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JohnH comments on Can somebody explain this to me?: The computability of the laws of physics and hypercomputation - Less Wrong
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I see a problem with this: There doesn't seem to be a way to tell if omega itself is in the laws of physics or some finite precision approximation to omega. Given any set of finite observable phenomena and any finite amount of time there will be some finite precision approximation to any real number which is sufficient in the equations to explain all observations, assuming the models used are otherwise correct and otherwise computable. How would one tell if the universe uses the real value Pi or a finite precision version of Pi whose finiteness is epsilon greater then what is needed to calculate any observable value?
How does one know the laws of physics won't suddenly change tomorrow, i.e., how does one distinguish a universe governed by a certain set of laws with one governed by an approximation of the same laws that stops working on a certain day?
You can't. However, if you somehow found an encoding of a physical constant that was highly compressible, such as 1.379[50 digits]0000000000000000, or some other sort of highly regular series, it would be strong evidence towards our universe being both computable and, indeed, computed. (No such constant has yet been found, but we haven't looked very hard yet)
Depending on what you mean by "constant"... The exponent in Coulomb's law is 2. To about 13 decimal places. I would expect some of the similar constants in other formulas to be comparably compressible.