Information Theory and Evolution

William Dembski, noted crackpot “intelligent design theorist,” is attempting to abuse information theory to support his notion that evolution is impossible. His first paper is dedicated to setting up a new mathematical framework for his theories, but really contains no new contribution. Its own claim is that:

But what if the item of knowledge learned is not the occurrence of an event but, rather, the change in probability distribution associated with an ensemble of events? This paper takes the usual account of information, which focuses on events, and generalizes it to probability distributions/measures. In so doing, it facilitates the assignment of “generalized bits” to arbitrary state transitions of physical systems.

Of course, this kind of thinking has been done by, for example, Kullback and Leibler, and the mutual information which he makes such a big deal out of is in fact just a special instance of the KL divergence. Another exciting “new generalization” is the first equation on page 8, which looks like a Renyi entropy to me. And the section on continuity spectra is something I’ve seen before, but I can’t find a reference.

Either we should junk the paper as of the “information theory, photosynthesis, and religion” type, or perhaps it’s just the warmup for more outrageous claims to follow.

UPDATE: Cosma Shalizi has the full critique. The information geometry is what I couldn’t figure out before. This critique found via Evolution Blog.

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