Whether you switch to something else like lambda calculus or a trivial CA doesn’t really matter. These all boil down to models with a few states and transitions and as such have simple physical realisations. When you have only a few states and transitions there isn’t much space to move about. This is the bedrock. It isn’t absolutely unique, sure, but the space is tight enough to have little impact on Solomonoff induction.
3^^^3 is a super gigantic monster number, and all these mind boggeling many shorter programs outputting things that are complex on a minimal state Turing machine (or lambda calculus, or minimal CA, or minimal...), where are you going to put all this? You can’t squeeze it into something that is as ultra trivial as the Wolfram/Smith UTM that has just 2 states and 3 symbols.
Toby:
Whether you switch to something else like lambda calculus or a trivial CA doesn’t really matter. These all boil down to models with a few states and transitions and as such have simple physical realisations. When you have only a few states and transitions there isn’t much space to move about. This is the bedrock. It isn’t absolutely unique, sure, but the space is tight enough to have little impact on Solomonoff induction.
3^^^3 is a super gigantic monster number, and all these mind boggeling many shorter programs outputting things that are complex on a minimal state Turing machine (or lambda calculus, or minimal CA, or minimal...), where are you going to put all this? You can’t squeeze it into something that is as ultra trivial as the Wolfram/Smith UTM that has just 2 states and 3 symbols.