Eugene Salamin wrote:

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I see no application of Godel incompleteness to physics. Questions such as whether the whole of physics is finitely describable are unanswerable, since, unlike mathematics, physics is limited by what can be measured rather than by what can be postulated.

I agree. One interesting paper I read claimed to show that if your physical theory predicts that some measureable quantity is equal to an uncomputable number, you'll never be able to verify your theory algorithmically! Of course, if the Church-Turing thesis is false for some physical system, then perhaps we could use that to verify it.

To obtain an uncomputable number as a measurement result requires measuring to infinite precision, and this is not possible.

Gene

It's not the infinite precision that's the important part, it's that you can't know how close your approximation to the number is. Say, for instance, the theory predicts Omega. You go and measure the appropriate property to a known accuracy, and then try to compute bits of Omega to compare it with. You can only prove a finite number of bits with any given algorithm. You could start enumerating programs and running them; if the "weight" of the halting programs exceeds the measured value, then you can falsify the theory. But if they're less than the measured number, there's no way to determine how close you are to the correct value, so you can never verify the theory to an arbitrary but finite accuracy algorithmically. -- Mike Stay staym@clear.net.nz http://www.cs.auckland.ac.nz/~msta039