Science > Physics > 2 and only 2 geometries where Euclidean is like Newton's absolute time and absolute space
| Topic: |
Science > Physics |
| User: |
"Archimedes Plutonium" |
| Date: |
23 Feb 2004 01:37:21 AM |
| Object: |
2 and only 2 geometries where Euclidean is like Newton's absolute time and absolute space |
I am going to have to revamp File 103 on FLT, and File 120 of "3 and
only 3 geometries" and File 125 of two proofs of the Riemann
Hypothesis in my website of www.iw.net/~a_plutonium/
I did not do much mathematics after 1997 and recently when I reviewed
my Riemann Hypothesis proof I realized that it is the p-adics that are
on the 1/2 Real line which means that lines are curved when out at
infinity. There are no straightlines. I have to change and revise my
Poincare Conjecture proof also.
But directly, I have to toss out my early 1990s proof of 3 and only 3
geometries
because it is really 2 and only 2 geometries. A lot of revision and I
can hack it if I go slowly.
What does this say about physic? It says alot. I was sort of
uncomfortable in the early 1990s with the statement of 3 and only 3
geometries idea. Because physics is dominated not by threesome but
duality of twosome. Particle to Wave and not triality but duality.
This is basic and fundamental in physics and so why should mathematics
be cloaked and dressed in triality when physics is duality.
That would mean that Riemannian and Lobachevskian are the only 2
geometries where the zeroness of Euclidean flat space is not a
geometry. Zeroness is contained in Riemannian geometry as well as
Lobachevskian.
If the Riemann Hypothesis has all the Natural Numbers on the 1/2 Real
Line and if the NaturalNumbers are really the P-adics, and since the
p-adics curve then there exists no straight lines. There exists no
Euclidean Geometry and Euclidean is just a human mental construct with
no physical substance. The same as Newtonian absolute space and
absolute time is just a human dreamed up mental construct.
I see alot of work ahead in revising that website of mine.
Archimedes Plutonium
whole entire Universe is just one big atom where dots
of the electron-dot-cloud are galaxies
(www.iw.net/~a_plutonium) website of the science of AP under revision
what used to be my old science website
www.newphys.se/elektromagnum/physics/LudwigPlutonium from years 1993
to 2004
.
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| User: "Archimedes Plutonium" |
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| Title: Does Euclidean geometry exist as a physical entity, or does only Riemannian and Lobachevskian |
25 Feb 2004 01:29:19 AM |
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(Archimedes Plutonium) wrote in message news:<618e71c0.0402222337.68df14d7@posting.google.com>...
I am going to have to revamp File 103 on FLT, and File 120 of "3 and
only 3 geometries" and File 125 of two proofs of the Riemann
Hypothesis in my website of www.iw.net/~a_plutonium/
I did not do much mathematics after 1997 and recently when I reviewed
my Riemann Hypothesis proof I realized that it is the p-adics that are
on the 1/2 Real line which means that lines are curved when out at
infinity. There are no straightlines. I have to change and revise my
Poincare Conjecture proof also.
Physics is duality and not triality. If I go by that presumption then
I have to concede that there are only really 2 geometries and not 3.
Of the three known geometries of Riem, Loba, and Eucl, I would bet
that Euclidean is the nonexistant one. The P-adics create a nice point
by point Riemannian geometry and they naturally curve back around. But
I have trouble forming Lobachevskian geometry with a one to one
correspondence with algebraic numbers. Perhaps the Doubly-Infinites?
Perhaps the negative Reals.
But then I have trouble with the Reals for they seem to be Euclidean
geometry. But are they really? Euclidean geometry is zero curvature.
But the number 0 exists in p-adics and doubly-infinites. The
complex-numbers I can rule out as just a gimmick that gives added
dimensions.
So I am faced with 3 number sets of P-adics, Reals, and
Doubly-Infinites. If physics is the final word on this that duality
exists but triality is nonsense, then I am going to have to find out
what 2 and only 2 geometries exist and that one of them is a mental
illusion for human minds. Just as Newtonian absolute space and
absolute time was just a mental illusion.
The most perfect match is P-adics to Riemannian Geometry because the
P-adics are all positive numbers which Riem geometry deals with only
positive quantities and they naturally curve back around such as in
10-adics the number ....99998 is equivalent of -2 and then ....99999
is equivalent to -1. So it is a beautiful matchup.
But I have trouble in finding a number set to matchup with
Lobachevskian Geometry. It cannot be the Reals because they have both
negative and positive but Loba requires only negative. So are the
Doubly-Infinites intrinsically negative quantities similar to the fact
that P-adics are intrinsically positive quantities?
Archimedes Plutonium
whole entire Universe is just one big atom where dots
of the electron-dot-cloud are galaxies
.
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| User: "Archimedes Plutonium" |
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| Title: cracks in Euclidean Geometry and why Reals are fake Re: Does Euclidean geometry exist as a physical entity, or does only Riemannian and Lobachevskian |
25 Feb 2004 01:32:13 PM |
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(Archimedes Plutonium) wrote in message news:<618e71c0.0402242329.aec237d@posting.google.com>...
(Archimedes Plutonium) wrote in message news:<618e71c0.0402222337.68df14d7@posting.google.com>...
I am going to have to revamp File 103 on FLT, and File 120 of "3 and
only 3 geometries" and File 125 of two proofs of the Riemann
Hypothesis in my website of www.iw.net/~a_plutonium/
I did not do much mathematics after 1997 and recently when I reviewed
my Riemann Hypothesis proof I realized that it is the p-adics that are
on the 1/2 Real line which means that lines are curved when out at
infinity. There are no straightlines. I have to change and revise my
Poincare Conjecture proof also.
Physics is duality and not triality. If I go by that presumption then
I have to concede that there are only really 2 geometries and not 3.
Of the three known geometries of Riem, Loba, and Eucl, I would bet
that Euclidean is the nonexistant one. The P-adics create a nice point
by point Riemannian geometry and they naturally curve back around. But
I have trouble forming Lobachevskian geometry with a one to one
correspondence with algebraic numbers. Perhaps the Doubly-Infinites?
Perhaps the negative Reals.
But then I have trouble with the Reals for they seem to be Euclidean
geometry. But are they really? Euclidean geometry is zero curvature.
But the number 0 exists in p-adics and doubly-infinites. The
complex-numbers I can rule out as just a gimmick that gives added
dimensions.
So I am faced with 3 number sets of P-adics, Reals, and
Doubly-Infinites. If physics is the final word on this that duality
exists but triality is nonsense, then I am going to have to find out
what 2 and only 2 geometries exist and that one of them is a mental
illusion for human minds. Just as Newtonian absolute space and
absolute time was just a mental illusion.
The most perfect match is P-adics to Riemannian Geometry because the
P-adics are all positive numbers which Riem geometry deals with only
positive quantities and they naturally curve back around such as in
10-adics the number ....99998 is equivalent of -2 and then ....99999
is equivalent to -1. So it is a beautiful matchup.
But I have trouble in finding a number set to matchup with
Lobachevskian Geometry. It cannot be the Reals because they have both
negative and positive but Loba requires only negative. So are the
Doubly-Infinites intrinsically negative quantities similar to the fact
that P-adics are intrinsically positive quantities?
Another major crack in Euclidean Geometry is that Real Numbers really
do not coincide with Euclidean Geometry, do they? Perhaps I am making
a statement or perhaps I am asking a question, for I am only at the
beginning of this inquiry.
If we look at the P-adics, they are all positive numbers, even the
zero point can be said to be positive and so they are ideal for
coinciding with Riemannian Geometry with its *positive curvature*.
P-adics are ideal for representing Riemannian Geometry, or, making a
1-to-1-correspondence. So one can say that P-adics are the points of
Riemannian Geometry and ideally such because the p-adics have a
natural curvature to them for as we start in the 10-adics with 0 and
then next is .000001 and next is .000002 and going way out it comes
back to ...99997
which we can conceive of as -3 then ....999998 which is -2 and
excitedly ....999
which is -1 and finally back to our starting point of 0. So the
P-adics can be said to be the actual algebraic points of Riemannian
Geometry.
But now inspecting Reals with the geometry of Euclid, it just simply
does not fit together does it. Because Euclid geometry is 0 curvature
and the only number in the Reals that obeys curvature is a single
point which is zero itself. The positive Reals disobey Euclidean
Geometry because they are positive signifying Riem geom and not
Euclidean and likewise the reverse for negative Reals for they signify
Lobachevskian geom. So one is left with the conclusion that the Reals
never represented the geometry entailed by Euclidean Geometry. Do the
Real Number system represent any geometry??? I suspect not. I suspect
the Reals are as mythical or imaginary as was Newtonian Mechanics of
absolute space and absolute time. Humans have minds that can dream up
things which really have no physical reality such as ghosts, witches,
and Newtonian absolute space and absolute time. Are the Real Numbers
another dream-up thing which has no physics reality? I suspect so.
But I am troubled with what numbers correspond to Lobachevskian
geometry. I would like to think that the negative REals suit the Loba
geometry, but that leaves the nasty question of the positive Reals. I
think I can draw some clues as what the numbers that make up
Lobachevskian Geometry from the P-adics making up Riemannian Geometry.
If I start with this claim: P-adics == Riemannian Geometry and accept
it as fully true, then there are some other numbers called
Doubly-Infinites. Doubly-Infinites are what the name implies. You see,
p-adics are infinite leftward strings. Doubly-Infinites would then be
numbers that are both infinite leftward but also infinite rightwards.
In some sense, the Real Numbers should be doubly-infinite. Perhaps
that is the reason the Reals are fake and nonphysical just as the
NaturalNumbers = finite-integers was a fake and dreamed-up illusions.
TEST: the test of the above would be to show that the Doubly-Infinites
are numbers that are all negative in sign value. What I mean is that
the P-adics are all positive (even ....9999 is positive but it can
represent -1).
So, if I can show that Doubly-Infinites are all negative, then I will
have shown a vast amount of knowledge and understanding. Because if I
can show the Doubly- Infinites are all negative in sign value then
these numbers are what compose Lobachevskian geometry.
And that where I have:
All-P-adics == Riemannian Geometry
I will also have
All-Doubly-Infinites == Lobachevskian Geometry
This would then conclude that REals as a number system were a fake
entity and would imply that the centuries of gaps and holes found in
Reals such as the myriad types of differentiation and integration
Lebesgue integral to name one is because the Reals are a
hodge-podge-mess just as Newtonian absolute space and absolute time
was a hodge-podge-mess that saddled Quantum Mechanics.
Driver Motivation for the above: what drives me to many of these
conclusions is that Quantum Mechanics is duality based and not
triality based. Physics is two-some in particle wave duality and not
threesome.
Because Physics is twosome, then geometries should be twosome and not
threesome. Therefore, geometry should have 2 and only 2 indepedent
geometries. So, I have a choice of 2 of these geometries that really
exist (1) Euclid (2) Riemannian (3) Lobachevskian. My choice is Riem
and Loba. And since there are only two entails that Algebraically in
Mathematics there exists only two real Number Systems. I am fully
confident that P-adics are one true number system. I suspect
Doubly-Infinites is the second truly existing number-system. Hence I
suspect the Reals to be a fake system just as Newtonian Absolute Space
and Absolute Time was a fake concept.
Research: All I need is hard-core evidence that Doubly-Infinites are
all negative numbers. If I can get that evidence, then all of my above
thoughts would be confirmed.
Archimedes Plutonium
whole entire Universe is just one big atom where dots
of the electron-dot-cloud are galaxies
(www.iw.net/~a_plutonium) website of the science of AP under revision
what used to be my old science website
www.newphys.se/elektromagnum/physics/LudwigPlutonium from years 1993
to 2004
.
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| User: "Archimedes Plutonium" |
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| Title: are Doubly-Infinites the points of Lobachevskian Geometry Re: cracks in Euclidean Geometry and why Reals are fake |
25 Feb 2004 09:45:45 PM |
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Earlier today I wrote:
(most snipped)
Research: All I need is hard-core evidence that Doubly-Infinites are
all negative numbers. If I can get that evidence, then all of my above
thoughts would be confirmed.
Let us look at a few P-adic of a 10-adic such as .....333333. and
.....67 and
......101100111000. And the question of sign value does not become an
issue for they are all of one sign. They are all of a positive number
sign value even though some of them can resemble a negative value such
as ....99998 which can be constrewed as -2. Not that it is -2 but has
the resemblance of -2. But all the P-adics thus have this *positive
value characteristic*.
But now take a look at Doubly-Infinites, can we likewise unravel what
sign value these numbers possess? Are they all a value opposite of
that of P-adics? Are they all *negative sign value* whereas p-adics
are *positive sign value*??
Let us write some Doubly-Infinites such as .....333333.67676767.....
Another Doubly-Infinite is .....99998.101100111000.........
The main question then is whether that infinite string rightwards
upsets the sign value of the infinite string leftwards so very much so
that the sign value of the entire number entity in question changes
from positive to negative.
P-adics are infinite strings leftward and are all positive valued
specimens. But what is the sign value of Doubly-Infinites? Does that
rightward infinite string force so much change upon the leftward
infinite string that the number specimen in question is transformed
into a "negative number"?
I am trying to get a handle on this question by contrasting actual
physical objects. And in contrast with Speed and Velocity and
Acceleration in Physics. If we are allowed to speed ahead with
velocity and with acceleration this would be the infinite leftward
string. But in our speeding and accelerating we are forced to pay
attention to little things, little distances would slow us down. In
going from 1 to 2 to 3 to 4 we can keep the speed. But if forced to
look at 1.3 between 1 and 2 and then 1.4 between 1 and 2 we are slowed
down.
Another physical model is the shape of a convex lens to a concave lens
in contrast to infinite leftward strings compared to doubly-infinites.
With no infinite rightward string to slow down the leftward string it
becomes convex in shape. But when details of numbers between two
consecutive rightward string numbers is demanded then a concave
surface is traversed.
What I am trying to convey is that P-adics are infinite leftward
strings and they are all positive numbers. But in Doubly Infinites,
because you have a infinite rightward string attached to a infinite
leftward string, that the rightward string concaves the path. So that
where the P-adic would form a convex lens surface, the Doubly-Infinite
forms the opposite surface of concave and thus the opposite sign of
negative vice positive.
Perhaps there is a better physics analogy to what a rightward minutia
detail string does to the macro large string that goes leftward. Or
perhaps mathematics itself can decide this case without any need to
refer to physics. But I doubt it because all of mathematics is a tiny
subset of physics.
Archimedes Plutonium
whole entire Universe is just one big atom where dots
of the electron-dot-cloud are galaxies
(www.iw.net/~a_plutonium) website of the science of AP under revision
what used to be my old science website
www.newphys.se/elektromagnum/physics/LudwigPlutonium from years 1993
to 2004
.
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| User: "Archimedes Plutonium" |
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| Title: infinite rightward strings tacked-on to p-adics serves as Orthogonality and makes Doubly-Infinites the points of Lobachevskian Geometry |
27 Feb 2004 01:45:17 AM |
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I wrote:
What I am trying to convey is that P-adics are infinite leftward
strings and they are all positive numbers. But in Doubly Infinites,
because you have a infinite rightward string attached to a infinite
leftward string, that the rightward string concaves the path. So that
where the P-adic would form a convex lens surface, the Doubly-Infinite
forms the opposite surface of concave and thus the opposite sign of
negative vice positive.
In p-adics of 10-adics take for example:
.......999997 and .......99998
both are positive numbers
and both have a Riemannian curvature because the entire 10-adics bend
back around joining up at 0. (Gee, I wish Abian were still around for
I would love to see his input).
But now let us look at several Doubly-Infinites near the two 10-adics
listed above.
Consider these Doubly-Infinites:
......99997.34343434....
.......99997.5555555....
.......99997.6700000....
......99997.75000.....
......99997.888888....
......999997.900000....
......999998.0000000010000.....
The talk of convex curvature as Riemannian formed by the P-adics and
the talk of concaveness that is Lobachevskian geometry and which I
intuit that the Doubly-Infinites form. Since p-adics are only infinite
strings leftward they form convexity shape. Doubly-Infinites also have
a leftward infinite string but it is the rightward infinite string
that creates an Orthogonality to the finality of where the point ends
up. When you tack on a infinite rightward string to a p-adic it
creates an Orthogonality and changes the convexity into concaveness.
It thus alters the positive sign value of what the p-adic possessed
and transforms it into a negative sign value because sign value is
merely a means of signifying a 180 degree change of direction.
Concaveness is 180 degree change of direction
So if we consider purely the P-adic of its infinite leftward string it
forms convexness like a convex lens. But if you take the same p-adics
and tack-on infinite rightward strings then they serve as
Orthogonality and the entire group of Doubly-Infinites become a
Lobachevskian surface or curve.
Archimedes Plutonium
whole entire Universe is just one big atom where dots
of the electron-dot-cloud are galaxies
(www.iw.net/~a_plutonium) website of the science of AP under revision
what used to be my old science website
www.newphys.se/elektromagnum/physics/LudwigPlutonium from years 1993
to 2004
.
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