I agree with Jimmy’s examples. Tim, the Solomonoff model may have some other fine print assumptions {see some analysis by Shane Legg here}, but “the earth having the same laws as space” or “laws not varying with time” are definitely not needed for the optimality proofs of the universal prior (though of course, to your point, uniformity does make our induction in practice easier, and time and space translation invariance of physical law do appear to be true, AFAIK.). Basically, assuming the universe is computable is enough to get the optimality guarantees. This doesn’t mean you might not still be wrong if Mars in empirical fact changes the rules you’ve learned on Earth, but it still provides a strong justification for using induction even if you were not guaranteed that the laws were the same, until you observed Mars to have different laws, at which point, you would assign largest weight to the simplest joint hypothesis for your next decision.
I agree with Jimmy’s examples. Tim, the Solomonoff model may have some other fine print assumptions {see some analysis by Shane Legg here}, but “the earth having the same laws as space” or “laws not varying with time” are definitely not needed for the optimality proofs of the universal prior (though of course, to your point, uniformity does make our induction in practice easier, and time and space translation invariance of physical law do appear to be true, AFAIK.). Basically, assuming the universe is computable is enough to get the optimality guarantees. This doesn’t mean you might not still be wrong if Mars in empirical fact changes the rules you’ve learned on Earth, but it still provides a strong justification for using induction even if you were not guaranteed that the laws were the same, until you observed Mars to have different laws, at which point, you would assign largest weight to the simplest joint hypothesis for your next decision.