If you’re running on the non-time-penalized solomonoff prior[...]a bunch of things break including anthropic probabilities and expected utility calculations
This isn’t true, you can get perfectly fine probabilities and expected utilities from ordinary Solmonoff induction(barring computability issues, ofc). The key here is that SI is defined in terms of a prefix-free UTM whose set of valid programs forms a prefix-free code, which automatically grants probabilities adding up to less than 1, etc. This issue is often glossed over in popular accounts.
If you use the UTMs for cartesian-framed inputs/outputs, sure; but if you’re running the programs as entire worlds, then you still have the issue of “where are you in time”.
Say there’s an infinitely growing conway’s-game-of-life program, or some universal program, which contains a copy of me at infinitely many locations. How do I weigh which ones are me?
It doesn’t matter that the UTM has a fixed amount of weight, there’s still infinitely many locations within it.
If you want to pick out locations within some particular computation, you can just use the universal prior again, applied to indices to parts of the computation.
What you propose, ≈”weigh indices by kolmogorov complexity” is indeed a way to go about picking indices, but “weigh indices by one over their square” feels a lot more natural to me; a lot simpler than invoking the universal prior twice.
I think using the universal prior again is more natural. It’s simpler to use the same complexity metric for everything; it’s more consistent with Solomonoff induction, in that the weight assigned by Solomonoff induction to a given (world, claw) pair would be approximately the sum of their Kolmogorov complexities; and the universal prior dominates the inverse square measure but the converse doesn’t hold.
It doesn’t matter? Like, if your locations are identical (say, simulations of entire observable universe and you never find any difference no matter “where” you are), your weight is exactly the weight of program. If you expect dfferences, you can select some kind of simplicity prior to weight this differences, because there is basically no difference between “list all programs for this UTM, run in parallel”.
This isn’t true, you can get perfectly fine probabilities and expected utilities from ordinary Solmonoff induction(barring computability issues, ofc). The key here is that SI is defined in terms of a prefix-free UTM whose set of valid programs forms a prefix-free code, which automatically grants probabilities adding up to less than 1, etc. This issue is often glossed over in popular accounts.
If you use the UTMs for cartesian-framed inputs/outputs, sure; but if you’re running the programs as entire worlds, then you still have the issue of “where are you in time”.
Say there’s an infinitely growing conway’s-game-of-life program, or some universal program, which contains a copy of me at infinitely many locations. How do I weigh which ones are me?
It doesn’t matter that the UTM has a fixed amount of weight, there’s still infinitely many locations within it.
If you want to pick out locations within some particular computation, you can just use the universal prior again, applied to indices to parts of the computation.
What you propose, ≈”weigh indices by kolmogorov complexity” is indeed a way to go about picking indices, but “weigh indices by one over their square” feels a lot more natural to me; a lot simpler than invoking the universal prior twice.
I think using the universal prior again is more natural. It’s simpler to use the same complexity metric for everything; it’s more consistent with Solomonoff induction, in that the weight assigned by Solomonoff induction to a given (world, claw) pair would be approximately the sum of their Kolmogorov complexities; and the universal prior dominates the inverse square measure but the converse doesn’t hold.
It doesn’t matter? Like, if your locations are identical (say, simulations of entire observable universe and you never find any difference no matter “where” you are), your weight is exactly the weight of program. If you expect dfferences, you can select some kind of simplicity prior to weight this differences, because there is basically no difference between “list all programs for this UTM, run in parallel”.
There could be a difference but only after a certain point in time, which you’re trying to predict / plan for.