#489 science book by AP-- The New Poincare Conjecture, not the old daft silly 1904 conjecture of a 4D sphere.
Archimedes Plutonium
Archimedes Plutonium
Old Math and Old Physics were smart enough to have Instantaneous Velocity, but too dumb and stupid to have Instantaneous Energy.On Saturday, May 30, 2026 at 4:24:23 PM UTC-5 Archimedes Plutonium wrote:(big snips)So how are they related???? Looking at the units of Action it is simply angular momentum.velocity = LT^-1energy = ML^2T^-2
action = ML^2 T^-1frequency = T^-1
Angular momentum = ML^2T^-1-------------------------------------------------------------------------------------------------------------------AP discovers the Integral is Angular Momentum is Instantaneous Energy while the Derivative as velocity is Instanteous speed.--------------------------------------------------------------------------------------------------------------------Physics has the Principle that Light is a constant maximum speed. It also has a less known Principle called Least Action which basically says that the motion of a particle follows the path of Least Action or Angular Momentum. I like to call it the Least Energy principle. And what it basically means is that Velocity is the dual of Angular Momentum, just as addition is the dual of subtraction; multiplication the dual of division; derivative the dual of integral; electricity the dual of magnetism.Old Math not only was stupid in never realizing calculus is geometry and seek a geometry proof of FTC, but they did manage to find "Instantaneous Velocity" in spite of their stupidity. But being dumb often means being sloppy, and Old Math --- finding intantaneous velocity, never followed through. Okay, you found instantaneous velocity but struggling to ever teach it, but you failed miserably in finding Instantaneous energy. And I suppose waiting for AP to discover it for you.
Archimedes Plutonium
So, what I am thinking here, for an elegant definition of Circle, I need two points-- center and a distance from center for radius.
So an elegant Plane definition is 1 point to define a plane, and that can be got from a Cylinder as Space. Where the points of the center-line define a unique circle.
That would leave Space to be elegantly defined as needing 0 points.
Summary:
0 points define Space.
1 point defines unique Plane.
2 points define unique circle in plane
Now this only will work if I can manage to say all of Physics is cylindrical. That a Cylinder defines Space.
So have to check into that. But already there are indications that a cylindrical coordinate system is the most General of all coordinate systems."
Archimedes Plutonium
Archimedes Plutonium
Aug 15, 2023, 2:25:26 PM
to Plutonium Atom Universe
AP's 253rd book of science: The math proof: 3 arbitrary points in Space, not collinear, determines a Unique Plane and the nonexistence of 4D // Math research
You see, I am trying to recollect what I had written in May of this year, and put off writing this book until now in August of 2023.
In the title I had written I found another proof that dimension of Space can only be 3rd dimension at tops, and cannot be 4th or higher.
So I am trying to recollect why I said that.
I know for sure I was very unhappy with making 3 arbitrary points in Space, noncollinear, form a unique plane as being a Axiom-Postulate. Very unhappy with that idea, and thus I found a derived theorem proof.
I do recall now the ellipse requiring just 3 arbitrary noncollinear points in Plane to form a unique ellipse. And that was resolved by a HourGlass type figure of 2 right triangles, smallest legs joined, one reversed and moved to one vertex point.
But I am trying to jog my memory as to how all of this proves Space can be 3rd dimension at tops.
It must have something to do with the fact that 3 arbitrary points, noncollinear in Space forms a Unique Plane, and so if Space had 4th dimension--- there then exists no way this plane can enter or intercept a 4th dimension.
So I am trying to jog my memory.
Apparently I had no proof of no 4th dimension and beyond, for I did not have a proper proof of theorem derived 3 arbitrary points, noncollinear determines a unique plane.
But now that I do have that proof, I can go on to prove Space has to be 3rd dimension and no higher.
And the proof of no 4th dimension space and higher is the fact and idea that how does a plane traverse or lie in this higher dimension. We can think of a 3rd dimensional space as being a packaging container full of Planes. A volume of planes makes 3rd dimension. If we had a 4th dimension, none of our planes picks up any added dimension.
So now, in 10 Grid, in 3rd dimension, we have 100 points on x-axis and 100 on y-axis and 100 on z-axis, not counting zero (0,0,0). In total that would be 100^3 = 1,000,000 coordinate points or 10^6. Now how many possible arrangements are there of 3 distinct points? Is it the horribly large number of 1,000,000 factorial? No, for that is permutation math. Here I have Combination math and we have 1,000,000*999,999*999,998/ 3*2*1 = some huge number, not as bad as 1,000,000 factorial.
Now in my earlier proof, each triangle yields a unique plane, but many different triangles are also in that same plane. And that is a stumbling block I fell on before. Each triangle does produce a unique plane for that triangle, but that plane once formed carries many different triangles.
Now, how do I separate out all the triangles that lie within one plane in the 10 Grid? How do I extract the number of unique planes in 10 Grid?
So I have this number as the total number of unique triangles in 10 Grid= 1,000,000*999,999*999,998/ 3*2*1 reduced to 1,000,000*333,333*499,999 which is the number of unique triangles in the 10 Decimal Grid.
Now in the 10 Grid, how many triangles would each plane on average carry? If I examine the xy plane, a flat plane as representative of an average plane I am looking for an average number of triangles that forms that plane through expansion of its sides via the parallel axiom. So here is a duplicate Combination problem. 10,000*9,999*9,998 / 3*2*1 = 10,000*3,333*4,999. And now I divide 1,000,000*333,333*499,999 by that of 10,000*3,333*4,999 to arrive at an approximate average number of distinct planes that reside in the Space of a 10 Grid. This is approximately 100*10*10 = 10,000. Is this a surprise?? That the total number of points in 10 Grid 3D Space is 1,000,000 and the total number of planes in 10 Grid is approximately 10,000.
Does that look right?
So then, back to the question of a 4th Dimension?
Archimedes Plutonium
Aug 16, 2023, 4:05:46 AM
to Plutonium Atom Universe
Alright, when I started writing this book back in May 2023, I thought I discovered a new proof that 3rd dimension was tops and there was no 4th or beyond. I based that on the idea each Grid system had a center, such as 10 Grid was (5,5,5) and 100 Grid was (50,50,50). Turns out that was not a proof.
But I still have a proof of no 4th dimension or higher based on this proof of 3 arbitrary noncollinear points in Space forms a unique plane. I arrived at that proof as a derived theorem using the Axiom of parallelism, by extending the sides of every triangle in 3D Space to construct a unique plane from that triangle. In essence, I replaced Old Math's proof of 3 arbitrary noncollinear points in Space forms a unique plane. Old Math had that as a axiom itself. So their proof was not a proof at all but a axiom.
The real proof as derived uses the parallel postulate of Euclid.
In Harold Jacobs GEOMETRY, 2nd edition, 1987, he lists the postulate 3 on page 51 saying "Postulate 3 If there are three noncollinear points, then there is exactly one plane that contains them.
On page 204, "Postulate 10 (The Parallel Postulate) Through a a point not on a line, there is exactly one line parallel to the line."
So, well, what AP did, by constructing 3 points as triangles and proving 3 arbitrary noncollinear points determines a unique plane, is AP proved it from using the parallel postulate and thus we do not need postulate 3. It is redundant.
And it is here, the parallel postulate itself denies the existence of 4th dimension or higher. So in one instance I throw out an axiom in Old Math Geometry, and use the Parallel axiom to prove it as a theorem.
Yet this same parallel postulate is going to throw out the 4th dimension and higher. And the way it does that, through consistency.
A 4th dimension or higher does not give a unique line parallel to given line from a point outside the given line.
There is a better way of stating Euclid's parallel postulate in the idea that a line parallel to another line is a perpendicular on one is a perpendicular on the other.
____________ B
____|________A
Every point on line A when drawn a perpendicular is a perpendicular on line B.
In 3rd dimension we have x-axis perpendicular to y-axis and we have z-axis perpendicular to x-axis and we have z-axis perpendicular to y-axis. We have 3 perpendicular tests. When we talk of 4th dimension we need a perpendicular to x and y and z. But no new axis is available to be perpendicular to x,y, z. But say there was such, some would call it a hidden dimension, or a curled up dimension. But the trouble is, it would destroy the Parallel Postulate Axiom.
So the reason dimension ends at 3rd, is that higher than 3rd destroys the Parallel Postulate.
And this is a new method of proof, a proof by consistency, that when a statement is made to be proven, and if it contradicts an existing axiom, it is a false statement.
Now do not confuse this proof method as Reductio Ad Absurdum, for that is not a valid proof method. Proof by Consistency is a class of itself, and not reductio ad absurdum.
Archimedes Plutonium
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Proof of the Poincare Conjecture; my 1990's proof revised
0 views
a_plu...@hotmail.com's profile photo
Nov 30, 2005, 9:37:51 PM
to
Since I am revising my entire mathematics files on my website this
Winter, I may as well revise this Poincare Conjecture that I offered in
the early 1990s. Since I am on the topic of topology, I deem it wise
to revise this Poincare Conjecture. Thing is that the Natural-Numbers
are the P-adics Integers has a direct influence on my Poincare
Conjecture proof.
In the below I have already decided to revise parts thereof.
--- quoting my website in part
http://www.iw.net/~a_plutonium/File126.html ---
Proof of the Poincare Conjecture
There are many reasons why PC is so easy to grasp as a conjecture but
tremendously difficult to prove and why it was outstanding for 100
years. Here to enumerate a few.
(1) Math definition of dimension has never been understood nor resolved
to this date. In physics only the 3rd dimension makes sense where
experimentation has shown that any dimension other than 3rd leads to
the wrong physics of Newtonian Classical. That alone should have
alerted the math community that there definition of higher dimensions
were pure illusions, Loch Ness monsters.
(2) As if dimension definition was not enough of a bugaboo, but the
concept of "completion with a point at infinity" to make the Eucl plane
into a sphere. Math people once they hear this idea they sheepishly
accept it as clear as broad daylight. But we should require a proof of
this. Prove that the Eucl plane can be point compactified to it turn it
into a sphere? Point deletions are always possible, but point
compactification is silly. Where do Plane compactifiers propose to put
that point? I ask you, where do you attach it?
(3) (Revison) The idea that P-adic Integers are the Native points of
Riem geom make a huge difference to the Poincare Conjecture because the
sphere is a perfect model of Riem geometry. And the engine of my proof
below is the infinite iteration of roots. So does the P-adic Integers
have a infinite iteration of roots?
POINCARE CONJECTURE (PC) PROVED
Brief description of proof. PC rests on the fact that the
infinite iteration of roots of any positive Real number always
converges to the number 1. And for ADICS the infinite squaring of any
ADIC when converted to base 2 converges to 2 points, both ...00. and
...01. These convergences are the SIMPLY CONNECTED.
NOTE: All topological objects of the sphere are determinable as
Riemannian geom objects OR, as positive Real number objects. In this
way the iteration of roots or the squaring of any Adic in base 2 is the
simply connected.
The statement which I claim is not a well-formulated statement
of the Poincare Conjecture1 is this. The 3-sphere, the space obtained
by completing R3 by a point at infinity, is the only closed
3-dimensional space whose fundamental group is trivial. I assert this
Poincare Conjecture is not a well-formulated conjecture, it is a fuzzy
idea, only the notion of a conjecture.
I give a well-formulated Poincare Conjecture as follows:
Riemannian geometry is the only geometry which is simply connected
where positive Reals forms a positive Gaussian curvature or the Adics
are Riemannian geometry.
PROOF OF THE WELL-FORMULATED POINCARE CONJECTURE.
All topological objects of the sphere are determinable as
Riemannian geom objects or, as positive Real number objects. In this
way the iteration of roots or the squaring of any Adic in base 2 is the
simply connected. It is
easily proved that a function built on the infinite iteration of roots
of any positive Real number always converges to the number 1. For
example, you take any positive Real number, then you take successive
square roots, successive cube roots, successive quadratic roots and so
on, of that number, then the convergence of all of these iterative
roots sequences, all of these iterative roots, is to the number 1. But
the iterative roots function does not work with any negative numbers,
since imaginary numbers come into action, and negative numbers occur in
all geometries except Riem. Where Riem. geom is positive gaussian
curvature and so no negative curvature (no negative number) can occur
in Riem. geometry. Thus the iterative roots sequence is the simply
connected concept of every loop shrunk to a point, which means there
are no holes in the geometry. So for Riem. geom, every loop can be
shrunk
to the number 1. But every other geometry except Riem. geom has
negative
numbers and thus there exists loops in them which are impossible to
shrink
to a point. Q.E.D.
--- end quoting http://www.iw.net/~a_plutonium/File126.html
Final Note: just tonight I was thinking and posting about the Jordan
Curve Theorem and I can see that the Poincare Conjecture is very much
related to the JCT. And in fact the definition of a circle on a torus
may well rely upon the Poincare conjecture.
Archimedes Plutonium
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies
Proof of the Poincare Conjecture; my 1990's proof revised
0 views
Nov 30, 2005, 9:37:51 PM
to
Since I am revising my entire mathematics files on my website this
Winter, I may as well revise this Poincare Conjecture that I offered in
the early 1990s. Since I am on the topic of topology, I deem it wise
to revise this Poincare Conjecture. Thing is that the Natural-Numbers
are the P-adics Integers has a direct influence on my Poincare
Conjecture proof.
In the below I have already decided to revise parts thereof.
--- quoting my website in part
http://www.iw.net/~a_plutonium/File126.html ---
Proof of the Poincare Conjecture
There are many reasons why PC is so easy to grasp as a conjecture but
tremendously difficult to prove and why it was outstanding for 100
years. Here to enumerate a few.
(1) Math definition of dimension has never been understood nor resolved
to this date. In physics only the 3rd dimension makes sense where
experimentation has shown that any dimension other than 3rd leads to
the wrong physics of Newtonian Classical. That alone should have
alerted the math community that there definition of higher dimensions
were pure illusions, Loch Ness monsters.
(2) As if dimension definition was not enough of a bugaboo, but the
concept of "completion with a point at infinity" to make the Eucl plane
into a sphere. Math people once they hear this idea they sheepishly
accept it as clear as broad daylight. But we should require a proof of
this. Prove that the Eucl plane can be point compactified to it turn it
into a sphere? Point deletions are always possible, but point
compactification is silly. Where do Plane compactifiers propose to put
that point? I ask you, where do you attach it?
(3) (Revison) The idea that P-adic Integers are the Native points of
Riem geom make a huge difference to the Poincare Conjecture because the
sphere is a perfect model of Riem geometry. And the engine of my proof
below is the infinite iteration of roots. So does the P-adic Integers
have a infinite iteration of roots?
POINCARE CONJECTURE (PC) PROVED
Brief description of proof. PC rests on the fact that the
infinite iteration of roots of any positive Real number always
converges to the number 1. And for ADICS the infinite squaring of any
ADIC when converted to base 2 converges to 2 points, both ...00. and
...01. These convergences are the SIMPLY CONNECTED.
NOTE: All topological objects of the sphere are determinable as
Riemannian geom objects OR, as positive Real number objects. In this
way the iteration of roots or the squaring of any Adic in base 2 is the
simply connected.
The statement which I claim is not a well-formulated statement
of the Poincare Conjecture1 is this. The 3-sphere, the space obtained
by completing R3 by a point at infinity, is the only closed
3-dimensional space whose fundamental group is trivial. I assert this
Poincare Conjecture is not a well-formulated conjecture, it is a fuzzy
idea, only the notion of a conjecture.
I give a well-formulated Poincare Conjecture as follows:
Riemannian geometry is the only geometry which is simply connected
where positive Reals forms a positive Gaussian curvature or the Adics
are Riemannian geometry.
PROOF OF THE WELL-FORMULATED POINCARE CONJECTURE.
All topological objects of the sphere are determinable as
Riemannian geom objects or, as positive Real number objects. In this
way the iteration of roots or the squaring of any Adic in base 2 is the
simply connected. It is
easily proved that a function built on the infinite iteration of roots
of any positive Real number always converges to the number 1. For
example, you take any positive Real number, then you take successive
square roots, successive cube roots, successive quadratic roots and so
on, of that number, then the convergence of all of these iterative
roots sequences, all of these iterative roots, is to the number 1. But
the iterative roots function does not work with any negative numbers,
since imaginary numbers come into action, and negative numbers occur in
all geometries except Riem. Where Riem. geom is positive gaussian
curvature and so no negative curvature (no negative number) can occur
in Riem. geometry. Thus the iterative roots sequence is the simply
connected concept of every loop shrunk to a point, which means there
are no holes in the geometry. So for Riem. geom, every loop can be
shrunk
to the number 1. But every other geometry except Riem. geom has
negative
numbers and thus there exists loops in them which are impossible to
shrink
to a point. Q.E.D.
--- end quoting http://www.iw.net/~a_plutonium/File126.html
Final Note: just tonight I was thinking and posting about the Jordan
Curve Theorem and I can see that the Poincare Conjecture is very much
related to the JCT. And in fact the definition of a circle on a torus
may well rely upon the Poincare conjecture.
Archimedes Plutonium
www.iw.net/~a_plutonium
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies
Archimedes Plutonium
Thanks very much Dik for the above table.
I suspect I have found a pattern that will help me to understand how
the P-adics are native numbers for Riem geometry. The pattern I see
above for the convergences of P-adic Integers is the pattern followed
in Atomic Physics of the s, p, d, f orbitals of electrons. The s
orbital is a sphere but the p and d and f orbitals are lobes extending
from the nucleus.
In Positive Reals as the surface of a sphere converges by iterative
roots to that of 1. For 2-adic integers iterative squaring also
converges to a sphere since podes and antipodes constitute one point.
But as for other p-adics and n-adics have lobes and the lobes have
convergence points.
I sense a pattern of the convergence points as the lobes of atomic
physics of the p, d and f orbitals of atoms.
We know that a sphere is a perfect model of Riemannian geometry, but we
do not know how lobes are also a model of Riemannian geometry, and if
the Adic Integers are the native-numbers of Riem geometry, then their
characteristics such as convergency is a window into Riem geometry.
Some features I have to work out are these:
(1) since Adic Integers constitute Riem geom of their native points,
then Adic Rationals constitute the native points of Loba geom, only
they have to be negative points so we would have to put a negative sign
in front of every Adic Rational.
Dik, I would suspect that Adic Rationals have no convergence. Is that
true?
(2) if I can get Riem geom parallel postulate + Lob geom parallel
postulate to equal that of Eucl geom parallel postulate in the fashion
of 2 + 0 + ...9999 = 1 where 1 represents one line parallel and 0
represents no lines parallel and ...9999 represents infinite number of
lines parallel. Then I will have accomplished a proof that putting a
donut hole inside the hole of a donut ends up with Eucl geom. But I
would have to have a equality, or equivalence or something similar to
equivalence for the Algebraic side of that equation of Riem geom + Loba
geom = Eucl geom. I am looking for something like this : Adic
Integers + Adic Rationals = Reals.
Only the Adic Rationals would all have a negative sign.
Now we know that when we fit a donut hole inside a hole of a donut that
there are still scars or cavities that does not make fully
3-dimensional Eucl geom. So I have to modify that equation to be
something else for it is not equality but something similar to
equality.
Likewise for the Algebra of
Adic Integers + Adic Rationals(negative numbers) = Reals
where the Adic Integers are the donut hole (sphere or lobes) and the
Adic Rationals are the donut (odd looking donut to accomodate lobes of
p, d, f electronic orbitals)
So it probably is not an equality or equivalence relationship and not
an equation but something weaker.
But as for now I will continue to use equality and continue to use the
add sign--
Riem geom + Loba geom = Eucl geom
Adic Integers + Adic Rationals (negative numbers) = Reals
Archimedes Plutonium
In the 1800s, Bernhard Riemann and Enrico Betti initiated the study of topological invariants of manifolds.[9][10] They introduced the Betti numbers, which associate to any manifold a list of nonnegative integers. Riemann showed that a closed connected two-dimensional manifold is fully characterized by its Betti numbers. As part of his 1895 paper Analysis Situs (announced in 1892), Poincaré showed that Riemann's result does not extend to higher dimensions.[11][12][13] To do this he introduced the fundamental group as a novel topological invariant, and exhibited examples of three-dimensional manifolds which have the same Betti numbers but distinct fundamental groups. He posed the question of whether the fundamental group is sufficient to topologically characterize a manifold (of given dimension), although he made no attempt to pursue the answer, saying only that it would "demand lengthy and difficult study".[12][13][14]
The primary purpose of Poincaré's paper was the interpretation of the Betti numbers in terms of his newly introduced homology groups, along with the Poincaré duality theorem on the symmetry of Betti numbers. Following criticism of the completeness of his arguments, he released a number of subsequent "supplements" to enhance and correct his work. The closing remark of his second supplement, published in 1900, said:[15][13]
orientable is simply connected, i.e., homeomorphic to a hypersphere.(In a modern language, taking note of the fact that Poincaré is using the terminology of simple-connectedness in an unusual way,[16] this says that a closed connected oriented manifold with the homology of a sphere must be homeomorphic to a sphere.[14]) This modified his negative generalization of Riemann's work in two ways. Firstly, he was now making use of the full homology groups and not only the Betti numbers. Secondly, he narrowed the scope of the problem from asking if an arbitrary manifold is characterized by topological invariants to asking whether the sphere can be so characterized.
However, after publication he found his announced theorem to be incorrect. In his fifth and final supplement, published in 1904, he proved this with the counterexample of the Poincaré homology sphere, which is a closed connected three-dimensional manifold which has the homology of the sphere but whose fundamental group has 120 elements. This example made it clear that homology is not powerful enough to characterize the topology of a manifold. In the closing remarks of the fifth supplement, Poincaré modified his erroneous theorem to use the fundamental group instead of homology:[17][13]
In this remark, as in the closing remark of the second supplement, Poincaré used the term "simply connected" in a way which is at odds with modern usage, as well as his own 1895 definition of the term.[12][16] (According to modern usage, Poincaré's question is a tautology, asking if it is possible for a manifold to be simply connected without being simply connected.) However, as can be inferred from context,[18]Poincaré was asking whether the triviality of the fundamental group uniquely characterizes the sphere.[14]
Throughout the work of Riemann, Betti, and Poincaré, the topological notions in question are not defined or used in a way that would be recognized as precise from a modern perspective. Even the key notion of a "manifold" was not used in a consistent way in Poincaré's own work, and there was frequent confusion between the notion of a topological manifold, a PL manifold, and a smooth manifold.[16][19] For this reason, it is not possible to read Poincaré's questions unambiguously. It is only through the formalization and vocabulary of topology as developed by later mathematicians that Poincaré's closing question has been understood as the "Poincaré conjecture" as stated in the preceding section.
However, despite its usual phrasing in the form of a conjecture, proposing that all manifolds of a certain type are homeomorphic to the sphere, Poincaré only posed an open-ended question, without venturing to conjecture one way or the other. Moreover, there is no evidence as to which way he believed his question would be answered.[14]
Archimedes Plutonium
The Klein bottleimmersed in three-dimensional space
The surface of the Earth requires (at least) two charts to include every point without plotting the same point more than once on the same chart. Here the globe is decomposed into charts around the North and South Poles.In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an -dimensional manifold, or -manifold for short, is a topological space with the property that each point has a neighborhood that is homeomorphic to an open subset of -dimensional Euclidean space.
-dimensional manifold, or One-dimensional manifolds include lines and circles, but not self-crossing curves such as a figure-eight. Two-dimensional manifolds are also called surfaces. Examples include the plane, the sphere, and the torus, and also the Klein bottle and real projective plane.
The concept of a manifold is central to many parts of geometry and modern mathematical physics because it allows complicated structures to be described in terms of well-understood topological properties of simpler spaces. Manifolds naturally arise as solution sets of systems of equations and as graphs of functions. The concept has applications in computer-graphics given the need to associate pictures with coordinates (e.g. CT scans).
Manifolds can be equipped with additional structure. One important class of manifolds are differentiable manifolds; their differentiable structure allows calculus to be done. A Riemannian metric on a manifold allows distances and angles to be measured. Symplectic manifolds serve as the phase spaces in the Hamiltonian formalismof classical mechanics, while four-dimensional Lorentzian manifoldsmodel spacetime in general relativity.
The study of manifolds requires working knowledge of calculus and topology.
Figure 1: The four charts each map part of the circle to an open interval, and together cover the whole circle.After a line, a circle is the simplest example of a topological manifold. Topology ignores bending, so a small piece of a circle is treated the same as a small piece of a line. Considering, for instance, the top part of the unit circle, x2 + y2 = 1, where the y-coordinate is positive (indicated by the yellow arc in Figure 1). Any point of this arc can be uniquely described by its x-coordinate. So, projection onto the first coordinate is a continuous and invertiblemapping from the upper arc to the open interval (−1, 1):
Such functions along with the open regions they map are called charts. Similarly, there are charts for the bottom (red), left (blue), and right (green) parts of the circle:
Together, these parts cover the whole circle, and the four charts form an atlas for the circle.
Archimedes Plutonium
Dimension proof, that 3rd is the last and final dimension// physics-math
by Archimedes Plutonium
This is AP's 213th 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: While looking for some old posts of 1994, a chance encounter; I ran across a post about Dimension. It does not take much to stimulate me on research of dimensions. I have been trying to proof in both math and physics that dimension does _not exist_ beyond 3rd dimension. That 3rd dimension is the last and final dimension, and I began looking for such a proof/s ever since 1991. There was the familiar proof that everyone knows-- adding a new perpendicular to existing 3 perpendiculars is impossible, for a 4th perpendicular only repeats one of the three already existing perpendiculars. But I wanted more than that proof. I wanted a proof out of physics. For it is physics that has spearheaded this crazy phenomenon of 4th dimension and higher. I wanted a proof directly out physics that ends the debate and discussion of higher dimensions. Fortunately I ran across this Usenet post/email of 1994, which offers a clear guidance as to how that proof of physics must go.
Cover Picture: Is my computer graphic of 3rd dimension from the erection of 3 axes, the x, y, and z axes as 3 perpendiculars from one another, and that a 4th would only be a repeat of one of the three existing axes.
-----------------------------
Table of Contents
-----------------------------
1) My history on the subject matter of this book.
2) My best opportunity for a physics proof that 3rd Dimension is last and final dimension.
3) My math proof experience; how much?
4) The Proof: in math and physics, 3 and only 3 dimensions exist.
5) Physics proof is always worth more than a mathematics proof.
6) Proof of 3rd dimension is last and final, because Volume and Voltage is all inclusive.
7) Physics 3rd dimension derives Coulomb constant 1*10^10 kg*m^3*s^-4*A^-2 from mass of neutron.
8) Proton+muon rest mass to be more precisely that of 1.61...*10^-27 kg, rather than their current 1.672... prefix.
---------
Text
---------
1) My history on the subject matter of this book.
An old email of 1994 on dimensions in physics and math// Needs a new look. While looking for posts of my suspension for 1 month from Usenet in 1994, by posting --- The Jew York Times. Looking through my archive of posts and emails I ran across this
Archimedes Plutonium<plutonium....@gmail.com>
Oct 3, 2022, 12:56:25 AM
to Plutonium Atom Universe
An old email of 1994 on dimensions in physics and math// Needs a new look.
While looking for posts of my suspension for 1 month from Usenet in 1994, by posting --- "The Jew York Times" over my anger of the newspaper The New York Times and their propaganda format in their science section, where most articles on physics had to have a reference to Einstein even though the science never warranted such a plug for Einstein. (See my published 209th published book:
Fair Journalism in reporting Science news-- The New York Times, Google, Wikipedia, NATURE, SCIENCE, magazines// Sociology by Archimedes Plutonium (Author)
So in looking in my archive of posts to Usenet for that 1994 suspension of my posting to Usenet, I happened to glance this Email post pertaining to dimension.
Looking through my archive of posts and emails I ran across this email. I have no idea who sent it. Whether they are still alive or not? But my science has grown and matured since 1994 and I have deep abiding belief that the world is 3rd dimension only, and higher dimensions are folly. So, will review the below and see if any thing comes of this.
Date: Sun, 26 Jun 94 22:09:31 EDT
To: Ludwig.P...@Dartmouth.EDU
Subject: Re: FAREWELL SCI.MATH FROM LP.
Newsgroups: sci.math
In-Reply-To: (2ulab0$9...@dartvax.dartmouth.edu>
Ludwig,
I don't think this will help you prove that there are only
three dimensions, but you might find it interesting, since it is
along the same line. It turns out that if you try to write down
an algebra, like the real number system, or complex numbers, you
can only do it in 1,2,4,or 8 dimensions. These solutions correspond
to real numbers, complex numbers, quaternions, and octonions, respectively.
It is a real math theorem which you can prove, although, of course,
it depends on how you define 'algebra'.
By the way, the QM description of a two-electron system requires
that one solve the Schroedinger equation in six dimensions. This is standard QM. How do you reconcile that with your claim that there are only three dimensions?
Archimedes Plutonium<plutonium....@gmail.com>
Oct 3, 2022, 1:12:13 AM
to Plutonium Atom Universe
Yes, I found who emailed me this missive back in 1994. The good news is that, I have some vital news on the subject and questions involved. One is bound to have more insight on the passing of 28 years elapsed time. I hope Mr. Ely is still alive and can read these posts.
Usenet title of thread in 1994:
IS THIS A THEOREM OF MATH
Ludwig Plutonium
Aug 3, 1994, 1:42:33 PM
to sci.math
It turns out that if you try to write down
an algebra, like the real number system, or complex numbers, you
can only do it in 1,2,4,or 8 dimensions. These solutions correspond
to real numbers, complex numbers, quaternions, and octonions,
respectively.
It is a real math theorem which you can prove, although, of course,
it depends on how you define 'algebra'.
I was supplied with that information and I want to confirm if true.
Thanks in advance.
Aug 3, 1994, 7:24:24 PM
to sci.math
In article <31p61m$k...@agate.berkeley.edu>,
je...@econ.berkeley.edu (Jeffrey Ely) writes:
>> It turns out that if you try to write down
>>an algebra, like the real number system, or complex numbers, you
>>can only do it in 1,2,4,or 8 dimensions. These solutions correspond
>>to real numbers, complex numbers, quaternions, and octonions,
>>respectively.
>Curiously enough you can also do it in Montana. The solution then
>corresponds to Montanans.
Out of all of Ludwig's oeuvre, what possessed you to select this
as worthy of posting to alt.usenet.kooks? It happens to be
a mathematical fact that the only finite dimensional alternative
division algebras over the reals are the reals R, the complex numbers C,
the quaternions H, and the octonions O; of dimensions 1, 2, 4,
and 8 respectively.
--
Gene Ward Smith/Brahms Gang/University of Toledo
gsm...@uoft02.utoledo.edu
PatT507
Aug 3, 1994, 7:30:08 PM
to sci.math
In article <31ooep$f...@dartvax.dartmouth.edu>,
Ludwig.P...@dartmouth.edu (Ludwig Plutonium) writes:
Re:Hopf Invariant One i.e Is this a theorem?
Yes it is a theorem. The only real division algebras are the reals,complex
numbers,quaternions and Cayley numbers.
J.F.Adams proved this theorem in the 60's. Actually he solved The Hopf
Invariant One problem of algebraic topology, which proves that these are
the only real division algebras.
Keith Conrad
Aug 3, 1994, 4:36:21 PM
to sci.math
Yes, Ludwig, the only real division algebras are the reals, complexes, and
quaternions. If you allow real algebras where every nonzero element
is invertible but multiplication is not necessarily associative or
commutative (so-called alternative division algebras) then the only
additional such algebra is the octonions. You can read a proof that any
finite dimensional (real) algebra must be one of these four in Jacobson's
Basic Algebra I. The fact that any real alternative division algebra
must be finite dimensional is not so easy to prove.
Since you seem to like the p-adics, I'll throw in the fact that there are
division algebras of arbitrarily large dimension over any p-adic field.
See the end of Jacobson's Basic Algebra II for that. So it is not true
in general that all (alternative) division algebras (over a general field)
must have dimensions 1,2,4 or 8.
Keith Conrad
Jeffrey Ely
Aug 3, 1994, 5:34:30 PM
to sci.math
In article <31ooep$f...@dartvax.dartmouth.edu>, Ludwig.P...@dartmouth.edu (Ludwig
Plutonium) says:
>
> It turns out that if you try to write down
>an algebra, like the real number system, or complex numbers, you
>can only do it in 1,2,4,or 8 dimensions. These solutions correspond
>to real numbers, complex numbers, quaternions, and octonions,
>respectively.
Curiously enough you can also do it in Montana. The solution then
corresponds to Montanans.
&&&&&&
Jeff Ely "The Sun's not yellow...
Department of Economics, UC Berkeley It's Chicken!"
je...@econ.berkeley.edu
&&&&&&
"...a man of great talent will normally pay less attention to other
people's foolishness than would a fool." -Proust
2) My best opportunity for a physics proof that 3rd Dimension is last and final dimension.
Archimedes Plutonium<plutonium....@gmail.com>
Oct 3, 2022, 1:26:20 AM
to Plutonium Atom Universe
>
> Ludwig,
> I don't think this will help you prove that there are only
> three dimensions, but you might find it interesting, since it is
AP: I think it will be another indicia of proof evidence that only 3 dimensions exist.
> along the same line. It turns out that if you try to write down
> an algebra, like the real number system, or complex numbers, you
> can only do it in 1,2,4,or 8 dimensions. These solutions correspond
> to real numbers, complex numbers, quaternions, and octonions, respectively.
> It is a real math theorem which you can prove, although, of course,
> it depends on how you define 'algebra'.
AP: Yes, I think that is the crux of the whole deal-- how do we define "algebra"
> By the way, the QM description of a two-electron system requires
> that one solve the Schroedinger equation in six dimensions. This is standard QM. How do you reconcile that with your claim that there are only three dimensions?
In the passing years, the 28 years, I learned the primal principle of all of science and physics-- All is Atom, and Atoms are nothing but electricity and magnetism.
So we go further to the next axioms, the axioms that come from the primal axiom. The axioms that are the laws of electromagnetism, what Maxwell found in the Maxwell Equations.
However we revise all of the Maxwell Equations, for some are seriously in error and flawed.
And these newer Equations of Electricity and Magnetism come as Six equations.
--- quoting from my textbook TEACHING TRUE PHYSICS, 1st year College ---
Mathematics has 6 operators, add, subtract, multiply, divide, integral, derivative. So Physics, as a reflection of mathematics, needs at least 6 laws of EM theory. If mathematics can do all of mathematics with 6 operators, it is no surprise that symmetry of science would call for 6 laws of EM physics. Much of science is like this, where a fact in math is also a fact in physics and vice versa. There is always symmetry in science, and that is because atoms are symmetrical entities. All is Atom, and atoms are nothing but electricity and magnetism.
Those 6 laws are these.
1) Magnetic monopole telling us what magnetism and electric current and magnetic field and electric field are.
2) New Ohm's law Voltage = capacitor-battery = quantity of current C times magnetic field times electric field. V= CBE. The equation of New Ohm's law is a math equation of volume Volume = length x width x height so we can expect that New Ohm's law is a measuring of volume in physics, volume of energy.
The next 4 laws are derivatives of all the possible 4 permutations of C, B, E, and V.
3) Rate of change of C, quantity current, C' = (V/(BE))' Faraday law.
4) Rate of change of B, magnetic field, B' = (V/(CE))' Ampere-Maxwell law.
5) Rate of change of E, electric field, E' = (V/(CB))' Coulomb law & gravity.
6) The rate of change of V= CBE as V' = (CBE)' as AC transformer law.
I need to start with those 6 laws and on units of electromagnetism and the definition of magnetic monopoles that composes electricity, and photon light-waves, and neutrinos.
Units
V = voltage
A = ampere current
s = seconds
C = Coulomb, amount of electricity = A*s
B = Magnetic field
E = Electric field
m = meters
kg = kilogram mass
More Units
Angular momentum L = kg*m^2/s
Pressure = kg/(m*s^2)
Action = kg*m^2/s where angular momentum = action and resembling both magnetic field and electric field but not equal to them.
Current = A, where the A represents Ampere
Quantity of Current = C = A*s where the C represents Coulomb
Magnetic Field B = m^2/ A*s^2 = m^2/ C*s
Electric Field is E = m^2/ A*s^2 = m^2/ C*s
Voltage = C*B*E = m^4 /A*s^3 = m^4 /C*s^2
Notice that there is no difference between Magnetic field and Electric field except the fact that one is perpendicular to the other as seen in the cover picture of bent circles at 90 degrees on a diameter.
Units are extremely important in Physics, and whenever mistakes are made, often, the blame is because of incorrect units, or a misunderstanding of units.
Here we need to pause a minute and review two other important Units of physics, the force unit and energy unit.
Force = kg*acceleration = kg*(meter/sec^2)
Energy = (kg)* (meter^2/sec^2) We ignore the 1/2 coefficient that is in kinetic energy.
Power (mechanical) = kg*(meter^2/sec^3)
Power (electrical) = meter^2/(A*sec^3)
3) My math proof experience; how much?
Somewhat strange to me, Mr. Ely, Berkeley, that someone in the Economics dept of Berkeley has so much interest in pure physics. Which is a good sign, for an economist who knows physics must be a highest quality economist!!! Or, it could be that you are actually a physicist just using a economics posting terminal. For I have the idea that someone who goes into Economics is desperately trying to get away from physics, chemistry, math.
But anyway, through the passage of time, 28 years in fact. I can answer your question and also bolster and support my hypothesis-- 3rd is the last and final dimension.
Notice there are 6 required laws to make Electromagnetic theory. At minimum you need those 6 and they describe all physics interactions. The Schrodinger Equation as you mention in your mail-post needs 6 dimensions. When really, what that means is the Schrodinger Equation requires the 6 laws of EM theory.
And the Schrodinger Equation describes 3 dimensional geometry. So you are confusing dimension with algebra. Algebra is defined as "minimal set of laws describing the system in play". You need 6 EM laws, to make the Schrodinger Equation work properly. And so, in conclusion, those 6 laws are 3 dimensional, the Schrodinger Equation is 3 dimensional.
Once you remove the confusion of dimension as algebra, then you conclude EM theory is 3 and only 3 dimensions and Schrodinger Equation is 3rd dimension.
Now someone will likely raise the question of the Dirac Equation. And questioning the dimension in Dirac Equation. Well fortunately for me in the passing of 28 years, I wrote a book on the Dirac Equation, ending up dismissing the Dirac Equation as a sham equation. Dirac was looking for a magnetic monopole most of his life, and it was right there in front of his nose-- the 0.5MeV particle that Thomson found in 1897. The true electron of atoms is the muon stuck inside a 840MeV proton torus doing the Faraday law.
So now going back in history, Dirac wanted to make the Schrodinger equation relativistic. Dirac never realized that the Schrodinger equation was Already relativistic. Because Dirac and Schrodinger had the wrong particle of the Atom's Electron.
So the Dirac equation ends up being a worthless pile of junk, a redundancy. The Dirac Equation one can jokingly say is the Schrodinger Equation-squared, for it was already relativistic.
The Dirac equation was Dirac's greatest mistake in physics. But his greatest achievement in physics far outweighs his mistake-- for the superb logical mind of Dirac knew that his Magnetic Monopole had to exist. Unfortunately, it was under his nose all along-- the 0.5MeV particle.
I think I figured this out, Berkeley had a physicist Dr Ely and did he have a economist son???? Mr. Jeffrey Ely, but which of the two wrote the physics message?
> Somewhat strange to me, Mr. Ely, Berkeley, that someone in the Economics dept of Berkeley has so much interest in pure physics. Which is a good sign!!! For I have the idea that someone who goes into Economics is desperately trying to get away from physics, chemistry, math.
>
I am going to use this as a proof that Space has 3 and only 3 dimensions. Old Physics confused algebra with dimension. The argument goes, that Schrodinger Equation is the highest form equation to do waves of physics and it is only 3rd dimension, for its results make no geometry sense in 4th or higher dimension.
Or, one could say, you cannot have a Faraday law if you had 4th or higher dimensions. This seems more practical of a proof, a proof that forbids because it destroys the Faraday law.
I thank the Ely folk for bringing that to my attention in 1994, and unable to respond with anything until now in 2022.
Anyway, I need to find out if this math theorem, Dr. Ely's mention of one, has a name to it.
And it looks to me as though, this proof of 3rd is highest and last dimension must involve the laws of electromagnetism. That Electromagnetism is encapsulated in the Schrodinger Equation, an equation that is strictly confined to 3D.
The proof will be along the lines that physics is built from the 6 laws of electromagnetism, all permutations of New Ohm's Law V = CBE. Those 6 laws become what mathematicians call "algebras". And that is quite logical and fanciful, for a law of physics is very much so, a algebra of mathematics.
The proof will look much like the idea, that if there exists more dimensions than 3, then there has to be more laws of physics and there has to be a larger Schrodinger Equation. A generalized Schrodinger Equation of which there has never been any experimental evidence for.
Now I wrote a book containing a generalization of the Faraday law. And of all places in Ecology biology where I wrote:
--- quote from my Ecology book ---
4) Generalized Faraday Law helps connect psychology with ethology with ecology.
What is the Generalized Faraday law? So let us have a brief review of what that law means. In the Faraday law we have a thrusting bar magnet through a closed loop coil of copper wire and it produces electricity in that copper coil. In Generalized Faraday law, we have a Light wave instead of a bar magnet thrusting through another Light Wave perpendicular to the first, or thrusting through DNA molecule and this produces electricity or messaging signals in the Light Wave or DNA. So as we watch Attenborough's The Green Planet and amazed at how leaves of plants or trees in a forest signal and message one another, --- they do it by Light waves thrusting through other Light waves or DNA, creating signals and messages.
--- end quoting my Ecology book ---
I called it a generalization of Faraday law but it is Faraday law itself. Maybe I should have called it something else. For it does not upset or disturb the fact that Faraday law is 3 dimensional and no more.
So to prove that a 4th dimension exists, we need something in EM theory of its 6 laws that we find in experiments but not find in any of the laws of EM theory. And to date, no such "new phenomenon" has ever been seen, not covered by EM theory.
However, there maybe a shortcut to the proof that 3rd dimension and no higher exists from the mere fact that speed of light is a maximum speed and a constant speed. It maybe the case that such is true only if 3rd dimension is the highest dimension. If a 4th dimension exists, I would have to show that the speed of light is not the maximum constant speed in Nature. But, here again, this is all part and parcel of EM theory. And I am not aware of any paradoxes in EM theory to go looking for a breakdown of EM theory.
Alright, I do not know why I was so naive as to think this was a singular theorem. It is the modern day wastrel theory of algebras, applied to physics. Reminds one of the Tycho Brahe collecting data, and that data only made sense once Kepler applied his laws to the data.
Algebras of mathematics into physics is wastrel game playing. And their conclusions are hypocrisy. Much of the Standard Model was this hypocrite game playing.
So I looked up the last one of these mentioned by Ely. The octonions, and realized that all this was game playing.
Instead of Physicists talking about "normed division algebra" what they really are talking about is that the EM laws of physics have perpendicularity of magnetic field to electric field.
When physicists talk about "noncommutative" what they really are talking about is the fact that 3 of the 6 laws of EM theory are divisions and hence noncommutative.
When physicists talk about "nonassociative but a weaker alternative" what they are talking about, unknown to them though, is EM theory that V' = (CBE)' the transformer law is nonassociative but is alternative.
When physicists talk about "power associative" what they are talking about, unknown to them though, is that V= CBE is a capacitor or battery in EM theory and is power associative.
On, down and down with every algebra description is replaced with a physics description of the 6 laws of EM theory.
Yes, physicists were in a total fog for most of the 20th century with their game playing algebra. And one of the great faults of that game-playing was they were for the most part too stupid to realize that EM theory is the center piece of physics, yet they opted for the silly and stupid General Relativity that sucked out most of the oxygen in the 20th century.
Mathematics algebra is playing games, playing with models that never matched physical reality.
--- quoting Wikipedia on Octonions ---
In mathematics, the octonions are a normed division algebra over the real numbers, a kind of hypercomplex number system....Octonions have eight dimensions; twice the number of dimensions of the quaternions, of which they are an extension. They are noncommutative and nonassociative, but satisfy a weaker form of associativity; namely, they are alternative. They are also power associative.
History
The octonions were discovered in 1843 by John T. Graves, inspired by his friend William Rowan Hamilton's discovery of quaternions. Graves called his discovery "octaves", and mentioned them in a letter to Hamilton dated 26 December 1843. He first published his result slightly later than Arthur Cayley's article. The octonions were discovered independently by Cayley and are sometimes referred to as "Cayley numbers" or the "Cayley algebra". Hamilton described the early history of Graves' discovery.
--- end quoting Wikipedia ---
Now I have had a lot of experience in math proofs, far more than most mathematicians, perhaps the greatest number of math proof, except Euclid and Archimedes of Ancient Greek times.
And the one item I have learned and picked up in all my math proofs, is the fact that once a theorem is given a proof, that it is not the be all and end all of that proof. The theorem through the years keeps nag nag nagging at you, to freshen up or simplify the theorem, even in some cases correct mistakes of the proof, such as my experience in the 6th Regular Polyhedron, finding out that computer graphics had polluted geometry such as the Goldberg Polyhedron. What I am trying to say is that a proof of mathematics will often follow you until you die, keep nagging.
When I proved that the slant cut of cone was not the ellipse but really the Oval, in 2016, it took several years later for me to reduce the proof to a simple concept-- cylinder and ellipse 2 axes of symmetry, cone and oval 1 axis of symmetry.
And so, I am almost positive that this proof that the world has 3 and only 3 dimensions and 4th and higher are b.s. (sorry, that is the best term for it). I am almost certain that this proof needs reduction.
4) The Proof: in math and physics, 3 and only 3 dimensions exist.
My proof so far is this:
Statement: In all the World, science, physics, math, there exists 3 and only 3 dimensions, no dimensions beyond 3rd.
Proof: The Schrodinger Equation is the pinnacle equation of quantum mechanics wave geometry. This equation is confined to 3rd dimension. It requires 6 algebras. Algebras of math directly corresponds to 6 laws of EM theory, the only 6 laws that describe all of EM theory. Thus, since Shrodinger Equation is 3rd dimension only. Means all of physics and hence all of mathematics is 3rd dimension and no higher.
That is a substantial and convincing proof. QED.
However, given my past history of proofs in math or physics (experiment + logic). I would easily wager a bet that I will soon come back with a sentence proof. Such as perhaps, if there is a 4th dimension, we would not have the Light Wave be Transverse with magnetic field perpendicular to electric field. Or something concerning speed of light.
That a 4th dimension or higher would totally destroy EM theory, the heart of all physics. The heart inside the Atomic theory.
5) Physics proof is always worth more than a mathematics proof.
Now a physics proof is always worth more than a math proof. This is because mathematics is a small subset inside of physics.
And that is some of the problem here. For if not for physics there would never be a 4th dimension or higher in mathematics. Most of the fault and blame for having higher dimensions than 3rd dimension can be placed at the lap of physics, with their silly 4th dimension as time or their 8 or 9 or 10 or 11 dimensions in their kook string theories.
Higher dimensions really are a physics kook basketweaving, underwater basketweaving, and then mathematics just went along with the insane ride.
But there are several pure math proofs that 3rd is the last and largest dimension.
#1 Standard Pure Math Proof that 3rd dimension is highest and last dimension.
Statement: 3rd dimension is the highest and last dimension of mathematics.
Proof:
The standard common math proof involves perpendicular axes. You start with the x-axis for 1 dimension. You add a second axes for y-axis and now you are in 2nd dimension, in graphing. Now you add a new perpendicular to the x-y plane for a 3rd axis, the z-axis and you now are in 3rd dimension. However, you cannot add a new 4th axis perpendicular to the x-y-z solid. There is no room, no place to put a new perpendicular axes, not already occupied by the x-y-z axes. A new one is not possible for it is a redundancy of one of x,y,z. QED
Now here the dumb silly physicist comes up with some really kook idea of "curled dimension". No more needs to be said, it is kookish and a kooks way of not admitting 3rd is the last dimension.
Now I found a new proof, other than the standard proof that 3rd is the highest and last dimension.
And I know I will receive much "flak" for offering this. And if it is true and valid proof, it probably is the world's most simple, most logical math proof, not physics but math proof that the World has 3rd dimension as last and highest dimension.
#2 Perhaps the worlds finest streamlined proof of pure math that 3rd dimension is last and highest dimension.
Statement: The 3rd dimension is last and final dimension in pure math.
Proof: The smallest closed figure of Geometry is the right triangle with one angle being 90 degree for electricity and magnetism. If there existed a 4th dimension, then the right triangle would not be the smallest closed figure, but that a square would be the smallest right angle closed figure. Since the Right Triangle is the smallest closed figure with a right angle implies dimension of 3 is highest and last dimension. Similarly, if a 5th dimension exists, then the smallest closed figure with right angles would be a pentagon, but no, we have smaller closed figures of 4-gon and 3-gon. QED.
This proof is actually a sentence proof of pure geometry math.
Proof: Right Triangle is the smallest closed figure of geometry, hence 3rd dimension is the last and final dimension. QED
This proof comes from the idiotic physicist with his curled dimensions and a rebuff to the stupid idea of curled dimension.
Now, I want a similar proof of physics that the 3rd dimension is last and final, a one liner proof. I cannot get that one liner proof from Schrodinger Equation proof.
Now, all those stupid in logic-- flak away,,, flak away,,,
Alright, I make a personal self note to myself in this post. I find myself always better able to think and to reason after I had a long night sleep. Maybe that is the case with nearly every human? Is it the case?? I may find good morsels of thought late at night before bed. But nothing compares to waking up after 10 hours of sleep and the start of a new day. Many humans are forced to wake up-- their jobs-- their family -- their livelihood.
But for me, everyday, I sleep in, and for good reason, because I have found that abundant sleep is the only means of crystal clear thinking, crystal clear logic.
So that I can pick up from yesterday, pick up all the pieces and find the final correct conclusion.
Last night I was working on proofs of 3 and only 3 dimensions. But not until now, this morning am I able to write crystal clear proofs of 3 and only 3 dimensions.
In fact I proved 3 and only 3 dimensions in both Mathematics and in Physics as my table of contents in one of my TEACHING TRUE PHYSICS textbooks.
It is my Senior year High School textbook that I had already proven that dimensions in math and in physics can only be 3 dimensions and any higher is nonexistent.
Let us glimpse the Table of Contents of that book:
TEACHING TRUE PHYSICS// Senior High School// Physics textbook series, book 3
by Archimedes Plutonium
Books in this series are.
Introduction to AP's TEACHING TRUE PHYSICS// Physics textbook series, book 1
TEACHING TRUE PHYSICS High School junior year, book 2
TEACHING TRUE PHYSICS High School senior year, book 3
TEACHING TRUE PHYSICS 1st year college, book 4
TEACHING TRUE PHYSICS Sophomore college, book 5
TEACHING TRUE PHYSICS Junior college, book 6
TEACHING TRUE PHYSICS Senior college, book 7
Preface: I believe that in knowing the history of a science is knowing half of that science. And that if you are amiss of knowing the history behind a science, you have only a partial understanding of the concepts and ideas behind the science. I further believe it is easier to teach a science by teaching its history than any other means of teaching. So for senior year High School, I believe physics history is the best way of teaching physics. And in later years of physics courses, we can always pick up on details. So I devote this senior year High School physics to a history of physics, but only true physics. And there are few books written on the history of physics, so I chose Asimov's The History of Physics, 1966 as the template book for this textbook. Now Asimov's book is full of error and mistakes, and that is disappointing but all of Old Physics is full of error. On errors and mistakes of Old Physics, the best I can do is warn the students, and the largest warning of all is that whenever someone in Old Physics says "electron" what they are talking about is really the Dirac magnetic monopole. And whenever they talk about the Rutherford-Bohr model of the atom, they are talking about huge huge grave mistakes, for the true atom is protons as 8 ringed toruses with a muon stuck inside of a proton doing the Faraday law and producing those magnetic monopoles as electricity. I use Asimov's book as a template but in the future, I hope to rewrite this textbook using no template at all, that is if I have time in the future.
Cover Picture: Is the book The History of Physics, by Isaac Asimov, 1966 and on top of the book are 4 cut-outs of bent circles representing magnetic monopoles which revolutionizes modern physics, especially the ElectroMagnetic theory.
What is a template book in writing? It means that I will use this book as much as possible to write this textbook. Reason: because I can then write 6 textbooks of this series in the time that it takes me to write one single textbook. And there is no point in science in rewriting what is already well known.
But, unlike the template book, I remove any mistakes, fakes, and overlooked ideas and materials. I correct the mistakes of Old Physics. And as can be seen in the first book of this series, the Introduction of Teaching True Physics, there are many and many mistakes of Old Physics, where there is a list of 100 fakes and mistakes.
---------------------------
Table of Contents
---------------------------
1) History of the volume of rectangular box V= L*W*H, and cube, earlier than 4,020 years ago, that starts physics.
2) Ancient Greek history of Atomic theory, magnetism and electricity.
3) Ancient Greek history of Magnetism and Electricity.
4) Classroom Demonstration of magnets moving iron filings, and silk-rubbed glass rod picking up paper; and the electroscope.
5) Kepler's three laws of planetary motion is electromagnetism.
6) Galileo starts Experimental physics, and physics of motion.
7) Gilbert's study on magnetism and his book De Magnete, 1600.
8) By 1687, Newton's F=ma becomes in modern times 2020 as F = m*a*(1/A), where m= mass, a= acceleration, A= current.
9) From 1662 through 1834, the Ideal Gas Law of Chemistry has the same math form of V= LWH and F = m*a*i or F = m*a*(1/A).
10) By 1785 Coulomb's law and 1823 Ampere's law of EM, and 1831 Faraday's law of Electromagnetic Induction.
11) Demonstration of the Faraday Law in the classroom and the Ampere Law.
12) By 1827 Ohm's law of Voltage = current*Resistance becomes New Ohms law V = iBE, where Resistance becomes B*E magnetic field times E electric field by 2016.
13) By 1860s Maxwell Equations, four equations that unify electricity to magnetism.
14) E= mc^2 = m*c*c, Russian Umov, energy equivalent to mass by speed of light times speed of light, 1873.
15) E = nhf, Planck's blackbody research that proves Universe is discrete quantized and not continuum, 1900.
16) Quantum Mechanics, 1900 through 1930, summarized to its importance.
17) Schrodinger Equation 1926, and Dirac Equation 1928; both are subset physics of the AP-EM Equations of 2016.
18) Notice that the entire history of physics starts with a math form of A = B*C*D, and ends with the math form of A=BCD and a secondary math form of x^2/a^2.
19) Unification of Units of Physics, of Force, Pressure, Magnetic field, Energy, Electric field, Voltage.
20) Unification of 4 Forces of Physics as all being electricity & magnetism, EM, 2016.
21) Conservation of Energy plus conservation of angular momentum plus conservation of force, 2018.
22) Correct Picture of Atoms interior makeup, design and function, 2019.
23) True Atomic Theory by 2020.
24) Atomic Energy from atoms; radioactive decay 2020 and the circuit math form of x^2/a^2.
25) AP's Magnetic Acceleration Law, a new EM Law, 2020.
26) Demonstration of the AP Magnetic Acceleration Law of Physics.
27) Units are essential for good true physics. And two math forms throughout physics, the dominant A= BCD and the secondary x^2/a^2.
28) (Optional reading) Appendix A: Research-Appendix for those thinking of going on in physics and about the Teaching True Physics series.
29) Appendix B: List of 116 fakes and mistakes of Old Physics.
30) Appendix C: List of Units Measure.
6) Proof of 3rd dimension is last and final, because Volume and Voltage is all inclusive.
The most simple proof in Physics that 3 and only 3 dimensions exists is the fact that the mathematics of all the important equations is structured as a Volume equation of Voltage = current*magnetic field * electric field.
We have Contradictions of science if we are to think that Volume of Voltage does not capture all of physics or all of mathematics in a given space or the entirety of Space.
So in my quest for the ultra proof of 3 and only 3 dimensions, I need not search for a contradiction in speed of light, nor a contradiction in a EM law such as Faraday. No, all I needed was to note--- volume in math is all consuming. Voltage in physics is all consuming of current of magnetic field of electric field.
If not all consuming, then we have contradictory physics and contradictory mathematics. When we have contradictory physics and contradictory math we have no science at all.
All the important equations of physics are a Volume formula of mathematics. All of the 6 laws of EM theory are based upon Voltage = iBE.
We can even make Newton's Force = mass*acceleration be a volume formula of force = mass* distance*(1/time^2) or writing it as Force = MLT^-2.
Even energy becomes a volume equation for math: E = m*c*c.
It is Volume that determines dimension of physics and of mathematics. If we ignore volume we become hypocrites with contradictory reasoning with dimensions beyond 3rd.
For a long time, very long time I was struggling with exponent powers where I see units that had exponents of 4th degree. Struggling in thinking that was 4th dimension with a exponent of 4th degree. Such as the units of Capacitance A^2*s^4 / kg*m^2. Struggling to think if that is a 4th dimension units with its seconds^4.
But now I no longer struggle, for that is merely arithmetic of seconds^4, because all of electricity and magnetism comes from a volume formula of Voltage = current*magnetic field*electric field. And although you can make some arithmetic combinations of current, B, E, and V to have a exponent of 4, it does not mean dimension. The 3rd dimension is existing to plot the current on x-axis, magnetic field on y-axis and electric field on z-axis.
Volume in math includes all and every. Voltage in physics includes all and every.
Alright, I am satisfied I have proven that in all the world, 3 and only 3 dimensions exist. The very best proof is that the most important equations in all of physics are Voltage = C*B*E, coulomb*magnetic field*electric field.
This connects up with mathematics, Volume = length*width*height.
Wearing a logical brain, we simply ask, if not everything is contained within volume, then we commit Contradictions of Logic, and no longer doing science.
The easiest proof that 3rd was the last and final dimension is the proof-- you start with x-axis, you do a perpendicular with y-axis, you do another perpendicular with z-axis. You have now run out of perpendiculars, for any more perpendicular is just a reiteration of x,y, or z.
This also ties into the triangle being the smallest closed geometry figure. If a 4th dimension existed, then the square would be the smallest closed geometry figure.
In Physics, the Schrodinger Equation is the pinnacle peak of wave mechanics. It is a equation grounded in 3rd dimension. A 4th dimension makes no sense to the Schrodinger equation. The Dirac equation is proven to be folly by myself recently in one of my books. You see, Dirac never knew that the 0.5MeV particle was the magnetic monopole and not the electron of Atoms. And so Dirac never knew that Schrodinger Equation was already a relativistic equation. Hence the Dirac equation ends up making the Schrodinger Equation doubly or squared relativistic, when Dirac should have let it alone for it was relativistic by itself.
7) Physics 3rd dimension derives Coulomb constant 1*10^10 kg*m^3*s^-4*A^-2 from mass of neutron.
If we couple the fact that Light Waves are closed loop circuits a right triangle being the smallest. And that Light Waves are Transverse for the most part, not always Transverse but for the most part. Then we see a 4th dimension cannot exist for then we would have to have Light Waves where the magnetic field is not perpendicular to the electric field.
Now the idea that the utmost equation of Physics is of form A = B*C*D, such as New Ohm's Law Voltage = C*B*E, and Volume = L*W*H. We also can include Energy E= mass*c*c which becomes Energy = mass*1*10^17m^2/sec^2. Mass of proton alone (840/945) 1.6*10^-27 kg = 1.4*10^-27 kg and multiply by 1*10^17m^2/sec^2 is 1.4^10^10.
When we place the mass of the neutron into mass*c*c, we end up with another important physics constant Coulomb constant 1*10^10 kg*m^3*s^-4*A^-2.
Sigma error is too large 1.4 versus 1.
On Thursday, October 6, 2022 at 11:04:45 PM UTC-5, Archimedes Plutonium wrote:
> Now the idea that the utmost equation of Physics is of form A = B*C*D, such as New Ohm's Law Voltage = C*B*E, and Volume = L*W*H. We also can include Energy E= mass*c*c which becomes Energy = mass*1*10^17m^2/sec^2. Mass of proton alone (840/945) 1.6*10^-27 kg = 1.4*10^-27 kg and multiply by 1*10^17m^2/sec^2 is 1.4^10^10.
>
> When we place the mass of the proton alone 840/945 into mass*c*c, we end up with another important physics constant Coulomb constant 1*10^10 kg*m^3*s^-4*A^-2.
>
> Sigma error is too large 1.4 versus 1.
>
Let me try it another way with 1/2 mass*v^2. For that Sigma Error is 1.4/1 is 40%.
So as listed in accurate measurement 8.9* 10^9 N*m^2*C^-2 as the Coulomb constant.
Now I apply the 1/2 in 1/2mv^2 for energy rather than the simple mass*c*c.
Applied to the neutron of 1.67*10^-27 kg, and 1/2 of that is 0.84*10^-27 kg.
Now let me take speed of light square value as 1*10^17meter^2/sec^2. Which ends up with 8.4*10^9 when what is needed is 8.9 for a sigma error of 8.9/8.4 is a 5% Sigma Error. I am going to accept that as being equality because in all electrical magnetic measurements, so much other electrical noise is present.
So here I claim the idea that Coulomb constant, naturally comes from electric permittivity 1/(4*pi*electric permittivity) but also comes directly from 1/2mv^2 of the neutron.
And the meaning in this context, is that a volume or voltage or Energy formulas of physics as A = B*C*D are all encompassing of the physics going on in that space. No other dimension by 3rd dimension, or else, we contradict all the physics going on in that Space. To say a 4th dimension exists is to say, you do not have all the energy of that Space in E = mc^2.
Alright I have been blessed with a cross-fertilization of ideas. My AP-EM equations of E' = (V/(C*B))' the derivative of Electric field, yields 3 terms. One of those terms is the Coulomb (or gravity force because E' makes gravity and Coulomb force be the same force), one of those terms is R, another term is 1/R and the last being 1/R^2.
So the force of Coulomb or gravity varies over the spectrum of R to 1/R to 1/R^2.
Now yesterday I discovered the Coulomb constant is merely 1/2 mv^2 when we substitute speed of light for velocity and using the mass of the neutron we find within Sigma Error we have the Coulomb constant as 1/(4*pi*(permittivity)) as 8.9*10^9N*m^2*C^-2
Well, pushing ever onwards upwards and higher for today. Take a look at permeability as 1.2*10^-6 N*A^-2. Then look at permittivity at 8.8*10^-12 F*m^-1.
So today, well, I am going to show that the R to 1/R to 1/R^2 is a progression and the values in constants of that progression follows as Permeability as R, then inverse permeability as 1/R and then inverse 1/R^2 as that of permittivity.
In other words, in Physics, R to 1/R to 1/R^2 is nothing more than a fancy mathematical replacement of permeability to inverse permeability to inverse permittivity.
So you ask, what has this got to do with 3rd dimension being the last and final dimension?
Well, the reason that electricity and magnetism are in 2nd dimension is because 3rd dimension is the last dimension.
In R, which is solid body rotation, we have the plain out in the open lines of force of magnetism of Permeability a 2nd dimension phenomenon in a 3D world.
The easiest proof in all the world from physics that 3rd dimension is last and final dimension is that of showing a bar magnet with its lines of force out in the open, and plain to see by all.
8) Proton+muon rest mass to be more precisely that of 1.61...*10^-27 kg, rather than their current 1.672... prefix.
Researchers of physics measurement in the future will find the Proton+muon rest mass to be more precisely that of 1.61...*10^-27 kg, rather than their current 1.672... prefix. The precision measurement will take into account the surrounding noise that interferes in accurate numbers. Of course, the 1.61... is the golden mean ratio 1.618033...
What it shows is that kilograms mass was already close to golden mean ratio, but now it must be seen as being a prefix of exactly 1.618033.... Same goes for neutron.
Likewise the neutron accurate measure in the future will be 1.61...*10^-27 kg, rather than 1.674... prefix.
Then when we do the math of 1/2mv^2 with speed of light we end up with a Coulomb constant of more precision as 8.0* 10^9 N*m^2*C^-2 as the Coulomb constant with prefix 8.0 rather than a prefix of 8.9.
You see the true physics has numbers already baked into the constants, and our measurements have too much background noise leading to less accuracy. But a 5% sigma error or less is acceptable.
AP
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plutonium dot archimedes at gmail dot com. Looking for a College or University press to hardcover publish all 317+ AP books of science, likely to become 500-600 maybe even 700 books by the time I die. E-books are too prone to unbalanced-unhinged censor-editors, who can easily make your books vanish by pulling a switch. Science should never have gatekeepers, who thwart access to true science.
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Archimedes Plutonium