Over at Uncommon Descent, Eric Holloway has declared that the critics of William Dembski’s 2002 book No Free Lunch actually accept that the No Free Lunch Theorem applies to evolution. He uses as his evidence the replies to Dembski’s use of the NFLT by Allen Orr and by David Wolpert (who co-wrote the original NFL paper). They had argued that evolution was a more complicated process than the simple model used in the NFLT, a model that for evolution would associate fitnesses with genotypes in a simple search for the genotype of highest fitness. So aren’t computer scientists (Wolpert) and biologists (Orr) implicitly acknowledging that the NFLT theorem applies to any such simple model, and prevents it from searching effectively?
But there have been other criticisms of Dembski’s use of the NFLT, and Holloway does not cite them. I summarized them in a 2007 article I wrote in Reports of the National Center for Science Education. And in the matter of the use of the NFLT my criticisms were actually not new — as I noted there, the fundamental point had been made many times since 2002, originally in a 2002 article by Richard Wein, and also in articles by Jason Rosenhouse (2002), Mark Perakh (2003), Jeffrey Shallit and Wesley Elsberry (2004), Erik Tellgren (2005), and Olle Häggström (2007). I will immodestly claim that my article is the clearest of these many clear articles.
So what is this oft-repeated criticism? When we have a simple model of evolution with genotypes and phenotypes, the NFLT argues that if we average over all the ways that set of fitnesses could be associated with the genotypes, that a simple model of search that climbs uphill on the fitness surface cannot do any better than a random search by pure mutation (one which is unaided by natural selection). That is disastrously bad. It sounds like it says that natural selection in such a model cannot work at all.
But notice the averaging part. It is critical to Wolpert and Macready’s theorem. In effect, it says that we are dealing with an infinitely rough fitness surface. If we change a genotype by making one mutation — changing a single position in its DNA — we arrive at a genotype whose fitness is randomly chosen from the whole set of possible fitnesses. In effect, a single mutation has the same effect as mutating every site in the genome simultaneously. (I apologize for shouting, but the point is not being noticed over at UD).
Of course real biology doesn’t work like this. Mutations are on average worse, but they mostly don’t instantly reduce the organism to rubble. In the real world, nearby genotypes are usually similar in fitness — often a bit worse but sometimes a bit better. In the NFLT world essentially all mutations are disastrous, and evolution would not work. So the No Free Lunch Theorem does not model real biology, not even in a simple model of evolution searching for genotypes of higher fitness on a fitness surface.
So far Holloway has not cited any of these criticisms, and when asked by a polite commenter whether there are any such criticisms, he has simply declared that
I spent some time reading the critics, and this bore [sic] my frustration. I could not find one author who treated Dembski’s work fairly! If someone could fairly refute Dembski’s work I’d be all over it, but I haven’t found anyone! Instead its all passive aggressive ad homineum [sic] and brow beating, with ample burning of strawmen, very tiring to read.
So the discussion at UD continues, hermetically sealed in a self-reinforcing bubble (though I notice now that in that discussion Elizabeth Liddle has tried to raise the relevant point).
Note added 8/29/2011: Eric Holloway has now replied to this post in a post he made recently at Uncommon Descent. For my response to this reply, see the two comments I have made below dated 8/29/2011 at 1:17am and the one following that.