme, is, well, eternal and never ending.

 

 

The general meaning of emotion derivatives of thought can be viewed as the manner in which the qualitative and/or quantitative aspects of thought as a function of thought very with emotion(s). The manner in which thoughts very with thought may be multi-thought dimensional wherein the dimensions of derivations can be multiple, and wherein the derivations can be taken in parallel, series parallel or serial manner The differentials can be partial or non-partial derivatives, or both partial and non-partial for a given computation.

 

In fact, since there is in theory, no limit to the numbers of qualitatively and quantitatively different thoughts, and perhaps no limit to the number of possible different types or classes of thoughts, wherein each person has his or her own unique thoughts, the number of thought dimensions that can effect thoughts is literally infinite, given the entirety of the set of created persons, and perhaps also literally infinite for each person as an individual, although we can not intellectually and intuitively understand this specific infinite number.

 

It is interesting to consider the ramifactions of being able to perform realistic calculations involving emotion derivatives of thought from a mathematical, theoretical, scientific,  and philosophical perspective.

 

Persons for which one or more nth order derivatives of thought with respect to emotion that have large absolute values would tend to have their thoughts highly influenced by thought, or at least for the thought under consideration with respect to the dimension of the specific thought type(s) or class(es) for which the differentiation(s) are performed. Perhaps a strong coupling between thought and emotion indicates a well integrated personality and commensurately, a high degree of thought capacity and a high degree of thought intelligence.

 

We would expect that disembodied human souls, ETI souls, and/or UTI souls in Heaven, Limbo, highly evolved bodily ETI persons, highly evolved UTI persons, and angels to have thought of all kinds and intensities which are highly subject to thought.

 

 

We can also consider two dimensional nth ordered derivatives of thought with respect to emotion and time, or with respect to t and T, respectively.

 

Given that TH[(e)(T)] =  TH[(t and/or w and/or a and/or i and/or m)(e)(T)], the following first order two dimensional derivatives of thought with respect to emotion and Time are possible.

 

 

d[dTH[(t)(T)]/dE]/dT, d[dTH[(w)(T)]/dE]/dT, d[dTH[(a)(T)]/dE]/dT, d[dTH[(i)(T)]/dE]/dT, d[dTH[(m)(T)]/dE]/dT, d[dTH[(t,w)(T)]/dE]/dT, d[dTH[(t,a)(T)]/dE]/dT, d[dTH[(t,i)(T)]/dE]/dT, d[dTH[(t,m)(T)]/dE]/dT, d[dTH[(w,a)(T)]/dE]/dT, d[dTH[(w,i)(T)]/dE]/dT, d[dTH[(w,m)(T)]/dE]/dT, d[dTH[(a,i)(T)]/dE]/dT, d[dTH[(a,m)(T)]/dE]/dT, d[dTH[(i,m)(T)]/dE]/dT, d[dTH[(t,w,a)(T)]/dE]/dT, d[dTH[(t,w,i)(T)]/dE]/dT, d[dTH[(t,w,m)(T)]/dE]/dT, d[dTH[(t,a,i)(T)]/dE]/dT, d[dTH[(t,a,m)(T)]/dE]/dT, d[dTH[(t,i,m)(T)]/dE]/dT, d[dTH[(w,a,i)(T)]/dE]/dT, d[dTH[(w,a,m)(T)]/dE]/dT, d[dTH[(w,i,m)(T)]/dE]/dT, d[dTH[(a,i,m)(T)]/dE]/dT, d[dTH[(t,w,a,i)(T)]/dE]/dT, d[dTH[(t,w,a,m)(T)]/dE]/dT, d[dTH[(t,w,i,m)(T)]/dE]/dT, d[dTH[(t,a,i,m)(T)]/dE]/dT, d[dTH[(w,a,i,m)(T)]/dE]/dT, d[dTH[(t,w,a,i,m)(T)]/dE]/dT.

 

 

Or more succinctly,  d[dTH(T)/dE]/dT = d[dTH[(T)(t and/or w and/or a and/or i and/or m)]/dE]/dT

 

or

 

d[dTH(T)/dT]/dE = d[dTH[(T)(t and/or w and/or a and/or i and/or m)]/dT]/dE

 

 

 

 

 

Or perhaps d[d TH[(e)(T)]/dE]/dT  = d[d TH [{[t(e)] and/or [w(e)] and/or [a(e)] and/or [i(e)] and/or [m(e)]}(T)]/dE]/dT

 

or

 

Or perhaps d[d TH[(e)(T)]/dT]/dE  = d[d TH [{[t(e)] and/or [w(e)] and/or [a(e)] and/or [i(e)] and/or [m(e)]}(T)]/dT]/dE

 

 

 

Likewise, we can take the second dual dimensioned thought-time derivatives of  TH as follows:

 

d[d[d[dTH[(t)(T)]/dE]/dT]/dE]/dT, d[d[d[dTH[(w)(T)]/dE]/dT]/dE]/dT, d[d[d[dTH[(a)(T)]/dE]/dT]/dE]/dT, d[d[d[dTH[(i)(T)]/dE]/dT]/dE]/dT, d[d[d[dTH[(m)(T)]/dE]/dT]/dE]/dT, d[d[d[dTH[(t,w)(T)]/dE]/dT]/dE]/dT, d[d[d[dTH[(t,a)(T)]/dE]/dT]/dE]/dT, d[d[d[dTH[(t,i)(T)]/dE]/dT]/dE]/dT, d[d[d[dTH[(t,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dTH[(w,a)(T)]/dE]/dT]/dE]/dT, d[d[d[dTH[(w,i)(T)]/dE]/dT]/dE]/dT, d[d[d[dTH[(w,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dTH[(a,i)(T)]/dE]/dT]/dE]/dT, d[d[d[dTH[(a,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dTH[(i,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dTH[(t,w,a)(T)]/dE]/dT]/dE]/dT, d[d[d[dTH[(t,w,i)(T)]/dE]/dT]/dE]/dT, d[d[d[dTH[(t,w,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dTH[(t,a,i)(T)]/dE]/dT]/dE]/dT, d[d[d[dTH[(t,a,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dTH[(t,i,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dTH[(w,a,i)(T)]/dE]/dT]/dE]/dT, d[d[d[dTH[(w,a,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dTH[(w,i,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dTH[(a,i,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dTH[(t,w,a,i)(T)]/dE]/dT]/dE]/dT, d[d[d[dTH[(t,w,a,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dTH[(t,w,i,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dTH[(t,a,i,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dTH[(w,a,i,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dTH[(t,w,a,i,m)(T)]/dE]/dT]/dE]/dT.

 

or as:

 

 

 

d[d[d[dTH[(t)(T)]/dE]/dT]/dT]/dE, d[d[d[dTH[(w)(T)]/dE]/dT]/dT]/dE, d[d[d[dTH[(a)(T)]/dE]/dT]/dT]/dE, d[d[d[dTH[(i)(T)]/dE]/dT]/dT]/dE, d[d[d[dTH[(m)(T)]/dE]/dT]/dT]/dE, d[d[d[dTH[(t,w)(T)]/dE]/dT]/dT]/dE, d[d[d[dTH[(t,a)(T)]/dE]/dT]/dT]/dE, d[d[d[dTH[(t,i)(T)]/dE]/dT]/dT]/dE, d[d[d[dTH[(t,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dTH[(w,a)(T)]/dE]/dT]/dT]/dE, d[d[d[dTH[(w,i)(T)]/dE]/dT]/dT]/dE, d[d[d[dTH[(w,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dTH[(a,i)(T)]/dE]/dT]/dT]/dE, d[d[d[dTH[(a,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dTH[(i,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dTH[(t,w,a)(T)]/dE]/dT]/dT]/dE, d[d[d[dTH[(t,w,i)(T)]/dE]/dT]/dT]/dE, d[d[d[dTH[(t,w,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dTH[(t,a,i)(T)]/dE]/dT]/dT]/dE, d[d[d[dTH[(t,a,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dTH[(t,i,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dTH[(w,a,i)(T)]/dE]/dT]/dT]/dE, d[d[d[dTH[(w,a,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dTH[(w,i,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dTH[(a,i,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dTH[(t,w,a,i)(T)]/dE]/dT]/dT]/dE, d[d[d[dTH[(t,w,a,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dTH[(t,w,i,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dTH[(t,a,i,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dTH[(w,a,i,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dTH[(t,w,a,i,m)(T)]/dE]/dT]/dT]/dE.

 

or as:

 

d[d[d[dTH[(t)(T)]/dT]/dE]/dE]/dT, d[d[d[dTH[(w)(T)]/dT]/dE]/dE]/dT, d[d[d[dTH[(a)(T)]/dT]/dE]/dE]/dT, d[d[d[dTH[(i)(T)]/dT]/dE]/dE]/dT, d[d[d[dTH[(m)(T)]/dT]/dE]/dE]/dT, d[d[d[dTH[(t,w)(T)]/dT]/dE]/dE]/dT, d[d[d[dTH[(t,a)(T)]/dT]/dE]/dE]/dT, d[d[d[dTH[(t,i)(T)]/dT]/dE]/dE]/dT, d[d[d[dTH[(t,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dTH[(w,a)(T)]/dT]/dE]/dE]/dT, d[d[d[dTH[(w,i)(T)]/dT]/dE]/dE]/dT, d[d[d[dTH[(w,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dTH[(a,i)(T)]/dT]/dE]/dE]/dT, d[d[d[dTH[(a,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dTH[(i,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dTH[(t,w,a)(T)]/dT]/dE]/dE]/dT, d[d[d[dTH[(t,w,i)(T)]/dT]/dE]/dE]/dT, d[d[d[dTH[(t,w,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dTH[(t,a,i)(T)]/dT]/dE]/dE]/dT, d[d[d[dTH[(t,a,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dTH[(t,i,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dTH[(w,a,i)(T)]/dT]/dE]/dE]/dT, d[d[d[dTH[(w,a,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dTH[(w,i,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dTH[(a,i,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dTH[(t,w,a,i)(T)]/dT]/dE]/dE]/dT, d[d[d[dTH[(t,w,a,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dTH[(t,w,i,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dTH[(t,a,i,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dTH[(w,a,i,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dTH[(t,w,a,i,m)(T)]/dT]/dE]/dE]/dT.

 

 

or as;

 

 

 

 

d[d[d[dTH(t)/dE]/dE]/dT]/dT, d[d[d[dTH(w)/dE]/dE]/dT]/dT, d[d[d[dTH(a)/dE]/dE]/dT]/dT, d[d[d[dTH(i)/dE]/dE]/dT]/dT, d[d[d[dTH(m)/dE]/dE]/dT]/dT, d[d[d[dTH(t,w)/dE]/dE]/dT]/dT, d[d[d[dTH(t,a)/dE]/dE]/dT]/dT, d[d[d[dTH(t,i)/dE]/dE]/dT]/dT, d[d[d[dTH(t,m)/dE]/dE]/dT]/dT, d[d[d[dTH(w,a)/dE]/dE]/dT]/dT, d[d[d[dTH(w,i)/dE]/dE]/dT]/dT, d[d[d[dTH(w,m)/dE]/dE]/dT]/dT, d[d[d[dTH(a,i)/dE]/dE]/dT]/dT, d[d[d[dTH(a,m)/dE]/dE]/dT]/dT, d[d[d[dTH(i,m)/dE]/dE]/dT]/dT, d[d[d[dTH(t,w,a)/dE]/dE]/dT]/dT, d[d[d[dTH(t,w,i)/dE]/dE]/dT]/dT, d[d[d[dTH(t,w,m)/dE]/dE]/dT]/dT, d[d[d[dTH(t,a,i)/dE]/dE]/dT]/dT, d[d[d[dTH(t,a,m)/dE]/dE]/dT]/dT,  d[d[d[dTH(t,i,m)/dE]/dE]/dT]/dT, d[d[d[dTH(w,a,i)/dE]/dE]/dT]/dT, d[d[d[dTH(w,a,m)/dE]/dE]/dT]/dT, d[d[d[dTH(w,i,m)/dE]/dE]/dT]/dT, d[d[d[dTH(a,i,m)/dE]/dE]/dT]/dT, d[d[d[dTH(t,w,a,i)/dE]/dE]/dT]/dT, d[d[d[dTH(t,w,a,m)/dE/dE, d[d[d[dTH(t,w,i,m)/dE]/dE]/dT]/dT, d[d[d[dTH(t,a,i,m)/dE]/dE]/dT]/dT, d[d[d[dTH(w,a,i,m)/dE]/dE]/dT]/dT, d[d[d[dTH(t,w,a,i,m)/dE]/dE]/dT]/dT..

 

or as:

 

d[d[d[dTH(t)/dT]/dE]/dT]/dE, d[d[d[dTH(w)/dT]/dE]/dT]/dE, d[d[d[dTH(a)/dT]/dE]/dT]/dE, d[d[d[dTH(i)/dT]/dE]/dT]/dE, d[d[d[dTH(m)/dT]/dE]/dT]/dE, d[d[d[dTH(t,w)/dT]/dE]/dT]/dE, d[d[d[dTH(t,a)/dT]/dE]/dT]/dE, d[d[d[dTH(t,i)/dT]/dE]/dT]/dE, d[d[d[dTH(t,m)/dT]/dE]/dT]/dE, d[d[d[dTH(w,a)/dT]/dE]/dT]/dE, d[d[d[dTH(w,i)/dT]/dE]/dT]/dE, d[d[d[dTH(w,m)/dT]/dE]/dT]/dE, d[d[d[dTH(a,i)/dT]/dE]/dT]/dE, d[d[d[dTH(a,m)/dT]/dE]/dT]/dE, d[d[d[dTH(i,m)/ dT]/dE]/dT]/dE, d[d[d[dTH(t,w,a)/dT]/dE]/dT]/dE, d[d[d[dTH(t,w,i)/dT]/dE]/dT]/dE, d[d[d[dTH(t,w,m)/dT]/dE]/dT]/dE, d[d[d[dTH(t,a,i)/dT]/dE]/dT]/dE, d[d[d[dTH(t,a,m)/dT]/dE]/dT]/dE,  d[d[d[dTH(t,i,m)/dT]/dE]/dT]/dE, d[d[d[dTH(w,a,i)/dT]/dE]/dT]/dE, d[d[d[dTH(w,a,m)/dT]/dE]/dT]/dE, d[d[d[dTH(w,i,m)/dT]/dE]/dT]/dE, d[d[d[dTH(a,i,m)/dT]/dE]/dT]/dE, d[d[d[dTH(t,w,a,i)/dT]/dE]/dT]/dE, d[d[d[dTH(t,w,a,m)/dE/dE, d[d[d[dTH(t,w,i,m)/dT]/dE]/dT]/dE, d[d[d[dTH(t,a,i,m)/dT]/dE]/dT]/dE, d[d[d[dTH(w,a,i,m)/dT]/dE]/dT]/dE, d[d[d[dTH(t,w,a,i,m)/dT]/dE]/dT]/dE..

 

or as:

 

d[d[d[dTH(t)/dT]/dT]/dE]/dE, d[d[d[dTH(w)/dT]/dT]/dE]/dE, d[d[d[dTH(a)/dT]/dT]/dE]/dE, d[d[d[dTH(i)/dT]/dT]/dE]/dE, d[d[d[dTH(m)/dT]/dT]/dE]/dE, d[d[d[dTH(t,w)/dT]/dT]/dE]/dE, d[d[d[dTH(t,a)/dT]/dT]/dE]/dE, d[d[d[dTH(t,i)/dT]/dT]/dE]/dE, d[d[d[dTH(t,m)/dT]/dT]/dE]/dE, d[d[d[dTH(w,a)/dT]/dT]/dE]/dE, d[d[d[dTH(w,i)/dT]/dT]/dE]/dE, d[d[d[dTH(w,m)/dT]/dT]/dE]/dE, d[d[d[dTH(a,i)/dT]/dT]/dE]/dE, d[d[d[dTH(a,m)/ dT]/dT]/dE]/dE, d[d[d[dTH(i,m)/ dT]/dT]/dE]/dE, d[d[d[dTH(t,w,a)/dT]/dT]/dE]/dE, d[d[d[dTH(t,w,i)/dT]/dT]/dE]/dE, d[d[d[dTH(t,w,m)/dT]/dT]/dE]/dE, d[d[d[dTH(t,a,i)/dT]/dT]/dE]/dE, d[d[d[dTH(t,a,m)/dT]/dT]/dE]/dE,  d[d[d[dTH(t,i,m)/dT]/dT]/dE]/dE, d[d[d[dTH(w,a,i)/dT]/dT]/dE]/dE, d[d[d[dTH(w,a,m)/dT]/dT]/dE]/dE, d[d[d[dTH(w,i,m)/dT]/dT]/dE]/dE, d[d[d[dTH(a,i,m)/dT]/dT]/dE]/dE, d[d[d[dTH(t,w,a,i)/dT]/dT]/dE]/dE, d[d[d[dTH(t,w,a,m)/dE/dE, d[d[d[dTH(t,w,i,m)/dT]/dT]/dE]/dE, d[d[d[dTH(t,a,i,m)/dT]/dT]/dE]/dE, d[d[d[dTH(w,a,i,m)/dT]/dT]/dE]/dE, d[d[d[dTH(t,w,a,i,m)/dT]/dT]/dE]/dE..

 

 

We can also take higher order duel dimensional derivatives of thought as a function of emotion and time but the symbolic expression of the set of such derivatives very soon becomes excessively lengthly to write and so these higher order derivatives as such are not mentioned here except to say that they would be computed in an analogous manner to the second order duel dimensional derivatives described above.

 

.

 

 

 

 

 

We can also express thought qualitatively, statistically, and perhaps with the use of some forms of real analyses as a derivative with respect to will or of w.

 

Given that TH(w) =  TH(t and/or w and/or a and/or i and/or m), the following first order derivatives of thought with respect to will are possible.

 

 

dTH(t)/dw, dTH(w)/dw, dTH(a)/dw, dTH(i)/dw, dTH(m)/dw, dTH(t,w)/dw, dTH(t,a)/dw, dTH(t,i)/dw, dTH(t,m)/dw, dTH(w,a)/dw, dTH(w,i)/dw, dTH(w,m)/dw, dTH(a,i)/dw, dTH(a,m)/dw, dTH(i,m)/dw, dTH(t,w,a)/dw, dTH(t,w,i)/dw, dTH(t,w,m)/dw, dTH(t,a,i)/dw, dTH(t,a,m)/dw, dTH(t,i,m)/dw, dTH(w,a,i)/dw, dTH(w,a,m)/dw, dTH(w,i,m)/dw, dTH(a,i,m)/dw, dTH(t,w,a,i)/dw, dTH(t,w,a,m)/dw, dTH(t,w,i,m)/dw, dTH(t,a,i,m)/dw, dTH(w,a,i,m)/dw, dTH(t,w,a,i,m)/dw.

 

 

Or more succinctly,  dTH/dw = dTH(t and/or w and/or a and/or i and/or m)/dw

 

 

Or perhaps dTH(w)/dw =d TH{[t(w)] and/or [w(w)] and/or [a(w)] and/or [i(w)] and/or [m(w)]}/dw.

 

 

Likewise, we can take the second will derivatives of  TH as follows:

 

 

 

d[dTH(t)/dw]/dw, d[dTH(w)/dw]/dw, d[dTH(a)/dw]/dw, d[dTH(i)/dw]/dw, d[dTH(m)/dw]/dw, d[dTH(t,w)/dw]/dw, d[dTH(t,a)/dw]/dw, d[dTH(t,i)/dw]/dw, d[dTH(t,m)/dw]/dw, d[dTH(w,a)/dw]/dw, d[dTH(w,i)/dw]/dw, d[dTH(w,m)/dw]/dw, d[dTH(a,i)/dw]/dw, d[dTH(a,m)/dw]/dw, d[dTH(i,m)/dw/dw, d[dTH(t,w,a)/dw]/dw, d[dTH(t,w,i)/dw]/dw, d[dTH(t,w,m)/dw]/dw, d[dTH(t,a,i)/dw]/dw, d[dTH(t,a,m)/dw]/dw,  d[dTH(t,i,m)/dw]/dw, d[dTH(w,a,i)/dw]/dw, d[dTH(w,a,m)/dw]/dw, d[dTH(w,i,m)/dw]/dw, d[dTH(a,i,m)/dw]/dw, d[dTH(t,w,a,i)/dw]/dw, d[dTH(t,w,a,m)/dw/dw, d[dTH(t,w,i,m)/dw]/dw, d[dTH(t,a,i,m)/dw]/dw, d[dTH(w,a,i,m)/dw]/dw, d[dTH(t,w,a,i,m)/dw]/dw..

 

 

or more succinctly, as d(dTH/dw)/dw = d[d TH(t and/or w and/or a and/or i and/or m)/dw]/dw = THw2

 

 

or as

 

 

d[dTH(w)/dw]/dw  = d[d TH{[t(w)] and/or [w(w)] and/or [a(w)] and/or [i(w)] and/or [m(w)]}/dw]/dw = THw2.

 

 

 

Likewise, we can take the third will derivatives of  TH as follows:

 

 

 

d[d[dTH(t)/dw]/dw]/dw, d[d[dTH(w)/dw]/dw]/dw, d[d[dTH(a)/dw]/dw]/dw, d[d[dTH(i)/dw]/dw]/dw, d[d[dTH(m)/dw]/dw]/dw, d[d[dTH(t,w)/dw]/dw]/dw, d[d[dTH(t,a)/dw]/dw]/dw, d[d[dTH(t,i)/dw]/dw]/dw, d[d[dTH(t,m)/dw]/dw]/dw, d[d[dTH(w,a)/dw]/dw]/dw, d[d[dTH(w,i)/dw]/dw]/dw, d[d[dTH(w,m)/dw]/dw]/dw, d[d[dTH(a,i)/dw]/dw]/dw, d[d[dTH(a,m)/dw]/dw]/dw, d[d[dTH(i,m)/dw/dw]/dw, d[d[dTH(t,w,a)/dw]/dw]/dw, d[d[dTH(t,w,i)/dw]/dw]/dw, d[d[dTH(t,w,m)/dw]/dw]/dw, d[d[dTH(t,a,i)/dw]/dw]/dw, d[d[dTH(t,a,m)/dw]/dw]/dw,  d[d[dTH(t,i,m)/dw]/dw]/dw, d[d[dTH(w,a,i)/dw]/dw]/dw, d[d[dTH(w,a,m)/dw]/dw]/dw, d[d[dTH(w,i,m)/dw]/dw]/dw, d[d[dTH(a,i,m)/dw]/dw]/dw, d[d[dTH(t,w,a,i)/dw]/dw]/dw, d[d[dTH(t,w,a,m)/dw/dw]/dw, d[d[dTH(t,w,i,m)/dw]/dw]/dw, d[d[dTH(t,a,i,m)/dw]/dw]/dw, d[d[dTH(w,a,i,m)/dw]/dw]/dw, d[d[dTH(t,w,a,i,m)/dw]/dw]/dw.

 

 

or more succinctly, as d[d(dTH/dw)/dw]/dw = d[d[d TH(t and/or w and/or a and/or i and/or m)/dw]/dw]/dw = THw3

 

 

or as

 

 

d[d[dTH(w)/dw]/dw]/dw  = d[d[d TH{[t(w)] and/or [w(w)] and/or [a(w)] and/or [i(w)] and/or [m(w)]}/dw]/dw]/dw = THw3.

 

 

We can also form the expressions;

 

 

d[d[f(TH)]/dw]/dw = d{d [TH[t(w)]]/dw and/or d[TH[w(w)]]/dw and/or d[TH[a(w)]]/dw and/or d[TH[i(w)]]/dw and/or d[TH[m(w)]]/dw}/dw  = f(THw)2

 

 

and

 

 

d[d[d[f(TH)]/dw]/dw]/dw = d{d{ d [TH[t(w)]]/dw and/or d[TH[w(w)]]/dw and/or d[TH[a(w)]]/dw and/or d[TH[i(w)]]/dw and/or d[TH[m(w)]]/dw}/dw}/dw  = f(THw)3A, where A stands for type A differentiation which is not to be confused with the meaning of so-called Type A personality as A is used as an ordinal in a totally different context here.

 

 

and

 

 

d[d[d[f(TH)]/dw]/dw]/dw = d{d[d [TH[t(w)]]/dw]/dw  and/or d[d [TH[w(w)]]/dw]/dw  and/or d[d [TH[a(w)]]/dw]/dw  and/or d[d [TH[i(w)]]/dw]/dw  and/or d[d [TH[m(w)]]/dw]/dw }/dw = f(THw)3B, where B stands for type B differentiation which is not to be confused with the meaning of so-called Type  B personality as B is used as an ordinal in a totally different context here .

 

 

In fact, one can form yet higher order derivatives of thought with respect to will as follows.

 

 

THw5 = d THw4/dw = d[dTHw3/dw]/dw

 

 

 

THw5 = dTHw4/dw =  d[d[d[d[d TH{[t(w)] and/or [w(w)] and/or [a(w)] and/or [i(w)] and/or [m(w)]}/dw]/dw]/dw]/dw]/dw.

 

 

 

f(THw)5A = d[f(THw)4A]/dw = d[d [f(THw)3A]/dw]/dw =  d{d{d{d{ d [TH[t(w)]]/dw and/or d[TH[w(w)]]/dw and/or d[TH[a(w)]]/dw and/or d[TH[i(w)]]/dw and/or d[TH[m(w)]]/dw}/dw}/dw]/dw]/dw

 

 

 

 

THw6 = d THw5/dw = d[d THw4/dw]/dw = d[d[dTHw3/dw]/dw]/dw

 

 

 

THw6 = dTHw5/dw = d[d[d[d[d[d TH{[t(w)] and/or [w(w)] and/or [a(w)] and/or [i(w)] and/or [m(w)]}/dw]/dw]/dw]/dw]/dw]/dw

 

 

 

f(THw)6A = d[f(THw)5A]/dw = d{ d{d{d{d{ d [TH[t(w)]]/dw and/or d[TH[w(w)]]/dw and/or d[TH[a(w)]]/dw and/or d[TH[i(w)]]/dw and/or d[TH[m(w)]]/dw}/dw}/dw]/dw]/dw]/dw

 

 

 

 

THw7 = dTHw6/dw

 

f(THw)7A = d[f(THw)6A]/dw

 

 

THw8 = d THw7/dw

 

f(THw)8A = d[f(THw)7A]/dw

 

 

 

THw9 = d THw8/dw

 

f(THw)9A = d[f(THw)8A]/dw

 

 

THw10…, THw11…, THw12 … etc.

 

 

Anyone for THw ensemble, or THw infinity scrapper, or THw (Aleph 0), or THw(Aleph 1), or THw (Aleph 2), or how about THw Aleph (Aleph 0), or THw Aleph (Aleph 1) , or THw Aleph (Aleph 2), or even THw Aleph (Aleph (Aleph 0)), or THw Aleph (Aleph (Aleph 1)), or THw Aleph (Aleph (Aleph 2)), and so on?

 

Thus, for the set of the sets of derivatives of THw1 through THw(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}.

 

For the set of the sets of derivatives of THw1 through THw (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)},…, {П(0,31)[R]}_{(Aleph 1)}.

 

For the set of the sets of derivatives of THw 1 through THw (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}.

 

For the set of the sets of derivatives of THw 1 through THw (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the derivative states in the set of the sets of derivatives of THw 1 through I(Aleph 0) is plausible equal to:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of THw 1 through THw (Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of THw 1 through THw (Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}}}.

 

For the set of the sets of derivatives of THw 1 through THw (Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous THw I(Aleph 0) derivative space at the level of 0/(Aleph 0), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of THw 1 through THw (Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of THw 1 through THw (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of THw 1 through THw (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of THw 1 through THw (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of THw 1 through THw (Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of THw 1 through THw (Aleph 1), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of THw 1 through  THw (Aleph 2), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of THw I1 through THw (Aleph 3), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous THw (Aleph 0) derivative space at the level of 0/(Aleph 1), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of THw 1 through THw (Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of THw 1 through THw (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of THw 1 through THw (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of THw 1 through  THw (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations  for the set of the sets of derivatives of THw 1 through THw (Aleph 0) is plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of THw 1 through THw (Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of THw 1 through THw (Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of THw 1 through THw (Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

 

For super-continuous THw (Aleph 0) derivative space at the level of 0/(Aleph 2), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of THw 1 through THw (Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of THw 1 through THw (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of THw 1 through THw (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of THw I1 through THw (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of THw 1 through THw (Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of THw I1 through THw (Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of THw 1 through THw (Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of THw I1 through THw (Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

Similar series can be developed for super-continuity at any applicable level such as 0/(Aleph 3), 0/(Aleph 4), 0/(Aleph 5),…, 0/(Aleph Ω), 0/(Aleph (Aleph 0)), …, 0/(Aleph (Aleph 1)), …, 0/(Aleph (Aleph 2)), …, 0/(Aleph (Aleph 3)),…, 0/(Aleph (Aleph Ω)),…, 0/(Aleph (Aleph (Aleph 0))), …, 0/(Aleph (Aleph (Aleph 1))),…, 0/(Aleph (Aleph (Aleph 2))),…, 0/(Aleph (Aleph (Aleph 3))),…, 0/(Aleph (Aleph  (Aleph Ω))), …

 

An so-on ad infinitum.

 

 

In addition to these numerical functions of THw as functions of summation series of product series functions, in order to really appreciate the enourmous complexity of the human soul in terms of its potential to evolve and be differentiated from all other souls in its characteristics, we would need to consider how every single category and even every single species of thought of the form THw can very. Since there may exist an arbitrarily high infinite number species of THw, the number of numerical functions of THw is utterly beyond recogning. I will cover such notions in terms of mathematical notation in yet another series of articles I will write on this general concept.

 

 

Perhaps these numbers are applicable when one considers that the human soul, in its accidental form and perhaps even in its substantial form stores all experience and other psychodynamics based phenomenon. Every experience adds to the accidental form of the human soul and this includes the souls of all those still alive on Earth, all those in Purgatory, all those in Heaven, all those in Hell, and all those in any Limbo.

Since the human soul can grow without limit in terms of its psychodynamic time –flow world line, such a consideration offers another mechanism where the number of derivative states, combinations of derivative states, and even super-continuity of the derivative state space can grow forever.

 

Folks, for those of you who might balk at me for including literally all souls in the above consideration, including the souls in Hell, as well as bodily extraterrestrial souls and the souls of so-called bodily ultraterrestials sometimes referred to as etherians in the new age UFO buff culture, my reply is that we simply do not understand the full scope of GOD’s Divine Economy. We may never fully comprehend the scope of the Divine Economy because such an utterly eternal scheme, is, well, eternal and never ending.

 

 

The general meaning of will derivatives of thought can be viewed as the manner in which the qualitative and/or quantitative aspects of thought as a function of will very with will. The manner in which thoughts very with will may be multi- will-aspect dimensional wherein the dimensions of derivations can be multiple, and wherein the derivations can be taken in parallel, series parallel or in serial manner. The differentials can be partial or non-partial derivatives, or both partial and non-partial for a given computation.

 

In fact, since there is in theory, no limit to the numbers of qualitatively and quantitatively different acts of will or volitional states, and perhaps no limit to the number of possible different types or classes of acts of will or volitional states, wherein each person has his or her own unique acts or will or volitional states, the number of volitional state dimensions that can effect thoughts is literally infinite, given the entirety of the set of created persons, and perhaps also literally infinite for each person as an individual, although we can not intellectually and intuitively understand this infinite number.

 

 

It is interesting to consider the ramifactions of being able to perform realistic calculations involving will derivatives of thought from a mathematical, theoretical, scientific,  and philosophical perspective.

 

Persons for which one or more nth order derivatives of thought with respect to will that have large absolute values would tend to have their thought thought highly influenced by will, or at least for the thoughts under consideration with respect to the dimension of the specific will act type(s) or class(es) for which the differentiation(s) are being performed. Perhaps a strong coupling between thought and will indicates a well integrated personality and commensurately, a high degree of thought capacity and a high degree of thought intelligence as well as perhaps very strong will power.

 

We would expect that disembodied human souls, ETI souls, and/or UTI souls in Heaven, Limbo, highly evolved bodily ETI persons, highly evolved UTI persons, and angels to have thoughts of all kinds and intensities which are highly subject to will.

 

 

We can also consider two dimensional ith ordered derivatives of thought with respect to will and time, or with respect to w and T, respectively.

 

Given that TH[(w)(T)] =  TH[(t and/or w and/or a and/or i and/or m)(w)(T)], the following first order two dimensional derivatives of thought with respect to will and Time are possible.

 

 

d[dTH[(t)(T)]/dw]/dT, d[dTH[(w)(T)]/dw]/dT, d[dTH[(a)(T)]/dw]/dT, d[dTH[(i)(T)]/dw]/dT, d[dTH[(m)(T)]/dw]/dT, d[dTH[(t,w)(T)]/dw]/dT, d[dTH[(t,a)(T)]/dw]/dT, d[dTH[(t,i)(T)]/dw]/dT, d[dTH[(t,m)(T)]/dw]/dT, d[dTH[(w,a)(T)]/dw]/dT, d[dTH[(w,i)(T)]/dw]/dT, d[dTH[(w,m)(T)]/dw]/dT, d[dTH[(a,i)(T)]/dw]/dT, d[dTH[(a,m)(T)]/dw]/dT, d[dTH[(i,m)(T)]/dw]/dT, d[dTH[(t,w,a)(T)]/dw]/dT, d[dTH[(t,w,i)(T)]/dw]/dT, d[dTH[(t,w,m)(T)]/dw]/dT, d[dTH[(t,a,i)(T)]/dw]/dT, d[dTH[(t,a,m)(T)]/dw]/dT, d[dTH[(t,i,m)(T)]/dw]/dT, d[dTH[(w,a,i)(T)]/dw]/dT, d[dTH[(w,a,m)(T)]/dw]/dT, d[dTH[(w,i,m)(T)]/dw]/dT, d[dTH[(a,i,m)(T)]/dw]/dT, d[dTH[(t,w,a,i)(T)]/dw]/dT, d[dTH[(t,w,a,m)(T)]/dw]/dT, d[dTH[(t,w,i,m)(T)]/dw]/dT, d[dTH[(t,a,i,m)(T)]/dw]/dT, d[dTH[(w,a,i,m)(T)]/dw]/dT, d[dTH[(t,w,a,i,m)(T)]/dw]/dT.

 

 

Or more succinctly,  d[dTH(T)/dw]/dT = d[dTH[(T)(t and/or w and/or a and/or i and/or m)]/dw]/dT

 

or

 

d[dTH(T)/dT]/dw = d[dTH[(T)(t and/or w and/or a and/or i and/or m)]/dT]/dw

 

 

 

 

 

Or perhaps d[d TH[(w)(T)]/dw]/dT  = d[d TH [{[t(w)] and/or [w(w)] and/or [a(w)] and/or [i(w)] and/or [m(w)]}(T)]/dw]/dT

 

or

 

Or perhaps d[d TH[(w)(T)]/dT]/dw  = d[d TH [{[t(w)] and/or [w(w)] and/or [a(w)] and/or [i(w)] and/or [m(w)]}(T)]/dT]/dw

 

 

 

Likewise, we can take the second dual dimension will -time derivatives of  TH as follows:

 

d[d[d[dTH[(t)(T)]/dw]/dT]/dw]/dT, d[d[d[dTH[(w)(T)]/dw]/dT]/dw]/dT, d[d[d[dTH[(a)(T)]/dw]/dT]/dw]/dT, d[d[d[dTH[(i)(T)]/dw]/dT]/dw]/dT, d[d[d[dTH[(m)(T)]/dw]/dT]/dw]/dT, d[d[d[dTH[(t,w)(T)]/dw]/dT]/dw]/dT, d[d[d[dTH[(t,a)(T)]/dw]/dT]/dw]/dT, d[d[d[dTH[(t,i)(T)]/dw]/dT]/dw]/dT, d[d[d[dTH[(t,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dTH[(w,a)(T)]/dw]/dT]/dw]/dT, d[d[d[dTH[(w,i)(T)]/dw]/dT]/dw]/dT, d[d[d[dTH[(w,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dTH[(a,i)(T)]/dw]/dT]/dw]/dT, d[d[d[dTH[(a,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dTH[(i,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dTH[(t,w,a)(T)]/dw]/dT]/dw]/dT, d[d[d[dTH[(t,w,i)(T)]/dw]/dT]/dw]/dT, d[d[d[dTH[(t,w,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dTH[(t,a,i)(T)]/dw]/dT]/dw]/dT, d[d[d[dTH[(t,a,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dTH[(t,i,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dTH[(w,a,i)(T)]/dw]/dT]/dw]/dT, d[d[d[dTH[(w,a,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dTH[(w,i,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dTH[(a,i,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dTH[(t,w,a,i)(T)]/dw]/dT]/dw]/dT, d[d[d[dTH[(t,w,a,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dTH[(t,w,i,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dTH[(t,a,i,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dTH[(w,a,i,m)(T)]/dw]/dT]/dw]/dT, d[d[d[dTH[(t,w,a,i,m)(T)]/dw]/dT]/dw]/dT.

 

or as:

 

 

 

d[d[d[dTH[(t)(T)]/dw]/dT]/dT]/dw, d[d[d[dTH[(w)(T)]/dw]/dT]/dT]/dw, d[d[d[dTH[(a)(T)]/dw]/dT]/dT]/dw, d[d[d[dTH[(i)(T)]/dw]/dT]/dT]/dw, d[d[d[dTH[(m)(T)]/dw]/dT]/dT]/dw, d[d[d[dTH[(t,w)(T)]/dw]/dT]/dT]/dw, d[d[d[dTH[(t,a)(T)]/dw]/dT]/dT]/dw, d[d[d[dTH[(t,i)(T)]/dw]/dT]/dT]/dw, d[d[d[dTH[(t,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dTH[(w,a)(T)]/dw]/dT]/dT]/dw, d[d[d[dTH[(w,i)(T)]/dw]/dT]/dT]/dw, d[d[d[dTH[(w,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dTH[(a,i)(T)]/dw]/dT]/dT]/dw, d[d[d[dTH[(a,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dTH[(i,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dTH[(t,w,a)(T)]/dw]/dT]/dT]/dw, d[d[d[dTH[(t,w,i)(T)]/dw]/dT]/dT]/dw, d[d[d[dTH[(t,w,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dTH[(t,a,i)(T)]/dw]/dT]/dT]/dw, d[d[d[dTH[(t,a,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dTH[(t,i,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dTH[(w,a,i)(T)]/dw]/dT]/dT]/dw, d[d[d[dTH[(w,a,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dTH[(w,i,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dTH[(a,i,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dTH[(t,w,a,i)(T)]/dw]/dT]/dT]/dw, d[d[d[dTH[(t,w,a,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dTH[(t,w,i,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dTH[(t,a,i,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dTH[(w,a,i,m)(T)]/dw]/dT]/dT]/dw, d[d[d[dTH[(t,w,a,i,m)(T)]/dw]/dT]/dT]/dw.

 

or as:

 

d[d[d[dTH[(t)(T)]/dT]/dw]/dw]/dT, d[d[d[dTH[(w)(T)]/dT]/dw]/dw]/dT, d[d[d[dTH[(a)(T)]/dT]/dw]/dw]/dT, d[d[d[dTH[(i)(T)]/dT]/dw]/dw]/dT, d[d[d[dTH[(m)(T)]/dT]/dw]/dw]/dT, d[d[d[dTH[(t,w)(T)]/dT]/dw]/dw]/dT, d[d[d[dTH[(t,a)(T)]/dT]/dw]/dw]/dT, d[d[d[dTH[(t,i)(T)]/dT]/dw]/dw]/dT, d[d[d[dTH[(t,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dTH[(w,a)(T)]/dT]/dw]/dw]/dT, d[d[d[dTH[(w,i)(T)]/dT]/dw]/dw]/dT, d[d[d[dTH[(w,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dTH[(a,i)(T)]/dT]/dw]/dw]/dT, d[d[d[dTH[(a,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dTH[(i,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dTH[(t,w,a)(T)]/dT]/dw]/dw]/dT, d[d[d[dTH[(t,w,i)(T)]/dT]/dw]/dw]/dT, d[d[d[dTH[(t,w,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dTH[(t,a,i)(T)]/dT]/dw]/dw]/dT, d[d[d[dTH[(t,a,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dTH[(t,i,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dTH[(w,a,i)(T)]/dT]/dw]/dw]/dT, d[d[d[dTH[(w,a,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dTH[(w,i,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dTH[(a,i,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dTH[(t,w,a,i)(T)]/dT]/dw]/dw]/dT, d[d[d[dTH[(t,w,a,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dTH[(t,w,i,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dTH[(t,a,i,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dTH[(w,a,i,m)(T)]/dT]/dw]/dw]/dT, d[d[d[dTH[(t,w,a,i,m)(T)]/dT]/dw]/dw]/dT.

 

 

or as;

 

 

 

 

d[d[d[dTH(t)/dw]/dw]/dT]/dT, d[d[d[dTH(w)/dw]/dw]/dT]/dT, d[d[d[dTH(a)/dw]/dw]/dT]/dT, d[d[d[dTH(i)/dw]/dw]/dT]/dT, d[d[d[dTH(m)/dw]/dw]/dT]/dT, d[d[d[dTH(t,w)/dw]/dw]/dT]/dT, d[d[d[dTH(t,a)/dw]/dw]/dT]/dT, d[d[d[dTH(t,i)/dw]/dw]/dT]/dT, d[d[d[dTH(t,m)/dw]/dw]/dT]/dT, d[d[d[dTH(w,a)/dw]/dw]/dT]/dT, d[d[d[dTH(w,i)/dw]/dw]/dT]/dT, d[d[d[dTH(w,m)/dw]/dw]/dT]/dT, d[d[d[dTH(a,i)/dw]/dw]/dT]/dT, d[d[d[dTH(a,m)/dw]/dw]/dT]/dT, d[d[d[dTH(i,m)/dw]/dw]/dT]/dT, d[d[d[dTH(t,w,a)/dw]/dw]/dT]/dT, d[d[d[dTH(t,w,i)/dw]/dw]/dT]/dT, d[d[d[dTH(t,w,m)/dw]/dw]/dT]/dT, d[d[d[dTH(t,a,i)/dw]/dw]/dT]/dT, d[d[d[dTH(t,a,m)/dw]/dw]/dT]/dT,  d[d[d[dTH(t,i,m)/dw]/dw]/dT]/dT, d[d[d[dTH(w,a,i)/dw]/dw]/dT]/dT, d[d[d[dTH(w,a,m)/dw]/dw]/dT]/dT, d[d[d[dTH(w,i,m)/dw]/dw]/dT]/dT, d[d[d[dTH(a,i,m)/dw]/dw]/dT]/dT, d[d[d[dTH(t,w,a,i)/dw]/dw]/dT]/dT, d[d[d[dTH(t,w,a,m)/dw/dw, d[d[d[dTH(t,w,i,m)/dw]/dw]/dT]/dT, d[d[d[dTH(t,a,i,m)/dw]/dw]/dT]/dT, d[d[d[dTH(w,a,i,m)/dw]/dw]/dT]/dT, d[d[d[dTH(t,w,a,i,m)/dw]/dw]/dT]/dT..

 

or as:

 

d[d[d[dTH(t)/dT]/dw]/dT]/dw, d[d[d[dTH(w)/dT]/dw]/dT]/dw, d[d[d[dTH(a)/dT]/dw]/dT]/dw, d[d[d[dTH(i)/dT]/dw]/dT]/dw, d[d[d[dTH(m)/dT]/dw]/dT]/dw, d[d[d[dTH(t,w)/dT]/dw]/dT]/dw, d[d[d[dTH(t,a)/dT]/dw]/dT]/dw, d[d[d[dTH(t,i)/dT]/dw]/dT]/dw, d[d[d[dTH(t,m)/dT]/dw]/dT]/dw, d[d[d[dTH(w,a)/dT]/dw]/dT]/dw, d[d[d[dTH(w,i)/dT]/dw]/dT]/dw, d[d[d[dTH(w,m)/dT]/dw]/dT]/dw, d[d[d[dTH(a,i)/dT]/dw]/dT]/dw, d[d[d[dTH(a,m)/dT]/dw]/dT]/dw, d[d[d[dTH(i,m)/ dT]/dw]/dT]/dw, d[d[d[dTH(t,w,a)/dT]/dw]/dT]/dw, d[d[d[dTH(t,w,i)/dT]/dw]/dT]/dw, d[d[d[dTH(t,w,m)/dT]/dw]/dT]/dw, d[d[d[dTH(t,a,i)/dT]/dw]/dT]/dw, d[d[d[dTH(t,a,m)/dT]/dw]/dT]/dw,  d[d[d[dTH(t,i,m)/dT]/dw]/dT]/dw, d[d[d[dTH(w,a,i)/dT]/dw]/dT]/dw, d[d[d[dTH(w,a,m)/dT]/dw]/dT]/dw, d[d[d[dTH(w,i,m)/dT]/dw]/dT]/dw, d[d[d[dTH(a,i,m)/dT]/dw]/dT]/dw, d[d[d[dTH(t,w,a,i)/dT]/dw]/dT]/dw, d[d[d[dTH(t,w,a,m)/dw/dw, d[d[d[dTH(t,w,i,m)/dT]/dw]/dT]/dw, d[d[d[dTH(t,a,i,m)/dT]/dw]/dT]/dw, d[d[d[dTH(w,a,i,m)/dT]/dw]/dT]/dw, d[d[d[dTH(t,w,a,i,m)/dT]/dw]/dT]/dw..

 

or as:

 

d[d[d[dTH(t)/dT]/dT]/dw]/dw, d[d[d[dTH(w)/dT]/dT]/dw]/dw, d[d[d[dTH(a)/dT]/dT]/dw]/dw, d[d[d[dTH(i)/dT]/dT]/dw]/dw, d[d[d[dTH(m)/dT]/dT]/dw]/dw, d[d[d[dTH(t,w)/dT]/dT]/dw]/dw, d[d[d[dTH(t,a)/dT]/dT]/dw]/dw, d[d[d[dTH(t,i)/dT]/dT]/dw]/dw, d[d[d[dTH(t,m)/dT]/dT]/dw]/dw, d[d[d[dTH(w,a)/dT]/dT]/dw]/dw, d[d[d[dTH(w,i)/dT]/dT]/dw]/dw, d[d[d[dTH(w,m)/dT]/dT]/dw]/dw, d[d[d[dTH(a,i)/dT]/dT]/dw]/dw, d[d[d[dTH(a,m)/ dT]/dT]/dw]/dw, d[d[d[dTH(i,m)/ dT]/dT]/dw]/dw, d[d[d[dTH(t,w,a)/dT]/dT]/dw]/dw, d[d[d[dTH(t,w,i)/dT]/dT]/dw]/dw, d[d[d[dTH(t,w,m)/dT]/dT]/dw]/dw, d[d[d[dTH(t,a,i)/dT]/dT]/dw]/dw, d[d[d[dTH(t,a,m)/dT]/dT]/dw]/dw,  d[d[d[dTH(t,i,m)/dT]/dT]/dw]/dw, d[d[d[dTH(w,a,i)/dT]/dT]/dw]/dw, d[d[d[dTH(w,a,m)/dT]/dT]/dw]/dw, d[d[d[dTH(w,i,m)/dT]/dT]/dw]/dw, d[d[d[dTH(a,i,m)/dT]/dT]/dw]/dw, d[d[d[dTH(t,w,a,i)/dT]/dT]/dw]/dw, d[d[d[dTH(t,w,a,m)/dw/dw, d[d[d[dTH(t,w,i,m)/dT]/dT]/dw]/dw, d[d[d[dTH(t,a,i,m)/dT]/dT]/dw]/dw, d[d[d[dTH(w,a,i,m)/dT]/dT]/dw]/dw, d[d[d[dTH(t,w,a,i,m)/dT]/dT]/dw]/dw..

 

We can also take higher order duel dimensional derivatives of thought as a function of will and time but the symbolic expression of the set of such derivatives very soon becomes excessively lengthly to write and so these higher order derivatives as such are not mentioned here except to say that they would be computed in an analogous manner to the second order duel dimensional derivatives described above.

 

 

We can also express emotion qualitatively, statistically, and perhaps with the use of some forms of real analysis as a derivative with respect to affect or of a.

 

Given that TH(a) =  TH(t and/or w and/or a and/or i and/or m), the following first order derivatives of thought with respect to affect are possible.

 

 

dTH(t)/da, dTH(w)/da, dTH(a)/da, dTH(i)/da, dTH(m)/da, dTH(t,w)/da, dTH(t,a)/da, dTH(t,i)/da, dTH(t,m)/da, dTH(w,a)/da, dTH(w,i)/da, dTH(w,m)/da, dTH(a,i)/da, dTH(a,m)/da, dTH(i,m)/da, dTH(t,w,a)/da, dTH(t,w,i)/da, dTH(t,w,m)/da, dTH(t,a,i)/da, dTH(t,a,m)/da, dTH(t,i,m)/da, dTH(w,a,i)/da, dTH(w,a,m)/da, dTH(w,i,m)/da, dTH(a,i,m)/da, dTH(t,w,a,i)/da, dTH(t,w,a,m)/da, dTH(t,w,i,m)/da, dTH(t,a,i,m)/da, dTH(w,a,i,m)/da, dTH(t,w,a,i,m)/da.

 

 

Or more succinctly, dTH/da = dTH(t and/or w and/or a and/or i and/or m)/da

 

 

Or perhaps dTH(a)/da =d TH{[t(a)] and/or [w(a)] and/or [a(a)] and/or [i(a)] and/or [m(a)]}/da.

 

 

Likewise, we can take the second affect derivatives of  TH as follows:

 

 

 

d[dTH(t)/da]/da, d[dTH(w)/da]/da, d[dTH(a)/da]/da, d[dTH(i)/da]/da, d[dTH(m)/da]/da, d[dTH(t,w)/da]/da, d[dTH(t,a)/da]/da, d[dTH(t,i)/da]/da, d[dTH(t,m)/da]/da, d[dTH(w,a)/da]/da, d[dTH(w,i)/da]/da, d[dTH(w,m)/da]/da, d[dTH(a,i)/da]/da, d[dTH(a,m)/da]/da, d[dTH(i,m)/da/da, d[dTH(t,w,a)/da]/da, d[dTH(t,w,i)/da]/da, d[dTH(t,w,m)/da]/da, d[dTH(t,a,i)/da]/da, d[dTH(t,a,m)/da]/da,  d[dTH(t,i,m)/da]/da, d[dTH(w,a,i)/da]/da, d[dTH(w,a,m)/da]/da, d[dTH(w,i,m)/da]/da, d[dTH(a,i,m)/da]/da, d[dTH(t,w,a,i)/da]/da, d[dTH(t,w,a,m)/da/da, d[dTH(t,w,i,m)/da]/da, d[dTH(t,a,i,m)/da]/da, d[dTH(w,a,i,m)/da]/da, d[dTH(t,w,a,i,m)/da]/da..

 

 

or more succinctly, as d(dTH/da)/da = d[d TH(t and/or w and/or a and/or i and/or m)/da]/da = THa2

 

 

or as

 

 

d[dTH(a)/da]/da  = d[d TH{[t(a)] and/or [w(a)] and/or [a(a)] and/or [i(a)] and/or [m(a)]}/da]/da = THa2.

 

 

 

Likewise, we can take the third affect derivatives of  TH as follows:

 

 

 

d[d[dTH(t)/da]/da]/da, d[d[dTH(w)/da]/da]/da, d[d[dTH(a)/da]/da]/da, d[d[dTH(i)/da]/da]/da, d[d[dTH(m)/da]/da]/da, d[d[dTH(t,w)/da]/da]/da, d[d[dTH(t,a)/da]/da]/da, d[d[dTH(t,i)/da]/da]/da, d[d[dTH(t,m)/da]/da]/da, d[d[dTH(w,a)/da]/da]/da, d[d[dTH(w,i)/da]/da]/da, d[d[dTH(w,m)/da]/da]/da, d[d[dTH(a,i)/da]/da]/da, d[d[dTH(a,m)/da]/da]/da, d[d[dTH(i,m)/da/da]/da, d[d[dTH(t,w,a)/da]/da]/da, d[d[dTH(t,w,i)/da]/da]/da, d[d[dTH(t,w,m)/da]/da]/da, d[d[dTH(t,a,i)/da]/da]/da, d[d[dTH(t,a,m)/da]/da]/da,  d[d[dTH(t,i,m)/da]/da]/da, d[d[dTH(w,a,i)/da]/da]/da, d[d[dTH(w,a,m)/da]/da]/da, d[d[dTH(w,i,m)/da]/da]/da, d[d[dTH(a,i,m)/da]/da]/da, d[d[dTH(t,w,a,i)/da]/da]/da, d[d[dTH(t,w,a,m)/da/da]/da, d[d[dTH(t,w,i,m)/da]/da]/da, d[d[dTH(t,a,i,m)/da]/da]/da, d[d[dTH(w,a,i,m)/da]/da]/da, d[d[dTH(t,w,a,i,m)/da]/da]/da.

 

 

or more succinctly, as d[d(dTH/da)/da]/da = d[d[d TH(t and/or w and/or a and/or i and/or m)/da]/da]/da = THa3

 

 

or as

 

 

d[d[dTH(a)/da]/da]/da  = d[d[d TH{[t(a)] and/or [w(a)] and/or [a(a)] and/or [i(a)] and/or [m(a)]}/da]/da]/da = THa3.

 

 

We can also form the expressions;

 

 

d[d[f(TH)]/da]/da = d{d [TH[t(a)]]/da and/or d[TH[w(a)]]/da and/or d[TH[a(a)]]/da and/or d[TH[i(a)]]/da and/or d[TH[m(a)]]/da}/da  = f(THa)2

 

 

and

 

 

d[d[d[f(TH)]/da]/da]/da = d{d{ d [TH[t(a)]]/da and/or d[TH[w(a)]]/da and/or d[TH[a(a)]]/da and/or d[TH[i(a)]]/da and/or d[TH[m(a)]]/da}/da}/da  = f(THa)3A, where A stands for type A differentiation which is not to be confused with the meaning of so-called Type A personality as A is used as an ordinal in a totally different context here.

 

 

and

 

 

d[d[d[f(TH)]/da]/da]/da = d{d[d [TH[t(a)]]/da]/da  and/or d[d [TH[w(a)]]/da]/da  and/or d[d [TH[a(a)]]/da]/da  and/or d[d [TH[i(a)]]/da]/da  and/or d[d [TH[m(a)]]/da]/da }/da = f(THa)3B, where B stands for type B differentiation which is not to be confused with the meaning of so-called Type  B personality as B is used as an ordinal in a totally different context here. .

 

 

In fact, one can form yet higher order derivatives of thoughts with respect to affect as follows.

 

 

THa5 = d THa4/da = d[dTHa3/da]/da

 

 

 

THa5 = dTHa4/da =  d[d[d[d[d TH{[t(a)] and/or [w(a)] and/or [a(a)] and/or [i(a)] and/or [m(a)]}/da]/da]/da]/da]/da.

 

 

 

f(THa)5A = d[f(THa)4A]/da = d[d [f(THa)3A]/da]/da =  d{d{d{d{ d [TH[t(a)]]/da and/or d[TH[w(a)]]/da and/or d[TH[a(a)]]/da and/or d[TH[i(a)]]/da and/or d[TH[m(a)]]/da}/da}/da]/da]/da

 

 

 

 

THa6 = d THa5/da = d[d THa4/da]/da = d[d[dTHa3/da]/da]/da

 

 

 

THa6 = dTHa5/da = d[d[d[d[d[d TH{[t(a)] and/or [w(a)] and/or [a(a)] and/or [i(a)] and/or [m(a)]}/da]/da]/da]/da]/da]/da

 

 

 

f(THa)6A = d[f(THa)5A]/da = d{ d{d{d{d{ d [TH[t(a)]]/da and/or d[TH[w(a)]]/da and/or d[TH[a(a)]]/da and/or d[TH[i(a)]]/da and/or d[TH[m(a)]]/da}/da}/da]/da]/da]/da

 

 

 

 

THa7 = dTHa6/da

 

f(THa)7A = d[f(THa)6A]/da

 

 

THa8 = d THa7/da

 

f(THa)8A = d[f(THa)7A]/da

 

 

 

THa9 = d THa8/da

 

f(THa)9A = d[f(THa)8A]/da

 

 

THa10…, THa11…, THa12 … etc.

 

 

Anyone for THa ensemble, or THa infinity scrapper, or THa (Aleph 0), or THa(Aleph 1), or THa (Aleph 2), or how about THa Aleph (Aleph 0), or THa Aleph (Aleph 1) , or THa Aleph (Aleph 2), or even THa Aleph (Aleph (Aleph 0)), or THa Aleph (Aleph (Aleph 1)), or THa Aleph (Aleph (Aleph 2)), and so on?

 

 

Thus, for the set of the sets of derivatives of THa1 through THa(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}.

 

For the set of the sets of derivatives of THa1 through THa (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)},…, {П(0,31)[R]}_{(Aleph 1)}.

 

For the set of the sets of derivatives of THa 1 through THa (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}.

 

For the set of the sets of derivatives of THa 1 through THa (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the derivative states in the set of the sets of derivatives of THa 1 through I(Aleph 0) is plausible equal to:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of THa 1 through THa (Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of THa 1 through THa (Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}}}.

 

For the set of the sets of derivatives of THa 1 through THa (Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous THa I(Aleph 0) derivative space at the level of 0/(Aleph 0), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of THa 1 through THa (Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of THa 1 through THa (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of THa 1 through THa (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of THa 1 through THa (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of THa 1 through THa (Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of THa 1 through THa (Aleph 1), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of THa 1 through  THa (Aleph 2), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of THa I1 through THa (Aleph 3), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous THa (Aleph 0) derivative space at the level of 0/(Aleph 1), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of THa 1 through THa (Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of THa 1 through THa (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of THa 1 through THa (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of THa 1 through  THa (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations  for the set of the sets of derivatives of THa 1 through THa (Aleph 0) is plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of THa 1 through THa (Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of THa 1 through THa (Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of THa 1 through THa (Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

 

For super-continuous THa (Aleph 0) derivative space at the level of 0/(Aleph 2), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of THa 1 through THa (Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of THa 1 through THa (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of THa 1 through THa (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of THa I1 through THa (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of THa 1 through THa (Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of THa I1 through THa (Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of THa 1 through THa (Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of THa I1 through THa (Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

Similar series can be developed for super-continuity at any applicable level such as 0/(Aleph 3), 0/(Aleph 4), 0/(Aleph 5),…, 0/(Aleph Ω), 0/(Aleph (Aleph 0)), …, 0/(Aleph (Aleph 1)), …, 0/(Aleph (Aleph 2)), …, 0/(Aleph (Aleph 3)),…, 0/(Aleph (Aleph Ω)),…, 0/(Aleph (Aleph (Aleph 0))), …, 0/(Aleph (Aleph (Aleph 1))),…, 0/(Aleph (Aleph (Aleph 2))),…, 0/(Aleph (Aleph (Aleph 3))),…, 0/(Aleph (Aleph  (Aleph Ω))), …

 

An so-on ad infinitum.

 

 

In addition to these numerical functions of THa as functions of summation series of product series functions, in order to really appreciate the enourmous complexity of the human soul in terms of its potential to evolve and be differentiated from all other souls in its characteristics, we would need to consider how every single category and even every single species of memory of the form THa can very. Since there may exist an arbitrarily high infinite number species of THa, the number of numerical functions of THa is utterly beyond recogning. I will cover such notions in terms of mathematical notation in yet another series of articles I will write on this general concept.

 

 

Perhaps these numbers are applicable when one considers that the human soul, in its accidental form and perhaps even in its substantial form stores all experience and other psychodynamics based phenomenon. Every experience adds to the accidental form of the human soul and this includes the souls of all those still alive on Earth, all those in Purgatory, all those in Heaven, all those in Hell, and all those in any Limbo.

Since the human soul can grow without limit in terms of its psychodynamic time –flow world line, such a consideration offers another mechanism where the number of derivative states, combinations of derivative states, and even super-continuity of the derivative state space can grow forever.

 

Folks, for those of you who might balk at me for including literally all souls in the above consideration, including the souls in Hell, as well as bodily extraterrestrial souls and the souls of so-called bodily ultraterrestials sometimes referred to as etherians in the new age UFO buff culture, my reply is that we simply do not understand the full scope of GOD’s Divine Economy. We may never fully comprehend the scope of the Divine Economy because such an utterly eternal scheme, is, well, eternal and never ending.

 

 

The general meaning of affect derivatives of thought can be viewed as the manner in which the qualitative and/or quantitative aspects of thought as a function of affect very with affect. The manner in which thoughts very with affect may be multi- affect-aspect dimensional wherein the dimensions of derivations can be multiple, and wherein the derivations can be taken in parallel, series parallel or in serial manner. The differentials can be partial or non-partial derivatives, or both partial and non-partial for a given computation.

 

In fact, since there is in theory, no limit to the numbers of qualitatively and quantitatively different affective states, and perhaps no limit to the number of possible different types or classes of affective states, wherein each person has his or her own unique affective rxperiences, the number of affect dimensions that can effect thoughts is literally infinite, given the entirety of the set of created persons, and perhaps also literally infinite for each person as an individual, although we can not intellectually and intuitively understand this infinite number.

 

 

It is interesting to consider the ramifactions of being able to perform realistic calculations involving affect derivatives of thought from a mathematical, theoretical, scientific,  and philosophical perspective.

 

Persons for which one or more nth order derivatives of thought with respect to affect that have large absolute values would tend to have their thoughts highly influenced by affect, or at least for the thoughts under consideration with respect to the dimension of the specific affect type(s) or class(es) for which the differentiation(s) are being performed. Perhaps a strong coupling between thought and affect indicates a well integrated personality and commensurately, a high degree of thought capacity and a high degree of thought intelligence as well as perhaps very strong affect power.

 

We would expect that disembodied human souls, ETI souls, and/or UTI souls in Heaven, Limbo, highly evolved bodily ETI persons, highly evolved UTI persons, and angels to have thoughts of all kinds and intensities which are highly subject to affect.

 

 

We can also consider that two dimensional nth ordered derivatives of thought with respect to affect and time, or with respect to a and T, respectively.

 

Given that TH[(a)(T)] =  TH[(t and/or w and/or a and/or i and/or m)(w)(T)], the following first order two dimensional derivatives of thought with respect to affect and Time are possible.

 

 

d[dTH[(t)(T)]/da]/dT, d[dTH[(w)(T)]/da]/dT, d[dTH[(a)(T)]/da]/dT, d[dTH[(i)(T)]/da]/dT, d[dTH[(m)(T)]/da]/dT, d[dTH[(t,w)(T)]/da]/dT, d[dTH[(t,a)(T)]/da]/dT, d[dTH[(t,i)(T)]/da]/dT, d[dTH[(t,m)(T)]/da]/dT, d[dTH[(w,a)(T)]/da]/dT, d[dTH[(w,i)(T)]/da]/dT, d[dTH[(w,m)(T)]/da]/dT, d[dTH[(a,i)(T)]/da]/dT, d[dTH[(a,m)(T)]/da]/dT, d[dTH[(i,m)(T)]/da]/dT, d[dTH[(t,w,a)(T)]/da]/dT, d[dTH[(t,w,i)(T)]/da]/dT, d[dTH[(t,w,m)(T)]/da]/dT, d[dTH[(t,a,i)(T)]/da]/dT, d[dTH[(t,a,m)(T)]/da]/dT, d[dTH[(t,i,m)(T)]/da]/dT, d[dTH[(w,a,i)(T)]/da]/dT, d[dTH[(w,a,m)(T)]/da]/dT, d[dTH[(w,i,m)(T)]/da]/dT, d[dTH[(a,i,m)(T)]/da]/dT, d[dTH[(t,w,a,i)(T)]/da]/dT, d[dTH[(t,w,a,m)(T)]/da]/dT, d[dTH[(t,w,i,m)(T)]/da]/dT, d[dTH[(t,a,i,m)(T)]/da]/dT, d[dTH[(w,a,i,m)(T)]/da]/dT, d[dTH[(t,w,a,i,m)(T)]/da]/dT.

 

 

Or more succinctly,  d[dTH(T)/da]/dT = d[dTH[(T)(t and/or w and/or a and/or i and/or m)]/da]/dT

 

or

 

d[dTH(T)/dT]/da = d[dTH[(T)(t and/or w and/or a and/or i and/or m)]/dT]/da

 

 

 

 

 

Or perhaps d[d TH[(a)(T)]/da]/dT  = d[d TH [{[t(a)] and/or [w(a)] and/or [a(a)] and/or [i(a)] and/or [m(a)]}(T)]/da]/dT

 

or

 

Or perhaps d[d TH[(a)(T)]/dT]/da  = d[d TH [{[t(a)] and/or [w(a)] and/or [a(a)] and/or [i(a)] and/or [m(a)]}(T)]/dT]/da

 

 

 

Likewise, we can take the second dual dimension affect -time derivatives of  TH as follows:

 

d[d[d[dTH[(t)(T)]/da]/dT]/da]/dT, d[d[d[dTH[(w)(T)]/da]/dT]/da]/dT, d[d[d[dTH[(a)(T)]/da]/dT]/da]/dT, d[d[d[dTH[(i)(T)]/da]/dT]/da]/dT, d[d[d[dTH[(m)(T)]/da]/dT]/da]/dT, d[d[d[dTH[(t,w)(T)]/da]/dT]/da]/dT, d[d[d[dTH[(t,a)(T)]/da]/dT]/da]/dT, d[d[d[dTH[(t,i)(T)]/da]/dT]/da]/dT, d[d[d[dTH[(t,m)(T)]/da]/dT]/da]/dT, d[d[d[dTH[(w,a)(T)]/da]/dT]/da]/dT, d[d[d[dTH[(w,i)(T)]/da]/dT]/da]/dT, d[d[d[dTH[(w,m)(T)]/da]/dT]/da]/dT, d[d[d[dTH[(a,i)(T)]/da]/dT]/da]/dT, d[d[d[dTH[(a,m)(T)]/da]/dT]/da]/dT, d[d[d[dTH[(i,m)(T)]/da]/dT]/da]/dT, d[d[d[dTH[(t,w,a)(T)]/da]/dT]/da]/dT, d[d[d[dTH[(t,w,i)(T)]/da]/dT]/da]/dT, d[d[d[dTH[(t,w,m)(T)]/da]/dT]/da]/dT, d[d[d[dTH[(t,a,i)(T)]/da]/dT]/da]/dT, d[d[d[dTH[(t,a,m)(T)]/da]/dT]/da]/dT, d[d[d[dTH[(t,i,m)(T)]/da]/dT]/da]/dT, d[d[d[dTH[(w,a,i)(T)]/da]/dT]/da]/dT, d[d[d[dTH[(w,a,m)(T)]/da]/dT]/da]/dT, d[d[d[dTH[(w,i,m)(T)]/da]/dT]/da]/dT, d[d[d[dTH[(a,i,m)(T)]/da]/dT]/da]/dT, d[d[d[dTH[(t,w,a,i)(T)]/da]/dT]/da]/dT, d[d[d[dTH[(t,w,a,m)(T)]/da]/dT]/da]/dT, d[d[d[dTH[(t,w,i,m)(T)]/da]/dT]/da]/dT, d[d[d[dTH[(t,a,i,m)(T)]/da]/dT]/da]/dT, d[d[d[dTH[(w,a,i,m)(T)]/da]/dT]/da]/dT, d[d[d[dTH[(t,w,a,i,m)(T)]/da]/dT]/da]/dT.

 

or as:

 

 

 

d[d[d[dTH[(t)(T)]/da]/dT]/dT]/da, d[d[d[dTH[(w)(T)]/da]/dT]/dT]/da, d[d[d[dTH[(a)(T)]/da]/dT]/dT]/da, d[d[d[dTH[(i)(T)]/da]/dT]/dT]/da, d[d[d[dTH[(m)(T)]/da]/dT]/dT]/da, d[d[d[dTH[(t,w)(T)]/da]/dT]/dT]/da, d[d[d[dTH[(t,a)(T)]/da]/dT]/dT]/da, d[d[d[dTH[(t,i)(T)]/da]/dT]/dT]/da, d[d[d[dTH[(t,m)(T)]/da]/dT]/dT]/da, d[d[d[dTH[(w,a)(T)]/da]/dT]/dT]/da, d[d[d[dTH[(w,i)(T)]/da]/dT]/dT]/da, d[d[d[dTH[(w,m)(T)]/da]/dT]/dT]/da, d[d[d[dTH[(a,i)(T)]/da]/dT]/dT]/da, d[d[d[dTH[(a,m)(T)]/da]/dT]/dT]/da, d[d[d[dTH[(i,m)(T)]/da]/dT]/dT]/da, d[d[d[dTH[(t,w,a)(T)]/da]/dT]/dT]/da, d[d[d[dTH[(t,w,i)(T)]/da]/dT]/dT]/da, d[d[d[dTH[(t,w,m)(T)]/da]/dT]/dT]/da, d[d[d[dTH[(t,a,i)(T)]/da]/dT]/dT]/da, d[d[d[dTH[(t,a,m)(T)]/da]/dT]/dT]/da, d[d[d[dTH[(t,i,m)(T)]/da]/dT]/dT]/da, d[d[d[dTH[(w,a,i)(T)]/da]/dT]/dT]/da, d[d[d[dTH[(w,a,m)(T)]/da]/dT]/dT]/da, d[d[d[dTH[(w,i,m)(T)]/da]/dT]/dT]/da, d[d[d[dTH[(a,i,m)(T)]/da]/dT]/dT]/da, d[d[d[dTH[(t,w,a,i)(T)]/da]/dT]/dT]/da, d[d[d[dTH[(t,w,a,m)(T)]/da]/dT]/dT]/da, d[d[d[dTH[(t,w,i,m)(T)]/da]/dT]/dT]/da, d[d[d[dTH[(t,a,i,m)(T)]/da]/dT]/dT]/da, d[d[d[dTH[(w,a,i,m)(T)]/da]/dT]/dT]/da, d[d[d[dTH[(t,w,a,i,m)(T)]/da]/dT]/dT]/da.

 

or as:

 

d[d[d[dTH[(t)(T)]/dT]/da]/da]/dT, d[d[d[dTH[(w)(T)]/dT]/da]/da]/dT, d[d[d[dTH[(a)(T)]/dT]/da]/da]/dT, d[d[d[dTH[(i)(T)]/dT]/da]/da]/dT, d[d[d[dTH[(m)(T)]/dT]/da]/da]/dT, d[d[d[dTH[(t,w)(T)]/dT]/da]/da]/dT, d[d[d[dTH[(t,a)(T)]/dT]/da]/da]/dT, d[d[d[dTH[(t,i)(T)]/dT]/da]/da]/dT, d[d[d[dTH[(t,m)(T)]/dT]/da]/da]/dT, d[d[d[dTH[(w,a)(T)]/dT]/da]/da]/dT, d[d[d[dTH[(w,i)(T)]/dT]/da]/da]/dT, d[d[d[dTH[(w,m)(T)]/dT]/da]/da]/dT, d[d[d[dTH[(a,i)(T)]/dT]/da]/da]/dT, d[d[d[dTH[(a,m)(T)]/dT]/da]/da]/dT, d[d[d[dTH[(i,m)(T)]/dT]/da]/da]/dT, d[d[d[dTH[(t,w,a)(T)]/dT]/da]/da]/dT, d[d[d[dTH[(t,w,i)(T)]/dT]/da]/da]/dT, d[d[d[dTH[(t,w,m)(T)]/dT]/da]/da]/dT, d[d[d[dTH[(t,a,i)(T)]/dT]/da]/da]/dT, d[d[d[dTH[(t,a,m)(T)]/dT]/da]/da]/dT, d[d[d[dTH[(t,i,m)(T)]/dT]/da]/da]/dT, d[d[d[dTH[(w,a,i)(T)]/dT]/da]/da]/dT, d[d[d[dTH[(w,a,m)(T)]/dT]/da]/da]/dT, d[d[d[dTH[(w,i,m)(T)]/dT]/da]/da]/dT, d[d[d[dTH[(a,i,m)(T)]/dT]/da]/da]/dT, d[d[d[dTH[(t,w,a,i)(T)]/dT]/da]/da]/dT, d[d[d[dTH[(t,w,a,m)(T)]/dT]/da]/da]/dT, d[d[d[dTH[(t,w,i,m)(T)]/dT]/da]/da]/dT, d[d[d[dTH[(t,a,i,m)(T)]/dT]/da]/da]/dT, d[d[d[dTH[(w,a,i,m)(T)]/dT]/da]/da]/dT, d[d[d[dTH[(t,w,a,i,m)(T)]/dT]/da]/da]/dT.

 

 

or as;

 

 

 

 

d[d[d[dTH(t)/da]/da]/dT]/dT, d[d[d[dTH(w)/da]/da]/dT]/dT, d[d[d[dTH(a)/da]/da]/dT]/dT, d[d[d[dTH(i)/da]/da]/dT]/dT, d[d[d[dTH(m)/da]/da]/dT]/dT, d[d[d[dTH(t,w)/da]/da]/dT]/dT, d[d[d[dTH(t,a)/da]/da]/dT]/dT, d[d[d[dTH(t,i)/da]/da]/dT]/dT, d[d[d[dTH(t,m)/da]/da]/dT]/dT, d[d[d[dTH(w,a)/da]/da]/dT]/dT, d[d[d[dTH(w,i)/da]/da]/dT]/dT, d[d[d[dTH(w,m)/da]/da]/dT]/dT, d[d[d[dTH(a,i)/da]/da]/dT]/dT, d[d[d[dTH(a,m)/da]/da]/dT]/dT, d[d[d[dTH(i,m)/da]/da]/dT]/dT, d[d[d[dTH(t,w,a)/da]/da]/dT]/dT, d[d[d[dTH(t,w,i)/da]/da]/dT]/dT, d[d[d[dTH(t,w,m)/da]/da]/dT]/dT, d[d[d[dTH(t,a,i)/da]/da]/dT]/dT, d[d[d[dTH(t,a,m)/da]/da]/dT]/dT,  d[d[d[dTH(t,i,m)/da]/da]/dT]/dT, d[d[d[dTH(w,a,i)/da]/da]/dT]/dT, d[d[d[dTH(w,a,m)/da]/da]/dT]/dT, d[d[d[dTH(w,i,m)/da]/da]/dT]/dT, d[d[d[dTH(a,i,m)/da]/da]/dT]/dT, d[d[d[dTH(t,w,a,i)/da]/da]/dT]/dT, d[d[d[dTH(t,w,a,m)/da/da, d[d[d[dTH(t,w,i,m)/da]/da]/dT]/dT, d[d[d[dTH(t,a,i,m)/da]/da]/dT]/dT, d[d[d[dTH(w,a,i,m)/da]/da]/dT]/dT, d[d[d[dTH(t,w,a,i,m)/da]/da]/dT]/dT..

 

or as:

 

d[d[d[dTH(t)/dT]/da]/dT]/da, d[d[d[dTH(w)/dT]/da]/dT]/da, d[d[d[dTH(a)/dT]/da]/dT]/da, d[d[d[dTH(i)/dT]/da]/dT]/da, d[d[d[dTH(m)/dT]/da]/dT]/da, d[d[d[dTH(t,w)/dT]/da]/dT]/da, d[d[d[dTH(t,a)/dT]/da]/dT]/da, d[d[d[dTH(t,i)/dT]/da]/dT]/da, d[d[d[dTH(t,m)/dT]/da]/dT]/da, d[d[d[dTH(w,a)/dT]/da]/dT]/da, d[d[d[dTH(w,i)/dT]/da]/dT]/da, d[d[d[dTH(w,m)/dT]/da]/dT]/da, d[d[d[dTH(a,i)/dT]/da]/dT]/da, d[d[d[dTH(a,m)/dT]/da]/dT]/da, d[d[d[dTH(i,m)/ dT]/da]/dT]/da, d[d[d[dTH(t,w,a)/dT]/da]/dT]/da, d[d[d[dTH(t,w,i)/dT]/da]/dT]/da, d[d[d[dTH(t,w,m)/dT]/da]/dT]/da, d[d[d[dTH(t,a,i)/dT]/da]/dT]/da, d[d[d[dTH(t,a,m)/dT]/da]/dT]/da,  d[d[d[dTH(t,i,m)/dT]/da]/dT]/da, d[d[d[dTH(w,a,i)/dT]/da]/dT]/da, d[d[d[dTH(w,a,m)/dT]/da]/dT]/da, d[d[d[dTH(w,i,m)/dT]/da]/dT]/da, d[d[d[dTH(a,i,m)/dT]/da]/dT]/da, d[d[d[dTH(t,w,a,i)/dT]/da]/dT]/da, d[d[d[dTH(t,w,a,m)/da/da, d[d[d[dTH(t,w,i,m)/dT]/da]/dT]/da, d[d[d[dTH(t,a,i,m)/dT]/da]/dT]/da, d[d[d[dTH(w,a,i,m)/dT]/da]/dT]/da, d[d[d[dTH(t,w,a,i,m)/dT]/da]/dT]/da..

 

or as:

 

d[d[d[dTH(t)/dT]/dT]/da]/da, d[d[d[dTH(w)/dT]/dT]/da]/da, d[d[d[dTH(a)/dT]/dT]/da]/da, d[d[d[dTH(i)/dT]/dT]/da]/da, d[d[d[dTH(m)/dT]/dT]/da]/da, d[d[d[dTH(t,w)/dT]/dT]/da]/da, d[d[d[dTH(t,a)/dT]/dT]/da]/da, d[d[d[dTH(t,i)/dT]/dT]/da]/da, d[d[d[dTH(t,m)/dT]/dT]/da]/da, d[d[d[dTH(w,a)/dT]/dT]/da]/da, d[d[d[dTH(w,i)/dT]/dT]/da]/da, d[d[d[dTH(w,m)/dT]/dT]/da]/da, d[d[d[dTH(a,i)/dT]/dT]/da]/da, d[d[d[dTH(a,m)/ dT]/dT]/da]/da, d[d[d[dTH(i,m)/ dT]/dT]/da]/da, d[d[d[dTH(t,w,a)/dT]/dT]/da]/da, d[d[d[dTH(t,w,i)/dT]/dT]/da]/da, d[d[d[dTH(t,w,m)/dT]/dT]/da]/da, d[d[d[dTH(t,a,i)/dT]/dT]/da]/da, d[d[d[dTH(t,a,m)/dT]/dT]/da]/da,  d[d[d[dTH(t,i,m)/dT]/dT]/da]/da, d[d[d[dTH(w,a,i)/dT]/dT]/da]/da, d[d[d[dTH(w,a,m)/dT]/dT]/da]/da, d[d[d[dTH(w,i,m)/dT]/dT]/da]/da, d[d[d[dTH(a,i,m)/dT]/dT]/da]/da, d[d[d[dTH(t,w,a,i)/dT]/dT]/da]/da, d[d[d[dTH(t,w,a,m)/da/da, d[d[d[dTH(t,w,i,m)/dT]/dT]/da]/da, d[d[d[dTH(t,a,i,m)/dT]/dT]/da]/da, d[d[d[dTH(w,a,i,m)/dT]/dT]/da]/da, d[d[d[dTH(t,w,a,i,m)/dT]/dT]/da]/da..

 

We can also take higher order duel dimensional derivatives of thought as a function of affect and time but the symbolic expression of the set of such derivatives very soon becomes excessively lengthly to write and so these higher order derivatives as such are not mentioned here except to say that they would be computed in an analogous manner to the second order duel dimensional derivatives described above.

 

.

 

 

We can also express thought qualitatively, statistically, and perhaps with the use of some forms of real analyses as a derivative with respect to  instinct or of i.

 

Given that TH(i) =  TH(t and/or w and/or a and/or i and/or m) or perhaps the following notation can be more appropriate in certain circumstances.

 

 

 

 

Thus the following first order derivatives of thought with respect to instinct are possible.

 

 

dTH(t)/di, dTH(w)/di, dTH(a)/di, dTH(i)/di, dTH(m)/di, dTH(t,w)/di, dTH(t,a)/di, dTH(t,i)/di, dTH(t,m)/di, dTH(w,a)/di, dTH(w,i)/di, dTH(w,m)/di, dTH(a,i)/di, dTH(a,m)/di, dTH(i,m)/di, dTH(t,w,a)/di, dTH(t,w,i)/di, dTH(t,w,m)/di, dTH(t,a,i)/di, dTH(t,a,m)/di, dTH(t,i,m)/di, dTH(w,a,i)/di, dTH(w,a,m)/di, dTH(w,i,m)/di, dTH(a,i,m)/di, dTH(t,w,a,i)/di, dTH(t,w,a,m)/di, dTH(t,w,i,m)/di, dTH(t,a,i,m)/di, dTH(w,a,i,m)/di, dTH(t,w,a,i,m)/di.

 

 

Or more succinctly,  dTH/di = dTH(t and/or w and/or a and/or i and/or m)/di

 

 

Or perhaps dTH(i)/di =d TH{[t(i)] and/or [w(i)] and/or [a(i)] and/or [i(i)] and/or [m(i)]}/di.

 

 

Likewise, we can take the second instinct derivatives of  TH as follows:

 

 

 

d[dTH(t)/di]/di, d[dTH(w)/di]/di, d[dTH(a)/di]/di, d[dTH(i)/di]/di, d[dTH(m)/di]/di, d[dTH(t,w)/di]/di, d[dTH(t,a)/di]/di, d[dTH(t,i)/di]/di, d[dTH(t,m)/di]/di, d[dTH(w,a)/di]/di, d[dTH(w,i)/di]/di, d[dTH(w,m)/di]/di, d[dTH(a,i)/di]/di, d[dTH(a,m)/di]/di, d[dTH(i,m)/di/di, d[dTH(t,w,a)/di]/di, d[dTH(t,w,i)/di]/di, d[dTH(t,w,m)/di]/di, d[dTH(t,a,i)/di]/di, d[dTH(t,a,m)/di]/di,  d[dTH(t,i,m)/di]/di, d[dTH(w,a,i)/di]/di, d[dTH(w,a,m)/di]/di, d[dTH(w,i,m)/di]/di, d[dTH(a,i,m)/di]/di, d[dTH(t,w,a,i)/di]/di, d[dTH(t,w,a,m)/di/di, d[dTH(t,w,i,m)/di]/di, d[dTH(t,a,i,m)/di]/di, d[dTH(w,a,i,m)/di]/di, d[dTH(t,w,a,i,m)/di]/di..

 

 

or more succinctly, as d(dTH/di)/di = d[d TH(t and/or w and/or a and/or i and/or m)/di]/di = THi2

 

 

or as

 

 

d[dTH(i)/di]/di  = d[d TH{[t(i)] and/or [w(i)] and/or [a(i)] and/or [i(i)] and/or [m(i)]}/di]/di = THi2.

 

 

 

Likewise, we can take the third instinct derivatives of  TH as follows:

 

 

 

d[d[dTH(t)/di]/di]/di, d[d[dTH(w)/di]/di]/di, d[d[dTH(a)/di]/di]/di, d[d[dTH(i)/di]/di]/di, d[d[dTH(m)/di]/di]/di, d[d[dTH(t,w)/di]/di]/di, d[d[dTH(t,a)/di]/di]/di, d[d[dTH(t,i)/di]/di]/di, d[d[dTH(t,m)/di]/di]/di, d[d[dTH(w,a)/di]/di]/di, d[d[dTH(w,i)/di]/di]/di, d[d[dTH(w,m)/di]/di]/di, d[d[dTH(a,i)/di]/di]/di, d[d[dTH(a,m)/di]/di]/di, d[d[dTH(i,m)/di/di]/di, d[d[dTH(t,w,a)/di]/di]/di, d[d[dTH(t,w,i)/di]/di]/di, d[d[dTH(t,w,m)/di]/di]/di, d[d[dTH(t,a,i)/di]/di]/di, d[d[dTH(t,a,m)/di]/di]/di,  d[d[dTH(t,i,m)/di]/di]/di, d[d[dTH(w,a,i)/di]/di]/di, d[d[dTH(w,a,m)/di]/di]/di, d[d[dTH(w,i,m)/di]/di]/di, d[d[dTH(a,i,m)/di]/di]/di, d[d[dTH(t,w,a,i)/di]/di]/di, d[d[dTH(t,w,a,m)/di/di]/di, d[d[dTH(t,w,i,m)/di]/di]/di, d[d[dTH(t,a,i,m)/di]/di]/di, d[d[dTH(w,a,i,m)/di]/di]/di, d[d[dTH(t,w,a,i,m)/di]/di]/di.

 

 

or more succinctly, as d[d(dTH/di)/di]/di = d[d[d TH(t and/or w and/or a and/or i and/or m)/di]/di]/di = THi3

 

 

or as

 

 

d[d[dTH(i)/di]/di]/di  = d[d[d TH{[t(i)] and/or [w(i)] and/or [a(i)] and/or [i(i)] and/or [m(i)]}/di]/di]/di = THi3.

 

 

We can also form the expressions;

 

 

d[d[f(TH)]/di]/di = d{d [TH[t(i)]]/di and/or d[TH[w(i)]]/di and/or d[TH[a(i)]]/di and/or d[TH[i(i)]]/di and/or d[TH[m(i)]]/di}/di  = f(THi)2

 

 

and

 

 

d[d[d[f(TH)]/di]/di]/di = d{d{ d [TH[t(i)]]/di and/or d[TH[w(i)]]/di and/or d[TH[a(i)]]/di and/or d[TH[i(i)]]/di and/or d[TH[m(i)]]/di}/di}/di  = f(THi)3A, where A stands for type A differentiation which is not to be confused with the meaning of so-called Type A personality as A is used as an ordinal in a totally different context here.

 

 

and

 

 

d[d[d[f(TH)]/di]/di]/di = d{d[d [TH[t(i)]]/di]/di  and/or d[d [TH[w(i)]]/di]/di  and/or d[d [TH[a(i)]]/di]/di  and/or d[d [TH[i(i)]]/di]/di  and/or d[d [TH[m(i)]]/di]/di }/di = f(THi)3B, where B stands for type B differentiation which is not to be confused with the meaning of so-called Type  B personality as B is used as an ordinal in a totally different context here .

 

 

In fact, one can form yet higher order derivatives of thoughts with respect to instinct as follows.

 

 

THi5 = d THi4/di = d[dTHi3/di]/di

 

 

 

THi5 = dTHi4/di =  d[d[d[d[d TH{[t(i)] and/or [w(i)] and/or [a(i)] and/or [i(i)] and/or [m(i)]}/di]/di]/di]/di]/di.

 

 

 

f(THi)5A = d[f(THi)4A]/di = d[d [f(THi)3A]/di]/di =  d{d{d{d{ d [TH[t(i)]]/di and/or d[TH[w(i)]]/di and/or d[TH[a(i)]]/di and/or d[TH[i(i)]]/di and/or d[TH[m(i)]]/di}/di}/di]/di]/di

 

 

 

 

THi6 = d THi5/di = d[d THi4/di]/di = d[d[dTHi3/di]/di]/di

 

 

 

THi6 = dTHi5/di = d[d[d[d[d[d TH{[t(i)] and/or [w(i)] and/or [a(i)] and/or [i(i)] and/or [m(i)]}/di]/di]/di]/di]/di]/di

 

 

 

f(THi)6A = d[f(THi)5A]/di = d{ d{d{d{d{ d [TH[t(i)]]/di and/or d[TH[w(i)]]/di and/or d[TH[a(i)]]/di and/or d[TH[i(i)]]/di and/or d[TH[m(i)]]/di}/di}/di]/di]/di]/di

 

 

 

 

THi7 = dTHi6/di

 

f(THi)7A = d[f(THi)6A]/di

 

 

THi8 = d THi7/di

 

f(THi)8A = d[f(THi)7A]/di

 

 

 

THi9 = d THi8/di

 

f(THi)9A = d[f(THi)8A]/di

 

 

THi10…, THi11…, THi12 … etc.

 

 

Anyone for THi ensemble, or THi infinity scrapper, or THi (Aleph 0), or THi(Aleph 1), or THi (Aleph 2), or how about THi Aleph (Aleph 0), or THi Aleph (Aleph 1) , or THi Aleph (Aleph 2), or even THi Aleph (Aleph (Aleph 0)), or THi Aleph (Aleph (Aleph 1)), or THi Aleph (Aleph (Aleph 2)), and so on?

 

 

Thus, for the set of the sets of derivatives of THi1 through THi(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}.

 

For the set of the sets of derivatives of THi1 through THi (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)},…, {П(0,31)[R]}_{(Aleph 1)}.

 

For the set of the sets of derivatives of THi 1 through THi (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}.

 

For the set of the sets of derivatives of THi 1 through THi (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the derivative states in the set of the sets of derivatives of THi 1 through I(Aleph 0) is plausible equal to:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of THi 1 through THi (Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of THi 1 through THi (Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}}}.

 

For the set of the sets of derivatives of THi 1 through THi (Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous THi I(Aleph 0) derivative space at the level of 0/(Aleph 0), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of THi 1 through THi (Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of THi 1 through THi (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of THi 1 through THi (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of THi 1 through THi (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of THi 1 through THi (Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of THi 1 through THi (Aleph 1), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of THi 1 through  THi (Aleph 2), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of THi I1 through THi (Aleph 3), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous THi (Aleph 0) derivative space at the level of 0/(Aleph 1), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of THi 1 through THi (Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of THi 1 through THi (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of THi 1 through THi (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of THi 1 through  THi (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations  for the set of the sets of derivatives of THi 1 through THi (Aleph 0) is plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of THi 1 through THi (Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of THi 1 through THi (Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of THi 1 through THi (Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

 

For super-continuous THi (Aleph 0) derivative space at the level of 0/(Aleph 2), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of THi 1 through THi (Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of THi 1 through THi (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of THi 1 through THi (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of THi I1 through THi (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of THi 1 through THi (Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of THi I1 through THi (Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of THi 1 through THi (Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of THi I1 through THi (Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

Similar series can be developed for super-continuity at any applicable level such as 0/(Aleph 3), 0/(Aleph 4), 0/(Aleph 5),…, 0/(Aleph Ω), 0/(Aleph (Aleph 0)), …, 0/(Aleph (Aleph 1)), …, 0/(Aleph (Aleph 2)), …, 0/(Aleph (Aleph 3)),…, 0/(Aleph (Aleph Ω)),…, 0/(Aleph (Aleph (Aleph 0))), …, 0/(Aleph (Aleph (Aleph 1))),…, 0/(Aleph (Aleph (Aleph 2))),…, 0/(Aleph (Aleph (Aleph 3))),…, 0/(Aleph (Aleph  (Aleph Ω))), …

 

An so-on ad infinitum.

 

 

In addition to these numerical functions of THi as functions of summation series of product series functions, in order to really appreciate the enourmous complexity of the human soul in terms of its potential to evolve and be differentiated from all other souls in its characteristics, we would need to consider how every single category and even every single species of thought of the form THi can very. Since there may exist an arbitrarily high infinite number species of THi, the number of numerical functions of THi is utterly beyond recogning. I will cover such notions in terms of mathematical notation in yet another series of articles I will write on this general concept.

 

 

Perhaps these numbers are applicable when one considers that the human soul, in its accidental form and perhaps even in its substantial form stores all experience and other psychodynamics based phenomenon. Every experience adds to the accidental form of the human soul and this includes the souls of all those still alive on Earth, all those in Purgatory, all those in Heaven, all those in Hell, and all those in any Limbo.

Since the human soul can grow without limit in terms of its psychodynamic time –flow world line, such a consideration offers another mechanism where the number of derivative states, combinations of derivative states, and even super-continuity of the derivative state space can grow forever.

 

Folks, for those of you who might balk at me for including literally all souls in the above consideration, including the souls in Hell, as well as bodily extraterrestrial souls and the souls of so-called bodily ultraterrestials sometimes referred to as etherians in the new age UFO buff culture, my reply is that we simply do not understand the full scope of GOD’s Divine Economy. We may never fully comprehend the scope of the Divine Economy because such an utterly eternal scheme, is, well, eternal and never ending.

 

 

The general meaning of instinct derivatives of thought can be viewed as the manner in which the qualitative and/or quantitative aspects of thought as a function of instinct very with instinct. The manner in which thoughts very with instinct may be multi- instinct-aspect dimensional wherein the dimensions of derivations can be multiple, and wherein the derivations can be taken in parallel, series parallel or in serial manner. The differentials can be partial or non-partial derivatives, or both partial and non-partial for a given computation.

 

In fact, since there is in theory, no limit to the numbers of qualitatively and quantitatively different instincts, and perhaps no limit to the number of possible different types or classes of instincts or potential instincts, wherein each person has his or her own unique instincts and instinctual experiences, the number of instinct dimensions that can effect thoughts is literally infinite, given the entirety of the set of created persons, and perhaps also literally infinite for each person as an individual, although we can not intellectually and intuitively understand this infinite number.

 

 

It is interesting to consider the ramifactions of being able to perform realistic calculations involving instinct derivatives of thought from a mathematical, theoretical, scientific,  and philosophical perspective.

 

Persons for which one or more nth order derivatives of thought with respect to instinct that have large absolute values would tend to have their thoughts highly influenced by instinct, or at least for the thoughts under consideration with respect to the dimension of the specific instinct act type(s) or class(es) for which the differentiation(s) are being performed. Perhaps a strong coupling between thought and instinct indicates a well integrated personality and commensurately, a high degree of thought capacity and a high degree of thought intelligence as well as perhaps very strong instinct power.

 

We would expect that disembodied human souls, ETI souls, and/or UTI souls in Heaven, Limbo, highly evolved bodily ETI persons, highly evolved UTI persons, and angels to have thoughts of all kinds and intensities which are perhaps  highly subject to advanced instincts such as spiritual instincts, spiritual intuitions, and even perhaps, psychic powers.

 

 

We can also consider that two dimensional nth ordered derivatives of thought with respect to instinct and time, or with respect to i and T, respectively.

 

Given that TH[(i)(T)] =  TH[(t and/or w and/or a and/or i and/or m)(i)(T)], the following first order two dimensional derivatives of thought with respect to instinct and Time are possible.

 

 

d[dTH[(t)(T)]/di]/dT, d[dTH[(w)(T)]/di]/dT, d[dTH[(a)(T)]/di]/dT, d[dTH[(i)(T)]/di]/dT, d[dTH[(m)(T)]/di]/dT, d[dTH[(t,w)(T)]/di]/dT, d[dTH[(t,a)(T)]/di]/dT, d[dTH[(t,i)(T)]/di]/dT, d[dTH[(t,m)(T)]/di]/dT, d[dTH[(w,a)(T)]/di]/dT, d[dTH[(w,i)(T)]/di]/dT, d[dTH[(w,m)(T)]/di]/dT, d[dTH[(a,i)(T)]/di]/dT, d[dTH[(a,m)(T)]/di]/dT, d[dTH[(i,m)(T)]/di]/dT, d[dTH[(t,w,a)(T)]/di]/dT, d[dTH[(t,w,i)(T)]/di]/dT, d[dTH[(t,w,m)(T)]/di]/dT, d[dTH[(t,a,i)(T)]/di]/dT, d[dTH[(t,a,m)(T)]/di]/dT, d[dTH[(t,i,m)(T)]/di]/dT, d[dTH[(w,a,i)(T)]/di]/dT, d[dTH[(w,a,m)(T)]/di]/dT, d[dTH[(w,i,m)(T)]/di]/dT, d[dTH[(a,i,m)(T)]/di]/dT, d[dTH[(t,w,a,i)(T)]/di]/dT, d[dTH[(t,w,a,m)(T)]/di]/dT, d[dTH[(t,w,i,m)(T)]/di]/dT, d[dTH[(t,a,i,m)(T)]/di]/dT, d[dTH[(w,a,i,m)(T)]/di]/dT, d[dTH[(t,w,a,i,m)(T)]/di]/dT.

 

 

Or more succinctly,  d[dTH(T)/di]/dT = d[dTH[(T)(t and/or w and/or a and/or i and/or m)]/di]/dT

 

or

 

d[dTH(T)/dT]/di = d[dTH[(T)(t and/or w and/or a and/or i and/or m)]/dT]/di

 

 

 

 

 

Or perhaps d[d TH[(i)(T)]/di]/dT  = d[d TH [{[t(i)] and/or [w(i)] and/or [a(i)] and/or [i(i)] and/or [m(i)]}(T)]/di]/dT

 

or

 

Or perhaps d[d TH[(i)(T)]/dT]/di  = d[d TH [{[t(i)] and/or [w(i)] and/or [a(i)] and/or [i(i)] and/or [m(i)]}(T)]/dT]/di

 

 

 

Likewise, we can take the second dual dimension instinct -time derivatives of  TH as follows:

 

d[d[d[dTH[(t)(T)]/di]/dT]/di]/dT, d[d[d[dTH[(w)(T)]/di]/dT]/di]/dT, d[d[d[dTH[(a)(T)]/di]/dT]/di]/dT, d[d[d[dTH[(i)(T)]/di]/dT]/di]/dT, d[d[d[dTH[(m)(T)]/di]/dT]/di]/dT, d[d[d[dTH[(t,w)(T)]/di]/dT]/di]/dT, d[d[d[dTH[(t,a)(T)]/di]/dT]/di]/dT, d[d[d[dTH[(t,i)(T)]/di]/dT]/di]/dT, d[d[d[dTH[(t,m)(T)]/di]/dT]/di]/dT, d[d[d[dTH[(w,a)(T)]/di]/dT]/di]/dT, d[d[d[dTH[(w,i)(T)]/di]/dT]/di]/dT, d[d[d[dTH[(w,m)(T)]/di]/dT]/di]/dT, d[d[d[dTH[(a,i)(T)]/di]/dT]/di]/dT, d[d[d[dTH[(a,m)(T)]/di]/dT]/di]/dT, d[d[d[dTH[(i,m)(T)]/di]/dT]/di]/dT, d[d[d[dTH[(t,w,a)(T)]/di]/dT]/di]/dT, d[d[d[dTH[(t,w,i)(T)]/di]/dT]/di]/dT, d[d[d[dTH[(t,w,m)(T)]/di]/dT]/di]/dT, d[d[d[dTH[(t,a,i)(T)]/di]/dT]/di]/dT, d[d[d[dTH[(t,a,m)(T)]/di]/dT]/di]/dT, d[d[d[dTH[(t,i,m)(T)]/di]/dT]/di]/dT, d[d[d[dTH[(w,a,i)(T)]/di]/dT]/di]/dT, d[d[d[dTH[(w,a,m)(T)]/di]/dT]/di]/dT, d[d[d[dTH[(w,i,m)(T)]/di]/dT]/di]/dT, d[d[d[dTH[(a,i,m)(T)]/di]/dT]/di]/dT, d[d[d[dTH[(t,w,a,i)(T)]/di]/dT]/di]/dT, d[d[d[dTH[(t,w,a,m)(T)]/di]/dT]/di]/dT, d[d[d[dTH[(t,w,i,m)(T)]/di]/dT]/di]/dT, d[d[d[dTH[(t,a,i,m)(T)]/di]/dT]/di]/dT, d[d[d[dTH[(w,a,i,m)(T)]/di]/dT]/di]/dT, d[d[d[dTH[(t,w,a,i,m)(T)]/di]/dT]/di]/dT.

 

or as:

 

 

 

d[d[d[dTH[(t)(T)]/di]/dT]/dT]/di, d[d[d[dTH[(w)(T)]/di]/dT]/dT]/di, d[d[d[dTH[(a)(T)]/di]/dT]/dT]/di, d[d[d[dTH[(i)(T)]/di]/dT]/dT]/di, d[d[d[dTH[(m)(T)]/di]/dT]/dT]/di, d[d[d[dTH[(t,w)(T)]/di]/dT]/dT]/di, d[d[d[dTH[(t,a)(T)]/di]/dT]/dT]/di, d[d[d[dTH[(t,i)(T)]/di]/dT]/dT]/di, d[d[d[dTH[(t,m)(T)]/di]/dT]/dT]/di, d[d[d[dTH[(w,a)(T)]/di]/dT]/dT]/di, d[d[d[dTH[(w,i)(T)]/di]/dT]/dT]/di, d[d[d[dTH[(w,m)(T)]/di]/dT]/dT]/di, d[d[d[dTH[(a,i)(T)]/di]/dT]/dT]/di, d[d[d[dTH[(a,m)(T)]/di]/dT]/dT]/di, d[d[d[dTH[(i,m)(T)]/di]/dT]/dT]/di, d[d[d[dTH[(t,w,a)(T)]/di]/dT]/dT]/di, d[d[d[dTH[(t,w,i)(T)]/di]/dT]/dT]/di, d[d[d[dTH[(t,w,m)(T)]/di]/dT]/dT]/di, d[d[d[dTH[(t,a,i)(T)]/di]/dT]/dT]/di, d[d[d[dTH[(t,a,m)(T)]/di]/dT]/dT]/di, d[d[d[dTH[(t,i,m)(T)]/di]/dT]/dT]/di, d[d[d[dTH[(w,a,i)(T)]/di]/dT]/dT]/di, d[d[d[dTH[(w,a,m)(T)]/di]/dT]/dT]/di, d[d[d[dTH[(w,i,m)(T)]/di]/dT]/dT]/di, d[d[d[dTH[(a,i,m)(T)]/di]/dT]/dT]/di, d[d[d[dTH[(t,w,a,i)(T)]/di]/dT]/dT]/di, d[d[d[dTH[(t,w,a,m)(T)]/di]/dT]/dT]/di, d[d[d[dTH[(t,w,i,m)(T)]/di]/dT]/dT]/di, d[d[d[dTH[(t,a,i,m)(T)]/di]/dT]/dT]/di, d[d[d[dTH[(w,a,i,m)(T)]/di]/dT]/dT]/di, d[d[d[dTH[(t,w,a,i,m)(T)]/di]/dT]/dT]/di.

 

or as:

 

d[d[d[dTH[(t)(T)]/dT]/di]/di]/dT, d[d[d[dTH[(w)(T)]/dT]/di]/di]/dT, d[d[d[dTH[(a)(T)]/dT]/di]/di]/dT, d[d[d[dTH[(i)(T)]/dT]/di]/di]/dT, d[d[d[dTH[(m)(T)]/dT]/di]/di]/dT, d[d[d[dTH[(t,w)(T)]/dT]/di]/di]/dT, d[d[d[dTH[(t,a)(T)]/dT]/di]/di]/dT, d[d[d[dTH[(t,i)(T)]/dT]/di]/di]/dT, d[d[d[dTH[(t,m)(T)]/dT]/di]/di]/dT, d[d[d[dTH[(w,a)(T)]/dT]/di]/di]/dT, d[d[d[dTH[(w,i)(T)]/dT]/di]/di]/dT, d[d[d[dTH[(w,m)(T)]/dT]/di]/di]/dT, d[d[d[dTH[(a,i)(T)]/dT]/di]/di]/dT, d[d[d[dTH[(a,m)(T)]/dT]/di]/di]/dT, d[d[d[dTH[(i,m)(T)]/dT]/di]/di]/dT, d[d[d[dTH[(t,w,a)(T)]/dT]/di]/di]/dT, d[d[d[dTH[(t,w,i)(T)]/dT]/di]/di]/dT, d[d[d[dTH[(t,w,m)(T)]/dT]/di]/di]/dT, d[d[d[dTH[(t,a,i)(T)]/dT]/di]/di]/dT, d[d[d[dTH[(t,a,m)(T)]/dT]/di]/di]/dT, d[d[d[dTH[(t,i,m)(T)]/dT]/di]/di]/dT, d[d[d[dTH[(w,a,i)(T)]/dT]/di]/di]/dT, d[d[d[dTH[(w,a,m)(T)]/dT]/di]/di]/dT, d[d[d[dTH[(w,i,m)(T)]/dT]/di]/di]/dT, d[d[d[dTH[(a,i,m)(T)]/dT]/di]/di]/dT, d[d[d[dTH[(t,w,a,i)(T)]/dT]/di]/di]/dT, d[d[d[dTH[(t,w,a,m)(T)]/dT]/di]/di]/dT, d[d[d[dTH[(t,w,i,m)(T)]/dT]/di]/di]/dT, d[d[d[dTH[(t,a,i,m)(T)]/dT]/di]/di]/dT, d[d[d[dTH[(w,a,i,m)(T)]/dT]/di]/di]/dT, d[d[d[dTH[(t,w,a,i,m)(T)]/dT]/di]/di]/dT.

 

 

or as;

 

 

 

 

d[d[d[dTH(t)/di]/di]/dT]/dT, d[d[d[dTH(w)/di]/di]/dT]/dT, d[d[d[dTH(a)/di]/di]/dT]/dT, d[d[d[dTH(i)/di]/di]/dT]/dT, d[d[d[dTH(m)/di]/di]/dT]/dT, d[d[d[dTH(t,w)/di]/di]/dT]/dT, d[d[d[dTH(t,a)/di]/di]/dT]/dT, d[d[d[dTH(t,i)/di]/di]/dT]/dT, d[d[d[dTH(t,m)/di]/di]/dT]/dT, d[d[d[dTH(w,a)/di]/di]/dT]/dT, d[d[d[dTH(w,i)/di]/di]/dT]/dT, d[d[d[dTH(w,m)/di]/di]/dT]/dT, d[d[d[dTH(a,i)/di]/di]/dT]/dT, d[d[d[dTH(a,m)/di]/di]/dT]/dT, d[d[d[dTH(i,m)/di]/di]/dT]/dT, d[d[d[dTH(t,w,a)/di]/di]/dT]/dT, d[d[d[dTH(t,w,i)/di]/di]/dT]/dT, d[d[d[dTH(t,w,m)/di]/di]/dT]/dT, d[d[d[dTH(t,a,i)/di]/di]/dT]/dT, d[d[d[dTH(t,a,m)/di]/di]/dT]/dT,  d[d[d[dTH(t,i,m)/di]/di]/dT]/dT, d[d[d[dTH(w,a,i)/di]/di]/dT]/dT, d[d[d[dTH(w,a,m)/di]/di]/dT]/dT, d[d[d[dTH(w,i,m)/di]/di]/dT]/dT, d[d[d[dTH(a,i,m)/di]/di]/dT]/dT, d[d[d[dTH(t,w,a,i)/di]/di]/dT]/dT, d[d[d[dTH(t,w,a,m)/di/di, d[d[d[dTH(t,w,i,m)/di]/di]/dT]/dT, d[d[d[dTH(t,a,i,m)/di]/di]/dT]/dT, d[d[d[dTH(w,a,i,m)/di]/di]/dT]/dT, d[d[d[dTH(t,w,a,i,m)/di]/di]/dT]/dT..

 

or as:

 

d[d[d[dTH(t)/dT]/di]/dT]/di, d[d[d[dTH(w)/dT]/di]/dT]/di, d[d[d[dTH(a)/dT]/di]/dT]/di, d[d[d[dTH(i)/dT]/di]/dT]/di, d[d[d[dTH(m)/dT]/di]/dT]/di, d[d[d[dTH(t,w)/dT]/di]/dT]/di, d[d[d[dTH(t,a)/dT]/di]/dT]/di, d[d[d[dTH(t,i)/dT]/di]/dT]/di, d[d[d[dTH(t,m)/dT]/di]/dT]/di, d[d[d[dTH(w,a)/dT]/di]/dT]/di, d[d[d[dTH(w,i)/dT]/di]/dT]/di, d[d[d[dTH(w,m)/dT]/di]/dT]/di, d[d[d[dTH(a,i)/dT]/di]/dT]/di, d[d[d[dTH(a,m)/dT]/di]/dT]/di, d[d[d[dTH(i,m)/ dT]/di]/dT]/di, d[d[d[dTH(t,w,a)/dT]/di]/dT]/di, d[d[d[dTH(t,w,i)/dT]/di]/dT]/di, d[d[d[dTH(t,w,m)/dT]/di]/dT]/di, d[d[d[dTH(t,a,i)/dT]/di]/dT]/di, d[d[d[dTH(t,a,m)/dT]/di]/dT]/di,  d[d[d[dTH(t,i,m)/dT]/di]/dT]/di, d[d[d[dTH(w,a,i)/dT]/di]/dT]/di, d[d[d[dTH(w,a,m)/dT]/di]/dT]/di, d[d[d[dTH(w,i,m)/dT]/di]/dT]/di, d[d[d[dTH(a,i,m)/dT]/di]/dT]/di, d[d[d[dTH(t,w,a,i)/dT]/di]/dT]/di, d[d[d[dTH(t,w,a,m)/di/di, d[d[d[dTH(t,w,i,m)/dT]/di]/dT]/di, d[d[d[dTH(t,a,i,m)/dT]/di]/dT]/di, d[d[d[dTH(w,a,i,m)/dT]/di]/dT]/di, d[d[d[dTH(t,w,a,i,m)/dT]/di]/dT]/di..

 

or as:

 

d[d[d[dTH(t)/dT]/dT]/di]/di, d[d[d[dTH(w)/dT]/dT]/di]/di, d[d[d[dTH(a)/dT]/dT]/di]/di, d[d[d[dTH(i)/dT]/dT]/di]/di, d[d[d[dTH(m)/dT]/dT]/di]/di, d[d[d[dTH(t,w)/dT]/dT]/di]/di, d[d[d[dTH(t,a)/dT]/dT]/di]/di, d[d[d[dTH(t,i)/dT]/dT]/di]/di, d[d[d[dTH(t,m)/dT]/dT]/di]/di, d[d[d[dTH(w,a)/dT]/dT]/di]/di, d[d[d[dTH(w,i)/dT]/dT]/di]/di, d[d[d[dTH(w,m)/dT]/dT]/di]/di, d[d[d[dTH(a,i)/dT]/dT]/di]/di, d[d[d[dTH(a,m)/ dT]/dT]/di]/di, d[d[d[dTH(i,m)/ dT]/dT]/di]/di, d[d[d[dTH(t,w,a)/dT]/dT]/di]/di, d[d[d[dTH(t,w,i)/dT]/dT]/di]/di, d[d[d[dTH(t,w,m)/dT]/dT]/di]/di, d[d[d[dTH(t,a,i)/dT]/dT]/di]/di, d[d[d[dTH(t,a,m)/dT]/dT]/di]/di,  d[d[d[dTH(t,i,m)/dT]/dT]/di]/di, d[d[d[dTH(w,a,i)/dT]/dT]/di]/di, d[d[d[dTH(w,a,m)/dT]/dT]/di]/di, d[d[d[dTH(w,i,m)/dT]/dT]/di]/di, d[d[d[dTH(a,i,m)/dT]/dT]/di]/di, d[d[d[dTH(t,w,a,i)/dT]/dT]/di]/di, d[d[d[dTH(t,w,a,m)/di/di, d[d[d[dTH(t,w,i,m)/dT]/dT]/di]/di, d[d[d[dTH(t,a,i,m)/dT]/dT]/di]/di, d[d[d[dTH(w,a,i,m)/dT]/dT]/di]/di, d[d[d[dTH(t,w,a,i,m)/dT]/dT]/di]/di..

 

We can also take higher order duel dimensional derivatives of thought as a function of instinct and time but the symbolic expression of the set of such derivatives very soon becomes excessively lengthly to write and so these higher order derivatives as such are not mentioned here except to say that they would be computed in an analogous manner to the second order duel dimensional derivatives described above.

 

 

 

These seemingly crazy differentials might have some use in extreme psychological states that can be experienced by souls who are departed and whose thoughts, although perhaps spiritualized, are nonetheless, not limited by a body and its brain.

 

 

Another type of being that might experience such extreme thought change capacities might be none other then some of our friends we believe to exist as pure body-less and brain-less spirits known as angels.

 

 

Since I have dared to speculate this far, perhaps we can speculate as to whether any intelligent extraterrestrials persons or any so-called ultra-terrestrials persons that are more cognitively evolved then we ordinary humans might be capable of experiencing large absolute valued terms of THn. Some such ETI and UTI persons may  have evolved over billions of years, or perhaps have far greater powers of sensation, thought, and intuition such as would seem plausible for any such persons and their civilizations who have not fallen from the state of innocence into the state of sin as we humans have, or perhaps such beings never had the option of  sanctifying grace opened to them but nonetheless may have been created at a naturally more perfect level then we humans, and who therefore might exhibit greater natural powers of thought and sensation.

 

 

 

 

 

 

 

 

 

 

 

 

We can also express thought qualitatively, statistically, and perhaps with the use of some forms of real analyses as a derivative with respect to memory or of m.

 

Given that TH(m) =  TH(t and/or w and/or a and/or i and/or m) or perhaps the following notation can be more appropriate in certain circumstances.

 

 

 

 

Thus,  the following first order derivatives of thought with respect to memory are possible.

 

 

dTH(t)/dm, dTH(w)/dm, dTH(a)/dm, dTH(i)/dm, dTH(m)/dm, dTH(t,w)/dm, dTH(t,a)/dm, dTH(t,i)/dm, dTH(t,m)/dm, dTH(w,a)/dm, dTH(w,i)/dm, dTH(w,m)/dm, dTH(a,i)/dm, dTH(a,m)/dm, dTH(i,m)/dm, dTH(t,w,a)/dm, dTH(t,w,i)/dm, dTH(t,w,m)/dm, dTH(t,a,i)/dm, dTH(t,a,m)/dm, dTH(t,i,m)/dm, dTH(w,a,i)/dm, dTH(w,a,m)/dm, dTH(w,i,m)/dm, dTH(a,i,m)/dm, dTH(t,w,a,i)/dm, dTH(t,w,a,m)/dm, dTH(t,w,i,m)/dm, dTH(t,a,i,m)/dm, dTH(w,a,i,m)/dm, dTH(t,w,a,i,m)/dm.

 

 

Or more succinctly,  dTH/dm = dTH(t and/or w and/or a and/or i and/or m)/dm

 

 

Or perhaps dTH(m)/dm =d TH{[t(m)] and/or [w(m)] and/or [a(m)] and/or [i(m)] and/or [m(m)]}/dm.

 

 

Likewise, we can take the second memory derivatives of  TH as follows:

 

 

 

d[dTH(t)/dm]/dm, d[dTH(w)/dm]/dm, d[dTH(a)/dm]/dm, d[dTH(i)/dm]/dm, d[dTH(m)/dm]/dm, d[dTH(t,w)/dm]/dm, d[dTH(t,a)/dm]/dm, d[dTH(t,i)/dm]/dm, d[dTH(t,m)/dm]/dm, d[dTH(w,a)/dm]/dm, d[dTH(w,i)/dm]/dm, d[dTH(w,m)/dm]/dm, d[dTH(a,i)/dm]/dm, d[dTH(a,m)/dm]/dm, d[dTH(i,m)/dm/dm, d[dTH(t,w,a)/dm]/dm, d[dTH(t,w,i)/dm]/dm, d[dTH(t,w,m)/dm]/dm, d[dTH(t,a,i)/dm]/dm, d[dTH(t,a,m)/dm]/dm,  d[dTH(t,i,m)/dm]/dm, d[dTH(w,a,i)/dm]/dm, d[dTH(w,a,m)/dm]/dm, d[dTH(w,i,m)/dm]/dm, d[dTH(a,i,m)/dm]/dm, d[dTH(t,w,a,i)/dm]/dm, d[dTH(t,w,a,m)/dm/dm, d[dTH(t,w,i,m)/dm]/dm, d[dTH(t,a,i,m)/dm]/dm, d[dTH(w,a,i,m)/dm]/dm, d[dTH(t,w,a,i,m)/dm]/dm..

 

 

or more succinctly, as d(dTH/dm)/dm = d[d TH(t and/or w and/or a and/or i and/or m)/dm]/dm = THm2

 

 

or as

 

 

d[dTH(m)/dm]/dm  = d[d TH{[t(m)] and/or [w(m)] and/or [a(m)] and/or [i(m)] and/or [m(m)]}/dm]/dm = THm2.

 

 

 

Likewise, we can take the third memory derivatives of  TH as follows:

 

 

 

d[d[dTH(t)/dm]/dm]/dm, d[d[dTH(w)/dm]/dm]/dm, d[d[dTH(a)/dm]/dm]/dm, d[d[dTH(i)/dm]/dm]/dm, d[d[dTH(m)/dm]/dm]/dm, d[d[dTH(t,w)/dm]/dm]/dm, d[d[dTH(t,a)/dm]/dm]/dm, d[d[dTH(t,i)/dm]/dm]/dm, d[d[dTH(t,m)/dm]/dm]/dm, d[d[dTH(w,a)/dm]/dm]/dm, d[d[dTH(w,i)/dm]/dm]/dm, d[d[dTH(w,m)/dm]/dm]/dm, d[d[dTH(a,i)/dm]/dm]/dm, d[d[dTH(a,m)/dm]/dm]/dm, d[d[dTH(i,m)/dm/dm]/dm, d[d[dTH(t,w,a)/dm]/dm]/dm, d[d[dTH(t,w,i)/dm]/dm]/dm, d[d[dTH(t,w,m)/dm]/dm]/dm, d[d[dTH(t,a,i)/dm]/dm]/dm, d[d[dTH(t,a,m)/dm]/dm]/dm,  d[d[dTH(t,i,m)/dm]/dm]/dm, d[d[dTH(w,a,i)/dm]/dm]/dm, d[d[dTH(w,a,m)/dm]/dm]/dm, d[d[dTH(w,i,m)/dm]/dm]/dm, d[d[dTH(a,i,m)/dm]/dm]/dm, d[d[dTH(t,w,a,i)/dm]/dm]/dm, d[d[dTH(t,w,a,m)/dm/dm]/dm, d[d[dTH(t,w,i,m)/dm]/dm]/dm, d[d[dTH(t,a,i,m)/dm]/dm]/dm, d[d[dTH(w,a,i,m)/dm]/dm]/dm, d[d[dTH(t,w,a,i,m)/dm]/dm]/dm.

 

 

or more succinctly, as d[d(dTH/dm)/dm]/dm = d[d[d TH(t and/or w and/or a and/or i and/or m)/dm]/dm]/dm = THm3

 

 

or as

 

 

d[d[dTH(m)/dm]/dm]/dm  = d[d[d TH{[t(m)] and/or [w(m)] and/or [a(m)] and/or [i(m)] and/or [m(m)]}/dm]/dm]/dm = THm3.

 

 

We can also form the expressions;

 

 

d[d[f(TH)]/dm]/dm = d{d [TH[t(m)]]/dm and/or d[TH[w(m)]]/dm and/or d[TH[a(m)]]/dm and/or d[TH[i(m)]]/dm and/or d[TH[m(m)]]/dm}/dm  = f(THm)2

 

 

and

 

 

d[d[d[f(TH)]/dm]/dm]/dm = d{d{ d [TH[t(m)]]/dm and/or d[TH[w(m)]]/dm and/or d[TH[a(m)]]/dm and/or d[TH[i(m)]]/dm and/or d[TH[m(m)]]/dm}/dm}/dm  = f(THm)3A, where A stands for type A differentiation which is not to be confused with the meaning of so-called Type A personality as A is used as an ordinal in a totally different context here.

 

 

and

 

 

d[d[d[f(TH)]/dm]/dm]/dm = d{d[d [TH[t(m)]]/dm]/dm  and/or d[d [TH[w(m)]]/dm]/dm  and/or d[d [TH[a(m)]]/dm]/dm  and/or d[d [TH[i(m)]]/dm]/dm  and/or d[d [TH[m(m)]]/dm]/dm }/dm = f(THm)3B, where B stands for type B differentiation which is not to be confused with the meaning of so-called Type  B personality as B is used as an ordinal in a totally different context here .

 

 

In fact, one can form yet higher order derivatives of thoughts with respect to memory as follows.

 

 

THm5 = d THm4/dm = d[dTHm3/dm]/dm

 

 

 

THm5 = dTHm4/dm =  d[d[d[d[d TH{[t(m)] and/or [w(m)] and/or [a(m)] and/or [i(m)] and/or [m(m)]}/dm]/dm]/dm]/dm]/dm.

 

 

 

f(THm)5A = d[f(THm)4A]/dm = d[d [f(THm)3A]/dm]/dm =  d{d{d{d{ d [TH[t(m)]]/dm and/or d[TH[w(m)]]/dm and/or d[TH[a(m)]]/dm and/or d[TH[i(m)]]/dm and/or d[TH[m(m)]]/dm}/dm}/dm]/dm]/dm

 

 

 

 

THm6 = d THm5/dm = d[d THm4/dm]/dm = d[d[dTHm3/dm]/dm]/dm

 

 

 

THm6 = dTHm5/dm = d[d[d[d[d[d TH{[t(m)] and/or [w(m)] and/or [a(m)] and/or [i(m)] and/or [m(m)]}/dm]/dm]/dm]/dm]/dm]/dm

 

 

 

f(THm)6A = d[f(THm)5A]/dm = d{ d{d{d{d{ d [TH[t(m)]]/dm and/or d[TH[w(m)]]/dm and/or d[TH[a(m)]]/dm and/or d[TH[i(m)]]/dm and/or d[TH[m(m)]]/dm}/dm}/dm]/dm]/dm]/dm

 

 

 

 

THm7 = dTHm6/dm

 

f(THm)7A = d[f(THm)6A]/dm

 

 

THm8 = d THm7/dm

 

f(THm)8A = d[f(THm)7A]/dm

 

 

 

THm9 = d THm8/dm

 

f(THm)9A = d[f(THm)8A]/dm

 

 

THm10…, THm11…, THm12 … etc.

 

 

Anyone for THm ensemble, or THm infinity scrapper, or THm (Aleph 0), or THm(Aleph 1), or THm (Aleph 2), or how about THm Aleph (Aleph 0), or THm Aleph (Aleph 1) , or THm Aleph (Aleph 2), or even THm Aleph (Aleph (Aleph 0)), or THm Aleph (Aleph (Aleph 1)), or THm Aleph (Aleph (Aleph 2)), and so on?

 

Thus, for the set of the sets of derivatives of THm1 through THm(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}.

 

For the set of the sets of derivatives of THm1 through THm (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)},…, {П(0,31)[R]}_{(Aleph 1)}.

 

For the set of the sets of derivatives of THm 1 through THm (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}.

 

For the set of the sets of derivatives of THm 1 through THm (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the derivative states in the set of the sets of derivatives of THm 1 through I(Aleph 0) is plausible equal to:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of THm 1 through THm (Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of THm 1 through THm (Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}}}.

 

For the set of the sets of derivatives of THm 1 through THm (Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous THm I(Aleph 0) derivative space at the level of 0/(Aleph 0), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of THm 1 through THm (Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of THm 1 through THm (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of THm 1 through THm (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of THm 1 through THm (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of THm 1 through THm (Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of THm 1 through THm (Aleph 1), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of THm 1 through  THm (Aleph 2), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of THm I1 through THm (Aleph 3), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous THm (Aleph 0) derivative space at the level of 0/(Aleph 1), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of THm 1 through THm (Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of THm 1 through THm (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of THm 1 through THm (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of THm 1 through  THm (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations  for the set of the sets of derivatives of THm 1 through THm (Aleph 0) is plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of THm 1 through THm (Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of THm 1 through THm (Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of THm 1 through THm (Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

 

For super-continuous THm (Aleph 0) derivative space at the level of 0/(Aleph 2), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of THm 1 through THm (Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of THm 1 through THm (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of THm 1 through THm (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of THm I1 through THm (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of THm 1 through THm (Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of THm I1 through THm (Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of THm 1 through THm (Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of THm I1 through THm (Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

Similar series can be developed for super-continuity at any applicable level such as 0/(Aleph 3), 0/(Aleph 4), 0/(Aleph 5),…, 0/(Aleph Ω), 0/(Aleph (Aleph 0)), …, 0/(Aleph (Aleph 1)), …, 0/(Aleph (Aleph 2)), …, 0/(Aleph (Aleph 3)),…, 0/(Aleph (Aleph Ω)),…, 0/(Aleph (Aleph (Aleph 0))), …, 0/(Aleph (Aleph (Aleph 1))),…, 0/(Aleph (Aleph (Aleph 2))),…, 0/(Aleph (Aleph (Aleph 3))),…, 0/(Aleph (Aleph  (Aleph Ω))), …

 

An so-on ad infinitum.

 

 

In addition to these numerical functions of THm as functions of summation series of product series functions, in order to really appreciate the enourmous complexity of the human soul in terms of its potential to evolve and be differentiated from all other souls in its characteristics, we would need to consider how every single category and even every single species of thought of the form THm can very. Since there may exist an arbitrarily high infinite number species of THm, the number of numerical functions of THm is utterly beyond recogning. I will cover such notions in terms of mathematical notation in yet another series of articles I will write on this general concept.

 

 

Perhaps these numbers are applicable when one considers that the human soul, in its accidental form and perhaps even in its substantial form stores all experience and other psychodynamics based phenomenon. Every experience adds to the accidental form of the human soul and this includes the souls of all those still alive on Earth, all those in Purgatory, all those in Heaven, all those in Hell, and all those in any Limbo.

Since the human soul can grow without limit in terms of its psychodynamic time –flow world line, such a consideration offers another mechanism where the number of derivative states, combinations of derivative states, and even super-continuity of the derivative state space can grow forever.

 

Folks, for those of you who might balk at me for including literally all souls in the above consideration, including the souls in Hell, as well as bodily extraterrestrial souls and the souls of so-called bodily ultraterrestials sometimes referred to as etherians in the new age UFO buff culture, my reply is that we simply do not understand the full scope of GOD’s Divine Economy. We may never fully comprehend the scope of the Divine Economy because such an utterly eternal scheme, is, well, eternal and never ending.

 

 

 

 

The general meaning of memory derivatives of thought can be viewed as the manner in which the qualitative and/or quantitative aspects of thought as a function of memory very with memory. The manner in which thoughts very with memory may be multi- memory-aspect dimensional wherein the dimensions of derivations can be multiple, and wherein the derivations can be taken in parallel, series parallel or in serial manner. The differentials can be partial or non-partial derivatives, or both partial and non-partial for a given computation.

 

In fact, since there is in theory, no limit to the numbers of qualitatively and quantitatively different memories, and perhaps no limit to the number of possible different types or classes of memories, wherein each person has his or her own unique memories, the number of memory dimensions that can effect thoughts is literally infinite, given the entirety of the set of created persons, and perhaps also literally infinite for each person as an individual, although we can not intellectually and intuitively understand this infinite number.

 

 

It is interesting to consider the ramifactions of being able to perform realistic calculations involving memory derivatives of thought from a mathematical, theoretical, scientific,  and philosophical perspective.

 

Persons for which one or more nth order derivatives of thought with respect to memory that have large absolute values would tend to have their thoughts highly influenced by memory, or at least for the thoughts under consideration with respect to the dimension of the specific memory act type(s) or class(es) for which the differentiation(s) are being performed. Perhaps a strong coupling between thought and memory indicates a well integrated personality and commensurately, a high degree of thought capacity and a high degree of thought intelligence as well as perhaps very strong memory power.

 

We would expect that disembodied human souls, ETI souls, and/or UTI souls in Heaven, Limbo, highly evolved bodily ETI persons, highly evolved UTI persons, and angels to have thoughts of all kinds and intensities which are perhaps  highly subject to powereful memorys such as spiritual memorys, psychological memories, emotional memories, intellectual memories, interpersonal memories, auto-biographical memories, and even perhaps, memories facilitated by advanced psychic powers.

 

 

We can also consider that two dimensional nth ordered derivatives of thought with respect to memory and time, or with respect to i and T, respectively.

 

Given that TH[(m)(T)] =  TH[(t and/or w and/or a and/or i and/or m)(m)(T)], the following first order two dimensional derivatives of thought with respect to memory and Time are possible.

 

 

d[dTH[(t)(T)]/dm]/dT, d[dTH[(w)(T)]/dm]/dT, d[dTH[(a)(T)]/dm]/dT, d[dTH[(i)(T)]/dm]/dT, d[dTH[(m)(T)]/dm]/dT, d[dTH[(t,w)(T)]/dm]/dT, d[dTH[(t,a)(T)]/dm]/dT, d[dTH[(t,i)(T)]/dm]/dT, d[dTH[(t,m)(T)]/dm]/dT, d[dTH[(w,a)(T)]/dm]/dT, d[dTH[(w,i)(T)]/dm]/dT, d[dTH[(w,m)(T)]/dm]/dT, d[dTH[(a,i)(T)]/dm]/dT, d[dTH[(a,m)(T)]/dm]/dT, d[dTH[(i,m)(T)]/dm]/dT, d[dTH[(t,w,a)(T)]/dm]/dT, d[dTH[(t,w,i)(T)]/dm]/dT, d[dTH[(t,w,m)(T)]/dm]/dT, d[dTH[(t,a,i)(T)]/dm]/dT, d[dTH[(t,a,m)(T)]/dm]/dT, d[dTH[(t,i,m)(T)]/dm]/dT, d[dTH[(w,a,i)(T)]/dm]/dT, d[dTH[(w,a,m)(T)]/dm]/dT, d[dTH[(w,i,m)(T)]/dm]/dT, d[dTH[(a,i,m)(T)]/dm]/dT, d[dTH[(t,w,a,i)(T)]/dm]/dT, d[dTH[(t,w,a,m)(T)]/dm]/dT, d[dTH[(t,w,i,m)(T)]/dm]/dT, d[dTH[(t,a,i,m)(T)]/dm]/dT, d[dTH[(w,a,i,m)(T)]/dm]/dT, d[dTH[(t,w,a,i,m)(T)]/dm]/dT.

 

 

Or more succinctly,  d[dTH(T)/dm]/dT = d[dTH[(T)(t and/or w and/or a and/or m and/or m)]/dm]/dT

 

or

 

d[dTH(T)/dT]/dm = d[dTH[(T)(t and/or w and/or a and/or i and/or m)]/dT]/dm

 

 

 

 

 

Or perhaps d[d TH[(m)(T)]/dm]/dT  = d[d TH [{[t(m)] and/or [w(m)] and/or [a(m)] and/or [i(m)] and/or [m(m)]}(T)]/dm]/dT

 

or

 

Or perhaps d[d TH[(m)(T)]/dT]/dm  = d[d TH [{[t(m)] and/or [w(m)] and/or [a(m)] and/or [i(m)] and/or [m(m)]}(T)]/dT]/dm

 

 

 

Likewise, we can take the second dual dimension memory -time derivatives of  TH as follows:

 

d[d[d[dTH[(t)(T)]/dm]/dT]/dm]/dT, d[d[d[dTH[(w)(T)]/dm]/dT]/dm]/dT, d[d[d[dTH[(a)(T)]/dm]/dT]/dm]/dT, d[d[d[dTH[(i)(T)]/dm]/dT]/dm]/dT, d[d[d[dTH[(m)(T)]/dm]/dT]/dm]/dT, d[d[d[dTH[(t,w)(T)]/dm]/dT]/dm]/dT, d[d[d[dTH[(t,a)(T)]/dm]/dT]/dm]/dT, d[d[d[dTH[(t,i)(T)]/dm]/dT]/dm]/dT, d[d[d[dTH[(t,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dTH[(w,a)(T)]/dm]/dT]/dm]/dT, d[d[d[dTH[(w,i)(T)]/dm]/dT]/dm]/dT, d[d[d[dTH[(w,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dTH[(a,i)(T)]/dm]/dT]/dm]/dT, d[d[d[dTH[(a,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dTH[(i,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dTH[(t,w,a)(T)]/dm]/dT]/dm]/dT, d[d[d[dTH[(t,w,i)(T)]/dm]/dT]/dm]/dT, d[d[d[dTH[(t,w,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dTH[(t,a,i)(T)]/dm]/dT]/dm]/dT, d[d[d[dTH[(t,a,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dTH[(t,i,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dTH[(w,a,i)(T)]/dm]/dT]/dm]/dT, d[d[d[dTH[(w,a,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dTH[(w,i,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dTH[(a,i,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dTH[(t,w,a,i)(T)]/dm]/dT]/dm]/dT, d[d[d[dTH[(t,w,a,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dTH[(t,w,i,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dTH[(t,a,i,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dTH[(w,a,i,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dTH[(t,w,a,i,m)(T)]/dm]/dT]/dm]/dT.

 

or as:

 

 

 

d[d[d[dTH[(t)(T)]/dm]/dT]/dT]/dm, d[d[d[dTH[(w)(T)]/dm]/dT]/dT]/dm, d[d[d[dTH[(a)(T)]/dm]/dT]/dT]/dm, d[d[d[dTH[(i)(T)]/dm]/dT]/dT]/dm, d[d[d[dTH[(m)(T)]/dm]/dT]/dT]/dm, d[d[d[dTH[(t,w)(T)]/dm]/dT]/dT]/dm, d[d[d[dTH[(t,a)(T)]/dm]/dT]/dT]/dm, d[d[d[dTH[(t,i)(T)]/dm]/dT]/dT]/dm, d[d[d[dTH[(t,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dTH[(w,a)(T)]/dm]/dT]/dT]/dm, d[d[d[dTH[(w,i)(T)]/dm]/dT]/dT]/dm, d[d[d[dTH[(w,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dTH[(a,i)(T)]/dm]/dT]/dT]/dm, d[d[d[dTH[(a,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dTH[(i,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dTH[(t,w,a)(T)]/dm]/dT]/dT]/dm, d[d[d[dTH[(t,w,i)(T)]/dm]/dT]/dT]/dm, d[d[d[dTH[(t,w,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dTH[(t,a,i)(T)]/dm]/dT]/dT]/dm, d[d[d[dTH[(t,a,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dTH[(t,i,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dTH[(w,a,i)(T)]/dm]/dT]/dT]/dm, d[d[d[dTH[(w,a,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dTH[(w,i,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dTH[(a,i,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dTH[(t,w,a,i)(T)]/dm]/dT]/dT]/dm, d[d[d[dTH[(t,w,a,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dTH[(t,w,i,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dTH[(t,a,i,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dTH[(w,a,i,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dTH[(t,w,a,i,m)(T)]/dm]/dT]/dT]/dm.

 

or as:

 

d[d[d[dTH[(t)(T)]/dT]/dm]/dm]/dT, d[d[d[dTH[(w)(T)]/dT]/dm]/dm]/dT, d[d[d[dTH[(a)(T)]/dT]/dm]/dm]/dT, d[d[d[dTH[(i)(T)]/dT]/dm]/dm]/dT, d[d[d[dTH[(m)(T)]/dT]/dm]/dm]/dT, d[d[d[dTH[(t,w)(T)]/dT]/dm]/dm]/dT, d[d[d[dTH[(t,a)(T)]/dT]/dm]/dm]/dT, d[d[d[dTH[(t,i)(T)]/dT]/dm]/dm]/dT, d[d[d[dTH[(t,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dTH[(w,a)(T)]/dT]/dm]/dm]/dT, d[d[d[dTH[(w,i)(T)]/dT]/dm]/dm]/dT, d[d[d[dTH[(w,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dTH[(a,i)(T)]/dT]/dm]/dm]/dT, d[d[d[dTH[(a,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dTH[(i,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dTH[(t,w,a)(T)]/dT]/dm]/dm]/dT, d[d[d[dTH[(t,w,i)(T)]/dT]/dm]/dm]/dT, d[d[d[dTH[(t,w,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dTH[(t,a,i)(T)]/dT]/dm]/dm]/dT, d[d[d[dTH[(t,a,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dTH[(t,i,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dTH[(w,a,i)(T)]/dT]/dm]/dm]/dT, d[d[d[dTH[(w,a,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dTH[(w,i,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dTH[(a,i,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dTH[(t,w,a,i)(T)]/dT]/dm]/dm]/dT, d[d[d[dTH[(t,w,a,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dTH[(t,w,i,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dTH[(t,a,i,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dTH[(w,a,i,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dTH[(t,w,a,i,m)(T)]/dT]/dm]/dm]/dT.

 

 

or as;

 

 

 

 

d[d[d[dTH(t)/dm]/dm]/dT]/dT, d[d[d[dTH(w)/dm]/dm]/dT]/dT, d[d[d[dTH(a)/dm]/dm]/dT]/dT, d[d[d[dTH(i)/dm]/dm]/dT]/dT, d[d[d[dTH(m)/dm]/dm]/dT]/dT, d[d[d[dTH(t,w)/dm]/dm]/dT]/dT, d[d[d[dTH(t,a)/dm]/dm]/dT]/dT, d[d[d[dTH(t,i)/dm]/dm]/dT]/dT, d[d[d[dTH(t,m)/dm]/dm]/dT]/dT, d[d[d[dTH(w,a)/dm]/dm]/dT]/dT, d[d[d[dTH(w,i)/dm]/dm]/dT]/dT, d[d[d[dTH(w,m)/dm]/dm]/dT]/dT, d[d[d[dTH(a,i)/dm]/dm]/dT]/dT, d[d[d[dTH(a,m)/dm]/dm]/dT]/dT, d[d[d[dTH(i,m)/dm]/dm]/dT]/dT, d[d[d[dTH(t,w,a)/dm]/dm]/dT]/dT, d[d[d[dTH(t,w,i)/dm]/dm]/dT]/dT, d[d[d[dTH(t,w,m)/dm]/dm]/dT]/dT, d[d[d[dTH(t,a,i)/dm]/dm]/dT]/dT, d[d[d[dTH(t,a,m)/dm]/dm]/dT]/dT,  d[d[d[dTH(t,i,m)/dm]/dm]/dT]/dT, d[d[d[dTH(w,a,i)/dm]/dm]/dT]/dT, d[d[d[dTH(w,a,m)/dm]/dm]/dT]/dT, d[d[d[dTH(w,i,m)/dm]/dm]/dT]/dT, d[d[d[dTH(a,i,m)/dm]/dm]/dT]/dT, d[d[d[dTH(t,w,a,i)/dm]/dm]/dT]/dT, d[d[d[dTH(t,w,a,m)/dm/dm, d[d[d[dTH(t,w,i,m)/dm]/dm]/dT]/dT, d[d[d[dTH(t,a,i,m)/dm]/dm]/dT]/dT, d[d[d[dTH(w,a,i,m)/dm]/dm]/dT]/dT, d[d[d[dTH(t,w,a,i,m)/dm]/dm]/dT]/dT..

 

or as:

 

d[d[d[dTH(t)/dT]/dm]/dT]/dm, d[d[d[dTH(w)/dT]/dm]/dT]/dm, d[d[d[dTH(a)/dT]/dm]/dT]/dm, d[d[d[dTH(i)/dT]/dm]/dT]/dm, d[d[d[dTH(m)/dT]/dm]/dT]/dm, d[d[d[dTH(t,w)/dT]/dm]/dT]/dm, d[d[d[dTH(t,a)/dT]/dm]/dT]/dm, d[d[d[dTH(t,i)/dT]/dm]/dT]/dm, d[d[d[dTH(t,m)/dT]/dm]/dT]/dm, d[d[d[dTH(w,a)/dT]/dm]/dT]/dm, d[d[d[dTH(w,i)/dT]/dm]/dT]/dm, d[d[d[dTH(w,m)/dT]/dm]/dT]/dm, d[d[d[dTH(a,i)/dT]/dm]/dT]/dm, d[d[d[dTH(a,m)/dT]/dm]/dT]/dm, d[d[d[dTH(i,m)/ dT]/dm]/dT]/dm, d[d[d[dTH(t,w,a)/dT]/dm]/dT]/dm, d[d[d[dTH(t,w,i)/dT]/dm]/dT]/dm, d[d[d[dTH(t,w,m)/dT]/dm]/dT]/dm, d[d[d[dTH(t,a,i)/dT]/dm]/dT]/dm, d[d[d[dTH(t,a,m)/dT]/dm]/dT]/dm,  d[d[d[dTH(t,i,m)/dT]/dm]/dT]/dm, d[d[d[dTH(w,a,i)/dT]/dm]/dT]/dm, d[d[d[dTH(w,a,m)/dT]/dm]/dT]/dm, d[d[d[dTH(w,i,m)/dT]/dm]/dT]/dm, d[d[d[dTH(a,i,m)/dT]/dm]/dT]/dm, d[d[d[dTH(t,w,a,i)/dT]/dm]/dT]/dm, d[d[d[dTH(t,w,a,m)/dm/dm, d[d[d[dTH(t,w,i,m)/dT]/dm]/dT]/dm, d[d[d[dTH(t,a,i,m)/dT]/dm]/dT]/dm, d[d[d[dTH(w,a,i,m)/dT]/dm]/dT]/dm, d[d[d[dTH(t,w,a,i,m)/dT]/dm]/dT]/dm..

 

or as:

 

d[d[d[dTH(t)/dT]/dT]/dm]/dm, d[d[d[dTH(w)/dT]/dT]/dm]/dm, d[d[d[dTH(a)/dT]/dT]/dm]/dm, d[d[d[dTH(i)/dT]/dT]/dm]/dm, d[d[d[dTH(m)/dT]/dT]/dm]/dm, d[d[d[dTH(t,w)/dT]/dT]/dm]/dm, d[d[d[dTH(t,a)/dT]/dT]/dm]/dm, d[d[d[dTH(t,i)/dT]/dT]/dm]/dm, d[d[d[dTH(t,m)/dT]/dT]/dm]/dm, d[d[d[dTH(w,a)/dT]/dT]/dm]/dm, d[d[d[dTH(w,i)/dT]/dT]/dm]/dm, d[d[d[dTH(w,m)/dT]/dT]/dm]/dm, d[d[d[dTH(a,i)/dT]/dT]/dm]/dm, d[d[d[dTH(a,m)/ dT]/dT]/dm]/dm, d[d[d[dTH(i,m)/ dT]/dT]/dm]/dm, d[d[d[dTH(t,w,a)/dT]/dT]/dm]/dm, d[d[d[dTH(t,w,i)/dT]/dT]/dm]/dm, d[d[d[dTH(t,w,m)/dT]/dT]/dm]/dm, d[d[d[dTH(t,a,i)/dT]/dT]/dm]/dm, d[d[d[dTH(t,a,m)/dT]/dT]/dm]/dm,  d[d[d[dTH(t,i,m)/dT]/dT]/dm]/dm, d[d[d[dTH(w,a,i)/dT]/dT]/dm]/dm, d[d[d[dTH(w,a,m)/dT]/dT]/dm]/dm, d[d[d[dTH(w,i,m)/dT]/dT]/dm]/dm, d[d[d[dTH(a,i,m)/dT]/dT]/dm]/dm, d[d[d[dTH(t,w,a,i)/dT]/dT]/dm]/dm, d[d[d[dTH(t,w,a,m)/dm/dm, d[d[d[dTH(t,w,i,m)/dT]/dT]/dm]/dm, d[d[d[dTH(t,a,i,m)/dT]/dT]/dm]/dm, d[d[d[dTH(w,a,i,m)/dT]/dT]/dm]/dm, d[d[d[dTH(t,w,a,i,m)/dT]/dT]/dm]/dm..

 

We can also take higher order duel dimensional derivatives of thought as a function of memory and time but the symbolic expression of the set of such derivatives very soon becomes excessively lengthly to write and so these higher order derivatives as such are not mentioned here except to say that they would be computed in an analogous manner to the second order duel dimensional derivatives described above.

 

 

 

These seemingly crazy differentials might have some use in extreme psychological states that can be experienced by souls who are departed and whose thoughts, although perhaps spiritualized, are nonetheless, not limited by a body and its brain.

 

 

Another type of being that might experience such extreme thoughts change capacities might be none other then some of our friends we believe to exist as pure body-less and brain-less spirits known as angels.

 

 

Since I have dared to speculate this far, perhaps we can speculate as to whether any intelligent extraterrestrials persons or any so-called ultra-terrestrials persons that are more cognitively evolved then we ordinary humans might be capable of experiencing large absolute valued terms of THn. Some such ETI and UTI persons may  have evolved over billions of years, or perhaps have far greater powers of sensation, thought, and intuition such as would seem plausible for any such persons and their civilizations who have not fallen from the state of innocence into the state of sin as we humans have, or perhaps such beings never had the option of  sanctifying grace opened to them but nonetheless may have been created at a naturally more perfect level then we humans, and who therefore might exhibit greater natural powers of thought and sensation.

 

We can also express thought qualitatively, statistically, and perhaps with the use of some forms of real analyses as a derivative of thought or of t

 

Given that TH(t) =  TH(t and/or w and/or a and/or i and/or m), the following first order derivatives of thought  with respect to thought are possible.

 

 

dTH(t)/dt, dTH(w)/dt, dTH(a)/dt, dTH(i)/dt, dTH(m)/dt, dTH(t,w)/dt, dTH(t,a)/dt, dTH(t,i)/dt, dTH(t,m)/dt, dTH(w,a)/dt, dTH(w,i)/dt, dTH(w,m)/dt, dTH(a,i)/dt, dTH(a,m)/dt, dTH(i,m)/dt, dTH(t,w,a)/dt, dTH(t,w,i)/dt, dTH(t,w,m)/dt, dTH(t,a,i)/dt, dTH(t,a,m)/dt, dTH(t,i,m)/dt, dTH(w,a,i)/dt, dTH(w,a,m)/dt, dTH(w,i,m)/dt, dTH(a,i,m)/dt, dTH(t,w,a,i)/dt, dTH(t,w,a,m)/dt, dTH(t,w,i,m)/dt, dTH(t,a,i,m)/dt, dTH(w,a,i,m)/dt, dTH(t,w,a,i,m)/dt.

 

 

Or more succinctly,  dTH/dt = dTH(t and/or w and/or a and/or i and/or m)/dt

 

 

Or perhaps dTH(t)/dt =d TH{[t(t)] and/or [w(t)] and/or [a(t)] and/or [i(t)] and/or [m(t)]}/dt.

 

 

Likewise, we can take the second thought derivatives of  TH as follows:

 

 

 

d[dTH(t)/dt]/dt, d[dTH(w)/dt]/dt, d[dTH(a)/dt]/dt, d[dTH(i)/dt]/dt, d[dTH(m)/dt]/dt, d[dTH(t,w)/dt]/dt, d[dTH(t,a)/dt]/dt, d[dTH(t,i)/dt]/dt, d[dTH(t,m)/dt]/dt, d[dTH(w,a)/dt]/dt, d[dTH(w,i)/dt]/dt, d[dTH(w,m)/dt]/dt, d[dTH(a,i)/dt]/dt, d[dTH(a,m)/dt]/dt, d[dTH(i,m)/dt/dt, d[dTH(t,w,a)/dt]/dt, d[dTH(t,w,i)/dt]/dt, d[dTH(t,w,m)/dt]/dt, d[dTH(t,a,i)/dt]/dt, d[dTH(t,a,m)/dt]/dt,  d[dTH(t,i,m)/dt]/dt, d[dTH(w,a,i)/dt]/dt, d[dTH(w,a,m)/dt]/dt, d[dTH(w,i,m)/dt]/dt, d[dTH(a,i,m)/dt]/dt, d[dTH(t,w,a,i)/dt]/dt, d[dTH(t,w,a,m)/dt/dt, d[dTH(t,w,i,m)/dt]/dt, d[dTH(t,a,i,m)/dt]/dt, d[dTH(w,a,i,m)/dt]/dt, d[dTH(t,w,a,i,m)/dt]/dt..

 

 

or more succinctly, as d(dTH/dt)/dt = d[d TH(t and/or w and/or a and/or i and/or m)/dt]/dt = THt2

 

 

or as

 

 

d[dTH(t)/dt]/dt  = d[d TH{[t(t)] and/or [w(t)] and/or [a(t)] and/or [i(t)] and/or [m(t)]}/dt]/dt = THt2.

 

 

 

Likewise, we can take the third thought derivatives of  TH as follows:

 

 

 

d[d[dTH(t)/dt]/dt]/dt, d[d[dTH(w)/dt]/dt]/dt, d[d[dTH(a)/dt]/dt]/dt, d[d[dTH(i)/dt]/dt]/dt, d[d[dTH(m)/dt]/dt]/dt, d[d[dTH(t,w)/dt]/dt]/dt, d[d[dTH(t,a)/dt]/dt]/dt, d[d[dTH(t,i)/dt]/dt]/dt, d[d[dTH(t,m)/dt]/dt]/dt, d[d[dTH(w,a)/dt]/dt]/dt, d[d[dTH(w,i)/dt]/dt]/dt, d[d[dTH(w,m)/dt]/dt]/dt, d[d[dTH(a,i)/dt]/dt]/dt, d[d[dTH(a,m)/dt]/dt]/dt, d[d[dTH(i,m)/dt/dt]/dt, d[d[dTH(t,w,a)/dt]/dt]/dt, d[d[dTH(t,w,i)/dt]/dt]/dt, d[d[dTH(t,w,m)/dt]/dt]/dt, d[d[dTH(t,a,i)/dt]/dt]/dt, d[d[dTH(t,a,m)/dt]/dt]/dt,  d[d[dTH(t,i,m)/dt]/dt]/dt, d[d[dTH(w,a,i)/dt]/dt]/dt, d[d[dTH(w,a,m)/dt]/dt]/dt, d[d[dTH(w,i,m)/dt]/dt]/dt, d[d[dTH(a,i,m)/dt]/dt]/dt, d[d[dTH(t,w,a,i)/dt]/dt]/dt, d[d[dTH(t,w,a,m)/dt/dt]/dt, d[d[dTH(t,w,i,m)/dt]/dt]/dt, d[d[dTH(t,a,i,m)/dt]/dt]/dt, d[d[dTH(w,a,i,m)/dt]/dt]/dt, d[d[dTH(t,w,a,i,m)/dt]/dt]/dt.

 

 

or more succinctly, as d[d(dTH/dt)/dt]/dt = d[d[d TH(t and/or w and/or a and/or i and/or m)/dt]/dt]/dt = THt3

 

 

or as

 

 

d[d[dTH(t)/dt]/dt]/dt  = d[d[d TH{[t(t)] and/or [w(t)] and/or [a(t)] and/or [i(t)] and/or [m(t)]}/dt]/dt]/dt = THt3.

 

 

We can also form the expressions;

 

 

d[d[f(TH)]/dt]/dt = d{d [TH[t(t)]]/dt and/or d[TH[w(t)]]/dt and/or d[TH[a(t)]]/dt and/or d[TH[i(t)]]/dt and/or d[TH[m(t)]]/dt}/dt  = f(THt)2

 

 

and

 

 

d[d[d[f(TH)]/dt]/dt]/dt = d{d{ d [TH[t(t)]]/dt and/or d[TH[w(t)]]/dt and/or d[TH[a(t)]]/dt and/or d[TH[i(t)]]/dt and/or d[TH[m(t)]]/dt}/dt}/dt  = f(THt)3A, where A stands for type A differentiation which is not to be confused with the meaning of so-called Type A personality as A is used as an ordinal in a totally different context here.

 

 

and

 

 

d[d[d[f(TH)]/dt]/dt]/dt = d{d[d [TH[t(t)]]/dt]/dt  and/or d[d [TH[w(t)]]/dt]/dt  and/or d[d [TH[a(t)]]/dt]/dt  and/or d[d [TH[i(t)]]/dt]/dt  and/or d[d [TH[m(t)]]/dt]/dt }/dt = f(THt)3B, where B stands for type B differentiation which is not to be confused with the meaning of so-called Type  B personality as B is used as an ordinal in a totally different context here .

 

 

In fact, one can form yet higher order derivatives of thoughts with respect to thought as follows.

 

 

THt5 = d THt4/dt = d[dTHt3/dt]/dt

 

 

 

THt5 = dTHt4/dt =  d[d[d[d[d TH{[t(t)] and/or [w(t)] and/or [a(t)] and/or [i(t)] and/or [m(t)]}/dt]/dt]/dt]/dt]/dt.

 

 

 

f(THt)5A = d[f(tTH)4A]/dt = d[d [f(THt)3A]/dt]/dt =  d{d{d{d{ d [TH[t(t)]]/dt and/or d[TH[w(t)]]/dt and/or d[TH[a(t)]]/dt and/or d[TH[i(t)]]/dt and/or d[TH[m(t)]]/dt}/dt}/dt]/dt]/dt

 

 

 

 

THt6 = d THt5/dt = d[d THt4/dt]/dt = d[d[dTHt3/dt]/dt]/dt

 

 

 

THt6 = dTHt5/dt = d[d[d[d[d[d TH{[t(t)] and/or [w(t)] and/or [a(t)] and/or [i(t)] and/or [m(t)]}/dt]/dt]/dt]/dt]/dt]/dt

 

 

 

f(THt)6A = d[f(THt)5A]/dt = d{ d{d{d{d{ d [TH[t(t)]]/dt and/or d[TH[w(t)]]/dt and/or d[TH[a(t)]]/dt and/or d[TH[i(t)]]/dt and/or d[TH[m(t)]]/dt}/dt}/dt]/dt]/dt]/dt

 

 

 

 

THt7 = dTHt6/dt

 

f(THt)7A = d[f(THt)6A]/dt

 

 

THt8 = d THt7/dt

 

f(THt)8A = d[f(THt)7A]/dt

 

 

 

THt9 = d THt8/dt

 

f(THt)9A = d[f(THt)8A]/dt

 

 

THt10…, THt11…, THt12 … etc.

 

 

Anyone for THt ensemble, or THt infinity scrapper, or THt (Aleph 0), or THt(Aleph 1), or THt(Aleph 2), or how about THt Aleph (Aleph 0), or THt Aleph (Aleph 1) , or THt Aleph (Aleph 2), or even THt Aleph (Aleph (Aleph 0)), or THt Aleph (Aleph (Aleph 1)), or THt Aleph (Aleph (Aleph 2)), and so on?

 

Thus, for the set of the sets of derivatives of THt1 through THt(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}.

 

For the set of the sets of derivatives of THt1 through THt (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)},…, {П(0,31)[R]}_{(Aleph 1)}.

 

For the set of the sets of derivatives of THt 1 through THt (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}.

 

For the set of the sets of derivatives of THt 1 through THt (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the derivative states in the set of the sets of derivatives of THt 1 through I(Aleph 0) is plausible equal to:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of THt 1 through THt (Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of THt 1 through THt (Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}}}.

 

For the set of the sets of derivatives of THt 1 through THt (Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous THt I(Aleph 0) derivative space at the level of 0/(Aleph 0), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of THt 1 through THt (Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of THt 1 through THt (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of THt 1 through THt (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of THt 1 through THt (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of THt 1 through THt (Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of THt 1 through THt (Aleph 1), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of THt 1 through  THt (Aleph 2), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of THt I1 through THt (Aleph 3), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous THt (Aleph 0) derivative space at the level of 0/(Aleph 1), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of THt 1 through THt (Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of THt 1 through THt (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of THt 1 through THt (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of THt 1 through  THt (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations  for the set of the sets of derivatives of THt 1 through THt (Aleph 0) is plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of THt 1 through THt (Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of THt 1 through THt (Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of THt 1 through THt (Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

 

For super-continuous THt (Aleph 0) derivative space at the level of 0/(Aleph 2), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of THt 1 through THt (Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of THt 1 through THt (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of THt 1 through THt (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of THt I1 through THt (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of THt 1 through THt (Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of THt I1 through THt (Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of THt 1 through THt (Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of THt I1 through THt (Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

Similar series can be developed for super-continuity at any applicable level such as 0/(Aleph 3), 0/(Aleph 4), 0/(Aleph 5),…, 0/(Aleph Ω), 0/(Aleph (Aleph 0)), …, 0/(Aleph (Aleph 1)), …, 0/(Aleph (Aleph 2)), …, 0/(Aleph (Aleph 3)),…, 0/(Aleph (Aleph Ω)),…, 0/(Aleph (Aleph (Aleph 0))), …, 0/(Aleph (Aleph (Aleph 1))),…, 0/(Aleph (Aleph (Aleph 2))),…, 0/(Aleph (Aleph (Aleph 3))),…, 0/(Aleph (Aleph  (Aleph Ω))), …

 

An so-on ad infinitum.

 

 

In addition to these numerical functions of THt as functions of summation series of product series functions, in order to really appreciate the enourmous complexity of the human soul in terms of its potential to evolve and be differentiated from all other souls in its characteristics, we would need to consider how every single category and even every single species of memory of the form THt can very. Since there may exist an arbitrarily high infinite number species of THt, the number of numerical functions of THt is utterly beyond recogning. I will cover such notions in terms of mathematical notation in yet another series of articles I will write on this general concept.

 

 

Perhaps these numbers are applicable when one considers that the human soul, in its accidental form and perhaps even in its substantial form stores all experience and other psychodynamics based phenomenon. Every experience adds to the accidental form of the human soul and this includes the souls of all those still alive on Earth, all those in Purgatory, all those in Heaven, all those in Hell, and all those in any Limbo.

Since the human soul can grow without limit in terms of its psychodynamic time –flow world line, such a consideration offers another mechanism where the number of derivative states, combinations of derivative states, and even super-continuity of the derivative state space can grow forever.

 

Folks, for those of you who might balk at me for including literally all souls in the above consideration, including the souls in Hell, as well as bodily extraterrestrial souls and the souls of so-called bodily ultraterrestials sometimes referred to as etherians in the new age UFO buff culture, my reply is that we simply do not understand the full scope of GOD’s Divine Economy. We may never fully comprehend the scope of the Divine Economy because such an utterly eternal scheme, is, well, eternal and never ending.

 

 

The general meaning of thought derivatives of thought can be viewed as the manner in which the qualitative and/or quantitative aspects of thought as a function of thought very with thought(s). The manner in which thoughts very with thought may be multi-thought dimensional wherein the dimensions of derivations can be multiple, and wherein the derivations can be taken in parallel, series parallel or serial manner The differentials can be partial or non-partial derivatives, or both partial and non-partial for a given computation.

 

In fact, since there is in theory, no limit to the numbers of qualitatively and quantitatively different thoughts, and perhaps no limit to the number of possible different types or classes of thoughts, wherein each person has his or her own unique thoughts, the number of thought dimensions that can effect thoughts is literally infinite, given the entirety of the set of created persons, and perhaps also literally infinite for each person as an individual, although we can not intellectually and intuitively understand this specific infinite number.

 

It is interesting to consider the ramifactions of being able to perform realistic calculations involving thought derivatives of thought from a mathematical, theoretical, scientific,  and philosophical perspective.

 

Persons for which one or more nth order derivatives of thought with respect to thought that have large absolute values would tend to have their thoughts highly influenced by thought, or at least for the thought under consideration with respect to the dimension of the specific thought type(s) or class(es) for which the differentiation(s) are performed. Perhaps a strong coupling between thought and thought indicates a well integrated personality and commensurately, a high degree of thought capacity and a high degree of thought intelligence.

 

We would expect that disembodied human souls, ETI souls, and/or UTI souls in Heaven, Limbo, highly evolved bodily ETI persons, highly evolved UTI persons, and angels to have thought of all kinds and intensities which are highly subject to thought.

 

 

We can also consider two dimensional nth ordered derivatives of thought with respect to thought and time, or with respect to t and T, respectively.

 

Given that TH[(t)(T)] =  TH[(t and/or w and/or a and/or i and/or m)(t)(T)], the following first order two dimensional derivatives of thought with respect to thought and Time are possible.

 

 

d[dTH[(t)(T)]/dt]/dT, d[dTH[(w)(T)]/dt]/dT, d[dTH[(a)(T)]/dt]/dT, d[dTH[(i)(T)]/dt]/dT, d[dTH[(m)(T)]/dt]/dT, d[dTH[(t,w)(T)]/dt]/dT, d[dTH[(t,a)(T)]/dt]/dT, d[dTH[(t,i)(T)]/dt]/dT, d[dTH[(t,m)(T)]/dt]/dT, d[dTH[(w,a)(T)]/dt]/dT, d[dTH[(w,i)(T)]/dt]/dT, d[dTH[(w,m)(T)]/dt]/dT, d[dTH[(a,i)(T)]/dt]/dT, d[dTH[(a,m)(T)]/dt]/dT, d[dTH[(i,m)(T)]/dt]/dT, d[dTH[(t,w,a)(T)]/dt]/dT, d[dTH[(t,w,i)(T)]/dt]/dT, d[dTH[(t,w,m)(T)]/dt]/dT, d[dTH[(t,a,i)(T)]/dt]/dT, d[dTH[(t,a,m)(T)]/dt]/dT, d[dTH[(t,i,m)(T)]/dt]/dT, d[dTH[(w,a,i)(T)]/dt]/dT, d[dTH[(w,a,m)(T)]/dt]/dT, d[dTH[(w,i,m)(T)]/dt]/dT, d[dTH[(a,i,m)(T)]/dt]/dT, d[dTH[(t,w,a,i)(T)]/dt]/dT, d[dTH[(t,w,a,m)(T)]/dt]/dT, d[dTH[(t,w,i,m)(T)]/dt]/dT, d[dTH[(t,a,i,m)(T)]/dt]/dT, d[dTH[(w,a,i,m)(T)]/dt]/dT, d[dTH[(t,w,a,i,m)(T)]/dt]/dT.

 

 

Or more succinctly,  d[dTH(T)/dt]/dT = d[dTH[(T)(t and/or w and/or a and/or i and/or m)]/dt]/dT

 

or

 

d[dTH(T)/dT]/dt = d[dTH[(T)(t and/or w and/or a and/or i and/or m)]/dT]/dt

 

 

 

 

 

Or perhaps d[d TH[(t)(T)]/dt]/dT  = d[d TH [{[t(t)] and/or [w(t)] and/or [a(t)] and/or [i(t)] and/or [m(t)]}(T)]/dt]/dT

 

or

 

Or perhaps d[d TH[(t)(T)]/dT]/dt  = d[d TH [{[t(t)] and/or [w(t)] and/or [a(t)] and/or [i(t)] and/or [m(t)]}(T)]/dT]/dt

 

 

 

Likewise, we can take the second dual dimensioned thought-time derivatives of  TH as follows:

 

d[d[d[dTH[(t)(T)]/dt]/dT]/dt]/dT, d[d[d[dTH[(w)(T)]/dt]/dT]/dt]/dT, d[d[d[dTH[(a)(T)]/dt]/dT]/dt]/dT, d[d[d[dTH[(i)(T)]/dt]/dT]/dt]/dT, d[d[d[dTH[(m)(T)]/dt]/dT]/dt]/dT, d[d[d[dTH[(t,w)(T)]/dt]/dT]/dt]/dT, d[d[d[dTH[(t,a)(T)]/dt]/dT]/dt]/dT, d[d[d[dTH[(t,i)(T)]/dt]/dT]/dt]/dT, d[d[d[dTH[(t,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dTH[(w,a)(T)]/dt]/dT]/dt]/dT, d[d[d[dTH[(w,i)(T)]/dt]/dT]/dt]/dT, d[d[d[dTH[(w,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dTH[(a,i)(T)]/dt]/dT]/dt]/dT, d[d[d[dTH[(a,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dTH[(i,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dTH[(t,w,a)(T)]/dt]/dT]/dt]/dT, d[d[d[dTH[(t,w,i)(T)]/dt]/dT]/dt]/dT, d[d[d[dTH[(t,w,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dTH[(t,a,i)(T)]/dt]/dT]/dt]/dT, d[d[d[dTH[(t,a,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dTH[(t,i,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dTH[(w,a,i)(T)]/dt]/dT]/dt]/dT, d[d[d[dTH[(w,a,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dTH[(w,i,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dTH[(a,i,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dTH[(t,w,a,i)(T)]/dt]/dT]/dt]/dT, d[d[d[dTH[(t,w,a,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dTH[(t,w,i,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dTH[(t,a,i,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dTH[(w,a,i,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dTH[(t,w,a,i,m)(T)]/dt]/dT]/dt]/dT.

 

or as:

 

 

 

d[d[d[dTH[(t)(T)]/dt]/dT]/dT]/dt, d[d[d[dTH[(w)(T)]/dt]/dT]/dT]/dt, d[d[d[dTH[(a)(T)]/dt]/dT]/dT]/dt, d[d[d[dTH[(i)(T)]/dt]/dT]/dT]/dt, d[d[d[dTH[(m)(T)]/dt]/dT]/dT]/dt, d[d[d[dTH[(t,w)(T)]/dt]/dT]/dT]/dt, d[d[d[dTH[(t,a)(T)]/dt]/dT]/dT]/dt, d[d[d[dTH[(t,i)(T)]/dt]/dT]/dT]/dt, d[d[d[dTH[(t,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dTH[(w,a)(T)]/dt]/dT]/dT]/dt, d[d[d[dTH[(w,i)(T)]/dt]/dT]/dT]/dt, d[d[d[dTH[(w,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dTH[(a,i)(T)]/dt]/dT]/dT]/dt, d[d[d[dTH[(a,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dTH[(i,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dTH[(t,w,a)(T)]/dt]/dT]/dT]/dt, d[d[d[dTH[(t,w,i)(T)]/dt]/dT]/dT]/dt, d[d[d[dTH[(t,w,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dTH[(t,a,i)(T)]/dt]/dT]/dT]/dt, d[d[d[dTH[(t,a,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dTH[(t,i,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dTH[(w,a,i)(T)]/dt]/dT]/dT]/dt, d[d[d[dTH[(w,a,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dTH[(w,i,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dTH[(a,i,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dTH[(t,w,a,i)(T)]/dt]/dT]/dT]/dt, d[d[d[dTH[(t,w,a,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dTH[(t,w,i,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dTH[(t,a,i,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dTH[(w,a,i,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dTH[(t,w,a,i,m)(T)]/dt]/dT]/dT]/dt.

 

or as:

 

d[d[d[dTH[(t)(T)]/dT]/dt]/dt]/dT, d[d[d[dTH[(w)(T)]/dT]/dt]/dt]/dT, d[d[d[dTH[(a)(T)]/dT]/dt]/dt]/dT, d[d[d[dTH[(i)(T)]/dT]/dt]/dt]/dT, d[d[d[dTH[(m)(T)]/dT]/dt]/dt]/dT, d[d[d[dTH[(t,w)(T)]/dT]/dt]/dt]/dT, d[d[d[dTH[(t,a)(T)]/dT]/dt]/dt]/dT, d[d[d[dTH[(t,i)(T)]/dT]/dt]/dt]/dT, d[d[d[dTH[(t,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dTH[(w,a)(T)]/dT]/dt]/dt]/dT, d[d[d[dTH[(w,i)(T)]/dT]/dt]/dt]/dT, d[d[d[dTH[(w,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dTH[(a,i)(T)]/dT]/dt]/dt]/dT, d[d[d[dTH[(a,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dTH[(i,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dTH[(t,w,a)(T)]/dT]/dt]/dt]/dT, d[d[d[dTH[(t,w,i)(T)]/dT]/dt]/dt]/dT, d[d[d[dTH[(t,w,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dTH[(t,a,i)(T)]/dT]/dt]/dt]/dT, d[d[d[dTH[(t,a,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dTH[(t,i,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dTH[(w,a,i)(T)]/dT]/dt]/dt]/dT, d[d[d[dTH[(w,a,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dTH[(w,i,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dTH[(a,i,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dTH[(t,w,a,i)(T)]/dT]/dt]/dt]/dT, d[d[d[dTH[(t,w,a,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dTH[(t,w,i,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dTH[(t,a,i,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dTH[(w,a,i,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dTH[(t,w,a,i,m)(T)]/dT]/dt]/dt]/dT.

 

 

or as;

 

 

 

 

d[d[d[dTH(t)/dt]/dt]/dT]/dT, d[d[d[dTH(w)/dt]/dt]/dT]/dT, d[d[d[dTH(a)/dt]/dt]/dT]/dT, d[d[d[dTH(i)/dt]/dt]/dT]/dT, d[d[d[dTH(m)/dt]/dt]/dT]/dT, d[d[d[dTH(t,w)/dt]/dt]/dT]/dT, d[d[d[dTH(t,a)/dt]/dt]/dT]/dT, d[d[d[dTH(t,i)/dt]/dt]/dT]/dT, d[d[d[dTH(t,m)/dt]/dt]/dT]/dT, d[d[d[dTH(w,a)/dt]/dt]/dT]/dT, d[d[d[dTH(w,i)/dt]/dt]/dT]/dT, d[d[d[dTH(w,m)/dt]/dt]/dT]/dT, d[d[d[dTH(a,i)/dt]/dt]/dT]/dT, d[d[d[dTH(a,m)/dt]/dt]/dT]/dT, d[d[d[dTH(i,m)/dt]/dt]/dT]/dT, d[d[d[dTH(t,w,a)/dt]/dt]/dT]/dT, d[d[d[dTH(t,w,i)/dt]/dt]/dT]/dT, d[d[d[dTH(t,w,m)/dt]/dt]/dT]/dT, d[d[d[dTH(t,a,i)/dt]/dt]/dT]/dT, d[d[d[dTH(t,a,m)/dt]/dt]/dT]/dT,  d[d[d[dTH(t,i,m)/dt]/dt]/dT]/dT, d[d[d[dTH(w,a,i)/dt]/dt]/dT]/dT, d[d[d[dTH(w,a,m)/dt]/dt]/dT]/dT, d[d[d[dTH(w,i,m)/dt]/dt]/dT]/dT, d[d[d[dTH(a,i,m)/dt]/dt]/dT]/dT, d[d[d[dTH(t,w,a,i)/dt]/dt]/dT]/dT, d[d[d[dTH(t,w,a,m)/dt/dt, d[d[d[dTH(t,w,i,m)/dt]/dt]/dT]/dT, d[d[d[dTH(t,a,i,m)/dt]/dt]/dT]/dT, d[d[d[dTH(w,a,i,m)/dt]/dt]/dT]/dT, d[d[d[dTH(t,w,a,i,m)/dt]/dt]/dT]/dT..

 

or as:

 

d[d[d[dTH(t)/dT]/dt]/dT]/dt, d[d[d[dTH(w)/dT]/dt]/dT]/dt, d[d[d[dTH(a)/dT]/dt]/dT]/dt, d[d[d[dTH(i)/dT]/dt]/dT]/dt, d[d[d[dTH(m)/dT]/dt]/dT]/dt, d[d[d[dTH(t,w)/dT]/dt]/dT]/dt, d[d[d[dTH(t,a)/dT]/dt]/dT]/dt, d[d[d[dTH(t,i)/dT]/dt]/dT]/dt, d[d[d[dTH(t,m)/dT]/dt]/dT]/dt, d[d[d[dTH(w,a)/dT]/dt]/dT]/dt, d[d[d[dTH(w,i)/dT]/dt]/dT]/dt, d[d[d[dTH(w,m)/dT]/dt]/dT]/dt, d[d[d[dTH(a,i)/dT]/dt]/dT]/dt, d[d[d[dTH(a,m)/dT]/dt]/dT]/dt, d[d[d[dTH(i,m)/ dT]/dt]/dT]/dt, d[d[d[dTH(t,w,a)/dT]/dt]/dT]/dt, d[d[d[dTH(t,w,i)/dT]/dt]/dT]/dt, d[d[d[dTH(t,w,m)/dT]/dt]/dT]/dt, d[d[d[dTH(t,a,i)/dT]/dt]/dT]/dt, d[d[d[dTH(t,a,m)/dT]/dt]/dT]/dt,  d[d[d[dTH(t,i,m)/dT]/dt]/dT]/dt, d[d[d[dTH(w,a,i)/dT]/dt]/dT]/dt, d[d[d[dTH(w,a,m)/dT]/dt]/dT]/dt, d[d[d[dTH(w,i,m)/dT]/dt]/dT]/dt, d[d[d[dTH(a,i,m)/dT]/dt]/dT]/dt, d[d[d[dTH(t,w,a,i)/dT]/dt]/dT]/dt, d[d[d[dTH(t,w,a,m)/dt/dt, d[d[d[dTH(t,w,i,m)/dT]/dt]/dT]/dt, d[d[d[dTH(t,a,i,m)/dT]/dt]/dT]/dt, d[d[d[dTH(w,a,i,m)/dT]/dt]/dT]/dt, d[d[d[dTH(t,w,a,i,m)/dT]/dt]/dT]/dt..

 

or as:

 

d[d[d[dTH(t)/dT]/dT]/dt]/dt, d[d[d[dTH(w)/dT]/dT]/dt]/dt, d[d[d[dTH(a)/dT]/dT]/dt]/dt, d[d[d[dTH(i)/dT]/dT]/dt]/dt, d[d[d[dTH(m)/dT]/dT]/dt]/dt, d[d[d[dTH(t,w)/dT]/dT]/dt]/dt, d[d[d[dTH(t,a)/dT]/dT]/dt]/dt, d[d[d[dTH(t,i)/dT]/dT]/dt]/dt, d[d[d[dTH(t,m)/dT]/dT]/dt]/dt, d[d[d[dTH(w,a)/dT]/dT]/dt]/dt, d[d[d[dTH(w,i)/dT]/dT]/dt]/dt, d[d[d[dTH(w,m)/dT]/dT]/dt]/dt, d[d[d[dTH(a,i)/dT]/dT]/dt]/dt, d[d[d[dTH(a,m)/ dT]/dT]/dt]/dt, d[d[d[dTH(i,m)/ dT]/dT]/dt]/dt, d[d[d[dTH(t,w,a)/dT]/dT]/dt]/dt, d[d[d[dTH(t,w,i)/dT]/dT]/dt]/dt, d[d[d[dTH(t,w,m)/dT]/dT]/dt]/dt, d[d[d[dTH(t,a,i)/dT]/dT]/dt]/dt, d[d[d[dTH(t,a,m)/dT]/dT]/dt]/dt,  d[d[d[dTH(t,i,m)/dT]/dT]/dt]/dt, d[d[d[dTH(w,a,i)/dT]/dT]/dt]/dt, d[d[d[dTH(w,a,m)/dT]/dT]/dt]/dt, d[d[d[dTH(w,i,m)/dT]/dT]/dt]/dt, d[d[d[dTH(a,i,m)/dT]/dT]/dt]/dt, d[d[d[dTH(t,w,a,i)/dT]/dT]/dt]/dt, d[d[d[dTH(t,w,a,m)/dt/dt, d[d[d[dTH(t,w,i,m)/dT]/dT]/dt]/dt, d[d[d[dTH(t,a,i,m)/dT]/dT]/dt]/dt, d[d[d[dTH(w,a,i,m)/dT]/dT]/dt]/dt, d[d[d[dTH(t,w,a,i,m)/dT]/dT]/dt]/dt..

 

 

We can also take higher order duel dimensional derivatives of thought as a function of thought and time but the symbolic expression of the set of such derivatives very soon becomes excessively lengthly to write and so these higher order derivatives as such are not mentioned here except to say that they would be computed in an analogous manner to the second order duel dimensional derivatives described above.

 

 

 

Now, the above variable of time, T,  can have multiple meanings or aspects. One such meaning is objective time and in such a case for large non-zero values of THn, where n = 1,2,3,…, the person experiencing such an thought or complex of thoughts  might not subjectively experience the thought(s) as occurring any faster than we ordinary humans do.

 

 

However, another interpretation of the variable of Time is subjective time. In such a case for large non-zero absolute values of THn, where n = 1,2,3,…, the person experiencing such an thought or complex of thoughts  would subjectively experience the thought(s) as occurring or changing faster than we ordinary humans experience, in fact the higher the absolute value of non-zero THn, especially for large n, the rate of change of thought with respect to time would progress at an incredible rate. We ordinary humans would likely be completely overwhelmed by subjective psychic experiences of such THn phenomenon.

 

 

Could there be other objective temporal dimensions beside the one objective temporal dimension that we know of, and the seemingly one subjective dimension of time that we experience? As someone who normally writes on the topic of exotic space craft propulsion systems such as proposed interstellar space craft propulsion systems, I am familiar with the theoretical paradigms that there may exist higher dimensions of space and perhaps more than one dimension of time, and so I say, never say never.

 

The above notation of derivatives and differential equations is just an infinitesimal glimpse of the number of possible equations as such and related constructs. Trust me, I can reasonably in good confidence re-assure you of such.

 

35) Just A Shadow Of A Glimpse Of The Utterly Limitless Number Derivatives of Will  With Respect To Time, Thought, Volition, Affect, Memory, Instinct, And Emotion  Where These Latter 6 Psychodynamic Parameter Are Likely Just An Infinitesimal Fraction Of The Number Of Possible Psychodynamic Parameters, Of Which In This Life, We Have  A Glimpse Of Relatively Few.

 

 

 

Will  as such can be a function or partially a function of emotion, will, affect, instinct, emotion and/or memory; and thought as such can be expressed as follows:

 

 

W(t), W(w), W(a), W(i), W(m), W(t,w), W(t,a), W(t,i), W(t,m), W(w,a), W(w,i), W(w,m), W(a,i), W(a,m), W(i,m), W(t,w,a), W(t,w,i), W(t,w,m), W(t,a,i), W(t,a,m), W(t,i,m), W(w,a,i), W(w,a,m), W(w,i,m), W(a,i,m), W(t,w,a,i), W(t,w,a,m), W(t,w,i,m), W(t,a,i,m), W(w,a,i,m), W(t,w,a,i,m)

 

W(t,e), W(w,e), W(a,e), W(i,e), W(m,e), W(t,w,e), W(t,a,e), W(t,i,e), W(t,m,e), W(w,a,e), W(w,i,e), W(w,m,e), W(a,i,e), W(a,m,e), W(i,m,e), W(t,w,a,e), W(t,w,i,e), W(t,w,m,e), W(t,a,i,e), W(t,a,m,e), W(t,i,m,e), W(w,a,i,e), W(w,a,m,e), W(w,i,m,e), W(a,i,m,e), W(t,w,a,i,e), W(t,w,a,m,e), W(t,w,i,m,e), W(t,a,i,m,e), W(w,a,i,m,e), W(t,w,a,i,m,e).

 

Note that some differential expressions involving  the form of functions of will, or W,  as a function of emotion, e, by itself, or in conjunction with any sub-set of the parameters of t,w,a,i,m, are not included to the same extent as many similar expressions including W, and these other parameters denoted by the small letters, t,w,a,i, and/or m in this section. A more comphrensive post will include the currently omitted explicit formulas incorporating the parameter, e. Note that capital e, or E, is a parameter that is often included in the differential equations herein, but then so in a slightly different context than e would have be included. The difference between e and E will become clear from the context of the specific formulas.

 

In all, there are (2 EXP n) – 1 = (2 EXP 6) – 1 = 63 expressions as such if one assumes the previous five dimensions of thought.

 

In this article, we will cover the notion of arbitrary finite and more or less arbitrarily infinity ordered derivatives of human, ETI, and UTI will with respect to time, thought, will, affect, memory, instinct, and emotion.

 

Even in the case where the first order derivatives as such are small in magnitude, this does not preclude non-zero first order derivatives of more or less arbitrary infinity orders with respect to the same psychodynamic variables. This is plausibly true since the derivatives described herein are not totally quantitative and in many respect are not quantitative. Also, for the quantitative aspects of such infinity ordered derivatives of  will, the complexity of the precise mathematical expressions may be such that there are an arbitrarily infinite number of  various infinite ordered derivatives such that the numerical infinities cancel out.

 

Another argument for the plausibility of  non-zero infinite order derivatives of will is that each aspect of human psychodynamic activity or states are immeadiately present to themselves in the sense that each such activity or change of state occurs within the complete and total simultaneous unity of the associated human person, more specifically within the associated human soul.

 

Yet another argument is that the difference in the various derivatives as such may be small even in the midst of a range of derivatives that spans infinite numbers of orders. Such small differences may be the result of infinities that cancel out, but may also be the result of non-numerically quantifiable aspects of the sets of such derivatives.

 

The Human Heart is so complex that I am not sure how the concepts described herein can be not valid even amidst the generally non violent or at least not too violent or not too over whelmingly strong effects of one psychodynamic parameter state on another.

 

So despite the fact that we do not notice infinitely rapid or infinite intra-reactive changes within our psychodynamic states, the arguments for the plausibility of non-zero infinite ordered derivatives of will with respect to other basic psychodynamic parameters or aspects is argued as above and mathematically categorized herein below.

 

 

 

 

Will  as such can be a function or partially a function of emotion, will, affect, instinct, emotion and/or memory; and thought as such can be expressed as follows:

 

 

W(t), W(w), W(a), W(i), W(m), W(t,w), W(t,a), W(t,i), W(t,m), W(w,a), W(w,i), W(w,m), W(a,i), W(a,m), W(i,m), W(t,w,a), W(t,w,i), W(t,w,m), W(t,a,i), W(t,a,m), W(t,i,m), W(w,a,i), W(w,a,m), W(w,i,m), W(a,i,m), W(t,w,a,i), W(t,w,a,m), W(t,w,i,m), W(t,a,i,m), W(w,a,i,m), W(t,w,a,i,m)

 

W(t,e), W(w,e), W(a,e), W(i,e), W(m,e), W(t,w,e), W(t,a,e), W(t,i,e), W(t,m,e), W(w,a,e), W(w,i,e), W(w,m,e), W(a,i,e), W(a,m,e), W(i,m,e), W(t,w,a,e), W(t,w,i,e), W(t,w,m,e), W(t,a,i,e), W(t,a,m,e), W(t,i,m,e), W(w,a,i,e), W(w,a,m,e), W(w,i,m,e), W(a,i,m,e), W(t,w,a,i,e), W(t,w,a,m,e), W(t,w,i,m,e), W(t,a,i,m,e), W(w,a,i,m,e), W(t,w,a,i,m,e).

 

 

 

Assuming that each of the above function f(W)  is perfectly continuous, the number of forms that the general emotion function, f(W), can have is plausibly equal to П(1,62)R where R is the number of real numbers.

 

Assuming that each of the above functions f(W) is super-continuous at the level of 0/(Aleph 0) where Aleph 0 is the number of integers, the number of forms that the general emotion function, f(W), can have is plausibly equal to П(1,62)[R x (Aleph 0)] where R is the number of real numbers.

 

Assuming that each of the above functions f(W) is super-continuous at the level of 0/(Aleph 1) where Aleph 1 is the number of real numbers according to the Continuum Hypotheses, the number of forms that the general will function, f(W), can have is plausibly equal to П(1,62)[R x (Aleph 1)] where R is the number of real numbers.

 

Assuming that each of the above functions f(W) is super-continuous at the level of 0/(Aleph 2) where Aleph 2 is is greater than Aleph 1 by a factor of infinity (the exact details of this infinity of which are a little more involve than the latter simple statement), the number of forms that the general will function, f(W), can have is plausibly equal to П(1,62)[R x (Aleph 2)] where R is the number of real numbers.

 

Assuming that each of the above functions f(W) is super-continuous at the level of 0/(Aleph 3) where Aleph 3 is is greater than Aleph 2 by a factor of infinity (the exact details of this infinity of which are a little more involve than the latter simple statement), the number of forms that the general will function, f(W), can have is plausibly equal to П(1,62)[R x (Aleph 3)] where R is the number of real numbers.

 

… and so on ad infinitum to, through, and beyond the following product series, П(1,62)[R x (Aleph 4)],   П(1,62)[R x (Aleph 5)],  П(1,62)[R x (Aleph 6)],…,  П(1,62)[R x (Aleph Ω)], …,  П(1,62)[R x (Aleph (Aleph 0))], …, П(1,62)[R x (Aleph (Aleph 1))], …, П(1,62)[R x (Aleph (Aleph 2))], … , П(1,62)[R x (Aleph (Aleph Ω))], …, П(1,62)[R x (Aleph (Aleph (Aleph 0)))] and so on perhaps in an ever lasting series even a  the latter level of abstraction.

 

Assuming that each of the above functions f(W) is super-continuous at the level of 0/(Aleph 2) where Aleph 2 is is greater than Aleph 1 by a factor of infinity (the exact details of this infinity of which are a little more involve than the latter simple statement), the number of forms that the general will function, f(W), can have is plausibly equal to П(1,62)[R x (Aleph 2)] where R is the number of real numbers.

 

 

We can summarize all of these combinations as follows in compact symbolism that is intuitively clear to follow:

 

 

W = W(t and/or w and/or a and/or i and/or m)

 

 

We can express W as a function of time as follows: W(T) =  W[(t and/or w and/or a and/or i and/or m),(T)] or perhaps the following notation can be more appropriate in certain circumstances.

 

 

W(T) = W{[t(T)] and/or [w(T)] and/or [a(T)] and/or [i(T)] and/or [m(T)]}.

 

 

Thus, the following first order derivatives of will with respect to time are possible.

 

 

dW(t)/dT, dW(w)/dT, dW(a)/dT, dW(i)/dT, dW(m)/dT, dW(t,w)/dT, dW(t,a)/dT, dW(t,i)/dT, dW(t,m)/dT, dW(w,a)/dT, dW(w,i)/dT, dW(w,m)/dT, dW(a,i)/dT, dW(a,m)/dT, dW(i,m)/dT, dW(t,w,a)/dT, dW(t,w,i)/dT, dW(t,w,m)/dT, dW(t,a,i)/dT, dW(t,a,m)/dT, dW(t,i,m)/dT, dW(w,a,i)/dT, dW(w,a,m)/dT, dW(w,i,m)/dT, dW(a,i,m)/dT, dW(t,w,a,i)/dT, dW(t,w,a,m)/dT, dW(t,w,i,m)/dT, dW(t,a,i,m)/dT, dW(w,a,i,m)/dT, dW(t,w,a,i,m)/dT.

 

 

Or more succinctly,  dW/dT = dW(t and/or w and/or a and/or i and/or m)/dT

 

 

Or perhaps dW(T)/dT =d W{[t(T)] and/or [w(T)] and/or [a(T)] and/or [i(T)] and/or [m(T)]}/dT.

 

 

Likewise, we can take the second time derivatives of  W as follows:

 

 

 

d[dW(t)/dT]/dT, d[dW(w)/dT]/dT, d[dW(a)/dT]/dT, d[dW(i)/dT]/dT, d[dW(m)/dT]/dT, d[dW(t,w)/dT]/dT, d[dW(t,a)/dT]/dT, d[dW(t,i)/dT]/dT, d[dW(t,m)/dT]/dT, d[dW(w,a)/dT]/dT, d[dW(w,i)/dT]/dT, d[dW(w,m)/dT]/dT, d[dW(a,i)/dT]/dT, d[dW(a,m)/dT]/dT, d[dW(i,m)/dT/dT, d[dW(t,w,a)/dT]/dT, d[dW(t,w,i)/dT]/dT, d[dW(t,w,m)/dT]/dT, d[dW(t,a,i)/dT]/dT, d[dW(t,a,m)/dT]/dT,  d[dW(t,i,m)/dT]/dT, d[dW(w,a,i)/dT]/dT, d[dW(w,a,m)/dT]/dT, d[dW(w,i,m)/dT]/dT, d[dW(a,i,m)/dT]/dT, d[dW(t,w,a,i)/dT]/dT, d[dW(t,w,a,m)/dT/dT, d[dW(t,w,i,m)/dT]/dT, d[dW(t,a,i,m)/dT]/dT, d[dW(w,a,i,m)/dT]/dT, d[dW(t,w,a,i,m)/dT]/dT..

 

 

or more succinctly, as d(dW/dT)/dT = d[d W(t and/or w and/or a and/or i and/or m)/dT]/dT = W2

 

 

or as

 

 

d[dW(T)/dT]/dT  = d[d W{[t(T)] and/or [w(T)] and/or [a(T)] and/or [i(T)] and/or [m(T)]}/dT]/dT = W2.

 

 

 

Likewise, we can take the third time derivatives of  W as follows:

 

 

 

d[d[dW(t)/dT]/dT]/dT, d[d[dW(w)/dT]/dT]/dT, d[d[dW(a)/dT]/dT]/dT, d[d[dW(i)/dT]/dT]/dT, d[d[dW(m)/dT]/dT]/dT, d[d[dW(t,w)/dT]/dT]/dT, d[d[dW(t,a)/dT]/dT]/dT, d[d[dW(t,i)/dT]/dT]/dT, d[d[dW(t,m)/dT]/dT]/dT, d[d[dW(w,a)/dT]/dT]/dT, d[d[dW(w,i)/dT]/dT]/dT, d[d[dW(w,m)/dT]/dT]/dT, d[d[dW(a,i)/dT]/dT]/dT, d[d[dW(a,m)/dT]/dT]/dT, d[d[dW(i,m)/dT/dT]/dT, d[d[dW(t,w,a)/dT]/dT]/dT, d[d[dW(t,w,i)/dT]/dT]/dT, d[d[dW(t,w,m)/dT]/dT]/dT, d[d[dW(t,a,i)/dT]/dT]/dT, d[d[dW(t,a,m)/dT]/dT]/dT,  d[d[dW(t,i,m)/dT]/dT]/dT, d[d[dW(w,a,i)/dT]/dT]/dT, d[d[dW(w,a,m)/dT]/dT]/dT, d[d[dW(w,i,m)/dT]/dT]/dT, d[d[dW(a,i,m)/dT]/dT]/dT, d[d[dW(t,w,a,i)/dT]/dT]/dT, d[d[dW(t,w,a,m)/dT/dT]/dT, d[d[dW(t,w,i,m)/dT]/dT]/dT, d[d[dW(t,a,i,m)/dT]/dT]/dT, d[d[dW(w,a,i,m)/dT]/dT]/dT, d[d[dW(t,w,a,i,m)/dT]/dT]/dT.

 

 

or more succinctly, as d[d(dW/dT)/dT]/dT = d[d[d W(t and/or w and/or a and/or i and/or m)/dT]/dT]/dT = W3

 

 

or as

 

 

d[d[dW(T)/dT]/dT]/dT  = d[d[d W{[t(T)] and/or [w(T)] and/or [a(T)] and/or [i(T)] and/or [m(T)]}/dT]/dT]/dT = W3.

 

 

We can also form the expressions;

 

 

d[d[f(W)]/dT]/dT = d{d [W[t(T)]]/dT and/or d[W[w(T)]]/dT and/or d[W[a(T)]]/dT and/or d[W[i(T)]]/dT and/or d[W[m(T)]]/dT}/dT  = f(W)2

 

 

and

 

 

d[d[d[f(W)]/dT]/dT]/dT = d{d{ d [W[t(T)]]/dT and/or d[W[w(T)]]/dT and/or d[W[a(T)]]/dT and/or d[W[i(T)]]/dT and/or d[W[m(T)]]/dT}/dT}/dT  = f(W)3A, where A stands for type A differentiation which is not to be confused with the meaning of so-called Type A personality as A is used as an ordinal in a totally different context here.

 

 

and

 

 

d[d[d[f(W)]/dT]/dT]/dT = d{d[d [W[t(T)]]/dT]/dT  and/or d[d [W[w(T)]]/dT]/dT  and/or d[d [W[a(T)]]/dT]/dT  and/or d[d [W[i(T)]]/dT]/dT  and/or d[d [W[m(T)]]/dT]/dT }/dT = f(W)3B, where B stands for type B differentiation which is not to be confused with the meaning of a  so-called Type  B personality as B is used as an ordinal in a totally different context here .

 

 

In fact, one can form yet higher order derivatives of will with respect to time as follows.

 

 

W5 = d W4/dT = d[dW3/dT]/dT

 

 

 

W5 = d W4/dT =  d[d[d[d[d W{[t(T)] and/or [w(T)] and/or [a(T)] and/or [i(T)] and/or [m(T)]}/dT]/dT]/dT]/dT]/dT.

 

 

 

f(W)5A = d[f(W)4A]/dT = d[d [f(W)3A]/dT]/dT =  d{d{d{d{ d [W[t(T)]]/dT and/or d[W[w(T)]]/dT and/or d[W[a(T)]]/dT and/or d[W[i(T)]]/dT and/or d[W[m(T)]]/dT}/dT}/dT]/dT]/dT

 

 

 

 

W6 = d W5/dT = d[d W4/dT]/dT = d[d[dW3/dT]/dT]/dT

 

 

 

W6 = dW5/dT = d[d[d[d[d[d W{[t(T)] and/or [w(T)] and/or [a(T)] and/or [i(T)] and/or [m(T)]}/dT]/dT]/dT]/dT]/dT]/dT

 

 

 

f(W)6A = d[f(W)5A]/dT = d{ d{d{d{d{ d [W[t(T)]]/dT and/or d[W[w(T)]]/dT and/or d[W[a(T)]]/dT and/or d[W[i(T)]]/dT and/or d[W[m(T)]]/dT}/dT}/dT]/dT]/dT]/dT

 

 

 

 

W7 = dW6/dT

 

f(W)7A = d[f(W)6A]/dT

 

 

W8 = d W7/dT

 

f(W)8A = d[f(W)7A]/dT

 

 

 

W9 = d W8/dT

 

f(W)9A = d[f(W)8A]/dT

 

 

W10…, W11…, W12 … etc.

 

 

Anyone for W ensemble, or W infinity scrapper, or W (Aleph 0), or W(Aleph 1), or W(Aleph 2), or how about W Aleph (Aleph 0), or W Aleph (Aleph 1) , or W Aleph (Aleph 2), or even W Aleph (Aleph (Aleph 0)), or W Aleph (Aleph (Aleph 1)), or W Aleph (Aleph (Aleph 2)), and so on?

 

We can also express will qualitatively, statistically, and perhaps with the use of some forms of real analyses as a derivative with respect to emotion or with respect to E.

 

Given that W(t) =  W(t and/or w and/or a and/or i and/or m), the following first order derivatives of will  with respect to emotion are possible.

 

 

dW(t)/dE, dW(w)/dE, dW(a)/dE, dW(i)/dE, dW(m)/dE, dW(t,w)/dE, dW(t,a)/dE, dW(t,i)/dE, dW(t,m)/dE, dW(w,a)/dE, dW(w,i)/dE, dW(w,m)/dE, dW(a,i)/dE, dW(a,m)/dE, dW(i,m)/dE, dW(t,w,a)/dE, dW(t,w,i)/dE, dW(t,w,m)/dE, dW(t,a,i)/dE, dW(t,a,m)/dE, dW(t,i,m)/dE, dW(w,a,i)/dE, dW(w,a,m)/dE, dW(w,i,m)/dE, dW(a,i,m)/dE, dW(t,w,a,i)/dE, dW(t,w,a,m)/dE, dW(t,w,i,m)/dE, dW(t,a,i,m)/dE, dW(w,a,i,m)/dE, dW(t,w,a,i,m)/dE.

 

 

Or more succinctly,  dW/dE = dW(t and/or w and/or a and/or i and/or m)/dE

 

 

Or perhaps dW(e)/dE =d W{[t(e)] and/or [w(e)] and/or [a(e)] and/or [i(e)] and/or [m(e)]}/dE.

 

 

Likewise, we can take the second emotion derivatives of  W as follows:

 

 

 

d[dW(t)/dE]/dE, d[dW(w)/dE]/dE, d[dW(a)/dE]/dE, d[dW(i)/dE]/dE, d[dW(m)/dE]/dE, d[dW(t,w)/dE]/dE, d[dW(t,a)/dE]/dE, d[dW(t,i)/dE]/dE, d[dW(t,m)/dE]/dE, d[dW(w,a)/dE]/dE, d[dW(w,i)/dE]/dE, d[dW(w,m)/dE]/dE, d[dW(a,i)/dE]/dE, d[dW(a,m)/dE]/dE, d[dW(i,m)/dE/dE, d[dW(t,w,a)/dE]/dE, d[dW(t,w,i)/dE]/dE, d[dW(t,w,m)/dE]/dE, d[dW(t,a,i)/dE]/dE, d[dW(t,a,m)/dE]/dE,  d[dW(t,i,m)/dE]/dE, d[dW(w,a,i)/dE]/dE, d[dW(w,a,m)/dE]/dE, d[dW(w,i,m)/dE]/dE, d[dW(a,i,m)/dE]/dE, d[dW(t,w,a,i)/dE]/dE, d[dW(t,w,a,m)/dE/dE, d[dW(t,w,i,m)/dE]/dE, d[dW(t,a,i,m)/dE]/dE, d[dW(w,a,i,m)/dE]/dE, d[dW(t,w,a,i,m)/dE]/dE..

 

 

or more succinctly, as d(dW/dE)/dE = d[d W(t and/or w and/or a and/or i and/or m)/dE]/dE = We2

 

 

or as

 

 

d[dW(e)/dE]/dE  = d[d W{[t(e)] and/or [w(e)] and/or [a(e)] and/or [i(e)] and/or [m(e)]}/dE]/dE = We2.

 

 

 

Likewise, we can take the third emotion derivatives of  W as follows:

 

 

 

d[d[dW(t)/dE]/dE]/dE, d[d[dW(w)/dE]/dE]/dE, d[d[dW(a)/dE]/dE]/dE, d[d[dW(i)/dE]/dE]/dE, d[d[dW(m)/dE]/dE]/dE, d[d[dW(t,w)/dE]/dE]/dE, d[d[dW(t,a)/dE]/dE]/dE, d[d[dW(t,i)/dE]/dE]/dE, d[d[dW(t,m)/dE]/dE]/dE, d[d[dW(w,a)/dE]/dE]/dE, d[d[dW(w,i)/dE]/dE]/dE, d[d[dW(w,m)/dE]/dE]/dE, d[d[dW(a,i)/dE]/dE]/dE, d[d[dW(a,m)/dE]/dE]/dE, d[d[dW(i,m)/dE/dE]/dE, d[d[dW(t,w,a)/dE]/dE]/dE, d[d[dW(t,w,i)/dE]/dE]/dE, d[d[dW(t,w,m)/dE]/dE]/dE, d[d[dW(t,a,i)/dE]/dE]/dE, d[d[dW(t,a,m)/dE]/dE]/dE,  d[d[dW(t,i,m)/dE]/dE]/dE, d[d[dW(w,a,i)/dE]/dE]/dE, d[d[dW(w,a,m)/dE]/dE]/dE, d[d[dW(w,i,m)/dE]/dE]/dE, d[d[dW(a,i,m)/dE]/dE]/dE, d[d[dW(t,w,a,i)/dE]/dE]/dE, d[d[dW(t,w,a,m)/dE/dE]/dE, d[d[dW(t,w,i,m)/dE]/dE]/dE, d[d[dW(t,a,i,m)/dE]/dE]/dE, d[d[dW(w,a,i,m)/dE]/dE]/dE, d[d[dW(t,w,a,i,m)/dE]/dE]/dE.

 

 

or more succinctly, as d[d(dW/dE)/dE]/dE = d[d[d W(t and/or w and/or a and/or i and/or m)/dE]/dE]/dE = We3

 

 

or as

 

 

d[d[dW(e)/dE]/dE]/dE  = d[d[d W{[t(e)] and/or [w(e)] and/or [a(e)] and/or [i(e)] and/or [m(e)]}/dE]/dE]/dE = We3.

 

 

We can also form the expressions;

 

 

d[d[f(W)]/dE]/dE = d{d [W[t(e)]]/dE and/or d[W[w(e)]]/dE and/or d[W[a(e)]]/dE and/or d[W[i(e)]]/dE and/or d[W[m(e)]]/dE}/dE  = f(We)2

 

 

and

 

 

d[d[d[f(W)]/dE]/dE]/dE = d{d{ d [W[t(e)]]/dE and/or d[W[w(e)]]/dE and/or d[W[a(e)]]/dE and/or d[W[i(e)]]/dE and/or d[W[m(e)]]/dE}/dE}/dE  = f(We)3A, where A stands for type A differentiation which is not to be confused with the meaning of so-called Type A personality as A is used as an ordinal in a totally different context here.

 

 

and

 

 

d[d[d[f(W)]/dE]/dE]/dE = d{d[d [W[t(e)]]/dE]/dE  and/or d[d [W[w(e)]]/dE]/dE  and/or d[d [W[a(e)]]/dE]/dE  and/or d[d [W[i(e)]]/dE]/dE  and/or d[d [W[m(e)]]/dE]/dE }/dE = f(We)3B, where B stands for type B differentiation which is not to be confused with the meaning of so-called Type  B personality as B is used as an ordinal in a totally different context here .

 

 

In fact, one can form yet higher order derivatives of will with respect to emotion as follows.

 

 

We5 = d We4/dE = d[dWe3/dE]/dE

 

 

 

We5 = dWet4/dE =  d[d[d[d[d W{[t(e)] and/or [w(e)] and/or [a(e)] and/or [i(e)] and/or [m(e)]}/dE]/dE]/dE]/dE]/dE.

 

 

 

f(We)5A = d[f(eW)4A]/dE = d[d [f(We)3A]/dE]/dE =  d{d{d{d{ d [W[t(e)]]/dE and/or d[W[w(e)]]/dE and/or d[W[a(e)]]/dE and/or d[W[i(e)]]/dE and/or d[W[m(e)]]/dE}/dE}/dE]/dE]/dE

 

 

 

 

We6 = d We5/dE = d[d We4/dE]/dE = d[d[dWe3/dE]/dE]/dE

 

 

 

We6 = dWe5/dE = d[d[d[d[d[d W{[t(e)] and/or [w(e)] and/or [a(e)] and/or [i(e)] and/or [m(e)]}/dE]/dE]/dE]/dE]/dE]/dE

 

 

 

f(We)6A = d[f(We)5A]/dE = d{ d{d{d{d{ d [W[t(e)]]/dE and/or d[W[w(e)]]/dE and/or d[W[a(e)]]/dE and/or d[W[i(e)]]/dE and/or d[W[m(e)]]/dE}/dE}/dE]/dE]/dE]/dE

 

 

 

 

We7 = dWe6/dE

 

f(We)7A = d[f(We)6A]/dE

 

 

We8 = d We7/dE

 

f(We)8A = d[f(We)7A]/dE

 

 

 

We9 = d We8/dE

 

f(Wet)9A = d[f(We)8A]/dE

 

 

We10…, We11…, We12 … etc.

 

 

Anyone for We ensemble, or We infinity scrapper, or We (Aleph 0), or We(Aleph 1), or We(Aleph 2), or how about We Aleph (Aleph 0), or We Aleph (Aleph 1) , or We Aleph (Aleph 2), or even We Aleph (Aleph (Aleph 0)), or We Aleph (Aleph (Aleph 1)), or WeAleph (Aleph (Aleph 2)), and so on?

 

Thus, for the set of the sets of derivatives of We1 through We(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}.

 

For the set of the sets of derivatives of We1 through We (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)},…, {П(0,31)[R]}_{(Aleph 1)}.

 

For the set of the sets of derivatives of We 1 through We (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}.

 

For the set of the sets of derivatives of We 1 through We (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the derivative states in the set of the sets of derivatives of We 1 through I(Aleph 0) is plausible equal to:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of We 1 through We (Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of We 1 through We (Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}}}.

 

For the set of the sets of derivatives of We 1 through We (Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous We I(Aleph 0) derivative space at the level of 0/(Aleph 0), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of We 1 through We (Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of We 1 through We (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of We 1 through We (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of We 1 through We (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of We 1 through We (Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of We 1 through We (Aleph 1), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of We 1 through  We (Aleph 2), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of We I1 through We (Aleph 3), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous We (Aleph 0) derivative space at the level of 0/(Aleph 1), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of We 1 through We (Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of We 1 through We (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of We 1 through We (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of We 1 through  We (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations  for the set of the sets of derivatives of We 1 through We (Aleph 0) is plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of We 1 through We (Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of We 1 through We (Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of We 1 through We (Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

 

For super-continuous We (Aleph 0) derivative space at the level of 0/(Aleph 2), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of We 1 through We (Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of We 1 through We (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of We 1 through We (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of We I1 through We (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of We 1 through We (Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of We I1 through We (Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of We 1 through We (Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of We I1 through We (Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

Similar series can be developed for super-continuity at any applicable level such as 0/(Aleph 3), 0/(Aleph 4), 0/(Aleph 5),…, 0/(Aleph Ω), 0/(Aleph (Aleph 0)), …, 0/(Aleph (Aleph 1)), …, 0/(Aleph (Aleph 2)), …, 0/(Aleph (Aleph 3)),…, 0/(Aleph (Aleph Ω)),…, 0/(Aleph (Aleph (Aleph 0))), …, 0/(Aleph (Aleph (Aleph 1))),…, 0/(Aleph (Aleph (Aleph 2))),…, 0/(Aleph (Aleph (Aleph 3))),…, 0/(Aleph (Aleph  (Aleph Ω))), …

 

An so-on ad infinitum.

 

 

In addition to these numerical functions of We as functions of summation series of product series functions, in order to really appreciate the enourmous complexity of the human soul in terms of its potential to evolve and be differentiated from all other souls in its characteristics, we would need to consider how every single category and even every single species of will of the form We can very. Since there may exist an arbitrarily high infinite number species of We, the number of numerical functions of We is utterly beyond recogning. I will cover such notions in terms of mathematical notation in yet another series of articles I will write on this general concept.

 

 

Perhaps these numbers are applicable when one considers that the human soul, in its accidental form and perhaps even in its substantial form stores all experience and other psychodynamics based phenomenon. Every experience adds to the accidental form of the human soul and this includes the souls of all those still alive on Earth, all those in Purgatory, all those in Heaven, all those in Hell, and all those in any Limbo.

Since the human soul can grow without limit in terms of its psychodynamic time –flow world line, such a consideration offers another mechanism where the number of derivative states, combinations of derivative states, and even super-continuity of the derivative state space can grow forever.

 

Folks, for those of you who might balk at me for including literally all souls in the above consideration, including the souls in Hell, as well as bodily extraterrestrial souls and the souls of so-called bodily ultraterrestials sometimes referred to as etherians in the new age UFO buff culture, my reply is that we simply do not understand the full scope of GOD’s Divine Economy. We may never fully comprehend the scope of the Divine Economy because such an utterly eternal scheme, is, well, eternal and never ending.

 

 

 

The general meaning of emotion derivatives of will can be viewed as the manner in which the qualitative and/or quantitative aspects of will as a function of will very with emotion(s). The manner in which will very with will may be multi-will dimensional wherein the dimensions of derivations can be multiple, and wherein the derivations can be taken in parallel, series parallel or serial manner The differentials can be partial or non-partial derivatives, or both partial and non-partial for a given computation.

 

In fact, since there is in theory, no limit to the numbers of qualitatively and quantitatively different volitions, and perhaps no limit to the number of possible different types or classes of volitions, wherein each person has his or her own unique volitions, the number of emotion dimensions that can effect will is literally infinite, given the entirety of the set of created persons, and perhaps also literally infinite for each person as an individual, although we can not intellectually and intuitively understand this specific infinite number.

 

It is interesting to consider the ramifactions of being able to perform realistic calculations involving emotion derivatives of will from a mathematical, theoretical, scientific,  and philosophical perspective.

 

Persons for which one or more nth order derivatives of will with respect to emotion that have large absolute values would tend to have their volitions highly influenced by emotion, or at least for the volitions under consideration with respect to the dimension of the specific volition type(s) or class(es) for which the differentiation(s) are performed. Perhaps a strong coupling between will and emotion indicates a well integrated personality and commensurately, a high degree of will capacity and a high degree of will intelligence.

 

We would expect that disembodied human souls, ETI souls, and/or UTI souls in Heaven, Limbo, highly evolved bodily ETI persons, highly evolved UTI persons, and angels to have volitions of all kinds and intensities which are highly subject to spiritual emotions.

 

 

We can also consider two dimensional nth ordered derivatives of will with respect to emotion and time, or with respect to E and T, respectively.

 

Given that W[(e)(T)] =  W[(t and/or w and/or a and/or i and/or m)(e)(T)], the following first order two dimensional derivatives of will with respect to emotion and Time are possible.

 

 

d[dW[(t)(T)]/dE]/dT, d[dW[(w)(T)]/dE]/dT, d[dW[(a)(T)]/dE]/dT, d[dW[(i)(T)]/dE]/dT, d[dW[(m)(T)]/dE]/dT, d[dW[(t,w)(T)]/dE]/dT, d[dW[(t,a)(T)]/dE]/dT, d[dW[(t,i)(T)]/dE]/dT, d[dW[(t,m)(T)]/dE]/dT, d[dW[(w,a)(T)]/dE]/dT, d[dW[(w,i)(T)]/dE]/dT, d[dW[(w,m)(T)]/dE]/dT, d[dW[(a,i)(T)]/dE]/dT, d[dW[(a,m)(T)]/dE]/dT, d[dW[(i,m)(T)]/dE]/dT, d[dW[(t,w,a)(T)]/dE]/dT, d[dW[(t,w,i)(T)]/dE]/dT, d[dW[(t,w,m)(T)]/dE]/dT, d[dW[(t,a,i)(T)]/dE]/dT, d[dW[(t,a,m)(T)]/dE]/dT, d[dW[(t,i,m)(T)]/dE]/dT, d[dW[(w,a,i)(T)]/dE]/dT, d[dW[(w,a,m)(T)]/dE]/dT, d[dW[(w,i,m)(T)]/dE]/dT, d[dW[(a,i,m)(T)]/dE]/dT, d[dW[(t,w,a,i)(T)]/dE]/dT, d[dW[(t,w,a,m)(T)]/dE]/dT, d[dW[(t,w,i,m)(T)]/dE]/dT, d[dW[(t,a,i,m)(T)]/dE]/dT, d[dW[(w,a,i,m)(T)]/dE]/dT, d[dW[(t,w,a,i,m)(T)]/dE]/dT.

 

 

Or more succinctly,  d[dW(T)/dE]/dT = d[dW[(T)(t and/or w and/or a and/or i and/or m)]/dE]/dT

 

or

 

d[dW(T)/dT]/dE = d[dW[(T)(t and/or w and/or a and/or i and/or m)]/dT]/dE

 

 

 

 

 

Or perhaps d[d W[(e)(T)]/dE]/dT  = d[d W [{[t(e)] and/or [w(e)] and/or [a(e)] and/or [i(e)] and/or [m(e)]}(T)]/dE]/dT

 

or

 

Or perhaps d[d W[(e)(T)]/dT]/dE  = d[d W [{[t(e)] and/or [w(e)] and/or [a(e)] and/or [i(e)] and/or [m(e)]}(T)]/dT]/dE

 

 

 

Likewise, we can take the second dual dimensioned emotion-time derivatives of  W as follows:

 

d[d[d[dW[(t)(T)]/dE]/dT]/dE]/dT, d[d[d[dW[(w)(T)]/dE]/dT]/dE]/dT, d[d[d[dW[(a)(T)]/dE]/dT]/dE]/dT, d[d[d[dW[(i)(T)]/dE]/dT]/dE]/dT, d[d[d[dW[(m)(T)]/dE]/dT]/dE]/dT, d[d[d[dW[(t,w)(T)]/dE]/dT]/dE]/dT, d[d[d[dW[(t,a)(T)]/dE]/dT]/dE]/dT, d[d[d[dW[(t,i)(T)]/dE]/dT]/dE]/dT, d[d[d[dW[(t,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dW[(w,a)(T)]/dE]/dT]/dE]/dT, d[d[d[dW[(w,i)(T)]/dE]/dT]/dE]/dT, d[d[d[dW[(w,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dW[(a,i)(T)]/dE]/dT]/dE]/dT, d[d[d[dW[(a,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dW[(i,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dW[(t,w,a)(T)]/dE]/dT]/dE]/dT, d[d[d[dW[(t,w,i)(T)]/dE]/dT]/dE]/dT, d[d[d[dW[(t,w,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dW[(t,a,i)(T)]/dE]/dT]/dE]/dT, d[d[d[dW[(t,a,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dW[(t,i,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dW[(w,a,i)(T)]/dE]/dT]/dE]/dT, d[d[d[dW[(w,a,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dW[(w,i,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dW[(a,i,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dW[(t,w,a,i)(T)]/dE]/dT]/dE]/dT, d[d[d[dW[(t,w,a,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dW[(t,w,i,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dW[(t,a,i,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dW[(w,a,i,m)(T)]/dE]/dT]/dE]/dT, d[d[d[dW[(t,w,a,i,m)(T)]/dE]/dT]/dE]/dT.

 

or as:

 

 

 

d[d[d[dW[(t)(T)]/dE]/dT]/dT]/dE, d[d[d[dW[(w)(T)]/dE]/dT]/dT]/dE, d[d[d[dW[(a)(T)]/dE]/dT]/dT]/dE, d[d[d[dW[(i)(T)]/dE]/dT]/dT]/dE, d[d[d[dW[(m)(T)]/dE]/dT]/dT]/dE, d[d[d[dW[(t,w)(T)]/dE]/dT]/dT]/dE, d[d[d[dW[(t,a)(T)]/dE]/dT]/dT]/dE, d[d[d[dW[(t,i)(T)]/dE]/dT]/dT]/dE, d[d[d[dW[(t,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dW[(w,a)(T)]/dE]/dT]/dT]/dE, d[d[d[dW[(w,i)(T)]/dE]/dT]/dT]/dE, d[d[d[dW[(w,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dW[(a,i)(T)]/dE]/dT]/dT]/dE, d[d[d[dW[(a,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dW[(i,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dW[(t,w,a)(T)]/dE]/dT]/dT]/dE, d[d[d[dW[(t,w,i)(T)]/dE]/dT]/dT]/dE, d[d[d[dW[(t,w,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dW[(t,a,i)(T)]/dE]/dT]/dT]/dE, d[d[d[dW[(t,a,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dW[(t,i,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dW[(w,a,i)(T)]/dE]/dT]/dT]/dE, d[d[d[dW[(w,a,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dW[(w,i,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dW[(a,i,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dW[(t,w,a,i)(T)]/dE]/dT]/dT]/dE, d[d[d[dW[(t,w,a,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dW[(t,w,i,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dW[(t,a,i,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dW[(w,a,i,m)(T)]/dE]/dT]/dT]/dE, d[d[d[dW[(t,w,a,i,m)(T)]/dE]/dT]/dT]/dE.

 

or as:

 

d[d[d[dW[(t)(T)]/dT]/dE]/dE]/dT, d[d[d[dW[(w)(T)]/dT]/dE]/dE]/dT, d[d[d[dW[(a)(T)]/dT]/dE]/dE]/dT, d[d[d[dW[(i)(T)]/dT]/dE]/dE]/dT, d[d[d[dW[(m)(T)]/dT]/dE]/dE]/dT, d[d[d[dW[(t,w)(T)]/dT]/dE]/dE]/dT, d[d[d[dW[(t,a)(T)]/dT]/dE]/dE]/dT, d[d[d[dW[(t,i)(T)]/dT]/dE]/dE]/dT, d[d[d[dW[(t,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dW[(w,a)(T)]/dT]/dE]/dE]/dT, d[d[d[dW[(w,i)(T)]/dT]/dE]/dE]/dT, d[d[d[dW[(w,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dW[(a,i)(T)]/dT]/dE]/dE]/dT, d[d[d[dW[(a,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dW[(i,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dW[(t,w,a)(T)]/dT]/dE]/dE]/dT, d[d[d[dW[(t,w,i)(T)]/dT]/dE]/dE]/dT, d[d[d[dW[(t,w,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dW[(t,a,i)(T)]/dT]/dE]/dE]/dT, d[d[d[dW[(t,a,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dW[(t,i,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dW[(w,a,i)(T)]/dT]/dE]/dE]/dT, d[d[d[dW[(w,a,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dW[(w,i,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dW[(a,i,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dW[(t,w,a,i)(T)]/dT]/dE]/dE]/dT, d[d[d[dW[(t,w,a,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dW[(t,w,i,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dW[(t,a,i,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dW[(w,a,i,m)(T)]/dT]/dE]/dE]/dT, d[d[d[dW[(t,w,a,i,m)(T)]/dT]/dE]/dE]/dT.

 

 

or as;

 

 

 

 

d[d[d[dW(t)/dE]/dE]/dT]/dT, d[d[d[dW(w)/dE]/dE]/dT]/dT, d[d[d[dW(a)/dE]/dE]/dT]/dT, d[d[d[dW(i)/dE]/dE]/dT]/dT, d[d[d[dW(m)/dE]/dE]/dT]/dT, d[d[d[dW(t,w)/dE]/dE]/dT]/dT, d[d[d[dW(t,a)/dE]/dE]/dT]/dT, d[d[d[dW(t,i)/dE]/dE]/dT]/dT, d[d[d[dW(t,m)/dE]/dE]/dT]/dT, d[d[d[dW(w,a)/dE]/dE]/dT]/dT, d[d[d[dW(w,i)/dE]/dE]/dT]/dT, d[d[d[dW(w,m)/dE]/dE]/dT]/dT, d[d[d[dW(a,i)/dE]/dE]/dT]/dT, d[d[d[dW(a,m)/dE]/dE]/dT]/dT, d[d[d[dW(i,m)/dE]/dE]/dT]/dT, d[d[d[dW(t,w,a)/dE]/dE]/dT]/dT, d[d[d[dW(t,w,i)/dE]/dE]/dT]/dT, d[d[d[dW(t,w,m)/dE]/dE]/dT]/dT, d[d[d[dW(t,a,i)/dE]/dE]/dT]/dT, d[d[d[dW(t,a,m)/dE]/dE]/dT]/dT,  d[d[d[dW(t,i,m)/dE]/dE]/dT]/dT, d[d[d[dW(w,a,i)/dE]/dE]/dT]/dT, d[d[d[dW(w,a,m)/dE]/dE]/dT]/dT, d[d[d[dW(w,i,m)/dE]/dE]/dT]/dT, d[d[d[dW(a,i,m)/dE]/dE]/dT]/dT, d[d[d[dW(t,w,a,i)/dE]/dE]/dT]/dT, d[d[d[dW(t,w,a,m)/dE/dE, d[d[d[dW(t,w,i,m)/dE]/dE]/dT]/dT, d[d[d[dW(t,a,i,m)/dE]/dE]/dT]/dT, d[d[d[dW(w,a,i,m)/dE]/dE]/dT]/dT, d[d[d[dW(t,w,a,i,m)/dE]/dE]/dT]/dT..

 

or as:

 

d[d[d[dW(t)/dT]/dE]/dT]/dE, d[d[d[dW(w)/dT]/dE]/dT]/dE, d[d[d[dW(a)/dT]/dE]/dT]/dE, d[d[d[dW(i)/dT]/dE]/dT]/dE, d[d[d[dW(m)/dT]/dE]/dT]/dE, d[d[d[dW(t,w)/dT]/dE]/dT]/dE, d[d[d[dW(t,a)/dT]/dE]/dT]/dE, d[d[d[dW(t,i)/dT]/dE]/dT]/dE, d[d[d[dW(t,m)/dT]/dE]/dT]/dE, d[d[d[dW(w,a)/dT]/dE]/dT]/dE, d[d[d[dW(w,i)/dT]/dE]/dT]/dE, d[d[d[dW(w,m)/dT]/dE]/dT]/dE, d[d[d[dW(a,i)/dT]/dE]/dT]/dE, d[d[d[dW(a,m)/dT]/dE]/dT]/dE, d[d[d[dW(i,m)/ dT]/dE]/dT]/dE, d[d[d[dW(t,w,a)/dT]/dE]/dT]/dE, d[d[d[dW(t,w,i)/dT]/dE]/dT]/dE, d[d[d[dW(t,w,m)/dT]/dE]/dT]/dE, d[d[d[dW(t,a,i)/dT]/dE]/dT]/dE, d[d[d[dW(t,a,m)/dT]/dE]/dT]/dE,  d[d[d[dW(t,i,m)/dT]/dE]/dT]/dE, d[d[d[dW(w,a,i)/dT]/dE]/dT]/dE, d[d[d[dW(w,a,m)/dT]/dE]/dT]/dE, d[d[d[dW(w,i,m)/dT]/dE]/dT]/dE, d[d[d[dW(a,i,m)/dT]/dE]/dT]/dE, d[d[d[dW(t,w,a,i)/dT]/dE]/dT]/dE, d[d[d[dW(t,w,a,m)/dE/dE, d[d[d[dW(t,w,i,m)/dT]/dE]/dT]/dE, d[d[d[dW(t,a,i,m)/dT]/dE]/dT]/dE, d[d[d[dW(w,a,i,m)/dT]/dE]/dT]/dE, d[d[d[dW(t,w,a,i,m)/dT]/dE]/dT]/dE..

 

or as:

 

d[d[d[dW(t)/dT]/dT]/dE]/dE, d[d[d[dW(w)/dT]/dT]/dE]/dE, d[d[d[dW(a)/dT]/dT]/dE]/dE, d[d[d[dW(i)/dT]/dT]/dE]/dE, d[d[d[dW(m)/dT]/dT]/dE]/dE, d[d[d[dW(t,w)/dT]/dT]/dE]/dE, d[d[d[dW(t,a)/dT]/dT]/dE]/dE, d[d[d[dW(t,i)/dT]/dT]/dE]/dE, d[d[d[dW(t,m)/dT]/dT]/dE]/dE, d[d[d[dW(w,a)/dT]/dT]/dE]/dE, d[d[d[dW(w,i)/dT]/dT]/dE]/dE, d[d[d[dW(w,m)/dT]/dT]/dE]/dE, d[d[d[dW(a,i)/dT]/dT]/dE]/dE, d[d[d[dW(a,m)/ dT]/dT]/dE]/dE, d[d[d[dW(i,m)/ dT]/dT]/dE]/dE, d[d[d[dW(t,w,a)/dT]/dT]/dE]/dE, d[d[d[dW(t,w,i)/dT]/dT]/dE]/dE, d[d[d[dW(t,w,m)/dT]/dT]/dE]/dE, d[d[d[dW(t,a,i)/dT]/dT]/dE]/dE, d[d[d[dW(t,a,m)/dT]/dT]/dE]/dE,  d[d[d[dW(t,i,m)/dT]/dT]/dE]/dE, d[d[d[dW(w,a,i)/dT]/dT]/dE]/dE, d[d[d[dW(w,a,m)/dT]/dT]/dE]/dE, d[d[d[dW(w,i,m)/dT]/dT]/dE]/dE, d[d[d[dW(a,i,m)/dT]/dT]/dE]/dE, d[d[d[dW(t,w,a,i)/dT]/dT]/dE]/dE, d[d[d[dW(t,w,a,m)/dE/dE, d[d[d[dW(t,w,i,m)/dT]/dT]/dE]/dE, d[d[d[dW(t,a,i,m)/dT]/dT]/dE]/dE, d[d[d[dW(w,a,i,m)/dT]/dT]/dE]/dE, d[d[d[dW(t,w,a,i,m)/dT]/dT]/dE]/dE..

 

 

We can also take higher order duel dimensional derivatives of will as a function of emotion and time but the symbolic expression of the set of such derivatives very soon becomes excessively lengthly to write and so these higher order derivatives as such are not mentioned here except to say that they would be computed in an analogous manner to the second order duel dimensional derivatives described above.

 

.

 

 

 

 

 

We can also express will qualitatively, statistically, and perhaps with the use of some forms of real analyses as a derivative with respect to thought or with respect to t.

 

Given that W(t) =  W(t and/or w and/or a and/or i and/or m), the following first order derivatives of will with respect to thought  are possible.

 

 

dW(t)/dt, dW(w)/dt, dW(a)/dt, dW(i)/dt, dW(m)/dt, dW(t,w)/dt, dW(t,a)/dt, dW(t,i)/dt, dW(t,m)/dt, dW(w,a)/dt, dW(w,i)/dt, dW(w,m)/dt, dW(a,i)/dt, dW(a,m)/dt, dW(i,m)/dt, dW(t,w,a)/dt, dW(t,w,i)/dt, dW(t,w,m)/dt, dW(t,a,i)/dt, dW(t,a,m)/dt, dW(t,i,m)/dt, dW(w,a,i)/dt, dW(w,a,m)/dt, dW(w,i,m)/dt, dW(a,i,m)/dt, dW(t,w,a,i)/dt, dW(t,w,a,m)/dt, dW(t,w,i,m)/dt, dW(t,a,i,m)/dt, dW(w,a,i,m)/dt, dW(t,w,a,i,m)/dt.

 

 

Or more succinctly,  dW/dt = dW(t and/or w and/or a and/or i and/or m)/dt

 

 

Or perhaps dW(t)/dt =d W{[t(t)] and/or [w(t)] and/or [a(t)] and/or [i(t)] and/or [m(w)]}/dt.

 

 

Likewise, we can take the second thought  derivatives of  W as follows:

 

 

 

d[dW(t)/dt]/dt, d[dW(w)/dt]/dt, d[dW(a)/dt]/dt, d[dW(i)/dt]/dt, d[dW(m)/dt]/dt, d[dW(t,w)/dt]/dt, d[dW(t,a)/dt]/dt, d[dW(t,i)/dt]/dt, d[dW(t,m)/dt]/dt, d[dW(w,a)/dt]/dt, d[dW(w,i)/dt]/dt, d[dW(w,m)/dt]/dt, d[dW(a,i)/dt]/dt, d[dW(a,m)/dt]/dt, d[dW(i,m)/dt/dt, d[dW(t,w,a)/dt]/dt, d[dW(t,w,i)/dt]/dt, d[dW(t,w,m)/dt]/dt, d[dW(t,a,i)/dt]/dt, d[dW(t,a,m)/dt]/dt,  d[dW(t,i,m)/dt]/dt, d[dW(w,a,i)/dt]/dt, d[dW(w,a,m)/dt]/dt, d[dW(w,i,m)/dt]/dt, d[dW(a,i,m)/dt]/dt, d[dW(t,w,a,i)/dt]/dt, d[dW(t,w,a,m)/dt/dt, d[dW(t,w,i,m)/dt]/dt, d[dW(t,a,i,m)/dt]/dt, d[dW(w,a,i,m)/dt]/dt, d[dW(t,w,a,i,m)/dt]/dt..

 

 

or more succinctly, as d(dW/dt)/dt = d[d W(t and/or w and/or a and/or i and/or m)/dt]/dt = Wt2

 

 

or as

 

 

d[dW(t)/dt]/dt  = d[d W{[t(t)] and/or [w(t)] and/or [a(t)] and/or [i(t)] and/or [m(t)]}/dt]/dt = Wt2.

 

 

 

Likewise, we can take the third thought derivatives of  W as follows:

 

 

 

d[d[dW(t)/dt]/dt]/dt, d[d[dW(w)/dt]/dt]/dt, d[d[dW(a)/dt]/dt]/dt, d[d[dW(i)/dt]/dt]/dt, d[d[dW(m)/dt]/dt]/dt, d[d[dW(t,w)/dt]/dt]/dt, d[d[dW(t,a)/dt]/dt]/dt, d[d[dW(t,i)/dt]/dt]/dt, d[d[dW(t,m)/dt]/dt]/dt, d[d[dW(w,a)/dt]/dt]/dt, d[d[dW(w,i)/dt]/dt]/dt, d[d[dW(w,m)/dt]/dt]/dt, d[d[dW(a,i)/dt]/dt]/dt, d[d[dW(a,m)/dt]/dt]/dt, d[d[dW(i,m)/dt/dt]/dt, d[d[dW(t,w,a)/dt]/dt]/dt, d[d[dW(t,w,i)/dt]/dt]/dt, d[d[dW(t,w,m)/dt]/dt]/dt, d[d[dW(t,a,i)/dt]/dt]/dt, d[d[dW(t,a,m)/dt]/dt]/dt,  d[d[dW(t,i,m)/dt]/dt]/dt, d[d[dW(w,a,i)/dt]/dt]/dt, d[d[dW(w,a,m)/dt]/dt]/dt, d[d[dW(w,i,m)/dt]/dt]/dt, d[d[dW(a,i,m)/dt]/dt]/dt, d[d[dW(t,w,a,i)/dt]/dt]/dt, d[d[dW(t,w,a,m)/dt/dt]/dt, d[d[dW(t,w,i,m)/dt]/dt]/dt, d[d[dW(t,a,i,m)/dt]/dt]/dt, d[d[dW(w,a,i,m)/dt]/dt]/dt, d[d[dW(t,w,a,i,m)/dt]/dt]/dt.

 

 

or more succinctly, as d[d(dW/dt)/dt]/dt = d[d[d W(t and/or w and/or a and/or i and/or m)/dt]/dt]/dt = Wt3

 

 

or as

 

 

d[d[dW(t)/dt]/dt]/dt  = d[d[d W{[t(t)] and/or [w(t)] and/or [a(t)] and/or [i(t)] and/or [m(t)]}/dt]/dt]/dt = Wt3.

 

 

We can also form the expressions;

 

 

d[d[f(W)]/dt]/dt = d{d [W[t(t)]]/dt and/or d[W[w(t)]]/dt and/or d[W[a(t)]]/dt and/or d[W[i(t)]]/dt and/or d[W[m(t)]]/dt}/dt  = f(Wt)2

 

 

and

 

 

d[d[d[f(W)]/dt]/dt]/dt = d{d{ d [W[t(t)]]/dt and/or d[W[w(t)]]/dt and/or d[W[a(t)]]/dt and/or d[W[i(t)]]/dt and/or d[W[m(t)]]/dt}/dt}/dt  = f(Wt)3A, where A stands for type A differentiation which is not to be confused with the meaning of so-called Type A personality as A is used as an ordinal in a totally different context here.

 

 

and

 

 

d[d[d[f(W)]/dt]/dt]/dt = d{d[d [W[t(t)]]/dt]/dt  and/or d[d [W[w(t)]]/dt]/dt  and/or d[d [W[a(t)]]/dt]/dt  and/or d[d [W[i(t)]]/dt]/dt  and/or d[d [W[m(t)]]/dt]/dt }/dt = f(Wt)3B, where B stands for type B differentiation which is not to be confused with the meaning of so-called Type  B personality as B is used as an ordinal in a totally different context here .

 

 

In fact, one can form yet higher order derivatives of will  with respect to thought  as follows.

 

 

Wt5 = d Wt4/dt = d[dWt3/dt]/dt

 

 

 

Wt5 = dWt4/dt =  d[d[d[d[d W{[t(t)] and/or [w(t)] and/or [a(t)] and/or [i(t)] and/or [m(w)]}/dt]/dt]/dt]/dt]/dt.

 

 

 

f(Wt)5A = d[f(Wt)4A]/dt = d[d [f(Wt)3A]/dt]/dt =  d{d{d{d{ d [W[t(t)]]/dt and/or d[W[w(t)]]/dt and/or d[W[a(t)]]/dt and/or d[W[i(t)]]/dt and/or d[W[m(t)]]/dt}/dt}/dt]/dt]/dt

 

 

 

 

Wt6 = d Wt5/dt = d[d Wt4/dt]/dt = d[d[dWt3/dt]/dt]/dt

 

 

 

Wt6 = dWt5/dt = d[d[d[d[d[d W{[t(t)] and/or [w(t)] and/or [a(t)] and/or [i(t)] and/or [m(w)]}/dt]/dt]/dt]/dt]/dt]/dt

 

 

 

f(Wt)6A = d[f(Wt)5A]/dt = d{ d{d{d{d{ d [W[t(t)]]/dt and/or d[W[w(t)]]/dt and/or d[W[a(t)]]/dt and/or d[W[i(t)]]/dt and/or d[W[m(t)]]/dt}/dt}/dt]/dt]/dt]/dt

 

 

 

 

Wt7 = dWt6/dt

 

f(Wt)7A = d[f(Wt)6A]/dt

 

 

Wt8 = d Wt7/dt

 

f(Wt)8A = d[f(Wt)7A]/dt

 

 

 

Wt9 = d Wt8/dt

 

f(Wt)9A = d[f(Wt)8A]/dt

 

 

Wt10…, Wt11…, Wt12 … etc.

 

 

Anyone for Wt ensemble, or Wt infinity scrapper, or Wt (Aleph 0), or Wt(Aleph 1), or Wt (Aleph 2), or how about Wt Aleph (Aleph 0), or Wt Aleph (Aleph 1) , or Wt Aleph (Aleph 2), or even Wt Aleph (Aleph (Aleph 0)), or Wt Aleph (Aleph (Aleph 1)), or Wt Aleph (Aleph (Aleph 2)), and so on?

 

Thus, for the set of the sets of derivatives of Wt1 through Wt(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Wt1 through Wt (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)},…, {П(0,31)[R]}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Wt 1 through Wt (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Wt 1 through Wt (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the derivative states in the set of the sets of derivatives of Wt 1 through I(Aleph 0) is plausible equal to:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Wt 1 through Wt (Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Wt 1 through Wt (Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}}}.

 

For the set of the sets of derivatives of Wt 1 through Wt (Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Wt I(Aleph 0) derivative space at the level of 0/(Aleph 0), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Wt 1 through Wt (Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Wt 1 through Wt (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Wt 1 through Wt (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Wt 1 through Wt (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Wt 1 through Wt (Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Wt 1 through Wt (Aleph 1), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Wt 1 through  Wt (Aleph 2), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Wt I1 through Wt (Aleph 3), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Wt (Aleph 0) derivative space at the level of 0/(Aleph 1), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Wt 1 through Wt (Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Wt 1 through Wt (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Wt 1 through Wt (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Wt 1 through  Wt (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations  for the set of the sets of derivatives of Wt 1 through Wt (Aleph 0) is plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Wt 1 through Wt (Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Wt 1 through Wt (Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Wt 1 through Wt (Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

 

For super-continuous Wt (Aleph 0) derivative space at the level of 0/(Aleph 2), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Wt 1 through Wt (Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Wt 1 through Wt (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Wt 1 through Wt (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Wt I1 through Wt (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Wt 1 through Wt (Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Wt I1 through Wt (Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Wt 1 through Wt (Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Wt I1 through Wt (Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

Similar series can be developed for super-continuity at any applicable level such as 0/(Aleph 3), 0/(Aleph 4), 0/(Aleph 5),…, 0/(Aleph Ω), 0/(Aleph (Aleph 0)), …, 0/(Aleph (Aleph 1)), …, 0/(Aleph (Aleph 2)), …, 0/(Aleph (Aleph 3)),…, 0/(Aleph (Aleph Ω)),…, 0/(Aleph (Aleph (Aleph 0))), …, 0/(Aleph (Aleph (Aleph 1))),…, 0/(Aleph (Aleph (Aleph 2))),…, 0/(Aleph (Aleph (Aleph 3))),…, 0/(Aleph (Aleph  (Aleph Ω))), …

 

An so-on ad infinitum.

 

 

In addition to these numerical functions of Wt as functions of summation series of product series functions, in order to really appreciate the enourmous complexity of the human soul in terms of its potential to evolve and be differentiated from all other souls in its characteristics, we would need to consider how every single category and even every single species of memory of the form Wt can very. Since there may exist an arbitrarily high infinite number species of Wt, the number of numerical functions of Wt is utterly beyond recogning. I will cover such notions in terms of mathematical notation in yet another series of articles I will write on this general concept.

 

 

Perhaps these numbers are applicable when one considers that the human soul, in its accidental form and perhaps even in its substantial form stores all experience and other psychodynamics based phenomenon. Every experience adds to the accidental form of the human soul and this includes the souls of all those still alive on Earth, all those in Purgatory, all those in Heaven, all those in Hell, and all those in any Limbo.

Since the human soul can grow without limit in terms of its psychodynamic time –flow world line, such a consideration offers another mechanism where the number of derivative states, combinations of derivative states, and even super-continuity of the derivative state space can grow forever.

 

Folks, for those of you who might balk at me for including literally all souls in the above consideration, including the souls in Hell, as well as bodily extraterrestrial souls and the souls of so-called bodily ultraterrestials sometimes referred to as etherians in the new age UFO buff culture, my reply is that we simply do not understand the full scope of GOD’s Divine Economy. We may never fully comprehend the scope of the Divine Economy because such an utterly eternal scheme, is, well, eternal and never ending.

 

 

The general meaning of thought derivatives of will can be viewed as the manner in which the qualitative and/or quantitative aspects of will as a function of thought very with acts of will(s). The manner in which acts of will very with thought may be multi-act-or will dimensional wherein the dimensions of derivations can be multiple, and wherein the derivations can be taken in parallel, series parallel or serial manner The differentials can be partial or non-partial derivatives, or both partial and non-partial for a given computation.

 

In fact, since there is in theory, no limit to the numbers of qualitatively and quantitatively different acts of will, and perhaps no limit to the number of possible different types or classes of acts of will, wherein each person has his or her own unique acts of will, the number of thought dimensions that can effect acts of will is literally infinite, given the entirety of the set of created persons, and perhaps also literally infinite for each person as an individual, although we can not intellectually and intuitively understand this specific infinite number.

 

It is interesting to consider the ramifactions of being able to perform realistic calculations involving thought derivatives of will from a mathematical, theoretical, scientific,  and philosophical perspective.

 

Persons for which one or more nth order derivatives of will with respect to thought that have large absolute values would tend to have their wills highly influenced by thought, or at least for the acts of will under consideration with respect to the dimension of the specific thought type(s) or class(es) for which the differentiation(s) are performed. Perhaps a strong coupling between will and thought indicates a well integrated personality and commensurately, a high degree of volitional capacity and a high degree of volitional intelligence.

 

We would expect that disembodied human souls, ETI souls, and/or UTI souls in Heaven, Limbo, highly evolved bodily ETI persons, highly evolved UTI persons, and angels to have acts of will of all kinds and intensities which are highly subject to thought.

 

 

The general meaning of thought  derivatives of will can be viewed as the manner in which the qualitative and/or quantitative aspects of will  as a function of thought very with thought. The manner in which vill very with thought may be multi- will-aspect dimensional wherein the dimensions of derivations can be multiple, and wherein the derivations can be taken in parallel, series parallel or in serial manner. The differentials can be partial or non-partial derivatives, or both partial and non-partial for a given computation.

 

In fact, since there is in theory, no limit to the numbers of qualitatively and quantitatively different acts of will or volitional states, and perhaps no limit to the number of possible different types or classes of acts of will or volitional states, wherein each person has his or her own unique acts or will or volitional states, the number of thoughts  state dimensions that can effect volitions is literally infinite, given the entirety of the set of created persons, and perhaps also literally infinite for each person as an individual, although we can not intellectually and intuitively understand this infinite number.

 

 

It is interesting to consider the ramifactions of being able to perform realistic calculations involving thought  derivatives of will from a mathematical, theoretical, scientific,  and philosophical perspective.

 

Persons for which one or more nth order derivatives of will  with respect to thought that have large absolute values would tend to have their will  highly influenced by thought, or at least for the volitions under consideration with respect to the dimension of the specific though type(s) or class(es) for which the differentiation(s) are being performed. Perhaps a strong coupling between thought and will indicates a well integrated personality and commensurately, a high degree of volitional capacity and a high degree of volitional intelligence as well as perhaps very strong will power.

 

We would expect that disembodied human souls, ETI souls, and/or UTI souls in Heaven, Limbo, highly evolved bodily ETI persons, highly evolved UTI persons, and angels to have volitions of all kinds and intensities which are highly subject to thought.

 

 

We can also consider two dimensional ith ordered derivatives of will  with respect to thought  and time, or with respect to w and T, respectively.

 

Given that W[(t)(T)] =  W[(t and/or w and/or a and/or i and/or m)(t)(T)], the following first order two dimensional derivatives of will with respect to thought and Time are possible.

 

 

d[dW[(t)(T)]/dt]/dT, d[dW[(w)(T)]/dt]/dT, d[dW[(a)(T)]/dt]/dT, d[dW[(i)(T)]/dt]/dT, d[dW[(m)(T)]/dt]/dT, d[dW[(t,w)(T)]/dt]/dT, d[dW[(t,a)(T)]/dt]/dT, d[dW[(t,i)(T)]/dt]/dT, d[dW[(t,m)(T)]/dt]/dT, d[dW[(w,a)(T)]/dt]/dT, d[dW[(w,i)(T)]/dt]/dT, d[dW[(w,m)(T)]/dt]/dT, d[dW[(a,i)(T)]/dt]/dT, d[dW[(a,m)(T)]/dt]/dT, d[dW[(i,m)(T)]/dt]/dT, d[dW[(t,w,a)(T)]/dt]/dT, d[dW[(t,w,i)(T)]/dt]/dT, d[dW[(t,w,m)(T)]/dt]/dT, d[dW[(t,a,i)(T)]/dt]/dT, d[dW[(t,a,m)(T)]/dt]/dT, d[dW[(t,i,m)(T)]/dt]/dT, d[dW[(w,a,i)(T)]/dt]/dT, d[dW[(w,a,m)(T)]/dt]/dT, d[dW[(w,i,m)(T)]/dt]/dT, d[dW[(a,i,m)(T)]/dt]/dT, d[dW[(t,w,a,i)(T)]/dt]/dT, d[dW[(t,w,a,m)(T)]/dt]/dT, d[dW[(t,w,i,m)(T)]/dt]/dT, d[dW[(t,a,i,m)(T)]/dt]/dT, d[dW[(w,a,i,m)(T)]/dt]/dT, d[dW[(t,w,a,i,m)(T)]/dt]/dT.

 

 

Or more succinctly,  d[dW(T)/dt]/dT = d[dW[(T)(t and/or w and/or a and/or i and/or m)]/dt]/dT

 

or

 

d[dW(T)/dT]/dt = d[dW[(T)(t and/or w and/or a and/or i and/or m)]/dT]/dt

 

 

 

 

 

Or perhaps d[d W[(t)(T)]/dt]/dT  = d[d W [{[t(t)] and/or [w(t)] and/or [a(t)] and/or [i(t)] and/or [m(t)]}(T)]/dt]/dT

 

or

 

Or perhaps d[d W[(t)(T)]/dT]/dt  = d[d W [{[t(t)] and/or [w(t)] and/or [a(t)] and/or [i(t)] and/or [m(t)]}(T)]/dT]/dt

 

 

 

Likewise, we can take the second dual dimension will -time derivatives of  W as follows:

 

d[d[d[dW[(t)(T)]/dt]/dT]/dt]/dT, d[d[d[dW[(w)(T)]/dt]/dT]/dt]/dT, d[d[d[dW[(a)(T)]/dt]/dT]/dt]/dT, d[d[d[dW[(i)(T)]/dt]/dT]/dt]/dT, d[d[d[dW[(m)(T)]/dt]/dT]/dt]/dT, d[d[d[dW[(t,w)(T)]/dt]/dT]/dt]/dT, d[d[d[dW[(t,a)(T)]/dt]/dT]/dt]/dT, d[d[d[dW[(t,i)(T)]/dt]/dT]/dt]/dT, d[d[d[dW[(t,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dW[(w,a)(T)]/dt]/dT]/dt]/dT, d[d[d[dW[(w,i)(T)]/dt]/dT]/dt]/dT, d[d[d[dW[(w,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dW[(a,i)(T)]/dt]/dT]/dt]/dT, d[d[d[dW[(a,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dW[(i,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dW[(t,w,a)(T)]/dt]/dT]/dt]/dT, d[d[d[dW[(t,w,i)(T)]/dt]/dT]/dt]/dT, d[d[d[dW[(t,w,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dW[(t,a,i)(T)]/dt]/dT]/dt]/dT, d[d[d[dW[(t,a,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dW[(t,i,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dW[(w,a,i)(T)]/dt]/dT]/dt]/dT, d[d[d[dW[(w,a,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dW[(w,i,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dW[(a,i,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dW[(t,w,a,i)(T)]/dt]/dT]/dt]/dT, d[d[d[dW[(t,w,a,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dW[(t,w,i,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dW[(t,a,i,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dW[(w,a,i,m)(T)]/dt]/dT]/dt]/dT, d[d[d[dW[(t,w,a,i,m)(T)]/dt]/dT]/dt]/dT.

 

or as:

 

 

 

d[d[d[dW[(t)(T)]/dt]/dT]/dT]/dt, d[d[d[dW[(w)(T)]/dt]/dT]/dT]/dt, d[d[d[dW[(a)(T)]/dt]/dT]/dT]/dt, d[d[d[dW[(i)(T)]/dt]/dT]/dT]/dt, d[d[d[dW[(m)(T)]/dt]/dT]/dT]/dt, d[d[d[dW[(t,w)(T)]/dt]/dT]/dT]/dt, d[d[d[dW[(t,a)(T)]/dt]/dT]/dT]/dt, d[d[d[dW[(t,i)(T)]/dt]/dT]/dT]/dt, d[d[d[dW[(t,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dW[(w,a)(T)]/dt]/dT]/dT]/dt, d[d[d[dW[(w,i)(T)]/dt]/dT]/dT]/dt, d[d[d[dW[(w,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dW[(a,i)(T)]/dt]/dT]/dT]/dt, d[d[d[dW[(a,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dW[(i,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dW[(t,w,a)(T)]/dt]/dT]/dT]/dt, d[d[d[dW[(t,w,i)(T)]/dt]/dT]/dT]/dt, d[d[d[dW[(t,w,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dW[(t,a,i)(T)]/dt]/dT]/dT]/dt, d[d[d[dW[(t,a,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dW[(t,i,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dW[(w,a,i)(T)]/dt]/dT]/dT]/dt, d[d[d[dW[(w,a,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dW[(w,i,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dW[(a,i,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dW[(t,w,a,i)(T)]/dt]/dT]/dT]/dt, d[d[d[dW[(t,w,a,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dW[(t,w,i,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dW[(t,a,i,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dW[(w,a,i,m)(T)]/dt]/dT]/dT]/dt, d[d[d[dW[(t,w,a,i,m)(T)]/dt]/dT]/dT]/dt.

 

or as:

 

d[d[d[dW[(t)(T)]/dT]/dt]/dt]/dT, d[d[d[dW[(w)(T)]/dT]/dt]/dt]/dT, d[d[d[dW[(a)(T)]/dT]/dt]/dt]/dT, d[d[d[dW[(i)(T)]/dT]/dt]/dt]/dT, d[d[d[dW[(m)(T)]/dT]/dt]/dt]/dT, d[d[d[dW[(t,w)(T)]/dT]/dt]/dt]/dT, d[d[d[dW[(t,a)(T)]/dT]/dt]/dt]/dT, d[d[d[dW[(t,i)(T)]/dT]/dt]/dt]/dT, d[d[d[dW[(t,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dW[(w,a)(T)]/dT]/dt]/dt]/dT, d[d[d[dW[(w,i)(T)]/dT]/dt]/dt]/dT, d[d[d[dW[(w,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dW[(a,i)(T)]/dT]/dt]/dt]/dT, d[d[d[dW[(a,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dW[(i,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dW[(t,w,a)(T)]/dT]/dt]/dt]/dT, d[d[d[dW[(t,w,i)(T)]/dT]/dt]/dt]/dT, d[d[d[dW[(t,w,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dW[(t,a,i)(T)]/dT]/dt]/dt]/dT, d[d[d[dW[(t,a,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dW[(t,i,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dW[(w,a,i)(T)]/dT]/dt]/dt]/dT, d[d[d[dW[(w,a,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dW[(w,i,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dW[(a,i,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dW[(t,w,a,i)(T)]/dT]/dt]/dt]/dT, d[d[d[dW[(t,w,a,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dW[(t,w,i,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dW[(t,a,i,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dW[(w,a,i,m)(T)]/dT]/dt]/dt]/dT, d[d[d[dW[(t,w,a,i,m)(T)]/dT]/dt]/dt]/dT.

 

 

or as;

 

 

 

 

d[d[d[dW(t)/dt]/dt]/dT]/dT, d[d[d[dW(w)/dt]/dt]/dT]/dT, d[d[d[dW(a)/dt]/dt]/dT]/dT, d[d[d[dW(i)/dt]/dt]/dT]/dT, d[d[d[dW(m)/dt]/dt]/dT]/dT, d[d[d[dW(t,w)/dt]/dt]/dT]/dT, d[d[d[dW(t,a)/dt]/dt]/dT]/dT, d[d[d[dW(t,i)/dt]/dt]/dT]/dT, d[d[d[dW(t,m)/dt]/dt]/dT]/dT, d[d[d[dW(w,a)/dt]/dt]/dT]/dT, d[d[d[dW(w,i)/dt]/dt]/dT]/dT, d[d[d[dW(w,m)/dt]/dt]/dT]/dT, d[d[d[dW(a,i)/dt]/dt]/dT]/dT, d[d[d[dW(a,m)/dt]/dt]/dT]/dT, d[d[d[dW(i,m)/dt]/dt]/dT]/dT, d[d[d[dW(t,w,a)/dt]/dt]/dT]/dT, d[d[d[dW(t,w,i)/dt]/dt]/dT]/dT, d[d[d[dW(t,w,m)/dt]/dt]/dT]/dT, d[d[d[dW(t,a,i)/dt]/dt]/dT]/dT, d[d[d[dW(t,a,m)/dt]/dt]/dT]/dT,  d[d[d[dW(t,i,m)/dt]/dt]/dT]/dT, d[d[d[dW(w,a,i)/dt]/dt]/dT]/dT, d[d[d[dW(w,a,m)/dt]/dt]/dT]/dT, d[d[d[dW(w,i,m)/dt]/dt]/dT]/dT, d[d[d[dW(a,i,m)/dt]/dt]/dT]/dT, d[d[d[dW(t,w,a,i)/dt]/dt]/dT]/dT, d[d[d[dW(t,w,a,m)/dt/dt, d[d[d[dW(t,w,i,m)/dt]/dt]/dT]/dT, d[d[d[dW(t,a,i,m)/dt]/dt]/dT]/dT, d[d[d[dW(w,a,i,m)/dt]/dt]/dT]/dT, d[d[d[dW(t,w,a,i,m)/dt]/dt]/dT]/dT..

 

or as:

 

d[d[d[dW(t)/dT]/dt]/dT]/dt, d[d[d[dW(w)/dT]/dt]/dT]/dt, d[d[d[dW(a)/dT]/dt]/dT]/dt, d[d[d[dW(i)/dT]/dt]/dT]/dt, d[d[d[dW(m)/dT]/dt]/dT]/dt, d[d[d[dW(t,w)/dT]/dt]/dT]/dt, d[d[d[dW(t,a)/dT]/dt]/dT]/dt, d[d[d[dW(t,i)/dT]/dt]/dT]/dt, d[d[d[dW(t,m)/dT]/dt]/dT]/dt, d[d[d[dW(w,a)/dT]/dt]/dT]/dt, d[d[d[dW(w,i)/dT]/dt]/dT]/dt, d[d[d[dW(w,m)/dT]/dt]/dT]/dt, d[d[d[dW(a,i)/dT]/dt]/dT]/dt, d[d[d[dW(a,m)/dT]/dt]/dT]/dt, d[d[d[dW(i,m)/ dT]/dt]/dT]/dt, d[d[d[dW(t,w,a)/dT]/dt]/dT]/dt, d[d[d[dW(t,w,i)/dT]/dt]/dT]/dt, d[d[d[dW(t,w,m)/dT]/dt]/dT]/dt, d[d[d[dW(t,a,i)/dT]/dt]/dT]/dt, d[d[d[dW(t,a,m)/dT]/dt]/dT]/dt,  d[d[d[dW(t,i,m)/dT]/dt]/dT]/dt, d[d[d[dW(w,a,i)/dT]/dt]/dT]/dt, d[d[d[dW(w,a,m)/dT]/dt]/dT]/dt, d[d[d[dW(w,i,m)/dT]/dt]/dT]/dt, d[d[d[dW(a,i,m)/dT]/dt]/dT]/dt, d[d[d[dW(t,w,a,i)/dT]/dt]/dT]/dt, d[d[d[dW(t,w,a,m)/dt/dt, d[d[d[dW(t,w,i,m)/dT]/dt]/dT]/dt, d[d[d[dW(t,a,i,m)/dT]/dt]/dT]/dt, d[d[d[dW(w,a,i,m)/dT]/dt]/dT]/dt, d[d[d[dW(t,w,a,i,m)/dT]/dt]/dT]/dt..

 

or as:

 

d[d[d[dW(t)/dT]/dT]/dt]/dt, d[d[d[dW(w)/dT]/dT]/dt]/dt, d[d[d[dW(a)/dT]/dT]/dt]/dt, d[d[d[dW(i)/dT]/dT]/dt]/dt, d[d[d[dW(m)/dT]/dT]/dt]/dt, d[d[d[dW(t,w)/dT]/dT]/dt]/dt, d[d[d[dW(t,a)/dT]/dT]/dt]/dt, d[d[d[dW(t,i)/dT]/dT]/dt]/dt, d[d[d[dW(t,m)/dT]/dT]/dt]/dt, d[d[d[dW(w,a)/dT]/dT]/dt]/dt, d[d[d[dW(w,i)/dT]/dT]/dt]/dt, d[d[d[dW(w,m)/dT]/dT]/dt]/dt, d[d[d[dW(a,i)/dT]/dT]/dt]/dt, d[d[d[dW(a,m)/ dT]/dT]/dt]/dt, d[d[d[dW(i,m)/ dT]/dT]/dt]/dt, d[d[d[dW(t,w,a)/dT]/dT]/dt]/dt, d[d[d[dW(t,w,i)/dT]/dT]/dt]/dt, d[d[d[dW(t,w,m)/dT]/dT]/dt]/dt, d[d[d[dW(t,a,i)/dT]/dT]/dt]/dt, d[d[d[dW(t,a,m)/dT]/dT]/dt]/dt,  d[d[d[dW(t,i,m)/dT]/dT]/dt]/dt, d[d[d[dW(w,a,i)/dT]/dT]/dt]/dt, d[d[d[dW(w,a,m)/dT]/dT]/dt]/dt, d[d[d[dW(w,i,m)/dT]/dT]/dt]/dt, d[d[d[dW(a,i,m)/dT]/dT]/dt]/dt, d[d[d[dW(t,w,a,i)/dT]/dT]/dt]/dt, d[d[d[dW(t,w,a,m)/dt/dt, d[d[d[dW(t,w,i,m)/dT]/dT]/dt]/dt, d[d[d[dW(t,a,i,m)/dT]/dT]/dt]/dt, d[d[d[dW(w,a,i,m)/dT]/dT]/dt]/dt, d[d[d[dW(t,w,a,i,m)/dT]/dT]/dt]/dt..

 

We can also take higher order duel dimensional derivatives of will as a function of thought  and time but the symbolic expression of the set of such derivatives very soon becomes excessively lengthly to write and so these higher order derivatives as such are not mentioned here except to say that they would be computed in an analogous manner to the second order duel dimensional derivatives described above.

 

 

 

We can also express will qualitatively, statistically, and perhaps with the use of some forms of real analysis as a derivative with respect to affect or of a.

 

Given that W(a) =  W(t and/or w and/or a and/or i and/or m), the following first order derivatives of will with respect to affect are possible.

 

 

dW(t)/da, dW(w)/da, dW(a)/da, dW(i)/da, dW(m)/da, dW(t,w)/da, dW(t,a)/da, dW(t,i)/da, dW(t,m)/da, dW(w,a)/da, dW(w,i)/da, dW(w,m)/da, dW(a,i)/da, dW(a,m)/da, dW(i,m)/da, dW(t,w,a)/da, dW(t,w,i)/da, dW(t,w,m)/da, dW(t,a,i)/da, dW(t,a,m)/da, dW(t,i,m)/da, dW(w,a,i)/da, dW(w,a,m)/da, dW(w,i,m)/da, dW(a,i,m)/da, dW(t,w,a,i)/da, dW(t,w,a,m)/da, dW(t,w,i,m)/da, dW(t,a,i,m)/da, dW(w,a,i,m)/da, dW(t,w,a,i,m)/da.

 

 

Or more succinctly, dW/da = dW(t and/or w and/or a and/or i and/or m)/da

 

 

Or perhaps dW(a)/da =d W{[t(a)] and/or [w(a)] and/or [a(a)] and/or [i(a)] and/or [m(a)]}/da.

 

 

Likewise, we can take the second affect derivatives of  W as follows:

 

 

 

d[dW(t)/da]/da, d[dW(w)/da]/da, d[dW(a)/da]/da, d[dW(i)/da]/da, d[dW(m)/da]/da, d[dW(t,w)/da]/da, d[dW(t,a)/da]/da, d[dW(t,i)/da]/da, d[dW(t,m)/da]/da, d[dW(w,a)/da]/da, d[dW(w,i)/da]/da, d[dW(w,m)/da]/da, d[dW(a,i)/da]/da, d[dW(a,m)/da]/da, d[dW(i,m)/da/da, d[dW(t,w,a)/da]/da, d[dW(t,w,i)/da]/da, d[dW(t,w,m)/da]/da, d[dW(t,a,i)/da]/da, d[dW(t,a,m)/da]/da,  d[dW(t,i,m)/da]/da, d[dW(w,a,i)/da]/da, d[dW(w,a,m)/da]/da, d[dW(w,i,m)/da]/da, d[dW(a,i,m)/da]/da, d[dW(t,w,a,i)/da]/da, d[dW(t,w,a,m)/da/da, d[dW(t,w,i,m)/da]/da, d[dW(t,a,i,m)/da]/da, d[dW(w,a,i,m)/da]/da, d[dW(t,w,a,i,m)/da]/da..

 

 

or more succinctly, as d(dW/da)/da = d[d W(t and/or w and/or a and/or i and/or m)/da]/da = Wa2

 

 

or as

 

 

d[dW(a)/da]/da  = d[d W{[t(a)] and/or [w(a)] and/or [a(w)] and/or [i(a)] and/or [m(a)]}/da]/da = Wa2.

 

 

 

Likewise, we can take the third affect derivatives of  W as follows:

 

 

 

d[d[dW(t)/da]/da]/da, d[d[dW(w)/da]/da]/da, d[d[dW(a)/da]/da]/da, d[d[dW(i)/da]/da]/da, d[d[dW(m)/da]/da]/da, d[d[dW(t,w)/da]/da]/da, d[d[dW(t,a)/da]/da]/da, d[d[dW(t,i)/da]/da]/da, d[d[dW(t,m)/da]/da]/da, d[d[dW(w,a)/da]/da]/da, d[d[dW(w,i)/da]/da]/da, d[d[dW(w,m)/da]/da]/da, d[d[dW(a,i)/da]/da]/da, d[d[dW(a,m)/da]/da]/da, d[d[dW(i,m)/da/da]/da, d[d[dW(t,w,a)/da]/da]/da, d[d[dW(t,w,i)/da]/da]/da, d[d[dW(t,w,m)/da]/da]/da, d[d[dW(t,a,i)/da]/da]/da, d[d[dW(t,a,m)/da]/da]/da,  d[d[dW(t,i,m)/da]/da]/da, d[d[dW(w,a,i)/da]/da]/da, d[d[dW(w,a,m)/da]/da]/da, d[d[dW(w,i,m)/da]/da]/da, d[d[dW(a,i,m)/da]/da]/da, d[d[dW(t,w,a,i)/da]/da]/da, d[d[dW(t,w,a,m)/da/da]/da, d[d[dW(t,w,i,m)/da]/da]/da, d[d[dW(t,a,i,m)/da]/da]/da, d[d[dW(w,a,i,m)/da]/da]/da, d[d[dW(t,w,a,i,m)/da]/da]/da.

 

 

or more succinctly, as d[d(dW/da)/da]/da = d[d[d W(t and/or w and/or a and/or i and/or m)/da]/da]/da = Wa3

 

 

or as

 

 

d[d[dW(a)/da]/da]/da  = d[d[d W{[t(a)] and/or [w(a)] and/or [a(a)] and/or [i(a)] and/or [m(a)]}/da]/da]/da = Wa3.

 

 

We can also form the expressions;

 

 

d[d[f(W)]/da]/da = d{d [W[t(a)]]/da and/or d[W[w(a)]]/da and/or d[W[a(a)]]/da and/or d[W[i(a)]]/da and/or d[W[m(a)]]/da}/da  = f(Wa)2

 

 

and

 

 

d[d[d[f(W)]/da]/da]/da = d{d{ d [W[t(a)]]/da and/or d[W[w(a)]]/da and/or d[W[a(a)]]/da and/or d[W[i(a)]]/da and/or d[W[m(a)]]/da}/da}/da  = f(Wa)3A, where A stands for type A differentiation which is not to be confused with the meaning of so-called Type A personality as A is used as an ordinal in a totally different context here.

 

 

and

 

 

d[d[d[f(W)]/da]/da]/da = d{d[d [W[t(a)]]/da]/da  and/or d[d [W[w(a)]]/da]/da  and/or d[d [W[a(a)]]/da]/da  and/or d[d [W[i(a)]]/da]/da  and/or d[d [W[m(a)]]/da]/da }/da = f(Wa)3B, where B stands for type B differentiation which is not to be confused with the meaning of so-called Type  B personality as B is used as an ordinal in a totally different context here. .

 

 

In fact, one can form yet higher order derivatives of volitions with respect to affect as follows.

 

 

Wa5 = d Wa4/da = d[dWa3/da]/da

 

 

 

Wa5 = dWa4/da =  d[d[d[d[d W{[t(a)] and/or [w(a)] and/or [a(a)] and/or [i(a)] and/or [m(a)]}/da]/da]/da]/da]/da.

 

 

 

f(Wa)5A = d[f(Wa)4A]/da = d[d [f(Wa)3A]/da]/da =  d{d{d{d{ d [W[t(a)]]/da and/or d[W[w(a)]]/da and/or d[W[a(a)]]/da and/or d[W[i(a)]]/da and/or d[W[m(a)]]/da}/da}/da]/da]/da

 

 

 

 

Wa6 = d Wa5/da = d[d Wa4/da]/da = d[d[dWa3/da]/da]/da

 

 

 

Wa6 = dWa5/da = d[d[d[d[d[d W{[t(a)] and/or [w(a)] and/or [a(a)] and/or [i(a)] and/or [m(a)]}/da]/da]/da]/da]/da]/da

 

 

 

f(Wa)6A = d[f(Wa)5A]/da = d{ d{d{d{d{ d [W[t(a)]]/da and/or d[W[w(a)]]/da and/or d[W[a(a)]]/da and/or d[W[i(a)]]/da and/or d[W[m(a)]]/da}/da}/da]/da]/da]/da

 

 

 

 

Wa7 = dWa6/da

 

f(Wa)7A = d[f(Wa)6A]/da

 

 

Wa8 = d Wa7/da

 

f(Wa)8A = d[f(Wa)7A]/da

 

 

 

Wa9 = d Wa8/da

 

f(Wa)9A = d[f(Wa)8A]/da

 

 

Wa10…, Wa11…, Wa12 … etc.

 

 

Anyone for Wa ensemble, or Wa infinity scrapper, or Wa (Aleph 0), or Wa(Aleph 1), or Wa (Aleph 2), or how about Wa Aleph (Aleph 0), or Wa Aleph (Aleph 1) , or Wa Aleph (Aleph 2), or even Wa Aleph (Aleph (Aleph 0)), or Wa Aleph (Aleph (Aleph 1)), or Wa Aleph (Aleph (Aleph 2)), and so on?

 

 

Thus, for the set of the sets of derivatives of Wa1 through Wa(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Wa1 through Wa (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)},…, {П(0,31)[R]}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Wa 1 through Wa (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Wa 1 through Wa (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the derivative states in the set of the sets of derivatives of Wa 1 through I(Aleph 0) is plausible equal to:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Wa 1 through Wa (Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Wa 1 through Wa (Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}}}.

 

For the set of the sets of derivatives of Wa 1 through Wa (Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Wa I(Aleph 0) derivative space at the level of 0/(Aleph 0), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Wa 1 through Wa (Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Wa 1 through Wa (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Wa 1 through Wa (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Wa 1 through Wa (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Wa 1 through Wa (Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Wa 1 through Wa (Aleph 1), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Wa 1 through  Wa (Aleph 2), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Wa I1 through Wa (Aleph 3), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Wa (Aleph 0) derivative space at the level of 0/(Aleph 1), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Wa 1 through Wa (Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Wa 1 through Wa (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Wa 1 through Wa (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Wa 1 through  Wa (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations  for the set of the sets of derivatives of Wa 1 through Wa (Aleph 0) is plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Wa 1 through Wa (Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Wa 1 through Wa (Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Wa 1 through Wa (Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

 

For super-continuous Wa (Aleph 0) derivative space at the level of 0/(Aleph 2), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Wa 1 through Wa (Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Wa 1 through Wa (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Wa 1 through Wa (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Wa I1 through Wa (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Wa 1 through Wa (Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Wa I1 through Wa (Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Wa 1 through Wa (Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Wa I1 through Wa (Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

Similar series can be developed for super-continuity at any applicable level such as 0/(Aleph 3), 0/(Aleph 4), 0/(Aleph 5),…, 0/(Aleph Ω), 0/(Aleph (Aleph 0)), …, 0/(Aleph (Aleph 1)), …, 0/(Aleph (Aleph 2)), …, 0/(Aleph (Aleph 3)),…, 0/(Aleph (Aleph Ω)),…, 0/(Aleph (Aleph (Aleph 0))), …, 0/(Aleph (Aleph (Aleph 1))),…, 0/(Aleph (Aleph (Aleph 2))),…, 0/(Aleph (Aleph (Aleph 3))),…, 0/(Aleph (Aleph  (Aleph Ω))), …

 

An so-on ad infinitum.

 

 

In addition to these numerical functions of Wa as functions of summation series of product series functions, in order to really appreciate the enourmous complexity of the human soul in terms of its potential to evolve and be differentiated from all other souls in its characteristics, we would need to consider how every single category and even every single species of will of the form Wa can very. Since there may exist an arbitrarily high infinite number species of Wa, the number of numerical functions of Wa is utterly beyond recogning. I will cover such notions in terms of mathematical notation in yet another series of articles I will write on this general concept.

 

 

Perhaps these numbers are applicable when one considers that the human soul, in its accidental form and perhaps even in its substantial form stores all experience and other psychodynamics based phenomenon. Every experience adds to the accidental form of the human soul and this includes the souls of all those still alive on Earth, all those in Purgatory, all those in Heaven, all those in Hell, and all those in any Limbo.

Since the human soul can grow without limit in terms of its psychodynamic time –flow world line, such a consideration offers another mechanism where the number of derivative states, combinations of derivative states, and even super-continuity of the derivative state space can grow forever.

 

Folks, for those of you who might balk at me for including literally all souls in the above consideration, including the souls in Hell, as well as bodily extraterrestrial souls and the souls of so-called bodily ultraterrestials sometimes referred to as etherians in the new age UFO buff culture, my reply is that we simply do not understand the full scope of GOD’s Divine Economy. We may never fully comprehend the scope of the Divine Economy because such an utterly eternal scheme, is, well, eternal and never ending.

 

 

The general meaning of affect derivatives of will can be viewed as the manner in which the qualitative and/or quantitative aspects of will as a function of affect very with affects(s). The manner in which acts of volition very with affect may be multi-act-of will dimensional wherein the dimensions of derivations can be multiple, and wherein the derivations can be taken in parallel, series parallel or serial manner The differentials can be partial or non-partial derivatives, or both partial and non-partial for a given computation.

 

In fact, since there is in theory, no limit to the numbers of qualitatively and quantitatively different acts of will, and perhaps no limit to the number of possible different types or classes of acts of will, wherein each person has his or her own unique acts of will, the number of volitional dimensions that can effect acts of will  is literally infinite, given the entirety of the set of created persons, and perhaps also literally infinite for each person as an individual, although we can not intellectually and intuitively understand this specific infinite number.

 

It is interesting to consider the ramifactions of being able to perform realistic calculations involving affect derivatives of will from a mathematical, theoretical, scientific,  and philosophical perspective.

 

Persons for which one or more nth order derivatives of will  with respect to affect that have large absolute values would tend to have their wills highly influenced by affect, or at least for the acts of will under consideration with respect to the dimension of the specific affect type(s) or class(es) for which the differentiation(s) are performed. Perhaps a strong coupling between will and affect indicates a well integrated personality and commensurately, a high degree of thought capacity and a high degree of volitional intelligence.

 

We would expect that disembodied human souls, ETI souls, and/or UTI souls in Heaven, Limbo, highly evolved bodily ETI persons, highly evolved UTI persons, and angels to have acts of will of all kinds and intensities which are highly subject to affect.

 

The general meaning of affect derivatives of will can be viewed as the manner in which the qualitative and/or quantitative aspects of will as a function of affect very with affect. The manner in which volitions very with affect may be multi- affect-aspect dimensional wherein the dimensions of derivations can be multiple, and wherein the derivations can be taken in parallel, series parallel or in serial manner. The differentials can be partial or non-partial derivatives, or both partial and non-partial for a given computation.

 

In fact, since there is in theory, no limit to the numbers of qualitatively and quantitatively different affective states, and perhaps no limit to the number of possible different types or classes of affective states, wherein each person has his or her own unique affective rxperiences, the number of affect dimensions that can effect volitions is literally infinite, given the entirety of the set of created persons, and perhaps also literally infinite for each person as an individual, although we can not intellectually and intuitively understand this infinite number.

 

 

It is interesting to consider the ramifactions of being able to perform realistic calculations involving affect derivatives of will from a mathematical, theoretical, scientific,  and philosophical perspective.

 

Persons for which one or more nth order derivatives of will with respect to affect that have large absolute values would tend to have their wills highly influenced by affect, or at least for the volitions under consideration with respect to the dimension of the specific affect type(s) or class(es) for which the differentiation(s) are being performed. Perhaps a strong coupling between will and affect indicates a well integrated personality and commensurately, a high degree of volitional capacity and a high degree of volitional intelligence as well as perhaps very strong affect power.

 

We would expect that disembodied human souls, ETI souls, and/or UTI souls in Heaven, Limbo, highly evolved bodily ETI persons, highly evolved UTI persons, and angels to have volitions of all kinds and intensities which are highly subject to affect.

 

 

We can also consider that two dimensional nth ordered derivatives of will with respect to affect and time, or with respect to a and T, respectively.

 

Given that W[(a)(T)] =  W[(t and/or w and/or a and/or i and/or m)(w)(T)], the following first order two dimensional derivatives of will with respect to affect and Time are possible.

 

 

d[dW[(t)(T)]/da]/dT, d[dW[(w)(T)]/da]/dT, d[dW[(a)(T)]/da]/dT, d[dW[(i)(T)]/da]/dT, d[dW[(m)(T)]/da]/dT, d[dW[(t,w)(T)]/da]/dT, d[dW[(t,a)(T)]/da]/dT, d[dW[(t,i)(T)]/da]/dT, d[dW[(t,m)(T)]/da]/dT, d[dW[(w,a)(T)]/da]/dT, d[dW[(w,i)(T)]/da]/dT, d[dW[(w,m)(T)]/da]/dT, d[dW[(a,i)(T)]/da]/dT, d[dW[(a,m)(T)]/da]/dT, d[dW[(i,m)(T)]/da]/dT, d[dW[(t,w,a)(T)]/da]/dT, d[dW[(t,w,i)(T)]/da]/dT, d[dW[(t,w,m)(T)]/da]/dT, d[dW[(t,a,i)(T)]/da]/dT, d[dW[(t,a,m)(T)]/da]/dT, d[dW[(t,i,m)(T)]/da]/dT, d[dW[(w,a,i)(T)]/da]/dT, d[dW[(w,a,m)(T)]/da]/dT, d[dW[(w,i,m)(T)]/da]/dT, d[dW[(a,i,m)(T)]/da]/dT, d[dW[(t,w,a,i)(T)]/da]/dT, d[dW[(t,w,a,m)(T)]/da]/dT, d[dW[(t,w,i,m)(T)]/da]/dT, d[dW[(t,a,i,m)(T)]/da]/dT, d[dW[(w,a,i,m)(T)]/da]/dT, d[dW[(t,w,a,i,m)(T)]/da]/dT.

 

 

Or more succinctly,  d[dW(T)/da]/dT = d[dW[(T)(t and/or w and/or a and/or i and/or m)]/da]/dT

 

or

 

d[dW(T)/dT]/da = d[dW[(T)(t and/or w and/or a and/or i and/or m)]/dT]/da

 

 

 

 

 

Or perhaps d[d W[(a)(T)]/da]/dT  = d[d W [{[t(a)] and/or [w(a)] and/or [a(a)] and/or [i(a)] and/or [m(a)]}(T)]/da]/dT

 

or

 

Or perhaps d[d W[(a)(T)]/dT]/da  = d[d W [{[t(a)] and/or [w(a)] and/or [a(a)] and/or [i(a)] and/or [m(a)]}(T)]/dT]/da

 

 

 

Likewise, we can take the second dual dimension affect -time derivatives of  W as follows:

 

d[d[d[dW[(t)(T)]/da]/dT]/da]/dT, d[d[d[dW[(w)(T)]/da]/dT]/da]/dT, d[d[d[dW[(a)(T)]/da]/dT]/da]/dT, d[d[d[dW[(i)(T)]/da]/dT]/da]/dT, d[d[d[dW[(m)(T)]/da]/dT]/da]/dT, d[d[d[dW[(t,w)(T)]/da]/dT]/da]/dT, d[d[d[dW[(t,a)(T)]/da]/dT]/da]/dT, d[d[d[dW[(t,i)(T)]/da]/dT]/da]/dT, d[d[d[dW[(t,m)(T)]/da]/dT]/da]/dT, d[d[d[dW[(w,a)(T)]/da]/dT]/da]/dT, d[d[d[dW[(w,i)(T)]/da]/dT]/da]/dT, d[d[d[dW[(w,m)(T)]/da]/dT]/da]/dT, d[d[d[dW[(a,i)(T)]/da]/dT]/da]/dT, d[d[d[dW[(a,m)(T)]/da]/dT]/da]/dT, d[d[d[dW[(i,m)(T)]/da]/dT]/da]/dT, d[d[d[dW[(t,w,a)(T)]/da]/dT]/da]/dT, d[d[d[dW[(t,w,i)(T)]/da]/dT]/da]/dT, d[d[d[dW[(t,w,m)(T)]/da]/dT]/da]/dT, d[d[d[dW[(t,a,i)(T)]/da]/dT]/da]/dT, d[d[d[dW[(t,a,m)(T)]/da]/dT]/da]/dT, d[d[d[dW[(t,i,m)(T)]/da]/dT]/da]/dT, d[d[d[dW[(w,a,i)(T)]/da]/dT]/da]/dT, d[d[d[dW[(w,a,m)(T)]/da]/dT]/da]/dT, d[d[d[dW[(w,i,m)(T)]/da]/dT]/da]/dT, d[d[d[dW[(a,i,m)(T)]/da]/dT]/da]/dT, d[d[d[dW[(t,w,a,i)(T)]/da]/dT]/da]/dT, d[d[d[dW[(t,w,a,m)(T)]/da]/dT]/da]/dT, d[d[d[dW[(t,w,i,m)(T)]/da]/dT]/da]/dT, d[d[d[dW[(t,a,i,m)(T)]/da]/dT]/da]/dT, d[d[d[dW[(w,a,i,m)(T)]/da]/dT]/da]/dT, d[d[d[dW[(t,w,a,i,m)(T)]/da]/dT]/da]/dT.

 

or as:

 

 

 

d[d[d[dW[(t)(T)]/da]/dT]/dT]/da, d[d[d[dW[(w)(T)]/da]/dT]/dT]/da, d[d[d[dW[(a)(T)]/da]/dT]/dT]/da, d[d[d[dW[(i)(T)]/da]/dT]/dT]/da, d[d[d[dW[(m)(T)]/da]/dT]/dT]/da, d[d[d[dW[(t,w)(T)]/da]/dT]/dT]/da, d[d[d[dW[(t,a)(T)]/da]/dT]/dT]/da, d[d[d[dW[(t,i)(T)]/da]/dT]/dT]/da, d[d[d[dW[(t,m)(T)]/da]/dT]/dT]/da, d[d[d[dW[(w,a)(T)]/da]/dT]/dT]/da, d[d[d[dW[(w,i)(T)]/da]/dT]/dT]/da, d[d[d[dW[(w,m)(T)]/da]/dT]/dT]/da, d[d[d[dW[(a,i)(T)]/da]/dT]/dT]/da, d[d[d[dW[(a,m)(T)]/da]/dT]/dT]/da, d[d[d[dW[(i,m)(T)]/da]/dT]/dT]/da, d[d[d[dW[(t,w,a)(T)]/da]/dT]/dT]/da, d[d[d[dW[(t,w,i)(T)]/da]/dT]/dT]/da, d[d[d[dW[(t,w,m)(T)]/da]/dT]/dT]/da, d[d[d[dW[(t,a,i)(T)]/da]/dT]/dT]/da, d[d[d[dW[(t,a,m)(T)]/da]/dT]/dT]/da, d[d[d[dW[(t,i,m)(T)]/da]/dT]/dT]/da, d[d[d[dW[(w,a,i)(T)]/da]/dT]/dT]/da, d[d[d[dW[(w,a,m)(T)]/da]/dT]/dT]/da, d[d[d[dW[(w,i,m)(T)]/da]/dT]/dT]/da, d[d[d[dW[(a,i,m)(T)]/da]/dT]/dT]/da, d[d[d[dW[(t,w,a,i)(T)]/da]/dT]/dT]/da, d[d[d[dW[(t,w,a,m)(T)]/da]/dT]/dT]/da, d[d[d[dW[(t,w,i,m)(T)]/da]/dT]/dT]/da, d[d[d[dW[(t,a,i,m)(T)]/da]/dT]/dT]/da, d[d[d[dW[(w,a,i,m)(T)]/da]/dT]/dT]/da, d[d[d[dW[(t,w,a,i,m)(T)]/da]/dT]/dT]/da.

 

or as:

 

d[d[d[dW[(t)(T)]/dT]/da]/da]/dT, d[d[d[dW[(w)(T)]/dT]/da]/da]/dT, d[d[d[dW[(a)(T)]/dT]/da]/da]/dT, d[d[d[dW[(i)(T)]/dT]/da]/da]/dT, d[d[d[dW[(m)(T)]/dT]/da]/da]/dT, d[d[d[dW[(t,w)(T)]/dT]/da]/da]/dT, d[d[d[dW[(t,a)(T)]/dT]/da]/da]/dT, d[d[d[dW[(t,i)(T)]/dT]/da]/da]/dT, d[d[d[dW[(t,m)(T)]/dT]/da]/da]/dT, d[d[d[dW[(w,a)(T)]/dT]/da]/da]/dT, d[d[d[dW[(w,i)(T)]/dT]/da]/da]/dT, d[d[d[dW[(w,m)(T)]/dT]/da]/da]/dT, d[d[d[dW[(a,i)(T)]/dT]/da]/da]/dT, d[d[d[dW[(a,m)(T)]/dT]/da]/da]/dT, d[d[d[dW[(i,m)(T)]/dT]/da]/da]/dT, d[d[d[dW[(t,w,a)(T)]/dT]/da]/da]/dT, d[d[d[dW[(t,w,i)(T)]/dT]/da]/da]/dT, d[d[d[dW[(t,w,m)(T)]/dT]/da]/da]/dT, d[d[d[dW[(t,a,i)(T)]/dT]/da]/da]/dT, d[d[d[dW[(t,a,m)(T)]/dT]/da]/da]/dT, d[d[d[dW[(t,i,m)(T)]/dT]/da]/da]/dT, d[d[d[dW[(w,a,i)(T)]/dT]/da]/da]/dT, d[d[d[dW[(w,a,m)(T)]/dT]/da]/da]/dT, d[d[d[dW[(w,i,m)(T)]/dT]/da]/da]/dT, d[d[d[dW[(a,i,m)(T)]/dT]/da]/da]/dT, d[d[d[dW[(t,w,a,i)(T)]/dT]/da]/da]/dT, d[d[d[dW[(t,w,a,m)(T)]/dT]/da]/da]/dT, d[d[d[dW[(t,w,i,m)(T)]/dT]/da]/da]/dT, d[d[d[dW[(t,a,i,m)(T)]/dT]/da]/da]/dT, d[d[d[dW[(w,a,i,m)(T)]/dT]/da]/da]/dT, d[d[d[dW[(t,w,a,i,m)(T)]/dT]/da]/da]/dT.

 

 

or as;

 

 

 

 

d[d[d[dW(t)/da]/da]/dT]/dT, d[d[d[dW(w)/da]/da]/dT]/dT, d[d[d[dW(a)/da]/da]/dT]/dT, d[d[d[dW(i)/da]/da]/dT]/dT, d[d[d[dW(m)/da]/da]/dT]/dT, d[d[d[dW(t,w)/da]/da]/dT]/dT, d[d[d[dW(t,a)/da]/da]/dT]/dT, d[d[d[dW(t,i)/da]/da]/dT]/dT, d[d[d[dW(t,m)/da]/da]/dT]/dT, d[d[d[dW(w,a)/da]/da]/dT]/dT, d[d[d[dW(w,i)/da]/da]/dT]/dT, d[d[d[dW(w,m)/da]/da]/dT]/dT, d[d[d[dW(a,i)/da]/da]/dT]/dT, d[d[d[dW(a,m)/da]/da]/dT]/dT, d[d[d[dW(i,m)/da]/da]/dT]/dT, d[d[d[dW(t,w,a)/da]/da]/dT]/dT, d[d[d[dW(t,w,i)/da]/da]/dT]/dT, d[d[d[dW(t,w,m)/da]/da]/dT]/dT, d[d[d[dW(t,a,i)/da]/da]/dT]/dT, d[d[d[dW(t,a,m)/da]/da]/dT]/dT,  d[d[d[dW(t,i,m)/da]/da]/dT]/dT, d[d[d[dW(w,a,i)/da]/da]/dT]/dT, d[d[d[dW(w,a,m)/da]/da]/dT]/dT, d[d[d[dW(w,i,m)/da]/da]/dT]/dT, d[d[d[dW(a,i,m)/da]/da]/dT]/dT, d[d[d[dW(t,w,a,i)/da]/da]/dT]/dT, d[d[d[dW(t,w,a,m)/da/da, d[d[d[dW(t,w,i,m)/da]/da]/dT]/dT, d[d[d[dW(t,a,i,m)/da]/da]/dT]/dT, d[d[d[dW(w,a,i,m)/da]/da]/dT]/dT, d[d[d[dW(t,w,a,i,m)/da]/da]/dT]/dT..

 

or as:

 

d[d[d[dW(t)/dT]/da]/dT]/da, d[d[d[dW(w)/dT]/da]/dT]/da, d[d[d[dW(a)/dT]/da]/dT]/da, d[d[d[dW(i)/dT]/da]/dT]/da, d[d[d[dW(m)/dT]/da]/dT]/da, d[d[d[dW(t,w)/dT]/da]/dT]/da, d[d[d[dW(t,a)/dT]/da]/dT]/da, d[d[d[dW(t,i)/dT]/da]/dT]/da, d[d[d[dW(t,m)/dT]/da]/dT]/da, d[d[d[dW(w,a)/dT]/da]/dT]/da, d[d[d[dW(w,i)/dT]/da]/dT]/da, d[d[d[dW(w,m)/dT]/da]/dT]/da, d[d[d[dW(a,i)/dT]/da]/dT]/da, d[d[d[dW(a,m)/dT]/da]/dT]/da, d[d[d[dW(i,m)/ dT]/da]/dT]/da, d[d[d[dW(t,w,a)/dT]/da]/dT]/da, d[d[d[dW(t,w,i)/dT]/da]/dT]/da, d[d[d[dW(t,w,m)/dT]/da]/dT]/da, d[d[d[dW(t,a,i)/dT]/da]/dT]/da, d[d[d[dW(t,a,m)/dT]/da]/dT]/da,  d[d[d[dW(t,i,m)/dT]/da]/dT]/da, d[d[d[dW(w,a,i)/dT]/da]/dT]/da, d[d[d[dW(w,a,m)/dT]/da]/dT]/da, d[d[d[dW(w,i,m)/dT]/da]/dT]/da, d[d[d[dW(a,i,m)/dT]/da]/dT]/da, d[d[d[dW(t,w,a,i)/dT]/da]/dT]/da, d[d[d[dW(t,w,a,m)/da/da, d[d[d[dW(t,w,i,m)/dT]/da]/dT]/da, d[d[d[dW(t,a,i,m)/dT]/da]/dT]/da, d[d[d[dW(w,a,i,m)/dT]/da]/dT]/da, d[d[d[dW(t,w,a,i,m)/dT]/da]/dT]/da..

 

or as:

 

d[d[d[dW(t)/dT]/dT]/da]/da, d[d[d[dW(w)/dT]/dT]/da]/da, d[d[d[dW(a)/dT]/dT]/da]/da, d[d[d[dW(i)/dT]/dT]/da]/da, d[d[d[dW(m)/dT]/dT]/da]/da, d[d[d[dW(t,w)/dT]/dT]/da]/da, d[d[d[dW(t,a)/dT]/dT]/da]/da, d[d[d[dW(t,i)/dT]/dT]/da]/da, d[d[d[dW(t,m)/dT]/dT]/da]/da, d[d[d[dW(w,a)/dT]/dT]/da]/da, d[d[d[dW(w,i)/dT]/dT]/da]/da, d[d[d[dW(w,m)/dT]/dT]/da]/da, d[d[d[dW(a,i)/dT]/dT]/da]/da, d[d[d[dW(a,m)/ dT]/dT]/da]/da, d[d[d[dW(i,m)/ dT]/dT]/da]/da, d[d[d[dW(t,w,a)/dT]/dT]/da]/da, d[d[d[dW(t,w,i)/dT]/dT]/da]/da, d[d[d[dW(t,w,m)/dT]/dT]/da]/da, d[d[d[dW(t,a,i)/dT]/dT]/da]/da, d[d[d[dW(t,a,m)/dT]/dT]/da]/da,  d[d[d[dW(t,i,m)/dT]/dT]/da]/da, d[d[d[dW(w,a,i)/dT]/dT]/da]/da, d[d[d[dW(w,a,m)/dT]/dT]/da]/da, d[d[d[dW(w,i,m)/dT]/dT]/da]/da, d[d[d[dW(a,i,m)/dT]/dT]/da]/da, d[d[d[dW(t,w,a,i)/dT]/dT]/da]/da, d[d[d[dW(t,w,a,m)/da/da, d[d[d[dW(t,w,i,m)/dT]/dT]/da]/da, d[d[d[dW(t,a,i,m)/dT]/dT]/da]/da, d[d[d[dW(w,a,i,m)/dT]/dT]/da]/da, d[d[d[dW(t,w,a,i,m)/dT]/dT]/da]/da..

 

We can also take higher order duel dimensional derivatives of will as a function of affect and time but the symbolic expression of the set of such derivatives very soon becomes excessively lengthly to write and so these higher order derivatives as such are not mentioned here except to say that they would be computed in an analogous manner to the second order duel dimensional derivatives described above.

 

.

 

 

We can also express will qualitatively, statistically, and perhaps with the use of some forms of real analyses as a derivative with respect to  instinct or with respect to i.

 

Given that W(i) =  W(t and/or w and/or a and/or i and/or m) or perhaps the following notation can be more appropriate in certain circumstances.

 

 

 

 

Thus the following first order derivatives of will with respect to instinct are possible.

 

 

dW(t)/di, dW(w)/di, dW(a)/di, dW(i)/di, dW(m)/di, dW(t,w)/di, dW(t,a)/di, dW(t,i)/di, dW(t,m)/di, dW(w,a)/di, dW(w,i)/di, dW(w,m)/di, dW(a,i)/di, dW(a,m)/di, dW(i,m)/di, dW(t,w,a)/di, dW(t,w,i)/di, dW(t,w,m)/di, dW(t,a,i)/di, dW(t,a,m)/di, dW(t,i,m)/di, dW(w,a,i)/di, dW(w,a,m)/di, dW(w,i,m)/di, dW(a,i,m)/di, dW(t,w,a,i)/di, dW(t,w,a,m)/di, dW(t,w,i,m)/di, dW(t,a,i,m)/di, dW(w,a,i,m)/di, dW(t,w,a,i,m)/di.

 

 

Or more succinctly,  dW/di = dW(t and/or w and/or a and/or i and/or m)/di

 

 

Or perhaps dW(i)/di =d W{[t(i)] and/or [w(i)] and/or [a(i)] and/or [i(i)] and/or [m(i)]}/di.

 

 

Likewise, we can take the second instinct derivatives of  W as follows:

 

 

 

d[dW(t)/di]/di, d[dW(w)/di]/di, d[dW(a)/di]/di, d[dW(i)/di]/di, d[dW(m)/di]/di, d[dW(t,w)/di]/di, d[dW(t,a)/di]/di, d[dW(t,i)/di]/di, d[dW(t,m)/di]/di, d[dW(w,a)/di]/di, d[dW(w,i)/di]/di, d[dW(w,m)/di]/di, d[dW(a,i)/di]/di, d[dW(a,m)/di]/di, d[dW(i,m)/di/di, d[dW(t,w,a)/di]/di, d[dW(t,w,i)/di]/di, d[dW(t,w,m)/di]/di, d[dW(t,a,i)/di]/di, d[dW(t,a,m)/di]/di,  d[dW(t,i,m)/di]/di, d[dW(w,a,i)/di]/di, d[dW(w,a,m)/di]/di, d[dW(w,i,m)/di]/di, d[dW(a,i,m)/di]/di, d[dW(t,w,a,i)/di]/di, d[dW(t,w,a,m)/di/di, d[dW(t,w,i,m)/di]/di, d[dW(t,a,i,m)/di]/di, d[dW(w,a,i,m)/di]/di, d[dW(t,w,a,i,m)/di]/di..

 

 

or more succinctly, as d(dW/di)/di = d[d W(t and/or w and/or a and/or i and/or m)/di]/di = Wi2

 

 

or as

 

 

d[dW(i)/di]/di  = d[d W{[t(i)] and/or [w(i)] and/or [a(i)] and/or [i(i)] and/or [m(i)]}/di]/di = Wi2.

 

 

 

Likewise, we can take the third instinct derivatives of  W as follows:

 

 

 

d[d[dW(t)/di]/di]/di, d[d[dW(w)/di]/di]/di, d[d[dW(a)/di]/di]/di, d[d[dW(i)/di]/di]/di, d[d[dW(m)/di]/di]/di, d[d[dW(t,w)/di]/di]/di, d[d[dW(t,a)/di]/di]/di, d[d[dW(t,i)/di]/di]/di, d[d[dW(t,m)/di]/di]/di, d[d[dW(w,a)/di]/di]/di, d[d[dW(w,i)/di]/di]/di, d[d[dW(w,m)/di]/di]/di, d[d[dW(a,i)/di]/di]/di, d[d[dW(a,m)/di]/di]/di, d[d[dW(i,m)/di/di]/di, d[d[dW(t,w,a)/di]/di]/di, d[d[dW(t,w,i)/di]/di]/di, d[d[dW(t,w,m)/di]/di]/di, d[d[dW(t,a,i)/di]/di]/di, d[d[dW(t,a,m)/di]/di]/di,  d[d[dW(t,i,m)/di]/di]/di, d[d[dW(w,a,i)/di]/di]/di, d[d[dW(w,a,m)/di]/di]/di, d[d[dW(w,i,m)/di]/di]/di, d[d[dW(a,i,m)/di]/di]/di, d[d[dW(t,w,a,i)/di]/di]/di, d[d[dW(t,w,a,m)/di/di]/di, d[d[dW(t,w,i,m)/di]/di]/di, d[d[dW(t,a,i,m)/di]/di]/di, d[d[dW(w,a,i,m)/di]/di]/di, d[d[dW(t,w,a,i,m)/di]/di]/di.

 

 

or more succinctly, as d[d(dW/di)/di]/di = d[d[d W(t and/or w and/or a and/or i and/or m)/di]/di]/di = Wi3

 

 

or as

 

 

d[d[dW(i)/di]/di]/di  = d[d[d W{[t(i)] and/or [w(i)] and/or [a(i)] and/or [i(i)] and/or [m(i)]}/di]/di]/di = Wi3.

 

 

We can also form the expressions;

 

 

d[d[f(W)]/di]/di = d{d [W[t(i)]]/di and/or d[W[w(i)]]/di and/or d[W[a(i)]]/di and/or d[W[i(i)]]/di and/or d[W[m(i)]]/di}/di  = f(Wi)2

 

 

and

 

 

d[d[d[f(W)]/di]/di]/di = d{d{ d [W[t(i)]]/di and/or d[W[w(i)]]/di and/or d[W[a(i)]]/di and/or d[W[i(i)]]/di and/or d[W[m(i)]]/di}/di}/di  = f(Wi)3A, where A stands for type A differentiation which is not to be confused with the meaning of so-called Type A personality as A is used as an ordinal in a totally different context here.

 

 

and

 

 

d[d[d[f(W)]/di]/di]/di = d{d[d [W[t(i)]]/di]/di  and/or d[d [W[w(i)]]/di]/di  and/or d[d [W[a(i)]]/di]/di  and/or d[d [W[i(i)]]/di]/di  and/or d[d [W[m(i)]]/di]/di }/di = f(Wi)3B, where B stands for type B differentiation which is not to be confused with the meaning of so-called Type  B personality as B is used as an ordinal in a totally different context here .

 

 

In fact, one can form yet higher order derivatives of will with respect to instinct as follows.

 

 

Wi5 = d Wi4/di = d[dWi3/di]/di

 

 

 

Wi5 = dWi4/di =  d[d[d[d[d W{[t(i)] and/or [w(i)] and/or [a(i)] and/or [i(i)] and/or [m(i)]}/di]/di]/di]/di]/di.

 

 

 

f(Wi)5A = d[f(Wi)4A]/di = d[d [f(Wi)3A]/di]/di =  d{d{d{d{ d [W[t(i)]]/di and/or d[W[w(i)]]/di and/or d[W[a(i)]]/di and/or d[W[i(i)]]/di and/or d[W[m(i)]]/di}/di}/di]/di]/di

 

 

 

 

Wi6 = d Wi5/di = d[d Wi4/di]/di = d[d[dWi3/di]/di]/di

 

 

 

Wi6 = dWi5/di = d[d[d[d[d[d W{[t(i)] and/or [w(i)] and/or [a(i)] and/or [i(i)] and/or [m(i)]}/di]/di]/di]/di]/di]/di

 

 

 

f(Wi)6A = d[f(Wi)5A]/di = d{ d{d{d{d{ d [W[t(i)]]/di and/or d[W[w(i)]]/di and/or d[W[a(i)]]/di and/or d[W[i(i)]]/di and/or d[W[m(i)]]/di}/di}/di]/di]/di]/di

 

 

 

 

Wi7 = dWi6/di

 

f(Wi)7A = d[f(Wi)6A]/di

 

 

Wi8 = d Wi7/di

 

f(Wi)8A = d[f(Wi)7A]/di

 

 

 

Wi9 = d Wi8/di

 

f(Wi)9A = d[f(Wi)8A]/di

 

 

Wi10…, Wi11…, Wi12 … etc.

 

 

Anyone for Wi ensemble, or Wi infinity scrapper, or Wi (Aleph 0), or Wi(Aleph 1), or Wi (Aleph 2), or how about Wi Aleph (Aleph 0), or Wi Aleph (Aleph 1) , or Wi Aleph (Aleph 2), or even Wi Aleph (Aleph (Aleph 0)), or Wi Aleph (Aleph (Aleph 1)), or Wi Aleph (Aleph (Aleph 2)), and so on?

 

Thus, for the set of the sets of derivatives of Wi1 through Wi(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Wi1 through Wi (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)},…, {П(0,31)[R]}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Wi 1 through Wi (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Wi 1 through Wi (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the derivative states in the set of the sets of derivatives of Wi 1 through I(Aleph 0) is plausible equal to:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Wi 1 through Wi (Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Wi 1 through Wi (Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}}}.

 

For the set of the sets of derivatives of Wi 1 through Wi (Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Wi I(Aleph 0) derivative space at the level of 0/(Aleph 0), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Wi 1 through Wi (Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Wi 1 through Wi (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Wi 1 through Wi (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Wi 1 through Wi (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Wi 1 through Wi (Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Wi 1 through Wi (Aleph 1), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Wi 1 through  Wi (Aleph 2), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Wi I1 through Wi (Aleph 3), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Wi (Aleph 0) derivative space at the level of 0/(Aleph 1), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Wi 1 through Wi (Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Wi 1 through Wi (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Wi 1 through Wi (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Wi 1 through  Wi (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations  for the set of the sets of derivatives of Wi 1 through Wi (Aleph 0) is plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Wi 1 through Wi (Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Wi 1 through Wi (Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Wi 1 through Wi (Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

 

For super-continuous Wi (Aleph 0) derivative space at the level of 0/(Aleph 2), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Wi 1 through Wi (Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Wi 1 through Wi (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Wi 1 through Wi (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Wi I1 through Wi (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Wi 1 through Wi (Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Wi I1 through Wi (Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Wi 1 through Wi (Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Wi I1 through Wi (Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

Similar series can be developed for super-continuity at any applicable level such as 0/(Aleph 3), 0/(Aleph 4), 0/(Aleph 5),…, 0/(Aleph Ω), 0/(Aleph (Aleph 0)), …, 0/(Aleph (Aleph 1)), …, 0/(Aleph (Aleph 2)), …, 0/(Aleph (Aleph 3)),…, 0/(Aleph (Aleph Ω)),…, 0/(Aleph (Aleph (Aleph 0))), …, 0/(Aleph (Aleph (Aleph 1))),…, 0/(Aleph (Aleph (Aleph 2))),…, 0/(Aleph (Aleph (Aleph 3))),…, 0/(Aleph (Aleph  (Aleph Ω))), …

 

An so-on ad infinitum.

 

 

In addition to these numerical functions of Wi as functions of summation series of product series functions, in order to really appreciate the enourmous complexity of the human soul in terms of its potential to evolve and be differentiated from all other souls in its characteristics, we would need to consider how every single category and even every single species of will of the form Wi can very. Since there may exist an arbitrarily high infinite number species of Wi, the number of numerical functions of Wi is utterly beyond recogning. I will cover such notions in terms of mathematical notation in yet another series of articles I will write on this general concept.

 

 

Perhaps these numbers are applicable when one considers that the human soul, in its accidental form and perhaps even in its substantial form stores all experience and other psychodynamics based phenomenon. Every experience adds to the accidental form of the human soul and this includes the souls of all those still alive on Earth, all those in Purgatory, all those in Heaven, all those in Hell, and all those in any Limbo.

Since the human soul can grow without limit in terms of its psychodynamic time –flow world line, such a consideration offers another mechanism where the number of derivative states, combinations of derivative states, and even super-continuity of the derivative state space can grow forever.

 

Folks, for those of you who might balk at me for including literally all souls in the above consideration, including the souls in Hell, as well as bodily extraterrestrial souls and the souls of so-called bodily ultraterrestials sometimes referred to as etherians in the new age UFO buff culture, my reply is that we simply do not understand the full scope of GOD’s Divine Economy. We may never fully comprehend the scope of the Divine Economy because such an utterly eternal scheme, is, well, eternal and never ending.

 

 

The general meaning of instinct derivatives of will can be viewed as the manner in which the qualitative and/or quantitative aspects of will as a function of instinct very with instinct(s). The manner in which volitions very with instinct may be multi-instinct dimensional wherein the dimensions of derivations can be multiple, and wherein the derivations can be taken in parallel, series parallel or serial manner The differentials can be partial or non-partial derivatives, or both partial and non-partial for a given computation.

 

In fact, since there is in theory, no limit to the numbers of qualitatively and quantitatively different acts of will, and perhaps no limit to the number of possible different types or classes of acts of will, wherein each person has his or her own unique acts of will, the number of instinct dimensions that can effect acts of will is literally infinite, given the entirety of the set of created persons, and perhaps also literally infinite for each person as an individual, although we can not intellectually and intuitively understand this specific infinite number.

 

It is interesting to consider the ramifactions of being able to perform realistic calculations involving instinct derivatives of will from a mathematical, theoretical, scientific,  and philosophical perspective.

 

Persons for which one or more nth order derivatives of will with respect to instinct that have large absolute values would tend to have their wills highly influenced by instinct, or at least for the acts of will under consideration with respect to the dimension of the specific instinct type(s) or class(es) for which the differentiation(s) are performed. Perhaps a strong coupling between will  and instinct indicates a well integrated personality and commensurately, a high degree of thought capacity and a high degree of thought intelligence.

 

We would expect that disembodied human souls, ETI souls, and/or UTI souls in Heaven, Limbo, highly evolved bodily ETI persons, highly evolved UTI persons, and angels to have acts of willl of all kinds and intensities which are highly subject to instinct.

 

 

 

The general meaning of instinct derivatives of will can be viewed as the manner in which the qualitative and/or quantitative aspects of will as a function of instinct very with instinct. The manner in which volitions very with instinct may be multi- instinct-aspect dimensional wherein the dimensions of derivations can be multiple, and wherein the derivations can be taken in parallel, series parallel or in serial manner. The differentials can be partial or non-partial derivatives, or both partial and non-partial for a given computation.

 

In fact, since there is in theory, no limit to the numbers of qualitatively and quantitatively different instincts, and perhaps no limit to the number of possible different types or classes of instincts or potential instincts, wherein each person has his or her own unique instincts and instinctual experiences, the number of instinct dimensions that can effect will is literally infinite, given the entirety of the set of created persons, and perhaps also literally infinite for each person as an individual, although we can not intellectually and intuitively understand this infinite number.

 

 

It is interesting to consider the ramifactions of being able to perform realistic calculations involving instinct derivatives of will from a mathematical, theoretical, scientific,  and philosophical perspective.

 

Persons for which one or more nth order derivatives of will with respect to instinct that have large absolute values would tend to have their wills highly influenced by instinct, or at least for the volitions under consideration with respect to the dimension of the specific instinct act type(s) or class(es) for which the differentiation(s) are being performed. Perhaps a strong coupling between will and instinct indicates a well integrated personality and commensurately, a high degree of will capacity and a high degree of volitional intelligence as well as perhaps very strong instinct power.

 

We would expect that disembodied human souls, ETI souls, and/or UTI souls in Heaven, Limbo, highly evolved bodily ETI persons, highly evolved UTI persons, and angels to have volitions of all kinds and intensities which are perhaps  highly subject to advanced instincts such as spiritual instincts, spiritual intuitions, and even perhaps, psychic powers.

 

 

We can also consider that two dimensional nth ordered derivatives of will with respect to instinct and time, or with respect to i and T, respectively.

 

Given that W[(i)(T)] =  W[(t and/or w and/or a and/or i and/or m)(i)(T)], the following first order two dimensional derivatives of will with respect to instinct and Time are possible.

 

 

d[dW[(t)(T)]/di]/dT, d[dW[(w)(T)]/di]/dT, d[dW[(a)(T)]/di]/dT, d[dW[(i)(T)]/di]/dT, d[dW[(m)(T)]/di]/dT, d[dW[(t,w)(T)]/di]/dT, d[dW[(t,a)(T)]/di]/dT, d[dW[(t,i)(T)]/di]/dT, d[dW[(t,m)(T)]/di]/dT, d[dW[(w,a)(T)]/di]/dT, d[dW[(w,i)(T)]/di]/dT, d[dW[(w,m)(T)]/di]/dT, d[dW[(a,i)(T)]/di]/dT, d[dW[(a,m)(T)]/di]/dT, d[dW[(i,m)(T)]/di]/dT, d[dW[(t,w,a)(T)]/di]/dT, d[dW[(t,w,i)(T)]/di]/dT, d[dW[(t,w,m)(T)]/di]/dT, d[dW[(t,a,i)(T)]/di]/dT, d[dW[(t,a,m)(T)]/di]/dT, d[dW[(t,i,m)(T)]/di]/dT, d[dW[(w,a,i)(T)]/di]/dT, d[dW[(w,a,m)(T)]/di]/dT, d[dW[(w,i,m)(T)]/di]/dT, d[dW[(a,i,m)(T)]/di]/dT, d[dW[(t,w,a,i)(T)]/di]/dT, d[dW[(t,w,a,m)(T)]/di]/dT, d[dW[(t,w,i,m)(T)]/di]/dT, d[dW[(t,a,i,m)(T)]/di]/dT, d[dW[(w,a,i,m)(T)]/di]/dT, d[dW[(t,w,a,i,m)(T)]/di]/dT.

 

 

Or more succinctly,  d[dW(T)/di]/dT = d[dW[(T)(t and/or w and/or a and/or i and/or m)]/di]/dT

 

or

 

d[dW(T)/dT]/di = d[dW[(T)(t and/or w and/or a and/or i and/or m)]/dT]/di

 

 

 

 

 

Or perhaps d[d W[(i)(T)]/di]/dT  = d[d W [{[t(i)] and/or [w(i)] and/or [a(i)] and/or [i(i)] and/or [m(i)]}(T)]/di]/dT

 

or

 

Or perhaps d[d W[(i)(T)]/dT]/di  = d[d W [{[t(i)] and/or [w(i)] and/or [a(i)] and/or [i(i)] and/or [m(i)]}(T)]/dT]/di

 

 

 

Likewise, we can take the second dual dimension instinct -time derivatives of  W as follows:

 

d[d[d[dW[(t)(T)]/di]/dT]/di]/dT, d[d[d[dW[(w)(T)]/di]/dT]/di]/dT, d[d[d[dW[(a)(T)]/di]/dT]/di]/dT, d[d[d[dW[(i)(T)]/di]/dT]/di]/dT, d[d[d[dW[(m)(T)]/di]/dT]/di]/dT, d[d[d[dW[(t,w)(T)]/di]/dT]/di]/dT, d[d[d[dW[(t,a)(T)]/di]/dT]/di]/dT, d[d[d[dW[(t,i)(T)]/di]/dT]/di]/dT, d[d[d[dW[(t,m)(T)]/di]/dT]/di]/dT, d[d[d[dW[(w,a)(T)]/di]/dT]/di]/dT, d[d[d[dW[(w,i)(T)]/di]/dT]/di]/dT, d[d[d[dW[(w,m)(T)]/di]/dT]/di]/dT, d[d[d[dW[(a,i)(T)]/di]/dT]/di]/dT, d[d[d[dW[(a,m)(T)]/di]/dT]/di]/dT, d[d[d[dW[(i,m)(T)]/di]/dT]/di]/dT, d[d[d[dW[(t,w,a)(T)]/di]/dT]/di]/dT, d[d[d[dW[(t,w,i)(T)]/di]/dT]/di]/dT, d[d[d[dW[(t,w,m)(T)]/di]/dT]/di]/dT, d[d[d[dW[(t,a,i)(T)]/di]/dT]/di]/dT, d[d[d[dW[(t,a,m)(T)]/di]/dT]/di]/dT, d[d[d[dW[(t,i,m)(T)]/di]/dT]/di]/dT, d[d[d[dW[(w,a,i)(T)]/di]/dT]/di]/dT, d[d[d[dW[(w,a,m)(T)]/di]/dT]/di]/dT, d[d[d[dW[(w,i,m)(T)]/di]/dT]/di]/dT, d[d[d[dW[(a,i,m)(T)]/di]/dT]/di]/dT, d[d[d[dW[(t,w,a,i)(T)]/di]/dT]/di]/dT, d[d[d[dW[(t,w,a,m)(T)]/di]/dT]/di]/dT, d[d[d[dW[(t,w,i,m)(T)]/di]/dT]/di]/dT, d[d[d[dW[(t,a,i,m)(T)]/di]/dT]/di]/dT, d[d[d[dW[(w,a,i,m)(T)]/di]/dT]/di]/dT, d[d[d[dW[(t,w,a,i,m)(T)]/di]/dT]/di]/dT.

 

or as:

 

 

 

d[d[d[dW[(t)(T)]/di]/dT]/dT]/di, d[d[d[dW[(w)(T)]/di]/dT]/dT]/di, d[d[d[dW[(a)(T)]/di]/dT]/dT]/di, d[d[d[dW[(i)(T)]/di]/dT]/dT]/di, d[d[d[dW[(m)(T)]/di]/dT]/dT]/di, d[d[d[dW[(t,w)(T)]/di]/dT]/dT]/di, d[d[d[dW[(t,a)(T)]/di]/dT]/dT]/di, d[d[d[dW[(t,i)(T)]/di]/dT]/dT]/di, d[d[d[dW[(t,m)(T)]/di]/dT]/dT]/di, d[d[d[dW[(w,a)(T)]/di]/dT]/dT]/di, d[d[d[dW[(w,i)(T)]/di]/dT]/dT]/di, d[d[d[dW[(w,m)(T)]/di]/dT]/dT]/di, d[d[d[dW[(a,i)(T)]/di]/dT]/dT]/di, d[d[d[dW[(a,m)(T)]/di]/dT]/dT]/di, d[d[d[dW[(i,m)(T)]/di]/dT]/dT]/di, d[d[d[dW[(t,w,a)(T)]/di]/dT]/dT]/di, d[d[d[dW[(t,w,i)(T)]/di]/dT]/dT]/di, d[d[d[dW[(t,w,m)(T)]/di]/dT]/dT]/di, d[d[d[dW[(t,a,i)(T)]/di]/dT]/dT]/di, d[d[d[dW[(t,a,m)(T)]/di]/dT]/dT]/di, d[d[d[dW[(t,i,m)(T)]/di]/dT]/dT]/di, d[d[d[dW[(w,a,i)(T)]/di]/dT]/dT]/di, d[d[d[dW[(w,a,m)(T)]/di]/dT]/dT]/di, d[d[d[dW[(w,i,m)(T)]/di]/dT]/dT]/di, d[d[d[dW[(a,i,m)(T)]/di]/dT]/dT]/di, d[d[d[dW[(t,w,a,i)(T)]/di]/dT]/dT]/di, d[d[d[dW[(t,w,a,m)(T)]/di]/dT]/dT]/di, d[d[d[dW[(t,w,i,m)(T)]/di]/dT]/dT]/di, d[d[d[dW[(t,a,i,m)(T)]/di]/dT]/dT]/di, d[d[d[dW[(w,a,i,m)(T)]/di]/dT]/dT]/di, d[d[d[dW[(t,w,a,i,m)(T)]/di]/dT]/dT]/di.

 

or as:

 

d[d[d[dW[(t)(T)]/dT]/di]/di]/dT, d[d[d[dW[(w)(T)]/dT]/di]/di]/dT, d[d[d[dW[(a)(T)]/dT]/di]/di]/dT, d[d[d[dW[(i)(T)]/dT]/di]/di]/dT, d[d[d[dW[(m)(T)]/dT]/di]/di]/dT, d[d[d[dW[(t,w)(T)]/dT]/di]/di]/dT, d[d[d[dW[(t,a)(T)]/dT]/di]/di]/dT, d[d[d[dW[(t,i)(T)]/dT]/di]/di]/dT, d[d[d[dW[(t,m)(T)]/dT]/di]/di]/dT, d[d[d[dW[(w,a)(T)]/dT]/di]/di]/dT, d[d[d[dW[(w,i)(T)]/dT]/di]/di]/dT, d[d[d[dW[(w,m)(T)]/dT]/di]/di]/dT, d[d[d[dW[(a,i)(T)]/dT]/di]/di]/dT, d[d[d[dW[(a,m)(T)]/dT]/di]/di]/dT, d[d[d[dW[(i,m)(T)]/dT]/di]/di]/dT, d[d[d[dW[(t,w,a)(T)]/dT]/di]/di]/dT, d[d[d[dW[(t,w,i)(T)]/dT]/di]/di]/dT, d[d[d[dW[(t,w,m)(T)]/dT]/di]/di]/dT, d[d[d[dW[(t,a,i)(T)]/dT]/di]/di]/dT, d[d[d[dW[(t,a,m)(T)]/dT]/di]/di]/dT, d[d[d[dW[(t,i,m)(T)]/dT]/di]/di]/dT, d[d[d[dW[(w,a,i)(T)]/dT]/di]/di]/dT, d[d[d[dW[(w,a,m)(T)]/dT]/di]/di]/dT, d[d[d[dW[(w,i,m)(T)]/dT]/di]/di]/dT, d[d[d[dW[(a,i,m)(T)]/dT]/di]/di]/dT, d[d[d[dW[(t,w,a,i)(T)]/dT]/di]/di]/dT, d[d[d[dW[(t,w,a,m)(T)]/dT]/di]/di]/dT, d[d[d[dW[(t,w,i,m)(T)]/dT]/di]/di]/dT, d[d[d[dW[(t,a,i,m)(T)]/dT]/di]/di]/dT, d[d[d[dW[(w,a,i,m)(T)]/dT]/di]/di]/dT, d[d[d[dW[(t,w,a,i,m)(T)]/dT]/di]/di]/dT.

 

 

or as;

 

 

 

 

d[d[d[dW(t)/di]/di]/dT]/dT, d[d[d[dW(w)/di]/di]/dT]/dT, d[d[d[dW(a)/di]/di]/dT]/dT, d[d[d[dW(i)/di]/di]/dT]/dT, d[d[d[dW(m)/di]/di]/dT]/dT, d[d[d[dW(t,w)/di]/di]/dT]/dT, d[d[d[dW(t,a)/di]/di]/dT]/dT, d[d[d[dW(t,i)/di]/di]/dT]/dT, d[d[d[dW(t,m)/di]/di]/dT]/dT, d[d[d[dW(w,a)/di]/di]/dT]/dT, d[d[d[dW(w,i)/di]/di]/dT]/dT, d[d[d[dW(w,m)/di]/di]/dT]/dT, d[d[d[dW(a,i)/di]/di]/dT]/dT, d[d[d[dW(a,m)/di]/di]/dT]/dT, d[d[d[dW(i,m)/di]/di]/dT]/dT, d[d[d[dW(t,w,a)/di]/di]/dT]/dT, d[d[d[dW(t,w,i)/di]/di]/dT]/dT, d[d[d[dW(t,w,m)/di]/di]/dT]/dT, d[d[d[dW(t,a,i)/di]/di]/dT]/dT, d[d[d[dW(t,a,m)/di]/di]/dT]/dT,  d[d[d[dW(t,i,m)/di]/di]/dT]/dT, d[d[d[dW(w,a,i)/di]/di]/dT]/dT, d[d[d[dW(w,a,m)/di]/di]/dT]/dT, d[d[d[dW(w,i,m)/di]/di]/dT]/dT, d[d[d[dW(a,i,m)/di]/di]/dT]/dT, d[d[d[dW(t,w,a,i)/di]/di]/dT]/dT, d[d[d[dW(t,w,a,m)/di/di, d[d[d[dW(t,w,i,m)/di]/di]/dT]/dT, d[d[d[dW(t,a,i,m)/di]/di]/dT]/dT, d[d[d[dW(w,a,i,m)/di]/di]/dT]/dT, d[d[d[dW(t,w,a,i,m)/di]/di]/dT]/dT..

 

or as:

 

d[d[d[dW(t)/dT]/di]/dT]/di, d[d[d[dW(w)/dT]/di]/dT]/di, d[d[d[dW(a)/dT]/di]/dT]/di, d[d[d[dW(i)/dT]/di]/dT]/di, d[d[d[dW(m)/dT]/di]/dT]/di, d[d[d[dW(t,w)/dT]/di]/dT]/di, d[d[d[dW(t,a)/dT]/di]/dT]/di, d[d[d[dW(t,i)/dT]/di]/dT]/di, d[d[d[dW(t,m)/dT]/di]/dT]/di, d[d[d[dW(w,a)/dT]/di]/dT]/di, d[d[d[dW(w,i)/dT]/di]/dT]/di, d[d[d[dW(w,m)/dT]/di]/dT]/di, d[d[d[dW(a,i)/dT]/di]/dT]/di, d[d[d[dW(a,m)/dT]/di]/dT]/di, d[d[d[dW(i,m)/ dT]/di]/dT]/di, d[d[d[dW(t,w,a)/dT]/di]/dT]/di, d[d[d[dW(t,w,i)/dT]/di]/dT]/di, d[d[d[dW(t,w,m)/dT]/di]/dT]/di, d[d[d[dW(t,a,i)/dT]/di]/dT]/di, d[d[d[dW(t,a,m)/dT]/di]/dT]/di,  d[d[d[dW(t,i,m)/dT]/di]/dT]/di, d[d[d[dW(w,a,i)/dT]/di]/dT]/di, d[d[d[dW(w,a,m)/dT]/di]/dT]/di, d[d[d[dW(w,i,m)/dT]/di]/dT]/di, d[d[d[dW(a,i,m)/dT]/di]/dT]/di, d[d[d[dW(t,w,a,i)/dT]/di]/dT]/di, d[d[d[dW(t,w,a,m)/di/di, d[d[d[dW(t,w,i,m)/dT]/di]/dT]/di, d[d[d[dW(t,a,i,m)/dT]/di]/dT]/di, d[d[d[dW(w,a,i,m)/dT]/di]/dT]/di, d[d[d[dW(t,w,a,i,m)/dT]/di]/dT]/di..

 

or as:

 

d[d[d[dW(t)/dT]/dT]/di]/di, d[d[d[dW(w)/dT]/dT]/di]/di, d[d[d[dW(a)/dT]/dT]/di]/di, d[d[d[dW(i)/dT]/dT]/di]/di, d[d[d[dW(m)/dT]/dT]/di]/di, d[d[d[dW(t,w)/dT]/dT]/di]/di, d[d[d[dW(t,a)/dT]/dT]/di]/di, d[d[d[dW(t,i)/dT]/dT]/di]/di, d[d[d[dW(t,m)/dT]/dT]/di]/di, d[d[d[dW(w,a)/dT]/dT]/di]/di, d[d[d[dW(w,i)/dT]/dT]/di]/di, d[d[d[dW(w,m)/dT]/dT]/di]/di, d[d[d[dW(a,i)/dT]/dT]/di]/di, d[d[d[dW(a,m)/ dT]/dT]/di]/di, d[d[d[dW(i,m)/ dT]/dT]/di]/di, d[d[d[dW(t,w,a)/dT]/dT]/di]/di, d[d[d[dW(t,w,i)/dT]/dT]/di]/di, d[d[d[dW(t,w,m)/dT]/dT]/di]/di, d[d[d[dW(t,a,i)/dT]/dT]/di]/di, d[d[d[dW(t,a,m)/dT]/dT]/di]/di,  d[d[d[dW(t,i,m)/dT]/dT]/di]/di, d[d[d[dW(w,a,i)/dT]/dT]/di]/di, d[d[d[dW(w,a,m)/dT]/dT]/di]/di, d[d[d[dW(w,i,m)/dT]/dT]/di]/di, d[d[d[dW(a,i,m)/dT]/dT]/di]/di, d[d[d[dW(t,w,a,i)/dT]/dT]/di]/di, d[d[d[dW(t,w,a,m)/di/di, d[d[d[dW(t,w,i,m)/dT]/dT]/di]/di, d[d[d[dW(t,a,i,m)/dT]/dT]/di]/di, d[d[d[dW(w,a,i,m)/dT]/dT]/di]/di, d[d[d[dW(t,w,a,i,m)/dT]/dT]/di]/di..

 

We can also take higher order duel dimensional derivatives of will as a function of instinct and time but the symbolic expression of the set of such derivatives very soon becomes excessively lengthly to write and so these higher order derivatives as such are not mentioned here except to say that they would be computed in an analogous manner to the second order duel dimensional derivatives described above.

 

 

 

These seemingly crazy differentials might have some use in extreme psychological states that can be experienced by souls who are departed and whose wills are  not limited by a body and its brain.

 

 

Another type of being that might experience such extreme will change capacities might be none other then some of our friends we believe to exist as pure body-less and brain-less spirits known as angels.

 

 

Since I have dared to speculate this far, perhaps we can speculate as to whether any intelligent extraterrestrials persons or any so-called ultra-terrestrials persons that are more cognitively evolved then we ordinary humans might be capable of experiencing large absolute valued terms of Wn. Some such ETI and UTI persons may  have evolved over billions of years, or perhaps have far greater powers of sensation, thought, and intuition such as would seem plausible for any such persons and their civilizations who have not fallen from the state of innocence into the state of sin as we humans have, or perhaps such beings never had the option of  sanctifying grace opened to them but nonetheless may have been created at a naturally more perfect level then we humans, and who therefore might exhibit greater natural powers of thought and sensation.

 

 

 

 

 

 

 

 

 

 

 

 

We can also express will qualitatively, statistically, and perhaps with the use of some forms of real analyses as a derivative with respect  memory or of m.

 

Given that W(m) =  W(t and/or w and/or a and/or i and/or m) or perhaps the following notation can be more appropriate in certain circumstances.

 

 

 

 

Thus the following first order derivatives of will with respect to memory are possible.

 

 

dW(t)/dm, dW(w)/dm, dW(a)/dm, dW(i)/dm, dW(m)/dm, dW(t,w)/dm, dW(t,a)/dm, dW(t,i)/dm, dW(t,m)/dm, dW(w,a)/dm, dW(w,i)/dm, dW(w,m)/dm, dW(a,i)/dm, dW(a,m)/dm, dW(i,m)/dm, dW(t,w,a)/dm, dW(t,w,i)/dm, dW(t,w,m)/dm, dW(t,a,i)/dm, dW(t,a,m)/dm, dW(t,i,m)/dm, dW(w,a,i)/dm, dW(w,a,m)/dm, dW(w,i,m)/dm, dW(a,i,m)/dm, dW(t,w,a,i)/dm, dW(t,w,a,m)/dm, dW(t,w,i,m)/dm, dW(t,a,i,m)/dm, dW(w,a,i,m)/dm, dW(t,w,a,i,m)/dm.

 

 

Or more succinctly,  dW/dm = dW(t and/or w and/or a and/or i and/or m)/dm

 

 

Or perhaps dW(m)/dm =d W{[t(m)] and/or [w(m)] and/or [a(m)] and/or [i(m)] and/or [m(m)]}/dm.

 

 

Likewise, we can take the second memory derivatives of  W as follows:

 

 

 

d[dW(t)/dm]/dm, d[dW(w)/dm]/dm, d[dW(a)/dm]/dm, d[dW(i)/dm]/dm, d[dW(m)/dm]/dm, d[dW(t,w)/dm]/dm, d[dW(t,a)/dm]/dm, d[dW(t,i)/dm]/dm, d[dW(t,m)/dm]/dm, d[dW(w,a)/dm]/dm, d[dW(w,i)/dm]/dm, d[dW(w,m)/dm]/dm, d[dW(a,i)/dm]/dm, d[dW(a,m)/dm]/dm, d[dW(i,m)/dm/dm, d[dW(t,w,a)/dm]/dm, d[dW(t,w,i)/dm]/dm, d[dW(t,w,m)/dm]/dm, d[dW(t,a,i)/dm]/dm, d[dW(t,a,m)/dm]/dm,  d[dW(t,i,m)/dm]/dm, d[dW(w,a,i)/dm]/dm, d[dW(w,a,m)/dm]/dm, d[dW(w,i,m)/dm]/dm, d[dW(a,i,m)/dm]/dm, d[dW(t,w,a,i)/dm]/dm, d[dW(t,w,a,m)/dm/dm, d[dW(t,w,i,m)/dm]/dm, d[dW(t,a,i,m)/dm]/dm, d[dW(w,a,i,m)/dm]/dm, d[dW(t,w,a,i,m)/dm]/dm..

 

 

or more succinctly, as d(dW/dm)/dm = d[d W(t and/or w and/or a and/or i and/or m)/dm]/dm = Wm2

 

 

or as

 

 

d[dW(m)/dm]/dm  = d[d W{[t(m)] and/or [w(m)] and/or [a(m)] and/or [i(m)] and/or [m(m)]}/dm]/dm = Wm2.

 

 

 

Likewise, we can take the third memory derivatives of  W as follows:

 

 

 

d[d[dW(t)/dm]/dm]/dm, d[d[dW(w)/dm]/dm]/dm, d[d[dW(a)/dm]/dm]/dm, d[d[dW(i)/dm]/dm]/dm, d[d[dW(m)/dm]/dm]/dm, d[d[dW(t,w)/dm]/dm]/dm, d[d[dW(t,a)/dm]/dm]/dm, d[d[dW(t,i)/dm]/dm]/dm, d[d[dW(t,m)/dm]/dm]/dm, d[d[dW(w,a)/dm]/dm]/dm, d[d[dW(w,i)/dm]/dm]/dm, d[d[dW(w,m)/dm]/dm]/dm, d[d[dW(a,i)/dm]/dm]/dm, d[d[dW(a,m)/dm]/dm]/dm, d[d[dW(i,m)/dm/dm]/dm, d[d[dW(t,w,a)/dm]/dm]/dm, d[d[dW(t,w,i)/dm]/dm]/dm, d[d[dW(t,w,m)/dm]/dm]/dm, d[d[dW(t,a,i)/dm]/dm]/dm, d[d[dW(t,a,m)/dm]/dm]/dm,  d[d[dW(t,i,m)/dm]/dm]/dm, d[d[dW(w,a,i)/dm]/dm]/dm, d[d[dW(w,a,m)/dm]/dm]/dm, d[d[dW(w,i,m)/dm]/dm]/dm, d[d[dW(a,i,m)/dm]/dm]/dm, d[d[dW(t,w,a,i)/dm]/dm]/dm, d[d[dW(t,w,a,m)/dm/dm]/dm, d[d[dW(t,w,i,m)/dm]/dm]/dm, d[d[dW(t,a,i,m)/dm]/dm]/dm, d[d[dW(w,a,i,m)/dm]/dm]/dm, d[d[dW(t,w,a,i,m)/dm]/dm]/dm.

 

 

or more succinctly, as d[d(dW/dm)/dm]/dm = d[d[d W(t and/or w and/or a and/or i and/or m)/dm]/dm]/dm = Wm3

 

 

or as

 

 

d[d[dW(m)/dm]/dm]/dm  = d[d[d W{[t(m)] and/or [w(m)] and/or [a(m)] and/or [i(m)] and/or [m(m)]}/dm]/dm]/dm = Wm3.

 

 

We can also form the expressions;

 

 

d[d[f(W)]/dm]/dm = d{d [W[t(m)]]/dm and/or d[W[w(m)]]/dm and/or d[W[a(m)]]/dm and/or d[W[i(m)]]/dm and/or d[W[m(m)]]/dm}/dm  = f(Wm)2

 

 

and

 

 

d[d[d[f(W)]/dm]/dm]/dm = d{d{ d [W[t(m)]]/dm and/or d[W[w(m)]]/dm and/or d[W[a(m)]]/dm and/or d[W[i(m)]]/dm and/or d[W[m(m)]]/dm}/dm}/dm  = f(Wm)3A, where A stands for type A differentiation which is not to be confused with the meaning of so-called Type A personality as A is used as an ordinal in a totally different context here.

 

 

and

 

 

d[d[d[f(W)]/dm]/dm]/dm = d{d[d [W[t(m)]]/dm]/dm  and/or d[d [W[w(m)]]/dm]/dm  and/or d[d [W[a(m)]]/dm]/dm  and/or d[d [W[i(m)]]/dm]/dm  and/or d[d [W[m(m)]]/dm]/dm }/dm = f(Wm)3B, where B stands for type B differentiation which is not to be confused with the meaning of so-called Type  B personality as B is used as an ordinal in a totally different context here .

 

 

In fact, one can form yet higher order derivatives of will with respect to memory as follows.

 

 

Wm5 = d Wm4/dm = d[dWm3/dm]/dm

 

 

 

Wm5 = dWm4/dm =  d[d[d[d[d W{[t(m)] and/or [w(m)] and/or [a(m)] and/or [i(m)] and/or [m(m)]}/dm]/dm]/dm]/dm]/dm.

 

 

 

f(Wm)5A = d[f(Wm)4A]/dm = d[d [f(Wm)3A]/dm]/dm =  d{d{d{d{ d [W[t(m)]]/dm and/or d[W[w(m)]]/dm and/or d[W[a(m)]]/dm and/or d[W[i(m)]]/dm and/or d[W[m(m)]]/dm}/dm}/dm]/dm]/dm

 

 

 

 

Wm6 = d Wm5/dm = d[d Wm4/dm]/dm = d[d[dWm3/dm]/dm]/dm

 

 

 

Wm6 = dWm5/dm = d[d[d[d[d[d W{[t(m)] and/or [w(m)] and/or [a(m)] and/or [i(m)] and/or [m(m)]}/dm]/dm]/dm]/dm]/dm]/dm

 

 

 

f(Wm)6A = d[f(Wm)5A]/dm = d{ d{d{d{d{ d [W[t(m)]]/dm and/or d[W[w(m)]]/dm and/or d[W[a(m)]]/dm and/or d[W[i(m)]]/dm and/or d[W[m(m)]]/dm}/dm}/dm]/dm]/dm]/dm

 

 

 

 

Wm7 = dWm6/dm

 

f(Wm)7A = d[f(Wm)6A]/dm

 

 

Wm8 = d Wm7/dm

 

f(Wm)8A = d[f(Wm)7A]/dm

 

 

 

Wm9 = d Wm8/dm

 

f(Wm)9A = d[f(Wm)8A]/dm

 

 

Wm10…, Wm11…, Wm12 … etc.

 

 

Anyone for Wm ensemble, or Wm infinity scrapper, or Wm (Aleph 0), or Wm(Aleph 1), or Wm (Aleph 2), or how about Wm Aleph (Aleph 0), or Wm Aleph (Aleph 1) , or Wm Aleph (Aleph 2), or even Wm Aleph (Aleph (Aleph 0)), or Wm Aleph (Aleph (Aleph 1)), or Wm Aleph (Aleph (Aleph 2)), and so on?

 

Thus, for the set of the sets of derivatives of Wm1 through Wm(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Wm1 through Wm (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)},…, {П(0,31)[R]}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Wm 1 through Wm (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Wm 1 through Wm (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the derivative states in the set of the sets of derivatives of Wm 1 through I(Aleph 0) is plausible equal to:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Wm 1 through Wm (Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Wm 1 through Wm (Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}}}.

 

For the set of the sets of derivatives of Wm 1 through Wm (Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Wm I(Aleph 0) derivative space at the level of 0/(Aleph 0), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Wm 1 through Wm (Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Wm 1 through Wm (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Wm 1 through Wm (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Wm 1 through Wm (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Wm 1 through Wm (Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Wm 1 through Wm (Aleph 1), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Wm 1 through  Wm (Aleph 2), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Wm I1 through Wm (Aleph 3), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Wm (Aleph 0) derivative space at the level of 0/(Aleph 1), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Wm 1 through Wm (Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Wm 1 through Wm (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Wm 1 through Wm (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Wm 1 through  Wm (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations  for the set of the sets of derivatives of Wm 1 through Wm (Aleph 0) is plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Wm 1 through Wm (Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Wm 1 through Wm (Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Wm 1 through Wm (Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

 

For super-continuous Wm (Aleph 0) derivative space at the level of 0/(Aleph 2), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Wm 1 through Wm (Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Wm 1 through Wm (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Wm 1 through Wm (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Wm I1 through Wm (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Wm 1 through Wm (Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Wm I1 through Wm (Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Wm 1 through Wm (Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Wm I1 through Wm (Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

Similar series can be developed for super-continuity at any applicable level such as 0/(Aleph 3), 0/(Aleph 4), 0/(Aleph 5),…, 0/(Aleph Ω), 0/(Aleph (Aleph 0)), …, 0/(Aleph (Aleph 1)), …, 0/(Aleph (Aleph 2)), …, 0/(Aleph (Aleph 3)),…, 0/(Aleph (Aleph Ω)),…, 0/(Aleph (Aleph (Aleph 0))), …, 0/(Aleph (Aleph (Aleph 1))),…, 0/(Aleph (Aleph (Aleph 2))),…, 0/(Aleph (Aleph (Aleph 3))),…, 0/(Aleph (Aleph  (Aleph Ω))), …

 

An so-on ad infinitum.

 

 

In addition to these numerical functions of Wm as functions of summation series of product series functions, in order to really appreciate the enourmous complexity of the human soul in terms of its potential to evolve and be differentiated from all other souls in its characteristics, we would need to consider how every single category and even every single species of acts of will of the form Wm can very. Since there may exist an arbitrarily high infinite number species of Wm, the number of numerical functions of Wm is utterly beyond recogning. I will cover such notions in terms of mathematical notation in yet another series of articles I will write on this general concept.

 

 

Perhaps these numbers are applicable when one considers that the human soul, in its accidental form and perhaps even in its substantial form stores all experience and other psychodynamics based phenomenon. Every experience adds to the accidental form of the human soul and this includes the souls of all those still alive on Earth, all those in Purgatory, all those in Heaven, all those in Hell, and all those in any Limbo.

Since the human soul can grow without limit in terms of its psychodynamic time –flow world line, such a consideration offers another mechanism where the number of derivative states, combinations of derivative states, and even super-continuity of the derivative state space can grow forever.

 

Folks, for those of you who might balk at me for including literally all souls in the above consideration, including the souls in Hell, as well as bodily extraterrestrial souls and the souls of so-called bodily ultraterrestials sometimes referred to as etherians in the new age UFO buff culture, my reply is that we simply do not understand the full scope of GOD’s Divine Economy. We may never fully comprehend the scope of the Divine Economy because such an utterly eternal scheme, is, well, eternal and never ending.

 

 

The general meaning of memory derivatives of will can be viewed as the manner in which the qualitative and/or quantitative aspects of will as a function of memory very with acts of will. The manner in which acts of will very with memory may be multi-act-of-will dimensional wherein the dimensions of derivations can be multiple, and wherein the derivations can be taken in parallel, series parallel or serial manner The differentials can be partial or non-partial derivatives, or both partial and non-partial for a given computation.

 

In fact, since there is in theory, no limit to the numbers of qualitatively and quantitatively different acts of will, and perhaps no limit to the number of possible different types or classes of acts of will, wherein each person has his or her own unique acts of will, the number of memory dimensions that can effect acts of will is literally infinite, given the entirety of the set of created persons, and perhaps also literally infinite for each person as an individual, although we can not intellectually and intuitively understand this specific infinite number.

 

It is interesting to consider the ramifactions of being able to perform realistic calculations involving memory derivatives of will from a mathematical, theoretical, scientific,  and philosophical perspective.

 

Persons for which one or more nth order derivatives of will with respect to memory that have large absolute values would tend to have their wills highly influenced by memory, or at least for the acts of will under consideration with respect to the dimension of the specific memory type(s) or class(es) for which the differentiation(s) are performed. Perhaps a strong coupling between will and memory indicates a well integrated personality and commensurately, a high degree of thought capacity and a high degree of volitional intelligence.

 

We would expect that disembodied human souls, ETI souls, and/or UTI souls in Heaven, Limbo, highly evolved bodily ETI persons, highly evolved UTI persons, and angels to have wills of all kinds and intensities which are highly subject to memory.

 

 

The general meaning of memory derivatives of will can be viewed as the manner in which the qualitative and/or quantitative aspects of will as a function of memory very with memory. The manner in which volitions very with memory may be multi- memory-aspect dimensional wherein the dimensions of derivations can be multiple, and wherein the derivations can be taken in parallel, series parallel or in serial manner. The differentials can be partial or non-partial derivatives, or both partial and non-partial for a given computation.

 

In fact, since there is in theory, no limit to the numbers of qualitatively and quantitatively different memories, and perhaps no limit to the number of possible different types or classes of memories, wherein each person has his or her own unique memories, the number of memory dimensions that can effect will is literally infinite, given the entirety of the set of created persons, and perhaps also literally infinite for each person as an individual, although we can not intellectually and intuitively understand this infinite number.

 

 

It is interesting to consider the ramifactions of being able to perform realistic calculations involving memory derivatives of will from a mathematical, theoretical, scientific,  and philosophical perspective.

 

Persons for which one or more nth order derivatives of will with respect to memory that have large absolute values would tend to have their wills highly influenced by memory, or at least for the volitions under consideration with respect to the dimension of the specific memory act type(s) or class(es) for which the differentiation(s) are being performed. Perhaps a strong coupling between will and memory indicates a well integrated personality and commensurately, a high degree of volitional capacity and a high degree of volitional  intelligence as well as perhaps very strong memory power.

 

We would expect that disembodied human souls, ETI souls, and/or UTI souls in Heaven, Limbo, highly evolved bodily ETI persons, highly evolved UTI persons, and angels to have volitions of all kinds and intensities which are perhaps  highly subject to powereful memorys such as spiritual memorys, psychological memories, emotional memories, intellectual memories, interpersonal memories, auto-biographical memories, and even perhaps, memories facilitated by advanced psychic powers.

 

 

We can also consider that two dimensional nth ordered derivatives of will with respect to memory and time, or with respect to i and T, respectively.

 

Given that W[(m)(T)] =  W[(t and/or w and/or a and/or i and/or m)(m)(T)], the following first order two dimensional derivatives of will with respect to memory and Time are possible.

 

 

d[dW[(t)(T)]/dm]/dT, d[dW[(w)(T)]/dm]/dT, d[dW[(a)(T)]/dm]/dT, d[dW[(i)(T)]/dm]/dT, d[dW[(m)(T)]/dm]/dT, d[dW[(t,w)(T)]/dm]/dT, d[dW[(t,a)(T)]/dm]/dT, d[dW[(t,i)(T)]/dm]/dT, d[dW[(t,m)(T)]/dm]/dT, d[dW[(w,a)(T)]/dm]/dT, d[dW[(w,i)(T)]/dm]/dT, d[dW[(w,m)(T)]/dm]/dT, d[dW[(a,i)(T)]/dm]/dT, d[dW[(a,m)(T)]/dm]/dT, d[dW[(i,m)(T)]/dm]/dT, d[dW[(t,w,a)(T)]/dm]/dT, d[dW[(t,w,i)(T)]/dm]/dT, d[dW[(t,w,m)(T)]/dm]/dT, d[dW[(t,a,i)(T)]/dm]/dT, d[dW[(t,a,m)(T)]/dm]/dT, d[dW[(t,i,m)(T)]/dm]/dT, d[dW[(w,a,i)(T)]/dm]/dT, d[dW[(w,a,m)(T)]/dm]/dT, d[dW[(w,i,m)(T)]/dm]/dT, d[dW[(a,i,m)(T)]/dm]/dT, d[dW[(t,w,a,i)(T)]/dm]/dT, d[dW[(t,w,a,m)(T)]/dm]/dT, d[dW[(t,w,i,m)(T)]/dm]/dT, d[dW[(t,a,i,m)(T)]/dm]/dT, d[dW[(w,a,i,m)(T)]/dm]/dT, d[dW[(t,w,a,i,m)(T)]/dm]/dT.

 

 

Or more succinctly,  d[dW(T)/dm]/dT = d[dW[(T)(t and/or w and/or a and/or m and/or m)]/dm]/dT

 

or

 

d[dW(T)/dT]/dm = d[dW[(T)(t and/or w and/or a and/or i and/or m)]/dT]/dm

 

 

 

 

 

Or perhaps d[d W[(m)(T)]/dm]/dT  = d[d W [{[t(m)] and/or [w(m)] and/or [a(m)] and/or [i(m)] and/or [m(m)]}(T)]/dm]/dT

 

or

 

Or perhaps d[d W[(m)(T)]/dT]/dm  = d[d W [{[t(m)] and/or [w(m)] and/or [a(i)] and/or [i(m)] and/or [m(m)]}(T)]/dT]/dm

 

 

 

Likewise, we can take the second dual dimension memory -time derivatives of  W as follows:

 

d[d[d[dW[(t)(T)]/dm]/dT]/dm]/dT, d[d[d[dW[(w)(T)]/dm]/dT]/dm]/dT, d[d[d[dW[(a)(T)]/dm]/dT]/dm]/dT, d[d[d[dW[(i)(T)]/dm]/dT]/dm]/dT, d[d[d[dW[(m)(T)]/dm]/dT]/dm]/dT, d[d[d[dW[(t,w)(T)]/dm]/dT]/dm]/dT, d[d[d[dW[(t,a)(T)]/dm]/dT]/dm]/dT, d[d[d[dW[(t,i)(T)]/dm]/dT]/dm]/dT, d[d[d[dW[(t,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dW[(w,a)(T)]/dm]/dT]/dm]/dT, d[d[d[dW[(w,i)(T)]/dm]/dT]/dm]/dT, d[d[d[dW[(w,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dW[(a,i)(T)]/dm]/dT]/dm]/dT, d[d[d[dW[(a,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dW[(i,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dW[(t,w,a)(T)]/dm]/dT]/dm]/dT, d[d[d[dW[(t,w,i)(T)]/dm]/dT]/dm]/dT, d[d[d[dW[(t,w,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dW[(t,a,i)(T)]/dm]/dT]/dm]/dT, d[d[d[dW[(t,a,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dW[(t,i,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dW[(w,a,i)(T)]/dm]/dT]/dm]/dT, d[d[d[dW[(w,a,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dW[(w,i,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dW[(a,i,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dW[(t,w,a,i)(T)]/dm]/dT]/dm]/dT, d[d[d[dW[(t,w,a,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dW[(t,w,i,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dW[(t,a,i,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dW[(w,a,i,m)(T)]/dm]/dT]/dm]/dT, d[d[d[dW[(t,w,a,i,m)(T)]/dm]/dT]/dm]/dT.

 

or as:

 

 

 

d[d[d[dW[(t)(T)]/dm]/dT]/dT]/dm, d[d[d[dW[(w)(T)]/dm]/dT]/dT]/dm, d[d[d[dW[(a)(T)]/dm]/dT]/dT]/dm, d[d[d[dW[(i)(T)]/dm]/dT]/dT]/dm, d[d[d[dW[(m)(T)]/dm]/dT]/dT]/dm, d[d[d[dW[(t,w)(T)]/dm]/dT]/dT]/dm, d[d[d[dW[(t,a)(T)]/dm]/dT]/dT]/dm, d[d[d[dW[(t,i)(T)]/dm]/dT]/dT]/dm, d[d[d[dW[(t,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dW[(w,a)(T)]/dm]/dT]/dT]/dm, d[d[d[dW[(w,i)(T)]/dm]/dT]/dT]/dm, d[d[d[dW[(w,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dW[(a,i)(T)]/dm]/dT]/dT]/dm, d[d[d[dW[(a,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dW[(i,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dW[(t,w,a)(T)]/dm]/dT]/dT]/dm, d[d[d[dW[(t,w,i)(T)]/dm]/dT]/dT]/dm, d[d[d[dW[(t,w,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dW[(t,a,i)(T)]/dm]/dT]/dT]/dm, d[d[d[dW[(t,a,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dW[(t,i,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dW[(w,a,i)(T)]/dm]/dT]/dT]/dm, d[d[d[dW[(w,a,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dW[(w,i,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dW[(a,i,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dW[(t,w,a,i)(T)]/dm]/dT]/dT]/dm, d[d[d[dW[(t,w,a,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dW[(t,w,i,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dW[(t,a,i,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dW[(w,a,i,m)(T)]/dm]/dT]/dT]/dm, d[d[d[dW[(t,w,a,i,m)(T)]/dm]/dT]/dT]/dm.

 

or as:

 

d[d[d[dW[(t)(T)]/dT]/dm]/dm]/dT, d[d[d[dW[(w)(T)]/dT]/dm]/dm]/dT, d[d[d[dW[(a)(T)]/dT]/dm]/dm]/dT, d[d[d[dW[(i)(T)]/dT]/dm]/dm]/dT, d[d[d[dW[(m)(T)]/dT]/dm]/dm]/dT, d[d[d[dW[(t,w)(T)]/dT]/dm]/dm]/dT, d[d[d[dW[(t,a)(T)]/dT]/dm]/dm]/dT, d[d[d[dW[(t,i)(T)]/dT]/dm]/dm]/dT, d[d[d[dW[(t,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dW[(w,a)(T)]/dT]/dm]/dm]/dT, d[d[d[dW[(w,i)(T)]/dT]/dm]/dm]/dT, d[d[d[dW[(w,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dW[(a,i)(T)]/dT]/dm]/dm]/dT, d[d[d[dW[(a,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dW[(i,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dW[(t,w,a)(T)]/dT]/dm]/dm]/dT, d[d[d[dW[(t,w,i)(T)]/dT]/dm]/dm]/dT, d[d[d[dW[(t,w,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dW[(t,a,i)(T)]/dT]/dm]/dm]/dT, d[d[d[dW[(t,a,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dW[(t,i,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dW[(w,a,i)(T)]/dT]/dm]/dm]/dT, d[d[d[dW[(w,a,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dW[(w,i,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dW[(a,i,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dW[(t,w,a,i)(T)]/dT]/dm]/dm]/dT, d[d[d[dW[(t,w,a,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dW[(t,w,i,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dW[(t,a,i,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dW[(w,a,i,m)(T)]/dT]/dm]/dm]/dT, d[d[d[dW[(t,w,a,i,m)(T)]/dT]/dm]/dm]/dT.

 

 

or as;

 

 

 

 

d[d[d[dW(t)/dm]/dm]/dT]/dT, d[d[d[dW(w)/dm]/dm]/dT]/dT, d[d[d[dW(a)/dm]/dm]/dT]/dT, d[d[d[dW(i)/dm]/dm]/dT]/dT, d[d[d[dW(m)/dm]/dm]/dT]/dT, d[d[d[dW(t,w)/dm]/dm]/dT]/dT, d[d[d[dW(t,a)/dm]/dm]/dT]/dT, d[d[d[dW(t,i)/dm]/dm]/dT]/dT, d[d[d[dW(t,m)/dm]/dm]/dT]/dT, d[d[d[dW(w,a)/dm]/dm]/dT]/dT, d[d[d[dW(w,i)/dm]/dm]/dT]/dT, d[d[d[dW(w,m)/dm]/dm]/dT]/dT, d[d[d[dW(a,i)/dm]/dm]/dT]/dT, d[d[d[dW(a,m)/dm]/dm]/dT]/dT, d[d[d[dW(i,m)/dm]/dm]/dT]/dT, d[d[d[dW(t,w,a)/dm]/dm]/dT]/dT, d[d[d[dW(t,w,i)/dm]/dm]/dT]/dT, d[d[d[dW(t,w,m)/dm]/dm]/dT]/dT, d[d[d[dW(t,a,i)/dm]/dm]/dT]/dT, d[d[d[dW(t,a,m)/dm]/dm]/dT]/dT,  d[d[d[dW(t,i,m)/dm]/dm]/dT]/dT, d[d[d[dW(w,a,i)/dm]/dm]/dT]/dT, d[d[d[dW(w,a,m)/dm]/dm]/dT]/dT, d[d[d[dW(w,i,m)/dm]/dm]/dT]/dT, d[d[d[dW(a,i,m)/dm]/dm]/dT]/dT, d[d[d[dW(t,w,a,i)/dm]/dm]/dT]/dT, d[d[d[dW(t,w,a,m)/dm/dm, d[d[d[dW(t,w,i,m)/dm]/dm]/dT]/dT, d[d[d[dW(t,a,i,m)/dm]/dm]/dT]/dT, d[d[d[dW(w,a,i,m)/dm]/dm]/dT]/dT, d[d[d[dW(t,w,a,i,m)/dm]/dm]/dT]/dT..

 

or as:

 

d[d[d[dW(t)/dT]/dm]/dT]/dm, d[d[d[dW(w)/dT]/dm]/dT]/dm, d[d[d[dW(a)/dT]/dm]/dT]/dm, d[d[d[dW(i)/dT]/dm]/dT]/dm, d[d[d[dW(m)/dT]/dm]/dT]/dm, d[d[d[dW(t,w)/dT]/dm]/dT]/dm, d[d[d[dW(t,a)/dT]/dm]/dT]/dm, d[d[d[dW(t,i)/dT]/dm]/dT]/dm, d[d[d[dW(t,m)/dT]/dm]/dT]/dm, d[d[d[dW(w,a)/dT]/dm]/dT]/dm, d[d[d[dW(w,i)/dT]/dm]/dT]/dm, d[d[d[dW(w,m)/dT]/dm]/dT]/dm, d[d[d[dW(a,i)/dT]/dm]/dT]/dm, d[d[d[dW(a,m)/dT]/dm]/dT]/dm, d[d[d[dW(i,m)/ dT]/dm]/dT]/dm, d[d[d[dW(t,w,a)/dT]/dm]/dT]/dm, d[d[d[dW(t,w,i)/dT]/dm]/dT]/dm, d[d[d[dW(t,w,m)/dT]/dm]/dT]/dm, d[d[d[dW(t,a,i)/dT]/dm]/dT]/dm, d[d[d[dW(t,a,m)/dT]/dm]/dT]/dm,  d[d[d[dW(t,i,m)/dT]/dm]/dT]/dm, d[d[d[dW(w,a,i)/dT]/dm]/dT]/dm, d[d[d[dW(w,a,m)/dT]/dm]/dT]/dm, d[d[d[dW(w,i,m)/dT]/dm]/dT]/dm, d[d[d[dW(a,i,m)/dT]/dm]/dT]/dm, d[d[d[dW(t,w,a,i)/dT]/dm]/dT]/dm, d[d[d[dW(t,w,a,m)/dm/dm, d[d[d[dW(t,w,i,m)/dT]/dm]/dT]/dm, d[d[d[dW(t,a,i,m)/dT]/dm]/dT]/dm, d[d[d[dW(w,a,i,m)/dT]/dm]/dT]/dm, d[d[d[dW(t,w,a,i,m)/dT]/dm]/dT]/dm..

 

or as:

 

d[d[d[dW(t)/dT]/dT]/dm]/dm, d[d[d[dW(w)/dT]/dT]/dm]/dm, d[d[d[dW(a)/dT]/dT]/dm]/dm, d[d[d[dW(i)/dT]/dT]/dm]/dm, d[d[d[dW(m)/dT]/dT]/dm]/dm, d[d[d[dW(t,w)/dT]/dT]/dm]/dm, d[d[d[dW(t,a)/dT]/dT]/dm]/dm, d[d[d[dW(t,i)/dT]/dT]/dm]/dm, d[d[d[dW(t,m)/dT]/dT]/dm]/dm, d[d[d[dW(w,a)/dT]/dT]/dm]/dm, d[d[d[dW(w,i)/dT]/dT]/dm]/dm, d[d[d[dW(w,m)/dT]/dT]/dm]/dm, d[d[d[dW(a,i)/dT]/dT]/dm]/dm, d[d[d[dW(a,m)/ dT]/dT]/dm]/dm, d[d[d[dW(i,m)/ dT]/dT]/dm]/dm, d[d[d[dW(t,w,a)/dT]/dT]/dm]/dm, d[d[d[dW(t,w,i)/dT]/dT]/dm]/dm, d[d[d[dW(t,w,m)/dT]/dT]/dm]/dm, d[d[d[dW(t,a,i)/dT]/dT]/dm]/dm, d[d[d[dW(t,a,m)/dT]/dT]/dm]/dm,  d[d[d[dW(t,i,m)/dT]/dT]/dm]/dm, d[d[d[dW(w,a,i)/dT]/dT]/dm]/dm, d[d[d[dW(w,a,m)/dT]/dT]/dm]/dm, d[d[d[dW(w,i,m)/dT]/dT]/dm]/dm, d[d[d[dW(a,i,m)/dT]/dT]/dm]/dm, d[d[d[dW(t,w,a,i)/dT]/dT]/dm]/dm, d[d[d[dW(t,w,a,m)/dm/dm, d[d[d[dW(t,w,i,m)/dT]/dT]/dm]/dm, d[d[d[dW(t,a,i,m)/dT]/dT]/dm]/dm, d[d[d[dW(w,a,i,m)/dT]/dT]/dm]/dm, d[d[d[dW(t,w,a,i,m)/dT]/dT]/dm]/dm..

 

We can also take higher order duel dimensional derivatives of will as a function of memory and time but the symbolic expression of the set of such derivatives very soon becomes excessively lengthly to write and so these higher order derivatives as such are not mentioned here except to say that they would be computed in an analogous manner to the second order duel dimensional derivatives described above.

 

 

 

These seemingly crazy differentials might have some use in extreme psychological states that can be experienced by souls who are departed and whose wills are not limited by a body and its brain.

 

 

Another type of being that might experience such extreme volition change capacities might be none other then some of our friends we believe to exist as pure body-less and brain-less spirits known as angels.

 

 

Since I have dared to speculate this far, perhaps we can speculate as to whether any intelligent extraterrestrials persons or any so-called ultra-terrestrials persons that are more cognitively evolved then we ordinary humans might be capable of experiencing large absolute valued terms of Wn. Some such ETI and UTI persons may  have evolved over billions of years, or perhaps have far greater powers of sensation, thought, and intuition such as would seem plausible for any such persons and their civilizations who have not fallen from the state of innocence into the state of sin as we humans have, or perhaps such beings never had the option of  sanctifying grace opened to them but nonetheless may have been created at a naturally more perfect level then we humans, and who therefore might exhibit greater natural powers of thought and sensation.

 

Given that W(w) =  W(t and/or w and/or a and/or i and/or m), the following first order derivatives of will  with respect to will are possible.

 

 

dW(t)/dW, dW(w)/dW, dW(a)/dW, dW(i)/dW, dW(m)/dW, dW(t,w)/dW, dW(t,a)/dW, dW(t,i)/dW, dW(t,m)/dW, dW(w,a)/dW, dW(w,i)/dW, dW(w,m)/dW, dW(a,i)/dW, dW(a,m)/dW, dW(i,m)/dW, dW(t,w,a)/dW, dW(t,w,i)/dW, dW(t,w,m)/dW, dW(t,a,i)/dW, dW(t,a,m)/dW, dW(t,i,m)/dW, dW(w,a,i)/dW, dW(w,a,m)/dW, dW(w,i,m)/dW, dW(a,i,m)/dW, dW(t,w,a,i)/dW, dW(t,w,a,m)/dW, dW(t,w,i,m)/dW, dW(t,a,i,m)/dW, dW(w,a,i,m)/dW, dW(t,w,a,i,m)/dW.

 

 

Or more succinctly,  dW/dW = dW(t and/or w and/or a and/or i and/or m)/dW

 

 

Or perhaps dW(w)/dW =d W{[t(w)] and/or [w(w)] and/or [a(w)] and/or [i(w)] and/or [m(w)]}/dW.

 

 

Likewise, we can take the second will derivatives of  W as follows:

 

 

 

d[dW(t)/dW]/dW, d[dW(w)/dW]/dW, d[dW(a)/dW]/dW, d[dW(i)/dW]/dW, d[dW(m)/dW]/dW, d[dW(t,w)/dW]/dW, d[dW(t,a)/dW]/dW, d[dW(t,i)/dW]/dW, d[dW(t,m)/dW]/dW, d[dW(w,a)/dW]/dW, d[dW(w,i)/dW]/dW, d[dW(w,m)/dW]/dW, d[dW(a,i)/dW]/dW, d[dW(a,m)/dW]/dW, d[dW(i,m)/dW/dW, d[dW(t,w,a)/dW]/dW, d[dW(t,w,i)/dW]/dW, d[dW(t,w,m)/dW]/dW, d[dW(t,a,i)/dW]/dW, d[dW(t,a,m)/dW]/dW,  d[dW(t,i,m)/dW]/dW, d[dW(w,a,i)/dW]/dW, d[dW(w,a,m)/dW]/dW, d[dW(w,i,m)/dW]/dW, d[dW(a,i,m)/dW]/dW, d[dW(t,w,a,i)/dW]/dW, d[dW(t,w,a,m)/dW/dW, d[dW(t,w,i,m)/dW]/dW, d[dW(t,a,i,m)/dW]/dW, d[dW(w,a,i,m)/dW]/dW, d[dW(t,w,a,i,m)/dW]/dW..

 

 

or more succinctly, as d(dW/dW)/dW = d[d W(t and/or w and/or a and/or i and/or m)/dW]/dW = Ww2

 

 

or as

 

 

d[dW(w)/dW]/dW  = d[d W{[t(w)] and/or [w(w)] and/or [a(w)] and/or [i(w)] and/or [m(w)]}/dW]/dW = Ww2.

 

 

 

Likewise, we can take the third will derivatives of  W as follows:

 

 

 

d[d[dW(t)/dW]/dW]/dW, d[d[dW(w)/dW]/dW]/dW, d[d[dW(a)/dW]/dW]/dW, d[d[dW(i)/dW]/dW]/dW, d[d[dW(m)/dW]/dW]/dW, d[d[dW(t,w)/dW]/dW]/dW, d[d[dW(t,a)/dW]/dW]/dW, d[d[dW(t,i)/dW]/dW]/dW, d[d[dW(t,m)/dW]/dW]/dW, d[d[dW(w,a)/dW]/dW]/dW, d[d[dW(w,i)/dW]/dW]/dW, d[d[dW(w,m)/dW]/dW]/dW, d[d[dW(a,i)/dW]/dW]/dW, d[d[dW(a,m)/dW]/dW]/dW, d[d[dW(i,m)/dW/dW]/dW, d[d[dW(t,w,a)/dW]/dW]/dW, d[d[dW(t,w,i)/dW]/dW]/dW, d[d[dW(t,w,m)/dW]/dW]/dW, d[d[dW(t,a,i)/dW]/dW]/dW, d[d[dW(t,a,m)/dW]/dW]/dW,  d[d[dW(t,i,m)/dW]/dW]/dW, d[d[dW(w,a,i)/dW]/dW]/dW, d[d[dW(w,a,m)/dW]/dW]/dW, d[d[dW(w,i,m)/dW]/dW]/dW, d[d[dW(a,i,m)/dW]/dW]/dW, d[d[dW(t,w,a,i)/dW]/dW]/dW, d[d[dW(t,w,a,m)/dW/dW]/dW, d[d[dW(t,w,i,m)/dW]/dW]/dW, d[d[dW(t,a,i,m)/dW]/dW]/dW, d[d[dW(w,a,i,m)/dW]/dW]/dW, d[d[dW(t,w,a,i,m)/dW]/dW]/dW.

 

 

or more succinctly, as d[d(dW/dW)/dW]/dW = d[d[d W(t and/or w and/or a and/or i and/or m)/dW]/dW]/dW = Ww3

 

 

or as

 

 

d[d[dW(w)/dW]/dW]/dW  = d[d[d W{[t(w)] and/or [w(w)] and/or [a(w)] and/or [i(w)] and/or [m(w)]}/dW]/dW]/dW = Ww3.

 

 

We can also form the expressions;

 

 

d[d[f(W)]/dW]/dW = d{d [W[t(w)]]/dW and/or d[W[w(w)]]/dW and/or d[W[a(w)]]/dW and/or d[W[i(w)]]/dW and/or d[W[m(w)]]/dW}/dW  = f(Ww)2

 

 

and

 

 

d[d[d[f(W)]/dW]/dW]/dW = d{d{ d [W[t(w)]]/dW and/or d[W[w(w)]]/dW and/or d[W[a(w)]]/dW and/or d[W[i(w)]]/dW and/or d[W[m(w)]]/dW}/dW}/dW  = f(Ww)3A, where A stands for type A differentiation which is not to be confused with the meaning of so-called Type A personality as A is used as an ordinal in a totally different context here.

 

 

and

 

 

d[d[d[f(W)]/dW]/dW]/dW = d{d[d [W[t(w)]]/dW]/dW  and/or d[d [W[w(w)]]/dW]/dW  and/or d[d [W[a(w)]]/dW]/dW  and/or d[d [W[i(w)]]/dW]/dW  and/or d[d [W[m(w)]]/dW]/dW }/dW = f(Ww)3B, where B stands for type B differentiation which is not to be confused with the meaning of so-called Type  B personality as B is used as an ordinal in a totally different context here .

 

 

In fact, one can form yet higher order derivatives of will with respect to will as follows.

 

 

Ww5 = d Ww4/dW = d[dWw3/dW]/dW

 

 

 

Ww5 = dWw4/dW =  d[d[d[d[d W{[t(w)] and/or [w(w)] and/or [a(w)] and/or [i(w)] and/or [m(w)]}/dW]/dW]/dW]/dW]/dW.

 

 

 

f(Ww)5A = d[f(Ww)4A]/dW = d[d [f(Ww)3A]/dW]/dW =  d{d{d{d{ d [W[t(w)]]/dW and/or d[W[w(w)]]/dW and/or d[W[a(w)]]/dW and/or d[W[i(w)]]/dW and/or d[W[m(w)]]/dW}/dW}/dW]/dW]/dW

 

 

 

 

Ww6 = d Ww5/dW = d[d Ww4/dW]/dW = d[d[dWt3/dW]/dW]/dW

 

 

 

Ww6 = dWw5/dW = d[d[d[d[d[d W{[t(w)] and/or [w(w)] and/or [a(w)] and/or [i(w)] and/or [m(w)]}/dW]/dW]/dW]/dW]/dW]/dW

 

 

 

f(Ww)6A = d[f(Ww)5A]/dW = d{ d{d{d{d{ d [W[t(w)]]/dW and/or d[W[w(w)]]/dW and/or d[W[a(w)]]/dW and/or d[W[i(w)]]/dW and/or d[W[m(w)]]/dW}/dW}/dW]/dW]/dW]/dW

 

 

 

 

Ww7 = dWw6/dW

 

f(Ww)7A = d[f(Ww)6A]/dW

 

 

Ww8 = d Ww7/dW

 

f(Ww)8A = d[f(Ww)7A]/dW

 

 

 

Ww9 = d Ww8/dW

 

f(Ww)9A = d[f(Ww)8A]/dW

 

 

Ww10…, Ww11…, Ww12 … etc.

 

 

Anyone for Ww ensemble, or Ww infinity scrapper, or Ww (Aleph 0), or Ww(Aleph 1), or Ww(Aleph 2), or how about Ww Aleph (Aleph 0), or Ww Aleph (Aleph 1) , or WwAleph (Aleph 2), or even Ww Aleph (Aleph (Aleph 0)), or Ww Aleph (Aleph (Aleph 1)), or Ww Aleph (Aleph (Aleph 2)), and so on?

 

Thus, for the set of the sets of derivatives of Ww1 through Ww(Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ww1 through Ww (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)},…, {П(0,31)[R]}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ww 1 through Ww (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ww 1 through Ww (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the derivative states in the set of the sets of derivatives of Ww 1 through I(Aleph 0) is plausible equal to:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ww 1 through Ww (Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ww 1 through Ww (Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)}}}.

 

For the set of the sets of derivatives of Ww 1 through Ww (Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31)[R]}₁ + {П(0,31)[R]}₂ + {П(0,31)[R]}₃ + … + {П(0,31)[R]}_Ω  + .. + {П(0,31)[R]}_{(Aleph 0)}+ … + {П(0,31)[R]}_{(Aleph 1)} + …+{П(0,31)[R]}_{(Aleph 2)} + …+{П(0,31)[R]}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Ww I(Aleph 0) derivative space at the level of 0/(Aleph 0), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Ww 1 through Ww (Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ww 1 through Ww (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ww 1 through Ww (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ww 1 through Ww (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Ww 1 through Ww (Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ww 1 through Ww (Aleph 1), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Ww 1 through  Ww (Aleph 2), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Ww I1 through Ww (Aleph 3), the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 0)}}₁ + {П(0,31){[R] x (Aleph 0)}}₂ + {П(0,31){[R] x (Aleph 0)}}₃ + … + {П(0,31){[R] x (Aleph 0)}}_Ω  + .. + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 0)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 0)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

For super-continuous Ww (Aleph 0) derivative space at the level of 0/(Aleph 1), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Ww 1 through Ww (Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ww 1 through Ww (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ww 1 through Ww (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ww 1 through  Ww (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations  for the set of the sets of derivatives of Ww 1 through Ww (Aleph 0) is plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ww 1 through Ww (Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Ww 1 through Ww (Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Ww 1 through Ww (Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 1)}}₁ + {П(0,31){[R] x (Aleph 1)}}₂ + {П(0,31){[R] x (Aleph 1)}}₃ + … + {П(0,31){[R] x (Aleph 1)}}_Ω  + .. + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 1)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 1)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

 

 

For super-continuous Ww (Aleph 0) derivative space at the level of 0/(Aleph 2), the following analogous formulas apply.

 

Thus, for the set of the sets of derivatives of Ww 1 through Ww (Aleph 0),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}.

 

For the set of the sets of derivatives of Ww 1 through Ww (Aleph 1),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}.

 

For the set of the sets of derivatives of Ww 1 through Ww (Aleph 2),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}.

 

For the set of the sets of derivatives of Ww I1 through Ww (Aleph 3),  the number of possible derivative states is plausibly equal to {П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}.

 

and so on ad infinitum.

 

The total number of subset combinations of the above derivative states is for the set of the sets of derivatives of Ww 1 through Ww (Aleph 0) plausibly equal to:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}}} – 1

 

For the set of the sets of derivatives of Ww I1 through Ww (Aleph 1) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)},…, {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)}}}- 1

 

For the set of the sets of derivatives of Ww 1 through Ww (Aleph 2) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)}}}

 

For the set of the sets of derivatives of Ww I1 through Ww (Aleph 3) derivative states, the total number is:

 

{2 EXP {{П(0,31){[R] x (Aleph 2)}}₁ + {П(0,31){[R] x (Aleph 2)}}₂ + {П(0,31){[R] x (Aleph 2)}}₃ + … + {П(0,31){[R] x (Aleph 2)}}_Ω  + .. + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 0)}+ … + {П(0,31){[R] x (Aleph 2)}}_{(Aleph 1)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 2)} + …+{П(0,31){[R] x (Aleph 2)}}_{(Aleph 3)}}}

 

and so on, ad infinitum.

 

Similar series can be developed for super-continuity at any applicable level such as 0/(Aleph 3), 0/(Aleph 4), 0/(Aleph 5),…, 0/(Aleph Ω), 0/(Aleph (Aleph 0)), …, 0/(Aleph (Aleph 1)), …, 0/(Aleph (Aleph 2)), …, 0/(Aleph (Aleph 3)),…, 0/(Aleph (Aleph Ω)),…, 0/(Aleph (Aleph (Aleph 0))), …, 0/(Aleph (Aleph (Aleph 1))),…, 0/(Aleph (Aleph (Aleph 2))),…, 0/(Aleph (Aleph (Aleph 3))),…, 0/(Aleph (Aleph  (Aleph Ω))), …

 

An so-on ad infinitum.

 

 

In addition to these numerical functions of Ww as functions of summation series of product series functions, in order to really appreciate the enourmous complexity of the human soul in terms of its potential to evolve and be differentiated from all other souls in its characteristics, we would need to consider how every single category and even every single species of will of the form Ww can very. Since there may exist an arbitrarily high infinite number species of Ww, the number of numerical functions of Ww is utterly beyond recogning. I will cover such notions in terms of mathematical notation in yet another series of articles I will write on this general concept.

 

 

Perhaps these numbers are applicable when one considers that the human soul, in its accidental form and perhaps even in its substantial form stores all experience and other psychodynamics based phenomenon. Every experience adds to the accidental form of the human soul and this includes the souls of all those still alive on Earth, all those in Purgatory, all those in Heaven, all those in Hell, and all those in any Limbo.

Since the human soul can grow without limit in terms of its psychodynamic time –flow world line, such a consideration offers another mechanism where the number of derivative states, combinations of derivative states, and even super-continuity of the derivative state space can grow forever.

 

Folks, for those of you who might balk at me for including literally all souls in the above consideration, including the souls in Hell, as well as bodily extraterrestrial souls and the souls of so-called bodily ultraterrestials sometimes referred to as etherians in the new age UFO buff culture, my reply is that we simply do not understand the full scope of GOD’s Divine Economy. We may never fully comprehend the scope of the Divine Economy because such an utterly eternal scheme, is, well, eternal and never ending.

 

 

The general meaning of will derivatives of will can be viewed as the manner in which the qualitative and/or quantitative aspects of will as a function of will very with acts of will(s). The manner in which acts of will very with acts of will may be multi-act-of-will dimensional wherein the dimensions of derivations can be multiple, and wherein the derivations can be taken in parallel, series parallel or serial manner The differentials can be partial or non-partial derivatives, or both partial and non-partial for a given computation.

 

In fact, since there is in theory, no limit to the numbers of qualitatively and quantitatively different acts of will, and perhaps no limit to the number of possible different types or classes of acts of will, wherein each person has his or her own unique acts of will, the number of volitional dimensions that can effect acts of will is literally infinite, given the entirety of the set of created persons, and perhaps also literally infinite for each person as an individual, although we can not intellectually and intuitively understand this specific infinite number.

 

It is interesting to consider the ramifactions of being able to perform realistic calculations involving volitional derivatives of will from a mathematical, theoretical, scientific,  and philosophical perspective.

 

Persons for which one or more nth order derivatives of will with respect to will that have large absolute values would tend to have their wills highly influenced by acts of will, or at least for the acts of will under consideration with respect to the dimension of the specific thought type(s) or class(es) for which the differentiation(s) are performed. Perhaps a strong coupling between voliton and will indicates a well integrated personality and commensurately, a high degree of thought capacity and a high degree of volitional intelligence.

 

We would expect that disembodied human souls, ETI souls, and/or UTI souls in Heaven, Limbo, highly evolved bodily ETI persons, highly evolved UTI persons, and angels to have wills of all kinds and intensities which are highly subject to acts of volition.

 

 

The general meaning of will derivatives of will can be viewed as the manner in which the qualitative and/or quantitative aspects of will as a function of will very with volitions(s). The manner in which will very with will may be multi-will dimensional wherein the dimensions of derivations can be multiple, and wherein the derivations can be taken in parallel, series parallel or serial manner The differentials can be partial or non-partial derivatives, or both partial and non-partial for a given computation.

 

In fact, since there is in theory, no limit to the numbers of qualitatively and quantitatively different volitions, and perhaps no limit to the number of possible different types or classes of volitions, wherein each person has his or her own unique volitions, the number of will dimensions that can effect will is literally infinite, given the entirety of the set of created persons, and perhaps also literally infinite for each person as an individual, although we can not intellectually and intuitively understand this specific infinite number.

 

It is interesting to consider the ramifactions of being able to perform realistic calculations involving will derivatives of will from a mathematical, theoretical, scientific,  and philosophical perspective.

 

Persons for which one or more nth order derivatives of will with respect to will that have large absolute values would tend to have their volitions highly influenced by will, or at least for the volitions under consideration with respect to the dimension of the specific volition type(s) or class(es) for which the differentiation(s) are performed. Perhaps a strong coupling between will and will indicates a well integrated personality and commensurately, a high degree of will capacity and a high degree of will intelligence.

 

We would expect that disembodied human souls, ETI souls, and/or UTI souls in Heaven, Limbo, highly evolved bodily ETI persons, highly evolved UTI persons, and angels to have volitions of all kinds and intensities which are highly subject to spiritual volitions.

 

 

We can also consider two dimensional nth ordered derivatives of will with respect to will and time, or with respect to E and T, respectively.

 

Given that W[(w)(T)] =  W[(t and/or w and/or a and/or i and/or m)(w)(T)], the following first order two dimensional derivatives of will with respect to will and Time are possible.

 

 

d[dW[(t)(T)]/dW]/dT, d[dW[(w)(T)]/dW]/dT, d[dW[(a)(T)]/dW]/dT, d[dW[(i)(T)]/dW]/dT, d[dW[(m)(T)]/dW]/dT, d[dW[(t,w)(T)]/dW]/dT, d[dW[(t,a)(T)]/dW]/dT, d[dW[(t,i)(T)]/dW]/dT, d[dW[(t,m)(T)]/dW]/dT, d[dW[(w,a)(T)]/dW]/dT, d[dW[(w,i)(T)]/dW]/dT, d[dW[(w,m)(T)]/dW]/dT, d[dW[(a,i)(T)]/dW]/dT, d[dW[(a,m)(T)]/dW]/dT, d[dW[(i,m)(T)]/dW]/dT, d[dW[(t,w,a)(T)]/dW]/dT, d[dW[(t,w,i)(T)]/dW]/dT, d[dW[(t,w,m)(T)]/dW]/dT, d[dW[(t,a,i)(T)]/dW]/dT, d[dW[(t,a,m)(T)]/dW]/dT, d[dW[(t,i,m)(T)]/dW]/dT, d[dW[(w,a,i)(T)]/dW]/dT, d[dW[(w,a,m)(T)]/dW]/dT, d[dW[(w,i,m)(T)]/dW]/dT, d[dW[(a,i,m)(T)]/dW]/dT, d[dW[(t,w,a,i)(T)]/dW]/dT, d[dW[(t,w,a,m)(T)]/dW]/dT, d[dW[(t,w,i,m)(T)]/dW]/dT, d[dW[(t,a,i,m)(T)]/dW]/dT, d[dW[(w,a,i,m)(T)]/dW]/dT, d[dW[(t,w,a,i,m)(T)]/dW]/dT.

 

 

Or more succinctly,  d[dW(T)/dW]/dT = d[dW[(T)(t and/or w and/or a and/or i and/or m)]/dW]/dT

 

or

 

d[dW(T)/dT]/dW = d[dW[(T)(t and/or w and/or a and/or i and/or m)]/dT]/dW

 

 

 

 

 

Or perhaps d[d W[(w)(T)]/dW]/dT  = d[d W [{[t(w)] and/or [w(w)] and/or [a(w)] and/or [i(w)] and/or [m(w)]}(T)]/dW]/dT

 

or

 

Or perhaps d[d W[(w)(T)]/dT]/dW  = d[d W [{[t(w)] and/or [w(w)] and/or [a(w)] and/or [i(w)] and/or [m(w)]}(T)]/dT]/dW

 

 

 

Likewise, we can take the second dual dimensioned will-time derivatives of  W as follows:

 

d[d[d[dW[(t)(T)]/dW]/dT]/dW]/dT, d[d[d[dW[(w)(T)]/dW]/dT]/dW]/dT, d[d[d[dW[(a)(T)]/dW]/dT]/dW]/dT, d[d[d[dW[(i)(T)]/dW]/dT]/dW]/dT, d[d[d[dW[(m)(T)]/dW]/dT]/dW]/dT, d[d[d[dW[(t,w)(T)]/dW]/dT]/dW]/dT, d[d[d[dW[(t,a)(T)]/dW]/dT]/dW]/dT, d[d[d[dW[(t,i)(T)]/dW]/dT]/dW]/dT, d[d[d[dW[(t,m)(T)]/dW]/dT]/dW]/dT, d[d[d[dW[(w,a)(T)]/dW]/dT]/dW]/dT, d[d[d[dW[(w,i)(T)]/dW]/dT]/dW]/dT, d[d[d[dW[(w,m)(T)]/dW]/dT]/dW]/dT, d[d[d[dW[(a,i)(T)]/dW]/dT]/dW]/dT, d[d[d[dW[(a,m)(T)]/dW]/dT]/dW]/dT, d[d[d[dW[(i,m)(T)]/dW]/dT]/dW]/dT, d[d[d[dW[(t,w,a)(T)]/dW]/dT]/dW]/dT, d[d[d[dW[(t,w,i)(T)]/dW]/dT]/dW]/dT, d[d[d[dW[(t,w,m)(T)]/dW]/dT]/dW]/dT, d[d[d[dW[(t,a,i)(T)]/dW]/dT]/dW]/dT, d[d[d[dW[(t,a,m)(T)]/dW]/dT]/dW]/dT, d[d[d[dW[(t,i,m)(T)]/dW]/dT]/dW]/dT, d[d[d[dW[(w,a,i)(T)]/dW]/dT]/dW]/dT, d[d[d[dW[(w,a,m)(T)]/dW]/dT]/dW]/dT, d[d[d[dW[(w,i,m)(T)]/dW]/dT]/dW]/dT, d[d[d[dW[(a,i,m)(T)]/dW]/dT]/dW]/dT, d[d[d[dW[(t,w,a,i)(T)]/dW]/dT]/dW]/dT, d[d[d[dW[(t,w,a,m)(T)]/dW]/dT]/dW]/dT, d[d[d[dW[(t,w,i,m)(T)]/dW]/dT]/dW]/dT, d[d[d[dW[(t,a,i,m)(T)]/dW]/dT]/dW]/dT, d[d[d[dW[(w,a,i,m)(T)]/dW]/dT]/dW]/dT, d[d[d[dW[(t,w,a,i,m)(T)]/dW]/dT]/dW]/dT.

 

or as:

 

 

 

d[d[d[dW[(t)(T)]/dW]/dT]/dT]/dW, d[d[d[dW[(w)(T)]/dW]/dT]/dT]/dW, d[d[d[dW[(a)(T)]/dW]/dT]/dT]/dW, d[d[d[dW[(i)(T)]/dW]/dT]/dT]/dW, d[d[d[dW[(m)(T)]/dW]/dT]/dT]/dW, d[d[d[dW[(t,w)(T)]/dW]/dT]/dT]/dW, d[d[d[dW[(t,a)(T)]/dW]/dT]/dT]/dW, d[d[d[dW[(t,i)(T)]/dW]/dT]/dT]/dW, d[d[d[dW[(t,m)(T)]/dW]/dT]/dT]/dW, d[d[d[dW[(w,a)(T)]/dW]/dT]/dT]/dW, d[d[d[dW[(w,i)(T)]/dW]/dT]/dT]/dW, d[d[d[dW[(w,m)(T)]/dW]/dT]/dT]/dW, d[d[d[dW[(a,i)(T)]/dW]/dT]/dT]/dW, d[d[d[dW[(a,m)(T)]/dW]/dT]/dT]/dW, d[d[d[dW[(i,m)(T)]/dW]/dT]/dT]/dW, d[d[d[dW[(t,w,a)(T)]/dW]/dT]/dT]/dW, d[d[d[dW[(t,w,i)(T)]/dW]/dT]/dT]/dW, d[d[d[dW[(t,w,m)(T)]/dW]/dT]/dT]/dW, d[d[d[dW[(t,a,i)(T)]/dW]/dT]/dT]/dW, d[d[d[dW[(t,a,m)(T)]/dW]/dT]/dT]/dW, d[d[d[dW[(t,i,m)(T)]/dW]/dT]/dT]/dW, d[d[d[dW[(w,a,i)(T)]/dW]/dT]/dT]/dW, d[d[d[dW[(w,a,m)(T)]/dW]/dT]/dT]/dW, d[d[d[dW[(w,i,m)(T)]/dW]/dT]/dT]/dW, d[d[d[dW[(a,i,m)(T)]/dW]/dT]/dT]/dW, d[d[d[dW[(t,w,a,i)(T)]/dW]/dT]/dT]/dW, d[d[d[dW[(t,w,a,m)(T)]/dW]/dT]/dT]/dW, d[d[d[dW[(t,w,i,m)(T)]/dW]/dT]/dT]/dW, d[d[d[dW[(t,a,i,m)(T)]/dW]/dT]/dT]/dW, d[d[d[dW[(w,a,i,m)(T)]/dW]/dT]/dT]/dW, d[d[d[dW[(t,w,a,i,m)(T)]/dW]/dT]/dT]/dW.

 

or as:

 

d[d[d[dW[(t)(T)]/dT]/dW]/dW]/dT, d[d[d[dW[(w)(T)]/dT]/dW]/dW]/dT, d[d[d[dW[(a)(T)]/dT]/dW]/dW]/dT, d[d[d[dW[(i)(T)]/dT]/dW]/dW]/dT, d[d[d[dW[(m)(T)]/dT]/dW]/dW]/dT, d[d[d[dW[(t,w)(T)]/dT]/dW]/dW]/dT, d[d[d[dW[(t,a)(T)]/dT]/dW]/dW]/dT, d[d[d[dW[(t,i)(T)]/dT]/dW]/dW]/dT, d[d[d[dW[(t,m)(T)]/dT]/dW]/dW]/dT, d[d[d[dW[(w,a)(T)]/dT]/dW]/dW]/dT, d[d[d[dW[(w,i)(T)]/dT]/dW]/dW]/dT, d[d[d[dW[(w,m)(T)]/dT]/dW]/dW]/dT, d[d[d[dW[(a,i)(T)]/dT]/dW]/dW]/dT, d[d[d[dW[(a,m)(T)]/dT]/dW]/dW]/dT, d[d[d[dW[(i,m)(T)]/dT]/dW]/dW]/dT, d[d[d[dW[(t,w,a)(T)]/dT]/dW]/dW]/dT, d[d[d[dW[(t,w,i)(T)]/dT]/dW]/dW]/dT, d[d[d[dW[(t,w,m)(T)]/dT]/dW]/dW]/dT, d[d[d[dW[(t,a,i)(T)]/dT]/dW]/dW]/dT, d[d[d[dW[(t,a,m)(T)]/dT]/dW]/dW]/dT, d[d[d[dW[(t,i,m)(T)]/dT]/dW]/dW]/dT, d[d[d[dW[(w,a,i)(T)]/dT]/dW]/dW]/dT, d[d[d[dW[(w,a,m)(T)]/dT]/dW]/dW]/dT, d[d[d[dW[(w,i,m)(T)]/dT]/dW]/dW]/dT, d[d[d[dW[(a,i,m)(T)]/dT]/dW]/dW]/dT, d[d[d[dW[(t,w,a,i)(T)]/dT]/dW]/dW]/dT, d[d[d[dW[(t,w,a,m)(T)]/dT]/dW]/dW]/dT, d[d[d[dW[(t,w,i,m)(T)]/dT]/dW]/dW]/dT, d[d[d[dW[(t,a,i,m)(T)]/dT]/dW]/dW]/dT, d[d[d[dW[(w,a,i,m)(T)]/dT]/dW]/dW]/dT, d[d[d[dW[(t,w,a,i,m)(T)]/dT]/dW]/dW]/dT.

 

 

or as;

 

 

 

 

d[d[d[dW(t)/dW]/dW]/dT]/dT, d[d[d[dW(w)/dW]/dW]/dT]/dT, d[d[d[dW(a)/dW]/dW]/dT]/dT, d[d[d[dW(i)/dW]/dW]/dT]/dT, d[d[d[dW(m)/dW]/dW]/dT]/dT, d[d[d[dW(t,w)/dW]/dW]/dT]/dT, d[d[d[dW(t,a)/dW]/dW]/dT]/dT, d[d[d[dW(t,i)/dW]/dW]/dT]/dT, d[d[d[dW(t,m)/dW]/dW]/dT]/dT, d[d[d[dW(w,a)/dW]/dW]/dT]/dT, d[d[d[dW(w,i)/dW]/dW]/dT]/dT, d[d[d[dW(w,m)/dW]/dW]/dT]/dT, d[d[d[dW(a,i)/dW]/dW]/dT]/dT, d[d[d[dW(a,m)/dW]/dW]/dT]/dT, d[d[d[dW(i,m)/dW]/dW]/dT]/dT, d[d[d[dW(t,w,a)/dW]/dW]/dT]/dT, d[d[d[dW(t,w,i)/dW]/dW]/dT]/dT, d[d[d[dW(t,w,m)/dW]/dW]/dT]/dT, d[d[d[dW(t,a,i)/dW]/dW]/dT]/dT, d[d[d[dW(t,a,m)/dW]/dW]/dT]/dT,  d[d[d[dW(t,i,m)/dW]/dW]/dT]/dT, d[d[d[dW(w,a,i)/dW]/dW]/dT]/dT, d[d[d[dW(w,a,m)/dW]/dW]/dT]/dT, d[d[d[dW(w,i,m)/dW]/dW]/dT]/dT, d[d[d[dW(a,i,m)/dW]/dW]/dT]/dT, d[d[d[dW(t,w,a,i)/dW]/dW]/dT]/dT, d[d[d[dW(t,w,a,m)/dW/dW, d[d[d[dW(t,w,i,m)/dW]/dW]/dT]/dT, d[d[d[dW(t,a,i,m)/dW]/dW]/dT]/dT, d[d[d[dW(w,a,i,m)/dW]/dW]/dT]/dT, d[d[d[dW(t,w,a,i,m)/dW]/dW]/dT]/dT..

 

or as:

 

d[d[d[dW(t)/dT]/dW]/dT]/dW, d[d[d[dW(w)/dT]/dW]/dT]/dW, d[d[d[dW(a)/dT]/dW]/dT]/dW, d[d[d[dW(i)/dT]/dW]/dT]/dW, d[d[d[dW(m)/dT]/dW]/dT]/dW, d[d[d[dW(t,w)/dT]/dW]/dT]/dW, d[d[d[dW(t,a)/dT]/dW]/dT]/dW, d[d[d[dW(t,i)/dT]/dW]/dT]/dW, d[d[d[dW(t,m)/dT]/dW]/dT]/dW, d[d[d[dW(w,a)/dT]/dW]/dT]/dW, d[d[d[dW(w,i)/dT]/dW]/dT]/dW, d[d[d[dW(w,m)/dT]/dW]/dT]/dW, d[d[d[dW(a,i)/dT]/dW]/dT]/dW, d[d[d[dW(a,m)/dT]/dW]/dT]/dW, d[d[d[dW(i,m)/ dT]/dW]/dT]/dW, d[d[d[dW(t,w,a)/dT]/dW]/dT]/dW, d[d[d[dW(t,w,i)/dT]/dW]/dT]/dW, d[d[d[dW(t,w,m)/dT]/dW]/dT]/dW, d[d[d[dW(t,a,i)/dT]/dW]/dT]/dW, d[d[d[dW(t,a,m)/dT]/dW]/dT]/dW,  d[d[d[dW(t,i,m)/dT]/dW]/dT]/dW, d[d[d[dW(w,a,i)/dT]/dW]/dT]/dW, d[d[d[dW(w,a,m)/dT]/dW]/dT]/dW, d[d[d[dW(w,i,m)/dT]/dW]/dT]/dW, d[d[d[dW(a,i,m)/dT]/dW]/dT]/dW, d[d[d[dW(t,w,a,i)/dT]/dW]/dT]/dW, d[d[d[dW(t,w,a,m)/dW/dW, d[d[d[dW(t,w,i,m)/dT]/dW]/dT]/dW, d[d[d[dW(t,a,i,m)/dT]/dW]/dT]/dW, d[d[d[dW(w,a,i,m)/dT]/dW]/dT]/dW, d[d[d[dW(t,w,a,i,m)/dT]/dW]/dT]/dW..

 

or as:

 

d[d[d[dW(t)/dT]/dT]/dW]/dW, d[d[d[dW(w)/dT]/dT]/dW]/dW, d[d[d[dW(a)/dT]/dT]/dW]/dW, d[d[d[dW(i)/dT]/dT]/dW]/dW, d[d[d[dW(m)/dT]/dT]/dW]/dW, d[d[d[dW(t,w)/dT]/dT]/dW]/dW, d[d[d[dW(t,a)/dT]/dT]/dW]/dW, d[d[d[dW(t,i)/dT]/dT]/dW]/dW, d[d[d[dW(t,m)/dT]/dT]/dW]/dW, d[d[d[dW(w,a)/dT]/dT]/dW]/dW, d[d[d[dW(w,i)/dT]/dT]/dW]/dW, d[d[d[dW(w,m)/dT]/dT]/dW]/dW, d[d[d[dW(a,i)/dT]/dT]/dW]/dW, d[d[d[dW(a,m)/ dT]/dT]/dW]/dW, d[d[d[dW(i,m)/ dT]/dT]/dW]/dW, d[d[d[dW(t,w,a)/dT]/dT]/dW]/dW, d[d[d[dW(t,w,i)/dT]/dT]/dW]/dW, d[d[d[dW(t,w,m)/dT]/dT]/dW]/dW, d[d[d[dW(t,a,i)/dT]/dT]/dW]/dW, d[d[d[dW(t,a,m)/dT]/dT]/dW]/dW,  d[d[d[dW(t,i,m)/dT]/dT]/dW]/dW, d[d[d[dW(w,a,i)/dT]/dT]/dW]/dW, d[d[d[dW(w,a,m)/dT]/dT]/dW]/dW, d[d[d[dW(w,i,m)/dT]/dT]/dW]/dW, d[d[d[dW(a,i,m)/dT]/dT]/dW]/dW, d[d[d[dW(t,w,a,i)/dT]/dT]/dW]/dW, d[d[d[dW(t,w,a,m)/dW/dW, d[d[d[dW(t,w,i,m)/dT]/dT]/dW]/dW, d[d[d[dW(t,a,i,m)/dT]/dT]/dW]/dW, d[d[d[dW(w,a,i,m)/dT]/dT]/dW]/dW, d[d[d[dW(t,w,a,i,m)/dT]/dT]/dW]/dW..

 

 

We can also take higher order duel dimensional derivatives of will as a function of will and time but the symbolic expression of the set of such derivatives very soon becomes excessively lengthly to write and so these higher order derivatives as such are not mentioned here except to say that they would be computed in an analogous manner to the second order duel dimensional derivatives described above.

 

 

 

 

Now, the above variable of time, T,  can have multiple meanings or aspects. One such meaning is objective time and in such a case for large non-zero values of Wn, where n = 1,2,3,…, the person experiencing such a volition or complex of volitions  might not subjectively experience the volitions(s) as occurring any faster than we ordinary humans do.

 

 

However, another interpretation of the variable of Time is subjective time. In such a case for large non-zero absolute values of Wn, where n = 1,2,3,…, the person experiencing such an act of will  or complex of acts of will  would subjectively experience the volitions(s) as occurring or changing faster than we ordinary humans experience, in fact the higher the absolute value of non-zero Wn, especially for large n, the rate of change of volition with respect to time would progress at an incredible rate. We ordinary humans would likely be completely overwhelmed by subjective psychic experiences of such Wn phenomenon.

 

 

Could there be other objective temporal dimensions beside the one objective temporal dimension that we know of, and the seemingly one subjective dimension of time that we experience? As someone who normally writes on the topic of exotic space craft propulsion systems such as proposed interstellar space craft propulsion systems, I am familiar with the theoretical paradigms that there may exist higher dimensions of space and perhaps more than one dimension of time, and so I say, never say never.

 

The above notation of derivatives and differential equations is just an infinitesimal glimpse of the number of possible equations as such and related constructs. Trust me, I can reasonably in good confidence re-assure you of such.

 

 

 

 

 

36) A Human Soul That Can Change Says Something Transcendently Remarkable About The Human Soul

 

Now, you can see that we have vaguely covered only psychodynamic 6 variables as well as time and  6 psychodynamic parameter variable derivatives as well as time derivatives .

 

The number of such expressions even at the general level considered herein is much, much, greater, and even greater  yet when one considers that the number of known psychodynamic variables is most likely, and in my opinion is, much, much,  greater that those known by psychologists and sociologists.

 

When we consider spirituality at the natural and supernatural level, most especially at the level of grace, then the number of general variables is as great as the number and forms of graces and individual vocations and spiritual natural and supernatural psychodynamic spectrum profiles.

 

In consideration that each natural and supernatural psychodynamic variable is lived out in each Human, ET, and UT person, in a unique manner, the complexity of the Soul’s set of natural and supernatural characteristics, features, and nuances is beyond comprehension.

This is especially true providing that the Human Soul in its characteristics and faculties is both super-continuous and very ontologically and existentially simple.

 

Such super-continuity and simplicity offer a human psyche with incomprehensibly vast infinite numbers of potential non-linear feed-back mechanisms or non-linear self-interaction mechanisms, of which in this life we experience only a miniscule portion of those that currently operate within our psyches.

 

Now by super-continuity, I mean continuous in a mathematical sense of 0/∞ at the least where the value of infinity can be Ω, Aleph 0, Aleph 1, Aleph 2, …, Aleph Ω, …, Aleph (Aleph 0),…, Aleph (Aleph 1),…, Aleph (Aleph 2),…, Aleph (Aleph Ω), …, Aleph (Aleph (Aleph 0)), …, Aleph (Aleph (Aleph 1)), …, Aleph (Aleph (Aleph 2)), … and this symbolic progression goes on in the form of this condensed notion perhaps forever and also utterly increasing.

 

Why do I make such a bold proclamation regarding the Human Soul? Simple! Because to paraphrase the Holy Bible, “Who but the Lord GOD Almighty can comprehend the tangled workings of the Human Heart? Who but the Lord GOD Almighty can comprehend the complexity of the Human  Heart? Who but the Lord GOD Himself is worthy of judging the intentions and actions of the Human Person beyond refute?” These are only paraphrases, but a good search of the Bible perhaps with the  aid of a concordance  will show you that the above paraphrases lie entirely within the translated meaning of the associated text.

 

Note that I covered only broad categories in developing the  above differential equations. Any hope at even finding a lower bounding limit to human complexity of Heart and Soul would necessarily need to take into account all possible types and forms of the above psychodynamic variables as well as the same for the possible  unlimited number of additional broad psychodynamic variables. Thus, each individual and specific possible thought, emotion, feeling, act of will, affective state, and memory would need to be known with maximal super-continuous precision.

 

Now we Humans are capable of change to an extreme degree and our daily waking consciousness and field of awareness is in constant flux. This is due to the dynamic nature of our conscious life processes. Such dynamism will continue in Heaven and also after the Resurrection of the Dead. Even the Souls who end up in Hell will have their own opportunity for dynamic self-reflection and situational awareness, although the Souls in Hell will undergo so sort of suffering(s) and deprivations of which we have no certain or detailed knowledge as to the specifics.

 

The Souls who go to any Limbo will also have a glorious dynamic life awaiting them and they will be so satisfied that they will not envy those who go to Heaven. In my humble opinion, perhaps the Souls who go to any Limbo, will have a compensatory increase in their natures, so as to make up for not being able to partake of the Beatific Vision.

 

This dynamism within the Human Soul can evolve for all eternity wherever a given Soul ends up. In a sense, a Soul that can change and which is in dynamic accidental flux with regards to its faculties is self-transcendent. This is because the Soul is thereby shown  to change at least with regards to its accidental properties with subjectively and objectively experience time or change and yet remain permanent or un-altered with respect to is essence or substantial nature.

 

My guess is that perhaps the Souls that go any Limbo will have their very nature improved thus perhaps indicating some sort of super-essential property(ies) or aspect(s) of the substance of these souls. However, let us not envy any currently unknown or non-humanly knowable DIVINE Providence for any Souls that go to Limbo. For in Heaven and in Limbo, there will be no inter-Heaven-Limbo rivalry and no experienced need for such either.

 

GOD may indeed have some currently unknown or not yet revealed plan for any Soul’s that go to any Limbo, but let us not get to concerned with such prospects as we need to focus on getting to Heaven.

 

Dynamic conscious sentience is a wonderful manifestation of natural and/or supernatural life of the Human Soul and by corollary, the Souls of any of our ET and UT brothers and sisters.

 

Note that a much more expansive discussion of the complexity of the Human Heart will be covered in a latter post on the subject of the Human Soul and also in a later post on the transcendent dignity of the Human Person.

 

37) The Soul As An Eternal Form

 

Now the human soul according to Saint Thomas Aquinas is the substantial form of the body. By substantial form, I do no mean that it has the same shape-form of the body or that it looks like the body. Instead, what is meant by the term is that it is the ideal, sort of in an abstract way, of what the body is just as say a perfect circle would be the abstract ideal of a geometric circle drawn on a black board during a geometry lecture. Another eternal form is that of GOD whose essence is goodness itself in its ideal form.

 

Now being that each human soul is unique and unrepeatable and is the substantial form of the body it will inform and is or will be united to, that is, the physically eternal form in nature of the body it will inform, each human soul is in a sense a unique eternal form that can be only the form it is and no other form. The number of such eternal forms is absolutely limit-less as can be intuited by the following argument.

 

For example, each real number,  whether positive or negative,  can be considered an abstract form or ideal that is independent of material reality. For instance, we can have three souls, three atoms, three DIVINE PERSONS, three angels and the like. Thus, the number three would have existence even if the physical universe suddenly ceased to exist along with all of its quantitatively  measurable accidents.

 

Well, given that each human soul is the substantial form of the human body it is or was united to, perhaps each human soul can be considered a more complex and rich eternal form than a mere number.

 

To see why, consider that the human soul is the vital natural life principle that constitutes each one of us as a human being. The human soul is the principle of unity, individuality, identity, and uniqueness and then so, a personal life principle as such. Thus,  the human soul is not merely a what but is rather a who. The human soul thus goes beyond a mere metaphysical spiritual entity and therefore is and has the characteristics of personal vital principle existentiality and reality to it.

 

Just as there are an unlimited number of real numbers, even an unlimited number of integers, and even the same for complex numbers, there are an absolutely unlimited number of possible uniquely charactered and personal identitied human souls.

 

Each human soul goes beyond the realm of a mere mathematical or logical entity type of form and exists as a personal life or vital principle type of form with its own unique identity.

 

 

38) The Soul As Self Transcendent.

 

Explaining the immortality of the human soul be reason alone or any natural immortality of the human soul in an absolutely certain and provable manner has been a problem that has vexed spiritual anthropologists since Plato’s time and continues to do so,  even  for contemporary Catholic theologians.

 

However, would a natural immortality of the soul really matter?

 

I will answer this question in the negative in multiple ways.

 

First, a human soul that is not naturally immortal and not naturally incorruptible is nonetheless, immortal, even in all cases for souls that go to Hell. Even in the case that the existence of  some souls would be temporarily disrupted by natural processes not known to  mankind, all such souls would have to be held to be immortal since  they would be re-created and reunited to their  immortalized and incorruptible human body at the End Of Time. Indeed, all souls must absolutely be said to be immortal even under the cases considered in this paragraph. Any soul whose existence might somehow be merely temporarily suspended,  which is a possibility that the Catholic Church does not recognize in terms of its official teachings on the subject, I am absolutely convinced that all such martyred souls will be Resurrected on the last day and  re-united to their  glorious, incorruptible, and immortal resurrected human body on the last day with additional glory as compensation for their martyrdom of  the temporary
Cross of soul death. We should have assurance that, in such a philosophically remote possibility, with the Cross of death comes eternal glory at the final Resurrection.

 

Second, each  human soul is in fact immortal, and will last forever, having the exact self-same identity for all eternity even in cases of souls that go to Hell. Consequently, assuming for the sake of argument that the human soul is not naturally immortal, but rather is held in existence when disconnected from its body at natural death until re-union with its Resurrected and Immortalized body at the End Of Time by an extra act of Divine Power, all human souls would have to be said to possess self-transcendence.

 

The reason for such self-transcendence can be gleaned from the fact that the human soul would continue to exist even though separated from its body at natural death in a fully alive and sentient form. Thus, the human soul would be immortal in spite of itself, or in transcendence of itself. This self-transcendence can be intuited from the fact that each human soul, even the souls that go on to eternal punishment remain unalterably the exact same person that they were created at conception and as they existed while united to their bodies in this life.

 

This principle of being the soul being the soul that it is,  and unalterable never any other soul or never anything or anyone else, last immutably for all eternity. This is so even for the case such that the human soul would be preserved after bodily death by a special act of GOD’s will. The fact that such a human soul would remain its own self and nothing else in an utterly immutable manner while being regenerated from moment to moment by GOD, no matter where or how a given soul will spend its eternity,  points to some principle within the human soul by which the soul is transcendent of its substantial and accidental properties.

 

Quite frankly, even the souls who go to Hell cannot not be the soul that they are as can be seen from the  consistency of eternal punishment. A human soul would have to be utterly physically eternal in order for the moral bindings of eternal punishment to be philosophically and logically self-consistent.

 

Third, if the human soul is immortal by grace and thus might not need an extra-special act of GOD’s will in order to exist after bodily death and before the Final Resurrection, then not only would the soul in all cases possess the supernatural character of gratuitous immortality, but the soul would be immortal in such a manner that it would not need any natural immortality to naturally live forever. In a certain manner, the soul would not need the would be aspect or characteristic of natural immortality to last forever. From the latter fact, it can be roughly intuited that the human soul that is gratuitously immortal is immortal in spite of itself or in spite of its natural would be immortality and is thus  self-transcendent.

 

Since even the souls that go to Hell are immortal, they must also be self-transcendent under the condition the ontological and existential mechanisms mentioned in the previous paragraph are operative.  Provided that human souls are immortal by grace only, then we will therefore necessarily need to draw the conclusion that even the souls condemned to Hell have a very significant level of grace, although nonetheless, not of the types that directly imply the Beatific Vision which they will miss out on. This is a cool concept for me as I can thereby be assured that any souls that go to Hell have supernatural goodness, at least ontological goodness as such, thus perhaps helping alleviate some of the extreme sadness I feel at the notion that some souls go to Hell in numbers known only to GOD. The souls who go to Hell might not ever appreciate this would be fact, but I would.

 

Fourth, even if the human soul can be said to be naturally immortal, contemporary Catholic teaching holds that all creatures whether physical, spiritual, or a combination of the physical and spiritual are maintained and sustained in existence by GOD’s almighty will. A soul that is thus gratuitously immortal might be an exception or perhaps a pseudo-exception to this rule, since it would be Divine Grace or a supernatural character within the soul by which it would be immortal, even in cases of souls who go to Hell.

 

If the human soul would be immortal be grace only, then there would be no additional need for sustenance in existence by GOD. This seems logical because the causative mechanism for the eternal duration of the human soul would not be GOD’s directly holding the human soul in existence, but rather it would be the supernatural aspect of the human soul in the form of certain grace of GOD. GOD never duplicates efforts where such duplication is not necessary or is logically inconsistent. In the latter sense, the existence of a gratuitously immortal soul would be more independent of GOD then would a naturally immortal soul held directly in existence by GOD’s sustaining might.

 

However, for all of you folks who long for the Glory Days of when the Scholasticism of Saint Thomas Aquinas reigned supreme in theological formation programs, have faith. I say this because Saint Thomas did not become the Church’s pre-eminent theologian for no reason at all, rather  instead, for obviously good reasons. Have joy and hope because Saint Thomas Aquinas taught the following regarding the human soul.

 

The human soul is: 1) Spiritual, 2) Naturally immortal, 3) Incorruptible per addends and per se, 4) Simple, 5) Unextended, 6) Without shape or size, 7) Non-material,   8]   Non-corporeal, 9) Rational, 10) Free,  11) A first created principle, 12) An essence or a being which exist per se, 13) Independent of the body for its existence and to some extent its operations in this life, 14) The substantial form of the body in the Ancient Greek philosophical sense of the word, 15) Directly created by God, 16) Immediately created by God, and if I am not mistaken, 17) Multiple meaning that it is completely and totally present and united to every portion of the human body that is alive.

 

For those who pray to find out that the above proposed 17 properties of the human soul are  real, you will either have your prayers answered in an affirmative matter or you will be given something better. GOD will always answer your prayers and will either give you what you ask for or, if not, then something better.

 

39) The Human Soul Ever New

 

Catholic theology is no stranger to the notion that GOD maintains all creatures in existence by HIS all sustaining might, and even accidental creatures indirectly by the accidental creatures subsistence in created first principles where are held in existence directly by GOD.

 

Presumably, the mechanism of DIVINE sustenance is applicable to Human Souls, ETI souls, and UTI souls, as well as for angels.

 

Now,  the Human Soul is accordingly the substantial form of the Human Body it is united to in the Platonic sense of the word “form”.

 

The Human Soul is also accordingly directly and immediately created at the moment of conception or created ex nihilo using no pre-existing material of any form.

Now each Human Soul is precisely the soul that it is in a divinely willed and absolute manner. By definition of the Human Soul as the life or vital principle of identity, individuality, distinction, and uniqueness that constitutes each one of us as human, it seems that the human soul is that aspect of our total being, body and soul, that utterly excels ontologically and existentially, at being our principle of identity, individuality, distinction, and uniqueness, and in short, of our personhood. This makes sense because the human soul is an eternal form, the substantial form of the body it will inform.

Now, how is this relevant to the topic introduced at the beginning of this article?

 

 

First, a Human Soul that is constantly being maintained in existence might be said to be eternally or perhaps temporally continuously regenerated. This re-generacy occurring from moment to moment or perhaps eternally all at once, is commensurate with the idea that the creation of each Human Soul is ever super-abounding. The Human Soul is ever new but yet ever its original self. This fact would seem to almost point to some aspect of the Human Soul by which it is self-transcendent of its mode of continual regeneration. For there must be something about the Human Soul that quite simply is eternally the same, no matter what are modes of the gratuitous, substantial, or accidental evolution of each Human Soul. Thus we seem to arrive at a hyper-metaphysical principle or hyper-substantial principle in Each Human Soul. Such a hyper-substantial principle may imply that as in all creatures, the existence of the Human Soul is not the same as its very core essence.

 

Second, a Human Soul that is constantly being maintained in existence or temporally or eternally continuously regenerated might in a sense be said to be continually existentially refreshed and by corollary substantially refreshed. Thus, each Human Soul might be said to be ever fresh or new or renewed thus implying a certain ontological newness of each soul. Thus, each Human Soul as such is never rotten or gross, but is ever fresh and substantially, existentially, and accidentally supple. This notion is in line with the notion that even the Souls who go to Hell and even the fallen angels have a nature which is inherently ontologically very good even though such souls may act in morally offensive manners.

 

Third, a Human Soul that is continuously refreshed,  either temporally or from eternity,  might be said to be created in an ever super-abundant manner. Since each Human Soul has an identity which is utterly immutably its own, such continuous regeneration, whether in time or from eternity, might be interpreted as an existential and/or substantial or essential growth of the Human Soul in a perpetual manner. Each Human Soul might thus be interpreted as continuously growing or becoming ontologically, existentially, substantially, and accidentally larger.

 

Just as the 4-D space time volume of a physical object in principle becomes larger along the 4^th dimension of ordinary Einsteinian space time or along the dimension of forward time extension into the future, a similar growth of the Human Soul along its world line might analogously follow as a mode of  perpetual growth in another sense than that of the mode of conjectural growth covered in the previous paragraph.

 

40) The Soul Intra-Reactivity

 

Now the Human Soul is self-reactive at least as far as the attributes of its faculties and its accidental properties are concerned.

 

Merely letting one’s mind wonder and intra-react causes new experiences and new psychodynamic accidents to become manifest. Even at the conscious level, the soul’s temporal flow of emotions, thoughts, feelings, impulses, acts of will,  and the like results in the continued development of psychodynamic structures. What happens at the sub-conscious level may be even more profound, and what happens at the unconscious level, is likely even more profound and involves the growth of the unconscious memory. Every conscious, sub-conscious, and unconscious experience adds to the accidental form of the Human Soul.

 

The intra-reactivity of the Human Soul presumably per dues eternally regardless of whether one ends up in Heaven, any Limbo, or Hell. In a sense, the soul continually builds on itself and continues to develop for all future eternity, even in cases where souls who do not make it to Heaven or any  Limbo, would never appreciate this reality.

 

The soul also reacts with its environment, and reacts to its reactions with the environment. It is hard to subjectively intuit in an experiential way how many primary levels of intra-reaction there are. For instance, we can be relatively sure that the soul reacts to its reactions to the external environment and that this second level interaction is one of the primary ones currently experienced in this life. Perhaps a case can be made for the soul’s reactions to its reactions to its reactions  to  the external environment as a third level. Might there exist many more levels, an ensemble of levels, an infinity scrapper of levels, or an arbitrarily infinite number of levels that are currently non-intuitive or cognitively perceptible by us in this life? It is hard to know for certain.

 

Now,  please do not feel that I am somehow sublimely self-aware simply because I have dared to ponder the above notions. I generally consciously operate at only at most the second level awareness and that is being aware of my reactions to my reactions to my environment. For instance, if I get pissed at an intimidating  fellow driver  acting rudely on the road here in the Northern Virginia area within the United States where I live, I can easily become unpleasantly aware of my temporarily feelings of anxiety and insecurity resulting from being flicked off or as a result of a macho stare down session with the rare verbal confrontations I have had with drivers here in the Washington D.C. metro area. By the way, also do not worry about my rare reactions as such, as I have made a decision about 8 years ago to always be different in such situations by calmly looking the other way when folks glare at me. Given the large number of folks who carry concealed firearms,  I decided it is better never to engage this behavior. Anyhow, that is another story all-together.

 

Now,  these levels of intra-reactivity, even if we are aware of only the first, second, and perhaps the third order of such reactivity on rare occasions, point to a sublimely non-linear psychodynamic intra-reactivity and to an awesome complexity within the Human Heart and  the Human Soul, not in terms of its substantial ontology which is simple and un-extended, but rather in terms of the complex existential structures within the faculties of the Human Soul such as within  the Heart, Intellect, Memory, and Will. I suppose that the more levels of such intra-reactivity there are, the more complex the psychodynamic existential and ontological underpinnings are for our conscious, sub-conscious, and un-conscious personal identities.

 

These non-linear psychodynamic attributes of intra-reactivity might be the reason for the realities which are summed up in the following paraphrases of Sacred Scripture;

 

“Who but the Lord GOD Almighty alone can comprehend the tangled workings of the Human Heart!”

 

“Who but the Lord GOD can judge the actions of the Human Person!”

Note that these are only paraphrases, but the meaning behind them is clearly supported by Sacred Scripture.

 

I will post an expanded version of these general by late this month.

 

 

 

 

41)  The Continuous Refreshment Of The Human Soul

 

Catholic theology is no stranger to the notion that GOD maintains all creatures in existence by HIS all sustaining might, and even accidental creatures indirectly by the accidental creatures subsistence in created first principles where are held in existence directly by GOD.Presumably, the mechanism of DIVINE sustenance is applicable to Human Souls, ETI souls, and UTI souls, as well as for angels.

 

 

Now the Human Soul is accordingly the substantial form of the Human Body it is united to in the Platonic sense of the word “form”. The Human Soul is also accordingly directly and immediately created at the moment of conception or created ex nihilo using no pre-existing material of any form.

 

 

Now each Human Soul is precisely the soul that it is in a divinely willed and absolute manner. By definition of the Human Soul as the life or vital principle of identity, individuality, distinction, and uniqueness that constitutes each one of us as human, it seems that the human soul is that aspect of our total being, body and soul, that utterly excels ontologically and existentially, at being our principle of identity, individuality, distinction, and uniqueness, and in short, of our personhood. This makes sense because the human soul is an eternal form, the substantial form of the body it will inform.

 

 

Now, how is this relevant to the topic introduced at the beginning of this article?

First, a Human Soul that is constantly being maintained in existence might be said to be eternally or perhaps temporally continuously regenerated. This re-generacy occurring from moment to moment or perhaps eternally all at once, is commensurate with the idea that the creation of each Human Soul is ever super-abounding. The Human Soul is ever new but yet ever its original self. This fact would seem to almost point to some aspect of the Human Soul by which it is self-transcendent of its mode of continual regeneration. For there must be something about the Human Soul that quite simply is eternally the same, no matter what are modes of the gratuitous, substantial, or accidental evolution of each Human Soul. Thus we seem to arrive at a hyper-metaphysical principle or hyper-substantial principle in Each Human Soul. Such a hyper-substantial principle may imply that as in all creatures, the existence of the Human Soul is not the same as its very core essence.

 

 

Second, a Human Soul that is constantly being maintained in existence or temporally or eternally continuously regenerated might in a sense be said to be continually existentially refreshed and by corollary substantially refreshed. Thus, each Human Soul might be said to be ever fresh or new or renewed thus implying a certain ontological newness of each soul. Thus, each Human Soul as such is never rotten or gross, but is ever fresh and substantially, existentially, and accidentally supple. This notion is in line with the notion that even the Souls who go to Hell and even the fallen angels have a nature which is inherently ontologically very good even though such souls may act in morally offensive manners.

 

 

Third, a Human Soul that is continuously refreshed,  either temporally or from eternity,  might be said to be created in an ever super-abundant manner. Since each Human Soul has an identity which is utterly immutably its own, such continuous regeneration, whether in time or from eternity, might be interpreted as an existential and/or substantial or essential growth of the Human Soul in a perpetual manner.

 

 

Each Human Soul might thus be interpreted as continuously growing or becoming ontologically, existentially, substantially, and accidentally larger.

Just as the 4-D space time volume of a physical object in principle becomes larger along the 4^th dimension of ordinary Einsteinian space time or along the dimension of forward time extension into the future, a similar growth of the Human Soul along its world line might analogously follow as a mode of  perpetual growth in another sense than that of the mode of conjectural growth covered in the previous paragraph.

 

 

42)  GOD KNEW US BEFORE HE FORMED US IN OUR MOTHER’S WOMB

 

Sacred Scripture attest to what we can refer to as fact if we believe in a divinely inspired Holy Bible that GOD knew us before we were formed in our mother’s womb.

 

In a certain limited sense, although not in an ontological substantial and accidental sense, each one of we humans has our roots in GOD’s utterly unfathomably unlimited imagination before the very foundation of the entire Cosmos. If you would like, you might loosely interpret this knowing as a very limited non-existential and non-ontological pre-existence yet without our pre-existing before we were procreated,  in a manner that we simply cannot understand at present.

 

What I am alluding to is not some form of previously life nor a substantial or personal existence before conception, but rather a sort of pre-existing root that led to our creation, a pre-existing root that was GOD’s perfect image of how and when HE would create us from all eternity.

 

The above paraphrase of Sacred Scripture shows just how intimate our existence and ontology is with GOD’s causal act of our creation and just how intimate this act of GOD’s will is with HIS ALMIGHTY INTELLECT.

 

From an existential and ontological standpoint in terms of our substance and accidents, soul and body, we  had no pre-existence or previous life before we were conceived in time in our body and directly and immeadiately created Human Soul.

 

The mystery of our creation, body and soul, and the relationship to our newly created selves to GOD’s  mental conception of how, why, and when we would be created is a profound mystery that is perhaps much more mysterious than the creation of the material Cosmos in terms of the Cosmos’ physical material composition and any non-physical material composition.

 

I am absolutely not trying to support the existence of re-incarnation or past lives as in so-called past life studies involving regressive hypnosis as I believe and the new Catechism Of The Catholic Church states that there is no re-incarnation and that is is appointed for men to be born only once.

 

I am merely trying to state the emphasis Scripture provides for us in terms of the revelation of the mysterious genesis of our creation with the ALMIGHTLY PERSONAL LOVE  that GOD has for Each One Of Us and which calls Each One Of Us by Name and which planned us from All Eternity.

 

If the mystery of the initial creation of the very physical cosmos in terms of its first principle, prime matter, directly and immeadiately created compositon,  is a mystery, then how much greater is the mystery of the creation of each  separate, individual, completely distinct, unique, and unrepeatable Human Soul.

 

The Human Soul, precisely because it is the separate, individual, completely distinct, unique, and unrepeatable life or vital principle that constitutes each one of us as  a free, unique, unrepeatable, autonomous, individual with a totally distinct identity, is in a sense much more of a mystery that the creation of the physical cosmos because each Human Soul, when created and united substantially to a newly conceived embryo in a real sense forms a entirely new and distinct separate microcosm that contains all of the basic elements of creation from those of the purely physical such as the mass-energy and space-time that define our physical bodies to the vegetative life principles that our bodies share with plants, cells, and bacteria, to the emotions, instincts, and senses we share with animals, to the rational, logical, and free volitional powers we share with any bodily ETI and UTI, to the purely spiritual element of our soul which we share in common with the pure spirits known as angels.

 

Each human person is in a sense a separate cosmos to the extent that each human person is a profoundly distinct being and GOD so loved us and so loves us that HE planned each one of us from all eternity, gave HIS only SON  to die on the Cross for each one of us, and calls each one of us as a distinct, autonomous, personal, free, vital, sentient, rational, individual,  and then so by our own very name.

 

43)  ALL HUMAN PERSONS,  ALIVE AND DECEASED,  SHARE A COMMON SOLIDARITY AS FREE AND RATIONAL SPIRITUAL PERSONS WHO EACH HAVE A SPIRITUAL AND IMMORTAL, DIRECTLY AND IMMEADIATELY CREATED SOUL.

 

All human persons, on Earth still, in Heaven, in any Limbo, in Purgatory, and even those unfortunate enough to be consined to Hell will last forever and will retain the natural attributes of their identity, souls, and personalities. When GOD states in Sacred Scripture and the Catholic Church states in Her Supreme and Ordinary Magesterium as well as in Her constant and un-erring tradition that each Human Soul is immortal, we can except these teachings as un-erring fact that cannot be altered for all eternity. Each Human Soul will live forever at least at the natural level regardless of where a given person ends up after death and regardless of the actual mechanism of the immortality of each Human Soul. GOD wills each Human Soul as Immortal and never takes back what HE grants in nature.

 

As Pope John Paul II mentioned in one of his books, I can’t recall which one at the moment, to the extend that the universal eternal life bestowed on humanity by virtue of Christ’s Death and Ressurection is lived out in a life beyond the grave for those consined to Hell is a complete mystery. However, John Paul II states that not even Sacred Scripture can be used to prove that Jude the traitor who handed Christ over to the Roman soldiers went to Hell. Pope John Paul II thus  calls all of us by the words  “Be Not Afraid!”

 

That a Hell exist is also unerring Catholic Doctrine and so we are advised to avoid going there at all personal cost. Why GOD would permit moral evil in HIS creatures and innocent material evil is in a real sense a profound and currenly vielded mystery, perhaps even to the highest Saints in Heaven. Want proof of this latter assertion? Then realize the fact the  just and the unjust at the Final Judgement will say to Our Lord as in the following paraphrase of Sacred Scripture, “Lord, when did we see you hungry, thirsty, alone, imprisoned, naked, or afflicted and when did we feed you, give  you to drink, visit you in prison, clothe you, comfort you when you where ill?” The Lord will accordingly reply as in the following paraphrase, “So long as you witnessed such  and did such for the least of my brethren, you did so unto me.”

 

Yes, it seems that moral theology and its teachings will not even be completely understood by even the just at Final Ressurection. Thus, those languishing in our prisons and in our psyche wards, or as homeless on our city streets, or as addicts in our substance abuse clinics, folks who even many Catholic Clergymen seem to want to ignore,  will in all likelihood be among the least of Christ Brethren who will be among the first. Those ignoring such poor souls who are in positions of authority within the Church and in civil leadership will likely be counted among the first who will be last and may even be turned away from Our Lord at the Final Judgement.

I thus present my case why those who would ordinarilly seem repulsive to those in so-called alpha positions in our society should never be shunned or neglected. There will indeed be many Lazarus’ and Mary Magdelines feasting at Our Lord’s table, perhaps many more than many of promenent Church and civil leaders would expect and like to admit.

 

44) An Ontological Simplicity To The Human Soul? Yes! An Organic Internal Ontological Structure To The Human Soul? Perhaps, And A Way To Arrive At The Great Mystery Of The Human  Heart!

 

Now theologians and philosophers, most especially, theologians who work under the guidelines set by the Vatican are familiar with the concept of a spiritual and immortal soul. What seems a little un-certain is whether or not each human soul is immortal by grace or by its very nature and I have not been able to determine a unanimous agreement among soul-geeks as to which mechanism is correct. If each human soul is immortal by grace, then by definition, even each human soul in Hell has a baseline level of grace instilled by Christ’s merituous  Life, Death on the Cross, and Resurrection. This grace would need to be deep as it would transform the very substance of the human soul in all cases. Regardless, the Catholic Church asserts that each human soul ever created is immortal and will at least naturally live forever.

 

 

But assuming that the human soul has no shape, extensity, and that it is ontologically simple, can anything be said regarding its structural simplicity? From the standpoint of a physicists, I am aware that  the current Standard Model paradigm holds that fundamental particles, both bosons and fermions alike, are simple but not without internal structure. Perhaps a similar heuristic principle can be applied to current understanding of the human soul. To see how consider the following points.

 

 

First, each human soul in its accidental form is imbued with its current and past experiences, both present and active and past and remembered. Every person having his or her own particular experiences can attest to the mental cataloguing  of such experiences and the structural relations between experiences in both current and previously memorized forms. The fact that a person can distinguish between one memorized experience and another is due to the relationships between dissimilar experiences that constitute the perceived uniqueness of each individual experiences. For clearly recalled experiences in the case where the experiences are what I would call para-identical or semi-identical, the subjective sense of when such experiences have occurred in the past by the person having had them still adds a structure to these experiences that sets them apart from each other. Memorized experiences can be cognitive events, intellectual events, volitional events, natural paranormal phenomenon events if such exist,  emotional events, affective events, social events, spiritual events, romantic and sexual events, instinctual events, sensory events, attitudinal events, and a whole host of others. In many cases, the experience categories listed above clearly overlap as very few if any experiences are imbued with only one such discriminating aspect.

 

 

Second, each one of we self-aware humans possesses an objective somato-sense or sense of kinesthesia or an overall sense of our body that has subjectively experienced structures. For example, we are aware that what feels like our hand or our head is subjectively differentiated from what feels like our foot or abdomen. In fact, to a more or less equal extent, but in some cases perhaps relatively extreme extents, we subjectively experience a large number of somato-sense differentiating elements within the sense of kinesthesia that we often experience as our complete body. This is evident to any person who has had their fingernails trimmed as they can feel a pair of scissors cut along the length of an individual fingernail starting with one side of the nail and propagating along the width of the nail to the other side as the nail is gradually but quickly trimmed. Needless to say, the number of examples of such high kinesthesia sense resolution is very large  given the large variety of tactile experiences one is capable of.

 

 

Third, each one of we self-aware humans is aware of our visual, and auditory perceptual fields, and the fantastic detail that the visual field presents to us, such as for example, when we look at a tree-covered mountain peak in the autumn and behold the nuances of the tree leave patterns, and the structure of the tree line, the various visible rocks, boulders, and the undulations in the ground surface of the peak. Another example is the viewing of a partly cloudy sky with all of the structural nuances contained within the clouds. Yet another example is one of an  autumn or winter clear star-lit midnight sky in a dark country location. You can tell by my examples that I have a strong out-doorsman, naturalist, aspect to my psychodynamic make-up. Each of these visual experiences in both static form and temporally varying form, whether presently experienced or memorized, has sensory or imagined structural elements similar in detail to those that are contained within a photographic image or a video or movie. Thus, there is a structural mechanism underwriting the various large scale and nuance-wise features of each visual memory  or current visual experience, each complex auditory memory or current auditory experience, and each tactile memory or current tactile experience.

 

 

I could give even more examples but by now the reader gets the picture.

As for yet another class of examples, consider the following.

 

 

First we are generally heuristically aware of the distinction between our emotions and thoughts although emotions and thoughts often run in parallel and intermesh with each other in normal psychologically healthy humans.

 

As an example, the thought or the concept of a little precious child being abducted and murdered by a stranger usually will elicit a very strong emotional response such as when such tragedies are reported on televised nightly news broadcasts.

 

Likewise, we can distinguish between emotionally pleasant spiritual experiences and an unpleasant visual-auditory emotional experience such as when we are charged by a snarling, teeth bearing dog, especially when the dog runs up to us in a surprising  or unforeseen manner while we are walking around a city block. So we can distinguish between advanced or spiritual emotions and more primitive emotions in the way that we categorize such in our day to day experiences.

 

Likewise, there are  heuristically distinguishable aspects to sexual experiences in terms of spiritual emotions, more primitive emotions and feelings which generally can include tactile feelings as non-limiting examples, and social aspects as well. Even a cerebral nuclear engineer who loves his work  can have emotional experiences connected with his working thinking as he or she is completing a design task out of sheer enjoyment of problem solving, the feeling of success accomplished, or in eager anticipation of bringing the designs to fruition.

 

As a physicist, I have sometimes pondered the potential joy of perhaps at some point getting involved in nuclear submarine nuclear reactor design because in general, I highly enjoy the subject of nuclear energy. If this joy was not present, then I would likely never want anything to do with nuclear reactor design and instead would find another outlet. Thus we can parse, sort, and categorize our psychic spheres because of the inherent structures we objectively and subjectively intuit in our complex of faculties we refer to as our personality, as our mind by some individuals, and more generally, as our psyche by sociologists and psychologists.

 

 

Second, as another example of commonly known heuristically principles regarding psychological anthropology, the human psyche is commonly categorized by the conscious mind, the sub-conscious mind, and the un-conscious mind. Each of these tri-partite divisions is equally valid  except that the quantity of stored information is held to be greatest in the un-conscious which accordingly is the repository of all unconscious memorized experiences. The sub-conscious contains stored experiences that are more or less open for recall on demand; and as such,  accordingly does not quite contain as much data and information as the unconscious. The conscious mind contains all current working experiences of  which a  person is presently aware and as such holds the least quantity of information.

 

 

Another Freudian division of psychic structure is in the categorizing of the ego, super-ego, and id. The ego is said to be the conscious self or identity of the person or that aspect of the human person’s psyche that the person identifies as being his or her self. The super-ego is the set of psychic norms or mores that directs and controls the expression of the id, which is the complex of instincts and impulses, conscious or sub-conscious, that typically can provide motives for acting. The super-ego can be loosely translated in meaning as being the set of moral and ethical guiding principles that guide one’s behavior such as one’s religious faith, attitudes of proper behavior learned from childhood, ethical guidelines in sensitivity training, and the like mechanisms.

 

 

Thirdly, it is natural for the human person to distinguish between his material and immaterial aspects. A person often will distinguish between one’s mind and one’s body such as when a particularly attractive women who as an academic super-achiever is  often hit upon by guys and where this woman will then  mention to her female friends that the guys don’t seem to realize that she also has a mind.

 

 

Even young children can learn to distinguish between their conscious inner self and their sensually perceived environment.

 

 

As yet another class of examples, consider the following taken from the heart of the science of the soul itself.

 

 

First, Scholastics typically categorize the human soul in a tripartite heuristic approach that involves the differentiation between the rational or intellective aspect of the human soul, the sensitive or a feeling aspects of the human soul, and the vegetative aspects of the human soul.

 

 

The rational aspects of the human soul accordingly pertain to the capacity for cognition, reason, free volition, and the spiritual or higher aspects of emotion as implied by the modifier “rational”.

 

 

The sensitive aspects of the human soul accordingly pertain to the emotions, feelings, and capacity for sensory experience and are said to be in common with non-human animal life-forms that exist on Earth.

 

 

The vegetative aspects of the human  soul are accordingly held to be the basic or bodily life sustaining aspects of the human soul and are said to be in common with the plant and other non-animal life-forms that exist on Earth. Animals are held to have souls that possess only the sensitive and vegetative aspects, but in light of the observed high degree on intuitive and intelligent actions by animals in modern animal behavioral studies, I doubt that animals cannot reason deductively and inductively. The notion that humans are the only species on Earth that can make rational and volitional choices is to me a hold-over from outmoded ways of religious thinking. Ask any service men or women who work alongside military work dogs and you will receive numerous accounts of such dogs putting their life on the line to defend their masters and their masters comrades, even to the point of the dogs being killed in action. These K-9 and military work dogs are indeed volitionally, rationally,  and lovingly loyal and can display all of the finesse of a NAVY SEAL by immediately de-escalating  and standing down at the command of their handler at the termination of  fierce combat situations.

 

 

Second, Scholastics also consider a distinction from among the faculties of the human soul such as distinctions between the intellect, the will, the heart or emotions, and the memory. The exact categorization is not completely consistent but you can see the general idea here.

 

 

Third, Scholastics in some cases also distinguish between the essence or the substance of the human soul and the faculties of the human soul and will even make a further distinction as to the accidental aspects of the human soul. Accordingly, each experience adds to the accidental form of the human  soul. The substance or essence of the human soul is accordingly a first created principle that subsists directly by GOD’s creation of each human soul directly and immediately upon human conception. The accidental aspects of the human soul really exist but subsist in or are dependent for their existence on the substantial or essential aspects of the soul much as a block of ice in its accidental form of being a solid cold state of water is an accidental feature of the more primitive material or substance of the constituent water which is composed of water molecules. However, is spiritual anthropology, the substance of the human soul is non-physical and so is not to be confused with the atomic or molecular composition of ordinary matter.

 

 

Fourth, metaphysics especially that which is  taught in theological formation programs within the Catholic Church distinguishes between the essence or nature of a creature and its existence. Accordingly, whereas GOD’s existence and essence and HIS characteristics are the same, for creatures this is not so. For example, it is often said that GOD is not simply just loving, but rather GOD is LOVE. For created persons, this is not the case as there is accordingly a fundamental distinction between a creatures existence and nature and the creatures characteristics. However, it is commonly held that the more elevated the species of creature, the closer is the approximation to indenticality between the creature’s essence or existence and its characteristics.

 

 

Now,  for those of you who want to believe in the natural immortality and natural incorruptibility of the soul, the great theologian of Saint Thomas Aquinas strongly and logically argued in favor of the natural immortality and incorruptibility of the soul. His writings on the subject are still in widespread teaching in formation programs and the new Catholic Catechism does not make counter arguments to Saint Thomas’ teachings, and in fact, it  seems to indorse the spirit of His teachings, although in not as great of detail in terms of the explanation of the immortality of the Human Soul.

 

Note, I also prefer to believe that the Human Soul is naturally immortal, and as a result, not immortal by grace.  But either way, I can assure the reader that each human soul possesses a sublimely great and transcendent dignity and will exist for ever.

 

Also, once again, note the Scholastic interpretation as promulgated by Saint Aquinas of the nature of the human soul, that is the human soul is:  1) Spiritual, 2) Naturally immortal, 3) Incorruptible per addends and per se, 4) Simple, 5) Unextended, 6) Without shape or size, 7) Non-material,   8]   Non-corporeal, 9) Rational, 10) Free,  11) A first created principle, 12) An essence or a being which exist per se, 13) Independent of the body for its existence and to some extent its operations in this life, 14) The substantial form of the body in the Ancient Greek philosophical sense of the word, 15) Directly created by God, 16) Immediately created by God, and if I am not mistaken, 17) Multiple meaning that it is completely and totally present and united to every portion of the human body that is alive.

 

The modern Catholic approach to the immortality of the soul is; however,  somewhat ambivalent about the spiritualistic extreme ideologies of Saint Thomas Aquinas described above, however its modern viewpoint backed by the full weight of the highest levels of the Church Hierarchy is that the human soul is: 1) Immortal, 2) Spiritual, 3) Rational, 4) Does not die when separated from its body at death, 4) Immediately created, 5) According to the index of the first addition of the new Catechism of the Catholic Church, directly created by God; 6) The seed of eternity we bear within ourselves, 7) Not reducible to the mere material world;   8]   The form of the body.

 

 

 

Here are some things that you can be assured are true regarding the Human Soul, that seemingly intangible innermost aspect of our natural being that has perplexed philosophers and theologians from antiquity.

 

Rest assure, some of the poor souls in purgatory who have no one to pray for them because, of phrases, such as “May they Rest in Peace” and similar phrases, when used by clergyman, and others, to indicate views points, such as “We really cannot know what happens after death.” or “The dead have fallen asleep to be awakened on the last day”, are of no consolation to these poor forgotten souls, who I assure every living adult human, are the very same persons they knew on Earth, and who I can assure everyone, are most fully alive, alert, conscious, affective, feeling, and sadly suffering.

 

Now; once again, read through these quotations from the new Catechism of the Catholic Church which was approved by the very highest levels of the Vatican during 1980s.

Part 1, Section 1, Chapter 1, SubSection 2

 

33 The human person: with his openness to truth and beauty, his sense of moral goodness, his freedom and the voice of his conscience, with his longings for the infinite and for happiness, man questions himself about God’s existence. In all this he discerns signs of his spiritual soul. The soul, the “seed of eternity we bear in ourselves, irreducible to the merely material”, 9 can have its origin only in God.

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 1

 

360 Because of its common origin the human race forms a unity, for “from one ancestor [God] made all nations to inhabit the whole earth”: 226

 

O wondrous vision, which makes us contemplate the human race in the unity of its origin in God. . . in the unity of its nature, composed equally in all men of a material body and a spiritual soul; in the unity of its immediate end and its mission in the world; in the unity of its dwelling, the earth, whose benefits all men, by right of nature, may use to sustain and develop life; in the unity of its supernatural end: God himself, to whom all ought to tend; in the unity of the means for attaining this end;. . . in the unity of the redemption wrought by Christ for all. 227.

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 2

 

363 In Sacred Scripture the term “soul” often refers to human life or the entire human person. 230 But “soul” also refers to the innermost aspect of man, that which is of greatest value in him, 231 that by which he is most especially in God’s image: “soul” signifies the spiritual principle in man.

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 2

 

366 The Church teaches that every spiritual soul is created immediately by God – it is not “produced” by the parents – and also that it is immortal: it does not perish when it separates from the body at death, and it will be reunited with the body at the final Resurrection. 235

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 2

 

367 Sometimes the soul is distinguished from the spirit: St. Paul for instance prays that God may sanctify his people “wholly”, with “spirit and soul and body” kept sound and blameless at the Lord’s coming. 236 The Church teaches that this distinction does not introduce a duality into the soul. 237 “Spirit” signifies that from creation man is ordered to a supernatural end and that his soul can gratuitously be raised beyond all it deserves to communion with God. 238.

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 4

 

382 “Man, though made of body and soul, is a unity” (GS 14 # 1). The doctrine of the faith affirms that the spiritual and immortal soul is created immediately by God.

 

Part 1, Section 2, Chapter 3, Article 11, SubSection 1, Heading 2

997 What is “rising”? In death, the separation of the soul from the body, the human body decays and the soul goes to meet God, while awaiting its reunion with its glorified body. God, in his almighty power, will definitively grant incorruptible life to our bodies by reuniting them with our souls, through the power of Jesus’ Resurrection.

 

Part 1, Section 2, Chapter 3, Article 12, SubSection 6

1052 “We believe that the souls of all who die in Christ’s grace . . . are the People of God beyond death. On the day of resurrection, death will be definitively conquered, when these souls will be reunited with their bodies” (Paul VI, CPG § 28].

 

Part 2, Section 2, Chapter 1, Article 1, SubSection 7, Heading 5

1280 Baptism imprints on the soul an indelible spiritual sign, the character, which consecrates the baptized person for Christian worship. Because of the character Baptism cannot be repeated (cf. DS 1609 and DS 1624).

 

Part 2, Section 2, Chapter 1, Article 2, SubSection 3

1304 Like Baptism which it completes, Confirmation is given only once, for it too imprints on the soul an indelible spiritual mark, the “character,” which is the sign that Jesus Christ has marked a Christian with the seal of his Spirit by clothing him with power from on high so that he may be his witness. 121

 

Part 3, Section 1, Chapter 1, Article 1

 

1705 By virtue of his soul and his spiritual powers of intellect and will, man is endowed with freedom, an “outstanding manifestation of the divine image.” 8

 

Part 3, Section 1, Chapter 1, Article 1

 

1711 Endowed with a spiritual soul, with intellect and with free will, the human person is from his very conception ordered to God and destined for eternal beatitude. He pursues his perfection in “seeking and loving what is true and good” (GS 15 § 2).

 

Part 3, Section 1, Chapter 2, Article 3, SubSection 2

 

1934 Created in the image of the one God and equally endowed with rational souls, all men have the same nature and the same origin. Redeemed by the sacrifice of Christ, all are called to participate in the same divine beatitude: all therefore enjoy an equal dignity.

 

Thus, we have at the very least, the above 13 aspects of the transcendent dignity of the Human Soul. In addition to these wonderful quotations, we have the Wisdom of Saint Thomas Aquinas, who held that the Human Soul is naturally immortal, spiritual, simple, unextended, incorruptible per addends and per se.

 

When Saint Thomas said that the Human Soul is the substantial form of the body, he was not saying that it physically looked like the body, rather he was using the Platonic or Aristotelian concept of eternal, immaterial, and perfect forms as the reified abstract ideal ideas that things represent.

 

Saint Thomas referred to the Soul as the substantial form of the body, ‘substantial” meaning a first created principle of being that is intrinsically independent of the body for its existence and for some of its more advanced operations.

 

Now once again, given the Scholastic interpretation of the nature of the human soul, that is the human soul is:  1) Spiritual, 2) Naturally immortal, 3) Incorruptible per addends and per se, 4) Simple, 5) Unextended, 6) Without shape or size, 7) Non-material,   8]   Non-corporeal, 9) Rational, 10) Free,  11) A first created principle, 12) An essence or a being which exist per se, 13) Independent of the body for its existence and to some extent its operations in this life, 14) The substantial form of the body in the Ancient Greek philosophical sense of the word, 15) Directly created by God, 16) Immediately created by God, and if I am not mistaken, 17) Multiple meaning that it is completely and totally present and united to every portion of the human body that is alive, we have much grounding through the use of natural reasoning that the human soul is naturally immortal and naturally indestructible. In all, we have at least the above 17 transcendent dignities of the human soul if Saint Thomas Aquinas is to be believed. In reality that are likely many additional transcendent dignities of the human soul regardless of whether the human soul is immortal by grace or instead, immortal by and in its very nature. Who knows, there may even be an infinite number of such dignities of the soul which are currently veiled to our knowledge and understanding by the wise providence of GOD. For if we knew everything there is to know about our souls, we would likely not so much delight in the mystery of the human person nor make efforts at self-improvements.

 

 

 

Now what about the structure of the human soul? If the human soul does have a structure, could it also have an ontological outside or external metaphysical surface and an innermost aspect or interior? Could not the human soul have a superficial exterior and a profoundly deep interior? I will refer to the statement within the new Catechism  Of The Catholic Church which makes reference to the human Heart or that innermost aspect of our being where we decide for or against GOD and which only we alone with GOD have access to. Perhaps this Heart is loosely translatable in meaning to the Heart of the Human Soul and thus implying an organic composition of the human soul, without implying a non-simplicity to the soul. This Human Heart might be metaphorically translated as being the Soul of the Soul while not introducing a duality to the human soul.

 

 

 

The fact that the Catechism Of The Catholic Church refers to the human heart as that aspect of our humanity by which we decide for or against GOD and by which we alone with GOD have access to seems to deepen the mystery of the spirituality of our humanity. Note that by the term  heart, I am not referring to the physical organ that pumps blood although some more or less anecdotal research seems to indicate that the physical organ may in some way seat some form of intelligence.

 

 
45) The Self In The Soul

 

A human soul is a human soul just as a child is a child, whether embryonic, in fetal form, near term, or new born.

 

 

I find that the most fascinating field of inquiry regarding created spiritual realities is that of the, spiritual and immortal, directly and immediately created,  human soul.

 

 

Now each human soul at the level of its natural existence retains the condition that it is naturally a human soul, for even the souls that are unfortunately consigned  to Hell are immortal, regardless of whether soul immortality is an inherent natural property of the human soul or is instead an immortality by grace only.

 

 

Now we know that a human soul cannot not be a human soul in essence or substance except for the possibility that GOD would have the power to somehow transubstantiate the human soul into something else. However, GOD never takes back what HE gives in nature and GOD has decided that each Human Soul should be immortal.

 

 

Now we can inquire as to how it is that a human soul is the soul that it is and no other human soul. Affirming that each human soul is and remains only the human soul that it is for all eternity no matter where it ends up after bodily death says that there is an aspect to each human soul that transcends the property of being a human soul.

 

 

There is something that makes my soul my soul and your soul your soul where your soul is not my soul and my soul is not your soul. This personal identity further differentiates human souls above and perhaps beyond the class of ontological and substantial soul-hood.

 

 

We can also contemplate what makes my soul me or your soul you, (or more correctly an aspect of me or of you) in such a way such that this inquiry is differentiated from the question as to what makes a soul the soul that it is and no other soul.

 

 

The human soul seems to be imbued with a transcendent property of self. Each human soul has self associated with it and this self by definition can only be the person possessing said human soul. Each human soul seems to have a dimension of self and by definition of a human person, body and soul in this life, and soul in the next life before the Final Resurrection, each human self can by definition only be the self that it is simply because the reality of a self remaining un-alterably itself is an a priori fact. If a self could not be itself, than the self becoming not itself would pose an ontological and logical contradiction since is order for a self not to be itself, it would need to become not itself at the point of transition thus resulting in the self not being itself in the transition in the first place. In short, there would remain no mechanism for the transition to take since  the self that the self would become afterward cannot be the self that it was before thereby forcing a distinction between ontological states defined by ontological information.

 

 

Now this brief digression might seem to be somewhat of a diatribe at first, however, I can assure the reader of this writing  that just as we have just barely scraped the surface of what is knowable about the physical cosmos, we have even less depth of our understanding about the wonderful reality of the human soul. The human soul seems to defy precise theological and philosophical understanding. Perhaps this is somehow related to Saint Thomas Aquinas referring to all of his theological works as empty straw after a mystical experience he underwent shortly before his passing.

 

 

Many folks in modern pop-culture, medicine, and theological studies put more focus on the human body that on the Human Soul. I have always done the reverse and must admit that I am a diehard old-school Scholastic soul freak.

 

 

Now do not get me wrong, I respect the human body as well as it will be Resurrected a spiritual and immortal body at the End of Time, however, I think we are losing something as a culture when the idea of the soul such as contemplated by like-minded folks seems immature or perhaps even psycho. I often have gotten looks of disapproval when I digress on the human soul in the instances where others or more likely I have brought the subject up for particular discussion.

 

 

Perhaps if more folks realized the mystery behind the human soul, procreations by such folks in valid marriages would not be interrupted by the sin of artificial contraception and sterilization operations. When there comes a time when there is something in a human embryo that seems transcendent to virtually all adult human persons and only when such occurs, the problem of figuring out how to stop legalized abortion will become tractable.

 

46) A Human Soul Can Substantially Survive Destruction Of Its Faculties And Purely Accidental Features.

 

Many theologians hold that the human soul is multiply present in the human body meaning that it is fully  united to each differential volumetric and massive element of the human body. But could the human soul also be completely present in every differential substantial and accidental sub-feature of the soul itself even where such differential elements are not considered to be the entirety of the human soul? To answer this question, we need to delve into the  subject of the human soul a little further.

 

 

First, many Catholic theologians from antiquity have theorized that if one or more of the soul’s faculties or semi-substantial accidental aspects were destroyed, the substance of the human soul would continue in its existence unharmed and un-phased. This notion is based on the concept that the essence of the human soul or its core substantial constitution is a created first principle meaning that it subsists in no other created reality and is instead created directly by GOD, ex nihilo.

 

 

Second, the human soul being ontologically simple and non-spatial or  non-spatially extended has no substantial sub-division and so each substantial element of the human soul is the entirely of the substantiality of the human soul as there is no way to subdivide the substantiality of the human soul.

 

 

Third, if there is no way to substantially divide the human soul, then there is no way that the human soul’s substantiality can be related in part to a limiting subset of the soul’s faculties and purely accidental aspects or features.

 

 

Thus, we seem to have a substantiality of the human soul which can even survive corruption of one or more of its faculties and certainly one or more of its purely accidental features.

 

 

This aspect of the substance of the human soul seems to allude to its remarkable incorruptibility since if the above reasoning is valid, then not even the destruction of the human soul’s intellect, free will, sensitive life, and memory could result in the destruction of the pure substantiality of the human soul.

 

 

 

Thus, we are affirmed that the human soul substantially transcends its facilities of intellect, will, sensitive life, and memory, and certainly its purely accidental features.

 

I always will have a love of the human soul and still see it as a mysterious aspect of the human person that seems to ever defy precise definition, even by the most astute Catholic theologians. But heck, part of the fun of being human is having  a sense of the mystique about all human persons, and this includes a sense of mystique regarding human sexuality. If more folks viewed human sexuality in spiritual terms instead of holding to an excessively spiritualistic rationalistic approach that demotes human sexuality to mere animalistic principles, and by modern psychodynamicists who view it as simply a primitive instinct, perhaps today youth would treat their sexualities with greater respect and realize what a great gift human sexuality is. This realization in turn would go a long way to reducing the practice of co-habitation, extra-marital sex, artificial contraception, abortion, so-called gay and lesbian marriages, and the rest of the sins of impurity that have increased in frequency in our modern culture.

 

 

Realizing the existence of a spiritual and immortal human soul in the spirit of Scholastic interpretation would go a long way in helping folks, even many daily mass attending folks, to love and respect the sanctity of all humans in this life and to love the sinner in spite of not-loving the sin.

 

 

With a greater respect for human life, youth in today’s culture could more readily excel in the virtue of purity and our current shortage of Catholic priests would be greatly mitigated.

 

 

47) The Glories For The Human Soul To Come.

The beatific vision might be analogous to an eighth and final sacrament while not being recognized as a sacrament by the Church, and indeed technically speaking, the Beatific Vision is not an actual sacrament.

 

 

However, the beatific vision is open to all folks, regardless of their faith based belief systems or ways of life so long as they die in the grace of GOD. Non-Catholics can be saved in vast numbers known only to GOD and those saved can include those of any faith provided they die in friendship with the Divine.

 

 

The beatific vision as a non-sacramental analogue to the 7 sacraments reaches its perfection is some-way by the process of Canonization whereby a soul in Heaven has the honor of being declared a Saint by the Catholic Church.

 

 

However, the beatitude of the just currently in Heaven, regardless of whether they must pass through Purgatory then to Heaven, go directly to Heaven but are never recognized via the process of Canonization, or eventually are canonized, is just the tip of the ice-burg.

 

 

We must realize that we are going to receive our bodies back at the Final Resurrection and this body will be spiritualized in a manner currently veiled to our understanding. Since grace effects the entire person in this life as a unity of body and soul, we can reasonably surmise that grace will affect our Resurrected Body at the End Of Time and that this grace bestowed on our Resurrected Body, to be immortalized incorruptible and spiritualized, will entail and extension of grace within the Human Person in the glorified Heavens to come.

 

 

While is this life, as Catholics, we are each a member of the real Mystical Body of Christ, and since we can surmise that just as the reward of the Beatific Vision and then the Final Resurrection into glory at the end of time entail a glorification of the Human Person, perhaps we will somehow more fully be incorporation into the Mystical Body of Christ upon attainment of the Beatific Vision and the Glories of the Final Resurrection.

The scenarios covered above are open to all persons, regardless of whether or not they are clergymen, consecrated religious and/or virgins, married folks, single lay persons, divorced or separated folks, or children.Our Lady is a perfect model of a married person who was and is Full Of Grace.

 

 

We need to consider once again as Catholics, whatever our vocation or state of life, that we are all called to become Saints and to the glories that will unfold in attainment of the Beatific Vision and then at the Final Resurrection on the Last Day. Since we will have all eternity to spend a dynamic life in beatitude with the TRIUNE GOD, and then so with each of HIS THREE DIVINE PERSONS, in the company of all of the Angels and Saints, and our family members, relatives, and friends, and all others who make it to Heaven, my guess is that having achieved all of this, we will have just started scraping an unlimited proverbial bucket full of untold riches and glories yet to be imagined as we will have all eternity to access to wonders of a perhaps ever growing creation.

 

 

In a modern civilization where most folks appear obsessed with heightening their career status, or are obsessed with intellectual, physical, and psychological prowess types of competition, perhaps we all need to step back and realize that this life is not our final destiny. For married folks, this means realizing that the children they can procreate are meant for and will last forever, as body and soul in this life, soul in the pre-Resurrection next life, and then again as body and soul after the Final Resurrection.

 

 

My guess is that the unfortunate reality of abortion and use of artificial contraception, even by many church going Catholics, are ultimately linked. I think we will only see an end to abortion when we see an end to legal artificial contraception prescriptions and indeed, and end to the practice of artificial contraceptives usage.

 

48) Created Relationships

 

I went to the local Burger King restaurant one morning  a few weeks ago and choose the drive thru service. I bought myself two large diet Cokes as a usual morning routine and sat in my car in the store’s parking lot and drank the first soda. As I was pondering on the complexity of creation, I was looking at the large night-time illuminable Burger King sign that that is located about a dozen meters away from Arlington Boulevard in Fairfax City, Virginia, USA.

 

 

As I was looking at the sign, I mused on the beauty and complexity of the logo and colored design patterns on the sign. I noted how  the image must be enormously complex simply by considering the relationship between each point location of the abstracted image in relation to every other point on the sign.

 

 

It occurred to me that in just one set of relations such as between one point and each of the other points on the sign, there is an (Infinity)(Infinity)(Infinity) of relations where each factor corresponds to the dimensional extent of the sign in each dimension of 3-Space. This is because each dimension of the abstracted sign image  is an infinite number of points long. Make a similar consideration for each point on the abstracted image and the number of such base-line simple relations is equal to Σ (1, [(Infinity)(Infinity)(Infinity)]): (Infinity)(Infinity)(Infinity).

 

 

I then considered the relations between any two points taken together and the rest of the points on the sign and realized the enormously infinite number of additional relations between the set of the two points and the remainder of the points on the sign. Simply draw a line segment between the two former points and one needs to consider the relationship between each of the other points on the sign and each point along the line segment and how the each of these relationships are further related to the location of the line segment end points. I then imagined repeating this analysis for any two arbitrary points on the sign and became stupefyingly aware of the vast infinities of existent relationships involved.

 

 

 

Then I considered the relations between any two three points taken together and the rest of the points on the sign and realized the ever greater  infinite number of additional relations between the set of the three points and the remainder of the points on the sign compared to the analogous case of the set of two points. Simply draw a triangle  connecting the three former points and one needs to consider the relationship between each of the other points on the sign and each point on  the triangle  and how each of these relationships are further related to the location of the triangles three vertex points. I then imagined repeating this analysis for any three arbitrary points on the sign and became even more stupefyingly aware of the vast infinities of existent relationships.

 

 

I mentally generalized the situation to all  sets of finite numbers of points and to all of the various sets of the (Infinity)(Infinity)(Infinity) number of points located on the 3-D abstract space defining the surface of the sign and the situation considered WOWed Me regarding the size of the set of the relations implied.

 

 

Now, just a few weeks  ago as I began to compose this article, I started to consider the case where one would take any two points on the sign and draw an arbitrary squiggly line between the former two points. I pictured a simple but rather sloppy sine-wave type curve and began to consider how each of the other points on the sign is related to each point on the sloppy curve and how each such relationship is related to the two arbitrarily chosen end points. I then mused that I could just as well have chosen any two points on the sign and  constructed a similar analysis. Then I came to realize that the number of shapes that could link the former arbitrarily chosen points is vastly infinite and how the set of relationships between each point on the sign with each point along each of each  arbitrarily considered curves is vastly infinite as is the number of said relationships to said arbitrarily chosen first two points. Consider similar cases for each set of two points on the sign and the total number of similar relations for the combined sets of any two points and the infinities of relations boggles the mind. Thus, I realized that that  analogous cases can be considered for each possible set of three points, four points, five points, …,  (Infinity)(Infinity)(Infinity) points on the Burger King sign.

 

 

Now in reality, space and time may be quantized thus greatly reducing the total number of relationships compared to the case of the continuous space described above, but nonetheless, in abstract space, the infinities  of the relationships are described as in the previous paragraphs for ordinary first level continuous space. For super-continuous space for ever increasing degrees of super-continuity, the infinities become ever greater.

 

 

Just now, I started contemplating the set relationships between each subset of the set of such relationships as described for the cases of the abstract continuous space given above. When summing all of the relationships for combined set of sub-sets, the size of the infinity utterly boggles the mind. When we take the analogous set of relationships involving the combined set, S₂,  of elements within the set of all of the sub-sets of the set of all of the sub-sets of the initial set, and the infinities become even more mind boggling. Consider the analogous case of the combined set, S₃, of elements within the set  of all of the sub-sets  of the set of all of the subsets of the set of all of the subsets of the initial set, and the infinities involve even  more stupefyingly large. We can likewise consider the analogous sets of relationships for each set in a series of  ever-larger  sets S_i where i is arbitrarily large but finite, and then the cases where i grows to ever greater infinite values utterly forever, world without end.

 

 

A similar  argument can be applied to the sets involving quantized space and time and mass and energy for which we can produce ever larger sets without end.

All of these utterly infinite numbers of inter-relations ships were gleamed from a casual glance of a fast food restaurant sign. How much more vast are the ever greater infinities of relationships for  the meta-case of the number of relationships contained within the set of all created reality, a created reality which we know grows at least with the creation of a brand new soul, ex nihilo, by GOD for each human conception.

 

 

Thus, we should applaud licit conceptions where ever they occur, and welcome the results of illicit conceptions while encouraging conceptions only within the confines of valid marriages, which for Catholics is ordinarily between two Catholics in the sacrament of Holy Matrimony. Even though I have chosen to live a single life, part of my life’s calling is to promote Holy Matrimony, because in the glories to be obtain therein, married couples put an un-repeatable and utterly eternal stamp on all creation by increasing the number of creatures in an non-revocable manners and even greater numbers of created relationships.

 

 

We should do more to foster good Catholic Marriages. Our Lady in her numerous Church Approved Apparitions does not nearly so much bemoan her predicted shortage of  modern day religious and clerical vocations as much as she chides us on the need for good Catholic families and stable marriages. By far and large, most persons will choose marriage as their vocation, whether Catholic or not. Should not we be doing more as Catholics to promote Holy Matrimony!

 

49) The Created Spiritual Fireworks Of Human Souls.

 

I thought that you would enjoy, this,  one of my latest articles on human nature. The article as you can tell is about the Human Soul. The Human Soul has a special place in my heart and is the most important created reality that we have access to.

 

 

Note that I am a Catholic; however, the general scope of the afterlife considerations made herein is applicable to all folks, regardless of whether or not they are from other Christian denominations, so-called non-denominational Christians, Jews, Hindus, Muslims, Buddhists, Taoists, Shinto, and the like, and the so-called  practitioners of New Age belief systems such as New Age space alien phenomenon buffs, and   even agnostics and atheists. All human persons are called by name to live out their lives in peace and charity to the extent that they are capable of and all are called to feast at the Heavenly Banquet at Our Lord’s supper table.  

 

Long after the last Mass is said, the last act of Consecration of the Sacred Species is made, the last confession is heard, the last baptisms are performed, the last confirmations are made, and the last installation into Holy Orders are carried out, each one of our Souls will be the temple of the Holy Spirit. In a significant sense, each Human Soul in Heaven will be a spiritual analogue to the bread and wine consecrated into the Body and Blood of Christ. In a real sense, we are already halfway there being that each person on Earth is an essential member of the Mystical Body of Christ by virtue of the universal graces merited by Christ Death on the Cross and Resurrection. Whereas the Lord is present under the appearance of ordinary bread and wine upon consecration of the bread and wine during Mass, each one of us, regardless of our vocation in Heaven, and more significantly after the Final Resurrection at the End of Time will in a sense replace that  Sacred Species,  in which the Holy Spirit dwells and in which the Holy Spirit is infused, much like one piece of wax, our soul, and another piece of wax, the Holy Spirit will be melted in stirred together, except that we will not lose our individuality nor identity, but instead will have it enormously enhanced. The Human Person is indeed truly a Temple of the Holy Trinity.

 

 

We as Catholics are given a special gift in that by virtue of each of the Sacraments of Baptism, and Confirmation, an indelible seal is imprinted on our Souls which imbues our Souls with a supernatural character that presumably per dues into eternity, even for the souls who unfortunately are consigned to Hell. Just as the famous slogan often recited by U.S. Marines, active duty, reservists, and retired, “Once a Marine, always a Marine!”, we as Catholics can rightfully say, “Once a Catholic, always a Catholic!”

 

 

For those gifted with the calling to Holy Orders, this Sacrament imbues its own indelible seal on the Souls of the Ordained Clergymen and is similar to the seals imprinted by Baptism and Confirmation. However, the laity should note that they too have a share in the Royal Priesthood as members of the Church and attenders of the Holy Mass as they participate in the presence of GOD at  Mass by their prayers during Mass.

 

 

All Catholics;  Clergymen, Consecrated Religious Men and Women, Married Folks, Single Persons, Divorced Persons, Alter Servers, and those with no current active participation in  the Church are called to be Saints and even to go directly to Heaven without Purgatorial Remediation. We end up in Purgatory first by our  freely chosen life-styles provided we die having been forgiven of all and any mortal sin. I personally like to believe that Our Lord offers and opportunity for final mercy to every one upon death although the Church does not include such a mechanism for Eternal Salvation in its teachings as far as I can tell.

 

 

For those who are married, your vocation offers its unique graces as marriage in Holy Matrimony is romance raised to  the level of its own Sacrament along with graces given by GOD. You conceive and bear children and as a result, leave a permanent and significant mark on creation for all eternity. Your calling to procreate causes a brand new human soul to be directly and immediately created which will last forever in absolutely all cases, thus resulting in an increase in the size of the set of human persons and also created spiritual elements.

 

 

In a way, entrance into Heaven directly or after Purgatorial remediation is analogous to an eighth and final Sacrament. So it is good not to fret in this life regarding the particular vocation you have chosen relative to vocations others may be called to. Each Human Person shares a fundamental moral equality before the Eternal Father and the Divine fireworks of the Beatific Vision is open to all who strive to live in peace and charity.

 

 

That being said, this past Independence day, I shared some personal time with my  in town siblings and nieces and nephews, and set of a good display of fireworks, and realized that the beautiful sparkles and brilliant colors represent in a very limited way, the beauty that GOD beholds in every Human Soul ever created as a divinely created spiritual sparkle of life, and the beauty we will behold in ourselves and in our loved ones in the life to come at the Lord’s Heavenly Banquette.

 

 

As a physicist who ponders the intricacies of the created physical world, I am mindful that this vast cosmos we look out into on a clear midnight belies the far greater richness of the world of the pure created spirits, angels and the souls of the deceased, and the even greater reality of GOD HIMSELF, ONE AND TRIUNE.

 

 

I am confident that I could never exhaust the range of questions that can be addressed in this life. Being that I am primarily an interstellar space craft propulsion physicist and am primarily a physics concepts and numbers kind of guy, my readership may be taken back a little bit by my speculations regarding the Human Soul. I will continue my life’s calling to work on concepts that can literally take us to the stars and beyond, however, if I can be said to have a secondary vocation, it would be to contemplate the wonders and the beauty of the Human Soul.

 

 

You may ask why someone who loves to tinker with interstellar propulsion physics also is thrilled about the Human Soul. Well,  all I can say is that my mother who is a devout Catholic did it to me.

 

 

Back when my family was living in Arlington Virginia on Lexington Street, while my dad was a Naval Officer stationed in the D.C. Area, I had the curiosity to ask my mother where my soul was located in my body. My mother answered something like, it is in the whole of you and that it is a form. At the time, I was playing with the toy known by the product name of  ”Colorforms” where one would take plastic electrostatically adhesive brightly colored renditions of articles of clothing and dress a template in the form of an outline of a person. I somehow seemed to obtain a glimpse that the soul was a form as of an abstract idealization although I by far lacked the intellectualized concept of eternal forms as taught in classes on ancient Greek philosophy.I was only about 4 years old when all this transpired and so I recommend that you do not shirk from talking to young children about such concepts when their question arises. 

 

The Human Soul in its accidental experienced form of daily waking and dreaming consciousness in an effervescent wonderfully sparkling reality that is dynamically changing and evolving. In a very interesting and ironic way, this spiritual and accidental effervescence is more existentially and  ontologically profound than the state of simply just being but having no  intra-personal and no interpersonal dynamism.

 

 

Since each Human Soul is immortal, an interesting mystery involves the fact that each Human Soul is the Soul that it is and also that it  remains the Soul that it precisely and exactly is for all eternity. This is a very important consideration being that the soul is the vital or life principle of identity, individuality, unity, distinction, and uniqueness that constitutes each human person as a unique, autonomous, free, and rational,  individual.

 

 

It is fascinating to consider that despite the dynamic time dependent changing of human daily waking consciousness, the human soul is eternally the self-same exact principle of identity, individuality, unity, distinction, and uniqueness that it was, is and will remain.

This utterly unchanging-ness of existential identity of the Human Soul with itself fascinates me as it seems to imply an existential and ontological aspect of each Human Soul that by far transcends its conscious experience or its daily waking conscious states in both the objective and subjective aspects of such states.

 

 

The possibility for the occurrence of major holistic personality changes throughout life  and  for dramatic emotional,  attitudinal, and cognitive changes during the daily wake sleep conscious life cycles of Human Persons coupled with the reality that each Human Person remains the exact self-same identical person that He or She is points to an intra-soul self-transcendence that is remarkable in scope.

 

 

The fact that each Human Soul that goes to Hell can remain exactly the same Soul and Human Person that it is for all eternity commensurate with eternal self-same moral responsibility and culpability for the Person’s actions and morally responsible thoughts and feelings,  even amidst the punishments in Hell which can vary in intensity and in qualitative form from Person to Person,  shows just how transcendent is the personal identity of each Human Soul with respect to it dynamically changing conscious intrapersonal and interpersonal experiences. The mere fact that each Human Soul that goes to Hell retains its exact self-same indenticality from this life, through divine judgment, and into Hell is really quite remarkable. The same argument can be made for souls that go to Heaven, Purgatory then Heaven, or to any Limbo.

 

 

The fact that the effervescence of the dynamic changing in the Human Soul is not identical with its self-same identity continuity, even among extreme discreet changes such as transition from this life to the next indicates that this effervescent fire somehow transcends the self-same indenticality of the Human Soul. Since every experience adds to the accidental from of the Human Soul, and is presumably conserved in the Soul’s faculty of the Unconsciousness, in a sense,  each instant of experienced effervescent dynamic activity is preserved for all eternity and so in a sense, is also immutably conserved.

 

 

 

Now consider that the most significant psychotic disorders are the various forms of schizophrenia. The fact that the continuity of the ontological aspects of self-identicality continues for all eternity also point to the transcendence of the aspect of the Human Soul that imbues the Soul with the quality of being the Soul or the Person that it is and no other Soul.  This is especially striking being that despite the untrue popular notion that schizophrenia implies the existence of multiple personalities or an over-abundance of conscious personal identities,  schizophrenia instead is associated with a deterioration of the personality to various extents instead of an overabundance of personality.

 

 

In fact, the dissociative disorder of Multiple Personality Disorder is an opposite to the psychotic disorders of the schizophrenias. There mere fact that the Soul of a schizophrenic remains the soul that it is for all eternity to the same extent as any other soul points to a profound transcendence of the ontological and existential self-sameness or identicality of the Human Soul with respect to not only its conscious daily waking activity, but also to the attributes and characteristics of the psychology of daily waking conscious personal identity. In short, the Souls of schizophrenics remain the exact same souls that they are and always were, throughout all eternity, and then so in the midst of at times profound conscious personal deterioration and the onset of disorganized behavior, thinking, and feeling.

 

50) Heaven Is Analogous To An  Eighth Sacrament

 

The beatific vision might be analogous to an eighth and final sacrament while not being recognized as a sacrament by the Church, and indeed technically speaking, the Beatific Vision is not an actual sacrament.

 

 

However, the beatific vision is open to all folks, regardless of their faith based belief systems or ways of life so long as they die in the grace of GOD. Non-Catholics can be saved in vast numbers known only to GOD and those saved can include those of any faith provided they die in friendship with the Divine.

 

 

The beatific vision as a non-sacramental analogue to the 7 sacraments reaches its perfection is some-way by the process of Canonization whereby a soul in Heaven has the honor of being declared a Saint by the Catholic Church.

 

 

However, the beatitude of the just currently in Heaven, regardless of whether they must pass through Purgatory then to Heaven, go directly to Heaven but are never recognized via the process of Canonization, or eventually are canonized, is just the tip of the ice-burg.

 

 

We must realize that we are going to receive our bodies back at the Final Resurrection and this body will be spiritualized in a manner currently veiled to our understanding. Since grace effects the entire person in this life as a unity of body and soul, we can reasonably surmise that grace will affect our Resurrected Body at the End Of Time and that this grace bestowed on our Resurrected Body, to be immortalized incorruptible and spiritualized, will entail and extension of grace within the Human Person in the glorified Heavens to come.

 

 

While is this life, as Catholics, we are each a member of the real Mystical Body of Christ, and since we can surmise that just as the reward of the Beatific Vision and then the Final Resurrection into glory at the end of time entail a glorification of the Human Person, perhaps we will somehow more fully be incorporation into the Mystical Body of Christ upon attainment of the Beatific Vision and the Glories of the Final Resurrection.

The scenarios covered above are open to all persons, regardless of whether or not they are clergymen, consecrated religious and/or virgins, married folks, single lay persons, divorced or separated folks, or children.Our Lady is a perfect model of a married person who was and is Full Of Grace.

 

 

We need to consider once again as Catholics, whatever our vocation or state of life, that we are all called to become Saints and to the glories that will unfold in attainment of the Beatific Vision and then at the Final Resurrection on the Last Day. Since we will have all eternity to spend a dynamic life in beatitude with the TRIUNE GOD, and then so with each of HIS THREE DIVINE PERSONS, in the company of all of the Angels and Saints, and our family members, relatives, and friends, and all others who make it to Heaven, my guess is that having achieved all of this, we will have just started scraping an unlimited proverbial bucket full of untold riches and glories yet to be imagined as we will have all eternity to access to wonders of a perhaps ever growing creation.

 

 

In a modern civilization where most folks appear obsessed with heightening their career status, or are obsessed with intellectual, physical, and psychological prowess types of competition, perhaps we all need to step back and realize that this life is not our final destiny. For married folks, this means realizing that the children they can procreate are meant for and will last forever, as body and soul in this life, soul in the pre-Resurrection next life, and then again as body and soul after the Final Resurrection.

 

 

My guess is that the unfortunate reality of abortion and use of artificial contraception, even by many church going Catholics, are ultimately linked. I think we will only see an end to abortion when we see an end to legal artificial contraception prescriptions and indeed, and end to the practice of artificial contraceptives usage.

 

 

51) The Plausible Nebulousity Of The Human Soul And How Such Would Actually Entail Something Profoundly Transcendent And Perhaps Incomprehensible In This Life About The Human Soul.

 

Now, we who work in the technical fields such as physics and engineering as I do and the other hard and soft sciences are familiar with the concept of a boundary condition. We are also familiar with transition regions and phase changes such as commonly occur in chemistry, thermodynamics, quantum atomic, nuclear, and molecular physics, and even theoretically in the evolution of our universe such as occurred, or so we think, during symmetry breaking events in early universal evolution.

Psychologist, psychiatrists, and sociologists are familiar with transitions or boundary conditions such as sensory thresholds, academic performance limits, transitions that can occur such as a sudden onset of psychotic symptoms or manic states, and the like.

Economists and business persons are familiar with transition points such as can occur for break even and profitable investments or bullish and bearish market  performance.

Mechanics, plumbers, pipe-fitters, electricians and the like are often very familiar with the performance of the tools and materials they work with.

Clergymen and religious focus on moral development and thresholds and dispositions to sin and to avoid temptations to sin.

Even drug cartel leaders and their distributors are familiar with social and financial transition points and popular outcries that could hurt their illicit trade.

Military leaders from generals and admirals to enlisted men and women are familiar with the potential kill ratio of their weapons, the threshold of human endurance under combat situations, and the transition points which can cause a military operation to be a success or go awry.

Lovers, especially passionate and intimate ones,  know when to approach their partners, and skilled ones are very good a climaxing the beautiful consummated act.

In short, we are all familiar with boundary conditions, phase changes, and the conditions that mark the existence of an event or element of creation.

Now, have you ever considered where the boundary of the soul exists between a soul and reality external to the soul? I had just started contemplating this aspect of human spiritual ontology about 2 weeks ago and decided that I just had to compose this post tonight.

The human body seems at least somewhat nebulously defined in terms of the spatial and/or temporal boundaries between living and non-living cellular tissue components. The transition between such states is hard to qualify because of the overlap of the probabilistic quantum wave functions that are associated with the positions of the atoms within the body, and indeed, also those associated with macroscopic tissue portions. Even aside from quantum mechanical considerations, the mere fact that cells are mostly water and that the water and metabolite flux that defines the physical and empirically scruitinizable aspects of cells and tissues is not perfectly defined in space and time alludes to such nebulosity. Who is to say that a water molecule that was just one of quadrillions with in a cell that is in the process of or has transitioned to the bulk of the fluid surrounding a given cell is still not part of the cell or no longer part of the cell.

Now back to the subject of the human soul. We Catholics generally hold that each human soul is created ex nihilo or directly and immediately at the point of human embryonic conception. However, due to the uncertainty in time and the lack of temporal definition and spatial definition at time and distance scales at or below the miniscule units of the Planck Time and Planck length , area, and volume, the meaning of the instant of conception simply may not exist because time theoretically appears not to be defined below the finite unit of the Planck time or perhaps not below arbitrarily smaller but finite units. Something cannot be created or happen at an instant if no such parameters exist in physical creation.

However, we know that a soul exists when it exists and does not exist before it exists. However, perhaps at or near the smallest unit of resolution of time, the human soul is gradually drawn into being and completed in existence over a period of time equal to or less than that of the Planck Time Unit, which by the way is very small at tp = {[h/(2π)]G/[C ⁵]} ^1/2   = 0.0000000000000000000000000000000000000000000539 second. The Planck Length is only 0.000000000000000000000000000000000016 meters, or only one hundred millionth of a trillionth of the diameter of the atomic nucleus.

Even though instant creation might not be defined in the physical world for the human soul, we know that if GOD nearly instantaneously gradually completes the soul from its lack of previous existence to its full existential state, HE lovingly, deliberately, and carefully crafts each human soul ex nihilo. It seems that since the Human Soul, may be the most important aspect of creation, or at least within our creation, GOD works hard and diligently to create each soul as HE is creating it even if such creation is nearly instantaneous. GOD working hard is not a sign of GOD’s struggling or excessive labor because GOD is utterly Almighty in HIS mental and volitional strength from both the objective standpoint and GOD’s own personal experience of HIS acts and might.

I think it is a great testament to human transcendental dignity and ephemerality if GOD works to create each human soul, even if over vanishingly finite time periods, physical universe time. This says something about the magnitude and dignity of the substantial principle, even if incomplete, of the spiritual and immortal human soul. After all, would you rather feel that your soul was created with just a careless and thoughtless Divine whim, or instead, that it was crafted with utmost control and personal loving deliberation and devotion.

However, the nebulosity of the boundary between what is one creature and what is another creature is intelligible by the complex web of inter-dependence and inter-relations that define one creature with respect to another. Now please do not think that I am delving into some New Age anti-personalism here, as the fact that each human person is judged by only his own free or semi-free actions and as such maintains an absolute distinction and unique moral identity from all other creatures and even from GOD HIMSELF. The fact that I as well as you are absolutely, solely,  and only responsible for our  morally binding personal choices and culpable influences on others, in spite of any accidental and perhaps substantial nebulosity in our bodies and perhaps even in our souls,   points to something utterly and transcendently profound about each human person, especially each human soul.

Clergyman should consider these thoughts, which in light of modern physics, seem inescapable. Clergymen, by virtue of the act of performing baptisms, the forgiveness of sins of penitents, and the consecration of the Sacred Species during Mass have a profound role to play as these sacramental acts are absolutely present and binding when they occur, even in the midst of what seems like a nebulosity of creatures given the interdependence and inter-relations among all creatures as mentioned in the new Catechism of the Catholic Church.

Regarding my speculations on human ontological nebulosity, you need not fret because you who are clergymen are well indoctrinated in rightfully so, in the notion that we are all parts of the mystical body of Christ. The mystical body of Christ is not just a social order of civil phenomenon, but is a real genuine body of which we are all members and inter-related to one another.

GOD BLESS!

Jim

53) THE HUMAN SOUL: A BEING OF LIGHT, A PERSON OF LIGHT.

 

 

 

The human soul is a created analogue of the Holy Trinity. The Holy Trinity has the Persons; GOD THE FATHER, GOD THE SON, and GOD THE HOLY SPIRIT. We have in our souls;  a heart, an intellect, and a will.

 

 

Often, when folks have out of body experiences, OOBEs, such as near death experiences, they claim to come before a beautiful warm intensely bright being of light. These persons will also in some cases claim to see what seems like glowing orbs which in some cases are perceived as dynamically shimmering and will often  feel that they become subjectively aware that these orbs are angels.

 

 

Folks having had near death so-called OOBEs often claim to have sensed of somato-sense or the shape and personalities of deceased loved ones who act as loving guides.

 

 

Now, let us step back a moment and consider the fact that all positive temperature bodies radiate, even supermassive black holes. This radiant heat is generally well approximated by a black body, i.e., a physical body that is perfectly absorptive of incident electromagnetic radiation and perfectly emissive of electromagnetic radiation. The hotter the body, the greater in general is the radiant thermal flux density of the radiation emitted by the body.

 

 

Now what if human souls have an analogue of black body radiation that has the nature of a dynamic field by which each human soul can interact with and be inter-related and in some sense be interdependent with respect to its environment.  This spiritual black body field might be what is responsible for phenomenon underpinning anecdotal accounts of lovers who claim to be able to sense their loved one’s intentions, or  in cases where folks perceive the creepiness of some stranger they feel is bent on doing them harm and the like.

 

 

It would seem that such black body analogues would be especially pertinent to any capacity for the disembodied human souls to interact with the aspects of creation they have access to and perhaps with other rational spirits by mental telepathic abilities. After all, if thoughts can be transferred from one spirit to another, it would seem plausible but not necessarily absolute critical that the egress of mental, emotional, sensual, volitional, and spiritual information from one soul or spirit to another followed by the entrance of the information into the mind, heart, and/or will of the spirit to which the communication is directed would require some sort of medium. After all, there is a definite existential boundary between the substance and accidental nature of one spirit and the substance and accidental nature of another spirit.

 

 

Even though the just in Heaven are united in one Mystical Body, a given soul in Heaven has a substance and accidental nature which is uniquely and solely its own and no one else’s. Any telepathic communication capability in the next life would imply information exchange between one spirit and another, and such transmission by definition requires information states within one spirit to be communicated out of the state of being solely within said first spirit and into the state of the recipient of the communication. In short, you cannot have communication with knowledge or information that does not cross the interpersonal; existential, substantial, and/or accidental boundaries that constitute each person as an individual.

 

 

Perhaps this medium is akin to black body radiation. Just as black body radiation tells us about the information content of a physical body, so might a spiritual analogue of black body radiation tell us about another soul or spirit in the afterlife.

 

 

Holographic Information Theory posits that the maximum possible entropy within a volume of space-time enclosed by an imaginary surface is directly proportional to the surface area of the enclosing surface in square Planck Length Units. The term holographic information theory thus posits that everything that can be known about the volume contained within the imaginary enclosure is thus encoded on the boundary surface much as a hologram on a credit card produces a 3-D image from an essentially 2-D surface. Note however, that such holographic images are not literally produced by 2-D substrates because the holographic effects actually require a slight thickness of  the image producing section of the credit card thus by definition, requiring a third dimension.

Perhaps the conjectured spiritual black body analogue in theory encodes information about a given soul or spirit in such a manner that telepathic communication is possible between the souls of the deceased and with  and among other species of spirits such as various levels or choirs of angels.

 

 

This spiritual black body radiation may in a sense be a property of the soul, if not just in accident, then in substance  in a similar manner that the electric field around an electron is an inherent and non-separable element from the fermionic massive substance of the electron itself. In a sense, the electric field around the electron or around any other charged fermion is  part of the substance of the fermion itself.

 

 

Thus, I would like to offer a rather prosaic and pleasant conjecture to the effect that each human soul is like a beautiful being of light, or spiritual light, by which each soul of the deceased has access to other spiritual creatures such as the souls of other deceased humans, any deceased bodily extraterrestrials,  any deceased bodily ultra-terrestrials, and the angels.

 

 

Just as the being of light often allegedly encountered in near death experience based encounters with the DIVINE is often described as more white than white, or as some form of clear transparent light that we cannot sense who have not experienced an OOBE, perhaps each human soul is a created analogue.

 

 

Each human soul, even the souls who may unfortunately have ended up in Hell, are ontologically very, very,  good even if they may have made terrible and unrepentant moral choices while here on Earth in this life. Modern Catholic understanding generally holds that even Satan Himself is inherently ontologically very, very, good, by virtue of his elevated nature or substance having perhaps been created with more natural power, intellect, and strength than any other creature.

 

 

No doubt, Satan now employs His nature for evil purposes and intentions, but nonetheless, He is loved by GOD just as any sinner is loved by GOD. That Satan in theory retains all of His natural powers and capabilities shows that He retains His natural elevated status in His ontological goodness, even  though His moral choices are reprehensible.

 

 

You have likely heard the phrase hate the sin but love the sinner. Well this is especially pertinent to our modern times especially within  the United States where the gulf between the rich and the educated and the poor and uneducated continues to widen with many well to do folks looking with distain on those who are poor, not college educated, mentally or emotionally disabled, and the like. These latter 4 conditions are usually no fault of the disadvantaged and so those with psychological and intellectual prowess who  look down on the unfortunate as free-loafers, low-lifes, or undesirables,  are also looking down on the sick, the homeless, the lonely, the imprisoned, the hungry, the naked. To those who mistreat these least brethren of the Lord with distain, the Lord will rebuke them at the End Of Time saying so long as you have done unto them, or failed to do unto them, you have done to me or failed to do for me.

 

 

Yes, it seems that even the just will be surprised at the Final Judgment as the just will too ask the Lord, when did we see you hungry, thirsty, naked, in prison, sick, lonely, or homeless, to which the Good Lord will respond the same way as He did for the ones He will rebuke. Rest assure, there will be many, many, Lazarus’ dinning in Glory with the Lord. These poorest of the poor are among the least who will be the among greatest.

 

 

 

Thus, we have pondered the Human Soul as a Being Of Light, As A Person Of Light. Pray for the Souls in Purgatory who are undergoing purifying hard times.

 

 

54) Perhaps A Substantial Self Transcendance Of The Human Soul As An Abstract Eternal Ideal Or Form

 

Those of us who are diehard Soul Freaks who  enjoy thinking about or contemplating the Human Soul I hope will really enjoy this post.  This post may seem strange coming from a 380 pound obese and overly corpulent guy who can and does multiple sets of rapid pushups in good form every day. However, no one ever accused me of being normal. In reality, I am a clown at heart and even once considered becoming a circus clown. Heck, back a couple or so decades ago during the famous NFL players strike, I started planning to contact my local team, the Washington Red Skins to see if I could tryout to become a so-called scab or new recruit replacement player.

Scholastic interpretation as promulgated by Saint Aquinas of the nature of the human soul, holds that the human soul is:  1) Spiritual, 2) Naturally immortal, 3) Incorruptible per addends and per se, 4) Simple, 5) Unextended, 6) Without shape or size, 7) Non-material,   8]   Non-corporeal, 9) Rational, 10) Free,  11) A first created principle, 12) An essence or a being which exist per se, 13) Independent of the body for its existence and to some extent its operations in this life, 14) The substantial form of the body in the Ancient Greek philosophical sense of the word, 15) Directly created by God, 16) Immediately created by God, and if I am not mistaken, 17) Multiple meaning that it is completely and totally present and united to every portion of the human body that is alive.

 

The modern Catholic approach to the immortality of the soul is somewhat ambivalent about the spiritualistic extreme ideologies of Saint Thomas Aquinas described above, however its modern viewpoint backed by the full weight of the highest levels of the Church Hierarchy is that the human soul is: 1) Immortal, 2) Spiritual, 3) Rational, 4) Does not die when separated from its body at death, 4) Immediately created, 5) According to the index of the first addition of the new Catechism of the Catholic Church, directly created by God; 6) The seed of eternity we bear within ourselves, 7) Not reducible to the mere material world;   8]   The form of the body.

 

From the new Catechism of the Catholic Church which was approved by the very highest levels of the Vatican during 1980s, we can trust that the following is true.

Part 1, Section 1, Chapter 1, SubSection 2

 

33 The human person: with his openness to truth and beauty, his sense of moral goodness, his freedom and the voice of his conscience, with his longings for the infinite and for happiness, man questions himself about God’s existence. In all this he discerns signs of his spiritual soul. The soul, the “seed of eternity we bear in ourselves, irreducible to the merely material”, 9 can have its origin only in God.

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 1

 

360 Because of its common origin the human race forms a unity, for “from one ancestor [God] made all nations to inhabit the whole earth”: 226

 

O wondrous vision, which makes us contemplate the human race in the unity of its origin in God. . . in the unity of its nature, composed equally in all men of a material body and a spiritual soul; in the unity of its immediate end and its mission in the world; in the unity of its dwelling, the earth, whose benefits all men, by right of nature, may use to sustain and develop life; in the unity of its supernatural end: God himself, to whom all ought to tend; in the unity of the means for attaining this end;. . . in the unity of the redemption wrought by Christ for all. 227.

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 2

 

363 In Sacred Scripture the term “soul” often refers to human life or the entire human person. 230 But “soul” also refers to the innermost aspect of man, that which is of greatest value in him, 231 that by which he is most especially in God’s image: “soul” signifies the spiritual principle in man.

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 2

 

366 The Church teaches that every spiritual soul is created immediately by God – it is not “produced” by the parents – and also that it is immortal: it does not perish when it separates from the body at death, and it will be reunited with the body at the final Resurrection. 235

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 2

 

367 Sometimes the soul is distinguished from the spirit: St. Paul for instance prays that God may sanctify his people “wholly”, with “spirit and soul and body” kept sound and blameless at the Lord’s coming. 236 The Church teaches that this distinction does not introduce a duality into the soul. 237 “Spirit” signifies that from creation man is ordered to a supernatural end and that his soul can gratuitously be raised beyond all it deserves to communion with God. 238.

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 4

 

382 “Man, though made of body and soul, is a unity” (GS 14 # 1). The doctrine of the faith affirms that the spiritual and immortal soul is created immediately by God.

 

Part 1, Section 2, Chapter 3, Article 11, SubSection 1, Heading 2

997 What is “rising”? In death, the separation of the soul from the body, the human body decays and the soul goes to meet God, while awaiting its reunion with its glorified body. God, in his almighty power, will definitively grant incorruptible life to our bodies by reuniting them with our souls, through the power of Jesus’ Resurrection.

 

Part 1, Section 2, Chapter 3, Article 12, SubSection 6

1052 “We believe that the souls of all who die in Christ’s grace . . . are the People of God beyond death. On the day of resurrection, death will be definitively conquered, when these souls will be reunited with their bodies” (Paul VI, CPG § 28].

 

Part 2, Section 2, Chapter 1, Article 1, SubSection 7, Heading 5

1280 Baptism imprints on the soul an indelible spiritual sign, the character, which consecrates the baptized person for Christian worship. Because of the character Baptism cannot be repeated (cf. DS 1609 and DS 1624).

 

Part 2, Section 2, Chapter 1, Article 2, SubSection 3

1304 Like Baptism which it completes, Confirmation is given only once, for it too imprints on the soul an indelible spiritual mark, the “character,” which is the sign that Jesus Christ has marked a Christian with the seal of his Spirit by clothing him with power from on high so that he may be his witness. 121

 

Part 3, Section 1, Chapter 1, Article 1

 

1705 By virtue of his soul and his spiritual powers of intellect and will, man is endowed with freedom, an “outstanding manifestation of the divine image.” 8

 

Part 3, Section 1, Chapter 1, Article 1

 

1711 Endowed with a spiritual soul, with intellect and with free will, the human person is from his very conception ordered to God and destined for eternal beatitude. He pursues his perfection in “seeking and loving what is true and good” (GS 15 § 2).

 

Part 3, Section 1, Chapter 2, Article 3, SubSection 2

 

1934 Created in the image of the one God and equally endowed with rational souls, all men have the same nature and the same origin. Redeemed by the sacrifice of Christ, all are called to participate in the same divine beatitude: all therefore enjoy an equal dignity.

 

No doubt, many of the quotes are truncated and so it is possible that I may have non-intentionally altered the spirit of the meaning of the Catechism, however, the general ideas expressed in the above quotations are essentially true.

Now, what if the human soul is immortal be grace only. Well then,  we would need to accept that even the souls who are consigned to eternal damnation have the eternal grace of immortality because all human souls are immortal.

Even in the case that some human souls might be accident-wise, accident-wise and faculty wise, or accident-wise, faculty-wise,  and substantially destroyed by mechanisms not clearly open to human understanding, all such damaged or destroyed souls will be Resurrected at the End Of Time and re-united with their body where  the Resurrected Human Body will be spiritualized and incorruptible. I would wager that any souls who might unfortunately face the prospects of natural soul death will be all the more rewarded with additional degrees of incorruptibility for having gone through the martyrdom and Cross of any soul death unknown to modern Catholic Dogma and Teaching. After all, what dies on a metaphorical Cross will be Resurrected with commensurately enhanced natural and supernatural glory.

Note that speculations on soul death are controversial and certainly not within the bounds of common consideration by the Catholic Church’s teaching authority and so I make the disclaimer that my speculations on the notion that some souls may unfortunately be damaged or destroyed by created events does not represent Catholic Dogma and Church Teaching. However, that absolutely all humans will be Resurrected as whole and complete persons, body and soul, at the End Of Time, is precisely Catholic Church Teaching and is the very backbone of hope for absolutely all Catholics, and implicitly, for all persons of any faith or lack thereof,  in this life.

 

Christ’s merits for us due to  HIS Crucifixion,  Death, Resurrection, Ascension, and Fatherhood of the World To Come by permission granted from His  ETERNAL FATHER or THE MAJESTY ON HIGH WHO  dwells in Unapproachable Light, are available to all human persons. Many, many, human persons who profess no religious belief system are in the state of grace regardless of whether or not they would ever be predisposed to assert the reality of the existence of a Saving GOD. I see many instances of noble, intimate, and caring behavior among folks, some of which do not hold to any religious belief system, and such kindness is an unmistakable sign of friendship with GOD.

Now what if the human soul is immortal by grace only or perhaps that it is not naturally incorruptible? Would this really matter all  that much?

I have struggled with these questions for 3 ½ decades and I must admit, sometimes in past decades out of worry, insecurity and sadness at the prospect that I could not prove to myself that the human soul was naturally incorruptible, I would cry myself silently asleep at night. I would at times even become angry with those who expressed their opinion that the human soul is immortal by grace only.

However, I ask again, Does it really matter?

My reply which was developed by flashes of abstractive insight over the past few days is that the human soul is likely naturally immortal, but that even if it is not, it would not really matter according to  the following arguments.

First, the human soul is commonly and universally traditionally held to be the substantial form of the body in the Platonic sense of an abstract eternal form or ideal. The phrase substantial does not mean a physical substance like material such as the maple syrup I will likely coat my waffles with  for breakfast tomorrow, a No! No! for me as I am a successful weight losing Weight Watcher and a very physically corpulent one at that with a current weight of 380 pounds and a height of only 5 feet 10 ½ inches. Rather the world substance means a first created principle that depends directly on GOD for existence and which therefor does not need any other created agent including the human brain for its existence and to some extent, does not even need the brain for some of  its operations  or activities in this life.  The use of the word form is not meant to be confused with the false notion that the human soul has the shape or geometric form of its body. The word form in the context of the Human Soul simply means that the soul is an abstract ideal much like the number one is a form or the notion of an absolutely perfect circle is an ideal form even though space-time-mass-energy quantization would prevent a perfect circle from ever being drawn in any physical recording medium, at least on this side of the Final Resurrection or before this universal glorification to come.  Any physical personal shape that those having had out of body experiences such as those having had near death experiences or those capable of the dubious phenomenon of astral-projection claim to experience is likely no more than that due to an energy body or a body made of residual electromagnetic energy that has somehow congealed and as such, any such energy body could not be the same as the human soul, nor would they be the same thing as the Resurrected and Glorified Human Body to be at the End Of Time. Any valid energy body experiences do not imply a separation of the Soul from the molecular  Body and in fact cannot because such separation only occurs upon non-recallable physical death.

The new Catholic Catechism drops the modifying preface substantial and merely refers to the Human  Soul as the form of the uma

 Human body but clearly affirms its existential distinction from the human body.

Now being that the Human Soul can be stated as the form of the human body and even the substantial form of the human body, we can extrapolate on this fact with the further understanding that the human soul is the very life principle of identity, individuality, uniqueness, and unity of the human person. Since the human soul is a form and  is most likely further qualifyable as a substantial form,  this ontological condition of being a form also necessarily incorporates the existential reality that each human soul is the very life principle of identity, individuality, uniqueness, and unity of the human person. Thus, the ontology of the soul being an eternal form spills over and is inseparably existentially blended with the nature or substance of the human soul as the very life principle of identity, individuality, uniqueness, and unity of the human person. Consequently, these later four properties of the human soul are ontologically related to the eternal form-ness of the human soul in a substantial if not essence-wise manner. This follows from the fact that the most truest and deepest aspect of the human soul is for it to be the specific very life principle of identity, individuality, uniqueness, and unity of the human person.

Since the human soul is an eternal form and a first created principle which is directly and immediately created ex nihilo according  to the great angelic Doctor of the Church,  Saint Thomas Aquinas and at least immediately created by GOD according to the new Catechisms of the Catholic Church, we know that ontologically, the soul is at its highest and most innermost aspects, an eternal form where this eternal form-ness has close association if not identicality with the soul as the very life principle of identity, individuality, uniqueness, and unity of the human person.

Perhaps even if the spiritual substance of the human soul is not naturally incorruptible per addends and per se, the fact that the human soul is an eternal ideal is eternally incorruptible since eternal forms are eternal and have existence independent of physical or spiritual created materiality.

Suppose some souls might unfortunately be accidentally, accidently and faculty-wise, accidently, faculty wise, and substantially be destroyed in mechanisms not clearly open to Church scrutiny. The fact that the such deceased souls are of an eternal form perhaps would ontologically persist even after complete substantial destruction  of the human soul. After all, what is a priori metaphysical truth can never be erased. It is likely that the moral truth within the Human Soul can also likewise never be erased even upon an instance of any unknown and unfortuitous substantial soul destruction.

I therefore quote Blessed Pope John Paul II which an exhortation to BE NOT AFRAID! In the midst of natural calamities known and unknown, wars global or local, and sickness and affliction, everything will work out for you in the end. There mere fact that you have taken an interest in reading this article  shows that you are,  at the very least,  in a certain measure of good standing before the Lord.

Heck, you are most likely in better standing than I am if you are Catholic because although I attend the Sacrament of Confession about twice per month and attend daily mass on most days, I will receive communion about only twice every two weeks. In fact,  my temperamental outburst on one of my websites yesterday over the fact that my computer has been hacked again tells me that in order for me to feel properly disposed to receive the Eucharist, I must first obtain Sacramental Absolution. A far out thinker, definitely yes! A Saint,  definitely no especially in consideration of my proneness to impulsive angry and judgmental rants on line.  For the record, I have prudently removed my antagonistic comments from the subject website.

I make the claim that I hereby permit folks to copy and distribute this material and to come up with further elaborations on the subject matter. I am merely staking a claim for the wordage and sequence of ideas expressed herein and the conceptual content to the extent that such is uniquely my work so that I can more readily incorporate these concepts in a book I will eventually write on the Human Soul.

In the meantime and according to my primary life’s vocation to be an advocate and concept validator and developer for the pro-life technology within the field of interstellar astronautics, I say.

“BEAM ME UP, SCOTTY!”

55) The Morality Of Absolutely Each And Every Human Soul As A Transcendent Aspect Of The Soul As Form

 

The morality in and of the human soul can be intuited by the fact that our eternal destiny is so much a consequence of the morally informed choices that we make.

 

Even the souls in Hell can be said to possess a morally informed nature for the reasons, some of them anecdotal, given below.

 

First, the souls in Hell suffer because they do not see GOD face to face in the Beatific Vision. The mere fact of the resulting suffering indicates an un-met need of the souls in Hell, otherwise there would be no pain in such deprivation. Thus, we can intuit the moral truth and moral aspects of the souls in Hell simply from the fact that they long to see GOD but know the cannot. This inner longing reveals a moral nature of the souls in Hell in the sense that, however dormant or latent, there is a desire to perhaps be in Heaven. These souls would not miss the Beatitude in Heaven if they were not is someway suffering due to such deprivation. In a sense, a need signifies a desire and a deprived all-consuming desire is one of the deepest reasons for and measures of suffering.

 

Second, is the Biblical account of the rich man in Hell who desires consolation when he sees Lazarus in Heaven. The rich man begs for a drop of quenching liquid, but when his desires are refused, the rich man begs that his relatives on Earth are warned so that they do not suffer the same fate as he does. Whatever the personal motives of the rich man, he had the morality to ask that his relatives would not suffer the same fate as he has. In a sense, such morality seems hard to distinguish from charity.

 

Third, I remember reading of an account in a popular spiritual book where two men lived squandering and revoltingly immoral life styles. I believe that at least one of these men was a military general. These two men made a pact that whoever died first would come back and tell the other what the afterlife is like. One of the two men died and according to the story, did not repent and as a result, went to Hell.

 

The condemned man at some point appeared to his still living comrade in  a profusely sweaty and overheated appearance, and with great discomfort, pleaded with his still living comrade not to continue living a depraved lifestyle or else the living comrade would suffer the same fate as the deceased man had.

 

Note that we need not shirk too much from the above third example, as modern Catholic understanding of the Sacraments of Baptism, Confirmation, and Holy Orders holds that each confer an indelible supernatural character or seal within the human souls of recipients, and that such characters per du into eternity, even amidst the metaphorical fires of Hell.

 

I don’t know, but this act of warning to me seems like an act of charity of the ultimate form since the condemned man evidently knew where he was to be consigned for all eternity. Yet, he was presented by GOD the opportunity to help save his living comrade and did so.

 

I am reasonably sure that in the annals of human history, past, present, and future, other cases of such almost bazaar seeming acts of charity will be revealed if additional ones have not been revealed already.

 

Fourth, every time a human person attends the Sacrament of Confession to come back into a state of grace, or into a higher level of grace such as when no unforgiving mortal sins are present, a moral predisposition is already manifested by the penitent  in his or her  knowing that  he or she needs to confess.

 

As for myself, a frequent attender of Confession, I can easily intuit a morally oriented human nature by the mere fact that I have often stood in a line for confession in a Church while at times being agitatedly anxious about whether the priest was  going to give me a good verbal slam dunk of sorts. In spite of perhaps some very heavy sins to confess at times and the distress of standing and waiting, I have frequently gone to confession and will continue to do so, because there is something deep within my psyche that draws me to confession, even in cases where I could in all probability and objectivity have had one or more mortal sins to confess.

 

Thus, it seems that the morality of human nature is inherent, absolutely ubiquitous, and eternal.

 

Now the human soul is the substantial form of the human body it informs according to Saint Thomas Aquinas. Even according to the new Catechism  Of  The Catholic Church which does not so much emphasis a more dualist Scholastic approach of understanding of the Human Soul, the Human Soul is the form of the Body it is united to. Here, we use the word “form” more in a Platonian and Aristotelian sense of the word as a perfect abstract ideal that really exists.

 

For example, a perfect circle or perfect square is an eternal form even though we could never draw a perfect circle or a perfect square, not even in theory,  due to the quantized nature of space and time and of mass and energy  as well as due to the Heisenberg Uncertainty Principle. Thusly, the human soul is an abstract eternal form of the body in some sense.

 

Perhaps the human soul as the eternal abstract ideal or form of the human body is more related to the human body’s substantial underpinnings or the raw featureless mass-energy composition of the human body and not so much to the accidental form of its physical and geometric extensity. Thus, perhaps the human soul can be an eternal abstract form without having any geometric or topological size, nor extension, of any sort.

 

If the human soul is indeed a form, an aspect of its form-hood or form-ness is to be the substantial form of the human brain which appears to be the seat of consciousness in the form of emotion, intellect, affect, sensation, and volition in this life.

 

To the extent that mass and energy can evolve to produce waking consciousness, as such definitely appears to have occurred in non-human animal life forms on Earth , many of which display noble behavior such as military service dogs  and K-9 police dogs, such a mechanism is also most likely largely prevalent in human rationality and noble conscious behavior.

 

To the extent that consciousness in the forms of emotion, affect, thought, memory, and will are generated within the brains of living humans and therefore appear to be at least somewhat of an aspect of raw mass energy, or if not, then specifically ordered mass energy in the form of a living human brain, then perhaps the human soul is a form-ness of said conscious, sub-conscious, and unconscious aspects of the living human brain.

 

Such a form-ness would entail the human soul as being the abstract eternal form of our brain based conscious faculties and states. This form-ness would be very profound.

 

Since I am a Scholastic, I do not buy the overzealous selling of the Theology Of The Body, that seems to be un-intentionally leading folks into a sort of moral cult of the body and into the denial of the existence of conscious human souls in the afterlife. Rest assure, the most fully alive and most dejected souls in Purgatory feel the same way when not receiving any personal prayers of the faithful for their release from Purgatory.  Our Lady Of Fatima emphasized prayers for the souls in Purgatory with Divinely inspired Wisdom.

 

To be in part the eternal,  abstract,  form of emotions, thoughts, active volitions, affects, feelings, and for especially 375 pound, more or less,  average height guys like myself on Weight Watchers who still love to eat, also basic primal consumptive drives such as tendencies toward gluttony,  is a wonderfully substantial aspect of the human soul. Perhaps I should not dwell on the later aspect. I have a sibling who would disapprove of such a broadcast. Note that I have greatly moderated my tendency toward gluttony, and no longer gulp down a half of a family size box of Cheerios at midnight, with the little Os occasionally rolling down my shirt onto the floor like a tire rolling down a hill. My past overeating was unfortunately a real freak show.

 

Since all humans, dead or alive, manifest some level of inherent pre-disposition to latent morality, this morality can be interpretable as a an inherent aspect of the human soul or an aspect of the substantial nature of the human soul.

 

This ideal or morality in the human soul is an eternal principle and abstract aspect of the human soul to the extent that morality exists in creatures. Since moral truths are higher than metaphysical truths, a likewise transcendental inherent aspect of the human soul is demonstrated especially that which is commensurate with the exalted status of moral truth over metaphysical truth.

 

 

The morally informed nature of the human person as intuited from an existence of a radically free human will in a sense attests to a certain  higher level or moral pre-disposition over any bodily intelligent extraterrestrial or any ultra-terrestrial races or species that have not sinned thus avoiding a fallen nature. We humans can radically go from serious mortal sin to radically sin-free states by Sacramental absolution and by making the intention to receive such forgiveness in an as common-place and ubiquitously ordinary act as standing in a line for the confessional.

 

 

Even for non-Catholics, free choices and apparent restoration from sinfully lifestyles abounds just as assuredly as public figures, politicians, Hollywood celebrities, and professional athletes, can go from a proud fall into disgrace and then change their ways and start not-for-profit organizations to feed the hungry, help the addicted and mentally ill, shelve the homeless, heal the sick, or to mentor the youth.

 

 

When we regain a sense of mystery about the human person especially with regard to all that goes on during embryonic conception, we will regain a sense of respect for the conjugal act and for human sexuality in general. Human sexuality has a profoundly spiritual dimension and such sublimity is sexy and attractive in its own right. Upon this realization, folks will see the error in the use of artificial contraception.

56) An Energy Body As Distinct From The Human Soul: A Sort Of Little Philosophically Understoood Middle Ground Between Soul And Body

Will any energy body or spirit body as distinct from the spiritual and immortal human soul also be Resurrected to a glorified state of incorruptibility?

My guess is that since the entire human person will be Resurrected Immortal as a complete unity, body and soul, any energy body or spirit body will also take part in this Resurrection and will too be glorified into a much more spiritualized and immortalized state.

I propose that any energy bodies or spirit bodies are not the same thing as the human soul. I also propose that certain created agents can destroy or annihilate the human energy body such as close proximity to the heart of a nuclear explosion, a supernova, a black hole, and a whole host of other mechanisms but I will spare the reader the unpleasant details due to the sensitivities that some folks would have one this subject matter. However, rest assured, if we humans do in fact have an energy body, even in cases where it might be temporarily destroyed, it too in all cases will arise incorruptible and immortal.

Could this energy body in its eventually glorified and recreated form be related to at least an aspect of the incorruptible life that will be definitely granted to the Resurrected Human body. My guess is that this may be the case but that the Human Physical Body itself will be spiritualized and immortalized with its very own incorruptible life. The degree of incorruptibility of the Resurrected Human Physical Body will be commensurate with the following paraphrase of Sacred Scripture. “What is sown in dishonor will arise incorruptible. The mortal Earthy body will arise a spiritual body.” And the list of wonderful qualifiers about the human body continues throughout a whole chapter in Sacred Scripture.

Even the souls who do not make it to Heaven or any Limbo will too have their bodies arise incorruptible, in fact so much so that not even the metaphorical fires of Hell will be able to consume it. However, realize that the phrase Fires of Hell is a metaphor and we cannot at this point have any clear or certain knowledge about the nature of suffering and deprivation of those who go there. We do not even know to what extent the eternal life universally merited by Christ’s conception, birth, life, Crucifixion, Resurrection, and Ascension into Heaven will be lived out in Hell. One thing is for sure, Catholic theologians generally hold that the Supernatural Sacramental Seal or quality inherently imprinted within the Souls of recipients as conferred  by Sacramental Baptism but which depends on Divine power as well as that for Sacramental Confirmation which also depends on Divine power,  per dues into eternity.  Thus, once a Catholic,  always a Catholic,  even amidst eternal damnation.

However, the energy body or spiritual body, if it exists, will arise incorruptible on the last day in all cases. You can be assured that just as I am confident enough to put these conditional speculations out there for all to see on my website, I stand de facto by my conclusion, the caveat being that we humans actually have an energy body, a notion that  the Catholic Church neither teaches nor endorses. However, no faith, not even the Catholic Faith has a monopoly on metaphysical truths regarding human spiritual ontology or spiritual anthropology.

As you can see by my numerous posts over the years on the subject of spiritual anthropology, I am on fire with zeal for speculative thinking about the nature of the Human Soul, any Human Energy Body, and the Resurrected Human Physical Body to be.

My zeal for spiritual topics comes about from a loosely conservative Catholic upbringing as I was Baptized soon after birth as were all of my siblings. My parents, all four grandparents, all 8 great grandparents, my step grandmother, all of my aunts and uncles, and cousins are also Catholic. I have an aunt,  Sister Joanne, who  is a Nun and a very devout and holy one at that.

My Catholic faith has ironically led me to devote my life to the subject of interstellar space craft propulsion system theoretical research and development and to  consider and conclude that there are likely literally infinite numbers of intelligent technological extraterrestrial and ultra-terrestrial civilizations out there of diverse ETI and UTI peoples that have bodies more or less similar to or analogous to our bodies and which are entirely distinct from the pure bodiless spirits known as the Angels. There are likewise,  in my opinion, an infinite number of body types for ETI and UTI as well as the same for these wonderful peoples personality trait  spectrum profiles.

However, do not worry! I am not bragging about my faith. I will happily admit that although I go to confession about twice per  month, and attend daily Mass, I only receive Sacramental Communion about three times per month. I have a great deal of  trouble completely avoiding sins that would ordinarily constitute the need to receive Sacramental absolution before receiving Sacramental Communion.  My sins range the  whole spectrum from sins of harsh impulsive temperamental language, excessive self-will, sins of impurity, gluttony although not so much anymore since I have successfully started Weight Watchers Online and have lost 45 pounds so far,  taking the Lord’s name in vain, and so on, and so on.

So despite my far out thinking, when you get right down to it, I have some serious moral weaknesses to work on, and morals are important just as moral truth is important, which is an entirely different form of truth than metaphysical truth and in some ways, far more profound and important.

For non-Catholics who are interested in learning more about the Catholic Faith and/or who would like to become Catholic, please do not be put off by some of the offensive moral grand-standing I have been guilty of in some of my previous posts. This moral grand-standing is not what the Catholic Faith is about, and I apologize to all those I have thusly offended or intimidated. Do not look up to me as an example, but rather look to Jesus, His Mother Mary, Each of the Three Divine Persons in Their Divinity, and GOD THRICE HOLY, THE HOLY TRINITY as ONE GOD HEAD, HE who the Ancient Hebrew Faith referred to as HE WHO IS and who revealed HIMSELF to Moses as I AM THAT I AM, or I AM, YEHWEY! GOD, Calls You By Name To An Ever Deeper Dynamic And Passionate Intimacy With Him. In fact, HE sent HIS ONLY SON,  to take on a Human Nature and to die on the Cross, just for you individually.

Talk to  a local priest, or Bishop, or give them an email of inquiry about how you can become Catholic and what you will need to do. For Catholics who have left the pews, come on back! The Church is still the same but the Holy Mother Church has likely matured in many ways during your absence from the Pews.

 

57) The Fire Of The Experiential Life Of The Human Soul And Its Capacity For Self Transcendence

 

Each human soul, to the extent that it is naturally alive, is teeming with conscious experience and activity. Those of us who are at least somewhat familiar with the field of psychology as I am and folks in general label this conscious activity in the following primary categories: 1) thoughts; 2) emotions; 3) feelings; 4) drives or instinctual impulses; 5) acts of will; free, semi-free, and non-free; 6) sensations; 7)  some would say psychic paranormal experiences; 8) intuitions; 9) memories which can have any of the previous 8 features; and 10) combinations thereof.

 

Regardless of whether a given human soul is united to a living body in this life, is in Heaven, Purgatory, any Limbo, or  even in Hell, the human soul at some natural level is teeming with consciousness in all of its possible broad categorical forms, that is of curse  the forms that are possible in each of the three or possibly four states and/or places after bodily death.

 

The state of the consciousness or personal subjective identity of each human soul is in constant flux as we go about our daily activities in this life. Yet despite this at times roiling cauldron of the fire of consciousness and experience, the fire burns on as personal experience and as part of the accidental aspects of our human soul, all of which despite being accidents, really exist.

 

Our consciousness seems to be an inherent aspect of our souls, and indeed it is because it defines the activity, psychodynamic energy, accidental features, and characteristics of the faculties of our soul which are generally characterized as the intellect, will, memory, heart, and power of sensation. We identify this at times roiling sea of consciousness as being our soul or our personal identity and rightfully so because it is, but nonetheless, it is not the full story of the Human Soul.

 

The fact that this at times roiling consciousness of subjective experience is in constant change throughout  our daily waking life and yet still seems ever to be our same selves indicates that this roiling psychodynamic activity is in a sense self-transcendent. Otherwise, how could we intimately experience such activity as our-selves in a stable manner with all of the constancy commensurate with continuous  experienced personal identity.

 

From an objective,  ontological, and  epistemological consideration, such a constant sea of change within the personal conscious psyche also affirms a substantial underpinning that is as enduring and personal as to its identity as a soul in Heaven, Purgatory, Limbo, and even in Hell remains itself in such an utterly stable manner commensurate with the possibility of  the immortality of the soul and the utterly eternally enduring existence of each human soul, no matter what its ultimate fate in the afterlife. Even the souls that go to Hell are unalterably themselves and have an un-alterability in their personal identity commensurate with the possibility of eternal punishment.

 

Even for the souls that go to Hell, the personal identity and therefore the substantial underpinnings of such identity must be of utmost stability throughout all eternity commensurate with the possibility of moral judgment and moral responsibility for their behavior while united to their human body while having lived here on Earth.

 

For clergymen who are utmost literalists in terms of traditional interpretation of the meaning of eternity for Hell, even you must admit that absolutely stable substantial and even conscious identity of each soul in Hell is required to a degree commensurate with the eternal  moral obligation and responsibility to which the soul is held in suffering for all eternity. If the souls in Hell had no personal stable identity, either objectively so and substantially, and consciously so and subjective, then they would not have a personal identity commensurate with being able to experience the pains of Hell for all eternity.

 

But let us not dwell too much on the sad reality of Hell as none of us should want to go there.

 

The same arguments can be made for souls that go to Heaven, either directly or from Purgatory, or to any Limbo. For souls that go to any three of these locations and/or states,  the personal conscious identity, perhaps even at the natural level is enhanced commensurate with spiritual health and well-being.

 

Thus we can intuit something about the dynamical activity of life in the human soul as implying a super-stable soul essence or soul substance amidst the change of  daily time-varying soul activity. This daily changing of soul activities seems to imply an extra-dimension of the soul  thereby making the soul all more full existentially, even at the natural level of the life of the soul. The continuous soul activity seems commensurate with the soul constantly becoming and already being on track at each point in subjective time to not be itself and as a result, seems implicit of soul self-transcendence, and even the transcendence of the soul’s dynamic life with respect to the eternally self-same soul essence or substance.

 

As long as the human soul can naturally evolve, even if only in accidental form, to a state that did not previously exist, the human soul should be held as capable of self-transcendence, at least with respect to its ability to change in future subjective time with respect to its present accidental state.

 

 

58)  Time And Souls

 

 

The body will be definitively granted its own incorruptible life at the Final Resurrection and will be a perfect body in look, form, and function just as Jesus’s Resurrected Body is such.

 

For all women who read my blog who may have issues with anorexia and/or bulimia, or who struggle with body image, the Lord wants you to know that He deeply beholds the beauty of your female body, and you will have a body that infinitely surpasses the beauty of the most gorgeous bodies on Earth at present, and which will be radiant beyond belief with natural and supernatural beauty at the substantial and accidental level. Your body will be spiritualized in a manner that is currently unknowable. And this spiritualized body will not be the same as any spirit body or energy body that those having near death experiences claim to experience, but rather will be both a real physical body and a real spiritual body that has unimaginably more depth to its existence that any temporary spirit or energy body could ever have.

 

But you also have an immortal and spiritual soul that will also be glorified at the Final Resurrection. The Catechism of the Catholic Church also refers to the human heart as the inner core of our being that only we and GOD alone have access to and by which we decide for or against GOD.

 

 

Ever wonder about the deep  meaning of the statement, “Time is all we got!”

 

Well consider that our souls are created at the point in time of our conception and that according to the new Catechism of the Catholic Church and also in its Revised Version, the human soul is immortal, spiritual, rational, radically endowed with free will, immediately created by GOD, and in the index of the original edition, directly created by GOD, and not reducible to the mere material world, the principle of unity and identity by which we most resemble GOD, and the list of wonderfuls goes on and on.

 

It seems likely that the past states of the human soul in terms of experiences, whether of a mental, volitional, emotional, effective, sensitive, romantic, or whatever level are conserved in the present state of each human soul, and so even in the subjective sense of personal identity, the human soul continues to grow with time and will always grow with subjective dynamically experienced  consciousness from a mental, volitional, emotional, effective, and sensitive standpoint, even in the next life, regardless of where we end up.

 

Since the human soul is simple and unextended in a metaphysical sense, might the objective nature, essence, substance, and existentiality of the human soul also grow for all eternity?

 

I am proposing that just as our physical universe may evolve and grow forever, or just as our multiverse may evolve and grow forever, as a unity in a present that evolves without temporal future limits, perhaps the human soul as a substantial unity simply grows along its own world line of subjectively experienced time, and thus since the soul is its own principle of life and identity at least as far as its spiritual aspects are concerned, perhaps it self grows for all of future subjectively experienced times steps in all cases, if not in a consciously controlled manner, then perhaps in an autonomous, automatic manner.

 

I know that life can be difficult in the culture that is obsessed with being thin, and model like in appearance, but remember you are wonderfully and beautifully made by GOD, and you will be infinitely gorgeous by all objective and subjective metrics upon your complete Resurrection at the End of Time.

 

I am especially speaking to all of you women and girls who have body image issues. Trust me, you are not alone, I have known folks with such conditions and I have a relative who has been hospitalized for eating disorders. I find that some of the most attractive and beautiful women have serious body image issues.

 

As a large guy, in fact a 369 pound husky large framed guy, although obese, because I am a guy, I am not as effected by body image if for no other reason than society is more forgiving of guys who are overweight  then of women.

 

Still the thought and realization that I need to respect my body since it will be a part of me for all eternity, has lead me back into a regular weight training and walking program. I took a 4  mile walk yesterday  and found the walk very refreshing.

 

For all those of you who are depressed about your body or your state of life, give a gentle outdoor walk for about 45 minutes a try. Do not over exercise, but try to get some sunlight every day. I have been making an effort to walk on most sunny days and my mood is more joyful yet calmer because of it.

 

60)  Emotions Are Great.

 

Emotions are great! While any human algorithmic reasoning process can in theory be duplicated by digital logic routines including computer applications, emotions are that sort of thing that has no shape, color, size, and no algorithm can simulate subjectively experienced emotion.  Moreover, each emotion is experienced within the context of the human person experiencing it and so even perfect telepathic transmission cannot allow signal receivers to experience the emotion of a transmitter in the way that the transmitter experiences the emotion with respect to himself or herself.

For example, an Al Qaeda terrorist cell member planning an attack experiences his or her plans as good or as something which is useful and pleasing to his or her agenda and internalizes the plan with a deep sense of motivation to perform the crime. Were a devout Catholic who borders on Sanctity somehow enabled to read the heart and mind of the person involved in planning an attack, the Catholic would likely be repulsed by  the experience of the telepathically transmitted thoughts, emotions, and sense of motivation transmitted from the terrorist. To the Catholic, the plans would likely be viewed with disgust whereas to the terrorist, the plans would likely be experienced with an eager sense of anticipation.

I could give countless other algorithmically described examples of which there are likely ensembles or more categories with perhaps utterly infinite numbers of perceptual and emotional nuances that could be experienced, transmitted, and/or telepathically received and so I will not provide any additional examples.

Emotions, be they base and primitive such as those associated with my early morning hours pig out in which I gobbled down 3,000 calories in a feeding frenzy  last month (LOL, for which I reminded myself of a shark),  or passionate, romantic, and erotic such as those experienced by lovers during sex, or perhaps  those  experienced by angels and the souls of the deceased as spiritual emotions, each emotion in itself has no inherent color, shape, and the like except for emotions associated with bodily somato-sense in which case, the person experiencing the emotion might feel as though the emotion has a shape in terms of the  its association with bodily somato-sense. Even in the latter case, the emotions and feelings are non-physical.

Mental sensory depictions such as those that are auditory and visual can indeed be duplicated in theory by the person experiencing the sensations such as by paintings, motion pictures, videos, sound recordings and the like, and to the extent that the imaginative or experienced color, shape, and tone patterns and auditory patterns can be duplicated by the person experiencing such sensory aspects to an extent that the person would recognize the similarity of the recordings or generated images with respect to his own personal visual and auditory experiences, the  recreated images can be duplicated by digital algorithms including computer applications. However, the purely emotional aspects of such images such as fear, joy, anger, disgust, and the like which are usually experienced along with emotionally charged images in a manner that is inseparable with the sensory images cannot be duplicated by algorithms to the extent that such emotions and feelings have no identicality labels by which they could be depicted within visual and auditory recording media commensurate with a person being able to say things such as, “Hey, look at that painting of my feelings or emotions!”. No doubt, however, that the visual and auditory content of such    emotional experiences can be represented as sure as I could take a photograph of a most delicious pepperoni and mushroom pizza and later recognize that the photo is of the pizza as I saw it when I took the photo. However, the photo would not have my subjectively experienced emotions and feelings regarding the taste of the Pizza in the form visual recordings of such emotions or feelings as they were subjectively experienced by me. No doubt, however, that the picture could be produced with odors and scents of the pizza that I would then recognize as being similar to that of the pizza. Mechanisms similar to the latter considerations are used all the time such as in printed advertisements for perfumes and colognes.

In short, there are aspects of subjectively experienced emotions that quite simply, seem to defy measuring and recording by the physical metrics of length, volume, surface area, optical light frequency distributions, and acoustic intensity and frequency patterns as such patterns are defined by physical metrics such as power,  energy  flux density,  energy flux density patterns, frequency, wavelength and the like.

So, whereas our algorithmic reasoning processes can be duplicated by digital applications, our emotions and feelings seem to have an ironically transcendent aspect by which the “what it is like for a person to experience a given emotion to himself or herself” seems to defy algorithmic duplication on purely physical media.

Perhaps we need to instruct students on how to respect their emotions, feelings, and drives, instead of enabling careless expressions of emotions and feelings such as those of a sexual or romantic nature in non-committed relationships in the forms of pre-marital or extra-marital sex. The enablement of such carelessness may be due in part to an excessive focus on rationality and academic achievement where students desire their abstract and algorithmic reasoning processes to be pure and advanced thus making it easier to casually and carelessly disregard emotions and feelings especially those of a sexual and romantic nature.

Now, I am not saying that everyone should be an emotional softy or warm slush ball, as in fact I tend to suppress many of my emotions perhaps as a result of my stoic German and Eastern European Catholic ancestry and family behavioral patterns that originated in those cultures, however, we in the rational thinking emphasizing modern cultures should step back to consider the possibility that emotions and feelings are not to be shunned as primitive or animalistic. When we do so, we devalue hearts and send a bad example to youth who are often looking for practical advice on how to express their sexual identities. Shunning sexuality in puritanical manners is a bad practice and can be scandalous to youth seeking wisdom on its proper expression.

Now, just how many forms emotions and feelings can be experienced is an utterly unbounded number. Consider all of the human persons who have ever been pro-created and who will  be so and you get an idea of the number of possible human emotions and feelings. Consider   the number of any bodily extra-terrestrial and bodily ultra-terrestrial persons that may have been pro-created and that will be pro-created and the numbers  of possible emotions  and feelings grows to unfathomable infinities. Consider the number of angels both good and bad and the number of sublimely spiritual emotions and feelings grows even higher.

Emotions have that ephemerality such that they are hard to define by algorithmic processes and yet are possessed by all animal life forms on Earth including human persons. Emotions are strange because they are ubiquitously experienced by animal life forms ranging from a bear that becomes dissed when tracked by a hunter, to the most astute of Catholic Monks and Shaolin Monks welcoming visitors to their monasteries with joy and gratitude.

The reality of emotions affirms the ephemerality and profundity of the Human Soul.  For emotions are accidental aspects of our spiritual heart which is a faculty of our spiritual and immortal Souls.

 

 

 

61)  Emotions: What Are They Made Of?

 

 

 

We are all familiar  with a child’s  inquiry to his mother or father about  what a penny is made of. We as adults often inquire about the nature of the wood out of which a nice piece of furniture is made or the materials out of which the latest sweaters are made.  Mechanics will some time remark on the particular alloy of construction of an expensive auto part to a customer whose vehicle he or she is servicing. Aerospace  engineers will often make mention of the newest composite materials out of which various portions of a new fighter plane being developed are made when presenting a summary of company progress on the R&D efforts to military officials. My brother John sometimes gave such reviews as part of company progress reports to top military officials while he worked for United Technologies, Pratt & Whitney Division as a highly skilled mechanical engineer. I do not know the details of the reports because the reports were obviously classified and since I have never had a security clearance, I would at present have no business knowing such details anyhow. In short, all of we humans have a mental schemata in the form of a tendency to ask what something is made of.

Now what about the seemingly  never, never, land of human emotions and feelings? Traditional Catholic Scholastic theologians commonly hold that there is a distinction between the substance of the human soul and its accidents and in some cases between the substance of the human soul and its non-essential aspects which are very close to the substance of the soul such as a soul’s faculties of intellect, heart, will, and memory.

To begin, we will briefly summarize conventional and current thinking about the human soul from a Catholic theological perspective.

Essentially, the Scholastic interpretation as promulgated by Saint Aquinas of the nature of the human soul, that is the human soul is:  1) Spiritual, 2) Naturally immortal, 3) Incorruptible per addends and per se, 4) Simple, 5) Unextended, 6) Without shape or size, 7) Non-material,   8]   Non-corporeal, 9) Rational, 10) Free,  11) A first created principle, 12) An essence or a being which exist per se, 13) Independent of the body for its existence and to some extent its operations in this life, 14) The substantial form of the body in the Ancient Greek philosophical sense of the word, 15) Directly created by God, 16) Immediately created by God, and if I am not mistaken, 17) Multiple meaning that it is completely and totally present and united to every portion of the human body that is alive.

The Catholic Church is currently somewhat ambivalent about the extreme spiritualism of Saint Thomas Aquinas and currently does not seek so much to explain the immortality of the human soul, but nonetheless, holds as a matter of faith that the human soul is immortal and that each human person whether consigned to Hell, in Purgatory, or in Heaven will be Resurrected as a full and complete human being at the Final Resurrection of the Dead, and then so to a nature that will be incorruptible.

 

Now read through these quotations from the new Catechism of the Catholic Church.

Part 1, Section 1, Chapter 1, SubSection 2

 

33 The human person: with his openness to truth and beauty, his sense of moral goodness, his freedom and the voice of his conscience, with his longings for the infinite and for happiness, man questions himself about God’s existence. In all this he discerns signs of his spiritual soul. The soul, the “seed of eternity we bear in ourselves, irreducible to the merely material”, 9 can have its origin only in God.

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 1

 

360 Because of its common origin the human race forms a unity, for “from one ancestor [God] made all nations to inhabit the whole earth”: 226

 

O wondrous vision, which makes us contemplate the human race in the unity of its origin in God. . . in the unity of its nature, composed equally in all men of a material body and a spiritual soul; in the unity of its immediate end and its mission in the world; in the unity of its dwelling, the earth, whose benefits all men, by right of nature, may use to sustain and develop life; in the unity of its supernatural end: God himself, to whom all ought to tend; in the unity of the means for attaining this end;. . . in the unity of the redemption wrought by Christ for all. 227.

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 2

 

363 In Sacred Scripture the term “soul” often refers to human life or the entire human person. 230 But “soul” also refers to the innermost aspect of man, that which is of greatest value in him, 231 that by which he is most especially in God’s image: “soul” signifies the spiritual principle in man.

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 2

 

366 The Church teaches that every spiritual soul is created immediately by God – it is not “produced” by the parents – and also that it is immortal: it does not perish when it separates from the body at death, and it will be reunited with the body at the final Resurrection. 235

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 2

 

367 Sometimes the soul is distinguished from the spirit: St. Paul for instance prays that God may sanctify his people “wholly”, with “spirit and soul and body” kept sound and blameless at the Lord’s coming. 236 The Church teaches that this distinction does not introduce a duality into the soul. 237 “Spirit” signifies that from creation man is ordered to a supernatural end and that his soul can gratuitously be raised beyond all it deserves to communion with God. 238.

 

Part 1, Section 2, Chapter 1, Article 1, Paragraph 6, SubSection 4

 

382 “Man, though made of body and soul, is a unity” (GS 14 # 1). The doctrine of the faith affirms that the spiritual and immortal soul is created immediately by God.

 

Part 1, Section 2, Chapter 3, Article 11, SubSection 1, Heading 2

997 What is “rising”? In death, the separation of the soul from the body, the human body decays and the soul goes to meet God, while awaiting its reunion with its glorified body. God, in his almighty power, will definitively grant incorruptible life to our bodies by reuniting them with our souls, through the power of Jesus’ Resurrection.

 

Part 1, Section 2, Chapter 3, Article 12, SubSection 6

1052 “We believe that the souls of all who die in Christ’s grace . . . are the People of God beyond death. On the day of resurrection, death will be definitively conquered, when these souls will be reunited with their bodies” (Paul VI, CPG § 28].

 

Part 2, Section 2, Chapter 1, Article 1, SubSection 7, Heading 5

1280 Baptism imprints on the soul an indelible spiritual sign, the character, which consecrates the baptized person for Christian worship. Because of the character Baptism cannot be repeated (cf. DS 1609 and DS 1624).

 

Part 2, Section 2, Chapter 1, Article 2, SubSection 3

1304 Like Baptism which it completes, Confirmation is given only once, for it too imprints on the soul an indelible spiritual mark, the “character,” which is the sign that Jesus Christ has marked a Christian with the seal of his Spirit by clothing him with power from on high so that he may be his witness. 121

 

Part 3, Section 1, Chapter 1, Article 1

 

1705 By virtue of his soul and his spiritual powers of intellect and will, man is endowed with freedom, an “outstanding manifestation of the divine image.” 8

 

Part 3, Section 1, Chapter 1, Article 1

 

1711 Endowed with a spiritual soul, with intellect and with free will, the human person is from his very conception ordered to God and destined for eternal beatitude. He pursues his perfection in “seeking and loving what is true and good” (GS 15 § 2).

 

Part 3, Section 1, Chapter 2, Article 3, SubSection 2

 

1934 Created in the image of the one God and equally endowed with rational souls, all men have the same nature and the same origin. Redeemed by the sacrifice of Christ, all are called to participate in the same divine beatitude: all therefore enjoy an equal dignity.

Now back to the subject of emotions.

I found the nerve to write and post this article this early moring after having some personal puzzlement over a child-like but hopefully not to childish inquiry as to what emotions are made of. Initially, I thought that I was onto some profound thinking in this regard. A few days later, especially yesterday, I begin to ponder the possibility that perhaps such a question is meaningless, or at the very least would be viewed as meaningless to ontologists and spiritual anthropologists. Folks as such who would hold such questions a naïve and meaningless would tend to view emotions as mere activity or processes and as not imbued with an underlying ontology or substance like accidental reality. However, upon contemplating how I might be laughed out of the podium of an academic conference by asking such a question, I began to formulate arguments in favor of my inquiry. The arguments proceed as follows.

We are all familiar with a coffee cup and how the cup in its real and concrete form is but an accidental arrangement of atoms comprising the materials out of which the coffee cup is made. Furthermore, any high school chemistry student will be able to explain at least at a cursory level that constituent atoms are comprised of electrons, protons, and neutrons.  An undergraduate physics student should be able to explain the composition of protons and neutrons as being made of two up quarks and one down quark and two down quarks and one up quark, respectively. A more advanced undergraduate physics student will see that the quarks are bound by gluons. A graduate student of physics will understand that most of the mass of the proton and the neutron is comprised of the relativistic kinetic energy of the quarks and the gluonic fields that bind the quarks. The graduate physics student should also be well aware of the various theories of unified fields and gauge transformations and should have at least an intuitive grasp of mixing parameters such as the electroweak mixing parameter, the weak-strong mixing parameter and the electro-weak-strong mixing parameter. Doctoral students in QCD or quantum-chromo-dynamics should be well versed in the understanding of lattice QCD computations including the various forms such algorithms take and the relative strengths and shortcomings from amongst the various methods. Post-doctoral QCD theorists will be well aware of the latest laboratory findings and models of the strong and weak interactions as well as the electromagnetic properties of quarks. Thus, even astute nuclear and sub-nuclear physicists often ask what material things are made of.

Now back to the point in a  first argument.

First, just as a coffee cup is in form an accidental arrangement atoms, the coffee cup still has reality that is concrete and tangible and still has existence, even though the form of the coffee cup is the aggregated arrangement and activity of atoms. The coffee cup can impart momentum, kinetic , and acoustic energy when dropped on the floor. The coffee cup in theory is so real as a form and is so existent as a form that in theory, should the coffee cup be accelerated to about 99.999999999 percent of the speed of light, and made to collide with the moon at such a velocity, many of the quarks themselves in the portion of the moon that would mediate the impact would be transformed into other particles, most likely in some cases, into particles yet to be discovered such as perhaps super-symmetric particles. Thus, to the extent that the coffee cup can be grabbed ahold of and accelerated as a form unit, and then made to collide with another object of similar or larger size, the cup in terms of its embodiment in its accidental form is decidedly quite real and capable of profound effects, even those that transmute the up quarks, down quarks, and electrons out of which the impacted portion of the Moon is made. Yes, the accidental form of the coffee cup is indeed quite real and quite existentially valid.

Well the same can be said regarding human emotions in my opinion even if most spiritual anthropologists would balk at my stated opinion of such. After all, emotions are real and concretely existing to the extent that they cause our everyday cognitive processes to be proverbially colored. Emotions are real and concretely existing to the extent that they can motivate a terrorist attack such as the one that brought down the World Trade Center in New York City on 9/11. Emotions are quite real and concretely existing to the extent that they can influence a human person’s decision to sacrifice his or her life to save a comrade in combat of to influence an act of terrorism so severe that even a wise Catholic clergyman  could be almost certain of the mortally sinful nature of such an act even given the understanding that only GOD can know the full intentions and scope of motivation for such acts. Yes, emotions are so real that they can lead a soul to eternal damnation or to canonized sainthood.

Just as we can make inquiry as to what a coffee cup is made of, we can also ask what emotions are made of. Yes there exists a dynamic activity aspect to  emotions, but we must be willing to at least entertain the notion that emotions exist and have an existential underpinning commensurate with the realness of emotions to wreak such havoc as providing a mechanism for the loss of sanctifying grace of a soul and in some cases, perhaps eternal damnation,  or the rise to sanctity of a soul and its eventual canonization.

From this reasoning by analogy alone, I am convinced that emotions have substance even if the existence of a spiritual materiality of emotions subsists in and is extrinsically dependent on the existence of the human soul, perhaps also mediated though the human spiritual faculty of the heart.

The second argument is as follows and requires acceptance of the reality of the Sacrifice of the Mass if one is to understand my reasoning.

We Catholics hold as a central tenant of our faith that  the sacred species of the bread and wine are transformed into the body and blood of Christ during the clerical prayers of consecration at Mass. The substance of the bread and wine is accordingly transubstantiated or transformed into another substance. Meanwhile, the accidental properties of the bread and wine, even the mass of the bread and wine and its QCD and QED (quantum-electro-dynamic) composition remains perceptibly identical in both its before and consecrated states. The atoms that comprise the accidental properties of the bread and wine continue to exist upon consecration and presumably also when the sacred species is digested within the human digestive system thereby resulting in the interruption of the Real Presence of Our Lord in the bread and wine.

The point to the preceding paragraph is to assert that the accidental properties of the sacred species are real and enduring even through the process of the transubstantiation of the bread and wine into the Body and Blood of Christ. Thus, we set the tone for the argument that accidents in material corporeal objects are real and can in theory and do an actually exist unaltered in at least some instances of transubstantiation. Such a conclusion is still valid even if Divine sustenance of the accidental properties of the bread and wine is required by a special act of GOD’s will. Even given the latter circumstance, the bread and wine in its accidental form has to really exist as a distinct reality from the transformed substance of the bread and wine simply because the accidental properties must have existence in the first place commensurate with already existing and continuing to exist upon  the consecratory prayers during Mass.

If the mere inanimate appearing accidental nature of the sacred species can continue unaltered in terms of its elemental, molecular, thermodynamic, and electrodynamic properties, and even in terms of its apparent mass-energy content to the extent that there is a continuity between the before, during, and after state with respect to the consecratory prayers, then we have grounds for further inductive, or more properly,  inductive-deductive arguments for the reasonableness of the actual existence accidental realities and by corollary, the less general categories of human emotions.

The third argument is presented from more or less ad hoc evidence for the possibility of hauntings or poltergeist activities.

Most traditionally minded clergymen will hold that hauntings are a deceptive work of Satan and in no way indicate the possibility of a human soul that has not received definitive judgment by GOD upon death. Personally, I feel that perhaps in some cases, the alleged dream like state of so-called Ghost –Souls may be a means for such souls to undergo salvific atonement by otherwise mortally sinful instances of suicide. In reality, the new Catechism of the Catholic Church asserts clearly and unambiguously, that GOD can provide a means of Salvific atonement for folks who have taken their own lives by means known only to GOD. For cases where the person committing suicide was in the state of grace upon death, then no such means would be required  as the obvious means for purification would be consignment to Purgatory unless the poor tortured soul was deemed to have so suffered in this life that GOD mercifully brings the soul immediately to its final reward without the need for Purgatorial remediation.

For those of you who have lost family or friends to suicide, do not despair for your loved ones’ salvation, because even the conservative Catechism of the Catholic Church clearly states that in many of not most circumstances, suicide is a result of mental illness and despair and so full culpability is not present thus resulting in the act not being mortally sinful and perhaps even no sin at all such as in the case of insanity and complete despair of persons who so take their own lives. A mortal sin can only be committed when at least the following conditions are met: 1) The person must have full freedom and deliberation in committing the act; 2) The person must have time to rationally review and reflect on the moral nature of the act; 3) The person must definitively and clearly know of the true moral seriousness of the act. Many theologians will add a fourth condition that the act must gravely offend GOD and not merely be an offense against GOD. It is therefore possible that a poor despairing  elderly woman who lost most of her children at the hands of a brutal occupying military power and who decided that she could not take it anymore and then overdosed on her blood pressure meds could in fact go straight to Heaven even if the Church would never recognize the women for beatification. In some instances of suicide, I am convinced that the act itself may have redeeming and sanctifying aspects due to the heavy cross of the humiliation of being overwhelmed by life’s circumstances even to the insidious humiliation of dying by one’s own  despairing acts.

Perhaps, just perhaps, many if not all real instances of hauntings or poltergeists are not due to the presence of deceased human person’s souls in a sort of dream like limbo state, but instead involve the release of emotional energy or quite simply, a sort of para-substantial material out of which emotions are composed that is distinct and more enduring then the subjectively , dynamically, and fleetingly experienced aspects of emotions  during daily life as emotional experiences come and go, wax and wane, and morph. The fact that even material objects that are removed  far from the objects initial  location at the scene of a tragic death such as by suicide or violent murder sometimes appear to give off bazaar material electromagnetic and acoustic, and even thermal emissions, and in some circumstances,  even holographic like projections of the deceased in the form of really hard to explain optical, electromagnetic, and acoustic emanations,  suggest that human emotions may imprint on surrounding physical objects present during the deceased daily lives and especially during the time of the tragic and untimely deaths.

Providing such hauntings are real, the argument is strong for the existence of emotional energy and for the validity of the question what emotions are made of.

What can be concluded from the above digressions assuming that the arguments are valid?

First, we can surmise that emotions have existence that is at least extrinsically independent of physical matter and energy even in the case that emotions are highly influence by and mediated as experiences by the physical human brain.

Second, another possibility is that emotions have a para-substantial or pseudo-substantial non-material component or underpinning.

Third, yet another possibility is that emotions are a fundamental aspect of raw physical otherwise inanimate matter but where the force or energy of emotions is greatly amplified within living animal brains including human brains. Do to the philosophical consistency of the notion of continued psychic  human identity after death, any emotions generated by the human brain per se would also continue to exist at least as remembered experiences by the souls of the deceased. Thus, even under the condition that emotions or so-called emotional energy is an aspect of raw inanimate physical mass-energy, such emotions or emotional energy would necessarily be able to decouple from the physical material world including the brains of the deceased to exist as an independent agent or reality, at least independent of the physical world and the deceased human brain.

Fourth, assuming that anyone or combination of the previous three consequences are real, emotions have a reality all their own and have an existence of their very own which is distinct from the existence of the physical world including live and deceased human brains and even which is distinct from the substance of the human soul. This philosophically appears true even under the condition that human emotions depend on the human soul for existence because such dependence is not the same as existential identicality for all of the reasons mentioned above.

The point is that human emotions are special and are to be cherished. We all have them, and as a person who actually used to be a frequent denialist of my emotions,  I humbly admit to the intensity of my emotions , feelings, and affect, and have come to a peaceful acceptance of my emotions and feelings and those of others. Quite frankly, I have come to think and feel that emotions are just plain fun and fantastic.

 

62)  What Color Is Your Soul?

 

What color is your Soul? I ask this question rhetorically but with a good bit of seriousness as I explain below.

Each human soul in the afterlife or each disembodied human soul must have an associated mechanism by which it can be identified by other souls it communicates with or by which it is recognized by other dis-embodied souls. I believe this associated mechanism to be some sort of natural appearance of the soul, which is perhaps altered or augmented by supernatural grace.

It does not seem enough to provide a refutation of a natural appearance of a human soul, or a natural appearance by which a supernatural gratuitous appearance of a given human soul would subsist in or be underwritten, by assuming that GOD provides a forced and direct mediation of such appearances.  If GOD was the sole source and the immediately direct cause and mechanism of mediation by which one soul would recognize another, what would be the point of the soul having objectively and subjectively observable characteristics? What would be the point of the soul having qualities by which it can affect other souls or be recognized by other dis-embodied Human Souls?

I thus propose that  human Souls of the deceased have  characteristics which are directly observable by other human Souls whereby a given human soul can recognize stranger Human Souls or the Human Souls of friends, deceased family members, relatives, and spouses, as well as human souls they may not have previously known but whom they have first met in Heaven, Purgatory, any Limbo, or Hell.

These observable characteristics would correspond to objective features of the observed human souls and perhaps may even involve features of the very substance of each human soul, although such direct observations would not necessarily be required for one to perceive, experience, or recognize a soul they are in the presence of or interacting with.

 

For example, we in this life can recognize a coffee cup or even the physical bodily presence of another human person;  however, we only observe the accidental aspects or features of said physical corporealities. We do not see or recognize any physical aspects of the human persons such as the prime matters or the most basic primitive ontological and substantial underpinnings  of the associated physical objects. Yes, we can in theory measure the mass of a coffee cup or weigh a living human person. We can even observe underlying chemical and isotopic identifiers of a living human body such as its DNA and other unique features. Heck, in theory, we could even identify and sense the sub-atomic and sub-nuclear aspects of a specific living human body through the acceleration a proton or an anti-proton to a kinetic energy of 10 TeV and then by  the directing of the particle into the  living human body whereupon the particle would collide with or interact with and transmute a portion of the body’s electronic, or quantum-chromo-dynamic constitution. However, we would still not directly observe the most primitive substantial underpinnings of the human body by which the mass-energy-space-time material composition of the given human body is made a physical reality instead of a spiritual reality or other non-physical reality.

 

A good example of an analogous mechanism to the latter is the Transubstantiation of the ordinary bread and wine into the Body and Blood of Christ during Mass. We could never hope to observe and recognize the Sacred Species as Christ in a laboratory setting except for the possible exceptions that Our Lord converts the accidental properties of the bread and wine into living tissues such as by Divine and miraculous intervention. Even the most sophisticated laboratory apparatus could not observe the substance of the Sacred Species.

Thus, a given human Soul even in the afterlife might only be observable through its accidental aspects much as a human body is identifiable through its accidental appearance. For those of you who delve into paranormal phenomenon such as mental telepathy or clairvoyance, you need not fret that perhaps the souls of the deceased can only be sensed by other such souls through spiritual accidental appearances, because, in the latter case, each human soul would still possess something untouchable and profoundly mysterious, even in the realms of Heaven, Purgatory, any Limbo, and Hell. The fact that we humans may have ontological aspects that forever remain hidden would be a great mystery and would point to something utterly profound about the natural created reality of each human soul. Given that we will have all eternity to access the wonders of creation, the mere reference to wonders of creation affirms that there will always be new and novel things to observe and learn in Heaven especially as suggested by the fact that we will never be bored in Heaven and that we will get our bodies back as immortal bodies, regardless of where we end up after death. A living immortalized body implies dynamic and changing experiences, otherwise why would we have immortalized bodily eyes and a dynamic thinking human brain. In order for such dynamism to be realized and not be eternally redundant and foreseeable, we are forced to conclude that there will always be yet to imagine experiences and discoveries, even within the domain of Heaven after the Final Resurrection of the Dead.

However, it may yet be the case that the very substance of the souls of the deceased can be metaphorically seen and recognized by other such souls, even if the ability of such seeing and recognizing is an eternally developing power or ability, a situation in itself which would provide novelty and profundity to each citizen of Heaven.

Although ontologically simple, each human soul is unique and utterly and absolutely uniquely itself. Yet each soul contains within a vast infinite ocean of existence of which in this life we catch notice of a surface glimmer as if by a metaphorical ray of sun-light reflecting off a mere surface ripple, according to a paraphrase of a great spiritual writer who lived roughly around the late 19^th early 20^th century. This vast ocean of existence, would apply to the un-observable existential aspects of our accidental composition such as our minds, heart,  wills, and the conscious, sub-conscious, and unconscious aspects of our psyches. It is philosophically consistent to make such a conclusion especially given the paradigm of modern psychodynamics that the human unconsciousness in each individual is a vast repository of experiences, both remembered and forgotten, and even those hard wired into our ontology by evolutionary processes.  Thus, even the accidental features of our personalities as a set may imply an ocean of existence so vast that we will be discovering things ever anew about our own selves and those we love and befriend in Heaven for all eternity.

The richness of attributes and characteristics of the substance of each and every human soul is likely to by far outclass those of the accidental aspects  of each and every human soul if for no other reason than that the substantial aspects of spiritual and even corporeal elements of creation are more ephemeral and epistemologically profound that directly observable accidents.

The point to this digression is that perhaps each and every human soul of the deceased may have not just one single color, but rather a multitude if not a vast unfathomable infinity of colors that even the souls in Heaven will have all eternity to explore and get to know, even at the level of the accidental nature of the human soul. How much more color in its varieties and intensities might  the very substance of each human soul have and  by which human souls in Heaven would have all eternity to explore.

Obviously, when using the word “color” above, I am not referring to the physical hues we see as we go about conducting our daily lives, but instead, am referring to any  sensible aspects of spiritual created realities of  the souls of the deceased.

 

63) Married Couples Of Fertile Age, Give A Soul The Ultimate Gift Of Being Created. Conceive A Child Before Or During Christmas.

 

How hot is the Human Soul? Seriously, I mean really “What temperature is the Human Soul?” Now you may be thinking “What kind of crazy crap is Jim Essig trying to sell me on now?” Well, I explain my thinking as follows.

 

Consider that the human soul has the capacity to interact with other creatures as well as interact or intra-act with itself.  This capacity to interact is associated with a certain dynamism or capacity for time dependent soul state change.

 

Now particles that interact with other particles or macroscopic bodies that interact with other macroscopic bodies have a temperature at least in the form of a kinetic energy of interaction. Interaction between bodies is only possible commensurate with a pre-engagement to full engagement based change of state. Such a change of state implies a thermodynamic gradient and thus a thermodynamic potentiality for the reactants to attain a state they did not previously have. The change of state can include particulate species or material(s) species composition change, change in temperature, change in geometric morphology, change in mass, change in electric and/or magnetic charge and distribution thereof, decomposition, and a whole host of other possible changes.

 

Since the human soul can change through interaction with other created agents and as well as with itself,  this potentiality for state change within the human soul is analogous to the thermodynamic  potential for physical systems to change based on the temperature of the systems. Thus, the analogy of a temperature of the human soul is self-evident.

 

The changes that are possible for the human soul to undergo include accidental, facultative, and even substantial.

 

Accidental changes include changes in immediate perceptual psychic spheres, changes in emotions, changes in feelings, changes in moods, changes in thoughts, changes in memory, and changes in volitional intention among others.

 

Facultative changes include changes within the intellect as a faculty, changes in the sensitive life as a faculty, changes in the power of volition or the will, and changes within the memory.  Changes within the intellect can include the subject of abstract knowledge, abstract cognitive ability, abstract intuitive ability, abstract logical reasoning ability, among others, Changes within the sensitive life include changes in sensory abilities, changes in capacity for emotions, changes in capacity for affect or emotional feelings, changes in level of instinct, changes in level of emotional and affective arousability such as in the capacity for sexual arousal among others.  Changes within the will include changes in capacity for free acts, changes in capacity for free self-determination,  changes in capacity for self-regulative behavior, and changes in capacity for strength of internal resolve,  among others.  Changes within the memory include changes in stored experiences and learned behaviors of the following classes: cognitive, emotional, affective, volitional, sensational, among others.

 

Facultative changes can also be classified in terms of Freudian Psychodynamics. Such changes can include changes to the conscious psyche, the sub-conscious psyche, and the unconscious psyche. Alternatively, the changes can be classified by those of the Freudian ID, the ego, and the superego.

 

Changes within the substance of the Human Soul can be considered possible such as through the administration of the Sacraments of Baptism, Confirmation, and Holy Orders. Each of these sacraments confers a sacramental seal or super-natural characteristic  within the soul  that presumably effects the very substance or essence of the souls of the recipients. These sacramental seals per due into eternity thus, once a Baptized Catholic, always a Baptized Catholic, one a confirmed Catholic, always a confirmed Catholic, and once a Priest, always a Priest.

 

In addition, the human soul can receive differing levels of Sanctifying Grace and thus receive objective moral capacities as a result of supernatural grace.

 

Thus, we seem to have two categorizations of Soul temperature. One category  is differentiation by ontology and that is according to accidentiality, falcultativeness, and substantiality. Thus, here there are actually three broad categories of temperature.  A second category is differentiation by supernaturality.In each of these two categories, there are many sub-categories as indicated by the above details. For supernaturality, there is a secondary primary sub-division and that is the distinction between characters associated with sacramental seals and characters associated with graces obtainable outside the confines of the reception of any or all of the three sacraments that so bestow the sacramental seals. The Holy Mother Church recognizes that vast numbers of persons in numbers known only to GOD can and do receive eternal salvation without ever receiving the any of the subject three sacraments. In the end, it is not the reception of the Sacraments and the seals they imbue the souls of the recipients who receive  them with that are of primary importance, but rather the metaphorical eighth sacrament of beholding GOD in the beatific vision in the Glory of Heaven with is open to all persons who die in the state of grace, no matter how such grace was obtained, even if by ways and means known only to GOD.

 

Each Human Soul that was ever created thus has multiple aspects of temperature. Here, the phrase temperature is used abstractly to denote spiritual thermodynamic potentialities for state changes which include ontological, existential, substantial, accidental, falcultative, natural, and supernatural aspects.

 

The fact that each Human Soul has a temperature so to speak points to something sublimely transcendent and even perhaps self-transcendent regarding the human soul. First, is the wide variety of dimensions of temperature as classified and categorized above. Second, and I am going out on a limb here, is that the Human Soul would continue to be a human soul even if at the spiritual analogue of absolute zero. Thus, there is something about the human soul that is what it is, even for a human soul that would lose the capacity for state change regardless of whether the state change is natural or supernatural; or substantial, facultative, or accidental.

 

Just as a massive boson or fermion continues to exist at absolute zero, so would a human soul at absolute zero. Since the substance of a Bose-Einstein condensate continues to exist in terms of the condensate’s invariant mass at temperatures that are slightly in excess of absolute zero even though the wave-functions of the constituent atoms overlap each other so that multiple atoms can occupy at least in part, the same space at the same time, the fermionic sub-atomic composition of each atom retains its identity, and the invariant mass of the individual atoms remains un-altered even if the spatial identity of the atoms is blurred to levels of greatly reduced individuality.

 

Likewise, each Human Soul has something mysteriously sublime such that even souls that would be metaphorically cooled to absolute zero would have a certain level of ontology that could not be lost or reduced to nothing. Since this fact even applies to souls under the condition that human souls have the capacity to receive Sacramental seals and sanctifying grace to an extent that modifies the substance of each soul receiving such supernatural attributes, there must be something more fundamental about each human soul than the so-called substantiality that could be thusly effected.

 

To the extent that this substantiality is present regardless of whether a given human soul would be reduced to a temperature of spiritual absolute zero in any subset of spiritual temperatures conjectured by analogy above, this super-substantiality may itself have multiple aspects thus implying a broadening of the super-substantial aspects of the human soul thereby implying a human soul that is far more ontologically and existentially richer than philosophers and theologians could have previously imagined.

 

The above conjecture is made more reasonable when one considers that  all human persons share a fundamental equality before  their Eternal  Creator regardless of whether or not they have received any of the sacraments, or are in the state of grace or not. The associated reference within the new Catechism of the Catholic Church affirms and paraphrases the meaning of the previous statement clearly and irrevocably. Sacred Scripture also indirectly affirms the above conjecture by implying that we are to love the sinner even though we hate the sin and that we are to love our enemies. Heck, in one reported  apparition, it was revealed that Our Lord still grieves over the loss of friendship with Satan. That’s how much GOD loves even the most morally imprudent of created persons. That’s how much we are called to love. That’s how serious it is to hate the sinner and feel that we are somehow inherently better than those who have not received any  subset of or all possible sacraments.

 

Please do not feel bad due to the implications of a greatly reduced pecking order in Heaven if my above arguments are sound, for such reasoning would then imply something mystically whimsical and mysteriously profound about each and every Human Soul ever created including yours.  However, the practice of artificial contraception and even  the undue use of the natural family planning methods can and do kill the potential of a given human soul to ever exist in any mode of being. That is how serious such sins are. That is why we the Catholic Faithfull must speak out in these regards.

 

It is not so much the poor uneducated inner city man or woman who relies on contraception who is at fault, but rather the educated professional mature Mass attending young couple who resorts to such methods while mocking  the poor unemployed inner city folks as bottom feeders, retards, or low-lifes. Many proverbial prostitutes are gaining entrance into Heaven before self-righteous pretty and elite Catholics are including the above mass attending young couples and the priests who are lax in the penance and advice they give to such young couples regarding such matters in the confessional.

 

Now do not be afraid that the above high status couples will not get to Heaven, because their psychological disposition in heart, intellect, and will  for devotion is a sign of grace. But rest assured, many of the first in this life will be among the least and many of the least or proverbial prostitutes will be the first. Sacred Scripture is clear in this general regard. Such young couples and  their confessors can turn the tide and attain great Sanctity such as the Italian female mother and physician who choose not to have surgery that would have saved her own life yet which would require killing the baby in her womb during the mid-part of the 20^th Century. This woman endured agonizing pain for several hours by rejecting medical intervention that would have killed her baby.  Most of the above referred to couples and their confessors will never be so tested, but nonetheless, they have the opportunity to attain great sainthood, even to the extent of becoming canonized, by simply following Church Teaching regarding matters of contraception and related Church teaching. It is just not that hard, and it can make you a Saint where you will have access to the wonders of creation and GOD for all eternity and find out a hell of a lot more about how wondrous each human soul is than from my brief digression given above which will prove trivial in the eternal scheme of things.

 

I in fact pray for the salvation of all such priests and young couples even to the extent that many more such persons will end up being canonized than would otherwise.

 

Why conceive as a young or fertile aged married couple?  Well, you procreate a human person and that involves inalterably influencing GOD’s decision in the affirmative to create a new spiritual and immortal soul. You permanently cause the size of the spiritual cosmos to grow in an irrevocable manner. That spiritual soul will honor you as a parent for all eternity and will also enjoy access to the wonders of all creation for all eternity. You enjoy in seeing a young toddler delight in a new toy as a Christmas present? Well the child you might now choose to conceive this Christmas as a present for him or her will delight infinitely more so in a humble, endearing, and child-like matter with unfettered enthusiasm and innocence at the wonders of creation for all eternity.

 

 

64) Does The Human Soul Have A Charge?

 

I am a kind of an oddball physicist who ardently believes in modern physics paradigms including the Big Bang cosmological model and in human evolutional development at least with regard to the Human Body but who also enjoys thinking about and writing on one of my favorite topics, the spiritual and immortal Human Soul.  I am sometimes scoffed at by even Catholics for my rigorous belief in the Big Bang model, ecological and geological evolution, and the evolutionary development of at least the bodily aspects of the Human Person as well as often scoffed at by pantheistically oriented, agnostic, or even atheistic folks, even some of my colleagues , for even adhering to the phrase, “Spiritual and Immortal Soul.” and for being a pro-life Catholic who is a member of the Knights Of Columbus.

 

Now I must ask a question I have been pondering as of late. “Is the Human Soul charged?” Seriously, I mean really “What is the Human Soul’s charge?” Now you may be thinking “Oh! Come on Big Jim! Stop drinking so many Coke Zeros and come back to Earth?” Well, I explain my thinking as follows.

 

Now do not feel slighted by a first impression that I might be  some sort of a cosmic consciousness, crystal interpreting, new age guru.  In the following argument for the plausibility of an analogue of charge within the Human Soul, I am in no way referring to physical electric charge. The spiritual charge I refer to is a purely spiritual reality that is abstracted from analogy to the physical force charges imbuing material bodies and fundamental and composite atomic and sub-atomic particles.

 

Consider that the human soul has the capacity to interact with other creatures as well as interact or intra-act with itself.  This capacity to interact is associated with a certain dynamism or capacity for time dependent soul state change. It is also associated with an ability of the Human Soul’s existence and ontology to extend beyond itself in terms of its effects on other creatures and to the extent that our actions and behaviors upset or please the HOLY TRIUNE GOD, THRICE HOLY, and EACH OF THE THREE DIVINE PERSONS,  the effects of our souls even influence GOD HIMSELF, in fact so much so, the HE sent HIS only SON to die on the Cross for our salvation as necessary for remediation of our disobedience.

 

Now particles that interact with other particles or macroscopic bodies that interact with other macroscopic bodies have a force charge of various forms to the extent that such particles feel each other’s presence in an interactive manner. Electrically charged particles such as leptons feel each others presence in an attractive or repulsive manner depending on the relative signs of the said electrical charges.   Quarks within protons and neutrons interact with each other via these constituent particles electric charges, but also via these particles strong force or gluon based charges, as well as via these particles weak force charges. The neutrinos interact with other weakly interacting particles via the weak force. All known particles;  charged leptons, un-charged leptons or the neutrino species, quarks, photons, gluons, weak force bosons, the still theoretical graviton, as well as gravity waves interact via the force of attraction of gravitation. Thus, there are several fundamental known force charges in the physical constitution within our universe. In addition, the Pauli Exclusion Principle inherent in fermionic repulsion acts to prevent identical fermionic species from occupying the same energy state in the same spatial location. It is the repulsive effects of the Exclusion Principle that prevent white dwarfs and neutron stars from collapsing further instead of the much smaller supporting role of the charge based repulsion of the electrons, quarks, that ultimately comprise bulk materials of these stellar bodies.

 

Interaction between bodies at a distance is only possible commensurate with a pre-engagement to full engagement based change of state. Such an ability to pre-engage from a distance is only possible via force charges. The change of state can include particulate species or material(s) species composition change, change in temperature, change in geometric morphology, change in mass, change in electric and/or magnetic charge and distributions thereof, decomposition, and a whole host of other possible changes.

 

Since the human soul can change its state(s) and the state(s) of other souls and other creatures, and perhaps even ancillary aspects of GOD HIMSELF through interaction with other created agents and also  with DIVINE REALITIES, the potential for such changes must exist in an imbuement of  the soul with a field like analogical capacity to cause change and to effect realities both within itself and also to effect external realities. Such realities can include existential, ontological, substantial, accidental, and facultative aspects of other creatures especially those having personal identities. This potentiality for state change within the human soul and entities external to the human soul is analogous to the force charge of physical systems and the ability of such systems to effect themselves and other systems via force charges. Thus, the analogy of a force charge  of the human soul seems self-evident.

 

The changes that are possible for the human soul to undergo include accidental, facultative, and even substantial. The changes that are possible for the human soul to effect external realities  include, existential, ontological,  accidental, facultative, and substantial aspects.

 

 

Accidental changes include changes in immediate perceptual psychic spheres, changes in emotions, changes in feelings, changes in moods, changes in thoughts, changes in memory, and changes in volitional intention among others.

 

Facultative changes include changes within the intellect as a faculty, changes in the sensitive life as a faculty, changes in the power of volition or the will, and changes within the memory.  Changes within the intellect can include the subject of abstract knowledge, abstract cognitive ability, abstract intuitive ability, abstract logical reasoning ability, among others, Changes within the sensitive life include changes in sensory abilities, changes in capacity for emotions, changes in capacity for affect or emotional feelings, changes in level of instinct, changes in level of emotional and affective arousability such as in the capacity for sexual arousal among others.  Changes within the will include changes in capacity for free acts, changes in capacity for free self-determination,  changes in capacity for self-regulative behavior, and changes in capacity for strength of internal resolve,  among others.  Changes within the memory include changes in stored experiences and learned behaviors of the following classes: cognitive, emotional, affective, volitional, sensational, among others.

 

Facultative changes can also be classified in terms of Freudian Psychodynamics. Such changes can include changes to the conscious psyche, the sub-conscious psyche, and the unconscious psyche. Alternatively, the changes can be classified by those of the Freudian ID, the ego, and the superego.

 

Changes within the substance of the Human Soul can be considered possible such as through the administration of the Sacraments of Baptism, Confirmation, and Holy Orders. Each of these sacraments confers a sacramental seal or super-natural characteristic  within the soul  that presumably effects the very substance or essence of the souls of the recipients. These sacramental seals per due into eternity thus, once a Baptized Catholic, always a Baptized Catholic, one a confirmed Catholic, always a confirmed Catholic, and once a Priest, always a Priest.

 

In addition, the human soul can receive differing levels of Sanctifying Grace and thus receive objective moral capacities as a result of supernatural grace.

 

These immaterial or non-physical aspects of capacities for a soul to effect itself are paralleled by capacities to produce similar changes in other spiritual creatures such as other Human Souls, the Souls of any bodily extra-terrestrials, the Souls of any bodily ultra-terrestrials, Angels good and bad, and even the Souls of lower forms of animal life especially intelligent animals that interact with created spiritual persons.

 

Thus, we seem to have two categorizations of Soul charge. One category is differentiation by ontology and that is according to accidentiality, falcultativeness, and substantiality. Thus, here there are actually three broad categories of metaphorical charge.  A second category is differentiation by supernaturality. In each of these two categories, there are many sub-categories as indicated by the above details. For supernaturality, there is a secondary primary sub-division and that is the distinction between characters associated with sacramental seals and characters associated with graces obtainable outside the confines of the reception of any or all of the three sacraments that so bestow the sacramental seals. The Holy Mother Church recognizes that vast numbers of persons in numbers known only to GOD can and do receive eternal salvation without ever receiving any of the subject three sacraments. In the end, it is not the reception of the Sacraments and the seals they imbue in the souls of the recipients who receive  them that are of primary importance, but rather the metaphorical eighth sacrament of beholding GOD in the Beatific Vision in the Glory of Heaven with is open to all persons who die in the state of grace,  no matter how such grace was obtained,  even if by ways and means known only to GOD.

 

Each Human Soul that was ever created thus has multiple aspects of charge. Here, the phrase charge  is used abstractly to denote spiritual potentialities for state changes which include ontological aspects, accidental aspect, facultative aspects,  natural aspects, and supernatural aspects.

 

The fact that each Human Soul has charges so to speak points to something sublimely transcendent and even perhaps self-transcendent regarding the human soul. First, is the wide variety of dimensions of charge as classified and categorized above. Second, and I am going out on a limb here, is that the Human Soul might continue to be a human soul even if having a spiritual analogue of zero charge.  An analogy to zero spiritual charge is the raw undifferentiated space time foam like underpinnings of the origins of the Big Bang once referred to a Yelm during roughly the middle of the 20^th Century by some Big Bang Theorists. Even in modern Chaotic Inflationary Theory, a raw undifferentiated prime matter or at least semi-substantial underpinning underwrites the birth of new universes  in new Big Bangs.  Thus, there is something about the human soul that is what it is, even for a human soul that would lose the capacity for state change regardless of whether the state change is natural or supernatural; or substantial, facultative, or accidental.

 

Just as a massive boson or fermion continues to have non-charge aspects, so would a human soul by analogy. Since the mass-energy equivalence of matter and antimatter particles undergoing Fermi-Dirac annihilation retains its energy equivalence despite destruction of the individual charges of say Fermi Dirac interacting charged leptons or quarks of the same flavor and  continues to exist in in the form of photonic and/or neutrino based energy forms, by analogy, the existence of some essential or super-essential aspects of Human Souls is plausible that is independent in its identity from the capacity of the Human Soul to influence itself and external substantial, accidental, and facultative realities be such realities spiritual or physical, a composite of spiritual and physical elements, or any intermediary forms of created entities perhaps currently unknowable to the Church in this world and in this life.

 

Thus,  perhaps each Human Soul has something mysteriously sublime such that  the Human Soul has an identity or super-substantial or super-essential aspect that exists independently of or at the very least has its own ontological identity and distinctness apart from any soul charge. This identity may be real even under the condition(s) that the charge aspects of Human Souls are so interiorly pervasive such that the human soul as a fundamental existential and ontological creation could not exist separately from its inherent charge. Since this notion plausibly even applies to souls under the condition that human souls have the capacity to receive Sacramental seals and sanctifying grace to an extent that modifies the substance of each soul receiving such supernatural attributes, there must be something more fundamental about each human soul than the so-called substantiality that could be thusly effected by potentialities inherent within Human Souls to receive such graces based on any spiritual charges of which the Human Soul would be inherently imbued with.

 

To the extent that this super-substantiality is present and identically distinct from any Soul charge, this super-substantiality may itself have multiple aspects thus implying a broadening of the super-substantial aspects of the human soul thereby implying a human soul that is far more ontologically and existentially rich than philosophers and theologians could have previously imagined.

 

The above conjecture is made more reasonable when one considers that  all human persons share a fundamental equality before  their Eternal  Creator regardless of whether or not they have received any of the sacraments, or are in the state of grace or not. The associated reference within the new Catechism of the Catholic Church affirms and paraphrases the meaning of the previous statement clearly and irrevocably. Sacred Scripture also indirectly affirms the above conjecture by implying that we are to love the sinner even though we hate the sin and that we are to love our enemies. Heck, in one reported apparition, it was revealed that Our Lord still grieves over the loss of friendship with Satan. That’s how much GOD loves even the most morally imprudent of created persons. That’s how much we are called to love. That’s how serious it is to hate the sinner and feel that we are somehow inherently better than those who have not received any  subset of all possible sacraments.

 

Please do not feel bad due to the implications of a reduced pecking order in Heaven if my above arguments are sound, for such reasoning would then imply something mystically whimsical and mysteriously profound about each and every Human Soul ever created including yours.  However, the practice of artificial contraception and even  the undue use of the natural family planning methods can and do kill the potential of a given human soul to ever exist in any mode of being. That is how serious such sins are. That is why we the Catholic Faithful must speak out in these regards to support Church teaching on artificial contraception and undue limitations on family growth through over exuberant use of natural family planning.

That natural family planning can in theory be overused is proved by the fact that perfect application of natural family planning by all Human Persons would lead to the extinction of the Human Species.  As someone interested in the UFO space alien phenomenon, I must say that our fellow rational creatures in the forms of ETI or so-called UTI would likely say something akin to “Oh, Brother!” should the human population become extinct at least in part due to over exuberant use of natural family planning for purposes of avoiding conceptions.

 

Why conceive as a young or fertile aged married couple?  Well, you procreate a human person and that involves inalterably influencing GOD’s decision in the affirmative to create a new spiritual and immortal soul. You permanently cause the size of the spiritual cosmos to grow in an irrevocable manner. That spiritual soul will honor you as a parent for all eternity and will also enjoy access to the wonders of all creation for all eternity. You enjoy in seeing a young toddler delight in a new toy as a Christmas present? Well the child you might now choose to conceive this Christmas as a present for him or her will delight infinitely more so in a humble, endearing, and child-like matter with unfettered enthusiasm and innocence at the wonders of creation for all eternity.

 

Ever see a young elementary school age little girl lavishly nurturing, petting, and playing with a new kitten given to her by her parents as a gift with giggles and grins of delight? Well the endearing love and spiritual emotions of an angel appointed to be a guardian of a newly conceived child, body and soul, is likely unfathomably more intense and rich, more loving, and more fun for the angel than the love and sentiment expressed by the little girl. I mean no offense to mothers holding their children of extreme importance in their rightfully and nobly chosen marital vocation, but rather am trying to affirm the supreme dignity of each Human Soul ever created. If the angels who are much lower than GOD can so exuberantly enjoy their little human child just conceived as a present, how much more does GOD love each Human Soul. Since GOD is the ultimate reference frame, GOD’s love for each Human Soul says something profound about the fundamental dignity and goodness of each Human Soul.

 

 

 

65)  Anecdotal Musings On The Nature Of The Human Soul By Reflections On The Very Speculative Concept Of Proton Fission.

 

 

As a physicist who works in the theoretical development of interstellar manned space travel concepts and who enjoys pondering the immensity of the physical cosmos and the opportunities for mankind to access the mineral and other resources of the universe, I am somewhat viewed as an oddball by both devout Catholics, clergymen, religious, and married and single lay-persons alike,  but also by fellow physics geeks, many of whom seem agnostic and unwilling to except the possibility of a personal and all-powerful Creator. I thought that the readership of E&T might enjoy the following personal anecdotes being that about at least half of the Catholic population of the Arlington Diocese grew up during roughly about the time that the ongoing Star Wars series of movies has been under production. As such, the following comments are not meant as a lecture but merely intended as a conversation piece to help any readers that distain modern cosmology and physics to realize that the grandeur of the domain of modern cosmology and physics need not detract from timeless cherished notions of an All Power GOD and CREATOR and the cherished notions of a spiritual and immortal soul. I present a personal anecdotal argument in support of the latter below.

 

Proton fission is more of a science fiction concept than an excepted plausibility that would entail the release of the binding and kinetic energy of the quarks that comprise protons.  The QCD process of confinement indicates that quarks cannot be unbound because the force of attraction between quarks does not diminish as the distance of separation is increased. After the gluonic field lines are suitably strained, the field lines metaphorically snap thereby resulting in the gluonic field line strain energy being converted to additional quarks. Thus, while attempting to separate a given set of quarks by pulling the quarks away from each other, the result accordingly is the conversion of gluonic strain energy into additional quarks.

 

As of the time of this writing, I have not been able to re-locate the source of the relevant science fiction story, however, the general idea is that  proton bombs would be as much as 1,200 times higher in yield than the maximum possible yield of a conventional atomic fission bomb having the same mass.

 

To get an intuitive grasp of how such a proton bomb could have such a high mass-specific yield, it is insightful to note that the invariant masses of the quarks that comprise a proton or a neutron are only on the order of one percent of the invariant mass of these particles. The rest of the mass is due to the relativistic kinetic energy of the constituent quarks as well as the inertia resulting from the gluonic binding fields.

 

Since the most efficient traditional atomic fission fuels permit at most about 1/1,200 of the fuel’s invariant mass to be converted into explosive energy, a so-called proton bomb of the conjectural forms described above would be almost as efficient if not just as efficient as a yield optimized matter-antimatter bomb.

 

Provided protons could somehow be induced to fission by low energy processes, perhaps the only massive particles produced by the fission would include a relativistic anti-muon or a relativistic positron such as perhaps due to the simplified case where nature strictly forbids violations of the electric charge conservative principle. Another option would entail the production of two to four muons and three to five antimuons which would then decay. The muons and antimuons could also be made to pair annihilate. Alternatively, combinations of:  1) muons, electrons, and antimuons; 2) muons positrons, and antimuons; 3) muons, electrons, antimuons, and positrons; 4) muons and positrons; or 5) anti-muons and electrons, perhaps along with the production of photons and/or neutrinos could result.

 

Whatever the final low energy artificially induced proton fission outcome, we should expect that the energy conservative principle and the charge conservative principle would hold as these are some of the most cherished principles in modern physics.

 

Standard Model theorists, especially traditional quantum-chromo-dynamicists, upon reading this post  would probably  enjoy giving me a gentle ribbing by asking me whether  I was smoking some “Wacky Tabacci” for writing these comments. However, I strongly feel that the ramifications of low to very low energy induced proton fission are so profound that we should not entirely dismiss such a possibility for all time as utterly impossible or unfeasible. The ramifications of such a technology would be as profound as taking any arbitrary supply of ordinary hydrogen and converting it into virtually pure energy at will. In all probability, if low energy proton fission is possible to control, then so would neutronic fission, and by corollary, also the conversion of ordinary nuclear matter into almost pure energy if not complete mass conversion to energy.   Imagine the gamma factors achievable for a very long and slender space train having  a mass ratio of say 10²⁴ or higher especially in cases where much of the instantaneous fraction of propulsion energy would be derived by interaction with the interstellar or intergalactic medium.

 

Proton fission rockets with a specific impulse of 1 C such as in cases where the protonic fuel is completely converted to energy and used as optimized thrust but where there are no other propulsion system energy inputs would yield gamma factors that are equal to 1/2 of the vehicles mass ratio. For the above space train example, the terminal gamma factor would be as high as 5 x 10²³. Compounding the instantaneous rate of propulsive power would result in an exponential growth in gamma factor for a given mass ratio and spent portion of fuel.  The determination of such a mechanism would make interstellar ramjets a proven possibility overnight and possibly permit perpetual acceleration in the ISR ship frame.

 

Proton fusion would be an ideal energy source because virtually all of the known baryonic mass within our universe is protonic and neutronic in nature with very little antimatter nucleons observed. Most of the hadronic baryonic mass is protonic of which all but a very small fraction is normal matter. The potential fuel supply for proton fission rockets is as large as the accessible regions of our universe, which by definition, in the infinite temporal limits of an eternally enduring universe, approaches a mass of infinity. Literally infinite gamma factors may present themselves as space craft performance boundary conditions in the temporal limits of infinity for eternal universes.

 

The evermore rarefication of the intergalactic medium would help in the above regards, but in eternally expanding universe models, despite the gradual thermodynamic heat death that may result, infinite gamma factors seem to be the only limit. Just how infinite is open to question, but since there are greater and lesser infinities such as the transfinite Aleph numbers, and since accordingly, there is no limit to the relative sizes of infinities of ever greater Aleph numbers, perhaps the mother nature limits us in the most absolute sense to ever higher infinite gamma factors.

 

Even if we never can travel faster than light, we may have all eternity to approach a gamma factor of Omega followed by Aleph 0, then Aleph 1, then Aleph 2 and so-on  ad infinitum commensurate with effective travel of an Omega followed by Aleph 0, then Aleph 1, then Aleph 2 and so- on  times the speed of light. Thus, travel into the future of an associated Omega followed by Aleph 0, then Aleph 1, then Aleph 2 and so-on ad infinitum times the number of years of ship frame travel time, in the background frame, is logically plausible. Yes, even if nature abhors superluminal inertial travel through space-time, Special Relativity can be the Cosmic Pilots best dream. As my brother John would say, “Oh Damn!”

 

As someone who was initially very disappointed to learn of the 1970s paradigm still held today that the speed of light in vacuu is the ultimate limit for signal and mass-energy propagation, I will not lose any sleep over the possibilities of infinite gamma factors. I would leap for joy and throw a huge party if I were to somehow mystically learn that such gamma factors are possible for us humans.

 

Do not count on the development of proton fission bombs or low energy initiated proton fission reactors anytime soon, however, we as a civilization that is inherently open to the infinite should at least keep an open mind regarding such concepts, even if only with a good degree of initial skepticism.

 

I feel obliged to respond to skeptical Standard Model theorists’ and conventional QCD theorists’ criticism by stating that, “Yes I have had several almost 2 quart cups of Coke Zero today (not quite Wacky Tabacci), but that we should be open to unexpected opportunities that nature throws our way.” After all, the mid-20^th Century nuclear physicists could not easily have foreseen the Standard Model as it is currently interpreted nor could they have clearly foreseen the full scope of the current QCD paradigm.

 

Now, it is an obvious fact that a live and awake human person under normal circumstances perceives his or her own self and his or her own environment as a time dependent changing one. We all under normal circumstances have a sense of the flow of time which we experience as flowing at a more or less subjectively normal rate.

 

Now for systems that are relativistically time dilated to an infinite extent such as a space craft traveling inertially through space at exactly the speed of light in a vacuum, crew members would perceive themselves as having a more or less normal progression of their time dependent consciousness stream flow. Now what if we could somehow cause the time dependent evolution of the quantum mechanical wave function probability amplitude defining the crew cabin and crew members bodies to evolve at a rate which is infinitely less than does that for ordinary background human civilization infrastructures such as within a house on a planet?

 

The result of such a slowing would be correspondence to the slowing of the rate of wave-function collapses within the space craft crew cabin and within the human bodies of the persons occupying it.

 

Since every subjective instant in perceived time or psychological time is normally followed by another perceived psychological time instant in a manner that seems more or less normal or routine to a given conscious individual, under the normal course of events in this life, there is always yet another instant to be perceived no matter what the objective granularity or scale of temporal resolution in the psychological time flow stream.

 

We can therefore in a limited sense say that conscious reality for a normal waking person abhors the elimination of yet another perceived step in psychological time, even in cases where the psychological time is perceived as continuously flowing as it normally is.

 

Given the experiences of those who have been knocked unconscious, re-awakened from a minimally conscious vegetative state, gone  through deep general anesthesia, have had a severe case of alcoholic or other substance based intoxication to the point of amnesia, or perhaps having been tasered,  upon re-gaining of consciousness, such persons routinely report that their sense of conscious awareness was continuous in such a manner that the subjective time passage from the before and after state of unconsciousness is zero in length. By this I mean that the person will often perceive zero passage of time between the before and after state of episodes of unconsciousness.

 

Thus, it really seems that the world of conscious life abhors a lack of perceived conscious continuity in our psychic lives.

 

There is, consequently, an aspect of our ontology by which we retain our personal sense of self even amongst the temporary corruption of our conscious awareness such as its objective time based interruption.

 

We therefore can intuit something higher within the human soul or the human person wherein the capacity for a continuous sense of self remains ever intacked even amidst the complete and temporary loss of consciousness.

 

Such an enduring aspect of our sense of self, and even more so, the enduring aspect of the capacity for continuity in the sense of self, seems to indicate something profoundly a-conscious or non-experiential about the nature of the human person. Since the psychic life in all of its conscious, sub-conscious, and unconscious aspects, is generally held to be identifiable to the human soul, we arrive at a plausible conclusion that there is something extra-conscious, extra-self-aware, or extra-experiential about the human soul. Otherwise, how would the human soul continue to exist through periods of subjective complete unconsciousness?

 

This extra-conscious-self aspect of the human soul seems consequently be a more primitive or more essential or primary ontological aspect of the human soul, even under the condition that our conscious self or our conscious identity may be an inherent aspect of our soul’s faculties and perhaps even a property  of the substantial aspects of our souls.

 

It seems that our conscious experiences can be interrupted completely in a subjective manner, but that our conscious sense of personal identity remains upon re-awakening. Our capacity for our conscious sense of personal identity continues even when our conscious sense of self is objectively terminated. Otherwise,  our conscious identity would not continue upon re-awakening.

 

We normally intuit the goodness of a creature with its moral disposition and its habitual morally informed behaviors. However, there is a profound difference between moral goodness and ontological goodness. For we humans on this side of life and perhaps even for the condemned souls and the fallen angels, an awareness of the ontological goodness of all angels, good and bad,  and human souls whether in Heaven, Hell, any Limbo, Purgatory, any Ghost-like state, or in this life, is not directly and intuitively seen. Yes, we can have an intuitive feeling about eerily evil intentions or the presence of evil, but such an intuition whether naturally or supernaturally motivated, generally manifests itself as a perception of hate or a potential for vengeance. We can seem to feel evil in the form of anger and hatred in others in an intuitive manner, but the idea the of ontological goodness of morally imprudent creatures especially of Satan and the fallen angels is unpleasantly accepted by many of folks, even those of Saintly dispositions.

 

Perhaps the previously conjectured  extra-conscious or extra-experiential aspect of the human soul and by corollary, even the souls of the condemned and the fallen angels, is somehow related to substantial or super-substantial ontological goodness. Perhaps even the accidental aspects of the condemned human souls and fallen angels have ontological goodness.

 

Now please do not worry that I am some sort of Satanist or evil worshiper. I am only trying to argue and see for myself the good of all rational creatures, even if such goodness is most significantly, of the ontological forms of super-substantiality, substantiality, and perhaps accidentiality.

 

That being said, nature does indeed seem to abhor a subjective discontinuity of a conscious sense of self or self-awareness, or even a sense of awareness of our environments in the ways such awareness is personalized.

 

The main point I am attempting to argue here is that a space craft traveling just under C and consequently experiencing very extreme but finite relativistic gamma factors but where the time dependent probability amplitudinal wave-function of the crew cabin and crew member’s bodies is slowed to an infinitesimal rate in such a manner that the geometric and morphological integrity of the crew cabin and crew members is retained for at least an arbitrarily small but finite time step, ship time, and for an arbitrarily infinite time, background time, would seem to abhor the elimination of a subjective sense of time passage by the crew members. In other words, nature may abhor any situation where an ever-following conscious time step for the crew would be eliminated by any would be impossibility of infinite duration of the crew members lives’ and the persistence of the crew cabin and overall ship, in the background reference frame.

 

It seems natural that in the normal course of life, there is always another conscious subjective time step. Thus, I present my argument for the plausibility of infinite effective time-dilation in non-destructive human crewed space craft  processes as well as a super-conscious, super-experiential, or if you will, and extra-conscious or extra-experiential aspect of the human soul.

 

Note that the cosmos may be as unfathomably large as it is unfathomably growing in size by GOD’s.

 
Almighty Power to Create. The power of GOD to create in a sense is unfathomably greater than HIS Almighty Power to destroy. If the Cosmos may be growing in its number of constituent elements be such elements physical and substantial, physical and accidental, spiritual such as human, any ETI, and any UTI souls, any additional angels GOD may create unbeknownst to modern Catholic theologians, and the like, the cosmos can be commensurately all the more able to be haven access to regarding its wonders for all eternity by the just in Heaven. We should not reject the possibility of an ever growing Cosmos and the possibility of ETI and bodily UTI life-forms, but should be open to the possibility of an ever more infinitely vast Cosmos that GOD perpetually adds to, and in doing so, we will get a glimpse of GOD’s Almighty Power to create, which consequently, says something profound about the very BEING of GOD, or the DIVINE ESSENSE, the HOLY TRINITY, Thrice Holy, HE WHO IS THAT HE IS, or YEHWEY.

 

Am I a pantheist? Absolutely not! I do not adhere to any Occult belief system or practices, and even feel that  the Eastern beliefs involving the notion of Qi such as in  dubious Eastern martial arts studies is a load of horse manure. I am very skeptical regarding the existence of natural telepathic abilities and other quasi-religious concepts such as astral projection, telekinesis and the like. However, I believe that in the eons to follow, we will likely have discovered intelligent extra-terrestrial and so-called intelligent bodily ultra-terrestrial civilizations and will have learned to travel to galaxies far, far away, and to travel temporal distances into the future that are a far, far, time ahead.

 

The Cosmos is good, indeed very good. How much more good is its CREATOR, THE TRIUNE GOD, THRICE HOLY. By realizing how unfathomable the cosmos may be, we realize how all the greater is the ETERNAL CREATOR. For all of you folks who have bagged the study of physics and cosmology at the college level because you became disappointed with the notion that the ultimate speed limit is equal to the speed of light in vaccu, I would like to invite you to renew your wanderlust for the beauty of the cosmos and the potential for the human technological civilization. For Special Relativity only puts an absolute upper bound on relativistic gamma factors of infinity. Just how infinite is open for philosophical discussion, but an infinite gamma factor of even Omega would enable the crew to travel an Omega of light years through space in one year ship time and an Omega of years into the future in one year ship time.

66) Does The Human Soul Have A Spin?

 

I am a kind of an oddball physicist who ardently believes in modern physics paradigms including the Big Bang cosmological model and in human evolutional development at least with regard to the Human Body but who also enjoys thinking about and writing on one of my favorite topics, the spiritual and immortal Human Soul.  I am sometimes scoffed at by even Catholics for my rigorous belief in the Big Bang model, ecological and geological evolution, and the evolutionary development of at least the bodily aspects of the Human Person as well as often scoffed at by pantheistically oriented, agnostic, or even atheistic folks, even some of my colleagues , for even adhering to the phrase, “Spiritual and Immortal Soul.” and for being a pro-life Catholic who is a member of the Knights Of Columbus.

Now I must ask a question I have been pondering as of late. “Does the Human Soul have a spin?” Seriously, I mean really “What is the Human Soul’s spin?” Now you may be thinking “Oh! Come on Big Jim! Stop drinking so many Coke Zeros and come back to Earth?” .  If you were my high-school history teacher, you would have asked me if I was smoking some “Wacky Tabacci”. Well, I explain my thinking as follows.

Do not worry that I am espousing a spatial or physical minimalist interpretation of the Human Soul by presenting the following notions of the analogue of particle or even a macroscopic body non-zero angular momentum within the ontology or existentiality of the Human Soul. The spiritual spin I am referring to is a purely spiritual reality that is abstracted from analogy to the physical spin imbued by material bodies and fundamental and composite atomic and sub-atomic particles.

 

Consider that the human soul has the capacity to interact with other creatures as well as interact or intra-act with itself in forms of interaction that repeat time after time.  This capacity to re-interact is associated with a certain dynamism or capacity for time dependent soul state change and time dependent capacity for the human soul to affect changes within and/or externally, of similar if not identical forms,  repeatedly. It is also associated with an ability of the Human Soul’s existence and ontology to extend beyond itself in terms of its effects on other creatures and to the extent that our actions and behaviors upset or please the HOLY TRIUNE GOD, THRICE HOLY, and EACH OF THE THREE DIVINE PERSONS,  the effects of our souls even influence GOD HIMSELF, in fact so much so, the HE sent HIS only SON to die on the Cross for our salvation as necessary for remediation of our disobedience.

 

Now particles that interact with other particles or macroscopic bodies that interact with other macroscopic bodies have a property abstractly labeled with the word spin. The value of spin that particles are imbued with effects how each of the species of particles will feel each other’s presence in an interactive manner. Electrically charged particles such as leptons feel each other’s presence in part by the fact that these particles belong to a class of particles having a spin which is equal to an odd integer multiple of ½ quantum spin units usually labeled simply  by the number 1/2 .   Quarks within protons and neutrons interact with each other  in part as a result of  the particles’ spins. The neutrinos interact with other weakly interacting particles via the weak force but also via the particles spin.  The charged leptons also interact at a distance by virtue of the particles’ electric charges. The quarks also have additional interactive mechanisms such as electric charge, and color force charge. In addition to interaction via electric charge, the quarks also interact amongst themselves via the strong and weak nuclear forces. All known particles;  charged leptons, un-charged leptons or the neutrino species, quarks, photons, gluons, weak force bosons, the still theoretical graviton, as well as gravity waves interact via the force of attraction of gravitation.

The so-called Pauli Exclusion Principle inherent in effective fermionic repulsion acts to prevent fermionic species from occupying the same energy state in the same spatial location. It is the repulsive effects of the Exclusion Principle that prevent white dwarfs and neutron stars from collapsing further instead of the much smaller supporting role of the charge based repulsion of the electrons, and quarks, that ultimately comprise the bulk materials of these stellar bodies.

Particles having a spin of an integer multiple of 1/2  are referred to a fermions and obey so-called Fermi-Dirac statistics. Particles such as photons (essentially electromagnetic waves), gluons (the strong nuclear force equivalent of photons), weak force bosons (the weak nuclear force equivalent of photons), the still theoretical graviton (essentially gravity waves), and the still theoretical Higgs Boson, are referred to as Bosons and accordingly do not experience the degeneracy pressures that prevent fermions from occupying the same energy state in the same space at the same time. Bosons have an even integer multiple of spin 1/2.

Thus, all known particles and yet to be discovered but theoretically plausible particles have spins taken from the set of  {0,  ±  1/2,  ± 1, ± 3/2, ± 2, …}. All particles of the same species have identical spins.

In quantum theory, the spin of a particle is related to how it appears under a given degree of rotation. For instance, my fat ass would appear identical under a full 360 degrees of rotation. For subatomic and atomic particles, the definition of rotational symmetry is a bit more abstract,  but you get the intuitive picture. I will spare the technical details of spin since this article is about the sublime and spiritual human soul and I do not want to lose the interest of folks schooled in liberal arts and the humanities but who are not well versed in modern physics.

 

Since the human soul can change its state(s) and the state(s) of other souls and other creatures, and perhaps even ancillary aspects of GOD HIMSELF through interaction with other created agents and also  with DIVINE REALITIES in manners that are periodic, identical or nearly so,  and repetitive, the potential for such  changes must exist in an imbuement of  the soul with a spin like analogical capacity to cause change and to effect realities both within itself and also to effect external realities. Such realities can include existential, ontological, substantial, accidental, and facultative aspects of other creatures especially those having personal identities. This potentiality for repetitive nearly identical state changes within the human soul and entities external to the human soul is analogous to quantum spin and rotational symmetry in physical systems.

 

The periodic changes that are possible for the human soul to undergo include accidental, facultative, and even substantial. The changes that are possible for the human soul to affect external realities include, existential, ontological, accidental, facultative, and substantial aspects.

 

 

Accidental periodic changes include changes in immediate perceptual psychic spheres, changes in emotions, changes in feelings, changes in moods, changes in thoughts, changes in memory, and changes in volitional intention,  among others.

 

Facultative periodic changes include changes within the intellect as a faculty, changes in the sensitive life as a faculty, changes in the power of volition or the will, and changes within the memory.  Periodic changes within the intellect can include the subject of abstract knowledge, abstract cognitive ability, abstract intuitive ability, abstract logical reasoning ability, among others. Periodic changes within the sensitive life include changes in sensory abilities, changes in capacity for emotions, changes in capacity for affect or emotional feelings, changes in level of instinct, changes in level of emotional and affective arousability such as in the capacity for sexual arousal among others.  Periodic changes within the will include changes in capacity for free acts, changes in capacity for free self-determination,  changes in capacity for self-regulative behavior, and changes in capacity for strength of internal resolve,  among others.  Periodic changes within the memory include changes in stored experiences and learned behaviors of the following classes: cognitive, emotional, affective, volitional, sensational, among others.

 

Periodic facultative changes can also be classified in terms of Freudian Psychodynamics. Such changes can include changes to the conscious psyche, the sub-conscious psyche, and the unconscious psyche. Alternatively, the periodic changes can be classified by those of the Freudian ID, the ego, and the superego.

 

One time periodic changes within the substance of the Human Soul can be considered possible such as through the administration of the Sacraments of Baptism, Confirmation, and Holy Orders. Each of these sacraments confers a sacramental seal or super-natural characteristic within the soul that presumably affects the very substance or essence of the souls of the recipients. These sacramental seals per due into eternity thus, once a Baptized Catholic, always a Baptized Catholic, one a confirmed Catholic, always a confirmed Catholic, and once a Priest, always a Priest. However, there is only one period over which such Sacraments can be administered since they cannot be repeated.

 

In addition, the human soul can receive differing levels of Sanctifying Grace and thus receive objective moral capacities as a result of supernatural grace. Similar bestowing of sanctifying grace can be applied to each human soul on Earth in a repetitive manner and thus provide for an interpretative analogue of spin.

 

These immaterial or non-physical aspects of capacities for a soul to periodically effect itself are paralleled by capacities to produce similar changes in other spiritual creatures such as other Human Souls, the Souls of any bodily extra-terrestrials, the Souls of any bodily ultra-terrestrials, Angels good and bad, and even the Souls of lower forms of animal life especially intelligent animals that interact with created spiritual persons.

 

Thus, we seem to have two categorizations of Soul spin. One category is differentiation by ontology and that is according to accidentiality, falcultativeness, and substantiality. Thus, here there are actually three broad categories of metaphorical spin.  A second category is differentiation by supernaturality. In each of these two categories, there are many sub-categories as indicated by the above details. For supernaturality, there is a secondary primary sub-division and that is the distinction between characters associated with sacramental seals and characters associated with graces obtainable outside the confines of the reception of any or all of the three sacraments that so bestow the sacramental seals. The Holy Mother Church recognizes that vast numbers of persons in numbers known only to GOD can and do receive eternal salvation without ever receiving any of the subject three sacraments. In the end, it is not the reception of the Sacraments and the seals they imbue in the souls of the recipients who receive them that are of primary importance, but rather the metaphorical eighth sacrament of beholding GOD in the Beatific Vision in the Glory of Heaven which is open to all persons who die in the state of grace, no matter how such grace was obtained, even if by ways and means known only to GOD.

 

Each Human Soul that was ever created thus has multiple aspects of spin. Here, the phrase spin  is used abstractly to denote spiritual potentialities for periodic state changes which include ontological aspects, accidental aspect, facultative aspects,  natural aspects, and supernatural aspects.

 

The fact that each Human Soul has spins so to speak points to something sublimely transcendent and even perhaps self-transcendent regarding the human soul. First, is the wide variety of dimensions of spin as classified and categorized above. Second, and I am going out on a limb here, is that the Human Soul might continue to be a human soul even if having a spiritual analogue of no spin, not even a spin of zero . Note that particles having a spin of zero still can be said to have a spin, it is just that its value is equal to zero.  An analogy of physical systems that have absolutely no spin at all might be  the raw undifferentiated space time foam like underpinnings of the origins of the Big Bang once referred to as Yelm during roughly the middle of the 20^th Century by some Big Bang Theorists. Even in modern Chaotic Inflationary Theory, a raw undifferentiated prime matter or at least semi-substantial underpinning underwrites the birth of new universes  in new Big Bangs.  Thus, there is something about the human soul that is what it is, even for a human soul that would lose the capacity for spin state change regardless of whether the state change is natural or supernatural; or substantial, facultative, or accidental.

 

Just as a charged massive boson  such as a W+ or W- weak force boson or fermion continues to have non-spin quantum related aspects, so would a human soul by analogy. Since the mass-energy equivalence of matter and antimatter particles undergoing Fermi-Dirac annihilation retains its energy equivalence despite destruction of the individual non-zero spins of say Fermi Dirac interacting charged leptons or quarks of the same flavor and  continues to exist in the form of photonic based energy, by analogy, the existence of some essential or super-essential aspects of Human Souls is plausible which is independent in its identity from the capacity of the Human Soul to influence itself and external substantial, accidental, and facultative realities; be such realities spiritual or physical, a composite of spiritual and physical elements, or any intermediary forms of created entities perhaps currently unknowable to the Church in this world and in this life.

 

Thus,  perhaps each Human Soul has something mysteriously sublime such that  the Human Soul has an identity or super-substantial or super-essential aspect that exists independently of or at the very least has its own ontological identity and distinctness apart from any soul spin. This identity may be real even under the condition(s) that the spin  aspects of Human Souls are so interiorly pervasive such that the human soul as a fundamental existential and ontological creation could not exist separately from its inherent spin. Since this notion plausibly even applies to souls under the condition that human souls have the capacity to receive Sacramental seals and sanctifying grace to an extent that modifies the substance of each soul receiving such supernatural attributes, there must be something more fundamental about each human soul than the so-called substantiality that could be thusly effected by potentialities inherent within Human Souls to receive such graces based on any spiritual spins of which the Human Soul would be inherently imbued with.

 

To the extent that this super-substantiality is present and identically distinct from any Soul spin, this super-substantiality may itself have multiple aspects thus implying a broadening of the super-substantial aspects of the human soul thereby implying a human soul that is far more ontologically and existentially rich than philosophers and theologians could have previously imagined.

Now, there is yet another class of physical spin in macroscopic systems that is not related to rotational symmetry and that is those based on macroscopic angular momentum or rotational kinetic energy. It is this rotational kinetic energy that presents visible features of say a rotating ice dancer at the International  Winter Olympics to appear repeatedly to the observers of the ice dancing event. The rate at which such features re-appear is related to the frequency of rotation which in turn is related to the rotational kinetic energy, moment of inertia,  and rotational momentum of the spinning ice dancer.

Thus, we humans tend to have a frequency by which we affect similar results in our own souls and in the souls of others, and well as within other external realities both physical and/or spiritual creatures, as well as presumably within GOD HIMSELF. Such effects can be natural such as choices of when to do our homework for college or grade-school, when to eat, when to party, or supernatural such as for my fellow Catholics  in when to attend Mass hopefully with proper intent and moral disposition when receiving Holy Communion, when to go to Confession, when to pray, and the like. Thus, the capacity for finite periods of  repetitive events  of similar nature or class within the Human Soul and within external realities that are brought about by the intra-actions and interactions of the Human Soul indicates an analogue of macroscopic rotational inertia in terms of non-zero rotational kinetic energy, non-zero rotational momentum, and non-zero moment of inertia. The range of such intra-actions and interactions includes the entire ranges described previously. Such effects can thus be substantially, falcultatively, accident-wise classified as well as naturally and/or supernaturally classified.

I will provide a much more extensive elaboration on spiritual soul spin in another post later this week which I hope will delight you with a much deeper sense of mystery and wonderment about the Human Soul.

67)  The Many Unique Degrees Of Human Soul Spins

 

Now each human person has a unique psychodynamic existential and behavioral personality structure. Each individual human person has his or her own behavioral cycles, repetitional  behavioral activities, and repetitional internal psychodynamic states. These repetitional sets of dynamics can in a sense be described by one or more spin states where the world spin in use as an abstract metaphor to the rotational symmetry of fundamental particles, and for macroscopic physical bodies, rotational symmetry as well as periodic or rotational velocity based relative position repetitions.

Such existential and behavioral  psychodynamic aspects include cognitive or intellectual; aspects, emotional aspects, affective aspects, sexual aspects, social aspects, intuitional aspects, spiritual aspects, paranormal or parapsychological aspects, and memory aspects which can include all of the former aspect, as well as other aspects.

Moreover, often times each type or class of behavioral dynamics is often cyclically repeated time and time again. The objective and even the subjective temporal periods of such repetitions can and usually varies with the passage of objective and subjective time. The relative objective and subjective temporal periodicity of one class or type of behaviors often varies with respect to one or more other types or classes.

Thus, in each human person, the number of fundamental degrees of spin or the number of different spins is at least as infinite as the number of possible distinct behavioral states involving one time or multiply repeated psychodynamic events. Since the number of types of human behavior and the number distinct psychodynamic states and possible changes or morphings of such psychodynamic states in limitless to unknown infinite sizes, it is conceivable that the number of possible spins of the human soul is commensurately infinite to an unknown and perhaps unknowable infinite degree.

Thus, based on the above reality, the complexity of the existentiality of the human soul in terms of its facultative and accidental structure is perhaps infinite to an unknowable extent.

Such a rich accidentiality and para-substantiality in all of its unknowably infinite richness must have a baseline substance or essential ontological principle in which it can subsist. In other words, the essence of the human soul must have an existential and ontological magnitude commensurate with it being able to existentially support and maintain the accidental and para-substantial or facultative richness of the psychodynamic aspects of the human psyche or soul.

Since a human person such as in a cryogenic sleep or near freezing hibernation state would have his or her will and consciousness in a complete inactive or static state, and his or her psychodynamic behavioristic activity would be renewed upon awakening where there would be a subjective and objective temporal continuity of personal conscious identity including but not limited to a particular individual’s sense of self, the per due-ance  of a substantial  and a facultative existentiality that is unique and personal must be real in order for the personalized accidentiality and personalized facultative aspects of the soul to survive or remain revivable upon awakening from the cryogenic sleep states.

If it be the case where the substance of the human soul could not exist without the soul’s faculties and accidents, then in order for the human spiritual components or his or her soul to continue existing as the same soul upon a given human persons complete cryogenic sleep, the soul must have some form of deeper level of existence and ontology that its substantial aspects.

Perhaps such sub-substantial and sub-essential aspects point to the reality of a form of meta-substance, meta-essence, super-substance or super-essence, pre-substance or pre-essence, of the Human Soul.

Such super-ontological aspects of a human soul would need to at least extrinsically if not intrinsically underwrite the richness of the substance of the human soul where such richness would be commensurate which the unknowably great infinite numbers of possible spins states of the human soul. Such a capacity for extrinsic or intrinsic underwriting would point to a profound existential, ontological, and perhaps more accurately the reality based greatness of the human soul.

Now since each human soul has unique psychodynamic traits and behavioral traits and a qualitative and perhaps quantitative unique set of spins and degrees of spin freedom, there must in each human person exist a soul that has a unique substance and therefor unique sub-substantial and sub-essential aspects commensurate with the reality that each human soul is a distinct person utterly forever, whether in Heaven, Purgatory, any Limbo, or any Hell,  and in this life.

The mere fact that the qualitative and quantitative aspects of soul spin states either collectively or individually considered is so radically unique for each human person and so rich in spiritual and psychodynamic patterns and texture points to some radically transcendent per due-ance of the substantial aspects and even more so, any sub-substantial and sub-essential aspects of the Human Soul.

Quite simply put, a human soul is the soul that he or she  is for all eternity and not even the deepest and hottest metaphorical flames of Hell in eternal damnation can erase this fact for each condemned human soul. This evidently true even if the human souls in Hell will require GOD to maintain them in existence for all eternity. If such eternal existential maintenance is required for the souls in Hell, then it is also by human nature required for the eternal existence of the Souls in Heaven and in any Limbo.

Any required Divine sustenance of Human Souls after the Final Resurrection of the Dead need not detract from the plausibility of the enormous existential and ontological magnitude of the human soul in its substantial, facultative, accidental,  and any sub-substantial or sub-ontological levels of its existence or its reality.

Any sub-substantial or sub-ontological levels of the Human Soul might provide a hint at where GOD as CREATOR  stops and where the Human Soul begins. Such a boundary condition may somehow be related to the Human Soul’s natural capacity to receive Divine Grace and the Sacramental Seals bestowed by the administration of each of the Catholic Sacraments of Baptism, Confirmation, and Holy Orders.

If Human Souls are immortal by grace only, then even the Human Souls in Hell must have a certain level of grace which would be universally bestowed on all Human Souls. This is evident since all Human Souls are immortal and can never finally die, even if under some circumstances, some souls would be destroyed in a temporary manner.

All Human Persons will be Resurrected as complete Body-Soul Natures at the Final Resurrection to Incorruptibility, even so for the Souls who go to Hell. Once eternally Resurrected, whether to Heaven, Hell, or any Limbo, there is no lapsing back into any state of non-existence. Note that the Catholic Church does not indorse and contemplate mechanisms by which the Human Soul could be temporarily eradicated, but I have written on  the subject of possible mechanisms by which such could happen. However, any souls that would die a soul death will be exceedingly well rewarded commensurate with such a martyrdom.

One mechanism of soul destruction that has some adherents is the close proximity of a human person to the heart of a nuclear explosion. I will spare the reader the details of this concept because of its unpleasant ramifications suffice it to say, that utterly and absolutely, all Human Persons will be eternally Resurrected on the Last Day, regardless of what can and would happen before then even in rare cases.

68) The Human Soul As The Substantial Form Of Body Defining Quantum And Thermodynamic Energy States And Informations.

 

What is matter?  What is energy? What is space? What is time? What is space-time? In short, what is the very substance or raw existential or ontological reality of physical corporeal being?

We humans and presumably also any bodily ETI and UTI are familiar with our sensory experiences, drives including those for sex, food, drink, sleep, warmth, and the whole host of other instinctual aspects of the human psyche. We are familiar with emotions, feelings, thoughts, volitions, intuitions and other higher psychic attributes. We are aware of ourselves and perhaps others directly in cases where any telepathic capacities are present. In short, we are somewhat aware of what it is like to be ourselves and for those in intimate relationships with the possibility of rudimentary telepathic capacities,  some folks would say they know what it is like for their intimate partner to be his or her own self to a very limited extent.

But what about matter? What particular dignity does mass-energy-space-time  (mest) have as considered a distinct class of created elements to  that of human spiritual and immortal souls, those of any bodily ETI and any bodily UTI,  and the pure spirits of angels,  do not have?

First,  mass-energy-space-time can do no evil in itself. Mass-energy-space-time has innocence to the extent that it cannot do evil. Since mest cannot do evil, it cannot be corrupted by or stained by its own sins which in fact cannot be committed by pure inanimate mest.

Second, mest is governed or predictable by  mathematically interpretable dynamics that quite simply never fail in its consistency except for miraculous Divine intervention. Human souls can fall in and out of the state of grace,  be stained by sin and can also be very unpredictable in terms of both human morally free, and evil, good, or morally neutral acts of volition. Such morally informed choices can have a corrupting effect on the accidental properties of the human soul but presumably not the Soul’s substantial or essential properties.

Third, mest and/or its substantial underpinning are the material elements of the Heavens or the Firmament which Sacred Scripture holds to be unshakable and incorruptible in its foundation set as such by GOD. Such unshakability may be commensurate with the unshakability of the mathematics we use to describe observable physical reality and the unshakability of the rules of logical deduction.

Fourth, even the physical cosmos or creation will be transformed or Resurrected on the Last Day. Our physical and mortal bodies will be spiritualized and immortalized incorruptible with the same qualities as Christ’s Resurrected body. It is interesting to note that Sacred Scripture primary speaks of the afterlife for we human persons in terms of the Final Bodily Resurrection of the Dead.

Even though our bodies are weak and corruptible, even my large husky but soft obese and padded body, all human bodies will arise incorruptible on the last day no matter where we will spend eternity.

The accidental aspects of the raw mest that comprise our bodies seems to be the aggregated statistical mechanical states, the quantum energy states, and the general relativistic states that define each atom and its constituent particles, and such in relation to all other atoms within the human body. Collectively, our bodies’ visible forms are defined by the polarizations, spins, energies, and other quantum properties of the constituent atoms.

Since a human body is only full and alive with its well defined unity by the associated accidental visible aspects open to scientific scrutiny by technological apparatus, such informations as a unity form producing aggregation will be Resurrected and glorified to an extent commensurate with spiritualization, immortalization, and incorruptibility of the Resurrected and glorified human body. In short, even the quantum-mechanical and statistical mechanical informational aspects of the Human Body will be Resurrected and glorified. Regardless, the new Catechism of the Catholic Church states that the human body will be given incorruptible life at the End of Time.

Since the entire physical cosmos appears to be on track to a transformative glorification also, perhaps the quantum mechanical and statistical mechanical informations that define it and each sub-portion thereof will also be glorified. This is a rather odd concept but seems plausible. The concept is also whimsically far out since one can question as to how mere quantum mechanical and statistical mechanical information can be exalted more than it already is. After all, information is what it is. None-the-less, I am proposing that the mere mathematicalized and set theory definable informations as such will be transformed in an existential if not ontological manner.

Since physical energy state informations define the visible aspects of the human body and make a live living human body a living body, we can expect that these informations will be ontologically transformed,  or perhaps to coin a new lexicography, realogically transformed into a much more exalted natural and supernatural state. By realogically, I mean a mode of reality that is not necessarily substantial or accidental but which underwrites the physical cosmos and the human body as the set of informations that define these physical entities.

Now since the Human Soul is the substantial form of the Human Body in a Platonian or Aristotelian sense of the word, the Human Soul is also the form of both the raw mest aspects of the Human Body as well as the distinguishing physical informations that define the body’s statistical mechanical and energy states. So in at least a limited sense even if only indirectly so, the Human Soul is so ephemeral that it is the substantial form of the raw physical and mathematical informations that thermodynamically and statistical mechanically define the Human Body. Since the nature of the Human Body for absolutely all Human Persons no matter where they spend their eternity is going to be resurrected to Incorruptibility, it would seem that each Human Soul to be re-united to its Human Body will likewise receive an additional degree of incorruptibility based on its substantial formality with the Human Body.

Now, I am not saying that each Human Soul in Hell united to its Human Body will not suffer in Hell, but rather and none-the-less, we must understand that we are all GOD’s children by virtue of Christ’s Conception, Birth, Life, Passion, Death, Resurrection, Ascension, and future coming in glory at the End Of Time. For Catholics, once a Catholic always a Catholic, once Baptized always Baptized, once Confirmed always Confirmed, once an Ordained Priest always an ordained Priest, and even more so,  once Resurrected in Body, always Resurrected in Body no matter where we spend eternity. As recounted in the book about Pope John Paul II written during His Reign,  Be Not Afraid,  Pope John Paul II is paraphrased there as saying that the extent to which eternal life is lived out in a life beyond the grave in damnation is profound and currently veiled mystery.

However, we can be assured that GOD’s eternal plan for creation in HIS Divine Economy has been far from exhaustively revealed. The hopes and dreams we have for the ever greater realization of the Divine Economy and the mysteries of creation will provide us delight for all eternity. Part of the fun of the Divine Economy is its eternal progression into existential and ontological vistas and horizons yet to be imagined.

69) The Dynamic Life Of The Human Soul: Another Spiritual Dimension

 

The spiritual and immortal human soul is the substantial form of the body according to Saint Thomas Aquinas and is the form of the body according to the new Catechism of the Catholic Church, that is,  in the Platonic or Aristotelian sense of the word, “form”.

Many physicists and physical minimalists may feel the human soul is of little importance compared with the human body and the physical world as a result of the conservative laws of physics that appear to rigorously enforce the mass-energy conservation principle and other conservative principles. Such folks may feel that since the Human Soul can be metaphorically stained by sin, it must not be as immutable or ontologically and/or existentially stable as space-time-mass-energy which is governed at the very least, by meta-stable conservative laws.

I would like to provide a counter-argument to the spirit of the physical minimalists point of view as structured below.

First, the spiritual and immortal human soul is essentially the substantial form, or form, life or vital principle in the human person. Since the human soul is immortal in absolutely all cases, it is utterly immortal.

 

Second,  because the human soul is changing in its activities and accidental properties, and is thus effervescently full of conscious, sub-conscious, and unconscious life experiences, and thus indeed is changing in terms of its accidental properties with time, it is a wonderful glittering sparkle of pure life. Thus, the human soul has a beauty and shimmering effervescence that no meta-stable, purely physical, entity or mode of being can have. Beauty is an ontologically transcendent principle that goes beyond and transcends any physical or spiritual immutability of any element of creation. The beauty of each human soul transcends its immortality but is an utterly inherent aspect of all human souls in the mind and heart of GOD and GOD is the ultimate reference point by which all things are relative.

 

Third, since each human soul is forever the soul that it is and is forever immortal, that fact that its accidental properties are time varying does not take away from its immortality which by definition is forever. Rather,  the time varying sparkling or effervescent shimmering of the human soul implies  another entire level to its existence. The human soul is immutably itself and immutability spiritual and immortal while at the same time having the capacity for time dependent change. Thus, the human soul has an additional ontological and existential richness as ontologically and existentially expressed in its shimmering effervescence.

 

Fourth, the founder of psychodynamic personality theory, Sigmund Freud, teaches us that each human experience, conscious, subconscious, or unconscious, is conserved forever in the human psyche even if only  in the vast repository of the unconscious mind of each human person. Thus, each thought, feeling, emotion, instinct, act of volition, intuition, and the like is forever preserved in the depths of the human soul.  This makes sense from the standpoint of Catholic spiritual anthropology which affirms that each experience adds to the accidental form of the human soul. It also make sense given the common faith-based belief that we will be rewarded to an extent at least partially based on what we have done or what we have failed to do in terms of free culpable acts or omissions.

 

Thus, a living human soul, spiritual and immortal in all cases, has an extra ontological and existential degree of effervescence. Yet each human soul is everlasting and immortal, no matter where it will eventually spend eternity.

 

Even the souls in Hell by virtue of their natural immortality are utterly immortal and to the extent that they experience time dependent changes in their conscious, sub-conscious, and unconscious suffering, they too have an eternal effervescence as an ontological and existential dimension that somehow in some way traditional theologians would likely not grasp. Even the souls in Hell serve at least one great purpose, and that is to be an existential and  moral reference by which morally virtuous and grace-filled rational creatures  can be distinguished (and rewarded) from those who have definitively chosen not to follow GOD.

 

This Christmas, when you are tempted to pray overly exuberantly for justice, and in some cases, for the eternal punishment of terrorists, those who sexually abuse children, rapists, drug dealers, death row inmates, and the like, remember that the Lord GOD loves all of these characters which many of otherwise refined and grace-filled Catholics and Christians tend to view with an irk-filled revulsion. The Lord died on the Cross and Rose from the Dead so that those who revile us would also be saved. Some of those like the Biblical Saint Paul were once the most notorious persecutors of the early Catholic Church. GOD can  and does raise up great Saints, even  from the ranks of terrorists, laypersons and clergymen who practice child abuse, drug dealers, rapists and the like.

 

In spite of the psychodynamic analysis that candidates post-humously must be subjected to in the current era in order to be considered for beatification and canonization, I am certain that some folks who would revile Church authorities as grave and habitual sinners can,  and in some cases,  do go straight to Heaven in numbers, ways, and means known only to GOD. It is kind of a shame that many conservative, and rightfully so,  Catholic clergymen often speak negatively of the practice of psychotherapy and psychiatry yet rely so much on modern psychometric testing to screen  candidates for priestly and religious formation.  Can’t have it both ways in my opinion.

 

Thus, in this Christmas season, let us try to bring joy to those who irk our sense of refined intellect and self-image such as a poor homeless beggar, those in jail or in prison, those confined to a psyche ward, or even an estranged family member. Better yet, pick an unsavory terrorist and/or an authoritarian dictator and say the Rosary for his or her salvation and if you are courageous enough, pray that they go straight to heaven when they leave this life and are thus eternally saved with utter certainty. Such a prayer will not likely be made even by many of pious clergymen and religious. However, such a prayer made on behalf of such unsavory characters will distinghuish those who are at least approaching Saint-hood from those who are of ordinary levels of grace in the life of the Church. If more Catholics prayed as such, we might soon enter an Era of Peace promised by Our Lady Of Fatima. If very few or no persons are willing to pray as such, than in all likelihood, the Era of Peace could never arrive before the Second Coming.

The good news is that by praying for the eternal salvation of those who revile us the most, those who irk us the most, and those who we distain with no sense of respect and with a great sense of disrespect, we will come one step closer to Sainthood. By praying for the eventual Canonization of such folks, we come even closer to Sainthood.

GOD BLESS!

70) The Entropy Of The  Human Soul And Its Objective Temporal Extension And Eternal Existential Growth

We in the modern science fiction culture infused 21^st Century Earth have all heard of sci-fi and government conspiracy theories of time travel, and physicists such as myself are generally aware of the pros and cons of theories of backward time travel, or of future and backward time travel. According to many of versions of the still speculative theories of such methods, the past and perhaps the future really exist as a backward and forward temporal extension from the present.

However, theoretically, space, and thus time are quantized at the level of the Planck Length and the Planck Time. These units are respectively, {[h/2π] G/[C³]}^1/2  and {[h/2π] G/[C⁵]}^1/2  or about 1.6 x 10^-35 meters and 5.39 x 10^-44 seconds respectively. Recent astronomical observations tentatively and very indirectly suggest an actual length quantization of less than about 10^-48 meters.

Thus, the extension of an object or an energy state for a distance greater than the Planck Time Length into the past or into the future might be discretized and therefore temporally composite with respect to the background.

Now entire assemblages of atoms and the atoms constituent particles and fields may have a backward and forward temporal extension that is smeared out to greater continuity with respect to the past and future simply because each atom, or each discreet quanta of mass and energy composing a large microscopic body or a macroscopic body may proverbially temporally march to its own Planck-Time ruler. Quite simply put, the ticks for each atom or quantized mass energy unit are likely not all centered amongst each other. The general concept here is analogous to two or more parallel rulers placed side to side in contact with each other  but being displaced from each other by less than one unit distance tick of the ruler.

Thus, the larger the system, the more ambiguity there is in a quantum Planck Time tick that would reference the temporal extension of the system or by which the system could be uniformly temporally measured.

The degree of smearing, S_mear, is likely to be at least m-fold for a system with m fundamental quantized particles. In reality, the system’s degree of smearing is likely to be closer to that defined as follows:

 

If N is the total number of particles or states, the degree of smearing is equal to:

S_mear = N = {{Σ_i exp [- U_i/[k_bT)]}/{exp [- U_i/[k_bT)]}}n_i

where n_i is the number of particles occupying level i or the number of feasible microstates corresponding to macrostate i; U_i is the energy of i; T stands for temperature; and k_B is the Boltzmann constant. This expression applies to systems defined by Boltzmann distributions.

Alternatively, S_mear  = Ω = exp [S/k_b]

 

where S is the system entropy and Ω is the number of microstates corresponding to the observed macrostate.

For systems that can be defined by a compound wave-function or a collective wave function, perhaps the smallest unit of time, conservatively for the system is equal to the Planck Time divided by N or {[h/2π] G/[C⁵]}^1/2 /N = {[h/2π] G/[C⁵]}^1/2/{{{Σ_i exp [- U_i/[k_bT)]}/{exp [- U_i/[k_bT)]}}n_i}

 or more generally for systems, {[h/2π] G/[C⁵]}^1/2/ Ω = {[h/2π] G/[C⁵]}^1/2 / {exp [S/k_b]}.

The beginning of all cosmic temporal rulers may have occurred at the very instant of the big bang after which quantum fluctuations cause the entire set of rulers, one for each energy state to become mismatched. For closed universes destined for re-collapse, the very ends of the rulers will line up at the same tick once again. Such an initial and final line up may imply an indistinguishability of the birth of our universe from its death should it be closed and destined for re-collapse. Should the universe re-inflate or rebound, the time dependent distribution of microstates will likely change due to quantum-statistical random-ness or semi-randomness, however, once again, there may be no distinction between the final collapse and re-expansion and the second collapse. The process might continue forever with all births and all collapses being indistinguishable in terms of boundary conditions. Should we learn how to travel at stupendously high gamma factors, and to cloak our space craft from the external universe, upon closely approaching the end state for our universe, provided it is closed, we should be able to tunnel or travel into any number of future versions of our cyclical big bang, provided our universe a cyclical closed one.

If our universe is infinitely large, say infinite in the sense of the least transfinite ordinal which I will refer to as Omega in terms of numbers microstates, then the number of possible universe versions is at least equal to  Omega = N = {{Σ_i exp [- U_i/[k_bT)]}/{exp [- U_i/[k_bT)]}}n_i  as a Boltzmann approximation and more generally, equal to Omega = Ω = exp [S/k_b].

If our universe is infinitely large, say infinite in the sense of the least transfinite Aleph number, Aleph 0,  which is the number of integers,  in terms of numbers microstates, then the number of possible universe versions is at least equal to  N = Aleph 0 = {{Σ_i exp [- U_i/[k_bT)]}/{exp [- U_i/[k_bT)]}}n_i  as a Boltzmann approximation and more generally, equal to Ω = Aleph 0 =  exp [S/k_b].

If our universe is infinitely large, say infinite in the sense of the second least transfinite Aleph number, Aleph 1,  which is the number of real numbers according to the continuum hypothesis,  in terms of numbers microstates, then the number of possible universe versions is at least equal to  N = Aleph 1 = {{Σ_i exp [- U_i/[k_bT)]}/{exp [- U_i/[k_bT)]}}n_i  as a Boltzmann approximation and more generally, equal to Ω = Aleph 1 = exp [S/k_b].

If our universe is infinitely large, say infinite in the sense of the third  least transfinite Aleph number, Aleph 2,  in terms of numbers microstates, then the number of possible universe versions is at least equal to  N = Aleph 2 = {{Σ_i exp [- U_i/[k_bT)]}/{exp [- U_i/[k_bT)]}}n_i  as a Boltzmann approximation and more generally, equal to Ω = Aleph 2 = exp [S/k_b].

On can proceed with similar conjectures with ever higher transfinite Aleph numbers such as Aleph i: i = 3,4,5,… ad infinitum.

For eternally open universes, such a past-future boundary in distinguishability would not apply but such a  universe would expand forever perhaps implying innumerable possible future phase changes and all of the additional entropy, order and disorder that would result, and the possibilities for life forms untold in number. One thing is for sure, achieving ever higher relativistic gamma factors permits us to travel ever further into the future of our universe from our present era, even if nature censors super-luminal energy and signal propagation in the traditional sense of the word.

71) The Subjective Time Dependent Growth Of The Human Soul And How The Human Soul Grows Itself Along The Axis Of Subjective Time.

 

We who are physicists and cosmologists are not adverse to contemplating a backward time and forward  time extension of our universe. As such, as a physicist who is also a soul freak, I naturally tend to contemplate the backward and forward temporal extension of the human soul at least in reference to its accidental properties and semi-substantial constitution such as the particular state of the soul’s so-called power parts or its faculties of heart, intellect, memory, and will. Modern psychodynamic theory classifies the human psyche into the conscious, sub-conscious, and unconscious mind or alternatively, into the Id, ego, and super ego.

 

Regardless, if the past really exists in the past and the physical universe also really extends along a future time axis, then by corollary, so does each human brain, and by association at the very least, so too does the accidental aspects of the human soul as well as its power parts or faculties.

 

However, psychologists and even physicists and cosmologists often make a distinction between objective time and subjective time where the latter is the sense of time flow which is related to the memory and awareness of past: personal activities, interaction with the external environment, interactions,  and intra-actions with one’s own psyche, and the like.

 

Objective time theoretically seems to be quantized at the Planck Time Unit level or at the level of temporal resolution equal to {[h/(2 π)] G/[C⁵]}^1/2 = 5.39 x 10^-44 second. Since the human soul is commonly and traditionally held to be substantial in nature as well as possessing an extreme degree of unity and individuality, perhaps the quantization of objective time does not imply a quantization of subjective time. Since the human soul is the spiritual and immortal, and also the vital or life principle: of unity, identity, individuality and uniqueness of each human person, perhaps its internal accidental and semi-substantial power part composition is perfectly continuous and even super-continuous in a qualitative sense and  also in reference to its subjective time dependent evolution and any analogous extension of such structural composition into any subjective past and into the future.

 

Perhaps the human soul grows not only in objective time in terms of its accidental and semi-substantial extension along the past-future objective temporal axis extension, but also the same along its subjective temporal axis. The extension of the human soul along its subjective future is a kind of irony because of the implications of human free will  and acausality commensurate with the frequent use of the faculty of free will by humans to make self-directed and informed free choices.

 

If indeed the subjective past really exists within the human soul, then by implication, the human soul grows in subjective temporal extension as it experiences daily life and as its faculties undergo subjective time dependent change. At the very least, the effects of the subjective past within the human soul are conserved in its present state.

 

Each human soul may in a sense grow itself along the subjective time axis because each human soul by virtue of its sub-conscious and unconscious minds stores memories of all past and present experiences. Simply by existing, the human soul seems capable of growing itself along the past-future subjective temporal axis if for no other reason than that each experience in the present and each experience within the past such as is recorded in the human faculty of memory continually effects the accidental and perhaps semi-substantial form of the human soul via self-interaction whether conscious, sub-conscious, or unconscious.

 

Thus, simply by naturally living, whether in Heaven, Hell, Purgatory, any Limbo, and in this life, the human soul seems epistemologically poised to grow in accidental and semi-substantial size by virtue of its own self-awareness, self-interaction, and interaction with the external environment in a manner that is likely qualitatively perfectly continuous or super-continuous.

 

Note that physical temporal continuity and super-continuity would imply a temporal resolution of (1/Ω) second, n(1/Ω) second, [1/(Aleph 0)] second, [n/(Aleph 0) ]second, [1/(Aleph 1)] second, [n/(Aleph 1)] second, [1/(Aleph 2)] second, [n/(Aleph 2)] second, and so-on ad infinitum. Note that  Ω is the least transfinite ordinal, Aleph 0 is the number of integers which is infinite, Aleph 1 is much greater than Aleph 0 by a factor of infinity and is the number of real numbers according to the Continuum Hypothesis, Aleph 2 is the  third least transfinite Aleph number and is greater than Aleph 1 by a factor of infinity, and so-on to ever greater transfinite Aleph numbers. Here, n can be either finite but less than one or infinitesimal.

 

Also a distinction not so much recognized by traditional spiritual anthropologists is made between the so-called semi-substantial aspects of the human soul and its essence or substance. Here, an immutability of the essence of the human soul is commonly interpreted by spiritual anthropologists as opposed to the dynamic aspects of its power parts or its faculties. However, some spiritual anthropologists hold that the human faculty of the free will can be viewed as if a nature all to its self since it is the most important faculty and is in fact the faculty by which we ultimately accept or reject the following of Christ.

GOD BLESS!

Jim

72)  Eternal Growth Of The Human Soul In And By Eternal Growth Of The Human Soul’s Vegetative Life

 

The following italicized text was taken from a previous chapter I had written;

“We in the modern science fiction culture infused 21^st Century Earth have all heard of sci-fi and government conspiracy theories of time travel, and physicists such as myself are generally aware of the pros and cons of theories of backward time travel, or of future and backward time travel. According to many of versions of the still speculative theories of such methods, the past and perhaps the future really exist as a backward and forward temporal extension from the present.

However, theoretically, space, and thus time are quantized at the level of the Planck Length and the Planck Time. These units are respectively, {[h/2π] G/[C³]}^1/2  and {[h/2π] G/[C⁵]}^1/2  or about 1.6 x 10^-35 meters and 5.39 x 10^-44 seconds respectively. Recent astronomical observations tentatively and very indirectly suggest an actual length quantization of less than about 10^-48 meters.

Thus, the extension of an object or an energy state for a distance greater than the Planck Time Length into the past or into the future might be discretized and therefore temporally composite with respect to the background.

Now entire assemblages of atoms and the atoms constituent particles and fields may have a backward and forward temporal extension that is smeared out to greater continuity with respect to the past and future simply because each atom, or each discreet quanta of mass and energy composing a large microscopic body or a macroscopic body may proverbially temporally march to its own Planck-Time ruler. Quite simply put, the ticks for each atom or quantized mass energy unit are likely not all centered amongst each other. The general concept here is analogous to two or more parallel rulers placed side to side in contact with each other  but being displaced from each other by less than one unit distance tick of the ruler.

Thus, the larger the system, the more ambiguity there is in a quantum Planck Time tick that would reference the temporal extension of the system or by which the system could be uniformly temporally measured.

The degree of smearing, S_mear, is likely to be at least m-fold for a system with m fundamental quantized particles. In reality, the system’s degree of smearing is likely to be closer to that defined as follows:

 

If N is the total number of particles or states, the degree of smearing is equal to:

S_mear = N = {{Σ_i exp [- U_i/[k_bT)]}/{exp [- U_i/[k_bT)]}}n_i

where n_i is the number of particles occupying level i or the number of feasible microstates corresponding to macrostate i; U_i is the energy of i; T stands for temperature; and k_B is the Boltzmann constant. This expression applies to systems defined by Boltzmann distributions.

Alternatively, S_mear  = Ω = exp [S/k_b]

 

where S is the system entropy and Ω is the number of microstates corresponding to the observed macrostate.

For systems that can be defined by a compound wave-function or a collective wave function, perhaps the smallest unit of time, conservatively for the system is equal to the Planck Time divided by N or {[h/2π] G/[C⁵]}^1/2 /N = {[h/2π] G/[C⁵]}^1/2/{{{Σ_i exp [- U_i/[k_bT)]}/{exp [- U_i/[k_bT)]}}n_i}

 or more generally for systems, {[h/2π] G/[C⁵]}^1/2/ Ω = {[h/2π] G/[C⁵]}^1/2 / {exp [S/k_b]}.

The beginning of all cosmic temporal rulers may have occurred at the very instant of the big bang after which quantum fluctuations cause the entire set of rulers, one for each energy state to become mismatched. For closed universes destined for re-collapse, the very ends of the rulers will line up at the same tick once again. Such an initial and final line up may imply an indistinguishability of the birth of our universe from its death should it be closed and destined for re-collapse. Should the universe re-inflate or rebound, the time dependent distribution of microstates will likely change due to quantum-statistical random-ness or semi-randomness, however, once again, there may be no distinction between the final collapse and re-expansion and the second collapse. The process might continue forever with all births and all collapses being indistinguishable in terms of boundary conditions. Should we learn how to travel at stupendously high gamma factors, and to cloak our space craft from the external universe, upon closely approaching the end state for our universe, provided it is closed, we should be able to tunnel or travel into any number of future versions of our cyclical big bang, provided our universe a cyclical closed one.

If our universe is infinitely large, say infinite in the sense of the least transfinite ordinal which I will refer to as Omega in terms of numbers microstates, then the number of possible universe versions is at least equal to  Omega = N = {{Σ_i exp [- U_i/[k_bT)]}/{exp [- U_i/[k_bT)]}}n_i  as a Boltzmann approximation and more generally, equal to Omega = Ω = exp [S/k_b].

If our universe is infinitely large, say infinite in the sense of the least transfinite Aleph number, Aleph 0,  which is the number of integers,  in terms of numbers microstates, then the number of possible universe versions is at least equal to  N = Aleph 0 = {{Σ_i exp [- U_i/[k_bT)]}/{exp [- U_i/[k_bT)]}}n_i  as a Boltzmann approximation and more generally, equal to Ω = Aleph 0 =  exp [S/k_b].

If our universe is infinitely large, say infinite in the sense of the second least transfinite Aleph number, Aleph 1,  which is the number of real numbers according to the continuum hypothesis,  in terms of numbers microstates, then the number of possible universe versions is at least equal to  N = Aleph 1 = {{Σ_i exp [- U_i/[k_bT)]}/{exp [- U_i/[k_bT)]}}n_i  as a Boltzmann approximation and more generally, equal to Ω = Aleph 1 = exp [S/k_b].

If our universe is infinitely large, say infinite in the sense of the third  least transfinite Aleph number, Aleph 2,  in terms of numbers microstates, then the number of possible universe versions is at least equal to  N = Aleph 2 = {{Σ_i exp [- U_i/[k_bT)]}/{exp [- U_i/[k_bT)]}}n_i  as a Boltzmann approximation and more generally, equal to Ω = Aleph 2 = exp [S/k_b].

On can proceed with similar conjectures with ever higher transfinite Aleph numbers such as Aleph i: i = 3,4,5,… ad infinitum.

For eternally open universes, such a past-future boundary in distinguishability would not apply but such a  universe would expand forever perhaps implying innumerable possible future phase changes and all of the additional entropy, order and disorder that would result, and the possibilities for life forms untold in number. One thing is for sure, achieving ever higher relativistic gamma factors permits us to travel ever further into the future of our universe from our present era, even if nature censors super-luminal energy and signal propagation in the traditional sense of the word.

Now, what about the application of time discreetizement for any objective time, past and future, extension of the Human Soul.

Since the human soul is a spiritual reality, it is not very physical and thus does not seem to be bound by the same cosmic aversions to locally infinite quantities. Thus,  the human soul might not have a temporal composition in any past- future extension.

Based on the above displaced center temporal ruler concept for purely physical systems, an effectively perfectly continuous past-future human soul extension is plausible based on  the Holy Bible based rhetorical questions paraphrased as follows: “Who but the Lord GOD, Hmself, can comprehend the tangled workings of the Human Heart. Who but GOD Himself can comprehend the complexity of the Human Heart and therefore judge Human intensions”.

Provided that the Human Heart is indeed infinitely complex, a past-future extensity of the Human Heart and therefore of the Human Soul would be effectively continuous with the number of human soul  elemental feature states being equal to Ω = exp [S/s_b] where s_b is the spiritual analogue of k_b, the Boltzmann constant.

The temporal discreetizment for the Human Soul may be effectively equal to Delta t = {[h/2π] G/[C⁵]}^1/2/ Ω = {[h/2π] G/[C⁵]}^1/2 / {exp [S/s_b]}.

The continuity of the Human Soul may be perfectly continuous, or super-continuous. For super-continuity, the number of pixilated spiritual informations  describing the Human Soul may be infinite of order Aleph 0, or perhaps Aleph 1, or perhaps Aleph 2, or perhaps Aleph 3, and so-on, ad infinitum.

Thus, the objective time resolution for a Human Soul may be equal to Delta t = {[h/2π] G/[C⁵]}^1/2/ Ω = {{[h/2π] G/[C⁵]}^1/2 / {f[Aleph i]}}  where i = 0, or 1, or 2, or 3, or … ad infinitum.

Thus, assuming that the past really exists and is conserved in the present, and that the future exists and is conserved from the present, each human soul from the time it was first conceived continues to grow or become larger and larger with the passage of objective physical time.

Such eternal growth of the human soul is plausible when considering that the human soul is a unity while at the same time being related to the human body to which it is united as the body’s substantial form. The human soul can thereby plausibly grow with its union with the body in an eternal manner and thus become ever existentially larger and with the passage of time, both in this life, and then in life after the Final Resurrection at the End Of Time. This eternal growth even applies to those eternally consigned to Hell who although missing out on the Beatitude of Heaven, still serve a mysterious purpose in the Divine Economy which is currently veiled to current understanding in this life and perhaps even in Heaven from amongst GOD’s creatures during the current era of history of the eternal unfolding of GOD’s plan according to HIS Divine economy. Absolutely all living folks should strive as an utmost important goal to avoid eternal condemnation, but I am convinced that the reason for Hell is nonetheless a great mystery that GOD has prudently chosen not to reveal to any of HIS creatures as of yet.

Now s_b may or may not have the same value for each human person because each psychodynamic constitution has its own strengths and weaknesses, and its own particular  existential  sub-regional aspect specific complexity and dynamics. In short, a given existential sub-portion of a given human soul has individual specific complexity and dynamical structure even if the human soul is spatially simple and unextended.

Thus,  for a given human soul which we will l