--- quoting Wikipedia on Pythagorean theorem proof---Proofs using constructed squaresRearrangement proof of the Pythagorean theorem.
(The area of the white space remains constant throughout the translation rearrangement of the triangles. At all moments in time, the area is always c2. And likewise, at all moments in time, the area is always a2 + b2.)Rearrangement proofsIn one rearrangement proof, two squares are used whose sides have a measure of and which contain four right triangles whose sides are a, b and c, with the hypotenuse being c. In the square on the right side, the triangles are placed such that the corners of the square correspond to the corners of the right angle in the triangles, forming a square in the center whose sides are length c. Each outer square has an area of (a + b)2 as well as 2ab + c2, with 2ab representing the total area of the four triangles. Within the big square on the left side, the four triangles are moved to form two similar rectangles with sides of length a and b. These rectangles in their new position have now delineated two new squares, one having side length a is formed in the bottom-left corner, and another square of side length b formed in the top-right corner. In this new position, this left side now has a square of area (a + b)2 as well as 2ab + a2 + b2. Since both squares have the area of (a + b)2 it follows that the other measure of the square area also equal each other such that 2ab + c2 = 2ab + a2 + b2. With the area of the four triangles removed from both side of the equation what remains is a2 + b2 = c2.
--- end quoting Wikipedia---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.Physics uses the Pythagorean theorem everywhere for the laws of Electromagnetism depend on the perpendicular, such as Faraday Law, and even the Light Ray where the Electric field is perpendicular to the Magnetic field.It looks as though the video above made it through.AP
The 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.
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]
Intermediate LOGIC // Teaching True Logic textbook series
by Archimedes Plutonium
This is AP's #370 published book of science published on Internet, Plutonium-Atom-Universe,
PAU newsgroup is this.
https://groups.google.com/forum/?hl=en#!forum/plutonium-atom-universe
Preface: This textbook is an expansion and detailing of my #366 textbook of Logic--- Elementary Logic. Here I want to expand and detail some ideas of Elementary Logic. I have not much of a concern over Truth Tables but a focus on the laws of logic.
I have prescribed that all science students seeking a degree in science be required to take two years mandatory logic in college or university. The Elementary and Intermediate Logic textbooks fulfills that requirement. But some, who found these two textbooks enjoyable, I recommend they take Advanced Logic where I make case studies of famous scientists and how Logic would have spared them that embarrassment of messing-up and screwing-up.
Cover picture: Pragmatism as the best philosophy system of all since its mechanism is the 'scientific method'. Meaning is future actions. Knowledge is in the "doing". Ideas for a pragmatist are weapons for purposeful action. My photograph picture of a new type of Rubik's Cube illustrating all of knowledge.
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Table of Contents
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1) What is Knowledge and where does Logic fit in?
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Text
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1) What is Knowledge and where does Logic fit in?
Archimedes Plutonium 3:11 AM, 11Mar2026 to Plutonium Atom Universe newsgroup.
In "Elementary Logic" textbook, I often stated that truth of ideas comes from the best available science on the topic. And we can make a list such as this of all knowledge evaluated by science
Physics
/
Chemistry
/
Astronomy, Geology
/
Biology which includes Sociology and language, medicine, political science,
history
/
Logic = statements + images
/
Mathematics = numbers + geometry figures
But the trouble with a diagram like that--- it does not show relationships such as math is connected directly to physics. The diagram should __not be linear__ but rather circular where one science influences other sciences.
A sphere would be nice to show this interconnectedness, but a modified Rubik's Cube would be even better.
A Rubik's Cube has 9 small cubes per 6 faces equals 54 small cubes. Now, if we give physics 9 small cubes then we have 54-9= 45 remaining small cubes. Now we give chemistry 4 small cubes and give biology 4 small cubes and so we have remaining 45-8 = 37. Now astronomy we give it 2 small cubes, geology 1 small cube, leaving us with 37-3= 34.
Now, surprisingly we need to give Logic 2 small cubes and give Mathematics 2 small cubes, for the reason that mathematics is split into two houses-- numbers and geometry figures. Logic is also split into two houses--- ideas and then images.
The images of the world, whether a eyesight image, a photograph a painting picture, is geometry, compared to say text of statements as algebra. Say, the difference of watching a movie of Noah's Ark and reading it in the Bible.
This geometrical-logic is the philosophy Pragmatism. And since pragmatism is the finest logic we can say that Logic = statements + images. Similar to Mathematics = numbers + geometry figures.
Now in the AP cube I wanted to give a sense of interconnectedness, where chemistry small cubes are near physics small cubes and where Logic and Math small cubes are near physics small cubes.
We can visualize other so called sciences like economics, political science, history as far away from the all physics face.
Archimedes Plutonium Mar 11, 2026, 3:25:02 AM to Plutonium Atom Universe newsgroup.
So what I have in mind is all the blue colored small squares be Physics, 4 for chemistry, 4 for biology, until all sciences are represented by a small square. Logic would have 2 small squares and math would have 2 and be near the Physics squares. This is how I can best relate the idea of interconnectedness of science.
AP's opinion:: if such a cube were manufactured, it would be utterly simple to play, for the rule would be to just get all the blue physics onto 1 face. Question:: Is the AP cube the Most Simple of all Cubes, after you have a cube that is totally all one color, where you actually do not need to move anything at all???? Silly people are always looking to make things difficult, when we should look to make things easy. Such as AP's books on Calculus, reducing calculus to just add or subtract 1 from exponent of polynomial , because the only valid function in all of math is the Polynomial. But few math professors have a 1/2 or more marble logical brain to ever understand that.
--- quoting Wikipedia---
An illustration of an unsolved Rubik's Cube
Archimedes Plutonium Mar 11, 2026, 3:35:38 AM to Plutonium Atom Universe newsgroup.
Homework: take a real light colored Rubik's cube and mark all 54 faces with a light pencil to erase later and see if you can fit Physics, Chemistry, Biology, etc. If no cube available, make sketches of the 6 faces with the sciences in each of the 54 small squares.
Archimedes Plutonium Mar2026, to Plutonium Atom Universe newsgroup.
Alright, I am momentarily stuck here and need to resolve the issue before I continue with the textbook.
I have arrived at the idea where all of philosophy, be it pragmatism or any other philosophy is a branch of Logic where Logic is split into geometry and into algebra.
When I do the logic syllogism: All men are mortal. Socrates is a man. Therefore Socrates is mortal. Is composed of 2 premisses and conclusion in statement form and is ____algebraic logic____
When I do logic by these pictures--- showing a slant cut in cylinder and showing a slant cut in cone--- concluding that the cylinder is ellipse slant cut and cone is oval slant cut. I am doing Geometry Logic as seen in pictures below.
However, this causes a huge problem of determining how much is a statement/s or premiss/s be that of algebra or that of geometry????
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 a algebraic component, but there is also a geometry component in or 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 at all algebraic.
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 and symbolic branch and then a branch that can be fully pictures and geometry.
These 2 pictures of slant cut in cylinder and cone is Geometry Logic, as well as the pictures of the proof of Pythagorean theorem.
--- quoting Wikipedia---
--- quoting Wikipedia---
--- quoting Wikipedia on Pythagorean theorem proof---
Rearrangement proof of the Pythagorean theorem.In one rearrangement proof, two squares are used whose sides have a measure of and which contain four right triangles whose sides are a, b and c, with the hypotenuse being c. In the square on the right side, the triangles are placed such that the corners of the square correspond to the corners of the right angle in the triangles, forming a square in the center whose sides are length c. Each outer square has an area of (a + b)2 as well as 2ab + c2, with 2ab representing the total area of the four triangles. Within the big square on the left side, the four triangles are moved to form two similar rectangles with sides of length a and b. These rectangles in their new position have now delineated two new squares, one having side length a is formed in the bottom-left corner, and another square of side length b formed in the top-right corner. In this new position, this left side now has a square of area (a + b)2 as well as 2ab + a2 + b2. Since both squares have the area of (a + b)2 it follows that the other measure of the square area also equal each other such that 2ab + c2 = 2ab + a2 + b2. With the area of the four triangles removed from both side of the equation what remains is a2 + b2 = c2.
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.
Physics uses the Pythagorean theorem everywhere for the laws of Electromagnetism depend on the perpendicular, such as Faraday Law, and even the Light Ray where the Electric field is perpendicular to the Magnetic field.
It looks as though the video above made it through.
The idea in the above pictures-images is that many, probably most ideas come from pictures-images on paper and the visual world, but also inside our brains and minds. Our brains and mind seldom makes sentence statements of ideas.
A review of Pragmatism philosophy and where all philosophies become the geometry branch of Logic.
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(1) Reality for a Pragmatist-- facts and data, only material and eye witness facts and data. And here we have to go down to "reliable sources" if not a, on the scene seeing for oneself. Even then, there maybe a magician in the report. So a Pragmatist is very tough on what is fact and data of reality. One of the recent researches of mine is Sleep and hypnosis, and I find that no hypnosis exists, never has and never will. Because if I wanted to sleep using hypnosis, I cannot. Hence, hypnosis is not a science but a sham, a magician trick.
(2) Ideas and the Meaning of those Ideas, for pragmatist are tools, instruments, weapons for purposeful future action. We must include concepts and definitions as ideas and Meaning. So we have in the first two Tenets of Pragmatism, we have facts, data, definitions and concepts. Now we must put those four-- facts, data, definitions, concepts into motion, and the last two tenets of Pragmatism do just that.
(3) Wisdom, Knowledge and Education is in the _doing_ the hands on experience. For a Pragmatist, that boils down to just one word- experiment.
(4) Truth is what _works_ and works in the long run. Truth for the Pragmatist is boiled down to be a "Law of Physics or Science". Because it is science laws that work in the long run. So when we speak about truth in the world, we are really talking about laws of science.
So we can make some equations comparing mathematics to Logic.
Math = algebra numbers + geometry figures
Logic = ideas as sentence statements or symbols + ideas from pictures-images
The ideas from pictures-images is the realm of philosophy. All philosophies are subjects that are pictures-images.
Some would say that a philosophy, as Abraham Kaplan lists them-- Pragmatism, Analytic Philosophy, Existentialism, Freud and Modern Philosophy, Communism, Buddhism, Chinese Philosophy, Indian Philosophy, Zen. That after reading his book, "The New World of Philosophy", 1961 in my teenage years, I came away with the impression that philosophy was a "attitude of behavior" to living life.
Many of us know people with a "attitude" and some call it a "personality".
Some philosophies you can ascribe "tenets" to them like above of the 4 tenets of pragmatism.
But many of the philosophies listed above we cannot even ascribe tenets to them, and have to have the "feeling of the philosophy".
When we lack this ability of describing the philosophy in sentences and statements, and tenets we thus describe the philosophy in pictures and images. Such as the sitting position of meditation in Buddhism.
Many philosophies, many religions rely more on pictures-images to get ideas across rather than on sentences of words to get ideas across. "Do as I do, is the teaching".
In "Introduction to Logic" #366, I defined Logic as the science that makes ideas clear and straight and manipulates ideas to form new ideas. There I did not break down ideas into two classes--- the algebraic statement idea and now we have a second type of idea which comes from pictures-images.
So where Mathematics has this equation Math = algebra numbers + geometry figures. That Logic has this equation Logic = algebra statements + pictures-images.
Intermediate LOGIC // Teaching True Logic textbook series
by Archimedes Plutonium
This is AP's #370 published book of science published on Internet, Plutonium-Atom-Universe,
PAU newsgroup is this.
https://groups.google.com/forum/?hl=en#!forum/plutonium-atom-universe
Math = algebra numbers + geometry figures
Logic = ideas as sentence statements or symbols + ideas from pictures-images
The ideas from pictures-images is the realm of philosophy. All philosophies are subjects that are pictures-images.
Some would say that a philosophy, as Abraham Kaplan lists them-- Pragmatism, Analytic Philosophy, Existentialism, Freud and Modern Philosophy, Communism, Buddhism, Chinese Philosophy, Indian Philosophy, Zen. That after reading his book, "The New World of Philosophy", 1961 in my teenage years, I came away with the impression that philosophy was a "attitude of behavior" to living life.
Many of us know people with a "attitude" and some call it a "personality".
Some philosophies you can ascribe "tenets" to them like above of the 4 tenets of pragmatism.
(1) Reality for a Pragmatist-- facts and data, only material and eye witness facts and data. And here we have to go down to "reliable sources" if not a, on the scene seeing for oneself. Even then, there maybe a magician in the report. So a Pragmatist is very tough on what is fact and data of reality. One of the recent researches of mine is Sleep and hypnosis, and I find that no hypnosis exists, never has and never will. Because if I wanted to sleep using hypnosis, I cannot. Hence, hypnosis is not a science but a sham, a magician trick.
(2) Ideas and the Meaning of those Ideas, for pragmatist are tools, instruments, weapons for purposeful future action. We must include concepts and definitions as ideas and Meaning. So we have in the first two Tenets of Pragmatism, we have facts, data, definitions and concepts. Now we must put those four-- facts, data, definitions, concepts into motion, and the last two tenets of Pragmatism do just that.
(3) Wisdom, Knowledge and Education is in the _doing_ the hands on experience. For a Pragmatist, that boils down to just one word- experiment.
But many of the philosophies listed above we cannot even ascribe tenets to them, and have to have the "feeling of the philosophy".
When we lack this ability of describing the philosophy in sentences and statements, and tenets we thus describe the philosophy in pictures and images. Such as the sitting position of meditation in Buddhism.
Many philosophies, many religions rely more on pictures-images to get ideas across rather than on sentences of words to get ideas across. "Do as I do, is the teaching".
In "Introduction to Logic" #366, I defined Logic as the science that makes ideas clear and straight and manipulates ideas to form new ideas. There I did not break down ideas into two classes--- the algebraic statement idea and now we have a second type of idea which comes from pictures-images.
Summary on what is Logic
-----------------------------------
Logic is the science that is larger than mathematics and contains all of mathematics inside of Logic. But Logic is small compared to physics for logic is a subset of physics. Physics is the science of everything. While logic is the science that makes ideas clear, straight and manipulates ideas into making new ideas. The truth of ideas is determined not by logic but the best available science at the moment--- physics, chemistry, biology, astronomy, geology, etc etc. The ideas of Logic come in two forms--- they can be either word-sentence algebra form or be a picture-image geometry form and often the case is any idea is a mixture of word-sentence and picture-image.
2) The Elements of Physics, Logic and Mathematics.
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.
My 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 Photon-Light-rays, protons, electrons, neutrons and many other subatomic particles. This viewpoint is a mistake.
These are all ______ subatomic particles______.
Photon-Light-rays
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 945MeV when fully grown
Alpha particles which are really helium atoms
Trouble with modern day physics, is few if any have logical brains or training in logic
AP
How much of science is a enterprise of asking questions??? I would say considerable and asking questions is text-word-sentence format, not picture format.A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z26 letters alphabet with 5 vowels, 21 consonantsSafe to say that hearing and phonetics comes first before visual seeing to create text-word-sentence ideas.