Anthropics would be one way of reading it, yes. Think of it as saying, in addition to wanting all of our Turing machines to add up to 1, we also want all of the computational elements inside our Turing machines to add up to 1 because we’re trying to guess which computational element ‘we’ might be. This might seem badly motivated in the sense that we can only say “Because our probabilities have to add up to 1 for us to think!” rather than being able to explain why magical reality fluid ought to work that way a priori, but the justification for a simplicity prior isn’t much different—we have to be able to add up all the Turing machines in their entirety to 1 in order to think. So Turing machines that use lots of tape get penalties to the probability of your being any particular or special element inside them. Being able to affect lots of other elements is a kind of specialness.
I’m confused because I had always thought it would be the exact opposite. To predict your observational history given a description of the universe, solomonoff induction needs to find you in it. The more special you are, the easier you are to find and thus the easier it is to find your observational history.
Anthropics would be one way of reading it, yes. Think of it as saying, in addition to wanting all of our Turing machines to add up to 1, we also want all of the computational elements inside our Turing machines to add up to 1 because we’re trying to guess which computational element ‘we’ might be. This might seem badly motivated in the sense that we can only say “Because our probabilities have to add up to 1 for us to think!” rather than being able to explain why magical reality fluid ought to work that way a priori, but the justification for a simplicity prior isn’t much different—we have to be able to add up all the Turing machines in their entirety to 1 in order to think. So Turing machines that use lots of tape get penalties to the probability of your being any particular or special element inside them. Being able to affect lots of other elements is a kind of specialness.
I’m confused because I had always thought it would be the exact opposite. To predict your observational history given a description of the universe, solomonoff induction needs to find you in it. The more special you are, the easier you are to find and thus the easier it is to find your observational history.