Solomonoff Induction has a free choice of variable, namely the use of the Universal Turing Machine (UTM) on which to run it, which is equivalent to the choice of language (e.g. whether to choose Python or C or some formalization of the english language). How to choose that variable is indeed kind of an open question, and not super obvious, but so are many other things about how to actually use SI in practice (obviously the same is true for less formal versions of Occam’s Razor).
However, you can still prove a substantial number of things about SI without knowing the UTM with which it is run, because as johnswentworth says, there is at most a fixed constant of difference in the length of the resulting programs and in many inference problems it makes sense to think about the convergent behavior over long periods of time/many pieces of evidence, for which all SI machines will converge to the same beliefs.
I do concretely think that this choice of open variable is a really big one, and not one that we should forget when reasoning about SI.
Solomonoff Induction has a free choice of variable, namely the use of the Universal Turing Machine (UTM) on which to run it, which is equivalent to the choice of language (e.g. whether to choose Python or C or some formalization of the english language). How to choose that variable is indeed kind of an open question, and not super obvious, but so are many other things about how to actually use SI in practice (obviously the same is true for less formal versions of Occam’s Razor).
However, you can still prove a substantial number of things about SI without knowing the UTM with which it is run, because as johnswentworth says, there is at most a fixed constant of difference in the length of the resulting programs and in many inference problems it makes sense to think about the convergent behavior over long periods of time/many pieces of evidence, for which all SI machines will converge to the same beliefs.
I do concretely think that this choice of open variable is a really big one, and not one that we should forget when reasoning about SI.