On Not Admitting You Are Wrong, or What Dembski and Wolfram Have in Common

Science often depends on experiments, and experiments are notoriously prone to error. Even if the experiment's results are correct, the conclusions may be wrong. And even if the experiment and conclusions are correct, they may represent only part of the truth. Sometimes scientists are simply wrong, and they need to admit it. While they don't do experiments, a similar obligation falls on mathematicians.

Most mathematicians and scientists recognize this obligation. In 1989, for example, the mathematician I. J. Good published a corrigendum to one of his previous papers. This wouldn't be noteworthy except that the paper he was correcting was published in 1941, nearly 50 years before.

Unfortunately, it doesn't always work that way. A classic case is that of René Blondlot (1849-1930), a French physicist who believed he had discovered a new kind of radiation, which he called "N-rays" in honor of Nancy, his native city. You can read about this case in Walter Gratzer's book The Undergrowth of Science, and I am following Gratzer's account here.

N-rays, Blondlot said, had all sorts of unusual properties. They could go through paper, wood, quartz, and mica, but not water or rock salt. They were emitted by animal and plant tissue. When N-rays hit the human eye, people could see better. Some other physicists confirmed his results, and found other strange properties of the rays. Blondlot's results were often based on very subjective data, such as a line of glowing phosphor increasing or decreasing in brightness based only on visual observations.

However, others failed to confirm his results, notably German physicists such as Heinrich Rubens, Otto Lummer, and Paul Drude, and English physicists such as Lord Rayleigh, Lord Kelvin, and William Crookes. Nationality began to influence the controversy: one Blondlot supporter later claimed the Germans could not detect the effect of the rays because "their sensibilities were inferior and were further blunted by their bruish diet of beer and sauerkraut" (Gratzer, p.20).

Ultimately, N-rays met their scientific death when R. W. Wood, a Johns Hopkins physicist, visited Blondlot's laboratory. In a 1904 letter published in Nature, he made a devastating revelation. While observing an experiment in a dark room in which the N-rays were refracted by an aluminum prism, Wood surreptitiously removed the prism from the apparatus. The French experimenters, unaware of Wood's actions, went on describing exactly the same phenomena as before.

But Blondlot and many of his supporters did not concede. One French scientist, Turpain, attempted to reproduce Blondlot's results, failed, and submitted his results to Comptes rendus for publication. They were rejected by the editor who said, "Your results can be explained simply by supposing that your eyes are insufficiently sensitive to appreciate the phenomena." (Gratzer, p. 21) Turpain replied, "If N-rays can only be observed by rare privileged individuals then they no longer belong to the domain of experiment." (ibid) When Blondlot died in 1930, his posthumous papers showed he continued to believe in and experiment on N-rays for many years after Wood's debunking.

The case of N-rays is a spectacular example of a failure of a scientist to admit he was wrong. Even in this case, though, science's self-correction won the day. After Wood's debunking, N-rays vanished from the scientific literature.

Blondlot's tale is a cautionary one. By contrast, I offer a case where the proper behavior was displayed, from Richard Dawkins' 1996 Richard Dimbleby lecture:


A formative influence on my undergraduate self was the response of a respected elder statesmen of the Oxford Zoology Department when an American visitor had just publicly disproved his favourite theory. The old man strode to the front of the lecture hall, shook the American warmly by the hand and declared in ringing, emotional tones: "My dear fellow, I wish to thank you. I have been wrong these fifteen years." And we clapped our hands red.


Admitting you are wrong is a basic part of the mathematical and scientific ethic. In the days of the Internet, mea culpas can be more public and more effectively distributed then ever before. For both of my published books, for example, I maintain public errrata pages. The errata and addenda for my 1996 book now take up ten pages!

But not everyone agrees. Take two controversial books published in the last few years: A New Kind of Science by Stephen Wolfram, and No Free Lunch, by William Dembski.

Wolfram's book was published in 2002. Roughly speaking, the main thesis is that even very simple interactions give rise to complex phenomena that are hard to predict. Over 1280 pages, this thesis is developed and applied to many different areas, including mathematics, physics, economics, and biology; it is touted as a genuine revolution in science. Critics, generally, speaking have not been kind. (See here for a compendium of many different reviews.) I find the book interesting, with many fascinating digressions. The pictures are nice. But the importance of the main thesis is wildly overstated, and Wolfram never really gives a formal definition of "complex" that would satisfy a mathematician or physicist; rather, he relies on an informal definition of complexity based on appearance to the human visual system. If he did use a more formal definition -- let's say Kolmogorov complexity -- then his claims become incoherent, trivial, or wrong.

Dembski's book was also published in 2002. Dembski defines a new kind of complexity, which he calls "specified complexity" or "complex specified information". He then discusses properties of this measure, which he claims satisfies a law called "The Law of Conservation of Information", and concludes that specified complexity cannot be generated by natural causes. He then finds specified complexity in biological structures such as the [sic] bacterial flagellum, and concludes the flagellum cannot have arisen through natural causes. Needless to say, most reviewers have not been kind to Dembski either. (See here for some reviews.) Like Wolfram, Dembki's definition of complexity suffers from subjectivity, as it depends critically on the knowledge base of the observer. When one tries to make the definition more precise, Dembski's claims become incoherent, trivial, or wrong.

The analogy between the work of Wolfram and Dembski is imperfect. Wolfram, for example, has a genuine record of achievement, winning a MacArthur "genius" grant, and creating the software system Mathematica. Many of his papers continue to be cited by scientists and mathematicians. By contrast, Dembski, though possessing numerous degrees, has had a negligible impact on mathematics and science.

Nevertheless, there is one thing they have in common, and this brings me back to the start of this entry. Neither Wolfram nor Dembski have seen fit to make available errata pages for their books. In this, they fail in their intellectual obligation. Back in October 2002, I sent Wolfram a list of various errata in his book. Eventually one of his assistants acknowledged the errors, but Wolfram has never made them public. (Some of them can be seen here, due to the persistence of Evangelos Georgiadis.) Considering the extensive web presence for A New Kind of Science, surely an errata page is not asking too much.

Similarly, in April 2002 I sent Dembski a review in which I pointed out many mistakes in No Free Lunch, but Dembski only acknowledged one of these errors publicly and it took him three years. (My review later appeared in the journal BioSystems.)

Both Wolfram and Dembski seem to be taking a page from Canadian feminist Nellie McClung, who reportedly said, "Never retract, never explain, never apologize –- get the thing done and let them howl!" This might be a good motto for a social activist, but for a scientist or mathematician it is a dereliction of duty. If you want to be taken seriously when you're right, it's a good idea to be upfront about it when you're wrong.