Rolf_Nelson2 comments on Complexity and Intelligence - Less Wrong

24 Post author: Eliezer_Yudkowsky 03 November 2008 08:27PM

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Comment author: Rolf_Nelson2 05 November 2008 05:28:22AM 0 points [-]

@Wei: p(n) will approach arbitrarily close to 0 as you increase n.

This doesn't seem right. A sequence that requires knowledge of BB(k), has O(2^-k) probability according to our Solomonoff Inductor. If the inductor compares a BB(k)-based model with a BB(k+1)-based model, then BB(k+1) will on average be about half as probable as BB(k).

In other words, P(a *particular* model of K-complexity k is correct) goes to 0 as k goes to infinity, but the conditional probability, P(a *particular* model of K-complexity k is correct | a sub-model of that particular model with K-complexity k-1 is correct), does not go to 0 as k goes to infinity.