AP's 222nd book of Science// Axes of Graphing; Axes of Symmetry; Axes of Dimension; New Math well defines them, whereas Old Math was in the weeds
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Archimedes Plutonium
Dec 13, 2021, 2:54:47 PM (yesterday)
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AP's 222nd book of Science// Axes of Graphing; Axes of Symmetry; Axes of Dimension; New Math well defines them, whereas Old Math was in the weeds

This book started by the answer to a reply in sci.math (see below). And before I publish this book I need to redact those names below --- still keeping the mathematics content. I already started the redaction, for I get too carried away in my discussion, as would anyone who is passionate about their work.

Everyone in Old Math was mixed up and confused by dimension, by symmetry and by graphing. So we really need to fix this ugly ill-defined sector of mathematics.

And the best way of doing this Well Defined Geometry, is to examine the Conic Sections and see what went wrong in a huge and ugly manner that lasted for over 2,000 years of error filled thinking.

The inability to realize that 3D is the top and highest possible dimension, and there is no 4th or higher dimension.

The inability to understand the difference between a Axes of Symmetry from a Coordinate System axes of Graph.

No-one in Old Math realized that the Cartesian Coordinate system of 3D, comes not from a x, y, z axes, axes perpendicular to one another. No, the 3D graph comes from two planes at perpendicular to one another. Planes in Graphing give us axes of symmetry, and that symmetry was why Ancient Greek mathematics up till 2016, could not see the slant cut in single cone is a Oval, never the ellipse.

The 3D coordinate system comes from 2 Planes perpendicular to one another. Now, take those 2 planes and intersect a single cone or a cylinder and you end up with surmising that the single cone has 1 axis of symmetry but the cylinder has 2 axes of symmetry.

In the long long history of geometry mathematics, everyone failed to include Symmetry axes. Totally forgot to include symmetry axes. And this is important for symmetry axes defines dimension. Notice that the symmetry axes are 2 while the Graph axes of x,y,z are 3. The symmetry axes are always 1 number less than the coordinate graph axes, because the symmetry axes comes from a Plane.

On Monday, December 13, 2021 at 1:36:54 PM UTC-6, Archimedes Plutonium wrote:
> On Monday, December 13, 2021 at 2:53:20 AM UTC-6, Hannu Poropudas wrote:
> > Please comment mathematics only of the subject (how to add additional 5-dimension for (3+1) dimensional flat space time?) of these posting of mine and nothing else.
> >
> > Best Regards,
> > Hannu Poropudas
> Well you failed to start at a proper beginning.
>
> Einstein and Minkowski Space-time are both washed up and washed out as failed math.
>
> Neither had a well educated background or understanding of Electricity & Magnetism.
>
> Neither could see that a slant cut in single cone is a Oval, never the ellipse. So with that being the case, neither Einstein or Minkowski had a level stable view of dimension of symmetry of geometry.
>
> And Hannu Poropudas when looking at a single cone and a slant cut in single cone, Hannu sees a Ellipse only because Hannu memorized from school that it is a ellipse and does not know that he is utterly wrong, the ellipse comes from a two axis symmetry-- the cylinder. The cone has just one axis of symmetry -- a cut through the apex and base diameter. If you cut the cone at midpoint of height, your two objects are not symmetrical objects. If you cut the cylinder at midpoint of height, your two objects are symmetrical.
>
> Einstein was too stupid to see the slant cut in single cone is a oval, never the ellipse.
>
> Minkowski was too stupid to see the slant cut in single cone is a oval, never the ellipse.
>
> Hannu Poropudas is too stupid to see the slant cut in single cone is a oval, never the ellipse.
>
> In fact, all three of these persons are so raw stupid, that they acknowledge a cone and cylinder are far far different geometry objects, yet ..., they imagine, like some nitwit, they imagine that a slant cut will deliver both a ellipse in the cone as well as a ellipse in the cylinder. I mean, really ... people in mathematics, who start out with two different objects and in the..., end up with a ellipse in both of them.
>
Archimedes Plutonium's profile photo
Archimedes Plutonium
Dec 13, 2021, 11:30:31 PM (yesterday)
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Alright, what I am doing here is making the case that to build or construct the Coordinate System of Graphing, especially for functions, is that you build it with 2 planes perpendicular to one another. And not build it with a starting line, the x-axis, then add on a second line perpendicular to x-axis so you now have the xy plane. Next you add on another third line perpendicular to the xy-plane, called the z-axis.

Something tells me that such a construction is muddle headed and in some respect wrong, although the error is not apparent to me fully as yet.

Something tells me the correct construction of the Coordinate System of 3rd dimension is to enter two planes, one plane perpendicular to the other and that creates the Graphing Coordinate System in 3rd dimension.

Why this is so, is because of Symmetry, the concept of symmetry was overlooked in math history and only recently in physics of quantum mechanics has symmetry received its fair share of attention it rightly deserves.

As to the error of lines, line x axis, line y axis, line z axis, that construction fails to solve Symmetry. And we easily look upon the single cone. Do we have a x axis symmetry, another as y axis symmetry, another as z axis symmetry. We are lost in this method. But if we place two planes that are the Graph Network we immediately can see that one plane has a symmetry for the single cone while the other plane does not. The plane at midpoint to height and parallel to base, that cuts the single cone into two parts and upon examination neither part looks like the other.

Another figure with only one axis of symmetry is the 3D wedge. A rectangular solid has 2 axes of symmetry. A sphere and cube and cylinder have 2 axes of symmetry.

The cone has 1 axis of symmetry a trapezoidal figure in 3D has 0 axes of symmetry.

The regular octahedron has 2 axes of symmetry, as well as the cube. I believe the regular tetrahedron, regular dodecahedron and the regular icosahedron have but 1 axis of symmetry, but that is just a quick judgement evaluation. This stuff is not easy.

And it is because Old Math neglected the idea of axes of symmetry, that they could never get a correct idea on Dimensions, that dimensions end at 3rd dimension, and why so many flakes and fruitcakes of math filled up math with higher dimensions.

AP, King of Science, especially Physics
Archimedes Plutonium's profile photo
Archimedes Plutonium
Dec 13, 2021, 11:59:48 PM (yesterday)
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So here I want a physics explanation for why a Graphing Coordinate System of Math must be built from 2 planes perpendicular to one another and cannot rightfully be built by 3 perpendicular lines as x,y, z axes. Why must there be 2 planes to build the Graph System.

And the best place to look for this demand on mathematics, is physics. It must have something to do with the AP-EM Equations of electricity & magnetism (what used to be called the Maxwell Equations, but they had too many mistakes).

So what is in Electrodynamics, its 6 laws that requires the graphing coordinate system of mathematics be built from 2 planes, and not 3 straight lines?

These are the 6 laws of EM theory.
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

And, sorry to say, I just cannot spot at the moment why this demand for 2 planes rather the old way of 3 straightlines, x, y, z.

But I can very well say that Calculus of dy/dx and dy*dx with its two power rules requires, demands, and forces a Plane for its domain, not that of a x-axis line and then a y-axis line.

So I think perhaps, that is all the justification I ever need, that you cannot do the Calculus by starting with x axis, then building y-axis then z-axis. No, I think you Logically must start Calculus with a Given Plane existing.

The error of Old Math is easy to spot, they used a line segment when dealing with symmetry, dimension and graph system, when they should have used the bare minimum of a Plane. Not a line segment, but a Plane itself must be used to start to talk about a Graph System, a symmetry and a dimension.

AP, King of Science, especially Physics

Archimedes Plutonium
1:07 PM (5 minutes ago)
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On Wednesday, December 15, 2021 at 7:51:30 AM UTC-6, timba...@gmail.com wrote:
> On Wednesday, December 15, 2021 at 5:32:40 AM UTC-5, Hannu Poropudas wrote:
> > tiistai 14. joulukuuta 2021 klo 14.58.24 UTC+2 timba...@gmail.com kirjoitti:
> > > On Tuesday, December 14, 2021 at 6:41:01 AM UTC-5, Hannu Poropudas wrote:
> > > > maanantai 13. joulukuuta 2021 klo 21.36.54 UTC+2 Archimedes Plutonium kirjoitti:
> > > > > On Monday, December 13, 2021 at 2:53:20 AM UTC-6, Hannu Poropudas wrote:
> > > > > > Please comment mathematics only of the subject (how to add additional 5-dimension for (3+1) dimensional flat space time?) of these posting of mine and nothing else.
> > > > > >
> > > > > > Best Regards,
> > > > > > Hannu Poropudas
> > > > > Well you failed to start at a proper beginning.
> > > > >
> > > > > Einstein and Minkowski Space-time are both washed up and washed out as failed math.
> > > > >
> > > > > Neither had a well educated background or understanding of Electricity & Magnetism.
> > > > >
> > > > > Neither could see that a slant cut in single cone is a Oval, never the ellipse. So with that being the case, neither Einstein or Minkowski had a level stable view of dimension of symmetry of geometry.
> > > > >
> > > > > And Hannu Poropudas when looking at a single cone and a slant cut in single cone, Hannu sees a Ellipse only because Hannu memorized from school that it is a ellipse and does not know that he is utterly wrong, the ellipse comes from a two axis symmetry-- the cylinder. The cone has just one axis of symmetry -- a cut through the apex and base diameter. If you cut the cone at midpoint of height, your two objects are not symmetrical objects. If you cut the cylinder at midpoint of height, your two objects are symmetrical.
> > > > >
> > > > > Einstein was too stupid to see the slant cut in single cone is a oval, never the ellipse.
> > > > >
> > > > > Minkowski was too stupid to see the slant cut in single cone is a oval, never the ellipse.
> > > > >
> > > > > Hannu Poropudas is too stupid to see the slant cut in single cone is a oval, never the ellipse.
> > > > >
> > > > > In fact, all three of these persons are so raw stupid, that they acknowledge a cone and cylinder are far far different geometry objects, yet in their raw stupidity, they imagine, like some nitwit, they imagine that a slant cut will deliver both a ellipse in the cone as well as a ellipse in the cylinder. I mean, really stupid ignorant people in mathematics, who start out with two different objects and in their stupidity, end up with a ellipse in both of them.
> > > > >
> > > > > So, Hannu, let us talk math, not your insane mathematics.
> > > > Yes, Theory of surfaces of second degree is not very simple.
> > > > Einstein et al. used simplified basic assumptions which
> > > > must be taken into account when dealing their theories.
> > > >
> > > > See for example
> > > >
> > > > Reference:
> > > >
> > > > Bronshtein-Semendyayev, 1973.
> > > > A Guide Book to Mathematics.
> > > > Springer Verlag.
> > > > Printed in Germany.
> > > > 783 pages. pp. 270-275 and pp. 275-276.
> > > > Surfaces of the second degree (canonical equations)
> > > > pp. 270-275.
> > > > Surfaces of the second degree (general theory).
> > > > pp. 275-276.
> > > >
> > > > Hannu Poropudas
> > > I believe you want to research Klein.
> > >
> > > https://arxiv.org/abs/1403.7780
> > >
> > > Ihttps://en.wikipedia.org/wiki/Kaluza%E2%80%93Klein_theory
> > >
> > > In my own recollection Einstein did meet with Klein and Klein worked independently on a 5D version.
> > > I pull a vacuum on Kaluza though.
> > > That said emag comes into supposedly clean 6D versions.
> > > I don't claim a complete understanding of those positions but am aware of them.
> > > To what degree electricity and magnetism are distinct concepts versus unified I view as an open problem still.
> > > This is not the status quo position, however.
> > >
> > > I am growing in favor of a form of analysis I call interdimensional analysis. It seems no matter where we look dimensional creep exists.
> > > Even in the sum: mathematicians claim that the operator exists on RxR and yields R. What a joke. Are we going to take every integral is infinite dimensional? Are the quants claiming just that in their 'configuration space'?
> > >
> > > There was an old man who walked the floor with a can of oil and meekly touched every shaft of the plant. When he died; and of course the filers were replaced years before; the men in the office were none the wiser.
> > >
> > > No: the gears were crushed long ago and the machine spins on.
> > > We are living in fictitious times, sir.
> > > The skills of the men in the 1800's far surpassed ours.
> > > In the cacophony of specialties that have accrued lays a large pile to digest...
> > No, I don't want to make this new fifth dimension with the electromagnetic
> > vector potential as was in your above reference.
> >
> > I'am now thinking that could it be possible to make an embedding two spaces: A. space-time and B. mirror-space-time into C. five dimensional space..
> >
> > C = A union B or C = A x B , I don't know which of these two set theoretic operations
> > should be usable here?
> >
> > Properties of A and B are:
> > 1. for both spaces time dimension would proceed same way as our familiar
> > time dimension.
> > 2. mirror-space-time would contain invisible DARK MATTER (?), say for example
> > invisible right neutrino matter (right-handed neutrinos?) and these two complex
> > conjugates , H-M-electron (not same as our familiar electron?) and H-M-mirror-electron
> > (not same as our familiar positron?)
> > 3. electron mass is only due expansion resistance of the Universe (H-M)..
> >
> > (in my experimental calculations (my recent posting in sci.physics.relativity,
> > where a kind of Stokes Law used is speculation of mine)
> >
> > I found three solutions for mass of electron and three solutions of
> > radius of electron.
> >
> > One real mass and one real radius (our familiar electron) and
> > two complex conjugate values of mass and two complex conjugate values of radius
> > (H-M-electron and H-M-mirror-electron).
> >
> > Arguments of all these three solutions for both mass and radius
> > are 0 degrees (real case), 120 degrees and 240 degrees (complex conjugate cases).)
> Well that is very P3 of polysign, which are the complex numbers in a new suit.
> Yeah, Stokes sounds good too.
> One curious fact though is that your mirror electron and its original are indistinguishable.
> So whether the plane deserves to be folded into a half plane deserves to be considered.
> The MU and the anti-MU are somewhat ordinary though. In P4 we see:
> * - = #
> * # = *
> * * = +
> * + = -
> so that the coverage is just as good as the original. To either side of NU lays a MU. The symmetry gets super-sloshed for the primes where powers of every sign can dance through the others... except the NU.
>
> Maybe rather than get lost in the kaleidoscopic effects you need to just focus on one electron on one side for now. Yes, your theory can produce a pair, but without the fundamentals of the one, the pair is a mere distraction.
> >
> > I peg you pardon, but I must distinguish different particles, and this is why
> > I gave names H-M-electron and H-M-mirror-electron for these new particles.
> >
> > My problem is now how to geometrize these all for calculations
> > C (5 D invisible space?) and
> > A (3+1 D Minkowski space-time) and
> > B (3+1 D invisible mirror-Minkowski space-time) ?
> >
> > Hannu Poropudas
> Hannu, suppose you had a rotor that could beget the unit vectors of your space as:
> U ^ n
> and that further when you need no more vectors this animal simply wraps around to your first vector again.
> Well, pretty quickly you'll find generality in a family of these things so that you'll see a
> U1, U2, U3, U4, ...
> and of course you'd like a breakpoint right around four for spacetime correspondence. There is little doubt that U1 is unidirectional; time. U2 is bidirectional; the familiar bipolar types and of course real line thinking; the basis of Cartesian space, which incidentally Minkowski and Einstein and everybody else as far as I know have relied upon. Yet you see U3 is your complex plane, and it did not come as a buildup of U2. No. It is every bit as fundamental as U2 and U1. Three unit vectors make up the plane of your H-M theory (is that Hannu-Minkowski? if so this is a misnomer. Possibly you'll need to shift that to H-G.) just as two unit vectors made up U2. Ah, you say, U2 needs just one unit vector... and what about U1? As I see it if I could take you through polysign theory within your own theory, and we have nearly done it in a paragraph, you will land more cleanly.
>
> Simply put the real numbers as a basis are fraudulent through their required use of the Cartesian product, which incidentally Descartes never made use of. I will not claim that the Cartesian product is broken, but that it is not fundamental. By what right can we insist upon two real lines, whose origins intersect exactly, and whose angles to one another are always ninety degrees, and claim these things to be independent of one another? We can leave them just there as a working representation, yet attack them as an invalid basis. Yet this is the basis of relativity theory, electromagnetics, etc.. We know that time is a misfit. You yourself are insisting on something rather different in your electron plane. Witness your own unit vectors in sum. Zero? Yes. Witness the unit vectors of the real line in sum. Zero? Yes.. This is how these systems come to be named polysign. We literally are generalizing sign:
> - 1 + 1 = 0 (P2)
> - 1 + 1 * 1 = 0 (P3)
> - 1 + 1 * 1 # 1 = 0 (P4)
> ...
> and of course I've left out P1 and its seemingly controversial behavior:
> - 1 = 0 (P1)
> yet these are graphical depictions; renderings; and time itself does render thus. The very term 'dimensional' is tied to the real line, which under polysign is a two-form. It happens to be quite accurate, so like the Cartesian product it can be respected yet not taken as fundamental to all. It almost looks as if I've raised the dimension of these systems by one, yet this is not the case. Every concrete instance can be resolved via the very zeros behaviors above which establish them. Take for instance in P2 a value such as:
> - 3 + 5
> and we see the resolution to + 2. Likewise in P3:
> - 3 + 5 * 1 = - 2 + 4
> and so in the reduced form we still have what could be called a two dimensional entity, yet the very terminology of 'dimension' is old-school here. We have broken into general dimensional mathematics via the generalization of sign, sir.

I sense there was a grave error throughout the history of mathematics with the idea of starting geometry with the Point, and then the Line (segment or infinite line).

That mathematics geometry should have started with the lowest figure in Physics which is the Plane. There is no "point or line" in Physics.

The smallest most primitive Physics geometry is the plane, a line with some width. For in electricity and magnetism, we see a circuit as a line with some width as copper wire.

Our imagination likes to think of the copper wire as a line, a line loop, but in reality, the most thin of copper wire is actually a thin, very thin plane.

AP

So what this book challenges is all of geometry. Starting with the Ancient Greeks of Euclid, for they missed "symmetry". And because of that missed symmetry concept, a foolish idea that the slant cut in single one could ever be an ellipse when in truth it is the oval that is the slant cut in single cone.

If the Ancient Greeks had used symmetry in their geometry, they would not have made that foolish mistake of conic sections as of Euclid and Apollonius.. If the Ancient Greeks had applied symmetry to their geometry they would have easily noticed that a cylinder has 2 axes of symmetry and the slant cut is truly a ellipse, but the single cone has just one axis of symmetry and thus the slant cut is a Oval, never the ellipse. But, having symmetry in Ancient Greek geometry mathematics would have been almost impossible, because symmetry comes from physics duality of Atoms and atomic structure. They did not have electrodynamics in Ancient Greek times. They did not know that physics has the duality of particle and wave and the duality of electricity to magnetism.

A single cone has 1 axis of symmetry. Symmetry means that if you cut a object in half from its midpoint, are the two separate pieces alike? Are the two parts the same? If the Same then you have a axis of symmetry. A single cone, if you cut from apex to base, it is symmetrical, but if you cut at midpoint of height, the two parts are vastly unlike to one another.

With a cylinder, which has 2 axes of symmetry, a cut at the midpoint of the height yields two parts that are identical.

So, why could not Ancient Greek geometry have symmetry in its axiom system? It could not have symmetry because symmetry depends upon Planes being the unit, not the point or line as units. The Plane is the provider of symmetry.. In physics, electromagnetism the plane is both electricity and magnetism. The point or line in electromagnetism are nonexistent. There is no point in electricity and magnetism, nor is there a line.

A copper wire, the thinnest copper wire is not a line but is a bandwidth, a plane is a copper wire.

So where math failed in geometry is that they started with two idealizations that never existed in the world. That existed only in screwed up imagination of a point and of a line.

Where geometry should have started with the Plane as the unit figure that starts all of geometry.

AP, King of Science, especially Physics

Alright, let us start with a little bit of how all of Geometry starts with Planes, not with points and lines, but with Planes.

So the huge problem of Ancient Greek Geometry, Euclid, Apollonius of Perga, et al, and right up to AP was there exists no continuum. Physics around 1900 first sighted the Discrete, the quantized space. Mathematicians were too stupid to acknowledge this truth for mathematics but instead went deeper and deeper into the weeds with fools like Cohen and his continuum hypothesis..

Not until AP proved the Fundamental Theorem of Calculus that out of necessity requires a Discrete Space, a quantized space circa 2013-2015. Quoting one of my older posts:
--- quote ---
History of discovery: can be pinned to the year 2013 where Grid Numbers replaces the Reals. I needed discrete numbers not a continuum and by 2013 I started True Calculus, where I need empty space gaps between discrete numbers, in order for calculus to exist.

--- end quote ---

So let us take a brief glimpse into why geometry cannot start with "point or line" for the point and line are fictions if Space is discrete and quantized.

AP, King of Science, especially Physics

In physics we have nothing that is a point, for a wave is a bandwidth. A atom and its subatomic particles can be considered the smallest entities, but those would be far more substance than what Geometry calls a "point".

So the concept of point in Old Geometry is akin to the concept in a fairy tale, where you ask your grandchildren or children, now daddy will tell you a story "imagine a far off castle on a hill,...."

The line in Old Geometry was seen as this _____________

When in reality the line in the world is like this ................... little dots separated by empty space. The dots can be atoms such as copper atoms or be protons separated from other protons by empty space.

So real true geometry never had what can be called a "solid line" a line that is continuous. Rather instead the line in geometry is a dot pattern of empty space from one dot to the next dot.

So in this true picture of Geometry, what is the most primitive unit? And it be the Plane, but the plane is also composed of dots with empty space in between.

This is a picture of a true real plane in true geometry.

.. . . . . . .
.. . . . . . .
.. . . . . . .
.. . . . . . .

So now what happens when that plane above intersects with another similar plane?

In Old Geometry the answer was a line is formed. In New Geometry the intersection of one plane with another plane, both discrete geometry with holes in between points means the intersection can be dot on dot, or dot on empty space, or empty space on empty space.

Now physics has a phenomenon in quantum mechanics called quantum tunnelling, where a substance inside a planar wall seeps right through the solid wall.. And this is natural when we consider the plane to be dots with empty space in between dots.

P.S. I am going slow on this because there is so much to write about. So much to explain, and believe you me, explaining can be awfully tiring.

AP, King of Science, especially Physics

Now the dots with empty space in between, these dots are also Planes. So I am building Geometry with the Plane not the point nor the line.

Some may say a plane is a large number of lines or line segments. No, not when you have empty space in between two neighboring points.

So in New Geometry, the most primitive geometry figure is the plane. And this makes perfect sense for physics electromagnetism. The most primitive substance besides empty space is the Atom, and the atom has subatomic particles inside the Atom. So we consider the atom as a plane in geometry. And those subatomic particles such as the photon and neutrino are further planes of narrow width forming a circuit. The proton is a bent plane forming a torus.. The muon, the atom's electron is a bent plane forming a ring of broader width than the photon or neutrino.

So, what was wrong in Old Math Geometry, that they could never grasp the single cone section at a slant was the Oval, never the ellipse, is because Old Math Geometry took the point and the line as the most primitive geometry figures, not the Plane.

AP, King of Science, especially Physics