cousin_it comments on Why no uniform weightings for ensemble universes? - Less Wrong

5 Post author: Will_Newsome 31 July 2011 10:05PM

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Comment author: cousin_it 01 August 2011 10:30:04AM *  0 points [-]

That in turn means that in our domain of programs a trillion bits long, exponentially more programs contain the compact subroutine than the literal print statement.

Are you sure this is right? There's exponentially many different print statements. Do you have an argument why they should have low combined weight?

Comment author: DanielVarga 01 August 2011 01:37:03PM *  0 points [-]

The number of N-bit print statements whose output starts with the n-bit Hamlet is exactly 2^(N-n). If K(Hamlet)=n/6, then there are at least 2^(N-n/6) programs whose output starts with Hamlet. Probably more.

EDIT: Ooops, I didn't prove anything about the structuredness of the remaining N-n bits, so this is not too useful in itself.

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