An Application of the No Free Lunch Theorem

[gumpzilla]

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Another way of saying it, is that for every possible search algorithm you can construct a terrain that is -EV. Therefore you can't design an algorithm better than any other.

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I'd never heard of this theorem before. It would be interesting to learn more about it.

That said, averaging over all possible cost functions can give you one measure of an algorithm's performance. But looking at how it performs against a realistic subset of cost functions, there can definitely be better or worse algorithms. "Always move downhill when possible" is going to be a very poor choice of algorithm for finding maxima.

And it seems to me that trying to use this theorem to discuss evolution, as Dembski is doing, is pretty laughable. For one thing, the whole context as I understand it - looking at survival as an optimization problem - already seems to spit out natural selection as a result, unless he's optimizing some particularly strange variable other than survivability. And trying to talk about how random mutation and natural selection aren't "better" than some other possible scheme misses the point as well, I think. The issue isn't whether random mutation and natural selection is the most efficient way to produce evolution, just whether it does at all. EDIT: Also, what exempts "intelligent change" from the NFL theorem, if you buy his line of reasoning?