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Posted by Richard Ruquist on September 3, 2001 12:16:32 UTC

The amount of logical or rational math may be infinite. That seems to be a logical conclusion from Goedel's theorem.

But enter Chaitin who now claims based on math research along the same lines as Goedel, that most mathematics is individual, isolated, and almost random solutions not connected to other solutions. These may be the extra solutions that Goedel talks about, But that is only a guess on my part.

Chaitin uses the analogy of rational islands in an ocean of irrational math. Now again I am not sure exactly what Chaitin means by rational. It's not irrational numbers that he means. I think it's more like axiomatic, logical systems of math that are islands in an ocean of isolated solutions. No idea how he arrives at this conclusion. As far as I can tell it's coming from his interpretation of his solutions. It may be quite intuitive.

Assuming all the above is true. Then the question is, does nature take advantage of all of the math or say does each universe sit on one island and have logical self-consistent laws of physics and chemistry and biology, etc. I hope the latter is correct. Goedel took away the possibility of ever deriving all math from axioms, but he did not take away the possibility of deriving all physics. The laws of physics could be limited, or maybe not.

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