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Penrose On Godel

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Posted by Richard Ruquist on January 22, 2002 15:59:15 UTC

What Godel says (according to Penrose)is that a given system of math, axioms plus derived theorems, will contain true solutions that cannot be derived from the axioms.

It is true that we know the solutions to be true (proven) based on larger systems of axioms that include the smaller system as a subset.

Does that make math imperfect. From all that I have read it does mean that math cannot be made rigorous. But that is because we cannot derive the emmergent solutions of a given system of math.

For me that is better than perfection. We are getting something for nothing. It means to me that nature, based on a fundamental set of postulates or laws, can evolve properties that go beyond what can be calculated from the laws. For me that is like magic, and I find that magical nature of nature appealing.

It still all comes from math. And it is math that we can ultimately know. Natural laws are finite- a finite number of axioms. But we math physicists can invent a larger system of math that includes nature's math as a subset, and which is able to prove the emergent properties of nature as well.

That is why research in math physics sometimes seems much more exotic than nature itself.

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