Phil_Goetz comments on Natural Selection's Speed Limit and Complexity Bound - Less Wrong

4 Post author: Eliezer_Yudkowsky 04 November 2007 04:54PM

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Comment author: Phil_Goetz 18 March 2008 02:08:00PM 0 points [-]

If you take a population of organisms, and you divide it arbitrarily into 2 groups, and you show the 2 groups to God and ask, "Which one of these groups is, on average, more fit?", and God tells you, then you have been given 1 bit of information.

But if you take a population of organisms, and ask God to divide it into 2 groups, one consisting of organisms of above-average fitness, and one consisting of organisms of below-average fitness, that gives you a lot more than 1 bit. It takes n lg(n) bits to sort the population; then you subtract out the information needed to sort each half, so you gain n lg(n) - 2(n/2)lg(n/2) = n[lg(n) - lg(n/2)]
= nlg(2) = n bits.

If you do tournament selection, you have n/2 tournaments, each of which gives you 1 bit, so you get n/2 bits per generation.