Science > Physics > Physics will now make all mathematical proofs and definitions, not
| Topic: |
Science > Physics |
| User: |
"Archimedes Plutonium" |
| Date: |
13 Feb 2005 03:54:35 PM |
| Object: |
Physics will now make all mathematical proofs and definitions, not |
Sun, 13 Feb 2005 14:10:05 +0000 (UTC) "E. E. Escultura" wrote:
(some big snips to save space)
I feel I did not address many big issues and want to address them before I leave this thread. And I have said some good points about EEE's thoughts and alot of bad points about EEE's thoughts and this is how it should be.
The good points is that EEE recognizes that the Natural-Numbers of Andrew Wiles FLT are a fake set. And that the world of mathematics needs to move into the direction of recognition that the Finite Integers/Counting Numbers/Natural Numbers become Infinite Integers as long as there is an endless adding of 1. The entire subject of Number Theory in mathematics is a fake subject because it does not have a full grasp that these Integers
are the Adics. And the reason Number-Theory has so many ancient unsolved problems and why FLT needs 100 pages of arcane arm twisting argument is because mathematicians fail to understand they are working with Infinite Integers and not Finite Integers. Physics had a similar history when Quantum Mechanics replaced Newtonian Mechanics yet the old physicists could not wrestle with the newfound knowledge and stubbornly stuck to the old
system.
So EEE deserves credit that FLT is false and that the numbers need repair.
But the bad points about EEE, I have not enumerated sufficiently and I want to do that.
Bad points:
(1) EEE is stuck with the idea that mathematicians and mathematics spearheads and is more fundamental than physicists and physics. Here EEE is very wrong because math and mathematicians are a tiny subdepartment of physics and it is physics that makes clear all and any piece of mathematics. It is physics, starting with 1990 and onwards through physics experiments that are the ultimate Proof of any mathematical claim.
Example: is FLT. It is not Andrew Wiles with some hornswaggle of an argument that is 100 or 200 pages long that is going to prove FLT. It is not EEE with some new set of axioms to define Reals or Integers that is going to solve FLT. It is Experimental Physicists who some day report that the Quantized Hall Effect of its strange and bizarre Rational Numbers are actually Adics and that a corner of physics requires out of necessity these
Adics to explain that corner of physics. Once that news is blaired out and validated by other experimental physicists and by theoretical physicists. That day is the day in which Physics will have proved FLT. Proved that the Natural-Numbers that Pythagoreas, that Archimedes, that Kepler, that Gauss, that Riemann, that Poincare had all thought were Finite Integers, were Natural-Numbers, were Counting Numbers were all wrong. And that
these numbers were really Infinite Integers and Adics.
So EEE is foolish to think that mathematicians and mathematics is going to solve any big and noteworthy thing in mathematics or in physics. It is physics that is going to solve all things in mathematics and in physics.
(2) Recently EEE has the claim of what he calls "new Reals". Here again he has failed to see the problem in terms of physics. To be a good mathematician means you have to be a good physicist first.
Example: Quantum Physics has duality. It does not have Tri-ality, nor Singl-ality, it has duality. The duality is Particle to Wave. This idea should have registered to EEE before he ran around after his so called "new Reals".
Back in the 1990s I wanted to know what the number set intrinsic to Loba geometry was. I hypothesized that the REals were the intrinsic set to Euclidean Geometry and that the Adics were the intrinsic set to Riem. geometry. In geometry we have three values of positive, zero and negative and thus we have three geometries of Riem, Eucl, and Loba. But in physics we have Duality not tri-ality. I was stuck and troubled with Doubly
Infinites. The Reals were rightward infinite strings and the Adics were leftward infinite strings. So, according to Physics I should stop with just the Reals and Adics because those two give Duality. That Double Infinites are just nonsense. But what about the 3 geometries, and should Duality say that one of those geometries is also nonsense?
When we look at the Adics they are disjoint infinite sets and they are spherical in behaviour for they come back around. The Adics are perfect description of Particles. When we look at the Reals they have embedded within themselves the Wave nature of physics with its periodic functions such as sin cosine tangent etc.
Perhaps the REals are really Loba geometry and not Euclidean but I have not yet worked that out in my mind. And that would leave Euclidean Geometry as a fictional geometry just as Newtonian Mechanics is a fictional physics. Both the Adics and the REals have a zero point. And so Euclidean GEometry is a geometry based on a single point of zero and nothing more. Whereas Riem geometry are all the Adics and Loba geometry is all the Reals
(if I work it out).
In light of that, when we look at EEE, as someone who ignores physics and thinks that math and math axioms champions all of math and all of physics, we see EEE claiming that his "new REals" are some singular super set. EEE fails to realize that physics Duality require the world of mathematics has 2 sets of numbers, both independent of each other and both describing a realm very much different from one another.
Again, it will be experimental-physicists who will prove my above notions and not some ivory towered mathematician who knows diddly about physics and experiments.
The reals, including the integers, are now embedded in the new reals and are now also well-defined by the axioms of the new reals. (They aren't in the real numbers) Therefore, numbers with periodic digits to the left or right are well-defined. Apparently, your adics are well-defined in the new reals.
(snip)
(3) The above paragraph by EEE fails to consider Physics. Physics duality is one of the most vital truths of our age. Physics is not tri-ality nor singular-ality. So physics demands there to be 2 sets of numbers that make up all of Algebra for mathematics. Since the 1990s I have proposed that these two sets be:
Reals ---- infinite strings rightward, with a finite portion leftwards
Adics ---- infinite strings leftward, with a finite portion rightwards
Those 2 sets satisfy physics of its Duality requirement. Adics are spherical in nature and disjoint and thus perfectly suited to be Particles. And REals are continuous in behaviour and able to have periodic functions such as the trig functions and thus perfectly suited to be the Wave Nature of physical reality.
There is room only for 2 sets according to Physics so the above Reals and Adics cover all the bases.
If EEE had learned or discovered more physics and had realized that Physics was the bases for mathematics, then he would have realized that his "new Reals" is a comedy trip.
Or the original papers on the subject:
1) Exact equations of Fermat's last theorem, Nonlinear Studies, Vol. 5, No. 2, 1998
2) The mathematics of the new physics, Applied Mathematics and Computation, Vol. 130, 2003
3) The new nonstandard analysis, Nonlinear Analysis and Phenomena, Vol. II, No. 1, 2005 (this is a new journal and this issue is due for release this month).
Regarding the adics they are presently ill-defined since the integers, as real numbers are ill-defined. Two of the axioms of the real number system, namely, the trichotomy and completeness axioms are false. Counterexamples to them were constructed by Brouwer (Benacerrap and Putnam, Philosphy of Math., Cambridge U Press, 1985)
and Banach-Tarski (Kline, Mathematics: The loss of certainty, Oxford U Press, 1980)
(snip)
(4) One gets the picture that EEE like Brouwer or Banach or Tarski or Wiles can sit in ivory towers and make mathematical proofs and can make mathematical arguments that have the ring of truth. But the reality of it all is that the Experimental Physicists allied with theoretical physicists from now and into the far future will be the persons Proving mathematical statements. Will be the persons correcting the axioms of the 20th century
and past centuries. It is the Experimental-Physicists that will announce some day that a corner of physics necessitates Adics and not Natural-Numbers. And then all of physics will be seen as containing Adics which were previously thought to be Natural-Numbers. And when that announcement comes FLT will be proven false. And all the old axioms dumped into the trashcan.
Mathematics is true only as it is USeful and true according to physics. Physics is the prover of all mathematical statements of all mathematical ideas because mathematics is just a tiny department inside of Physics.
A real number is determined by its digits. Therefore, it is ill-defined unless there is an algorithm or procedure for computting its digits. For example, a nonperiodic decimal is ill-defined unless such algorithm or procdure exists. In some cases this requirement is not enough. In the case of a normal number, that is, a number whose digits are obtained from the basic integers, is unknown until it is actually constructed.
(5) EEE never really understood the blemish of the Successor Axiom in that it forces the Natural-Numbers to become Adics. The Successor Axiom is the endless adding of 1. And the not-so-bright mathematicians of the 20th century never put their minds to the rigor of logic to realize if the Successor Axiom was included in the Peano axioms that those Counting Numbers cannot be controlled. Can not be halted and said that you must be a
finite-integer and never cross over into becoming infinite-integer as a adic.
EEE never spent time on talking long and hard on the contradiction and inconsistency that the Successor Axiom is in the Peano axioms and simultaneously is in the method of producing the Adics. So if you have a Successor in the Finite Integers and have a Successor in the Adics and yet like Wiles claim those two sets are distinct is a failure of a prudent mind. You cannot have an endless adding of one and call your set Finite Integers
and have an endless adding of 1 and call that set the Adics and say they are distinct and different sets.
So, in the 1990s and 2000-2005 EEE never talked in depth about the Successor Axiom and how it is contradictory to Adics and Natural-Numbers. Instead EEE has latched onto his new crank turnwheel of "algorithm and procedure for producing digits". But, EEE, is not the Successor axiom of endless adding of 1 a algorithm and procedure for producing digits? Is not the next Adic achieved by the procedure of endless adding of 1? Seems that
EEE has another lapse of logic here and is not focused.
Archimedes Plutonium
www.iw.net/~a_plutonium
whole entire Universe is just one big atom where dots
of the electron-dot-cloud are galaxies
.
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| User: "Babylonian" |
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| Title: Re: Physics will now make all mathematical proofs and definitions, not mathematicians Re: The counterexamples to FLT |
13 Feb 2005 05:14:04 PM |
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Not physics! Chemistry!! As in your synthesis of
Carbon-RadiumPoloLanthanide from Arsenic Sulfo-Plutokryptonide and
Plutonium Sulfohydride:
AsSPuKr + PuSH --> CRaPoLa
Eureka!!!
.
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| User: "Archimedes Plutonium" |
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| Title: FLT will prove integers are Riem geometry and RH to prove Reals are Lobageometry |
15 Feb 2005 12:02:53 PM |
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Sun, 13 Feb 2005 15:54:35 -0600 Archimedes Plutonium wrote:
Back in the 1990s I wanted to know what the number set intrinsic to Loba geometry was. I hypothesized that the REals were the intrinsic set to Euclidean Geometry and that the Adics were the intrinsic set to Riem. geometry. In geometry we have three values of positive, zero and negative and thus we have three geometries of Riem, Eucl, and Loba. But in physics we have Duality not tri-ality. I was stuck and troubled with Doubly
Infinites. The Reals were rightward infinite strings and the Adics were leftward infinite strings. So, according to Physics I should stop with just the Reals and Adics because those two give Duality. That Double Infinites are just nonsense. But what about the 3 geometries, and should Duality say that one of those geometries is also nonsense?
When we look at the Adics they are disjoint infinite sets and they are spherical in behaviour for they come back around. The Adics are perfect description of Particles. When we look at the Reals they have embedded within themselves the Wave nature of physics with its periodic functions such as sin cosine tangent etc.
Perhaps the REals are really Loba geometry and not Euclidean but I have not yet worked that out in my mind. And that would leave Euclidean Geometry as a fictional geometry just as Newtonian Mechanics is a fictional physics. Both the Adics and the REals have a zero point. And so Euclidean GEometry is a geometry based on a single point of zero and nothing more. Whereas Riem geometry are all the Adics and Loba geometry is all the Reals
(if I work it out).
There are two major cracks in Reals that when fixed, I believe will reveal the REals as Lobachevskian geometry, the intrinsic points of Loba geometry. One of those cracks I mentioned in detail years ago by talking about the plethora of definitions of the integral and derivative. Math is riddled with scores and scores of different definitions for integral and derivative of calculus. If the Reals were Euclidean geometry then one definition
of integral and one definition of derivative should suffice for all applications.
The other crack is the Riemann Hypothesis. If the Reals were Euclidean geometry and if the Natural-Numbers all lined up in a straight line at the 1/2 REal mark then RH would have been proven true by Mr. Riemann himself.
But I suspect the reason RH is improvable by the old mathematics is because the Reals do not form a Euclidean Geometry of points. I believe the Reals form a Lobachevskian geometry and bend with a negative curvature.
Because the REals bend with a negative curvature is the reason that calculus needs a plethora of different definitions for the integral and derivative to work as the REals bend.
We have a sense that the Adics bend positively as they stretch further out for we know that .....9998 is -2 and we know that ....9999 is -1. So the Adics bend like on the surface of a ball or sphere and as these numbers get larger and larger they bend and come back around to their starting point of 0 itself.
So the Adics as a set of numbers are the intrinsic points of Riemannian Geometry.
Now as for the Reals, I am hypothesizing that they bend also but bend negatively such as a saddle is negative curvature. So the reason for these cracks of plethora of definitions for integral and derivative of calculus and for the improvability of the Riemann Hypothesis is because the Reals are not flat Euclidean geometry points but are the intrinsic points of Lobachevskian Geometry.
Archimedes Plutonium
www.iw.net/~a_plutonium
whole entire Universe is just one big atom where dots
of the electron-dot-cloud are galaxies
.
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