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The TOE and imperfect mathematics 
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#1
Jan2610, 03:10 AM

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Hello..
I read somewhere that Mathematics is an imperfect science...basically a science with ultimately unprovable assumptions. Could that be the reason for the problem of squaring relativity & quantum mechanics? Thanks for any and all responses. Bye G. 


#2
Jan2610, 08:39 AM

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It's true that mathematics relies on axioms (statements that you don't try to prove), but this is obviously necessary. Every proof takes some set of statements as its starting point, so in order to even try to prove the axioms, you'd have to write down another set of axioms.
These things have nothing to do with why it's so difficult to find a quantum theory of gravity. Also, mathematics isn't science. Science makes statements about results of experiments, mathematics doesn't. 


#3
Jan2610, 10:06 AM

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#4
Jan2610, 10:10 AM

P: 2,828

The TOE and imperfect mathematics
It could also very well be that a quantum theory of gravity requires entirely new mathematics. 


#5
Jan2610, 10:30 AM

P: 370

The adjective imperfect is silly and useless in this context. Nothing in life is perfect, although mathematics probably comes closer than anything else in meeting this impossible criterion. Mathematics is not a science at all. The modern definition of science relates to understanding the real world via experiments. Sure, mathematics is a useful tool in many branches of science, but mathematics extends much beyond the real world. It is an abstraction and a language independent of physical reality. The last words make some sense. The scope of most (if not all) mathematical frameworks are based on a small number of starting postulates that are unproven assumptions. Or, at least they are not mathematically provable with logic in the framework of that particular mathematics. However, one can offer nonmathematical evidence (i.e. akin to a courtroom type of proof, or scientific evidence) of situations where the starting assumptions seem to apply. This is necessary whenever mathematics is used as a realworld tool, with applied math in science being one of the best examples of this. 


#6
Feb110, 11:37 PM

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P: 194

Two big theorems came out that brought the hilbert program to a sudden stop. 1. Godel's Theorem of incompleteness. 2. Allan Turing's halting problem. These theorems killed the idea of a certain mathematics (and logic). In a basic nutshell, the theorems created statements that could not be proved (not assumptions, statements (BIG DIFFERENCE)). In addition, there is more recent work that makes the uncertainty greater. Chaitin recently (in math years) published a proof that tied a type of incompleteness into data itself. In a basic nutshell, it is a number that can not be computed. Does any of this mathematics have impacts on physics? Absolutely, incompleteness is already a fact of life in computer science through Turing machines and Chaitin's work. The physics TOE is likely dead in its tracks because of this mathematics. But I think the whys and hows have been poorly communicated. Stephen Hawking made an attempt to explain why it kills the TOE, but I think most people have a very difficult time understanding it. In a fashion, incompleteness is a knowledge of systems or a limitation of mathematics when dealing with systems. The problem with creating a TOE is that physics is complicated enough to spark incompleteness (IE: it is a system covered by incompleteness). In other words, physicist will be unable to construct enough axioms so that they can formulate the TOE. So they essential end up with a framework that they already have. 


#7
Feb110, 11:43 PM

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