The “Born Probabilities” section was 11 dang paragraphs of “they’re the best fit to our observations and Occam’s razor.” :(
It was 8 paragraphs of “Here is why Occam’s razor is entitled to explain the Born probabilities just like the rest of physics.” Insofar as the Born probabilities are mysterious at all, this is what needs to be resolved. Do you disagree?
This is not necessarily true. The sequence HHHHHHHHHH has a lower Kolmogorov complexity than HTTTTHTHTT. So this weighting of observers by complexity has observable consequences in that we will see simpler strings more often than a uniform distribution would predict. But we don’t, which makes this idea unlikely.
Your reasoning applies verbatim to Solomonoff induction itself, which is the first clue that someone has thought through it before. In fact, I strongly suspect that Solomonoff thought through it.
What you are saying is that truly random processes are rare under the Solomonoff prior. But it should be clear that the total mass on random processes is comparable to the total mass on deterministic processes. So we should not be surprised in general to find ourselves in a universe in which random processes exist. Once we have observed a phenomenon to be random in the past, switching from randomness to some simple law (like always output H) is unlikely for the same reason that arbitrarily changing the laws of physics is unlikely.
Yes, but then I never thought they were relatively mysterious anyhow, for the reasons you describe. They’re a natural law, and that’s what science is for. Neither have I ever heard any physics professors or textbooks say they’re mysterious. An “explanation” of the Born probabilities would be deriving them, and some other parts of quantum mechanics, from a simpler underlying framework.
What you are saying is that truly random processes are rare under the Solomonoff prior. But it should be clear that the total mass on random processes is comparable to the total mass on deterministic processes.
“Comparable,” but not the same. Qualitative estimates are not enough here.
switching from randomness to some simple law (like always output H) is unlikely for the same reason that arbitrarily changing the laws of physics is unlikely.
Nope. Changing from random to simple would reduce the size of the turing machine needed to generate the output, because a specific random string needs a lot of specification but a run of heads does not. This lowers the complexity and makes it more likely by your proposed prior. The reason that this is bad for your proposed prior and not for Solomonoff induction is because one is about your experience and one is about just the universe. So even in a multiverse where all of you “happen,” thus satisfying Solomonoff induction, your prior adds this extra weighting that makes it more likely for you to observe HHHHHHHHHH.
Short PRNGs seem to exist, and a Turing machine that could produce my subjective experiences up until now would seem to need one already. So I don’t think it’s necessarily the case that the Turing machine to output a description of an Everett branch in which I observe HHHHHH after a bunch of random-like events is shorter than the one to output a description of an Everett branch in which I observe HTTHHHT after a bunch of random-like events.
It was 8 paragraphs of “Here is why Occam’s razor is entitled to explain the Born probabilities just like the rest of physics.” Insofar as the Born probabilities are mysterious at all, this is what needs to be resolved. Do you disagree?
Your reasoning applies verbatim to Solomonoff induction itself, which is the first clue that someone has thought through it before. In fact, I strongly suspect that Solomonoff thought through it.
What you are saying is that truly random processes are rare under the Solomonoff prior. But it should be clear that the total mass on random processes is comparable to the total mass on deterministic processes. So we should not be surprised in general to find ourselves in a universe in which random processes exist. Once we have observed a phenomenon to be random in the past, switching from randomness to some simple law (like always output H) is unlikely for the same reason that arbitrarily changing the laws of physics is unlikely.
Yes, but then I never thought they were relatively mysterious anyhow, for the reasons you describe. They’re a natural law, and that’s what science is for. Neither have I ever heard any physics professors or textbooks say they’re mysterious. An “explanation” of the Born probabilities would be deriving them, and some other parts of quantum mechanics, from a simpler underlying framework.
“Comparable,” but not the same. Qualitative estimates are not enough here.
Nope. Changing from random to simple would reduce the size of the turing machine needed to generate the output, because a specific random string needs a lot of specification but a run of heads does not. This lowers the complexity and makes it more likely by your proposed prior. The reason that this is bad for your proposed prior and not for Solomonoff induction is because one is about your experience and one is about just the universe. So even in a multiverse where all of you “happen,” thus satisfying Solomonoff induction, your prior adds this extra weighting that makes it more likely for you to observe HHHHHHHHHH.
Short PRNGs seem to exist, and a Turing machine that could produce my subjective experiences up until now would seem to need one already. So I don’t think it’s necessarily the case that the Turing machine to output a description of an Everett branch in which I observe HHHHHH after a bunch of random-like events is shorter than the one to output a description of an Everett branch in which I observe HTTHHHT after a bunch of random-like events.