Tuesday, January 17, 2012

Follow up to critics agreeing with Dembski re: NFL

Copied from Uncommon Descent:


Joe Felsenstein (Zoologist) at Panda’s Thumb responded [1] to my previous article [2] showing that a couple critics, Wolpert in particular who created the NFL, actually agree with Dembski.
He refers me to a paper he wrote [3] where he explains that the problem with Dembski’s argument is the relevant fitness landscape for evolution is not under the domain of the NFL.  While he may be right, I’m skeptical since Wolpert explicitly denies this in his paper.
Here is the quote again:
“In general in biological coevolution scenarios (e.g., evolutionary game theory), there is no notion of a champion being produced by the search and subsequently pitted against an antagonist in a “bake-off”. Accordingly, there is no particular signifcance to results for C’s that depend on f.
This means that so long as we make the approximation, reasonable in real biological systems, that x’s are never revisited, all of the requirements of Ex. 1 are met. This means that NFL applies.” [formatting mine] [4]
Additionally, there are other reasons I am skeptical.  For one, while there are a few domains where the NFL doesn’t apply, the NFL applies to most.  It may be that evolution just happens to be concerned with the extremely small subset where the NFL doesn’t apply.  But even if it does, even within this select group, most of the group is mostly random.  While there are relevant cites within other papers by Wolpert and other authors on the NFL (which I can dig up if requested), it is easy to just see this result mathematically.  According to Kolmogrov complexity, the majority of the landscapes will be completely random in structure.  Of the rest, only a small subset has any significant amount of structure, and this subset shrinks at an exponential rate as your landscape size increases.  So, given the timescales and number of creatures and variety of environments that evolution posits for its effectivity, it is highly unlikely the landscape is suitably structured for any manner of effective search.
Second, Dr. Felsenstein’s big promise that obviates any concerns about the NFL is:
“They have overlooked the NFL theorem’s unrealistic assumptions about the random way that fitnesses are associated with genotypes, which in effect assumes mutations to have disastrously bad fitness. ”
As far as I know, the current consensus of population geneticists is that mutations do indeed have disastrously bad fitness.
Finally, perhaps Dr. Felsenstein is right after all and evolution does happen to possess the extremely rare and valuable fitness landscape whereby algorithmic search is significantly effective to be worthwhile.  In this case Dembski would be indeed wrong about the applicability of the NFL.  However, given the high specificity of such a landscape, this would mean that evolution itself is intelligently designed to an extraordinary degree.
[1] http://www.pandasthumb.org/archives/2011/08/criticisms-of-d.html#comment-panels
[2] http://www.uncommondescent.com/intelligent-design/critics-agree-with-dembski-the-no-free-lunch-theorem-applies-to-evolution/
[3] http://ncse.com/rncse/27/3-4/has-natural-selection-been-refuted-arguments-william-dembski
[4] http://cs.calstatela.edu/wiki/images/1/15/Wolpert-Coevolution.pdf

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