I think that’s roughly correct, but it is useful...
‘The best UTM is the one that figures out the right answer the fastest’ is true, but not very useful.
Another way to frame it would be: after one has figured out the laws of physics, a good-for-these-laws-of-physics Turning machine is useful for various other things, including thermodynamics. ‘The best UTM is the one that figures out the right answer the fastest’ isn’t very useful for figuring out physics in the first place, but most of the value of understanding physics comes after it’s figured out (as we can see from regular practice today).
Also, we can make partial updates along the way. If e.g. we learn that physics is probably local but haven’t understood all of it yet, then we know that we probably want a local machine for our theory. If we e.g. learn that physics is causally acyclic, then we probably don’t want a machine with access to atomic unbounded fixed-point solvers. Etc.
I agree that this seems maybe useful for some things, but not for the “Which UTM?” question in the context of debates about Solomonoff induction specifically, and I think that’s the “Which UTM?” question we are actually kind of philosophically confused about. I don’t think we are philosophically confused about which UTM to use in the context of us already knowing some physics and wanting to incorporate that knowledge into the UTM pick, we’re confused about how to pick if we don’t have any information at all yet.
I think roughly speaking the answer is: whichever UTM you’ve been given. I aim to write a more precise answer in an upcoming paper specifically about Solomonoff induction. The gist of it is that the idea of a “better UTM” U_2 is about as absurd as that of a UTM that has hardcoded knowledge of the future: yes such UTMs exists, but there is no way to obtain it without first looking at the data, and the best way to update on data is already given by Solomonoff induction.
I think that’s roughly correct, but it is useful...
Another way to frame it would be: after one has figured out the laws of physics, a good-for-these-laws-of-physics Turning machine is useful for various other things, including thermodynamics. ‘The best UTM is the one that figures out the right answer the fastest’ isn’t very useful for figuring out physics in the first place, but most of the value of understanding physics comes after it’s figured out (as we can see from regular practice today).
Also, we can make partial updates along the way. If e.g. we learn that physics is probably local but haven’t understood all of it yet, then we know that we probably want a local machine for our theory. If we e.g. learn that physics is causally acyclic, then we probably don’t want a machine with access to atomic unbounded fixed-point solvers. Etc.
I agree that this seems maybe useful for some things, but not for the “Which UTM?” question in the context of debates about Solomonoff induction specifically, and I think that’s the “Which UTM?” question we are actually kind of philosophically confused about. I don’t think we are philosophically confused about which UTM to use in the context of us already knowing some physics and wanting to incorporate that knowledge into the UTM pick, we’re confused about how to pick if we don’t have any information at all yet.
I think roughly speaking the answer is: whichever UTM you’ve been given. I aim to write a more precise answer in an upcoming paper specifically about Solomonoff induction. The gist of it is that the idea of a “better UTM” U_2 is about as absurd as that of a UTM that has hardcoded knowledge of the future: yes such UTMs exists, but there is no way to obtain it without first looking at the data, and the best way to update on data is already given by Solomonoff induction.