Here we go again! Dembski is back on the scene with his latest version of his mathematical attempts to demonstrate that the natural world is impossible.
http://www.designinference.com/documents/2005.03.Searching_Large_Spaces.pdf
It’s highly technical, but certainly not beyond many Dopers. And the gist, in case you are unfamiliar with the guy, is that there is “No Free Lunch” in the sense Dembski means: the natural world cannot possibly, by any possible process or happenstance state, account for highly functional complexity.
Here he is just happening to apply his math to evolution:
[quote]
Even if we accept the full efficacy of evolutionary mechanisms to evolve biological structures and functions, the challenge that displacement poses to evolutionary biology still stands. A larger environment bestows a nonuniform probability qua assisted search. Fine. Presumably this nonuniform probability, which is defined over the search space in question, splinters off from richer probabilistic structures defined over the larger environment. We can, for instance,
imagine the search space being embedded in the larger environment, and such richer probabilistic structures inducing a nonuniform probability (qua assisted search) on this search space, perhaps by conditioning on a subspace or by factorizing a product space. But, if the larger environment is capable of inducing such probabilities, what exactly are the structures of the larger environment that endow it with this capacity? Are any canonical probabilities defined over this larger environment (e.g., a uniform probability)? Do any of these higherlevel probabilities induce the nonuniform probability that characterizes effective search of the original search space? What stochastic mechanisms might induce
such higher-level probabilities?
For any interesting instances of biological evolution, we don’t know the answer
to these questions. But suppose we could answer these questions. As soon as we could, the No Free Lunch Regress would kick in, applying to the larger environment once its probabilistic structure becomes evident. And so, this probabilistic structure would itself require explanation in terms of stochastic mechanisms. On the other hand, lacking answers to these questions, we lack a stochastic mechanism to explain the nonuniform probabilities (and corresponding assisted searches) that the larger environment is supposed to induce and that makes effective search of the original space possible. In either case, the No Free Lunch Regress blocks our attempts to account for assisted searches in terms of stochastic mechanisms.
Evolutionary biologists at this point sometimes object that evolutionary mechanisms like Darwinian natural selection are indeed a free lunch because they are so simple, generating, as Richard Dawkins (1987: 316) puts it, biological complexity out of “primeval simplicity.” But ascribing simplicity to these mechanisms betrays wishful thinking. The information that assisted searches bring to otherwise blind searches is measurable and substantial, and discloses an underlying complexity (see section 4). Just because it’s possible to describe the mechanism that assists a search in simple terms does not mean that the mechanism, as actually operating in nature and subject to countless contingencies
(Michael Polanyi called them boundary conditions), is in fact simple.
A final question therefore presents itself, namely, Is it even reasonable,
whether in biology or elsewhere, to think that the assisted searches that successfully locate small targets in large spaces should be conceived as purely the result of stochastic mechanisms? What if, additionally, they inevitably result from a form of intelligence that is not reducible to stochastic mechanisms–a form of intelligence that transcends chance and necessity? The No Free Lunch Regress,
by demonstrating the incompleteness of stochastic mechanisms to explain assisted searches, fundamentally challenges the materialist dogma that reduces all intelligence to chance and necessity.