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Douglas_Knight comments on Born rule or universal prior? - Less Wrong Discussion

7 Post author: cousin_it 29 June 2011 11:27PM

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Comment author: Douglas_Knight 30 June 2011 03:31:03AM 0 points [-]

I don't know what Legg says in your link, but there are variants of the universal prior in which "the coin is fair" has small complexity, because nature has access to random numbers.

Comment author: cousin_it 30 June 2011 06:51:42AM 1 point [-]

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.

Comment author: Douglas_Knight 30 June 2011 04:00:25PM 4 points [-]

"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.

Comment author: cousin_it 10 July 2011 09:17:14PM *  0 points [-]

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 :-(

Comment author: Wei_Dai 10 July 2011 09:56:30PM *  3 points [-]

These two pages from the 1997 edition of "An Introduction to Kolmogorov Complexity and Its Applications" seem relevant.

Comment author: cousin_it 11 July 2011 08:25:46AM *  0 points [-]

Thanks a lot! I'm now convinced that the claim is true, but have no idea why :-) Will try to work through the proof.

Comment author: timtyler 01 July 2011 06:43:02PM 0 points [-]

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.

Haven't seen too any of those. Have they even been seriously proposed? This certainly isn't what people usually mean by "Solomonoff induction".

Comment author: jsalvatier 30 June 2011 03:08:45PM *  0 points [-]

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.

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