#447 book of science for AP---- SPACE = Magnetic Field + Electric Field by Archimedes Plutonium.
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Archimedes Plutonium
Jan 12, 2026, 9:48:48 PM (4 days ago) Jan 12
to Plutonium Atom Universe
My first book where the title is just one word. Maybe my last and only book with a one word title.
If I am successful with this adventure or exploit, I will have accomplished one of the most beautiful theories in all of physics, that the composition of Space is because of the habitation of EM photons, the electromagnetic spectrum itself makes empty space.
It is not that empty space exists and then matter trespasses into it or that Light photons wander in and out of empty space. No, the idea I put forward here is that Space is formed by Light-Photons. And only recently can I start to put mathematics to the test to see if correct.
---quoting my #446 book---
Although I would have preferred to say REVERSE, rather than Inverse. Something about inverse that does not agree with me.
Anyway, a very important book, indeed, for I am chasing after that elusive but beautiful theory that SPACE = Magnetic Field + Electric Field. And now I think I am getting very very close.
I recently noticed in doing the revised Hertzsprung-Russell Diagram of this function that looks like Y--> 10- x. And if that were graphed in a square that was 10 by 10.
Now we roll the square to the right in a 90 degree roll and end up with a square where the function is now the inverse of what it was previously as that of Y--> x, the identity function.
|\
|___\ roll that square 90 degrees and you end up with
| /
|/___
the 90 degree roll causes the x-axis to become the y-axis and vice versa.
So then I look up to see what physics forces follow this Y--> 10 -x and come to find out that not only the Hertzsprung-Russell Diagram but the Coulomb force law and also the Ideal Gas Law of PV = nRT.
Now I look to see what New Ohm's Law when graphed looks like. And would you not believe it-- it follows Y--> x. New Ohm's law is different from Old Physics of V = i R for we include magnetic field and electric field as that of V = CBE.
So, well, I have the Ideal Gas Law when graphed follow Y-->10 - x the inverse of New Ohm's law graph of Y--> x.
For decades now, ever since I fixed Old Physics Ohm's law to be a true law of physics by replacing resistance with B*E, I have been vocal on the idea that New Ohm's law and Ideal Gas Law were both equal expressions of the math formula Volume = length*width*height.
But Inverses tell me a different story in that I cannot say Ideal Gas Law has the same formula as New Ohm's Law.
And during those decades, I could never seem to get Pressure be Voltage or get three variables on one side of the equation as in C*B*E. I could only have P*V on one side.
But now, seeing there is some form of Inverse relationship, if I multiply both sides by T temperature I get this.
PV = nR(1/T)
TPV = nR or some other variant such as V = nR (T*P) looking more like New Ohm's Law.
Then I can begin to relate Voltage with Volume (or perhaps pressure) and relate temperature with E or B field or both as some form of resistance.
Which is worthy of a entire book devoted to Inverses.
AP, King of Science
#446 science book of AP-- INVERSES// physics by Archimedes Plutonium
Archimedes Plutonium
Jan 12, 2026, 9:53:22 PM (4 days ago) Jan 12
to Plutonium Atom Universe
Title is more than 1 word, and I was referring to my #446 book of INVERSES. sorry
Archimedes Plutonium
Jan 13, 2026, 2:24:00 AM (4 days ago) Jan 13
to Plutonium Atom Universe
Tough subject. I need to find experiments and observations to prove the claim.
The claim is simple to state, simple to understand, simple to recognize. However, it is mindboggling in many respects.
Old Physics claims
-------------------------------
Old Physics claims Space exists independent of matter and photons and when you introduce matter or photons into Space, they can roam freely and occupy Space.
AP believes Space is itself formed by the Photons that traverse there. If no photons available, no Space exists there.
Now I use the ideas of my #446 book titled with one word INVERSES. What in the world is the inverse of Space. This is easy, because quantum mechanics duality says that Time is the dual of Space, and so, Time is the Inverse of Space.
If Space exists only when photons are present to create Space, then they are at the Speed of Light, and in motion and in perpetual motion. The inverse of that is complete rest with no motion. If the Universe in its entirety had no motion, everything stuck and frozen in place, no motion with respect to anything, then such a Universe has ____no time____.
No Space, means no photons existing there. No Time, means no motion.
Now, are there any observations that lends credence to the above claims of AP???
Just tonight I pulled up this report.
pp
--- quoting CBS report---
X-SciTech
50 years later, mystery of bizarre radio echoes solved
By Jeanna Bryner
May 13, 2016 / 10:48 AM EDT / Livescience.com
Add CBS News on Google
More than 50 years after weird radio echoes were detected coming from Earth's upper atmosphere, two scientists say they've pinpointed the culprit. And it's complicated.
In 1962, after the Jicamarca Radio Observatory was built near Lima, Peru, some unexplainable phenomenon was reflecting the radio waves broadcast by the observatory back to the ground to be picked up by its detectors. The mysterious cause of these echoes was sitting at an altitude of between 80 and 100 miles (130 and 160 kilometers) above sea level.
"As soon as they turned this radar on, they saw this thing," study researcher Meers Oppenheim, of the Center for Space Physics at Boston University, said, referring to the anomalous echo. "They saw all sorts of interesting phenomena that had never been seen before. Almost all of it was explained within a few years." [In Photos: Mysterious Radar Blob Puzzles Meteorologists]
The Jicamarca Radio Observatory, which was built in 1961, studies the equatorial ionosphere.
Jicamarca Radio Observatory (JRO), Public Domain
Peculiar radar echoes
Though the other phenomena detected by the observatory got explanations, these radar echoes continued to baffle scientists.
To see what was happening at that altitude, researchers at the time sent rockets, equipped with antennas and particle detectors, through the region. The instruments, which were designed to detect radar waves, "saw almost nothing," Oppenheim said.
Adding more peculiarity to the puzzle, the phenomenon showed up only during daylight hours, vanishing at night. The echo would appear at dawn every day at about 100 miles (160 km) above the ground, before descending to about 80 miles (130 km) and getting stronger. Then at Noon, the echo would start to rise back again toward its starting point at 100 miles above the ground. When plotted on a graph, the echoes appeared as a necklace shape.
Radar echoes plotted over the course of two days show how the signal emerged at dawn, descended toward the ground, and then rose again over the course of the day.
Jorge Chau
And in 2011, during a partial solar eclipse seen over the National Atmospheric Research Laboratory in India, the echo went silent.
"And then there was a solar flare, and it sort of went a little nuts," Oppenheim said. "There was a solar flare, and the echo got really strong."
The sun takes charge
Now, with a lot of supercomputing effort, Oppenheim and Yakov Dimant, also at the Center for Space Physics, have simulated the bizarre radar echoes to find the culprit -- the sun. [Infographic: Explore Earth's Atmosphere, Top to Bottom]
Ultraviolet radiation from the sun, it seems, slams into the ionosphere (the part of Earth's upper atmosphere located between 50 and 370 miles, or 80 and 600 km, above sea level), where the radio echoes were detected, they said. Then, the radiation, in the form of photons (particles of light), strips molecules in that part of the atmosphere of their electrons, resulting in charged particles called ions -- primarily, positively charged of their electrons, resulting in charged particles called ions, primarily positively charged oxygen -- and a free electron (a negatively charged particle that is not attached to an atom or molecule).
That ultra-energized electron, or photoelectron, zips through the atmosphere, which, at this altitude, is much cooler than the photoelectron, Oppenheim said.
Making waves
Using a computer simulation, the scientists allowed these high-energy electrons to interact with other, less energized particles.
Because these high-energy electrons are racing through a cool, slow environment in the ionosphere, so-called kinetic plasma instabilities (turbulence, in a sense) occur. The result: The electrons start vibrating with different wavelengths.
"One population of very energetic particles moving through a population of much less energetic particles -- it's like running a violin bow across the strings. The cold population will start developing resonant waves," Oppenheim explained.
"The next step is that those electron waves have to cause the ions to start forming waves too, and they do," Oppenheim said.
Though this last step isn't clearly understood, he explained that periodic waves of ions bunch up with no dominant wavelength winning out. "It's a whole set of wavelengths; it's a whole froth of wavelengths," he said.
That "froth" of wavelengths was strong enough to reflect radio waves back to the ground and to form the mysterious radar echoes.
"The reason it wasn't figured out for a long time is that it's a complicated mechanism," Oppenheim said.
As for why the rockets missed the bizarre echoes, Oppenheim pointed to the messy nature of the waves.
"Turns out, it looks like what the rockets saw is what we see with our simulation," he said. "You don't see strong coherent waves. What you see is sort of a froth of low-level waves, above the noise of thermal material," and those waves are sort of like "foam on the top of sea waves," he added.
50 years later, mystery of bizarre radio echoes solved
By Jeanna Bryner
May 13, 2016 / 10:48 AM EDT / Livescience.com
Add CBS News on Google
More than 50 years after weird radio echoes were detected coming from Earth's upper atmosphere, two scientists say they've pinpointed the culprit. And it's complicated.
In 1962, after the Jicamarca Radio Observatory was built near Lima, Peru, some unexplainable phenomenon was reflecting the radio waves broadcast by the observatory back to the ground to be picked up by its detectors. The mysterious cause of these echoes was sitting at an altitude of between 80 and 100 miles (130 and 160 kilometers) above sea level.
"As soon as they turned this radar on, they saw this thing," study researcher Meers Oppenheim, of the Center for Space Physics at Boston University, said, referring to the anomalous echo. "They saw all sorts of interesting phenomena that had never been seen before. Almost all of it was explained within a few years." [In Photos: Mysterious Radar Blob Puzzles Meteorologists]
The Jicamarca Radio Observatory, which was built in 1961, studies the equatorial ionosphere.
Jicamarca Radio Observatory (JRO), Public Domain
Peculiar radar echoes
Though the other phenomena detected by the observatory got explanations, these radar echoes continued to baffle scientists.
To see what was happening at that altitude, researchers at the time sent rockets, equipped with antennas and particle detectors, through the region. The instruments, which were designed to detect radar waves, "saw almost nothing," Oppenheim said.
Adding more peculiarity to the puzzle, the phenomenon showed up only during daylight hours, vanishing at night. The echo would appear at dawn every day at about 100 miles (160 km) above the ground, before descending to about 80 miles (130 km) and getting stronger. Then at Noon, the echo would start to rise back again toward its starting point at 100 miles above the ground. When plotted on a graph, the echoes appeared as a necklace shape.
Radar echoes plotted over the course of two days show how the signal emerged at dawn, descended toward the ground, and then rose again over the course of the day.
Jorge Chau
And in 2011, during a partial solar eclipse seen over the National Atmospheric Research Laboratory in India, the echo went silent.
"And then there was a solar flare, and it sort of went a little nuts," Oppenheim said. "There was a solar flare, and the echo got really strong."
The sun takes charge
Now, with a lot of supercomputing effort, Oppenheim and Yakov Dimant, also at the Center for Space Physics, have simulated the bizarre radar echoes to find the culprit -- the sun. [Infographic: Explore Earth's Atmosphere, Top to Bottom]
Ultraviolet radiation from the sun, it seems, slams into the ionosphere (the part of Earth's upper atmosphere located between 50 and 370 miles, or 80 and 600 km, above sea level), where the radio echoes were detected, they said. Then, the radiation, in the form of photons (particles of light), strips molecules in that part of the atmosphere of their electrons, resulting in charged particles called ions -- primarily, positively charged of their electrons, resulting in charged particles called ions, primarily positively charged oxygen -- and a free electron (a negatively charged particle that is not attached to an atom or molecule).
That ultra-energized electron, or photoelectron, zips through the atmosphere, which, at this altitude, is much cooler than the photoelectron, Oppenheim said.
Making waves
Using a computer simulation, the scientists allowed these high-energy electrons to interact with other, less energized particles.
Because these high-energy electrons are racing through a cool, slow environment in the ionosphere, so-called kinetic plasma instabilities (turbulence, in a sense) occur. The result: The electrons start vibrating with different wavelengths.
"One population of very energetic particles moving through a population of much less energetic particles -- it's like running a violin bow across the strings. The cold population will start developing resonant waves," Oppenheim explained.
"The next step is that those electron waves have to cause the ions to start forming waves too, and they do," Oppenheim said.
Though this last step isn't clearly understood, he explained that periodic waves of ions bunch up with no dominant wavelength winning out. "It's a whole set of wavelengths; it's a whole froth of wavelengths," he said.
That "froth" of wavelengths was strong enough to reflect radio waves back to the ground and to form the mysterious radar echoes.
"The reason it wasn't figured out for a long time is that it's a complicated mechanism," Oppenheim said.
As for why the rockets missed the bizarre echoes, Oppenheim pointed to the messy nature of the waves.
"Turns out, it looks like what the rockets saw is what we see with our simulation," he said. "You don't see strong coherent waves. What you see is sort of a froth of low-level waves, above the noise of thermal material," and those waves are sort of like "foam on the top of sea waves," he added.
--- end quoting CBS report---
ppp
AP writes:: Old Physics has the idea that if you hit photons into matter, some reflect back. Hit photons in a gas, few reflect back, and hit photons into empty space and none reflect back. But in AP theory, Space itself is photons and some reflect back. Photons = Space.
AP
Archimedes Plutonium
Jan 13, 2026, 9:46:30 PM (3 days ago) Jan 13
to Plutonium Atom Universe
So, what I am doing here is with the help of INVERSES, is to match the Ideal Gas Law with New Ohm's Law with the formula of Volume in geometry.
Ideal Gas Law
PV = nR T
New Ohm's Law
Voltage = C * B* E where * signifies a generalized multiplication-- cross product or dot product etc
Geometry volume in 3D
Volume = length * width * depth
So for a decade or more now, I have been trying to get PV = nRT look like V = C*B*E. But the temperature T is stubborn with PV/T or the pressure P is stubborn with nRT/P.
With INVERSES (my #446 book), I can justify making Ideal Gas Law be the same as New Ohm's Law. That then puts me closer to the realization that Space itself is ____not pre-existing___ but is formed by Photons the form Space.
This could explain why the Cosmos of galaxies has what are called Voids.
AP, King of Science
Archimedes Plutonium
Jan 13, 2026, 10:11:31 PM (3 days ago) Jan 13
to Plutonium Atom Universe
p
A map of galaxy voids
---end quoting Wikipedia---
--- quoting Wikipedia on Voids---
pp
Large-scale structure
A map of galaxy voidsThe structure of the Universe can be broken down into components that can help describe the characteristics of individual regions of the cosmos. These are the main structural components of the cosmic web:
- Voids – vast, largely spherical[6] regions with very low cosmic mean densities, up to 100 megaparsecs (Mpc) in diameter.[7]
- Walls – the regions that contain the typical cosmic mean density of matter abundance. Walls can be further broken down into two smaller structural features:
---end quoting Wikipedia---
ppp
AP writes:: Of course Earth is in the Virgo Supercluster, and if we look outwards we are relatively in the middle surrounded by these almost circular Voids.
Archimedes Plutonium
Jan 14, 2026, 9:50:56 PM (2 days ago) Jan 14
to Plutonium Atom Universe
If I am ever going to solve this on what is Space??? I am going to have to unify Volume with that of the factorial Arrangements Possible.
Math Geometry needs a new geometry for that of Factorial and to find where Volume equals factorial.
1! = 1
2! = 2
3! = 6
4! =24
5!=120
6!=720
7!=5,040
8!=40,320
9!=362,880
10!=3,628,800
11!=39,916,800
12!=479,001,600
13!=6,227,020,800
14!=8.718×10¹⁰
15!=1.308×10¹²
16!=2.0923×10¹³
17!=3.557×10¹⁴
18!=6.402×10¹⁵
19!=1.216×10¹⁷
20!=2.433×10¹⁸
21!=5.109×10¹⁹
22!=1.124×10²¹
23!=2.585×10²²
24!=6.204×10²³
25!=1.551×10²⁵
26!=4.0329×10²⁶
The exponential function in base 10.
1 goes to 10^1
2 goes to 10^2
3 goes to 10^3
4 goes to 10^4
.
.
.
24 goes to 10^24 where the factorial is still smaller
25 goes to 10^25 where the factorial surpasses exponential function
So, what I need to do to solve what SPACE truly is, is to make more clear the Geometry of factorial. To tie in factorial with Coulomb Interactions of Photon-Light.
253! = 5.1734609926400789218043308997295e+499
300! = 3.0605751221644063603537046129727e+614
19^(22x22) = 8.2554901045277384397095530071882e+618
22^(22x22) = 5.4022853245302743024619692001681e+649
AP, King of Science
Archimedes Plutonium
Jan 14, 2026, 10:22:27 PM (2 days ago) Jan 14
to Plutonium Atom Universe
In mathematics the infinity borderline is 1*10^604.
The plutonium isotope 231Pu and 244Pu fall short of 10^604.
Somewhere between isotope 253 and 300 lies a element of 1*10^604.
If I successfully solve "what is Space?" then I will have also solved "what is Time?". Because Time is the inverse of Space. But it is far easier to solve what is Space than to solve what is Time.
With Time, we have to consider everything comes to rest, with no motion in atoms or anything else in the Cosmos.
With Space, I need only find the geometry understanding of What is factorial relative to Volume. I need more to the Factorial than the idea--- Total Possible Arrangements.
I reflect back in my education to the Harold Jacobs book Mathematics A Human Endeavor, 1970, page 317 asking the total number of ways of seating 14 people at a table. The answer is a factorial 14 = 87,178,291,200.
So, my burden is to Make A New Geometry for Factorial.
AP
Archimedes Plutonium
Jan 15, 2026, 12:32:52 AM (2 days ago) Jan 15
to Plutonium Atom Universe
Here is an old post of mine about the subject of Minimum Coulomb Interactions, which is one of the biggest mistakes Halliday & Resnick made in their excellent physics textbooks.
Subject: re-examining old post about Coulomb force Re: Minimum Coulomb
Interactions for plutonium?
From: Archimedes Plutonium <plutonium....@gmail.com>
Injection-Date: Wed, 21 Mar 2018 05:48:45 +0000
re-examining old post about Coulomb force Re: Minimum Coulomb Interactions for plutonium?
This is now March 2018 and the below is an old post of mine of May 1994 discussing the number of Coulomb Interactions in an instant of time in order for an atom to exist of its internal subatomic particles. I need to review that idea in light of the fact Real-Electron = muon and the .5MeV particle is Dirac's magnetic monopole and the proton is really 840MeV.
On Tuesday, May 10, 1994 at 7:33:12 PM UTC-5, Ludwig Plutonium wrote:
> Sorry to break me self-imposed limit of no more than 3 posts per 24
> hours. But this is important I feel because it is in Halliday & Resnick
> text which I feel was the best physics text ever made for University
> and College. I think H&R's 1986 was the best but their latest edition
> of PHYSICS, 1992, are going to hell in a handbasket, other than being
> on acid free paper 1992 is of lower quality than their 1986 edition
> because it has speculative physics in it-- it treats the big bang as a
> forgone conclusion and also it talks of neutron stars as if they are
> true science when it will turn out that pulsars are strange quark
> matter stars. I think it is essential that the authors of such widely
> used physics texts throw in cautionary words such as "speculative"
> whenever possible.
> I have shown the below passage of H&R to Dartmouth physics
> professors, math professors, all came back to me with somewhat the same
> reply as what Scott gives.
> I am of the opinion that H&R is so widely used and so heavily picked
> over that H&R are correct in their text. That neon has as a minimum
> number of Coulomb Interactions derived by (2^20x2x2x2), where the
> exponent 20 comes from the 10 protons and 10 electrons of neon.
> Continuing in the same line of reasoning for plutonium. The total
> number of minimum Coulomb interactions of the 94 protons and 94
> electrons of a plutonium atom is (2^188x2x2x2) or about 6.3 x10^57.
> The number (2^188x2x2x2) comes from 4 possible quantum numbers of
> (n,L,mL,ms) and each having at least a minimum of 2 choices with the
> first quantum number having 2^188 minimum possible quantum energy
> states based on the potential energy function substituted into the
> Schroedinger equation, in order for the Schroedinger equation to be
> solved rigorously.
> I strongly believe H&R were correct commonsensewise. If we see the
> Coulomb interaction as the means of holding protons and electrons
> together in an atom. Think of the protons and electrons as balls
> exchanging photons. That to keep 94 protons to 94 electrons would
> require at minimum 6.3 x 10^57 photons exchanged at any one instant. To
> imagine 10 protons and 10 electrons held together by only 210 photons
> shot between them to keep them as an atom strains credulity.
>
> In article <10MAY199...@csa5.lbl.gov>
> sic...@csa5.lbl.gov (SCOTT I CHASE) writes:
>
> > In article <2qmrk9$n...@dartvax.dartmouth.edu>, Ludwig.P...@dartmouth.edu (Ludwig Plutonium) writes...
> > >pages 1190-1191 of PHYSICS Part 2 extended version Halliday & Resnick
> > >1986
> > >
> > > "For atoms with substantially more than one electron the potential
> > >energy function that we must substitute into the Schroedinger equation
> > >involves the Coulomb interaction between many pairs of particles and
> > >can rapidly become hopelessly complicated. In neon, for example, it can
> > >be shown that, including the nucleus and the ten electrons, there are
> > >no fewer than about 2 X 10^7 independent pairs of charges whose Coulomb
> > >interactions must be taken into account if the Schroedinger equation is
> > >to be solved rigorously. At this level of complexity rigorous solutions
> > >are not possible, and we must rely on methods that are both approximate
> > >and numerical."
> > >
> > >What are the minimum Coulomb Interactions for plutonium?
> >
> > I don't know how Halliday and/or Resnick arrived at this number, but I
> > believe it to be wrong. Neon has a total of 20 charges, 60 if you foolishly
> > treat it at the quark level. The number of distinct pairs of objects which
> > you can form from a set of 20 is 20*21/2 = 210. Believe me, that's more
> > than enough to make your Schroedinger equation unsolvable.
Well, back then, in May 1994, my name was still Ludwig Plutonium, not yet changed legally to Archimedes Plutonium.
And what was disturbing for me was the Coulomb Interactions for the EM force. Of course we all know it to be inverse square. But, we like a number for it to keep all the subatomic particles to stay and reside inside an atom.
The Coulomb force is often viewed metaphorically, or by analogy to tennis players. They hit a tennis ball (photon) back and forth-- so to speak-- keeping them together, like a proton shots a photon to the muon and the muon shots it back to the proton-- binding the two together in an atom.
I like that analogy, that picture, and it provides a number value to the Coulomb Force. As to how many interactions occur in an instant of time.
So yes of course, I would be askance if I thought what keeps 10 protons to 10 muons in a neon atom together is a mere 190, or 210, or even 2x10^7.
So, back in 1994-- my best guess of the number of interactions per instant of time was (2^20x2x2x2) where the exponent 20 comes from 10 protons in neon and 10 muons (back then I did not know real electron = muon).
AP writes in 2026:: what struck me as horribly mistaken was to think that Halliday & Resnick and the entire rest of the physics community believed that the Coulomb Interactions going on inside Neon were a paltry meager few 2*10^7 Coulomb Interactions. When, for me, it was more on the lines of 20! =2.433×10¹⁸ Coulomb Interactions due to the 10 protons and 10 muons inside of Neon.
Interactions for plutonium?
From: Archimedes Plutonium <plutonium....@gmail.com>
Injection-Date: Wed, 21 Mar 2018 05:48:45 +0000
re-examining old post about Coulomb force Re: Minimum Coulomb Interactions for plutonium?
This is now March 2018 and the below is an old post of mine of May 1994 discussing the number of Coulomb Interactions in an instant of time in order for an atom to exist of its internal subatomic particles. I need to review that idea in light of the fact Real-Electron = muon and the .5MeV particle is Dirac's magnetic monopole and the proton is really 840MeV.
On Tuesday, May 10, 1994 at 7:33:12 PM UTC-5, Ludwig Plutonium wrote:
> Sorry to break me self-imposed limit of no more than 3 posts per 24
> hours. But this is important I feel because it is in Halliday & Resnick
> text which I feel was the best physics text ever made for University
> and College. I think H&R's 1986 was the best but their latest edition
> of PHYSICS, 1992, are going to hell in a handbasket, other than being
> on acid free paper 1992 is of lower quality than their 1986 edition
> because it has speculative physics in it-- it treats the big bang as a
> forgone conclusion and also it talks of neutron stars as if they are
> true science when it will turn out that pulsars are strange quark
> matter stars. I think it is essential that the authors of such widely
> used physics texts throw in cautionary words such as "speculative"
> whenever possible.
> I have shown the below passage of H&R to Dartmouth physics
> professors, math professors, all came back to me with somewhat the same
> reply as what Scott gives.
> I am of the opinion that H&R is so widely used and so heavily picked
> over that H&R are correct in their text. That neon has as a minimum
> number of Coulomb Interactions derived by (2^20x2x2x2), where the
> exponent 20 comes from the 10 protons and 10 electrons of neon.
> Continuing in the same line of reasoning for plutonium. The total
> number of minimum Coulomb interactions of the 94 protons and 94
> electrons of a plutonium atom is (2^188x2x2x2) or about 6.3 x10^57.
> The number (2^188x2x2x2) comes from 4 possible quantum numbers of
> (n,L,mL,ms) and each having at least a minimum of 2 choices with the
> first quantum number having 2^188 minimum possible quantum energy
> states based on the potential energy function substituted into the
> Schroedinger equation, in order for the Schroedinger equation to be
> solved rigorously.
> I strongly believe H&R were correct commonsensewise. If we see the
> Coulomb interaction as the means of holding protons and electrons
> together in an atom. Think of the protons and electrons as balls
> exchanging photons. That to keep 94 protons to 94 electrons would
> require at minimum 6.3 x 10^57 photons exchanged at any one instant. To
> imagine 10 protons and 10 electrons held together by only 210 photons
> shot between them to keep them as an atom strains credulity.
>
> In article <10MAY199...@csa5.lbl.gov>
> sic...@csa5.lbl.gov (SCOTT I CHASE) writes:
>
> > In article <2qmrk9$n...@dartvax.dartmouth.edu>, Ludwig.P...@dartmouth.edu (Ludwig Plutonium) writes...
> > >pages 1190-1191 of PHYSICS Part 2 extended version Halliday & Resnick
> > >1986
> > >
> > > "For atoms with substantially more than one electron the potential
> > >energy function that we must substitute into the Schroedinger equation
> > >involves the Coulomb interaction between many pairs of particles and
> > >can rapidly become hopelessly complicated. In neon, for example, it can
> > >be shown that, including the nucleus and the ten electrons, there are
> > >no fewer than about 2 X 10^7 independent pairs of charges whose Coulomb
> > >interactions must be taken into account if the Schroedinger equation is
> > >to be solved rigorously. At this level of complexity rigorous solutions
> > >are not possible, and we must rely on methods that are both approximate
> > >and numerical."
> > >
> > >What are the minimum Coulomb Interactions for plutonium?
> >
> > I don't know how Halliday and/or Resnick arrived at this number, but I
> > believe it to be wrong. Neon has a total of 20 charges, 60 if you foolishly
> > treat it at the quark level. The number of distinct pairs of objects which
> > you can form from a set of 20 is 20*21/2 = 210. Believe me, that's more
> > than enough to make your Schroedinger equation unsolvable.
Well, back then, in May 1994, my name was still Ludwig Plutonium, not yet changed legally to Archimedes Plutonium.
And what was disturbing for me was the Coulomb Interactions for the EM force. Of course we all know it to be inverse square. But, we like a number for it to keep all the subatomic particles to stay and reside inside an atom.
The Coulomb force is often viewed metaphorically, or by analogy to tennis players. They hit a tennis ball (photon) back and forth-- so to speak-- keeping them together, like a proton shots a photon to the muon and the muon shots it back to the proton-- binding the two together in an atom.
I like that analogy, that picture, and it provides a number value to the Coulomb Force. As to how many interactions occur in an instant of time.
So yes of course, I would be askance if I thought what keeps 10 protons to 10 muons in a neon atom together is a mere 190, or 210, or even 2x10^7.
So, back in 1994-- my best guess of the number of interactions per instant of time was (2^20x2x2x2) where the exponent 20 comes from 10 protons in neon and 10 muons (back then I did not know real electron = muon).
AP writes in 2026:: what struck me as horribly mistaken was to think that Halliday & Resnick and the entire rest of the physics community believed that the Coulomb Interactions going on inside Neon were a paltry meager few 2*10^7 Coulomb Interactions. When, for me, it was more on the lines of 20! =2.433×10¹⁸ Coulomb Interactions due to the 10 protons and 10 muons inside of Neon.
Archimedes Plutonium
Jan 15, 2026, 12:59:53 AM (2 days ago) Jan 15
to Plutonium Atom Universe
So I am looking for a New Geometry Interpretation of Factorial. Going far beyond the idea of "Total Possible Arrangement".
8!=40,320
9!=362,880
10!=3,628,800
11!=39,916,800
12!=479,001,600
13!=6,227,020,800
14!=8.718×10¹⁰
15!=1.308×10¹²
16!=2.0923×10¹³
17!=3.557×10¹⁴
18!=6.402×10¹⁵
19!=1.216×10¹⁷
20!=2.433×10¹⁸
21!=5.109×10¹⁹
22!=1.124×10²¹
23!=2.585×10²²
24!=6.204×10²³
Naturally, since the inverse square law is prevalent throughout Electromagnetism, I may as well try the inverse square law to make Factorial equal to Volume.
Math Geometry needs a new geometry for that of Factorial and to find where Volume equals factorial.
1! = 1 versus 10
2! = 2 versus 100
3! = 6 versus 1000
4! =24 versus 10,000
5!=120 versus 100,000
6!=720 versus 1,000,000
7!=5,040 versus 10,000,000
2! = 2 versus 100
3! = 6 versus 1000
4! =24 versus 10,000
5!=120 versus 100,000
6!=720 versus 1,000,000
7!=5,040 versus 10,000,000
8!=40,320
9!=362,880
10!=3,628,800
11!=39,916,800
12!=479,001,600
13!=6,227,020,800
14!=8.718×10¹⁰
15!=1.308×10¹²
16!=2.0923×10¹³
17!=3.557×10¹⁴
18!=6.402×10¹⁵
19!=1.216×10¹⁷
20!=2.433×10¹⁸
21!=5.109×10¹⁹
22!=1.124×10²¹
23!=2.585×10²²
24!=6.204×10²³
25!=1.551×10²⁵ versus 10^25
26!=4.0329×10²⁶ versus 10^26
26!=4.0329×10²⁶ versus 10^26
Geometry Volume is Length x Width x Depth.
Coulomb Interactions are seen as pencil ellipse closed loop connections from one particle to another. I imagine it as lines filling up the space of a given volume.
Let me try first on 5! =120 as volume of 5x4x3 =60 trying to get 120 rather than 60. Looking at 6! and where 6! =720. Here I have 6x5x4=120. Just what I wanted.
See if that works on 6!, where 6!=720 and find a volume that matches 720. Looking at 7!=5,040 and now using 7x6x5=210. No go.
Let me try Inverse square law on the factorial to bring it down.
For 5!=120 I use the 4, the nearest perfect square.
120/ sqrt4 =60
For 6!=720, the nearest perfect square is still 4, 720/2=360 and a No Go.
Let me experiment some more to find how to Equilibrate Volume to factorial.
AP, King of Science
Message has been deleted
Archimedes Plutonium
Jan 15, 2026, 3:11:43 AM (2 days ago) Jan 15
to Plutonium Atom Universe
So if you joined me late in this discussion, here is what I am up to. The Factorial Function is one of the steepest rising functions in all of Mathematics. The factorial function though has __no real geometry value__. It does have value as the Total Possible Arrangements given n particles about a geometry figure, like that of seating 14 guests at a table.
Volume in geometry does have huge geometry value. It also is steeply rising function.
So, what I am doing here, is making Factorial be another Volume. And the way I am going about it is using the Inverse Square law that so often frequents Electromagnetism laws of physics.
1! = 1 versus 10
2! = 2 versus 100
3! = 6 versus 1000
4! =24 versus 10,000
5!=120 versus 100,000
6!=720 versus 1,000,000
7!=5,040 versus 10,000,000
Volume in geometry does have huge geometry value. It also is steeply rising function.
So, what I am doing here, is making Factorial be another Volume. And the way I am going about it is using the Inverse Square law that so often frequents Electromagnetism laws of physics.
The question arises as to whether the Inverse square law of physics comes directly out of pure math Factorial function. That would be a beautiful and surprising result. For come to think about it, inverse square laws in pure math are absent, as far as I know, but abundant in physics.
I am thinking that the inverse square law applied to Factorial will tame the function enough so that it becomes another volume function. For volume I am going to use the pure cube.
I am thinking that the inverse square law applied to Factorial will tame the function enough so that it becomes another volume function. For volume I am going to use the pure cube.
1! = 1 versus 10
2! = 2 versus 100
3! = 6 versus 1000
4! =24 versus 10,000
5!=120 versus 100,000
6!=720 versus 1,000,000
7!=5,040 versus 10,000,000
Starting with 5! and the volume of 5x5x5 =125. That is close enough for me.
6! =720 and compare to 6x6x6= 216. What do I have to do to 720 to come close to 216 using a inverse square? Well 720/2^2 = 180. I am using only integers.
7!=5,040 and compare 7x7x7=343 then 5040/4^2= 315
8!=40,320 and compare to 8x8x8= 512 then 40320/ 9^2=497.
9!=362,880 and compare to 9x9x9= 729 then 362880/ 22^2 =749
Is there a pattern starting to emerge????
AP
6! =720 and compare to 6x6x6= 216. What do I have to do to 720 to come close to 216 using a inverse square? Well 720/2^2 = 180. I am using only integers.
7!=5,040 and compare 7x7x7=343 then 5040/4^2= 315
8!=40,320 and compare to 8x8x8= 512 then 40320/ 9^2=497.
9!=362,880 and compare to 9x9x9= 729 then 362880/ 22^2 =749
Is there a pattern starting to emerge????
AP
Archimedes Plutonium
Jan 15, 2026, 4:40:24 AM (2 days ago) Jan 15
to Plutonium Atom Universe
Rather than a cube, let me see if a rectangular box volume gives me more accurate results as inverse square of factorial.
1! = 1 versus 10
2! = 2 versus 100
3! = 6 versus 1000
4! =24 versus 10,000
5!=120 versus 100,000
6!=720 versus 1,000,000
7!=5,040 versus 10,000,000
2! = 2 versus 100
3! = 6 versus 1000
4! =24 versus 10,000
5!=120 versus 100,000
6!=720 versus 1,000,000
7!=5,040 versus 10,000,000
Starting with 5! and the volume of 3x4x5 =60. But 5! is 120. The square root of 2 in inverse square would give me exactly 60, but can I use square root of 2???? However, I notice this 4x5x6=120 exactly. So maybe a box with one parameter larger.
6! =720 and compare to 4x5x6= 120, while 5x6x7=210 . What do I have to do to 720 to come close to 210 using a inverse square? Well 720/2^2 = 180. I am using only integers.
7!=5,040 and compare 6x7x8=336 then 5040/4^2= 315
8!=40,320 and compare to 7x8x9= 504 then 40320/ 9^2=497.
9!=362,880 and compare to 8x9x10= 720 then 362880/ 22^2 =749
6! =720 and compare to 4x5x6= 120, while 5x6x7=210 . What do I have to do to 720 to come close to 210 using a inverse square? Well 720/2^2 = 180. I am using only integers.
7!=5,040 and compare 6x7x8=336 then 5040/4^2= 315
8!=40,320 and compare to 7x8x9= 504 then 40320/ 9^2=497.
9!=362,880 and compare to 8x9x10= 720 then 362880/ 22^2 =749
Archimedes Plutonium
Jan 15, 2026, 6:27:19 PM (2 days ago) Jan 15
to Plutonium Atom Universe
Alright, I was holding back on bringing in the Stirling approximation formula of Factorial. I did do some research on it decades back. I am not getting any closer to a Geometry Interpretation of Factorial so instead, bring in the Stirling formula. It is very close and so, if I can reinterpret the Stirling formula into a pure geometry interpretation, then I will be highly satisfied.
I was using cubes and rectangular boxes, while Stirling apparently is using spheres, perhaps circles because he has pi, but also "e".
n! approximately equal to Sqrt[2pi*n] (n/e)^n
Example check for 5! done roughly where pi = 3.1, e= 2.7
sqrt[2*3.1*5](5/2.7)^5 approx= 5.5*(1.8^5) approx= 5.5*18.8 approx = 103.4
Example check for 6! roughly done
sqrt[2*3.1*6](6/2.7)^6 approx= 6.1*(2.2^6) approx= 6.1*113.2 approx= 691
These results were far better than I was getting.
So all I need do now is interpret the Stirling approximation to be some form of geometry volume or area or a combination of the two.
AP, King of Science
Archimedes Plutonium
Jan 15, 2026, 6:44:32 PM (2 days ago) Jan 15
to Plutonium Atom Universe
I wrote this about the Stirling approximation formula of Factorial in 2018 to sci.math.
Archimedes Plutonium
Mar 7, 2023, 3:02:06 PM
to sci.math
On Tuesday, February 21, 2017 at 7:41:35 AM UTC-6, Peter Percival wrote:
> Archimedes Plutonium wrote:
> > Alright, using the Tool::
> >
> > The Polynomial Generator is this tool::
> >
> >
> > For 2 coordinate points, (x0, y0) (x1, y1), we produce the 1st degree polynomial, a straightline or line segment
> >
> > P(x) = y0(x-x1) / (x0-x1)
> > + y1(x-x0) / (x1-x0)
> >
> > For 3 coordinate points, (x0, y0) (x1, y1) (x2, y2), we produce the 2nd degree polynomial, a compilation-curve
> >
> > P(x) = y0(x-x1)(x-x2) / (x0-x1)(x0-x2)
> > +y1(x-x0)(x-x2) / (x1-x0)(x1-x2)
> > +y2(x-x0)(x-x1) / (x2-x0)(x2-x1)
> >
> > For 4 coordinate points, (x0, y0) (x1, y1) (x2, y2) (x3, y3), we produce the 3rd degree polynomial, a compilation curve
> >
> > P(x) = y0(x-x1)(x-x2)(x-x3) / (x0-x1)(x0-x2)(x0-x3)
> > +y1(x-x0)(x-x2)(x-x3) / (x1-x0)(x1-x2)(x1-x3)
> > +y2(x-x0)(x-x1)(x-x3) / (x2-x0)(x2-x1)(x2-x3)
> > +y3(x-x0)(x-x1)(x-x2) / (x3-x0)(x3-x1)(x3-x2)
> >
> > Factorial function:
> > x x!
> > 0 0
> I think 0! = 1.
> > 1 1
> > 2 2
> > 3 6
> > 4 24
> > 5 120
> > 6 720
> >
> > Now using the tool I get Y = 252x^2 - 2172x + 4680 from 4 to 6.
> >
> > Now, what I want to do with that is bound the factorial by a far easier function, one that is far easier to use such as a linear function. The easiest at the moment is the linear function for (0,0) (6,720) and using the tool for 2 points I have:
> >
> > P(x) = y0(x-x1) / (x0-x1)
> > + y1(x-x0) / (x1-x0)
> >
> > 720(x)/6
> >
> > 120x
> >
> > So, we have our first approximation of factorial function as Y = 120x
> >
> > Let us test it out
> >
> > x y
> > 0 0
> > 1 120
> > 2 240
> > 3 360
> > 4 480
> > 5 600
> > 6 720
> >
> > Not looking good at all
> >
> > So would an exponent do better?
> Stirling's approximation is sqrt(2 pi x)*(x/e)^x, so any polynomial will
> only work well for a few values of x. x! will soon overtake any poly in
> x because of the exponential nature of the function (the "^x" bit).
>
>
>
> --
> Do, as a concession to my poor wits, Lord Darlington, just explain
> to me what you really mean.
> I think I had better not, Duchess. Nowadays to be intelligible is
> to be found out. -- Oscar Wilde, Lady Windermere's Fan
Peter, I tried Stirling's and horribly off of 24, 120, 720. Besides, the Polynomials give fast and easy derivatives and integrals. While Stirling's formula is a nightmare to differentiate and integrate.
Y = 252x^2 -2172x + 4680 for x in interval of 4,5,6 yields exact numbers as polynomial for Factorial.
For 6, I have 9072 -13032 + 4680 = 720
For 5, I have 6300 -10860 +4680 = 120
For 4, I have 4032 -8688 +4680 = 24
Now in Old Math, their calculus, Peter Percival, they had for their integrals, their tables on integrals would have a constant C along with the answer. I am wondering what the justification Old Math had for their constants. Such as for example Integral e^u du = e^u + C. Another example Integral sin (u) du = -cos(u) + C.
So, Peter, what I am thinking here is that Old Math never had a justification, for this C constant. But then, if all functions of mathematics were actually and truly polynomials. Then the justification, a __valid justification__ for having a Constant is because the only valid functions in mathematics are polynomials and the bard just never bothered to convert sine or e^x to a polynomial. Never converted factorial to a polynomial over an interval.
For now, as I integrate the Factorial of 4 to 6 polynomial Y = 252x^2 -2172x + 4680, I end up by the power rule of converting 4680 to be 4680x.
When all of mathematics recognizes the only valid functions of mathematics are Polynomials, then the C constant in integration makes perfect sense for it captures that 4680. But Old Math has no explanation of the C constant.
And for derivative, we need not the C constant, but rather it throws out the 4680.
Derivative of Y = 252x^2 -2172x + 4680 is Y' = 504x -2172
Integral of Y = 252x^2 -2172x + 4680 is Integral-Y = (252/3)x^3 -(2172/2)x^2 + 4680x
Peter, I dare say, Stirling's formula is inaccurate and a nightmare to differentiate or integrate.
My point is-- Old Math Calculus is an abomination of science, a torture chamber for students. When all of Calculus is just polynomial functions governed by the Power Rules of derivative and integral.
Everyday that we have classes in calculus of Old Math is a torture chamber of propaganda, not of doing math, but of anti-math.
AP
Archimedes Plutonium's profile photo
Archimedes Plutonium
Mar 7, 2023, 4:16:41 PM
to
Now one of the greatest beauties of all functions of mathematics be polynomial functions and only polynomial functions is the beauty that the mind of a person can always relate one polynomial with a different polynomial. In Old Math that cesspool of thought, no-one can relate a sine to a exponential to a hyperbolic to a logarithmic to a trigonometric and thousands and thousands of bs functions.
When math has one and only one type of function, the mind of a individual person can relate a function with the next one.
And of course, the polynomial function that everyone knows so well is Y = x with its derivative slope is 1. So how does the Factorial function as polynomial in interval 4 to 6 compare? Y = 252x^2 - 2172x + 4680 and its derivative is 504x - 2172 and we take the point x=5 for a derivative slope is 504*5 - 2172 is equal to 348. That is a huge slope compared to say Y= x with its slope of 1.
You see, when mathematics turns its existing cesspool of Old Math into proper true math, a High School student can do calculus. Can take the derivative of the Factorial Function for the power-rules are simple and easy. A High School student can take the derivative of Y = 252x^2 - 2172x + 4680, while, no High School student can take the derivative and integral of Sterling's formula for Factorial, much less understand it.
And this is the whole entire problem of modern day mathematics education. We have professors in colleges paid more for their outside research in "publish or perish" and not a thought in making the classroom a environment of teaching true math, easy so easy that High School kids can do calculus. No, we have professors spending more time on publishing some mindless math and their classrooms torture chambers for students.
I bet there is not a single calculus classroom in the entire globe of Earth where students sit and learn without taking notes. For when you have a math class of students participating and not a "notetaking factory" you actually have education going on in that classroom.
If I were a calculus teacher, one day I would go into class and split up the room into groups of students, and have them convert 4factorial, 5factorial, 6factorial into a Polynomial function, then before the bell rings take the derivative and integral of their polynomial function.
Now, that is might fine classroom math teaching. And not a silly stupid notetaking mill, where the math professor is more eager to get back to his/her publishing of a paper of fake math.
AP
Mar 7, 2023, 3:02:06 PM
to sci.math
On Tuesday, February 21, 2017 at 7:41:35 AM UTC-6, Peter Percival wrote:
> Archimedes Plutonium wrote:
> > Alright, using the Tool::
> >
> > The Polynomial Generator is this tool::
> >
> >
> > For 2 coordinate points, (x0, y0) (x1, y1), we produce the 1st degree polynomial, a straightline or line segment
> >
> > P(x) = y0(x-x1) / (x0-x1)
> > + y1(x-x0) / (x1-x0)
> >
> > For 3 coordinate points, (x0, y0) (x1, y1) (x2, y2), we produce the 2nd degree polynomial, a compilation-curve
> >
> > P(x) = y0(x-x1)(x-x2) / (x0-x1)(x0-x2)
> > +y1(x-x0)(x-x2) / (x1-x0)(x1-x2)
> > +y2(x-x0)(x-x1) / (x2-x0)(x2-x1)
> >
> > For 4 coordinate points, (x0, y0) (x1, y1) (x2, y2) (x3, y3), we produce the 3rd degree polynomial, a compilation curve
> >
> > P(x) = y0(x-x1)(x-x2)(x-x3) / (x0-x1)(x0-x2)(x0-x3)
> > +y1(x-x0)(x-x2)(x-x3) / (x1-x0)(x1-x2)(x1-x3)
> > +y2(x-x0)(x-x1)(x-x3) / (x2-x0)(x2-x1)(x2-x3)
> > +y3(x-x0)(x-x1)(x-x2) / (x3-x0)(x3-x1)(x3-x2)
> >
> > Factorial function:
> > x x!
> > 0 0
> I think 0! = 1.
> > 1 1
> > 2 2
> > 3 6
> > 4 24
> > 5 120
> > 6 720
> >
> > Now using the tool I get Y = 252x^2 - 2172x + 4680 from 4 to 6.
> >
> > Now, what I want to do with that is bound the factorial by a far easier function, one that is far easier to use such as a linear function. The easiest at the moment is the linear function for (0,0) (6,720) and using the tool for 2 points I have:
> >
> > P(x) = y0(x-x1) / (x0-x1)
> > + y1(x-x0) / (x1-x0)
> >
> > 720(x)/6
> >
> > 120x
> >
> > So, we have our first approximation of factorial function as Y = 120x
> >
> > Let us test it out
> >
> > x y
> > 0 0
> > 1 120
> > 2 240
> > 3 360
> > 4 480
> > 5 600
> > 6 720
> >
> > Not looking good at all
> >
> > So would an exponent do better?
> Stirling's approximation is sqrt(2 pi x)*(x/e)^x, so any polynomial will
> only work well for a few values of x. x! will soon overtake any poly in
> x because of the exponential nature of the function (the "^x" bit).
>
>
>
> --
> Do, as a concession to my poor wits, Lord Darlington, just explain
> to me what you really mean.
> I think I had better not, Duchess. Nowadays to be intelligible is
> to be found out. -- Oscar Wilde, Lady Windermere's Fan
Peter, I tried Stirling's and horribly off of 24, 120, 720. Besides, the Polynomials give fast and easy derivatives and integrals. While Stirling's formula is a nightmare to differentiate and integrate.
Y = 252x^2 -2172x + 4680 for x in interval of 4,5,6 yields exact numbers as polynomial for Factorial.
For 6, I have 9072 -13032 + 4680 = 720
For 5, I have 6300 -10860 +4680 = 120
For 4, I have 4032 -8688 +4680 = 24
Now in Old Math, their calculus, Peter Percival, they had for their integrals, their tables on integrals would have a constant C along with the answer. I am wondering what the justification Old Math had for their constants. Such as for example Integral e^u du = e^u + C. Another example Integral sin (u) du = -cos(u) + C.
So, Peter, what I am thinking here is that Old Math never had a justification, for this C constant. But then, if all functions of mathematics were actually and truly polynomials. Then the justification, a __valid justification__ for having a Constant is because the only valid functions in mathematics are polynomials and the bard just never bothered to convert sine or e^x to a polynomial. Never converted factorial to a polynomial over an interval.
For now, as I integrate the Factorial of 4 to 6 polynomial Y = 252x^2 -2172x + 4680, I end up by the power rule of converting 4680 to be 4680x.
When all of mathematics recognizes the only valid functions of mathematics are Polynomials, then the C constant in integration makes perfect sense for it captures that 4680. But Old Math has no explanation of the C constant.
And for derivative, we need not the C constant, but rather it throws out the 4680.
Derivative of Y = 252x^2 -2172x + 4680 is Y' = 504x -2172
Integral of Y = 252x^2 -2172x + 4680 is Integral-Y = (252/3)x^3 -(2172/2)x^2 + 4680x
Peter, I dare say, Stirling's formula is inaccurate and a nightmare to differentiate or integrate.
My point is-- Old Math Calculus is an abomination of science, a torture chamber for students. When all of Calculus is just polynomial functions governed by the Power Rules of derivative and integral.
Everyday that we have classes in calculus of Old Math is a torture chamber of propaganda, not of doing math, but of anti-math.
AP
Archimedes Plutonium's profile photo
Archimedes Plutonium
Mar 7, 2023, 4:16:41 PM
to
Now one of the greatest beauties of all functions of mathematics be polynomial functions and only polynomial functions is the beauty that the mind of a person can always relate one polynomial with a different polynomial. In Old Math that cesspool of thought, no-one can relate a sine to a exponential to a hyperbolic to a logarithmic to a trigonometric and thousands and thousands of bs functions.
When math has one and only one type of function, the mind of a individual person can relate a function with the next one.
And of course, the polynomial function that everyone knows so well is Y = x with its derivative slope is 1. So how does the Factorial function as polynomial in interval 4 to 6 compare? Y = 252x^2 - 2172x + 4680 and its derivative is 504x - 2172 and we take the point x=5 for a derivative slope is 504*5 - 2172 is equal to 348. That is a huge slope compared to say Y= x with its slope of 1.
You see, when mathematics turns its existing cesspool of Old Math into proper true math, a High School student can do calculus. Can take the derivative of the Factorial Function for the power-rules are simple and easy. A High School student can take the derivative of Y = 252x^2 - 2172x + 4680, while, no High School student can take the derivative and integral of Sterling's formula for Factorial, much less understand it.
And this is the whole entire problem of modern day mathematics education. We have professors in colleges paid more for their outside research in "publish or perish" and not a thought in making the classroom a environment of teaching true math, easy so easy that High School kids can do calculus. No, we have professors spending more time on publishing some mindless math and their classrooms torture chambers for students.
I bet there is not a single calculus classroom in the entire globe of Earth where students sit and learn without taking notes. For when you have a math class of students participating and not a "notetaking factory" you actually have education going on in that classroom.
If I were a calculus teacher, one day I would go into class and split up the room into groups of students, and have them convert 4factorial, 5factorial, 6factorial into a Polynomial function, then before the bell rings take the derivative and integral of their polynomial function.
Now, that is might fine classroom math teaching. And not a silly stupid notetaking mill, where the math professor is more eager to get back to his/her publishing of a paper of fake math.
AP
Archimedes Plutonium
Jan 15, 2026, 6:55:21 PM (2 days ago) Jan 15
to Plutonium Atom Universe
So, well, I am here to figure-out and find a GEOMETRIC INTERPRETATION of the Factorial function.
I strongly believe it is a Inverse Square Law such as the Laws of Electromagnetism.
The Stirling formula is a exceptionally close approximation.
So, now the question is, is the Stirling formula a Inverse square Law such as Coulomb law, such as gravity law??
Factorial n! approx equal Sqrt[2pi*n] (n/e)^n
AP
Archimedes Plutonium
Jan 15, 2026, 9:00:27 PM (2 days ago) Jan 15
to Plutonium Atom Universe
Alright, my hypothesis is showing itself to be true. For if I divide both sides of Stirling formula by Sqrt[2pi*n] gives us the Inverse Square laws found throughout Electromagnetism physics
Factorial n! approx equal Sqrt[2pi*n] (n/e)^n
n! / Sqrt[2pi*n] = (n/e)^n
All of us, I included have our education of geometry with a misconception. We believe Volume is the utmost end of Geometry measure. Nothing higher than Volume. And in Straightline geometry volume is distance cubed or is a rectangular box volume.
But the laws of electromagnetism are all formed with inverse-square laws which is a sphere. This is not volume of a sphere but something about arrangements of particles Photon-Light as a geometry measure. Not about volume of sphere but the arrangement of Photons from a center forming Coulomb Interactions with other Photons a distance from the center.
AP
Archimedes Plutonium
Jan 15, 2026, 9:21:41 PM (2 days ago) Jan 15
to Plutonium Atom Universe
I must include this in my other book --- INVERSES.
| *
| *
| *
So I made a square cutout of a used envelope to draw on. Pretending it is the 1000 Grid to graph the factorial function.
It crudely looks like this.
| *
| *
|* *_______
The factorial function sort of looks like the letter J, only not perpendicular.
Now, I rotate by 90 degrees my square cutout of a used envelope, from left to right.
And now my x-axis is the y-axis and my y-axis is now my x-axis looking like this.
| *
| *
|_____*__
Sorry, there are no letters in the alphabet that comes close to looking like that arc.
If we combine the two functions, one an inverse of the other in a form of addition such as Y_1 + Y_2
We end up with a function that is a straightline that looks like this.
______>
|
|
|
|_________
The identity function of math is this.
| *
| *
| * _______
If we draw that on a used envelope square cutout and rotate from left to right by a 90 degree rotation we end up with this.
| *
| *
| ______*
If we combined these two inverse functions by addition into being one function Y_1 + Y_2 we end up with this.
_______>
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|
| _______
So, what does this tell us about Inverse functions???
They are __not equal__. But they are duals in the fact that their addition becomes a function that is the maximum straightline height of the grid they are graphed in. So if I graphed the Factorial function in 1000 Grid with 1 to 6 where 6 goes to 720. Then the inverse added to factorial would be a straight line across the top of the grid as that of Y--> 1000.
Inverses functions are not equals to the original function.
AP, King of Science
Archimedes Plutonium
Jan 16, 2026, 2:51:29 AM (24 hours ago) Jan 16
to Plutonium Atom Universe
I use Harold Jacobs textbooks a-lot for reference because of the many pictures they have. I am limited of making pictures, even simply diagrams.
94! = 1.087366E +146
100! = 9.33262E +157
105! = 1.081396E +168
135! = 2.69047E +230
137! = 5.012888E +234
250! = 3.23285E +492
253! = 5.17346E+499
260! = 3.83019E+516
270! = 6.66211E +540
280! = 1.67722E + 565
290! = 6.03161E + 589
294! = 4.414933E +599
295! = 1.302405E + 602
296! = 3.855119E + 604
300! = 3.060575E +614
527! = 1.910144E +1207
528! = 1.008556E +1210
840! = 2.808718E + 2093
945! = 1.82649E +2403
19^(22x22) = 8.2554901E+618 22^(22x22) = 5.402285324E+649
22^450 = 1.23085E + 604
19^470 = 1.03321E +601
(Thanks, source CalculatorSoup; Edward Furey, Large exponents and factorials)
So, well, I have conquered this Hypothesis that Space is equal to Magnetic Field + Electric Field by showing there is a Geometry above and beyond Volume as we know it in Euclidean straightline geometry. Our notion of Volume ends with rectangular boxes and cubes where we have Volume = lengthx width x height. But, there is a far larger parameter in Geometry that goes beyond volume. Hard as that may appear. It is not the dumb foolish 4th dimension, no, it is still in 3rd dimension, the last and final dimension.
So if you look on page 566 and 567 of Jacobs GEOMETRY, 1987, second edition, you will see pictures of how he derives the sphere volume then the sphere surface area.
Look at that picture of small pyramids whose base forms polygons and the vertex of pyramid is the center of the sphere.
Replace pyramids with a pencil ellipse a closed circuit of Photon-Light. And the idea here is that a center of a sphere is a single atom, say this atom is gold, as it emits Electromagnetic Radiation in Light Photons. As these Photons hit other atoms outside the gold atom they form another concentric sphere. Spheres inside of more spheres.
This conception of Space is far more complex and complicated than our old notion of Space as boxes and cubes of volume.
Volume is exponent of 3. While Factorial goes far beyond exponents.
Why the simple number of 296 in the factorial goes all the way up to the exponent number 10^604. And we look to chemistry of what element has 296 neutrons+protons and it is the last nucleosynthesized element 118 in the inert gas column of the periodic table.
94! = 1.087366E +146
100! = 9.33262E +157
105! = 1.081396E +168
135! = 2.69047E +230
137! = 5.012888E +234
250! = 3.23285E +492
253! = 5.17346E+499
260! = 3.83019E+516
270! = 6.66211E +540
280! = 1.67722E + 565
290! = 6.03161E + 589
294! = 4.414933E +599
295! = 1.302405E + 602
296! = 3.855119E + 604
300! = 3.060575E +614
527! = 1.910144E +1207
528! = 1.008556E +1210
840! = 2.808718E + 2093
945! = 1.82649E +2403
19^(22x22) = 8.2554901E+618 22^(22x22) = 5.402285324E+649
22^450 = 1.23085E + 604
19^470 = 1.03321E +601
(Thanks, source CalculatorSoup; Edward Furey, Large exponents and factorials)
What I am putting together here is a Geometry Idea that goes far beyond Volume. The idea of concentric spheres going outward from a center.
AP, King of Science
Archimedes Plutonium
Jan 16, 2026, 9:12:25 PM (6 hours ago) Jan 16
to Plutonium Atom Universe
So, when I went to University 1968-1972 to study science, I took chemistry and the textbook at that time was Chemistry: A Conceptual Approach by Mortimer 1967 and on page 38 shows the 2p orbitals. What I would call elongated spheres or "lobes".
Now I look in Chemistry: The Central Science, 5th edition Brown, LeMay, Bursten, 1991 pages 188-189. Showing the 2p orbital not as lobes but rather as adjacent spheres. Seems like the "lobe picture" had disappeared, somewhat from 1967 to 1991. And on the prior page 188 the 1s is a sphere, the 2s is concentric spheres with nodes in between and 3s with 2 nodes in between.
So, this is where I am taking Geometry of the Factorial.
In Plane Euclidean geometry of straightlines and volume being a cube or box of straightlines covered by the mathematics of V= lengthx width x height. Where exponents side^2 or side^3 for square and cube suffice. Here I am going far beyond those limitations to where Factorial involves concentratic layered spheres. Where the inverse square law found throughout Electromagnetic Laws of Physics abound. And that the Factorial function itself is a inverse square law.
I am going to assert the claim that the geometry inside a Atom is the geometry found in the whole of the Universe at large, especially in a Atom Totality Universe of Plutonium.
Volume in straightline geometry is no longer the maximum parameter of geometry. Rather instead, the maximum parameter of geometry involves the Factorial as atomic orbitals.
On page 1212 of Physics: Part 2: Extended Version by Halliday & Resnick, 1986 shows the energy formula of hydrogen atom orbitals as this.
E = - (m_e *e^4)/(8permittivity*h^2) * (Z^2/n^2)
Which to me, looks much like a manipulation of the Stirling formula for Factorial. n! = Sqrt[2pi*n] (n/e)^n
By the way on page 1194 H&R has their p-orbital by 1986 look more like two adjacent spheres rather than the "lobe like picture".
AP, King of Science
Archimedes Plutonium
1:24 AM (1 hour ago) 1:24 AM
to Plutonium Atom Universe
Praise must be given to the Scotsman James Stirling 1692-1770 for devising the Factorial approximation. How did he do it? Was it a guessing process? Did he simply line up n! on one side of the equation then on the other side line up n^n, then start including constants?
This is the magical way that all of Science works, we inherit the fruits of past generations and are then able to utilize them and push science into the future.
But I may have left a false impression along the way. The exponent function can always be made larger than the factorial function. Consider these two functions.
n^n versus n!
1 1
2^2 2!
3^3 3!
4^4 4!
In this situation, the exponential function is always ahead of the factorial after 1.
I likely gave the false impression that the factorial is always ahead of the exponent.
Exponent 2 has geometry meaning of area in plane geometry and exponent 3 means cube volume in 3D. But exponent 4 and higher have no geometry meaning.
AP
Archimedes Plutonium
2:02 AM (1 hour ago) 2:02 AM
to Plutonium Atom Universe
On Saturday, January 17, 2026 at 12:24:59 AM UTC-6 Archimedes Plutonium wrote:
Praise must be given to the Scotsman James Stirling 1692-1770 for devising the Factorial approximation. How did he do it? Was it a guessing process? Did he simply line up n! on one side of the equation then on the other side line up n^n, then start including constants?This is the magical way that all of Science works, we inherit the fruits of past generations and are then able to utilize them and push science into the future.But I may have left a false impression along the way. The exponent function can always be made larger than the factorial function. Consider these two functions.n^n versus n!1 12^2 2!3^3 3!4^4 4!In this situation, the exponential function is always ahead of the factorial after 1.I likely gave the false impression that the factorial is always ahead of the exponent.Exponent 2 has geometry meaning of area in plane geometry and exponent 3 means cube volume in 3D. But exponent 4 and higher have no geometry meaning.
And so here we could have some sort of Arm's Race in numbers, who can be the fastest rising numbers. If we take the Factorial of n!, it rises faster than n^n.
n^n versus factorial n!
1 1
2^2 2
3^3 factorial of 3! = 720
4^4 24!
How would exponent out best factorial here?? Notice that the 2 in factorial is stuck.
But hard to get something natural in the exponent to outbest factorial-n! .
The infinity borderline in mathematics is 1*10^604 with algebraic closure at 1*10^1208. It is easy to see that we can get both of these large numbers by the third step in the factorial arms race.
So that 296! = 3.855119E + 604 which by the way is chemical element 118 of its total Coulomb Interactions inside the Atom to hold it together.
So how do we turn the base number 3 (2 spins around 2, like 1 spins around 1). So then 3! is 6 and 6! is 720 already far far past 296.
If calculus was the judge between these two competitors-- exponent and factorial, it would be the factorial that wins.
But then again it all seems to boil down to Geometry. If there is no Geometry Meaning for n^n or for factorial n! then they are meaningless altogether.
AP, King of Science
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