371st AP textbook of science--- Advanced True Logic// logic textbook by Archimedes Plutonium This is AP's 371st published book of science published on Internet, Plutonium-Atom-Universe, PAU newsgroup is this. Please read this textbook for free ..
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Archimedes Plutonium
Sep 9, 2026, 7:57:56 AMSep 9
to Plutonium Atom Universe
Advanced True Logic// logic textbook by Archimedes Plutonium
This is AP's 371st published book of science published on Internet, Plutonium-Atom-Universe,
PAU newsgroup is this. Please read this textbook for free on Internet.
https://groups.google.com/forum/?hl=en#!forum/plutonium-atom-universe
Prologue: Rutherford, Geiger, Marsden undertook a famous experiment from 1906-1913 in that they were on a quest to understand the interior of an atom in the Gold Foil Experiment where they shot alpha particles into gold atoms. Their conclusion was that since some alpha particles bounced back to the source at 180 degrees, that Atoms had a dense nucleus. They sadly overlooked the fact that the bounced back alpha particles exited faster than what they entered the gold atom, meaning that Atoms have No Nucleus, but instead have a Proton Torus with thrusting Muons inside that bounced back the incoming alpha particles. If Rutherford, Geiger, Marsden had taken Logic while in college or university, they would probably have gotten the correct answer to the interior of atoms.
Preface: This textbook is for seniors or graduate students in college or university who have had at least 2 years of Logic covered before. I intend to pick apart errors in thinking, especially science, due to a lack of logical foresight. I firmly believe that once you know logic well, --- you have wisdom. Wisdom is the end result of knowing logic well.
Cover Picture: 6) Quantum Mechanics is discrete, not a continuum.
Cover picture:
Cover Picture of this book should be a picture of Planck's starting of Quantum Mechanics with his famous formula E = h f. I especially like the picture in a Google search of Planck that shows a ladder versus a continuous inclined plane.
If all those seeking a PhD in math from year 1900 onwards, had been forced to take Logic in College, then it likely would have happened that one of these professors would have asked the question--- "If Planck finds discreteness in physics, then, should not the true numbers of mathematics be discrete also?"
Instead of AP discovering that the true numbers of math are not the Reals for they are a continuum, but rather the Decimal Grid Numbers, by 2013. If math professors had been forced to take Logic before getting a degree; I am guessing it would not have taken 113 years to pose that question-- math numbers need to be discrete, not continuous.
Max Planck starts Quantum Mechanics, 1900
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--- quoting a Google search of Planck quantum theory---
--- end quoting a Google search of Planck quantum theory---
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Archimedes Plutonium
Sep 9, 2026, 8:38:20 AMSep 9
to Plutonium Atom Universe
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Table of Contents
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1) Introduction
2) Start with the first shining bright Logic used by humanity-- Neanderthals discovery that flint struck on iron pyrite produces fire.
3) Thales of Miletus (626 - 548 BC) -- static electricity and magnetism.
4) Leucippus (5th century BC) and Democritus (460-370 BC) greatest of all science theories, the Atomic Theory
Now we come to the greatest science theory and idea in all the world, the Atomic theory, and its extension which says the total Universe itself has to be a single big Atom, and plutonium fits all the important numbers of math and physics.
5) Euclid (300BC) starts deductive geometry, but messes up on Axiom of Point.
6) Apollonius of Perga (240-190 BC) and his geometry and conic sections.
7) Aristarchus of Samos 270BC-- systematized the experimental science of Astronomy
I need to include Eratosthenes 276-194 BC along with Aristarchus as astronomers, thousand years ahead of their time because they had great logical skills.
8) Kepler 1571-1630, Galileo 1564-1642, Newton 1643-1727, all they needed to do was argue the force of gravity is magnetism.
9) Newton 1643-1727, Leibniz 1646-1716, the Calculus, if only they had logically reasoned it was geometry.
10) Maxwell 1831-1879, Unification of Electricity with Magnetism but the equations are full of error and asymmetry.
11) Heinrich Hertz 1887 Experiment, a magnificent experiment into radio-pulses but no-one had enough logical brains to see its many vast insights into electricity and magnetism and the whole of the science of psychology.
12) Max Planck, 1900 announcement of physics is discrete--- the birth of quantum mechanics, contrasted by math professors moron response by digging deeper into continuity with Reals.
13) Rutherford-Geiger-Marsden-Bohr Experiment of 1906-1913, illogical interpretation for Atoms have ___no nucleus___.
14) Pierre Curie 1859-1906, Dirac 1902-1984 their steadfast logical minds won them victory of truth--- magnetic monopoles exist and are abundant.
15) John Bell 1928-1990, a giant of logical mind with his Bell inequality and Superdeterminism Principle.
16) AP; it is logic that carried me to be the King of Science. That is how important Logic is. And, what is the point of a College or University education if at the end, you come out and cannot think straight, think clearly, think correctly? I would contend your education was squandered.
17) Summary.
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Text
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1) Introduction
This is the 5th logic textbook in the series of High School or 1st year College Logic, Elementary Logic, History of Logic, Intermediate Logic, and finally Advanced True Logic.
For a decade now, I have been harping and harping that students in College and Universities seeking a degree in science to mandatorily take 2 years of Logic to help them think straight and think clearly and correctly by taking and understanding logic. It certainly helped me, otherwise I would not have risen to become the King of Science.
But I had a huge problem with the mandatory taking of 2 years of Logic in College and University. There does not exist Logic textbooks that have Logic correct. All the textbooks on logic before AP's 4 textbooks, have not one of the 4 simple connectors of Logic correct, but full of error. The connectors of AND, OR, Equal-Not, and If-->Then are all messed up and in horrible error. So how could I insist College and University students take Logic when no textbook worthy of logic exists. That is the reason I write these 4 Logic textbooks. They are all for free on the Internet in this newsgroup of PAU.
This textbook of Advanced Logic will be an Analysis of the History of Science and the mistakes made when you ------ lack logic skills -----. All the more reason, for every scientist of the future to take 2 years of Logic in College or University.
The Prologue, is about the story of the great experiment of Rutherford, Geiger, Marsden, although they erred in their conclusion. They lacked sufficient Logic skills to realize if the bounced back particles are moving faster at exit than upon entrance, means they slammed into something with greater momentum that pushed them back at a faster speed. That greater momentum was 79 Muons thrusting through a 79 Proton torus of each gold atom. When 79 Muons moving at almost the speed of light slams into a alpha particle, it will bounce the alpha particle backwards with a greater speed of exit than of entrance.
Thus, AP gets the credit for the correct interior of Atoms, sadly, no longer does Rutherford, Geiger, Marsden. And this story will happen over and over again to all scientists who lack logic skills.
The Preface, is about the story of Max Planck in year 1900 where he starts the fabulously successful Quantum Mechanics Physics. Quantum means "discrete", not continuous. What Max Planck did and discovered is true. What I am complaining about is why all the mathematics professors after year 1900 were so stupid and ignorant as to never raise the question--- if physics is discrete with holes and gaps from one number to the next number. Should not mathematics also be discrete, and that continuity is a mirage, a aberration, a delusion and illusion of the mind. Are not the Reals of mathematics, just plain phony and stupid because they are continuous???? Well, AP answers that question by the year 2013, when I discovered you cannot have Calculus when the numbers of mathematics are continuous. You need holes and gaps from one number to the next successor number in order to have calculus exist. So, here, the logic is this---- math professors are not forced to take logic in university and thus, end up being mostly stupid in a career in mathematics. Most of their proofs are fake and phony, most of their questions are unsound. So bad are math professors, that not one of them is able to admit slant cut of cone is a oval, not a ellipse.
As of this writing, AP discovered that the slant cut of cone is Oval, not ellipse in year 2016, and widely broadcast that news over the Internet sci.math, sci.physics, and to my surprise, not a single professor of mathematics--- Andrew Wiles of Oxford, Terence Tao of UCLA, Thomas Hales of University Pittsburgh, Ken Ribet of Princeton, John Baez UC Riverside, not a one can understand why they are math failures, failing at the most simple level of geometry, for a cone has 1 axis of symmetry, a cylinder has 2 axes of symmetry, the same as a ellipse requires 2 axes of symmetry. They run and hide whenever you ask them "what is the slant cut of a cone?" They are not math educators but failures.
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2--- quoting Wikipedia, the free encyclopedia---
2--- end quoting Wikipedia---
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Archimedes Plutonium
Sep 9, 2026, 10:39:49 PMSep 9
to Plutonium Atom Universe
So when you educate and train physicists without teaching them Logic or how to think straight, clear and correctly, your picture of the Atom and a proton and electron and a neutron becomes lunatic like these pictures.
--- quoting Wikipedia---
Atom
An illustration of the helium atom, depicting the nucleus (pink) and the electron clouddistribution (black). The nucleus (upper right) in helium-4 is in reality spherically symmetric and closely resembles the electron cloud, although for more complicated nuclei this is not always the case. The black bar is one angstrom(10−10 m or 100 pm).
Classification
Smallest recognized division of a chemical element
Properties
Mass range
1.67×10−27 to 4.52×10−25 kg
Electric charge
zero (neutral), or ion charge
Diameterrange
62 pm (He) to 520 pm (Cs) (data page)
Components
Electrons and a compact nucleusof protons and neutrons
Atoms are the basic particles of the chemical elements and the fundamental building blocks of matter. An atom consists of a nucleus of protons and generally neutrons, surrounded by an electromagnetically bound swarm of electrons. The chemical elements are distinguished from each other by the number of protons that are in their atoms. For example, any atom that contains 11 protons is sodium, and any atom that contains 29 protons is copper. Atoms with the same number of protons but a different number of neutrons are called isotopes of the same element.
Atoms are extremely small, typically around 100 picometersacross. A human hair is about a million carbon atoms wide. Atoms are smaller than the shortest wavelength of visible light, which means humans cannot see atoms with conventional microscopes. They are so small that accurately predicting their behavior using classical physics is not possible due to quantum effects.
More than 99.94% of an atom's mass is in the nucleus.[1]Protons have a positive electric charge and neutrons have no charge, so the nucleus is positively charged. The electrons are negatively charged, and this opposing charge is what binds them to the nucleus. If the numbers of protons and electrons are equal, as they normally are, then the atom is electrically neutral as a whole. A charged atom is called an ion. If an atom has more electrons than protons, then it has an overall negative charge and is called a negative ion (or anion). Conversely, if it has more protons than electrons, it has a positive charge and is called a positive ion (or cation).
The electrons of an atom are attracted to the protons in an atomic nucleus by the electromagnetic force. The protons and neutrons in the nucleus are attracted to each other by the nuclear force. This force is usually stronger than the electromagnetic force that repels the positively charged protons from one another. Under certain circumstances, the repelling electromagnetic force becomes stronger than the nuclear force. In this case, the nucleus splits and leaves behind different elements. This is a form of nuclear decay.
Bohr model
Main article: Bohr model
The Bohr model of the atom, with an electron making instantaneous "quantum leaps" from one orbit to another with gain or loss of energy. This model of electrons in orbits is obsolete.A problem in classical mechanics is that an accelerating charged particle radiates electromagnetic radiation, causing the particle to lose kinetic energy. Circular motion counts as acceleration, which means that an electron orbiting a central charge should spiral down into that nucleus as it loses speed. In 1913, the physicist Niels Bohr proposed a new model in which the electrons of an atom were assumed to orbit the nucleus but could only do so in a finite set of orbits, and could jump between these orbits only in discrete changes of energy corresponding to absorption or radiation of a photon.[20] This quantization was used to explain why the electrons' orbits are stable and why elements absorb and emit electromagnetic radiation in discrete spectra.[21] Bohr's model could only predict the emission spectra of hydrogen, not atoms with more than one electron.
The current consensus model
The modern model of atomic orbitals draws zones where an electron is most likely to be found at any moment.In 1925, Werner Heisenberg published the first consistent mathematical formulation of quantum mechanics (matrix mechanics).[30] One year earlier, Louis de Broglie had proposed that all particles behave like waves to some extent,[31] and in 1926 Erwin Schrödinger used this idea to develop the Schrödinger equation, which describes electrons as three-dimensional waveforms rather than points in space.[32] A consequence of using waveforms to describe particles is that it is mathematically impossible to obtain precise values for both the positionand momentum of a particle at a given point in time. This became known as the uncertainty principle, formulated by Werner Heisenberg in 1927.[30] In this concept, for a given accuracy in measuring a position one could only obtain a range of probable values for momentum, and vice versa.[33] Thus, the planetary model of the atom was discarded in favor of one that described atomic orbital zones around the nucleus where a given electron is most likely to be found.[34][35] This model was able to explain observations of atomic behavior that previous models could not, such as certain structural and spectral patterns of atoms larger than hydrogen.
[many snips]
Illustration of a nuclear fusion process that forms a deuterium nucleus, consisting of a proton and a neutron, from two protons. A positron (e+)—an antimatterelectron—is emitted along with an electron neutrino.The number of protons and neutrons in the atomic nucleus can be modified, although this can require very high energies because of the strong force. Nuclear fusion occurs when multiple atomic particles join to form a heavier nucleus, such as through the energetic collision of two nuclei. For example, at the core of the Sun protons require energies of 3 to 10 keV to overcome their mutual repulsion—the coulomb barrier—and fuse together into a single nucleus.[46] Nuclear fission is the opposite process, causing a nucleus to split into two smaller nuclei—usually through radioactive decay. The nucleus can also be modified through bombardment by high energy subatomic particles or photons. If this modifies the number of protons in a nucleus, the atom changes to a different chemical element.[47][48]
Electron cloud
See also: Electronegativity
A potential well, showing, according to classical mechanics, the minimum energy V(x) needed to reach each position x. Classically, a particle with energy E is constrained to a range of positions between x1 and x2.The electrons in an atom are attracted to the protons in the nucleus by the electromagnetic force. This force binds the electrons inside an electrostatic potential well surrounding the smaller nucleus, which means that an external source of energy is needed for the electron to escape. The closer an electron is to the nucleus, the greater the attractive force. Hence electrons bound near the center of the potential well require more energy to escape than those at greater separations.
Electrons, like other particles, have properties of both a particle and a wave. The electron cloud is a region inside the potential well where each electron forms a type of three-dimensional standing wave—a wave form that does not move relative to the nucleus. This behavior is defined by an atomic orbital, a mathematical function that characterises the probability that an electron appears to be at a particular location when its position is measured.[51] Only a discrete (or quantized) set of these orbitals exist around the nucleus, as other possible wave patterns rapidly decay into a more stable form.[52] Orbitals can have one or more ring or node structures, and differ from each other in size, shape and orientation.[53]
3D views of some hydrogen-like atomic orbitals showing probability density and phase (g orbitals and higher are not shown)Each atomic orbital corresponds to a particular energy level of the electron. The electron can change its state to a higher energy level by absorbing a photon with sufficient energy to boost it into the new quantum state. Likewise, through spontaneous emission, an electron in a higher energy state can drop to a lower energy state while radiating the excess energy as a photon. These characteristic energy values, defined by the differences in the energies of the quantum states, are responsible for atomic spectral lines.[52]
The amount of energy needed to remove or add an electron—the electron binding energy—is far less than the binding energy of nucleons. For example, it requires only 13.6 eV to strip a ground-state electron from a hydrogen atom,[54] compared to 2.23 millioneV for splitting a deuterium nucleus.[55] Atoms are electrically neutral if they have an equal number of protons and electrons. Atoms that have either a deficit or a surplus of electrons are called ions. Elec
--- end quoting Wikipedia---
Summary when a Physicist who has no logical brain talks about Atoms. He/she shows balls, neutron balls, proton balls, tiny tiny electron balls or electron cloud outside a nucleus. This is what happens when a physicist has no logical brain--- balls balls balls. If a physicist had a logical brain would know that geometry comes from function-job-task. A proton is the coil in Faraday Law-structure and the electron is the bar magnet in Faraday law-structure. That means the Proton is a Coil in the shape of a torus, and inside the proton torus is found the electron as a muon bar magnet thrusting through the proton torus producing new electricity. This new electricity has to be stored somewhere and hence we have created the neutron which is parallel plates surrounding the proton torus. This new electricity in the form of 0.5MeV magnetic monopoles travel from the proton torus to a neutron. A neutron grows from 1 eV all the way out to 945MeV.
This is why I complain about physics and chemistry education, no logic, and no logical brains. For if 2 years of Logic were required to get a degree in physics and chemistry, the professors have a chance to think straight, clear and correctly.
On Tuesday, September 8, 2026 at 6:09:12 AM UTC-5 Archimedes Plutonium wrote:
Alright, so I pulled out my slinky toy model of a Proton Torus with Muon inside.Now for uranium-238 there would be 92 X 840 =77,280 rings as one big torus, and inside would be a chain of 92 muons each 105 rings thrusting through the uranium atom proton torus in the Faraday Law.So, a Neutron in New Physics is a Parallel Plate Capacitor that stores and grows from 1 eV all the way out to 945MeV when fully grown after some 140 million years of Faraday Law Growth.Now in the reading above of how to turn 238U into 239Pu by radiating the Uranium atom with a Neutron, begs the question of how does the Uranium + Neutron transform over into a 94 x 840 =78,960 rings of 1 MeV each for the Plutonium 239 Proton Torus??????This developing 239Pu Atom has to take the Neutron into its 77,280 rings plus alter an existing neutron in the 238U, an existing neutron converting to a 840 rings with 105 rings added to the muons inside.The easiest way possible according to my eyes would be to make a snip of the 77,280 rings (if all the rings are connected like in a slinky toy, and make a snip into the neutron 945 rings (neutron converted into a torus of 840 + 105).Then join the new muon inside with the 92 muons then join the new proton addition of 840 new rings. Making a 239Np atom.Now the 239Np atom takes one of its Neutrons and converts it from parallel plate capacitor to that of 840 proton rings with 105 muon rings. And does the process all over again of a snip cut into the huge 78,120 rings of Np and allows 105 muon rings inside, then attaches the new second proton torus of 78,120 + 840 =78,960 rings to make 239Pu.Now Old Dumb Physics talks about a double Beta decay in this entire process. They maybe correct.New Physics would question if the snip cuts into the 238U then the 239Np is the Cause of the double Beta decay of two magnetic monopoles of 0.5MeV????Are the two snip cuts to form 239Np then 239Pu, the after-effect that is seen as 2 Beta decays???????I will have to ponder this question for awhile, to make more progress.AP, King of Science
Archimedes Plutonium
Sep 10, 2026, 1:01:18 AMSep 10
to Plutonium Atom Universe
You see, the information I need to tell us that the Proton and Muon and Neutron are rings of 1 MeV, is that in a Atomic bomb blast, most of the radiation that comes out will be in the 1 MeV range, of X-rays. This would tell us that the architecture of the Proton of the Muon of the Neutron are rings of 1 MeV.
Attribute
Atmospheric Blast (Ground/Air Burst)
Space / High-Altitude Blast
Initial X-ray Output
70% to 80% of total weapon energy
70% to 80% of total weapon energy
X-ray Range
Absorbed within meters by the air
Travels hundreds of miles through space
What it turns into
The nuclear fireball, blast waves, and heat
Stays pure X-ray radiation until hitting an object
Primary Danger to Humans
Blinding heat, shockwaves, and gamma radiation
High-altitude radiation and electrical grid failure (EMP)
So I make a Google search under "How much x rays in a Atomic bomb blast" and I get these hits.
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Inside the exploding nuclear core of an atomic bomb, roughly 70% to 80% of the total energy is initially released in the form of soft X-rays. However, how much of that reaches a person on the ground depends entirely on whether the bomb is detonated in the atmosphere or in space. [1, 2]
1. In an Atmospheric Blast (Like Hiroshima or Nagasaki)
If the atomic bomb explodes in the air, virtually zero X-rays reach the ground.
- The Air Blockade: Earth's atmosphere is extremely dense and opaque to X-rays. Within a matter of microseconds, the surrounding air absorbs almost 100% of these X-rays. [1]
- The Fireball Effect: As the air absorbs this massive amount of X-ray energy, it heats up to millions of degrees, creating the iconic, blinding nuclear fireball. [1]
Note: While people on the ground suffer from devastating ionizing radiation, it comes from gamma rays and neutrons, not X-rays. [1]
2. In a High-Altitude / Space Blast
If an atomic bomb is detonated in the vacuum of space (above 30 to 100 km), the situation changes entirely. [1]
- Direct Exposure: Because there is no air to absorb them, the X-rays travel unhindered for hundreds of miles.
- Weapon Effects: Instead of a giant atmospheric shockwave, the bomb produces a massive, blinding burst of X-rays, alongside a powerful Electromagnetic Pulse (EMP) that can fry electronics over an entire continent. [1]
Directly Comparing the Scenarios
Attribute
Atmospheric Blast (Ground/Air Burst)
Space / High-Altitude Blast
Initial X-ray Output
70% to 80% of total weapon energy
70% to 80% of total weapon energy
X-ray Range
Absorbed within meters by the air
Travels hundreds of miles through space
What it turns into
The nuclear fireball, blast waves, and heat
Stays pure X-ray radiation until hitting an object
Primary Danger to Humans
Blinding heat, shockwaves, and gamma radiation
High-altitude radiation and electrical grid failure (EMP)
If you are researching a specific aspect of nuclear physics, let me know if you want to explore how the Electromagnetic Pulse (EMP) forms or how modern hydrogen bombs use these X-rays internally to trigger a secondary explosion. [1]
- Basic Nuclear Physics and Weapons Effects - acq.osd.milEMP is a very short duration pulse of low-frequency, or long-wavelength, electromagnetic radiation (EMR). The source for all nucle...
Show all
AI can make mistakes, so double-check responses
Web results
the blast and shock wave: 50% of total energy · thermal radiation: 35% of total energy · ionizing radiation: 5% of total energy (more in a neutron bomb) · residual ...Read more
Prompt radiation consists of the neutrons and gamma rays emitted as a nuclear bomb explodes and during the first minute thereafter. About 85 percent of the ...Read more
Mar 2, 2022 — Lethal direct radiation extends nearly a mile from a 10-kiloton explosion. With most weapons, though, direct radiation is of little significance ...Read more
A nuclear blast will most always create enough prompt radiation (neutrons and gamma rays) within 500 meters to kill ahuman.
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Archimedes Plutonium
Sep 10, 2026, 1:06:09 AMSep 10
to Plutonium Atom Universe
Some more hits of a Google search for "How much x ray from Atomic bomb blast"
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Missing: x | Show results with: x
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Archimedes Plutonium
Sep 10, 2026, 1:26:14 AMSep 10
to Plutonium Atom Universe
You see, Old Physics, which is mostly dumb physics, for they do not train their scientists by taking Logic to think straight, think clearly and think correctly, ends up,....... ends up with making the Proton a ball that does nothing but lounge around in a dense nucleus, and a neutron another ball about the same size as the proton ball, and the electron about 2,000 times tinier of a ball that seems to float around outside this dense nucleus. Such a moron picture of the Atom is what happens when physicists never have to take Logic in college or university.
On the other hand, AP, who took two years of Logic in University 1968-1972, and that logic helped me to realize some 45 years later in 2016-2017, that the proton, neutron, electron had to be more, far far more than stupid do nothing balls lounging around.
That the greatest laws of physics--- the Electromagnetic Laws such as Ohms law, Faraday law, Coulomb law, Ampere law and others defined and built what the Proton, Neutron, Electron actually are.
So, well, if AP is correct in the Proton Torus and Neutrons and parallel plate capacitors, the muons inside the proton torus as more rings of 1 MeV each. That in a Atomic Bomb blast 80%, and likely 90% of the outcoming energy is X-ray radiation as the bomb blast cuts and severs all those rings in plutonium.
A individual 239Pu Atom has 94 x 840 =78,960 rings of 1 MeV each, and the neutrons of this individual atom would have 145 x 945 =137,025 rings of 1 MeV each, and we should not forget the Muons inside the proton torus as 94 x 105= 9,870 rings of 1 MeV each, making a total of rings of 225,855 x-rays of 1MeV for each individual plutonium atom in the blast.
I guess with the available evidence, AP is correct, and the Old Physics is ready for the junk pile.
Archimedes Plutonium
Sep 11, 2026, 12:47:27 AMSep 11
to Plutonium Atom Universe
1) Start with the first shining bright Logic used by humanity-- Neanderthals discovery that flint struck on iron pyrite produces fire.
I am starting Advanced Logic with the story of making fire by Neanderthals in England some 400,000 years ago. I am paralleling my history of logic textbook, "The History of Logic", my #369 science book.
Of course, well humanity a long time ago evolved from apes some 10 million years ago and they evolved because they were gifted with throwing rocks for their benefit. The Throwing Ape eventually evolved into humanity. Rocks and stones would be the first advancement of humanity, but it is difficult to place the science of Logic into throwing rocks and stones some 10 million years ago.
Although it would be logical to collect a lot of rocks and stones to be prepared to defend oneself or defend a group of proto-humans, or to use in hunting, logical foresight.
But, rather, I chose to begin the story of Advanced Logic with humanity some 400,000 years ago who had to clearly use Logic in finding that two special rocks of Flint and of Iron Pyrite when struck together produced many sparks.
This is the Logic of Equal-Not connector of the 4 simple connectors of Logic--- AND, OR, Equal-Not, If-->Then. For the Equal-Not told the Neanderthals that those sparks are the same equal of campfire sparks.
We definitely can say without a doubt, 400,000 years ago in England, a group of Neanderthals (by the way, they were the same species as Cro-magnon, homo sapiens for many humans present today have Neanderthal genes in them, and that could not have happened if different species), a group of Neanderthals in England figured out that if you create sparks from striking flint on iron pyrite that those sparks were Equal to their campfire.
It is __logical__ to say those humans with Neanderthal genes are modern day humans, for species definition in Darwin evolution is that a different species cannot mate with another different species. So, how is it possible to be a different species yet mate with one another. On PBS TV was a long program series on human evolution and the hostess erred many a times with her placement of Neanderthals as a different species.
These Neanderthals logically learned flint AND iron pyrite. They logically learned the sparks of the rocks Equals their campfire. They logically learned that If__ their campfire goes out Then__ the flint AND iron pyrite, will give them a new campfire.
Now my textbook on the History of Logic talks mostly about Logic successes, but in this textbook of Advanced Logic I talk mostly of Logic failures because the person or scientist lacked logic to reason correctly.
But let me open Advanced Logic with the success story of Neanderthals in England, 400,000 years ago successfully using Logic to make campfires.
Now I turn to two more success stories before talking mostly about logic failures. Let me talk of Thales success and of Leucippus-Democritus success. The story of the Atomic theory is central in any science history. Electricity is the Atomic Theory. And humanity would not progress far if not for electricity. Electricity is the future and it comes from Atomic theory.
2) Thales of Miletus (626 - 548 BC) -- static electricity and magnetism.
Archimedes Plutonium Mar 30, 2026, 2:43:01 AM to Plutonium Atom Universe newsgroup.
Thales of Miletus (626 - 548 BC) -- static electricity and magnetism
Alright this is an excellent idea of making the Scientific Method be nothing but the 6 Connectors of Logic, except, I need to scramble the order around.
For Logic the order of presentation is Existential quantifier, then Not-Equal, then AND, then OR, then IF-->Then, then finally Universal quantifier.
For Scientific Method, the order seems to be Existential quantifier, then AND, then IF-->Then for the hypothesis making of several hypothesis, then conducting experiments is the OR, then Not-Equal and OR for analysis of data from experiments and finally Universal quantifier if your hypothesis is a law of science, or even a rule.
Scientific Method from various sources on Internet
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Step 1-- Make observations and ask many questions.
Step 2-- Research the subject matter and Review the literature on the subject.
Step 3-- Formulate a Hypothesis of what you think is going on.
Step 4-- Conduct Experiments pertaining to your hypothesis.
Step 5-- Collect data from the experiment/s and analyze the data.
Step 6-- Draw conclusions, and publish the results.
Step 1-- Make observations and ask many questions.
No, I think the Scientific Method starts with a Observation of Existence and a curiosity of an idea. I think science is curiosity.
Step 2-- Research the subject matter and Review the literature on the subject.
This is good, and would be Not-Equal. Is the idea equal to known ideas and whether the new idea is not equal to known ideas.
Step 3-- Formulate a Hypothesis of what you think is going on.
Yes this is the IF--> Then hypothesis.
Step 4-- Conduct Experiments pertaining to your hypothesis.
Step 5-- Collect data from the experiment/s and analyze the data.
Yes this is the AND connector, both step 4 and step 5 is one step, the doing of experiments and collecting data and information.
Step 6-- Draw conclusions, and publish results.
Yes, we also need to decide between competing hypotheses and ideas and this is the OR where we have Deciding Experiments.
Step 6 would be the Universal quantifier where the idea that started the research and experiments may be a new law of science or a rule of science and the conclusion should be published for others to do the experiments.
Yes, at first I was not sure I could get a pattern of the Scientific Method using strictly just the 6 connectors of Logic, now I am sure that is the case.
In other words, the Scientific Method is the sequence of the Logic Connectors.
Let me try it out using the Earth's first science experiment by Neanderthals some 400,000 years ago in England starting a fire with flint and iron pyrite.
Scientific Method from various sources on Internet
-----------------------------------------------------------------
Step 1-- Make observations and ask many questions.
Step 2-- Research the subject matter and Review the literature on the subject.
Step 3-- Formulate a Hypothesis of what you think is going on.
Step 4-- Conduct Experiments pertaining to your hypothesis.
Step 5-- Collect data from the experiment/s and analyze the data.
Step 6-- Draw conclusions, and publish results.
Step 1-- Make observations and ask many questions.
The Scientific Method starts with a Observation of Existence and a curiosity of a idea. I think science is curiosity.
With Neanderthal fire making 400,000 years ago, they had a tool industry already of flint and iron pyrite, as hand tools, to cut or to grind or as axes. One day a Neanderthal smashed flint against iron pyrite and to his/her amazement, sparks flew off.
Step 2-- Research the subject matter and Review the literature on the subject.
This is good, and would be Not-Equal. Is the idea equal to known ideas and whether the new idea is not equal to known ideas.
Of course Neanderthal had no books or libraries or science journals. What they did have is a mind with ideas. And one or several of them seeing sparks would ask the question--- are the sparks equal to fire of the campfire?? Equal to campfire or not campfire.
Step 3-- Formulate a Hypothesis of what you think is going on.
Yes this is the IF--> Then hypothesis.
Here the Neanderthals would have formed a hypothesis, If the sparks are fire, then we can form a new fire with tinder of leaves or dry grass.
Step 4-- Conduct Experiments pertaining to your hypothesis. Step 5-- Collect data from the experiment/s and analyze the data.
Yes this is the AND connector, both step 4 and step 5 is one step, the doing of experiments and collecting data and information.
Here the Neanderthals using the AND connector-- collect leaves and dry grass and strike flint against iron pyrite AND see if fire starts.
Step 6-- Draw conclusions.
Yes, we also need to decide between competing hypotheses and ideas and this is the OR where we have Deciding Experiments.
Here the Neanderthals had no competing hypothesis and the fire making was successful with the AND connector. So I have to wait in History of Logic for another science experiment that does need the OR connector. Fortunately, the next great Science experiment in human history is Thales with magnetism and the Lodestone and with static electricity of rubbing amber on fur. The Thales experiment goes all the way out to OR connector and then to Universal quantifier.
Step 6 would be the Universal quantifier where the idea that started the research and experiments may be a new law-structure of science or a rule of science and the conclusion should be published for others to repeat the experiments, making sure it is a universal law-structure.
The Neanderthal fire experiment goes out to AND and stops there. But the Thales science experiment of Lodestone magnetism and static electricity goes through the entire gamut of Scientific Method as delineated by the 6 connectors of Logic.
I suspect there are monuments on Miletus commemorating Thales. However, I insist a International Monument be erected with a tourist center showing the Lodestone magnet and the Amber rubbed in fur giving static electricity.
A monument in Surrey England for fire making 400,000 years ago. And here a monument of where the first science experiments of truly magnificent in electricity and magnetism for the Primal Axiom over all science is = All is Atom and Atoms are nothing but electricity and magnetism.
In fact, all these famous persons in the History of Logic should have an International Monument.
Yes, I could not complete the Scientific Method with all 6 connectors for Fire Making by Neanderthals, but I sure can complete it using Thales scientific experiment discovery of magnetism and static electricity.
In other words, the Scientific Method is the sequence of the Logic Connectors.
Let me try it out with Thales electricity, magnetism.
Scientific Method from various sources on Internet
-------------------------------------------------------------------
Step 1-- Make observations and ask many questions.
Step 2-- Research the subject matter and Review the literature on the subject.
Step 3-- Formulate a Hypothesis of what you think is going on.
Step 4-- Conduct Experiments pertaining to your hypothesis.
Step 5-- Collect data from the experiment/s and analyze the data.
Step 6-- Draw conclusions.
Step 7-- Universal quantifier
Step 1-- Make observations and ask many questions.
So there was Thales, we do not have his writings to know exactly his discoveries, so I am going to play around here. Did he discover the properties of magnetism with Lodestone first or did he discover rubbing amber in fur and then seeing a attraction to small objects?
Let me say he discovered them roughly in one year. He made observations that the Lodestone attracted iron nails and called it a Magnet for the rock came from Magnesia. And he observed that rubbed amber attracts small objects.
Thales says --- there exists Lodestone and there exists Amber and fur and nails and small paper of his time.
The Existential quantifier.
Step 2-- Research the subject matter and Review the literature on the subject.
This is good, and would be Not-Equal. Is the idea equal to known ideas and whether the new idea is not equal to known ideas.
Thales would have seen that the attraction of nails by lodestone equals the attraction of small paper or feathers or straw by Amber.
Step 3-- Formulate a Hypothesis of what you think is going on.
Yes this is the IF--> Then hypothesis.
Thales would have logically reasoned If lodestone attracts iron nails and if rubbed Amber attracts small paper, Then Lodestone and Amber share some force of attraction.
Step 4-- Conduct Experiments pertaining to your hypothesis. Step 5-- Collect data from the experiment/s and analyze the data.
Yes this is the AND connector, both step 4 and step 5 is one step, the doing of experiments and collecting data and information.
Here Thales may have experimented to see if the Lodestone attracts Amber. Or if the Lodestone attracts the fur. Or if the Lodestone attracts paper.
He may have experimented to see if rubbed amber attracts a tiny piece of iron nail.
Now he makes a Hypothesis that inside the Amber exists tiny lodestones that do the attracting. So tiny they cannot attract big nails only tiny nails.
Step 6-- Draw conclusions, and publish results.
Yes, we also need to decide between competing hypotheses and ideas and this is the OR where we have Deciding Experiments.
Thales makes a competing Hypothesis, Either the Amber is composed of tiny lodestones or it is not.
Here Thales needs to perform a Deciding Experiment.
So he smashes nails to get iron flakes, iron filings.
Now he sets up the Deciding Experiment, the OR connector of Logic.
Will the rubbed Amber in fur pick up any iron filings?????
Step 6 would be the Universal quantifier where the idea that started the research and experiments may be a new law of science or a rule of science and the conclusion should be published for others to do the experiments.
Based on his Experiments, Thales concludes that no Universal or does he conclude a Universal law????
Leave the reader to find out.
4) Leucippus (5th century BC) and Democritus (460-370 BC) greatest of all science theories, the Atomic Theory
Now we come to the greatest science theory and idea in all the world, the Atomic theory, and its extension which says the total Universe itself has to be a single big Atom, and plutonium fits all the important numbers of math and physics.
Archimedes Plutonium
Sep 11, 2026, 7:17:33 AMSep 11
to Plutonium Atom Universe
Archimedes Plutonium Mar 30, 2026, 2:53:23 AM to Plutonium Atom Universe newsgroup.
Now we come to the greatest science theory and idea in all the world, the Atomic theory, and its extension which says the total Universe itself has to be a single big Atom, and plutonium fits all the important numbers of math and physics.
You see, you really cannot have the greatest of all science theories not be universal. Even Feynman in his splendid 3 volume set of Lectures on Physics, at the outset, says the greatest science theory of all time--- the Atomic theory.
This is the science of Logic in its finest form, finest application.
Atom Totality Theory in long Logic Argument
------- Facts and definitions of Atom Totality ------
1) All Matter is one of 118 Chemical Elements of the Periodic Table of Chemical Elements. This is the definition of Matter and Matter has rest mass. Reason:: Chemistry's Periodic Table of Chemical Elements.
2) The 118 Chemical Elements are each Atoms, and a atom is defined as having three components --- Protons, Muons, Neutrons for which these three components engage in the Faraday and Ampere law and Capacitor law and other Electromagnetic Laws. Reason:: Physics Atomic Theory.
3) The Proton is a coil torus and all the protons form a single torus, with muons inside this proton torus act as bar magnets thrusting through the proton torus in the Faraday law producing new electricity and electromagnetic radiation. Reason:: Proton +Muon inside equals 938MeV, and neutron equals 940MeV, both within sigma error of 945MeV with the AP EM laws of physics that all elementary particles have a function in the EM laws such as proton is the coil in Faraday law and muon the true electron of Atoms is the bar magnet in Faraday law.
4) The electricity and electromagnetic radiation produced by proton-muons is storaged in neutrons as parallel plate capacitors. But some of the radiation is emitted out of the atom such as starshine and sunshine. Emitted out as EM radiation but still connected with the atom of origin until absorbed by a new atom. Reason:: AP EM laws of electromagnetism.
5) Stars and Sun shine not from fusion but from Faraday law, and it is the Faraday law that builds stars and planets and other astronomical bodies. As the storage of electricity in Faraday law proton-muon builds up neutrons to become new hydrogen atoms or other atoms. Reason:: fusion depends on probability of collisions, while Faraday law is assured certainty of producing electricity energy from a perpetual motion thrusting muon inside a proton torus coil. Stars and Sun shine so dependably that fusion is unable to supply this dependable energy.
---------- Facts and definitions of Space where few if any matter exists -----
6) What is not matter, is empty space full of Electromagnetic Radiation pencil ellipses of Light Waves and subatomic particles traveling through the Cosmos. The empty space of a plutonium atom matches the empty space seen in Astronomy where there are few galaxies, and stars. Rutherford-Geiger-Marsden gold leaf experiment points to empty space similar to astronomy empty space. Reason:: Rutherford-Geiger-Marsden gold leaf experiment 1906-1913.
7) EM radiation is a circuit, although a pencil-ellipse, it is always connected with the atom that gave it birth, until the radiation is absorbed in other atoms. Reason:: The laws of electromagnetism form the electromagnetic spectrum.
8) Space can be empty of Atoms, but is always containing electromagnetic radiation, pencil ellipses of Light waves going at the speed of light in closed loop pencil ellipses always connected with the Atom of origin or the Atom it is absorbed by. Reason:: Particle to Wave duality of Quantum Mechanics.
9) Subatomic particles that escape an atom, are always connected with its original atom via the EM radiation is a closed loop, until the subatomic particle is absorbed by a new atom. Reason:: Coulomb law of electromagnetism.
10) All subatomic particles or EM energy outside an Atom are all connected to their atom of origin until absorbed by a new atom and then connected to the new atom. Reason:: Coulomb law of electromagnetism.
------- Growth in an Atom Totality -----
11) Growth in Atom Totality is caused by Faraday and Ampere law and Capacitor law, especially in Faraday law where a thrusting bar magnet through a coil of wire produces new electricity the 0.5MeV Dirac magnetic monopoles which have rest mass but also in the EM radiation given off in Faraday law. This is a conversion of Space into new mass. And the Sun and stars shine from Faraday law, not fusion. As each atom is composed of protons which has muons inside the proton torus doing the Faraday law. Reason:: Universal laws of Electromagnetism.
12) In Astronomy, the galaxies form rings which is a small part of a Cosmic Proton torus and the galaxies form Cosmic Muons thrusting through the Cosmic Proton producing electricity and radiation. We see and measure this in the form of cosmic gamma rays. Astronomy sees this as the Ring of Galaxies in 3rd layer as reported by Caltech. Plutonium Atom Totality has 94 x 840 = 78960 Cosmic Proton Rings and we are beginning to see just 2 or 3 of these rings in our corner of the Plutonium Atom Totality. The muons inside this Cosmic Proton torus are a bar magnet that is 94 x 105 = 9870 connected Cosmic Muon Chain inside the Cosmic Proton. We seem to have a nexus of galaxies in that some are moving perpendicular to one another in the Ring in the 3rd layer. Reason:: Applying observations of science to the laws of electromagnetism.
13) Chemistry sees this as the concentration of high atomic number elements in ore deposits as a direct result of Faraday law growth. Elements created as ores in planets, moons and asteroids. Reason:: Faraday law of electromagnetism.
----- Concluding the Atom Totality is a single big atom of plutonium ------
14) The Universe itself has mass and matter. Reason:: Everyday observation of the world we live in.
15) Hence the Universe is one of the 118 chemical elements, and the plutonium atom fits the special numbers of math and physics such as pi = 3.14... as 22/7 and e = 2.718... as 19/7, the Fine Structure Constant, the best fit. Reason:: Fulfillment of the Atomic Theory as Universal Generalization law-- all matter comes down to being one of the 118 known chemical elements.
16) The Atom Totality is different from the atoms it contains inside the Atom Totality, simply as a mass and size difference. For a Plutonium atom found inside the Plutonium Atom Totality is many times exponentially smaller mass and size. Reason:: One atom contains all the other atoms inside itself. Plus, the Symmetry of Physics is restored-- one atom whole containing all other atoms of the universe preserves symmetry.
17) The Atom Totality must be a single Atom, for the growth pattern is Atoms giving birth to new atoms via Faraday law. The Universe cannot be a molecule for the growth pattern is not set up to create molecules. Reason:: Faraday law give rise to new electricity which is storaged in neutrons as parallel plate capacitors that keep growing until the neutron forms a new atom of hydrogen, then the hydrogen neutron forms helium, and so on.
18) The Atom Totality must be true, otherwise the Atomic Theory is a mere and meager rule and not a law or theory of science. Laws and theories of science are Universal, while a rule of science is sometimes correct, often wrong. Reason:: The Scientific Method in working order.
19) The Atom Totality as a Law and Theory of science propounds the axiomatic principle of science--- All is Atom and Atoms are nothing but electricity and magnetism. Meaning that all science reduces to the laws of electromagnetism. Reason:: Atomic theory and Electromagnetic laws are one and the same.
----- Purpose of Life in an Atom Totality -------
20) Purpose of life in an Atom Totality is to nucleosynthesize heavy elements impossible to nucleosynthesize in stars or supernova. Life was not needed in prior Atom Totalities of helium up to lead as Faraday Law could build an atom twice the atomic number and spontaneous fission into the newly created Atom Totality. But life in Atom Totalities were required to create new Atom Totalities beyond lead. This would mean that life, intelligent life to do nucleosynthesis, existed for billions and billions of years long before planet Earth and humans arrived in the Plutonium Atom Totality. Whether life lives after spontaneous fission into a new Atom Totality is unknown at this time. I am guessing life lives through the birth of a new Atom Totality. Reason:: If Atoms are all that exists, makes logical sense that life is created to further increase more Atoms.
21) As Life nucleosynthesizes Element 192 it will __spontaneously fission__ into a Curium Atom Totality. Life is uniformly spread throughout the Universe and its mission is to create the next Atom Totality. Reason:: Today we, as life on Earth, has nucleosynthesized element 118. We have a long ways to go before nucleosynthesizing element 192.
22) As Element 192 is formed by bombarding Curium with other Curium atoms until two fuse together to briefly form Element 192 which immediately decays into the Curium Atom Totality in equal parts, one curium atom being particle the other being wave (one being electricity rest mass, the other curium atom being magnetism energy). The need for the Atom Totality to be an even proton number-- atomic number--- is so that the spontaneous fission creates two equal atoms. One to give the rest mass Curium Atom Totality and the other to give the energy of the Curium Atom Totality. Reason:: Our best state of physics knowledge at present.
23) If humanity saves itself from extinction and oblivion by making Europa our permanent new home in the next 1,000 years, because our Sun has gone Red Giant phase and will swallow Earth in due course. Then on Europa, after we become settled in, our mission there will be to build cyclotrons to bombard curium atoms into other curium atoms hoping to get two to fuse and nucleosynthesize element 192 and create the New Curium Atom Totality. We will likely have competitors in billions of other solar systems in the Universe. It is a race to create the New God-- Curium Atom Totality. Reason:: How physics works and reveals the truth.
-----------
Another logical argument that the Universe is a single atom of Plutonium.
One would think that God, our creator would not hide from us. Be behind the scenes and never apparent to humans. One would think the creator of life would be apparent and obvious to all intelligent life. And, well, everyday we get up and start to work, we see materials all around us. We see these materials and know they are composed of Atoms. And so, the argument goes. Our Creator is visible every day of our life, all around us in all forms and shapes and color. Even our own bodies are atoms, atoms of the creator. All is Atom and Atoms are nothing but electricity and magnetism.
5) Euclid (300BC) starts deductive geometry, but messes up on Axiom of Point.
Aug 17, 2026, 4:46:49 PM
to Plutonium Atom Universe
6) Concept of Well-defined in Logic.
Old Math failed at the starting line of Geometry, with their fatally flawed Axiom or Postulate of that of "Point".
No wonder Old Math could never do a geometry proof of Fundamental Theorem of Calculus.
No wonder that Physics started the truth of geometry in year 1900 with Max Planck kicking off the century with Quantum Mechanics saying physics is discrete, yet the fools and cranks of math still in their cesspool of continuums.
I shall go through all the math history books here at home that talks about the First Axiom of geometry.
Old Math:: A point has no length, no width, no depth.
New Math:: A point must have at minimum a length of 1*10^-604 length and that same amount for width and depth. Note--- at minimum but in most circumstances it can have larger proportions.
Examples: area of rectangle and volume of rectangular box.
The area of a rectangle is length by width. Suppose a point has no dimension. In 1000 Grid the induction element is 0.001, in 100 Grid the induction element is 0.01 and in 10 Grid the induction element is 0.1. In 10 Grid we start with 0 and add 0.1 gives us the first number. Add 0.1 to 0.1 gives us the next number 0.2 and so on adding the increment 0.1 gets us to 10, the last number in 10 Grid. In 10 Grid, the smallest Grid of numbers there are exactly 100 numbers in total not counting 0.
The area of a rectangle in 10 Grid such as a rectangle of 3 units long by 2 units width is a multiplication of length x width. |||||| is a figure of 3 units long by 2 units wide.
What makes it possible to have a formula of Length x Width for area of rectangle is that a number as a geometry point cannot be 0 long, 0 wide. The point in geometry in 10 Grid must be 0.1 long and 0.1 wide. Thus, you get the correct answer of 6 square units.
What makes it possible to have a formula for volume of rectangular box as Length x Width x Depth in 1000 Grid is that each point in math in 1000 Grid has a 0.001 length, and a 0.001 width and a 0.001 depth in order for a rectangular box that is 4 long, 3 wide and 2 depth comes out to be 24 cubic units.
ANALYSIS
-------------
We can analyze the fatal flaw of Old Math's axiom on what a point is by pure Logic.
A Point is something, otherwise it is nothing.
If a point has no length, no width, no depth, then it has 0 length, 0 width, 0 depth.
Hence a point is nothing for zero is nothing.
But a point is something and not nothing.
Therefore, A point must have some tiny finite length, finite width, finite depth. The minimum amount of metric for a point would be the Infinity Borderline and the induction element is 1*10^-604.
Common Sense Explanation
------------------------------------
Physics is the material world science. The smallest thing in physics would be a point of math. Atoms are too big to be points, for they have subatomic particles. The smallest subatomic particle is the magnetic monopole of the 0.5MeV particle. Hence, the Point in Physics is the dimension of the magnetic monopole.
Note: Old Physics and Old Chemistry were confused for the 0.5MeV particle is not the electron of Atoms, but rather instead the muon the 105 MeV particle is the true electron of Atoms.
The failure of Old Math to have a valid definition or postulate or axiom of "Point" contributed to the gargantuan failure of Old Math to understand what the Calculus was; with the derivative as part of the function graph, where the true numbers of mathematics have to be discrete with empty space in between one point and the next point.
Now, with Point having a tiny tiny finite size, we can backtrack and thus make Exacting Precision in Geometry figures such as a Circle is at minimum a 96-Regular Polygon when mapped on a Decimal Grid system.
Now I am going to go through a list of books that present Euclid's axiom of "point". For it is a Flawed Axiom that is self-contradictory.
GEOMETRY, 2nd edition Harold Jacobs, 1987, page 50 starts to talk about "points". Jacobs is following a practice that I suspect is dubious and flawed in that he insists on not defining "point".
Which reminds me of Edwin Moise "Elementary Geometry from an Advanced Standpoint" 3rd edition, 1990, pages, 43, 44, who does not define point and thinks that the axioms will specify what a "point" is. I am dubious of this claim.
Morris Kline, "Mathematical Thought From Ancient to Modern Times" volume 1, 1972, page 58, and where Kline writes the Euclid Elements definition of "point" as "1. A point is that which has no part." "2. A line is breadthless length."
AP writes: this caught me by surprise for I had remembered the Euclid definition as a Point has no length, no width, no depth. Could it be that "no parts" is the same as "no length, no width, no depth" ? No, I beg to differ that those two ideas are not the same. So I looked through other books to see if that was truly Euclid's definition of "point". So I go to Britannica-Great Books to see if "no parts" was Euclid's axiom.
Britannica "Great Books of the Western World" 1952, page 1, Book One Euclid Definitions 1. A point is that which has no part. 2. A line is breadthless length. 3. The extremities of a line are points. 4. A straight line is a line which lies evenly with the points on itself. 5. A surface is that which has length and breadth only. 6. The extremities of a surface are lines. 7. A plane surface is a surface which lies evenly with the straight lines on itself.
AP writes:: I see room for a-lot of mistakes there, especially the difference between straight-line and curved line. For AP, no continuum curves exist but rather instead, a large collection of tiny fine straight line segments all connected together to appear like a curve.
But let me get back to this idea of Point as having "no parts" and Point as having "no length, no width, no depth" to me those two are different definitions. And that the concept of Point from Euclid to 2026 AP was fatally flawed.
As I wrote earlier the true definition of Point must involve the infinity borderline which by tractrix computation is 1*10^-604. Hence, all points have at minimum 1*10^-604 length, and that amount of width and that amount of depth. When working in 10 Grid and borrowing up to 10000 Grid then the length, width and depth of a point can be 1*10^-4 long, wide, deep.
Modern day math with Quantum Mechanics Physics updates the definition of Point so that it is no longer a Self Contradictory definition.
A Point is Something. If it has no parts, or if it is metrically described as no length, no width, no depth means it is 0 long, 0 wide, 0 deep and 0 is Nothing. But a Point must be Something. Hence we have a self contradiction here. Proving that a Point must have some tiny finite metric. And this makes absolutely Common Sense for we know the length of a line distance is the summation of all its points. If points are 0, then all lines are 0 length.
Well-defined Numbers or else you have no Calculus
-------------------------------------------------------------------
Archimedes Plutonium Aug 3, 2026, 2:32:06 AM to Plutonium Atom Universe newsgroup.
Include this proof.
Archimedes Plutonium<plutonium....@gmail.com>
Aug 2, 2026, 6:26:31 PM (8 hours ago)
to Plutonium Atom Universe
So, now, already we are going to have an important proof in this research of Circle determination.
Statement:: The Reals cannot be the numbers of mathematics because any three noncollinear points in plane does not determine a unique circle. To find a circle from 3 arbitrary noncollinear points requires the perpendicular bisector. But many numbers are not divisible by 2. You can imagine them but geometry goes beyond imagination and wants you to put a compass needle into a midpoint or a circle center.
Proof:: The Decimal Grid Numbers starting with the smallest Grid of 10 grid are all numbers ending in 0s digits rightward 0, 0.1, 0.2, ...9.8, 9.9, 10. When the Decimal Grid Numbers are the true numbers of mathematics, given any two Grid numbers, you can find a midpoint distance between them. For example 1000 - 5.5 = 994.5 and divide by 2 = 497.25.
But using the Reals, we are caught in a fallacy of all irrational numbers cannot be divided by 2, and left in a Twilight Zone of Belief that a number like pi/2 or sqrt3/2. In other words, when we can no longer talk about a number without having a 2 divide into it, means, that math went berserk in believing such stupid numbers exist.
Decimal Grid numbers have nothing Irrational. For the entire concept of Irrational was a fake and a fiction.
The true numbers of math can all be written out without having a "dangling divide by 2".
QED
Archimedes Plutonium 12:30 AM to Plutonium Atom Universe newsgroup.
Explanation of Proof that Reals are fake numbers
------------------------------------------------
So we were trying to do a circle of geometry given 3 random points, noncollinear, where we measure the distance then find a midpoint which would thus be a perpendicular bisector to find a unique circle center.
In doing geometry we draw the circle by using a compass where the needle pokes a hole into the center and the pencil draws the circle that includes the 3 points on the circle.
Trouble with Reals when the distance length of A to B is irrational like pi or say square root 2 or square root of 3 or even that of Rationals, for A, B need not be irrationals to make it impossible to draw the unique circle but Rationals like 2/3, or 1/3 or many other Rationals. For 2/3 is 0.66666..... of endless 6 digit and where the center of the circle if distance length is 0.6666.... is 0.33333....... endless digit 3 in Old Math.
You see, it is impossible for our compass needle to poke a hole into pi/2, or sqrt3 / 2 or even find 0.3333..... as center.
Of course, in practice by engineers or dumb mathematicians they say 0.33333 is close enough and forget about all the 3 digits yonder.
But Math is all about precision, and never sloppy.
So, what is wrong here??? What is wrong is that the Reals are phony and junk numbers. They were created by math professors who never took Logic or failed logic. For they accepted the Reals as being a collection of different types of numbers to fulfill their idea of a continuum. They wanted a set of numbers that were continuous. Yet too stupid to stand up and listen to Max Planck in year 1900 when he announces that all of Physics is discrete in energy called Quantum Mechanics. Quantum means discrete, and discrete means a hole in between one number and the next number on the number line. The smallest discrete set of numbers in Decimal Grid Numbers is the 10 Grid which is a set of numbers, 100 of them not counting zero and looks like this 0, .1, .2, .3, . . .9.8, 9.9, 10. The next higher Grid is 100 Grid, next is the 1000 Grid on up to the 10^604 Grid and stops there because that is the infinity borderline.
The special thing to notice about Decimal Grid Numbers, is they all end to the right in a string of 0 digits.
This empowers the Decimal Grid numbers to always be divisible by 2, every last one of them divisible by 2. So that you can use a compass needle to poke a hole in a number.
No funny stupid numbers like pi/2 or square root 3/ 2 or the Rationals of .666.../2 or 2.173173173.../2.
Every Decimal Grid Number is divisible by 2 and leaves as answer, another decimal grid number for which you can take your Compass Needle and directly poke a hole into the number to actually draw the geometry circle.
This is Precision, and the reason Math Professors cannot see or understand their failings, is they are never required to take Logic in college before getting a degree in mathematics.
All Math Professors who teach the Reals failed Logic, because the Reals with their continuum will not allow you to have a valid proof of the Fundamental Theorem of Calculus, FTC. That is a proof that the derivative is inverse the integral and vice versa. If you try to prove FTC using the continuum of Reals you fail, and Old Math does a horrible failure with their dumb Limit-Analysis of a wiggle waggle dance on x and y axis. That is not a proof but a hornswaggle propaganda. Calculus is geometry and FTC can only be proven true by a geometry proof. Here is AP's most simple FTC proof.
Before I explain function, derivative, integral, let me show you pictures which sums it all up. These pictures are actually a proof of the biggest theorem-proof in calculus, called the Fundamental Theorem of Calculus.
From this:
B
/|
/ |
m /----|
/ |
|A |
|____|
a b
The trapezoid roof has to be a straight-line segment (the derivative)
so that it can be hinged at a midpoint m, and swiveled down to form rectangle for
integral. The area of the rectangle is the integral.
To this:
__m__
| |
| |
| |
---------
a b
So, we have two items in Calculus for this theorem, we have a derivative, the straight line segment A to B with m in the middle. And we have the rectangle area which we call the integral.
We draw in m, the midpoint because that is where we have a hinge, we imagine a hinge there. In fact, some teachers will build this model in wood working class just to use in math class.
So, Calculus has two items-- the derivative which is the rooftop, the straightline. And the other item, the integral which is the rectangle area.
I should include this proof of drawing a circle in my Logic textbook series to show how lousy Old Math was in almost everything it ever did, due to lack of Logic.
When Max Planck introduced quantum mechanics to physics in year 1900, every mathematician in the world should have had their ears and eyes perked up and listening and asking the question--- is not the continuum utter stupid mind-rot???
All of Logic requires WELL DEFINED Definitions
---------------------------------------------------------------------------
Two examples of Poor definitions-- physics -- "charge" and maths "point".
Two examples of Well Defined definitions-- biology's "DNA" and maths AP geometry proof of Fundamental Theorem of Calculus.
Now I am going to go through a list of books that present Euclid's axiom of "point". For it is a Flawed Axiom that is self-contradictory.
GEOMETRY, 2nd edition Harold Jacobs, 1987, page 50 starts to talk about "points". Jacobs is following a practice that I suspect is dubious and flawed in that he insists on not defining "point".
Which reminds me of Edwin Moise "Elementary Geometry from an Advanced Standpoint" 3rd edition, 1990, pages, 43, 44, who does not define point and thinks that the axioms will specify what a "point" is. I am dubious of this claim.
Clayton Dodge "Numbers & Mathematics" 2nd edition, 1975, pages 26 and 27 says:
"It follows that not all terms can be explicitly defined, for we do not have an endless supply of terms upon which to draw. And, of course, it is unthinkable to commit the "sin of circularity" by defining point in terms of line (say, as the intersection of two lines), and then turning around and defining line in terms of point (as a special collection of points)."
AP writes:: You see, Dodge, Moise, Jacobs would have immensely benefited if in college or university they had studied Logic for 2 years to know that what Logic says about Well Defining something, instead of leaving up to their notions.
In Logic, you have a choice--- you can well define "point" from other parameters. Or, you can use "point" in an axiom-postulate that describes what a point is. Either one you can use.
Continuing with Dodge : "How, then, are the primitive terms to be given precise meanings? By the postulates. These assumed statements involve the primitive terms and state their properties implicitly. The statement,
two points determine exactly one line,
tells something about points and lines."
AP writes:: Sorry to say, Euclid in Ancient Greek times had a better grasp of math geometry and of Logic than does Dodge, Moise, Jacobs.
For Euclid recognized that math proof is composed of (1) well defined terms (2) axiom-postulates (3) theorems as proofs using (1), (2).
A point needs to be Well Defined. It cannot be defined as having no length, no width, no depth for then it is Nothing, nothing at all and not a point.
Let me repeat what Euclid himself in Ancient Greek times does to "point". He defines "point" and defines "line". But if you make a point have a tiny length, tiny width and tiny depth, then you can have area and volume, otherwise you have nothing.
Britannica "Great Books of the Western World" 1952, page 1, Book One Euclid Definitions 1. A point is that which has no part. 2. A line is breadthless length. 3. The extremities of a line are points. 4. A straight line is a line which lies evenly with the points on itself. 5. A surface is that which has length and breadth only. 6. The extremities of a surface are lines. 7. A plane surface is a surface which lies evenly with the straight lines on itself.
What is needed is Physics with physical reality. Physics has Distance measured by a metric most often in meters.
No, what Dodge, Moise, Jacobs fail in realizing is that Physics is a Meta set above math geometry and which can easily provide a definition of point. Once a well-defined point and line is given then axioms of point and line can further detail what point and line are.
AP Definition of Point: A point has a minimal length, minimal width and minimal depth given a specific Decimal Grid System. The smallest metric is 1*10^-604 because the infinity borderline itself is 1*10^604. In other words, a Point in geometry is an entity that has the smallest finite metrics, otherwise there is empty space at that location.
You see, Dodge, Moise, Jacobs are living with a self contradiction, on one hand they say a point is Something, but a Something that is Nothing.
One of my best history of math books is Cajori, "A History of Mathematics", 1991.
I am curious to see if Cajori adds some new light or new angle on well-defined concept of "point".
--- quoting Cajori, page 26---
The Pythagoreans called a point "unity in position," but this is a statement of a philosophical theory rather than a definition. Plato objected to calling a point a "geometrical fiction." He defined a point as the "beginning of a line" or as "an indivisible line," and a line as "length without breadth." He called the point, line, surface, the "boundaries" of the line, surface, solid, respectively. Many of the definitions in Euclid are to be ascribed to the Platonic school.
--- end quoting Cajori---
AP writes:: Keep in mind it was Plato with his many students who gave a proof that the 5 Platonic Solids are the only existing regular polyhedron. You need immense well defined definitions and axioms to pull off a proof like that.
I was looking for when the first Graph paper was in use in the world. Wikipedia says the Metropolitan Museum of Art owns a pattern book dated to 1596 in which each page bears a grid printed with a woodblock.
The first commercial "coordinate paper" is attributed to Dr. Buxton of England.
I would have guessed Rene Descartes (1596-1650) would have used graph paper.
Cajori mentions Karl von Staudt (1798-1867) as graphic statics.
So, I wonder if Descartes had graph paper in his research?
Aug 18, 2026, 3:41:44 AM
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A strange but haunting idea comes to mind, not in 10 Grid, not in 100 Grid but say in 1000 Grid where it really blossoms.
In Decimal Grid Systems the true numbers and points of geometry are at the intersection lines of graph paper and in between are holes as empty space, as no numbers, no coordinate points.
So in True Geometry we have a lattice where in between every point is empty space, a tiny square of empty space. And where no curves exist for you need a microscope to see that a curve is actually tiny straight line segments.
So, the new idea here is and a haunting strange idea.
What if we made the tiny square between 4 coordinate points a Geometry Point itself.
So in 1000 Grid where the holes are 0.001 long and wide
* *
* *
What if we gave that hole as square and call it a coordinate point.
Or, well, say in 10^6 Grid, that hole would be so tiny compared to 10^3 Grid.
What I am trying to say, if we count in the holes as coordinate points, can we then find a Grid such that a mix of true coordinate points and using empty space holes, can we say the Curve can exist in such a structure.
A curve where the true point goes into a hole as coordinate point and thus call it a smooth curve.
Before this idea, I kept saying, a curve was reaching such a tiny Grid say 10^20 Grid, that you need a microscope to see that they are fine straight line segments.
Maybe I just best leave it at that--- fine straight line segments, for I cannot see any use in mixing true points with empty space squares as coordinate points.
Or, well perhaps I can see a use--- what if we graph a function as just the holes as points, because then we resemble some sort of continuity where the only break in continuity are the dot-points for the holes are large squares compared to dot points.
If I can find a use for making holes as the coordinate points, I surely will take this much more seriously.
AP, King of Science
Aug 18, 2026, 3:50:14 AM
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Conjecture:: In any grid system, 10 Grid, 100 Grid, 1000 Grid, whatever, no full circle can be drawn that is a dense concentration of points. We can make a dense concentration of points if we borrow from higher grids. But, can a circle be drawn in any graph paper to which that circle has no points involved at all, where the circle remains totally within empty space and does not intersect a single coordinate point???? I am guessing Yes.
If True, I am guessing that math can then resemble the Particle Wave duality of physics. The particle is the grid points, the intersection points. The wave form lies within the empty space.
AP
Aug 18, 2026, 6:01:15 PM
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p
Well-defined Point in Math Geometry
------------------------------------------------------
You see, Old Math had a definition of point as a contradiction in terms. They thought a point has no length, no width, no depth. In other words a point is Nothing at all. A contradiction, for a point has to be something, not nothing.
Well-defined Point in Math Geometry
------------------------------------------------------
You see, Old Math had a definition of point as a contradiction in terms. They thought a point has no length, no width, no depth. In other words a point is Nothing at all. A contradiction, for a point has to be something, not nothing.
So a point in physical reality must have some dimensions of length, width, depth. And the question then becomes, where do we find those small microscopic dimensions that a point has???? We go to Huygens and the history of the curve Tractrix.
We go back to the history of Tractrix by Huygens. And we look for when the area of a circle involved is equal to the area of the tractrix under the function graph. The answer is that when pi digits has its first three zeros in a row at 10^-601, 10^-602 and 10^-603, does the area of Tractrix becomes equal to the area of specific starting circle.
pp
--- quoting Wikipedia---
Tractrix
Tractrix created by the end of a pole (lying flat on the ground). Its other end is first pushed then dragged by a finger as it spins out to one side.
Tractrix created by the end of a pole (lying flat on the ground). Its other end is first pushed then dragged by a finger as it spins out to one side.In geometry, a tractrix (from Latin trahere 'to pull, drag'; plural: tractrices) is the curve along which an object moves, under the influence of friction, when pulled on a horizontal plane by a line segmentattached to a pulling point (the tractor) that moves at a right angle to the initial line between the object and the puller at an infinitesimal speed. It is therefore a curve of pursuit. It was first introduced by Claude Perrault in 1670, and later studied by Isaac Newton(1676) and Christiaan Huygens (1693).[1]
--- end quoting Wikipedia---
ppp
Aug 18, 2026, 6:32:26 PM
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Max Planck in year 1900 said that all of physics is discrete, not a continuum. However, math professors were morons and could never ask the question, if all of physics is discrete, should not all of mathematics be discrete??? When you are a moron in logic, you never ask those questions.
So in Geometry math we have graphing of functions on graph paper.
--- quoting Wikipedia---
Graph paper
Mathematical tool
--- end quoting Wikipedia---
So the question becomes, Since all of Physics is Discrete, then all of math geometry must also be discrete, the question becomes when does the empty space holes become equal to the small finite dimension of a point??? Where a Point that is well-defined and has a tiny length, a tiny width, and a tiny depth. The answer comes from watching a Tractrix, when its area under the graph equals the representative circle area. That is the numbers 10^-601, 10^-602, 10^-603 digit place value of pi.
Here are those digits of pi---
3.141592653589793238462643383279502884197169399375105820974944592307816406286 208998628034825342117067982148086513282306647093844609550582231725359408128481 117450284102701938521105559644622948954930381964428810975665933446128475648233 786783165271201909145648566923460348610454326648213393607260249141273724587006 606315588174881520920962829254091715364367892590360011330530548820466521384146 951941511609433057270365759591953092186117381932611793105118548074462379962749 567351885752724891227938183011949129833673362440656643086021394946395224737190 702179860943702770539217176293176752384674818467669405132000568127145263560827 785771342757789609173637178721468440901224953430146549585371050792279689258923 542019956112129021960864034418159813629774771309960518707211349999998372978049
Aug 18, 2026, 6:39:56 PM
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In other words, the world looks continuous, when a point is so small that you need a microscope to see the points.
Look at that largest graph paper where the empty space is large.
Now look at the graph paper of those 4 graphs above with the smallest holes of empty space.
When you make the holes of empty space so small, that you cannot tell empty space from the size of an actual POINT in the plane, that is where you can have curves like the circle, like the ellipse, like the tractrix, but still, in actuality they are a string of so very fine straightline segments, but the human eye cannot tell that they are such, but sees them as smooth curves.
AP
Aug 19, 2026, 12:45:15 AM
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Please indulge with me for a moment, where we make the graph paper--- turned around --- instead of square blocks with points as intersection, we make round circles as Points and the interspace between circles we make those be the empty space.
So look at a typical graph paper such as above. You see the Points of Geometry are the intersection lines, and where the empty space is all that in between. Here we make dots as the Points of geometry. We see this in some of the below pictures.
I bring this up, because, when we make dots as the Points, we can more easily draw Curves as the joining of one dot to the next dot.
Now Physics may also allow this Total Conversion, where dots are the points and where empty space is hyperbolic empty space. Notice below the Rhino with all those curves and some empty space.
What I am saying is, Convert tiny squares in Graph paper to be round dots, which are now the Points of Geometry. And where the hyperbolic empty space is now replacement of the tiny squares.
Note: Take special notice of that 2D rhino below, for the Dot Circles makes that figure to be 3D. The artist there on that Rhino, is a most exquisite artist and has found a secret of making 2D appear to be 3D. I would go so far as to say, that artist has created a new category of Art Work, an exquisite category.
AP, King of Science
pp
--- quoting a Google search of "circle packing"---
ppp
Aug 19, 2026, 6:22:51 PM
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The question becomes, can a rhinoceros can be drawn using squares instead of circles??? I would guess--- NO.
Aug 19, 2026, 6:32:40 PM
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The Logical Point of Math Geometry
--------------------------------------------------------
So, well, Old Math had the dumb stupid idea that a geometry point has no length, no width, no depth.
So, anyone believing in that stupidity, has no logical marbles.
If Something has no length, no width, no depth, means....... LOGICALLY it is Nothing.
It is not a point unless it has a finite length, a finite width, a finite depth.
A something has a finite dimensions even though it is microscopic small, it must be a finite number.
So, no math professor from Ancient Greek Euclid had enough logical brains to understand that Something requires finite length, finite width, finite depth.
No-one in the history of Math had enough logical brains to understand that if you have Finite versus Infinite, Logically means, -------- You have to have a borderline between finite and infinite.
With no borderline, means there is nothing finite, nor infinite. All is one, if there is no borderline.
But no math professor in the entire history of public education, no math professor was forced or required to take Logic in College or University to help that person to think straight, think clearly, think correctly.
And so, well, no wonder math professors were sucked in and fooled by thinking a Point can exist that has no length, no width, no depth.
AP, King of Science
Aug 19, 2026, 6:43:27 PM
Aug 19, 2026, 8:16:13 PM
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Is the Tractrix Unique Curve in that it is the only one that goes to infinity--- infinite Reach, but finite internal area????
----------------------------------------------
So Huygens studied and researched the Tractrix and found out key essential features thereof.
Then along comes AP in 2009, realizing that Geometry and Number-Algebra theory of mathematics is required to have a borderline between finite and infinity, but where to look?????? The answer came from Huygens Tractrix. Look for where the INFINITE REACH of the Tractrix equals the area of a circle of radius 1, of the area of the Tractrix under the function graph curve.
The first time that the area of Tractrix under function graph curve in 1st Quadrant Only equals the area of unit radius circle is in the digits of pi at 10^-601, 10^-602, 10^-603 where the tractrix adds on area, but the circle adds NO more area in those three digits. The Tractrix fully caught up to the circle area, and may have even surpassed the circle area (as yet to be found out).
Borderline between finite and infinity
Now this mistake in not having a correct Infinity in math, affects the Calculus by a large measure, a large degree. It is impossible to have a correct calculus, when you have a bozo-kook understanding of what is infinity.
This is probably the biggest mistake in all of pure mathematics for it
affects all other mathematics. Of course the other sciences, especially physics rarely needs to know what the correct proper infinity is. However, it does show up frequently in the best physics-- quantum electrodynamics, in which it is
often used to eliminate infinities that crop up in calculations. This physics math procedure is called Renormalization-- getting rid of the infinities.
The trouble with Old Math, is, well, they were terribly shoddy in logic, in thinking straight and clear. For a logical person, knows, that if you have a concept of finite versus infinite, the only way to handle those two concepts is to realize a border must go between them so that you can tell if any given number is finite or infinite. Otherwise, there is no infinity, if there is no borderline.
There is only one way you can have a concept of finite, by having a
concept of infinity, and the only way you can have both, is that a
borderline exists between them.
I have pinpointed that borderline from tractrix-circle analysis, from
algebraic analysis of algebraic completeness, and from angles of
regular polyhedra. The borderline in microinfinity is 1*10^-604 and in
macroinfinity is 1*10^604.
The easiest way to see the borderline is to see where pi digits ends in a three zero digits in a row.
3.141592653589793238462643383279502884197169399375105820974944592307816406286 208998628034825342117067982148086513282306647093844609550582231725359408128481 117450284102701938521105559644622948954930381964428810975665933446128475648233 786783165271201909145648566923460348610454326648213393607260249141273724587006 606315588174881520920962829254091715364367892590360011330530548820466521384146 951941511609433057270365759591953092186117381932611793105118548074462379962749 567351885752724891227938183011949129833673362440656643086021394946395224737190 702179860943702770539217176293176752384674818467669405132000
Since the Universe 3rd dimension, one would suspect that where pi digits are there first three digits in a row of 000, that such would be the borderline at infinity.
Now, for physics, that infinity is 1*10^604 for large and 1*10^-604 for the small, makes perfect sense, since in physics, it is extremely, extremely difficult to find anything above 10^200 or smaller than 10^-200, to give the reader a sense of proportion.
Now, for physics, that infinity is 1*10^604 for large and 1*10^-604 for the small, makes perfect sense, since in physics, it is extremely, extremely difficult to find anything above 10^200 or smaller than 10^-200, to give the reader a sense of proportion.
Back to the starting question, is there another curve that is infinite in reach yet finite in area. I mean---- a specific curve with a programmed formula. The Tractrix program is push a rod along the x-axis or pull a stop watch on the x-axis.
Not just any imagined curve, but a curve with a program of formation.
AP, King of Science
Aug 19, 2026, 9:02:37 PM
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Tracing through the Logic of the Geometry Point
-------------------------------------------------------------------------
It must have some dimensions, even though they are microscopic.
For something to exist, it cannot be zero length, zero width, zero depth. Something has dimensions, and Nothing has zero dimensions.
We look for the Infinity borderline in mathematics. It must have a infinity borderline else, everything is finite, and no infinity exists.
The only curve that I know of that has finite Area yet Infinite REACH is the tractrix.
From the Tractrix, it catches up the corresponding unit radius circle in area at the digit place value of 10^-601, 10^-602, 10^-603, meaning that 1^10^604 and beyond and its inverses are all infinite numbers.
That means the circle of 10^-603 is the smallest possible Finite number to exist and a radius of a circle of that amount is the length the width and depth of a Geometry Point.
With the Geometry point of that dimension, we can draw any curve as a string of circle-dot-points.
AP, King of Science
Aug 19, 2026, 11:26:21 PM
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So, looking at this picture in the Google search of tiling the plane with circles instead of with squares.
Can you see that hexagon that outlines 6 circles that surround a interior circle? The emtpy space between circles as points are small hyperbolic V shaped empty space. While in a plane tiled by squares, the empty space is huge.
But the main reason I point you to this above figure, is when the POINT in geometry is a circle and not a intersection of lines in a graph, the Points as circles allows us to draw Curves, and the circle is a great curve.
AP
Aug 20, 2026, 3:41:08 AM
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So let us examine the square packing that is regular graph paper where the empty space is large, and the points are the mere intersections of horizontal and vertical lines.
Contrast that with a graph paper made of circles where the circle itself is the Point and the empty space are these hyperbolic quadrilaterals looking somewhat like this. In circle graph paper, the points take up most of the paper.
<^>
In regular graph paper the holes of empty space are squares and take up most of the paper.
___
| |
But better yet, when we have circle hexagonal packing as graph paper our holes are as tiny as possible with a hyperbolic triangle. And in circle hexagonal packing, we see that the world's smallest circle is 6 points.
--- quoting Wikipedia---Graph paperMathematical tool
Aug 20, 2026, 3:57:01 AM
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Now the below is interesting as it is a ellipse in 2D composed of just 6 points.
Previously I said the world's smallest circle, since all points have a finite length, finite width, finite depth. And below we see the world's smallest ellipse composed of just 6 points. The difference between circle and ellipse is the center of the circle is a Point identical to the 6 circles that form the circle. In the ellipse, the center is 2 points approximately half the size of the ellipse 6 points.
So I can make up at least two theorems of Geometry.
Theorem A:: The smallest circle in the world is composed of 6 points with the center of the circle the 7th point.
Proof:: Just look at the picture.
Theorem B:: The smallest ellipse in the world is composed of 6 points with the center being 2 circles approximately half the size of a ellipse circle. Proof: Just look at the picture.
A-lot of geometry proofs in New Math are simple statements of --- just look at the picture.
Old Math was too illogical and ignorant, for they never required mathematicians to take logic and end up with stodgy, stiff, dull proofs, like their invalid proof of Fundamental Theorem of Calculus using limit analysis, wiggle waggle dance on x,y axes.
pp
ppp
Aug 20, 2026, 5:39:19 PM
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Now in that image below we can get a oval if we remove one of the smaller blue circles. and put a red circle where the missing blue circle was.
This would lead to the Theorem C:: The smallest possible Oval is composed of a odd number of Circle Points. The smallest ellipse and circle in geometry would be composed of 6 circle Points.
Now we have to investigate whether the Ancient Greek Axiom --- two points determine a Unique Line once we Well-Defined what a Point is.
But first, we have to Summarize what we have so far. We have, in fact, two types of geometry, one where a Graph is horizontal and vertical lines intersection that are Coordinate Points with empty space being large squares, and the other is where the Graph is round circles as Points and the hyperbolic triangle or hyperbolic quadrilateral are empty space.
In the square space, we cannot form smooth curves like circles or ellipses or tractrix. But in the square space we do have the Axiom that 2 points determine a unique straight line segment. Even though the Point has a finite length, finite width, finite depth.
On the other hand in round circle space, I am not sure that 2 Points as circles has a unique line, for the lines in round circle space are smooth curves.
What it looks like is that once we Well Define Point, the question of all the other axioms of geometry are up for scrutiny.
Aug 20, 2026, 9:20:38 PM
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So geometry is forced to Well-Define a Coordinate Point of the plane or 3D.
A coordinate Point must have a tiny finite dimension of length, width, depth. We found that the infinity borderline is 1*10^604 with inverse. It is where pi has 3 zero digits in a row at 10^-601, 10^-602, 10^-603.
Geometry can be either the square or cube geometry or the circle or sphere geometry.
Every point in geometry must have a length width and depth.
And every point in geometry can be either a square or a circle in 2D, or a cube or sphere in 3D.
We cannot get any smooth curve in Square tiling the plane, but if we slide over the circles in 2D we have smooth curves appear. The smallest circle and ellipse are 6 coordinate points, as shown in pictures earlier.
So Geometry, logically starts with Well Defined Coordinate Points, and they come in two types.
This means, we have to scrutinize the next Axiom of geometry that says--- two points determine a unique straight line segment.
Obviously that axiom needs correction.
It is alright for the square-lattice geometry but falls apart in the circle lattice geometry.
So how do we fix this second axiom???
AP, King of Science
Aug 21, 2026, 12:08:35 AM
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As I am working to solve this problem of how the Axiom--- two points determine a unique line segement given the well-defined point is either a square or round circle with finite dimensions, an Extraordinary Idea comes to mind. And I need a proof of this idea.
You see, 6 circles makes the smallest circle in the world and how do we draw lines connecting those points???
Conjecture:: I have a square in the plane, now, I rotate the same square to where the vertices become the 4 midpoints of the 4 sides of original square. The conjecture is, is the area of what sticks out from the original square, the same area as what an enclosed circle is inside the original square, subtracted from the square area????
Example: A square of side 2 has area 2^2 = 4. The area of enclosed circle has radius 1 and thus area of 3.14 x 1^2 =3.14. Thus 4-3.14 =0.86. The question I am asking in the Conjecture is when I rotate the same square above a given square, the maximum area that sticks out, jutts out, whether that area is 0.86, so that a small triangle of 0.86/4 =0.215 composes those 4 triangles?
Now, nowhere would a question like that ever come up, unless one is trying to mediate the problem of Points of geometry as both square lattice and circle lattice.
AP, King of Science
Aug 21, 2026, 1:28:16 AM
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I always like to do modeling first, for it is quicker, easier and more compelling than doing algebra.
If I take two identical squares, one on top of the other and the bottom one stationary, top one rotate on center axis over the other square, the vertices of the top square etch out a disc on each square side and the 4 discs match the area of 0.86 described below in the enclosed circle.
So now, I have always believed in a line a having only length, no width no depth. In New Math, a point has a tiny length, width and depth. This demands and forces that a line itself has more than just a length but also a tiny width and tiny depth.
The Line in Geometry can be either a straight line or a curved line segment.
Sadly, I need to go back through all my previous books where I said no curves exist in math, only tinier fine straight line segments.
When I claimed above that those 6 Points as circles forms the world's smallest circle other than the point itself, I have to view those 6 points as a curved line segment that connects any two of those 6 points.
In a square lattice we form straight line segments. In a circle lattice we form curved line segments or we can form straight line segments.
Aug 21, 2026, 5:23:23 PM
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Alright, yesterday I found myself in a predicament but has it solved for the time being.
I wanted to know that starting out with the true axiom of Point, for it has a tiny finite dimension of length, width, depth.
You see, if stupid mathematicians were forced to take Logic in college and university would more easily come to understand that something with no length, no width, no depth is NOTHING and being nothing means it does not exist.
Now the next Axiom of mathematics to exist, given the first axiom is the coordinate point. The second axiom following the first axiom would have to be what a line is in geometry. We know a Point has a tiny finite length, width, depth on the order of 10^-603 or 10^-604, so our Second Axiom wants to establish what a Line is all about when we say Two Points determine a Unique Line segment.
We draw inspiration, always from physics. We see in physics Quantum Mechanics and duality--- particle-wave duality, better yet electricity-magnetism duality. Which of the two in physics, the electricity or the magnetism is the particle???? Well, both need a circuit. You have no electricity without a circuit. You have no magnetism without Lines of Force.
So the categories of particle to wave is a stupid and error filled description of Physics, of physics professors that are dumb in logic. It is Particle to Circuit Duality.
In Physics, we Truly have Electricity to Magnetism duality. And if you prefer, you can call that Particle to Circuit Duality. A photon of Light is a Circuit because all its energy has no rest mass. It is ____not a ray of Light____ but a circuit of light. A proton or muon or magnetic monopole are particles for they have rest mass.
But now, well, I can replace particle and circuit duality with a geometry concept of Square and of Circle duality.
So, start with a drawing. Draw a square that is sides 2 by 2. Its area obviously is 4. Now inside the square draw a maximum circle enclosed by the square. Its radius is 1, and its area turns out to be 3.14... Now we go further and draw another square inside the circle we found of area 3.14... This smaller square has sides of 1.414 using the pythagorean theorem of 1^2 + 1^2 = s^2 where s = 1.414.... The area of this new square is what??? It is obviously area of 2. Our original starting square had area of 4, and this new square is 1/2 of that. Now we ask, is the new circle we enclose within the square of area 2, is that new circle 1/2 the area of previous circle of area of 3.14???? Yes of course for area of circle is pi r^2 and the radius is 0.707 when squared is 0.5 and that is one half the area of 3.14...
So what we have here in terms of algebra, is the circles infinite regression by 1/2 and the squares infinite regression of 1/2.
All my life long until now, I viewed the Line, whether finite or infinite as having length but no width and no depth
---------------------------------------------------------------
It is time for a change, in that a Coordinate Point in True Geometry has a finite length, a finite width and a finite depth.
A coordinate point in geometry, like Physics can come in two types, a duality. A coordinate point can be a square or it can be a circle. This is another duality in Nature, for we have particle to circuit, and electricity to magnetism and now a square to a circle.
What is the Axiom now, for 2 Points determine a Unique Line?
--------------------------------------------------------
I have already shown that 2 points in the plane determines a Unique Circle, where one of the points is the center of circle and the other point serves as a distance radius with that point on the Rim of the circle.
In Old Geometry, they had only one idea on 2 points determine a unique line. We accept that idea but place it into the Square Lattice Plane. The Circle Lattice Plane has all circles. The square-lattice plane is our familiar old Graph paper.
So our Second Axiom of Geometry: 2 Points in Plane determine a unique line in Square Lattice Plane, but, we must not forget those same two points determines a unique circle if we replace square lattice with circle lattice.
Now, how do we re-imagine a Line, or line segment that has length, but also a finite width and depth???
------------------------------------------------
This is the tricky part of this examination of Line. Somehow we have to consider a line to infinity or a line segment is like a Wire, the thinnest wire imaginable and where that wire can switch from being round circular to square straight.
In other words, sad for me, for now we have curves that Exist, when decades ago I said no curves exist but are tiny fine straight line segments. Sadly, because I have to go back and make massive editing of all my prior books.
When in Physics reality we have 4 microscopic points such as this
* *
* *
Those four points could be both a circle curve and the points part of the circle lattice, or they can be a square with points from square-lattice and straight line segments between the four points.
Now looking at the world's smallest circle in this picture again.
So, looking at this picture in the Google search of tiling the plane with circles instead of with squares.
How should we see those 6 points drawn as a Curve, a circle curve???
We take a fine wire that goes through the 6 circle centers plus passes through the points of intersection of each 6 circles.
Since those are microscopic points, our curved line will appear more like a band, a tube like wire.
For straight lines horizontal, vertical, diagonal, we duality shift out of circle lattice and into square lattice. The points are square, and the wire of straight line are rectangular boxes.
AP, King of Science
Aug 21, 2026, 9:14:55 PM
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I find no hardship, in these 30 years of writing science, except that of having to go back and edit and correct previous ideas. Somehow that lays a psychological burden on my mind. Having to go back and where I wrote ___ no curves exist, for they are ever smaller fine straightline segments strung together___.
So here, I find that while correcting the first two axioms of geometry math--- points have finite dimensions, and two points determine a unique line, they can also determine a unique curved line like a circle.
The burden of going back weighs heavily on my mind.
But it shows the Importance, essential importance of having Logic in science. This development, afterall, arose in writing a Logic textbook for High School and 1st year college. Who would have thought that such a project would end up revolutionizing all of geometry, first by correcting geometries 1st axiom--- what is a point and then geometries 2nd axiom-- two points determine a unique line.
But these changes are all warranted by Physics for physics has duality of electricity to magnetism, of particle to circuit and so math geometry has a duality of point as square lattice and point as circle lattice. A duality of straightline versus curved line and the two can switch from one to the other.
AP
Aug 22, 2026, 12:23:12 AM
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How should we see those 6 points drawn as a Curve, a circle curve???
My mistake in the below description and correction to it.
We take a broad wire that goes through the 6 circle centers plus passes through the points of intersection of each 6 circles where the wire even envelopes some of the empty space of hyperbolic triangles..
Aug 22, 2026, 12:38:11 AM
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In fact, we can picture this circle of 6 points in the plane by a circle that is in 3rd Dimension that like a ring goes around the 6 planar points.
The same can be done in Square lattice of straightlines. Where we take a square slightly larger than the planar squares and move it along the straightline Points to well define the horizontal, diagonal especially, and vertical lines in Square lattice plane.
P.S. Is there any immediate gifts when points of geometry have this duality of being either square or circle with finite length, finite width, finite depth.
There is an exceedingly important feature of Quantum Mechanics that is little understood. It is called quantum intrinsic spin. It is a quantum number of 1/2. It is in the Stern-Gerlach Experiment, for we have N, L, M_L and finally M_s a spin quantum number.
When we look at a Point in Geometry as having finite dimensions of length, width, depth and can switch from a Square Lattice to a Circle Lattice, there and back, we are dealing with a SPIN.
AP, King of Science
Aug 22, 2026, 4:46:57 AM
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So, well, Revising all the Geometry Axioms and starting as the first axiom the Point, being well defined. Logic says that if something has no length, no width, no depth then nothing there exists and so you have no point. To fix that error of Logic, you have to say a Point, a Coordinate Point must have a tiny finite length, a tiny finite width and a tiny finite depth.
That as the first axiom of geometry forces us to define distance length and forces us to have 1st dimension, 2nd dimension and 3rd dimension for a Point is a 3rd dimension object.
The second axiom of geometry would well define what is meant by 2 Points determine a unique line. The points can be square-lattice points or can be circle lattice points.
We have to go to the Tractrix to find a infinity borderline to tell us the limit of distance length, for it is 10^-603 region where we have three zero digits in a row in pi digits and the Tractrix area under the function graph has caught up with the unit circle area for the first time. Remember, a Tractrix is one of those figures that has Infinite Reach, yet still having finite area.
So what would be a third axiom in the revised Geometry axioms??? I dare not use Euclid's axioms for they are ancient. I rather look at some modern set of axioms.
Looking in Jacobs GEOMETRY, 2nd edition, 1987, on page 647, he calls them postulates, while I call them axioms. And he lists the first 7 postulates.
Interestingly he does not give Points as a axiom.
Let me quote Jacobs first 5 axioms.
Postulate 1 : If there are two points, then there is exactly one line that contains them.
Postulate 2 : If there is a line, then there are at least two points on the line.
Postulate 3 : If there are three noncollinear points, then there is exactly one plane that contains them.
Postulate 4 : If two points lie in a plane, then the line that contains them lies in the plane.
Postulate 5 : The Ruler Postulate : The points on a line can be numbered so that
(a) to every point there corresponds exactly one real number called its coordinate,
(b) to every real number there corresponds exactly one point,
(c) to every pair of points there corresponds exactly one real number called the distance between the points,
(d) and the distance between two points is the absolute value of the difference between their coordinates.
AP writes: Well Harold Jacobs makes some mistakes above that need correction.
Postulate 1 : If there are two points, then there is exactly one line that contains them.
This should read--- Given any two points, they determine a unique line.
That is much better logically for the word "exactly" is out of place and you need the word "determine".
Postulate 2 : If there is a line, then there are at least two points on the line.
Jacobs probably never studied logic, for when you say "Given any two points determines a unique line." Is in logic a If A then B, and if B then A ends up being A = B. So that one sentence covers both postulate 1 and 2.
Postulate 3 : If there are three noncollinear points, then there is exactly one plane that contains them.
AP writes: Yes, I am looking for a plane axiom in the my revised axioms. But I will need to well define plane because points are 3 dimensional with length, width, depth. And according to Jacobs, a plane ends up being a vast sheet of points which have depth, yet his plane has no depth.
So another major fault of Old Geometry, is they all knew that volume of a rectangular box was its length multiplied by planes of width x depth. But if the planes have 0 depth, there is always 0 volume in the multiplication. This is another major flaw of Old Geometry.
Postulate 4 : If two points lie in a plane, then the line that contains them lies in the plane.
AP writes: no complaint, but keep in mind the points are 3D, the line is 3D and the plane is 3D.
Postulate 5 : The Ruler Postulate : The points on a line can be numbered so that
(a) to every point there corresponds exactly one real number called its coordinate,
(b) to every real number there corresponds exactly one point,
(c) to every pair of points there corresponds exactly one real number called the distance between the points,
(d) and the distance between two points is the absolute value of the difference between their coordinates.
AP writes: A-lot of mistakes here. The above should read like this.
Postulate 5 : The Ruler Postulate : The points on a line can be numbered so that
(a) to every point there corresponds exactly one Decimal Grid number called its coordinate,
(b) to every Decimal Grid number there corresponds exactly one point, and Decimal Grid numbers have no negative numbers.
(c) to every pair of points there corresponds exactly one Decimal Grid number called the distance between the points,
(d) and the distance between two points is the absolute value of the difference between their coordinates.
So far, AP has two axioms and looking for his third in New Geometry.
AP axioms
---------------
1) A point in geometry is a 3 dimensional figure with a tiny finite length, finite width, and finite depth. The limit of this finite is the infinity borderline 10^-603 ending at 1*10^-604 as determined by the 3 zero digits in a row in pi.
2) Two points determine a unique circle in 3D space using circle-lattice points, and a straight line in 3D using a square-lattice points.
3) Three noncollinear points determines a unique plane. Since points are 3 dimensional with length, width, depth a plane is 3 dimensional with length, width, depth. But the depth of a plane must be a quantum discrete 1 point.
Also, in the definition of plane, it can be either a square-lattice plane or a circle-lattice plane and cannot mix the two. Perhaps the lattices can switch from one form into another.
Just today in the mail I received SCIENCE NEWS, Sept 2026 and they have an article on Static electricity saying "But what actually causes electric charge to leap from one object to another remains elusive. Centuries of efforts by scientists have failed to solve its mysteries--"
We all know that circuits of electricity require smooth curves, for if you have vertices in a circuit, the magnetic monopoles 0.5MeV particles tend to leap off at the vertex.
AP, King of Science
Aug 22, 2026, 6:42:41 AM
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On Saturday, August 22, 2026 at 4:46:57 AM UTC-5 Archimedes Plutonium wrote:
(snipped)
AP axioms---------------1) A point in geometry is a 3 dimensional figure with a tiny finite length, finite width, and finite depth. The limit of this finite is the infinity borderline 10^-603 ending at 1*10^-604 as determined by the 3 zero digits in a row in pi.
2) Two points determine a unique circle in 3D space using circle-lattice points, and a unique straight line segment in 3D using a square-lattice points.
3) Three noncollinear points determines a unique plane. Since points are 3 dimensional with length, width, depth a plane is 3 dimensional with length, width, depth. But the depth of a plane must be a quantum discrete 1 point.Also, in the definition of plane, it can be either a square-lattice plane or a circle-lattice plane and cannot mix the two. Perhaps the lattices can switch from one form into another.Just today in the mail I received SCIENCE NEWS, Sept 2026 and they have an article on Static electricity saying "But what actually causes electric charge to leap from one object to another remains elusive. Centuries of efforts by scientists have failed to solve its mysteries--"We all know that circuits of electricity require smooth curves, for if you have vertices in a circuit, the magnetic monopoles 0.5MeV particles tend to leap off at the vertex.
Now I need to be really careful here about the Plane definition because on whether a surface of a sphere is a plane that is 1 point thick?
A sphere surface as plane would be a closed-plane contrasted to the Old Geometry plane as not closed but open.
Because if the sphere surface or ellipsoid surface or Ovum surface are planes, or even triangular wedges surface or rectangular boxes surface of 1 point thick are planes then I may get into trouble with the prior axiom of " Two points determine a unique circle or a unique straightline segment.
If not careful, I could easily have two axioms contradict one another, quite rapidly.
AP
Aug 22, 2026, 5:20:13 PM
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Some Good news, some bad news. First the bad news.
I need to start over with the axioms because the ones I have deliver a contradictory Plane.
The big problem is the number Zero which stands for "nothing" when it should be something.
In Ancient Greek times, they had a physical problem of not being able to Square the Circle.
In modern times, AP is having the physical problem of being able to "poke a hole with a compass into a point that is zero". Poking a hole into nothing is logically unsustainable.
The Good news is I have resolved the physical problem of Squaring the Circle by noting the fact, that when you start with a square and find the inscribed circle, then find the circumscribing circle of that same square, then, finding the inscribed square of the larger circle, that the 2 circles are equal in area by a factor of 1/2 and the 2 squares are equal in area by that same factor of 1/2. In other words a square and circle are duals of one another.
Duality is what I need to start the axioms of geometry in order to get the true axioms of the Plane.
Start with Axiom 1 :: as duality exists in forms such as electricity to magnetism, as particle to circuit, as geometry to numbers, as circles to squares, as nothing to something for within something lies nothing and within nothing lies something. Duality means one form switches into the other form because they are one and the same.
I could not get a plane of geometry without contradicting my other axioms, so what is Axiom 2 when Axiom 1 is duality???
Axiom 2 : The point in geometry must have a tiny microscopic length, width, depth that is obtained from the inverse of the infinity borderline and is the number 1*10^-604, where 10^-601, 10^-602, 10^-603 are the place value digits of pi where it has 3 zeros in a row so that the Tractrix area catches up with the unit circle area. Tractrix has infinite reach but finite area.
Axiom 3: A point with at minimum has a length of 1*10^-604 and the same for width and depth. This insures that one can poke a hole in a point with a compass and produce a circle from that point, and the circle produced from that point produces a square, inside the circle and outside the circle in which the two squares are equal in area by a factor of 1/2 inversely a factor of 2.
Now I need to bring in Jacobs Ruler Measure Axiom (Postulate). I need to do that because I cannot poke a hole into the number 0. Strange, that I have to start with 1 then gain the number 2 to determine where 0 lies.
Axiom 4:: now I introduce the Line in Geometry where a Point is having length, width, depth that I can poke a hole and use a compass to construct a circle then square. A line is constructed from 2 points as a straightline as the sides of a square, or as the radius of a circle with one point as center and the other point as rim of circle. Two points determine a unique line whether a circle or straightline. Notice, zero is not involved.
Axiom 5:: is the Ruler Measure axiom
The Ruler Postulate : The points on a line can be numbered so that
(a) to every point there corresponds exactly one Decimal Grid number called its coordinate,
(b) to every Decimal Grid number there corresponds exactly one point, and Decimal Grid numbers have no negative numbers.
(c) to every pair of points there corresponds exactly one Decimal Grid number called the distance between the points,
(a) to every point there corresponds exactly one Decimal Grid number called its coordinate,
(b) to every Decimal Grid number there corresponds exactly one point, and Decimal Grid numbers have no negative numbers.
(c) to every pair of points there corresponds exactly one Decimal Grid number called the distance between the points,
(d) and the distance between two points is the absolute value of the difference between their coordinates,
(e) and, once we have 1 and 2 in integers Decimal Grid, we draw the circle from point 1 to 2 and the radius comes back around 360 degrees to the number 0 and we can then say we form a "poke hole by compass needle" that creates a Zero number hole, even though zero is empty space and has no length, width, depth,
(f) and this axiom introduces angle into geometry, where the full circle is 360 degrees and the square has 4 right angles of 90 degrees.
Axiom 6:: So we have a Point, and a Line, now we need an axiom of the Plane. That axiom of Plane involves the extension of all the numbers on the line from 0 to infinity borderline and all the Points of the plane having all the finite numbers of length and width, but only 1 unit thickness, a quantization discrete unit thickness. The dimensions of point are x,y,z and the x,y can have any numbers to infinity borderline, but the z value has only one value, that of the value of distance from 0 to the Decimal Grid induction number. In 10 Grid it is 0.1, in 100 Grid it is 0.01, in 1000 Grid it is 0.001 out to infinity borderline.
The above eliminates the Contradictions.
Axiom 7 :: the axiom of volume:: Space is composed of 3 dimensions represented by x, y, z axes. In two dimensions we have Planes, in one dimension we have lines. In 2 dimensions we have area, and in 3 dimensions we have volume. The calculation of area is length times width. The calculation of volume is the length of planes that compose the geometry figure.
So in New Math of revised Euclid Axioms, since planes have a small depth, we just multiply the number of planes which is the length of the figure to obtain the volume. In Old Math, Old Geometry, their volume was a multiplication by zero which ends up being 0 volume.
Now there was tremendous raucous in the history of Euclid axioms over the parallel postulate, when there never needed to be any raucous. Next I examine how New Math, New Geometry views the Parallel Postulate.
AP, King of Science
Aug 23, 2026, 12:34:43 AM
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Alright, let us inspect what New True Geometry, when a point has a tiny finite length, width and depth possess, related to the Parallel Postulate.
First, let me describe how I handled the so called alleged 3 types of geometry of Euclidean flat, Riemannian elliptic and the Lobachevsky hyperbolic, which came out of the Parallel Postulate. I accepted the 3 types myself, until I saw a better idea. Some year in the past I came up with the idea that Euclidean Geometry was equal to Riem geometry unioned with Loba geometry. In other words, Riem and Loba geometry were fragmented Euclidean plane geometry and thus Only One Geometry existed.
Mind you, these 3 types of geometry in Old Math were considered independent. I considered them all just one of Euclidean Geometry.
But now, that I am creating a New True Geometry, let us inspect the Parallel Postulate that so fascinated Old Math math professors and which lead them astray. It all starts with the fact that Old Math professors were logically stupid fools who could never think straight. For example, they all believed a Point has no length, no width, no depth. If they had taken Logic, they may have scraped a few marbles together in their empty heads and realized ----- If a point has no length, no width, no depth, it is nothing, for it does not exist but is empty space and not a point at all. For a Point to exist and be Something, it must have at least a finite length, but it does not even have that much.
So AP comes along and says--- alright--- A Point to exist has a finite length a finite width and a finite depth in Order for a phsyics tool, a compass needle to poke a hole into the Point and draw a circle or measure the distance to another point.
Let us investigate a Point with length, width, depth affects the Parallel Postulate.
According to Harold Jacobs, GEOMETRY, 2nd edition, 1987, page 649 describes the parallel postulate as his 10th postulate.
Postulate 10:: The Parallel Postulate : Through a point not on a line, there is exactly one line parallel to the line.
Here again, I have to correct Harold for he is lackadaisical when it comes to logic. His postulate should have read--- Through a point not on a line in the plane, there is exactly one and only one line parallel to the given line. Jacobs missed that for in 3D space there are infinite lines parallel.
But here, in New True Geometry we are going to alter the meaning of what it means to be parallel. A change in which we can actually measure if lines are parallel, and not rely on the dumb notion of do the lines intersect as being the definition of parallel.
I bring in the concept of Perpendicular whenever there is the concept of Parallel.
Are these two lines parallel???
_________A_________
_________B_________
If I connect A and B with a line segment and find out that that angle is 90 degrees and correspondingly all Points on both lines if their associated points have a perpendicular between them, means the two lines are parallel.
You see, we could just as well state a Perpendicular Postulate instead of a Parallel Postulate.
Through a point not on a line in the plane, there is exactly one and only one line perpendicular to the given line.
AP's Axiom for Parallel or Perpendicular.
Through a point not on a line in the plane, there is exactly one and only one line parallel to the given line and one and only one perpendicular from the point to the given line.
The beauty of AP's Parallel or Perpendicular axiom is that it allows me to have a axiom for given a plane and a point not in the plane in 3D Space, there is one and only one plane parallel or perpendicular to the given plane.
You see the beauty of AP's Parallel or Perpendicular axiom is that I handle not just lines in plane; I handle planes themselves.
I correspond every point on one line with a test case line and see if a perpendicular connects them. Also a entire plane is checking of corresponding points and if a perpendicular is the connection.
In the AP axiom of Parallel, does this lunacy-idiocy of 3 types of geometry arise???? No, for there never arises this folly that 2 or more lines are parallel as in Loba geometry or that no lines are parallel as in Riem. geometry.
You see, what led Old Math, Old Geometry astray, is, there definition of being Parallel was not well defined--- for, how do you test if two lines or two planes intersect. While AP's definition has you test corresponding points if there is a perpendicular between them.
AP
Aug 23, 2026, 4:25:48 AM
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Alright I need to review the history of Non-Euclidean Geometry to find out if they (math professors) made the same ridiculous and stupid mistake as they did in their phony proof of Fundamental Theorem of Calculus, FTC.
Math professors Logic mistake in their "limit analysis" dance around the x and y axis in FTC is what Logic calls the Fallacy of Irrelevancy. Just as in voodoo witchcraft where someone dances around to cure a person of disease. The dance is Irrelevant to the disease. Yet math professors who never take Logic while in school, are deaf dumb and blind in thinking that a limit analysis dance will show the derivative is inverse the integral in FTC. No wonder Univ. Virginia Reddit Steve Huffman calls UCLA Terence Tao and University Eindhoven Scott Contini as Lunatics. To think that a voodoo witchcraft dance will cure a disease is the same as Tao and Contini thinking a limit analysis dance shows derivative inverse to integral in FTC.
So does Non-Euclidean geometry come from another Logic Fallacy of Irrelevancy???? Looking at Harold Jacobs discussion in his textbook 1987, pages 581 through 593, gives a rather detailed analysis of that history.
And I was reading the history of Non-Euclidean geometry in Wikipedia, paying close attention to the idea, that the math professors were trying to find a "contradiction" between a ---- tampered Parallel Postulate---- and the rest of Euclid's axioms.
Well, the problem with looking for a contradiction by math professors--- is that Euclid's axioms were flawed such as --- What is a Point.
Saccheri, Lobachevsky, Riemann, Gauss, none of them had valid axioms to compare the Parallel Postulate up against and see the contradiction.
AP has a logical mind, and can see that a Axiom of duality would cause elliptic and hyperbolic when joined together be Euclidean geometry, and not three separate independent geometries.
So what axioms would a Elliptic geometry violate and cause a contradiction????
What axioms would Hyperbolic geometry violate and cause a contradiction????
My first axiom of duality, my first axiom exposes Elliptic and Hyperbolic as being fragments of Euclidean.
My second axiom of What is the Point in Geometry, requires a point to be a cube simultaneously a sphere in 3D, and be a square and simultaneously a circle in 2D. Both elliptic and hyperbolic geometry would be contradicted for neither can accommodate both square and circle or cube and sphere.
My third axiom is contradicted by a elliptic and hyperbolic geometry for the points have to be uniform in size, which is impossible to have in elliptic and hyperbolic geometry.
My fourth axiom is contradicted by elliptic and hyperbolic geometry for the 2 points determine a unique line is not possible.
My fifth axiom is contradicted by elliptic and hyperbolic geometry for that is the axiom of Ruler Measure. It is impossible to set up a numbering system in elliptic or hyperbolic geometry that consistently gives distance measure or angle measure. Talk about a barbed wire fence entanglement of the mind!!!!
My sixth axiom of establishing a plane in geometry, is impossible if the geometry is elliptic or hyperbolic. One would start with cross sections into a sphere or horse-saddle which quickly degenerates into ugly inconsistencies such as a polar cap on sphere or a undescribable cross sections of horse saddle.
My seventh axiom of volume has a horrible time with hyperbolic where it appears nothing is finite.
AP summarizes:: So you see, when Old Math has professors who know little to nothing about Logic, their discoveries end up mostly as barbed wire entanglements of error filled nonsense.
AP, King of Science
Aug 23, 2026, 5:50:02 PM
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In New Math, New True Geometry, we use Logic to derive true geometry, true calculus. We are no longer as dumb as a math professor who never studied logic, and never knows how to think straight, think clearly, think correctly.
I could not get a plane of geometry without contradicting my other axioms, so what is Axiom 2 when Axiom 1 is duality???
Axiom 2 : The point in geometry must have a tiny microscopic length, width, depth that is obtained from the inverse of the infinity borderline and is the number 1*10^-604, where 10^-601, 10^-602, 10^-603 are the place value digits of pi where it has 3 zeros in a row so that the Tractrix area catches up with the unit circle area. Tractrix has infinite reach but finite area.
Now I need to bring in Jacobs Ruler Measure Axiom (Postulate). I need to do that because I cannot poke a hole into the number 0. Strange, that I have to start with 1 then gain the number 2 to determine where 0 lies.
Axiom 4:: now I introduce the Line in Geometry where a Point is having length, width, depth that I can poke a hole and use a compass to construct a circle then square. A line is constructed from 2 points as a straightline as the sides of a square, or as the radius of a circle with one point as center and the other point as rim of circle. Two points determine a unique line whether a circle or straightline. Notice, zero is not involved.
Axiom 5:: is the Ruler Measure axiom
The Ruler Postulate : The points on a line can be numbered so that
(a) to every point there corresponds exactly one Decimal Grid number called its coordinate,
(b) to every Decimal Grid number there corresponds exactly one point, and Decimal Grid numbers have no negative numbers.
(c) to every pair of points there corresponds exactly one Decimal Grid number called the distance between the points,
(d) and the distance between two points is the absolute value of the difference between their coordinates,
(e) and, once we have 1 and 2 in integers Decimal Grid, we draw the circle from point 1 to 2 and the radius comes back around 360 degrees to the number 0 and we can then say we form a "poke hole by compass needle" that creates a Zero number hole, even though zero is empty space and has no length, width, depth,
(f) and this axiom introduces angle into geometry, where the full circle is 360 degrees and the square has 4 right angles of 90 degrees.
The above eliminates the Contradictions.
Axiom 7 :: the axiom of volume:: Space is composed of 3 dimensions represented by x, y, z axes. In two dimensions we have Planes, in one dimension we have lines. In 2 dimensions we have area, and in 3 dimensions we have volume. The calculation of area is length times width. The calculation of volume is the length of planes that compose the geometry figure.
Our first axiom in geometry is Physics duality. If physics, the king of science has quantum duality, then geometry has quantum duality of particle to circuit, of electricity to magnetism, of straight line to circle, of numbers to geometry figures, of integral to derivative, of energy to time.
So, why is Geometry only Euclidean, which has squares and circles composing it?? Why cannot there be a Elliptic geometry and a Hyperbolic geometry, called Riemannian and Lobachevskian geometries respectively. Why can they not exist??
Riemannian and Lobachevskian geometries are bogus nonexistent geometries because they are dependent on Euclidean geometry. They cannot exist outside of Euclidean geometry. The formula is this.
Euclidean geometry = Riemannian geometry Unioned Lobachevskian geometry.
That must be true due to the First Axiom of geometry--- Duality exists in geometry, and a Point in geometry must be both a square and a circle simultaneously. Just as in physics, all is electricity and magnetism, both exist simultaneously and together. Neither electricity nor magnetism exist independently without the other.
And we can see the truth of this in geometry by Harold Jacobs 1987 GEOMETRY, pages 580 and 581 with his two definitions.
Definition: A great circle of a sphere is a set of points that is the intersection of the sphere and a plane containing the center.
Definition: Polar points are the points of intersection of a line through the center of the sphere with the sphere.
What Jacobs was trying to get across is in Riemannian (elliptic geometry) there are no Parallel lines parallel from a line and a point not on the line, the Parallel Postulate.
But Jacobs had no logic brain when he wrote his Non-Euclidean geometry chapter, for, well, where is his model of Lobachevskian geometry (hyperbolic geometry). When I was young in college in the very early 1970s the best model for Lobachevskian was a saddle shape figure, but still that is horribly inadequate. Then some kookish math professors came up with the Pseudosphere. They cannot even draw the pseudosphere.
A person that is Logical would look at this situation and say this---- look, you can model a sphere as Elliptic geometry but you have absolutely no model whatsoever for Hyperbolic geometry, and because of this difficulty, we say that Hyperbolic geometry is nonexistent and is imagination gone amok.
Secondly, because you dream up the pseudosphere as the model of Hyperbolic geometry, we can logically say that the sphere of Elliptic geometry is also ignorant and false.
Thirdly, we can look at the first five axioms of true geometry and realize that both Elliptic and Hyperbolic geometry break and violate all 5 axioms. And the easiest contradiction that Elliptic and Hyperbolic geometries impose on geometry, is that--- There Exists No Straight Line within Elliptic or Hyperbolic Geometry. If a geometry cannot accommodate a straightline, then it is fakery garbage.
You see, if math professors had taken Logic while in school, some of them would have been bright enough to realize that if you cannot form a straightline in Elliptic nor Hyperbolic geometries, then these are fake geometries.
List of Geometries first 7 Axioms
---------------------------------------------------
Axiom 1 :: as duality exists in forms such as electricity to magnetism, as particle to circuit, as geometry to numbers, as circles to squares, as nothing to something for within something lies nothing and within nothing lies something. Duality means one form switches into the other form because they are one and the same.
Duality of straightline to curved line.
Dualities exist together, simultaneously, unable to be seperated.
I could not get a plane of geometry without contradicting my other axioms, so what is Axiom 2 when Axiom 1 is duality???
Axiom 2 : The point in geometry must have a tiny microscopic length, width, depth that is obtained from the inverse of the infinity borderline and is the number 1*10^-604, where 10^-601, 10^-602, 10^-603 are the place value digits of pi where it has 3 zeros in a row so that the Tractrix area catches up with the unit circle area. Tractrix has infinite reach but finite area.
Axiom 3: A point has at minimum has a length of 1*10^-604 and the same for width and depth. This insures that one can poke a hole in a point with a compass and produce a circle from that point, and the circle produced from that point produces a square, inside the circle and outside the circle in which the two squares are equal in area by a factor of 1/2 inversely a factor of 2.
Now I need to bring in Jacobs Ruler Measure Axiom (Postulate). I need to do that because I cannot poke a hole into the number 0. Strange, that I have to start with 1 then gain the number 2 to determine where 0 lies.
Axiom 4:: now I introduce the Line in Geometry where a Point is having length, width, depth that I can poke a hole and use a compass to construct a circle then square. A line is constructed from 2 points as a straightline as the sides of a square, or as the radius of a circle with one point as center and the other point as rim of circle. Two points determine a unique line whether a circle or straightline. Notice, zero is not involved.
Axiom 5:: is the Ruler Measure axiom
The Ruler Postulate : The points on a line can be numbered so that
(a) to every point there corresponds exactly one Decimal Grid number called its coordinate,
(b) to every Decimal Grid number there corresponds exactly one point, and Decimal Grid numbers have no negative numbers.
(c) to every pair of points there corresponds exactly one Decimal Grid number called the distance between the points,
(d) and the distance between two points is the absolute value of the difference between their coordinates,
(e) and, once we have 1 and 2 in integers Decimal Grid, we draw the circle from point 1 to 2 and the radius comes back around 360 degrees to the number 0 and we can then say we form a "poke hole by compass needle" that creates a Zero number hole, even though zero is empty space and has no length, width, depth,
(f) and this axiom introduces angle into geometry, where the full circle is 360 degrees and the square has 4 right angles of 90 degrees.
Axiom 6:: So we have a Point, and a Line, now we need an axiom of the Plane. That axiom of Plane involves the extension of the Decimal Grid Numbers on the line from 0 to infinity borderline and all the Points of the plane having all the finite numbers of length and width, but only 1 unit thickness, a quantization discrete unit thickness. The dimensions of point are x,y,z and the x,y can have any numbers to infinity borderline, but the z value has only one value, that of the value of distance from 0 to the Decimal Grid induction number. In 10 Grid it is 0.1, in 100 Grid it is 0.01, in 1000 Grid it is 0.001 out to infinity borderline.
The Plane can have all numbers for x and y, but only a unit number for depth.
The above eliminates the Contradictions.
Axiom 7 :: the axiom of volume:: Space is composed of 3 dimensions represented by x, y, z axes. In two dimensions we have Planes, in one dimension we have lines. In 2 dimensions we have area, and in 3 dimensions we have volume. The calculation of area is length times width. The calculation of volume is the length of planes that compose the geometry figure.
Aug 23, 2026, 9:25:23 PM
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On Sunday, August 23, 2026 at 5:50:02 PM UTC-5 Archimedes Plutonium wrote:
(snipped)
And we can see the truth of this in geometry by Harold Jacobs 1987 GEOMETRY, pages 580 and 581 with his two definitions.Definition: A great circle of a sphere is a set of points that is the intersection of the sphere and a plane containing the center.Definition: Polar points are the points of intersection of a line through the center of the sphere with the sphere.What Jacobs was trying to get across is in Riemannian (elliptic geometry) there are no Parallel lines parallel from a line and a point not on the line, the Parallel Postulate.But Jacobs had no logic brain when he wrote his Non-Euclidean geometry chapter, for, well, where is his model of Lobachevskian geometry (hyperbolic geometry). When I was young in college in the very early 1970s the best model for Lobachevskian was a saddle shape figure, but still that is horribly inadequate. Then some kookish math professors came up with the Pseudosphere. They cannot even draw the pseudosphere.
Jacobs was not trained in Logic to think logically, and 99% of math professors have only a 1/2 marble of a brain of logic.
So in the above definition, Jacobs is saying take a sphere as elliptic Riemannian geometry and take a Euclidean flat space plane cut into the sphere at its center. You see, here, if Jacobs and 99% of math professors had taken Logic while in school, they had a chance of perceiving or realizing, ----- whoa----- the sphere is in Riemann geometry but here you want me to apply a plane that does not exist in Riemann geometry ---- meaning what??? Meaning, that the only truly existing geometry is Euclidean that has both, simultaneously straight lines and curved lines in a circle.
Is the trouble the world over, where we train students to become math professors, like what Reddit's Steve Huffman complains about UCLA Terence Tao or Oxford's Andrew Wiles or Univ Eindhoven Scott Contini none of which have any logical marbles in their brain, and all they can do is read and memorize math and prattle that memorization off.
The reason no Old Math professor could do a valid proof of the Fundamental Theorem of Calculus, is that none of them had a single logical marble in their head to understand a limit analysis dance on x,y axes is a Fallacy of Irrelevancy.
What is the Fallacy that mathematicians make when they claim Geometry has 3 types--- Euclidean, Riemannian, Lobachevskian??? What is their fallacy and error, for only one geometry exists--- Euclidean and Euclidean can be fragmented into elliptic and hyperbolic.
The fallacy they commit is not Irrelevancy, but is the error of never Well-Defined terms or axioms. These morons of math start geometry with a Point having no length, no width, no depth. And it is a duty of a student to ask such a moron math professor--- like Tao, like Wiles, like Hales--- if that is true, then a Point is nothing, has no existence.
So, when math professors are forced to take logic in college, at least they have a reasonable chance that when they hear a Point has no length, no width, no depth, that their brain may arrive at the idea, a point requires a tiny length, a tiny width and a tiny dept, and then it is Something rather than nothing.
AP
Aug 24, 2026, 12:33:17 AM
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Without a straightline instead of a curved line, you cannot have Calculus. The Derivative would not exist in a elliptic or hyperbolic geomety. No straightline, no grid, no function graph, no calculus.
ppp
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Archimedes Plutonium
Sep 21, 2026, 9:28:46 PMSep 21
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I am in constant editing and revision of this textbook, thanks, AP.
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Archimedes Plutonium
Oct 21, 2026, 6:49:25 PM (2 days ago) Oct 21
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I need a ending chapter in each one of these 5 textbooks of Logic, a happy ending chapter.
I have lived for 76 years now, and in that lifetime, have found that Happiness occurs, at least for me, when I have things in Order. Even now, as I come home after a day of working outside, to fix dinner and have a bit of rest, I find that my work of the day was putting things in better Order, and this gives me happiness.
Happiness is not how rich you are, nor how bright and educated you are, nor how much entertainment you have, nor how much leisure you have, nor how many friends you have. No, happiness is about Order and working towards order in your life. And this is where Logic helps a person. Logic is also a process of making Order out of chaos and disorder.
Logic is not just a great tool for doing science, but is a tool for making our lives be as happy as possible.
AP
Logic is a science that helps people being and becoming happy. For happiness is getting a life in Order and order is happiness. Logic figures a way to obtain and hold onto Order.
One can be happy without being logical, but a lifetime of facing problems, for a lifetime is a long string-sequence of solving problems, and without logic helping you, risks much much unhappiness.
Logic is a science that can help people be and become happy.
AP
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