I didn’t follow all of that, but your probability count after shooting seems wrong. IIUC, you claim that the probabilities go from {1/2 uncopied, 1⁄4 copy #1, 1⁄4 copy #2} to {1/2 uncopied, 1⁄2 surviving copy}. This is not right. The hypotheses considered in Solomonoff induction are supposed to describe your entire history of subjective experiences. Some hypotheses are going to produce histories in which you get shot. Updating on not being shot is just a Bayesian update, it doesn’t change the complexity count. Therefore, the resulting probabilities are {2/3 uncopied, 1⁄3 surviving copy}.
This glosses over what Solomonoff induction thinks you will experience if you do get shot, which requires a formalism for embedded agency to treat properly (in which case the answer becomes, ofc, that you don’t experience anything), but the counting principle remains the same.
Hm. I agree that this seems reasonable. But how do you square this with what happens if you locate yourself in a physical hypothesis by some property of yourself? Then it seems straightforward that when there are two things that match the property, they need a bit to distinguish the two results. And the converse of this is that when there’s only one thing that matches, it doesn’t need a bit to distinguish possible results.
I think it’s very possible that I’m sneaking in an anthropic assumption that breaks the property of Bayesian updating. For example, if you do get shot, then Solomonoff induction is going to expect the continuation to look like incomprehensible noise that corresponds to the bridging law that worked really well so far. But if you make an anthropic assumption and ask for the continuation that is still a person, you’ll get something like “waking up in the hospital after miraculously surviving” that has experienced a “mysterious” drop in probability relative to just before getting shot.
The fact that one copy gets shot doesn’t mean that “there’s only one thing that matches”. In spacetime the copy that got shot still exists. You do have hypotheses of the form “locate a person that still lives after time t and track their history to the beginning and forward to the future”, but those hypotheses are suppressed by 2−K(t).
I didn’t follow all of that, but your probability count after shooting seems wrong. IIUC, you claim that the probabilities go from {1/2 uncopied, 1⁄4 copy #1, 1⁄4 copy #2} to {1/2 uncopied, 1⁄2 surviving copy}. This is not right. The hypotheses considered in Solomonoff induction are supposed to describe your entire history of subjective experiences. Some hypotheses are going to produce histories in which you get shot. Updating on not being shot is just a Bayesian update, it doesn’t change the complexity count. Therefore, the resulting probabilities are {2/3 uncopied, 1⁄3 surviving copy}.
This glosses over what Solomonoff induction thinks you will experience if you do get shot, which requires a formalism for embedded agency to treat properly (in which case the answer becomes, ofc, that you don’t experience anything), but the counting principle remains the same.
Hm. I agree that this seems reasonable. But how do you square this with what happens if you locate yourself in a physical hypothesis by some property of yourself? Then it seems straightforward that when there are two things that match the property, they need a bit to distinguish the two results. And the converse of this is that when there’s only one thing that matches, it doesn’t need a bit to distinguish possible results.
I think it’s very possible that I’m sneaking in an anthropic assumption that breaks the property of Bayesian updating. For example, if you do get shot, then Solomonoff induction is going to expect the continuation to look like incomprehensible noise that corresponds to the bridging law that worked really well so far. But if you make an anthropic assumption and ask for the continuation that is still a person, you’ll get something like “waking up in the hospital after miraculously surviving” that has experienced a “mysterious” drop in probability relative to just before getting shot.
The fact that one copy gets shot doesn’t mean that “there’s only one thing that matches”. In spacetime the copy that got shot still exists. You do have hypotheses of the form “locate a person that still lives after time t and track their history to the beginning and forward to the future”, but those hypotheses are suppressed by 2−K(t).