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Stone pseudomagic square on exterior of La Sagrada Familia cathedral, Barcelona, Spain [Photo by DHB, (c) 2011]

Does information theory refute evolution?
David H. Bailey
1 Jan 2017 (c) 2017
Introduction
Both traditional creationists and intelligent design scholars have invoked probability arguments in criticisms of biological evolution. They argue that certain features of biology are so fantastically improbable that they could never have been produced by a purely natural, "random" process, even assuming the billions of years of history asserted by geologists and astronomers. They often equate the hypothesis of evolution to the absurd suggestion that monkeys randomly typing at a typewriter could compose a selection from the works of Shakepeare [Dembski1998; Foster1991; Hoyle1981; Lennox2009].
Dembski's information theory arguments
Intelligent design writer William Dembski invokes both probability and information theory (the mathematical theory of information content in data) in his arguments against Darwinism [Dembski1998, Dembski1999; Dembski2002; Dembski2004; Dembski2007]. Robert Koons, a colleague of Dembski's, writes in the jacket of Dembski's book Intelligent Design, "William Dembski is the Isaac Newton of information theory, and since this is the Age of Information, that makes Dembski one of the most important thinkers of our time." [Dembski1999]. So are these flattering assessments (by fellow intelligent design scholars) well deserved?
Difficulties with Dembski's arguments
To begin with, it is important to note that Dembski's works are not based on peerreviewed mathematical material. Indeed, a recent check of the mathematical literature identified only one publication by Dembski in the area of probability theory, and none in the specific areas covered by his books [Elsberry2011].
Also, although Dembski's books are marketed to the lay public, they include highly technical analysis and obscure notation that is readable only by experts. If anything, there appears to be gratuitous usage of obscure mathematical notation and mathematical concepts in these books [Perakh2004, pg. 2728; Perakh2005; Shallit2002].
In any event, mathematicians who have examined Dembski's books are not persuaded by his reasoning. Mark Perakh concludes that Dembski's results are mostly wishful thinking, with significant errors of reasoning. For example, Perakh observes that Dembski's "Law of Conservation of Information" contradicts the second law of thermodynamics, a wellknown scientific principle [Perakh2004, pg. 103106] (see also
Thermodynamics).
Indeed, there is no "conservation" law with respect to any of the most widely employed measures of information (Shannon, Kolmogorov or Chaitin) employed in information theory research. Richard Wein, in a review of Dembski's book No Free Lunch [Dembski2002], bluntly concludes that it is "pseudoscientific rhetoric aimed at a mathematically unsophisticated audience" [Wein2002].
The most extensive analyses of Dembski's writings to date have been published by Wesley Elsberry (a computational biologist at Michigan State University) and Jeffrey Shallit (a mathematician at the University of Waterloo in Canada) [Elsberry2011; Shallit2004]. For instance, these authors analyze an example presented by Dembski, wherein a New Jersey official, appointed to randomly assign the order of political parties in local elections, assigned the Democratic candidate first in all but one of the 41 elections (and thus his assignment was highly suspect). Dembski calculates the probability of this event as 42 x 2^{41}, or roughly 1.9 x 10^{11}. But Elsberry and Shallit point out that Dembski only considers one possibility, namely that the official's selections arose by the flipping of a fair coin. He does not consider other possibilities such as (paraphrased) [Elsberry2011]:
 The official had no choice in all but one of the cases, since a mobster was holding a gun to his head.
 The official is the victim of a brain condition that renders him unable to write "Republican" except on one occasion.
 The official attempted to use a fair coin, but unbeknown to him he was using a coin that had been weighted.
 Acting in response to evolutionary pressures over many years, the official sought to enhance his social status among his peers, all of whom happened to be Democrats.
The point of these humorous items is that there are always other possibilities to exclude other than a simple cointossing scenario. Elsberry and Shallit note that if, as Dembski argues, the design hypothesis can be inferred simply by ruling out hypotheses of chance and necessity, then any observed event with a sufficiently complicated or obscure causal history could be mistakenly be assigned to design. For example, in 1967 astronomer Jocelyn Bell observed a long series of pulses, with period 1.337 seconds, in the light coming from a distant star. Applying Dembski's rules for design (e.g., by assessing "complex specified information"), one would have concluded that this was indisputable evidence of an extraterrestrial intelligence. In fact, the source later turned out to be a rotating neutron star [Elsberry2011].
Elsberry and Shallit conclude their analysis of Dembski's writings as follows [Elsberry2011]:
We have argued that Dembski's justification for "intelligent design" is flawed in many respects. His concepts of complexity and information are either orthogonal or opposite to the use of these terms in the literature. His concept of specification is problematic and illdefined. Dembski's use of the term "complex specified information" is inconsistent, and his proof of the "Law of Conservation of Information" is flawed. Finally, his claims about the limitations of natural causes and computation are incorrect. We conclude that there is no reason to accept his claims.
Conclusions
In short, professional mathematicians who have studied Dembski's material in detail have concluded that these arguments are deeply flawed. Dembski's central argument, namely that there is a "Law of Conservation of Information" that rules out natural evolution of highly complex biological structures, is without foundation. And it is not clear that any of his arguments are valid in an evolutionary biology context.
In any event, it is clear that it is extremely unwise to base one's religious faith on information theory analyses. Why look to information theory to "prove" God, particularly when there are very serious questions as to whether such reasoning is valid? One is reminded of a passage in the New Testament (1 Cor. 14:8): "For if the trumpet gives an uncertain sound, who shall prepare himself for the battle?"
See English text, Origin and Probability for additional related discussion.
[See Bibliography].