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cousin_it comments on Born rule or universal prior? - Less Wrong Discussion
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Comments (35)
You can't have a variant of the universal prior that makes all incoming bitstrings equiprobable regardless of their K-complexity, because that would be the uniform prior.
"Nature has access to random bits" is a very different claim than "nature outputs the uniform distribution."
Many versions of Solomonoff induction, including, I believe, the original, predict that if so far the even bits of the output are all 0 and the odd bits have full complexity, that description will continue to be true in the future.
I'm having trouble figuring out a proof for your last claim... But then again, maybe I'm just being stupid because two other people have tried to explain it to me and I didn't understand their attempts either :-(
These two pages from the 1997 edition of "An Introduction to Kolmogorov Complexity and Its Applications" seem relevant.
Thanks a lot! I'm now convinced that the claim is true, but have no idea why :-) Will try to work through the proof.
Haven't seen too any of those. Have they even been seriously proposed? This certainly isn't what people usually mean by "Solomonoff induction".
Can you explain you can't have a language that has some encoding for random bits as well as encodings for deterministic bits? Doesn't seem like such a language would imply a uniform prior.
Edit: Even though I don't have the math background to understand this stuff, I love it when it gets discussed here.