Distant spiral galaxy NGC4603 [Courtesy NASA]

Does information theory refute evolution?

David H. Bailey
Updated 27 August 2022 (c) 2022


Both traditional creationists and intelligent design scholars have invoked probability and information theory 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, or that an explosion in an aircraft shop could produce a working airliner [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 peer-reviewed 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. 27-28; 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 well-known scientific principle [Perakh2004, pg. 103-106] (see also Thermodynamics). 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]:

  1. The official had no choice in all but one of the cases, since a mobster was holding a gun to his head.
  2. The official is the victim of a brain condition that renders him unable to write "Republican" except on one occasion.
  3. The official attempted to use a fair coin, but unbeknown to him he was using a coin that had been weighted.
  4. 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 coin-tossing 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 ill-defined. 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.

Do probability and information theory calculations matter?

One general criticism that applies to all arguments dealing with probability, information and evolution, either from Dembski or others, is that it is not at all clear that such highly mathematical models are truly applicable to a highly complex, real-world phenomenon such as evolution. Evolution is a much more complicated process than anything that can be modeled well with such an approach, and virtually all such attempts, particularly those by creationist and intelligent design writers, are fallacious. For additional details and discussion, see Probability.

For example, as mentioned above, Dembski's information theory arguments can be seen as an elaboration on the principle that the overall process of nature is to greater disorder, whereas evolution has led to highly complex, ordered organisms such as us. But there is much more (in fact, many orders of magnitude more) energy and entropy available to life on Earth than is needed to explain evolution. Even at the molecular level, DNA and the mechanisms of cell reproduction and evolution are continually bombarded by both random thermal jostling and cosmic-ray-induced "errors," and these disturbances, together with the ever-present forces of natural selection, are the sources of long-term evolutionary change. So it is not at all clear that information theory has anything meaningful to say here, one way or the other. See Thermodynamics for additional discussion.

Computer programs produced by evolutionary processes

The fact that the information theory arguments against evolution cannot possibly be valid can be seen by the rise of computer programs that mimic the process of biological evolution to produce novel solutions to engineering problems, in many cases superior to the best human efforts. This approach has been termed "genetic algorithms" or "evolutionary computing." As a single example, in 2017 Google researchers generated 1000 image recognition algorithms, each of which were trained using state-of-the-art deep neural networks to recognize a selected set of images. They then used an array of 250 computers, each running two algorithms, to identify an image. Only the algorithm that scored higher proceeded to the next iteration, where it was changed somewhat, mimicking mutations in natural evolution. Google researchers found that their scheme could achieve accuracies as high as 94.6% [Gershgorn2017].

Closely related are advances in artificial intelligence, in which a set of computer programs "compete" to produce a superior program. One notable example is the 2016 defeat of the world's top Go player by a computer program named AlphaGo, developed by DeepMind (a subsidiary of Alphabet, Google's parent company), in an event that surprised observers who had not expected this for decades, if ever. Then in 2017, DeepMind announced even more remarkable results: their researchers had started from scratch, programming a computer with only the rules of Go, together with a "deep learning" algorithm, and then had the program play games against itself. Within a few days it had advanced to the point that it defeated the earlier champion-beating AlphaGo program 100 games to zero. After one month, the program's rating was as far above the world champion as the world champion was above a typical amateur [Greenmeier2017].

Look to nature

In any event, arguments such as Dembski's, which in effect attempt to establish that evolution can't happen naturally, are overwhelmingly refuted by the many instances of evolution occurring in the natural world, and as evidenced overwhelmingly in analysis of DNA between organisms. See DNA, English text, Novelty and Probability for additional discussion.


In short, professional mathematicians who have studied Dembski's material in detail have concluded that these arguments are deeply flawed. Dembski central argument, namely that a "Law of Conservation of Information" or similar principle rules out the 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.

But one does not need to be an expert in information theory to see that these arguments cannot possibly be correct -- one need only look to nature, to the many published instances of evolution in action producing novel structures and features, together with the growing usage of "genetic algorithms" and the like in computer science and engineering, which in many cases has produced designs and programs superior to the best human efforts.

In a larger context, one has to question whether highly technical issues such as information theory have any place in a discussion of religion. Why attempt to "prove" God with information theory, particularly when there are very serious questions as to whether such reasoning is valid? One is reminded of a passage in the New Testament: "For if the trumpet gives an uncertain sound, who shall prepare himself for the battle?" [1 Cor. 14:8]. It makes far more sense to leave such matters to peer-reviewed scientific research.

For additional information, see Complexity, Creationism, English text, Novelty, Origin and Probability.


[See Bibliography].