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?
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.
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.