What is often left-out in the discussion of the Pythagorean Theorem is the geometry that you Need a 90degree angle.
And the importance of this theorem, linking numbers to 90 degrees if you hand me lengths 3.5, 4, 5, that it cannot form a right-triangle. It forms a triangle, but not a right-triangle. When three numbers A,B,C obey A^2 + B^2 = C^2 those three numbers form a right angle triangle, and those three numbers are called Pythagorean triples. Some Pythagorean triples are <3,4,5> another is <5,12,13>, another is <8,15,17>, etc. The Pythagorean Theorem makes what physics calls quantum duality of magnetism to electricity or particle to circuit, makes in mathematics a duality of number to that of geometry.
Physics uses the Pythagorean theorem everywhere for the law-structures of Electromagnetism depend on the perpendicular, the 90 degree right-angle, such as Faraday law-structure, where only the 90 degree component of the magnetic field in the thrusting bar magnet through copper wire coil translates into electric current in the galvanometer reading.
It looks as though the video above of the proof of the Pythagorean theorem made it through.
Now since Logic is the science of communicating well formed-straight and clear ideas, and correct ideas, we had better know what "ideas" are in the first place. And so we see ideas can come in two forms: one of word-sentence-statement and another in pictures-images.
However, this causes a huge problem of determining how much is a statement/s or premiss/s be that of algebra words-sentence or that of geometry of picture-images????
And one can say, that every algebra statement has a mix of algebra with geometry and every geometry statement has a mix of both.
For example: Statement: Jack ran up the hill until he reached the top. Jack walked down the hill, after he reached the top.
So, in that Logic Statement, we can see there is an algebraic component, but there is also a geometry component in our minds as we form pictures of the events that occurred.
You see, my big problem here is that Old Logic saw all of logic as just "algebraic statements". While New Logic sees statements of Logic can be totally geometrical and not all algebraic. Or a mixture of the two forms.
For example: It is dark nighttime and you turn off the light, nearby the bed. You have a few steps to walk to get to the bed. You turned off the light, but your mind geometrically remembers you have to avoid a cord and avoid a table top. And all of that is possible because the mind has a geometry picture of those next events that take place.
So here I need to spend some time on furnishing New Logic with two branches--- an algebraic symbolic branch and then a branch that can be fully pictures and geometry.
Those 2 pictures earlier, above, of slant cut in cylinder and cone is Geometry Logic, as well as the pictures of the proof of Pythagorean theorem.
The Ideas of Logic come in two forms and often mixed together-- as algebraic form of words-sentences-statements and the geometry picture-image form of idea.
Part 2. Fundamental Elements of Physics of Logic and of Mathematics.
Part 2. Fundamental Elements of Physics of Logic and of mathematics.
Archimedes Plutonium Mar 15, 2026, 5:40:00 PM to Plutonium Atom Universe newsgroup.
The Elements of Physics, Mathematics and Logic
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Since physics dominates the world of ideas and where Logic is a subset of physics and where mathematics in total is a subset of Logic, we should spend some time on exposing what the fundamental elements of physics, logic and mathematics are.
For Physics the base elements of that science are Atoms, and chemistry enshrines the elements in what it calls the Periodic Table of Chemical Elements.
This is a chart of the Atomic Theory, the greatest single science theory in all of human history.
Atoms are the base foundation elements of Physics.
In 5th edition, "Chemistry: The Central Science", by Brown, LeMay, Bursten, goes up to element 105 Ha with 262 nucleons. But looking in Wikipedia, they go up to 118 Og with 294 nucleons.
The elements of Physics are the Atoms, one of 118 known chemical elements. The mistake and huge mistake most people make is that they see the world not composed of these 118 elements but rather see the world of atoms as swimming inside a ocean of subatomic particles such as Light-photons, protons, electrons, neutrons and many other subatomic particles. And swimming around inside of what they think and see as "empty space". This viewpoint is a mistake.
These are a list of ______ subatomic particles______.
Light-photons
Electrons as Muons of 105 MeV as stuck inside a hydrogen atom proton
Magnetic Monopoles of 0.5MeV
Protons as 840MeV proton toruses
Neutrons as growing from 1MeV all the way up to 945MeV when fully grown
Archimedes Plutonium Mar 15, 2026, 9:38:33 PM to Plutonium Atom Universe newsgroup.
When I was taking Logic in college-- 1968-1972 at University of Cincinnati for my degree in mathematics, I took 2 years of Logic one taught from Introduction to Logic, Copi, and one taught from Introduction to Symbolic Logic, Thomason. I remember the thought in both classes, a lack of science in examples or even the comparison of science and math to that of logic. If I look in the index for subject matter for "physics" or for "mathematics" I find nothing in either Thomason or Copi.
But to Copi's credit on page 417, he describes how Pauli in 1930 gave a logical solution to the contradiction of the neutrino and the conservation of energy. Pauli, logically, declared a new particle.
All Old Logic textbooks are junk for the singular reason, alone, they do not recognize the role of Science as the truth giver of the basic elements of Logic---- IDEAS.
The basic Elements of Physics are the atoms, 1 of 118 known chemical atoms. And Atoms in the Atomic Theory---- All things are made up of Atoms or parts of atoms and compose the entire Universe, and the Universe itself is one of those 1 in 118 atoms--- specifically plutonium. In Elementary Logic textbook you learned that the Universe itself must be one of those 118 elements in the Periodic Table. Do you remember why it "must be so"? It must be so, otherwise the Atomic theory of physics is not a universal law-structure. It is a mere rule that is sometimes true but often wrong.
Now in Ancient Greek Atomic Theory the empty space makes up a vast part of the Universe, of dark empty space. But recently in my researches, we find that Microwave Light-photons make up 10^7 more than the rest-mass matter of the universe. This means, in a sense, the entire universe is a single big Plutonium Atom and the dark empty space we see, is occupied by Microwave Photons. In other words, every atom is full of either rest mass particles or photon radiation and _____ no dark empty space vacuum____.
The basic Elements of Mathematics are what?? Is there anyone in this classroom who knows the basic elements of Mathematics??? Probably not, because virtually 100% of math professors in all colleges and universities across the world do not know the basic Elements of Mathematics.
The basic elements of Math are numbers and geometry figures, for the numbers are the Decimal Grid Systems starting with 10 Grid, next 100 Grid, next 1000 Grid until we end up and reach 10^604 Grid where the infinity borderline lies.
Here are all the integer numbers of mathematics for the first 100 integers.
91, 92, 93, 94, 95 96, 97, 98, 99, 100
81, 82, 83, 84, 85, 86, 87, 88, 89, 90
71, 72, 73, 74, 75, 76, 77, 78, 79, 80
61, 62, 63, 64, 65, 66, 67, 68, 69, 70
51, 52, 53, 54, 55, 56, 57, 58, 59, 60
41, 42, 43, 44, 45, 46, 47, 48, 49, 50
31, 32, 33, 34, 35, 36, 37, 38, 39, 40
21, 22, 23, 24, 25, 26, 27, 28, 29, 30
11, 12, 13, 14, 15, 16, 17, 18, 19, 20
01, 02, 03, 04, 05, 06, 07, 08, 09, 10
00
This is the 10 Grid with a counting successor unit as .1 because you get the next number from any given number by adding .1.
9.1, 9.2, 9.3, 9.4, 9.5 9.6, 9.7, 9.8, 9.9, 10.0
8.1, 8.2, 8.3, 8.4, 8.5, 8.6, 8.7, 8.8, 8.9, 9.0
7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8, 7.9, 8.0
6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7, 6.8, 6.9, 7.0
5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8, 5.9, 6.0
4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9, 5.0
3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9, 4.0
2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 3.0
1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0
0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0
00
The 10 Grid if we ignore 0 has exactly 100 elements. How many elements would the next higher Grid, the 100 Grid have??
Homework: Write out the __last 100 elements__ of the Decimal 100 Grid. Careful, your last number should be 100.00.
Archimedes Plutonium Mar 15, 2026, 10:18:25 PM to Plutonium Atom Universe newsgroup.
Now Mathematics has two sets of Elements--- numbers for algebra and geometry figures for geometry. The two branches of elements are connected through Pythagorean Theorem and is the reason that theorem is so important in mathematics. Numbers are dual to geometry figures. In Logic, the Existential quantifier is dual to Universal quantifier, and in physics the electricity is dual to magnetism.
It is easy to list all the Number elements of math although time consuming as we list 10 Grid, 100 Grid, 1000 Grid on up to and including 10^604 Grid.
If you do not know it yet, Old Math with their Reals, rationals, irrationals, complex, imaginary and all manner of silly stupid numbers were fools of mathematics. So dumb has the mathematics community become that in the year 1900, Max Planck in Germany showed the world that Physics, all of Physics obeys Quantum Mechanics. Quantum means "discrete". The Decimal Grid numbers are discrete. The Reals are of the continuum and are stupid silly numbers. The endless fools of Old Math never stood up and realized what Planck had discovered, instead, they doubled down into insanity with Cohen seeking ever more continuums. Rather than admitting Quantum Mechanics changed not only physics but all of mathematics.
The geometry branch of Elements of Mathematics is difficult to list, for geometry figures are an enormous list of varying types. We can start off with Point, then line segment, then line out to infinity. But we have to be careful for in True Geometry because Space is Discrete, has ____ no curved line segment or line beyond infinity____. A curved line is a string of small tiny straight-line-segments strung together. And so small are the tiny straight lines that our eyes and mind are fooled into thinking it is a smooth curve line, no, it is tiny straight lines strung together. The smaller the segments, the more the figure looks like a smooth curve.
Geometry Figure Elements
------------------------------------------
Point
Straight line segment
Straight line to infinity borderline
Closed straight line figures triangle, square, rectangle, trapezoid
Curved-straight line figures that are closed -- circle, ellipse, oval (remembering that if we examined these figures under a microscope, they would be tiny straight line figures strung together)
Many more, in fact so many more that a picture or image may contain 10^12 such geometry figures
So to my comment earlier, that while I was in college a teenager and reaching age 21-22, in logic classrooms, I noticed an absence of the sciences like physics or mathematics discussed in Logic. It is as if the subject of logic in academics had become a down-trodden feeble annoying subject that could only once in awhile open its mouth about physics and math and the other sciences.
What AP textbooks on Logic is beginning to show is that Logic is filled with science and that logic dominates over math, all of math and that it is Logic, so powerful that it is tearing down vast swathes of Old Physics with their purported nucleus of Atoms that never existed and their messed up view of thinking Sun and stars shine from fusion, when in truth, they shine from Faraday law-structure.
AP logic textbooks puts Logic back on center stage of wherever science is done, whether it be physics on down to psychology.
No longer is logic some shadow subject.... and I recommend 2 years mandatory course to get a science degree.
Archimedes Plutonium Mar 16, 2026, 4:29:12 AM to Plutonium Atom Universe newsgroup.
Since mathematics has 2 Elements to construct it (1) numbers-algebra, (2) geometry figures, that it stands to reason that Logic, the superior set over mathematics must have 2 Elements that builds Logic and those would be (1) word-sentence-statement Ideas and (2) pictures-images as Ideas.
Then we would have to go back to Physics and ask if the Elements also come in a duality? We have in Physics the Atomic Theory where atoms are all the Elements. But, as noted earlier, atoms have subatomic particles and especially Electromagnetic Photons. These photons fill up the space all inside an atom and all the space outside of the atom/s. In other words the universe has ___ no empty space___. So the 2 Elements of Physics are (1) Atoms (2) Space which is subatomic particles such as photons that is the Space between atoms.
Now the Elements of Logic (1) word-sentence ideas (2) picture-images as ideas allows us to build a science of Psychology, plus a science of Mind-Brain, plus a science of Language. This is all possible when a science has Dualistic Elements.
Science of Psychology built from word sentence + picture-images
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All life has DNA. The geometry of DNA is a double helix. A Photon-Light is a closed circuit pencil ellipse. When we inspect a Photon it is also a double helix of E-field and B-field, which I have named "pure DNA".
|__|__]___[##]___\___/___| one Photon segment can look like this of its E and B field
Another can look like this [__]___\___[____|_##]___|____|
These photons are composed of bits of geometry such as |__| is a bit of geometry such as a square or rectangle. And one Light-photon can inscribe an entire picture such as a photograph of you or a photograph of me.
Part 3. Theory of the Mind and the basis of the science of Psychology comes from Physics.
Since ideas are the elements of Logic, and come in two forms--- word-sentence-statement form or in picture-image form, the next logical question to ask is where do the Ideas themselves originate from? For most of my life, I thought all ideas come from inside my body from the brain, specifically. But when I discovered the Atom Totality theory in 1990, along with that theory comes Quantum Mechanics entanglement which John Bell summarized with his concept of "superdeterminism". As the years rolled by after 1990 and I gradually got an appreciation and sense of what Superdeterminism means, I ended up with the realization that the Mind and brain of a human body only process ideas that come from outside the body. That ideas come from the control-center of the Atom Totality as if it were a TV station broadcaster or a radio station broadcaster.
That Quantum Mechanics of a Atom Totality Universe, a Plutonium Atom Totality Universe Control Center shoots Photons into our bodies which are picked up in the kidney and brains as antennae and process those Photons to be our every thought and idea. In other words, every living organism mind is a TV station receiving broadcasts from the Atom Totality Control Center.
In astronomy, where is this control center? I am not sure because I do not yet know if our galaxy, The Milky Way is in the Cosmic Muon or Cosmic Proton or one of the Cosmic Neutrons (neutrons are capacitor batteries). If I had to guess, the Cosmic Protons are likely to be the control center of the Cosmos. But then again, it could well be the Cosmic Neutrons for we can say that the batteries of a car are the brains of a car.
So the elements of Logic are Ideas and ideas come in two forms-- word-sentence-statement algebra or in picture-image geometry form.
So, let us investigate how Ideas can come from outer space and are shot into our mind-brain where they are thence received.
Archimedes Plutonium Mar 13, 2026, 8:52:02 PM to Plutonium Atom Universe newsgroup.
Theory of the Mind
------------------------
A theory of the mind has to account for both memory and where new ideas come from.
In a Plutonium Atom Totality, new ideas come from the Atom Control Central as it shoots photons into our body and gives us new thoughts.
But, where is Memory in an Atom Totality. Here the brain is the memory station and the brain is a large capacitor.
A capacitor is where photons are like electricity, just go round and round in the brain.
The photons of Light are pure DNA, and pure DNA is geometrical. The ATGC of DNA are geometry figures such as squares, triangles, circles etc.
When we see something in life our eyes form a image of the sight and that is converted to photons-of-Light that is storaged in the brain as electric current going round and round.
When a new thought comes into our mind from the Atom Control Central it can link up with one of these photons going around and around in our brain, link up and where we relive the images.
Now, I have learned that the modern technology of Cloud for computers works in such a way that if I send a message that is too large. The Cloud divides up the message leaving tags on each message to reassemble into one document upon receipt by another computer. In this manner, we can think of human memory in psychology as to where a tagged Light photon going round and round in the mind, meets up with its counterpart tagged Light photon, and in that instant of time we experience a "Memory of thought".
How Much of an Idea is an algebra statement or an image statement?
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Since Memory is all stored images, means that all ideas from memory start out as Geometry.
Archimedes Plutonium Mar 14, 2026, 4:20:46 AM to Plutonium Atom Universe newsgroup.
If this theory pans out as true, it will certainly be one of my finest science discoveries ever.
It will change all of psychology as a science.
It will give structure to the Brain-Mind and well define both.
So let me go slowly on explaining this.
A few days ago, I was starting to get into trouble about what constitutes an Idea for Logic????
We are all familiar with Logic statements like this.
All men are mortal. Socrates is a man.
Therefore Socrates is mortal.
Plenty of ideas in those statements.
But then I ran into a difficulty.
Are there images, or pictures statements of logic??
Seems reasonable that instead of just words as logic ideas, that a picture probably packs far more ideas in a single image or picture than a sentence or words.
So, then, I fell into this vast pit of wondering if Images and Pictures should be allowed as Ideas, as statements as premisses even as conclusions.
And what I ended up saying, is that the Mind itself starts out all ideas as being Images, as pictures, that DNA is geometry and that Photon-Light is perfect DNA. That electricity is perfect DNA.
Hence, the Mind is a battery capacitor of electric signals all made up of perfect DNA, and that Memories are these constant circuits of the brain of this electric signals. When we have a past memory, we simply turn on a switch that gives us some of those electric currents full of past pictures revealing themselves in our mind, or that one tagged light-photon is tagged with another to form a Memory, much like modern day computers and phones tag up messages in the Cloud computing and why so much electricity in data-centers are needed. Where we make the skies the brains of modern day life.
Of course, during the waking day-- our eyes capture images of the world and our eyes transform those images into electric currents that hold those pictures in our mind as a battery-capacitor.
Few of our Ideas are sentences of words. Most of our Ideas are images and pictures.
Like reading a magazine. Each sentence can be construed as an algebraic idea. But each sentence forms a picture in our mind as the idea.
Our Minds as Memories does not hold the algebraic sentence, no, it transforms the algebra of words and we hold in our mind-memory a picture.
Archimedes Plutonium Mar 14, 2026, 3:04:17 PM to Plutonium Atom Universe newsgroup.
So there I was, several days back-ago. I had arrived upon this Logic idea, that a statement or premiss need not be a sentence, but be, actually a whole entire picture or image.
A sentence being a algebra of words.
A picture or image being a geometry.
And, come to think of it, whenever one reads or writes a sentence that forms a Statement or Premiss of Logic, it is extremely difficult to keep that sentence to not form a picture or imagine.
In other words, I had a fight on my hands a few days back-ago.
And the resolution of this--- is spectacular. It involves a complete revolution in the science of Psychology.
Our brains are the hardware of a Mind of Thoughts. And all thought is ---- Pictures and Imagines. Plants do not have a word-sentence format.
The bodies of plants and animals is composed of DNA. These are molecules constructed from ATCG which are geometric figures. The Photon-Light is actually perfect DNA and is electric current.
What this resolves into being is that the Brain is an organ that is a battery capacitor, in which it circulates electric current all composed of geometry figures. These figures were formed from the eyes seeing the world around us and making pictures that are transcribed into electric current. We can recall such a long past picture because we have that picture circulating around in our head as long as we live.
In other words images and pictures are turned into electric current that is kept circulating in our brain and is our Memory when one tagged message intersects with another tagged message.
Archimedes Plutonium Mar 14, 2026, 3:13:09 PM to Plutonium Atom Universe newsgroup.
I need pictures of the brain and try to see if I can make out the image of a car battery as Parallel Plate Capacitor.
All those folds, can we say the folds are like parallel-plates?????
So that the electric currents that are constantly flowing around and around remain in the brain forming a Mind and Memory.
[pictures of the brain]
--- quoting Wikipedia---
free encyclopedia
Brain
Details
Part of
Nervous system
Identifiers
Latin
cerebrum
Greek
ἐγκέφαλος (enképhalos)
MeSH
D001921
NeuroNames
21
TA98
A14.1.03.001
TA2
5415
Anatomical terminologyThe brain is an organ that serves as the center of the nervous system in all vertebrate and most invertebrateanimals. It consists of nervous tissue and is typically located in the head (cephalization), usually near organs for special senses such as vision, hearing, and olfaction. Being the most specialized organ, it is responsible for receiving information from the sensory nervous system, processing that information (thought, cognition, and intelligence) and the coordination of motor control(muscle activity and endocrine system).
While invertebrate brains arise from paired segmental ganglia (each of which is only responsible for the respective body segment) of the ventral nerve cord, vertebrate brains develop axially from the midline dorsal nerve cord as a vesicular enlargement at the rostral end of the neural tube, with centralized control over all body segments. All vertebrate brains can be embryonically divided into three parts: the forebrain (prosencephalon, subdivided into telencephalon and diencephalon), midbrain (mesencephalon) and hindbrain(rhombencephalon, subdivided into metencephalon and myelencephalon). The spinal cord, which directly interacts with somatic functions below the head, can be considered a caudal extension of the myelencephalon enclosed inside the vertebral column. Together, the brain and spinal cord constitute the central nervous system in all vertebrates.
In humans, the cerebral cortex contains approximately 14–16 billion neurons,[1] and the estimated number of neurons in the cerebellum is 55–70 billion.[2] Each neuron is connected by synapses to several thousand other neurons, typically communicating with one another via cytoplasmic processes known as dendrites and axons. Axons are usually myelinated and carry trains of rapid micro-electric signal pulses called action potentialsto target specific recipient cells in other areas of the brain or distant parts of the body. The prefrontal cortex, which controls executive functions, is particularly well developed in humans.
--- end quoting Wikipedia---
Archimedes Plutonium Mar 14, 2026, 4:57:29 PM to Plutonium Atom Universe newsgroup.
I have never really understood this physiological brain structure of neurons, axon, synapse, until now.
Until now, for it is beginning to make sense, as the eyes are like a Photo-Camera and wants the picture to be converted into a electric current that stays trapped inside the brain, going around and around, like electricity in a car battery.
--- quoting Wikipedia---
Cellular structure
Neurons generate electrical signalsthat travel along their axons. When an electrical impulse reaches a junction called a synapse, it causes a neurotransmitter to be released, which binds to receptors on other cells and thereby alters their electrical activity.The brains of all species are composed primarily of two broad classes of brain cells: neurons and glial cells. Glial cells (also known as glia or neuroglia) come in several types, and perform a number of critical functions, including structural support, metabolic support, insulation, and guidance of development. Neurons, however, are usually considered the most important cells in the brain.[8] In humans, the cerebral cortex contains approximately 14–16 billion neurons,[1] and the estimated number of neurons in the cerebellum is 55–70 billion.[2] Each neuron is connected by synapses to several thousand other neurons. The property that makes neurons unique is their ability to send signals to specific target cells, sometimes over long distances.[8] They send these signals by means of an axon, which is a thin protoplasmic fiber that extends from the cell body and projects, usually with numerous branches, to other areas, sometimes nearby, sometimes in distant parts of the brain or body. The length of an axon can be extraordinary: for example, if a pyramidal cell (an excitatory neuron) of the cerebral cortex were magnified so that its cell body became the size of a human body, its axon, equally magnified, would become a cable a few centimeters in diameter, extending more than a kilometer.[9] These axons transmit signals in the form of electrochemical pulses called action potentials, which last less than a thousandth of a second and travel along the axon at speeds of 1–100 meters per second. Some neurons emit action potentials constantly, at rates of 10–100 per second, usually in irregular patterns; other neurons are quiet most of the time, but occasionally emit a burst of action potentials.[10]
ppp
and which contain four right triangles whose sides are 
