While listening to this podcast yesterday, I was startled by the section on the choice of Turing machine in Solomonoff induction, and the fact that it seems arbitrary. (I had been thinking about similar questions, but in relation to Dust Theory).
One approach could be to take the set of all possible turing machines T, and for each pair of turing machines t1,t2∈T find the shortest/fastest program p1 on 2 so that p1 on 2 emulates t1 on t2. Then, if p1 on 2 is shorter/faster than p2 on 1, one can say that t1 is simpler than t2 (I don’t know if this would always intuitively be true). For example, python with witch can emulate python without witch in a shorter program that vice versa (this will only make sense if you’ve listened to the podcast).
Maybe this would give a total order over Turing machines with a maximum. One could then take the simplest Turing machine and use that one for Solomonoff induction.
epistemic status: a babble
While listening to this podcast yesterday, I was startled by the section on the choice of Turing machine in Solomonoff induction, and the fact that it seems arbitrary. (I had been thinking about similar questions, but in relation to Dust Theory).
One approach could be to take the set of all possible turing machines T, and for each pair of turing machines t1,t2∈T find the shortest/fastest program p1 on 2 so that p1 on 2 emulates t1 on t2. Then, if p1 on 2 is shorter/faster than p2 on 1, one can say that t1 is simpler than t2 (I don’t know if this would always intuitively be true). For example, python with witch can emulate python without witch in a shorter program that vice versa (this will only make sense if you’ve listened to the podcast).
Maybe this would give a total order over Turing machines with a maximum. One could then take the simplest Turing machine and use that one for Solomonoff induction.