Mathematicians and Evolution
As recently highlighted here, mathematics is an academic locale where scientific skepticism of Neo-Darwinism can survive the current political climate! Discovery Institute recently received an e-mail from someone commenting on the Scientific Dissent from Darwinism List where over 600 Ph.D. scientists from various fields agree that they are "skeptical of claims for the ability of random mutation and natural selection to account for the complexity of life." This skeptic of evolutionary-skepticism e-mailer wrote "I'm a mathematician and certainly am NOT qualified to support such a statement. Only evolutionary biologists are qualified to respond here." While the Dissent from Darwinism list does contain individuals trained in evolutionary biology, the question remains "Is the objection valid?"
The truth is that mathematics has a strong tradition of giving cogent critique of evolutionary biology. After all, Darwin's theory of evolution by natural selection is fundamentally based upon an algorithm which uses a mathematically describable trial and error process to attempt to produce complexity. Population genetics is rife with mathematics. In fact, one criticism of the alleged transitional fossil sequences for whales is that they represent evolutionary change on too rapid a timescale to be mathematically feasible. It seems that there is no good reason why those trained in mathematics cannot comment on the ability of the Neo-Darwinian mutation-selection process to generate the complexity of life.
One of the best known mathematical forays into evolution was the 1966 Wistar Symposium, held in Philadelphia, where mathematicians and other scientists from related fields congregated to assess whether Neo-Darwinism is mathematically feasible. The conference was chaired by Nobel Laureate Sir Peter Medawar. The general consensus of many meeting participants was that Neo-Darwinism was simply not mathematically tenable.
The proceedings of that conference, Mathematical Challenges to the Neo-Darwinian Interpretation of Evolution (Wistar Institute Press, 1966, No. 5), reports various challenges to evolution presented by respected mathematicians and similar scholars at the conference. For example, the conference chair Sir Peter Medawar stated at the outset:
"[T]he immediate cause of this conference is a pretty widespread sense of dissatisfaction about what has come to be thought as the accepted evolutionary theory in the English-speaking world, the so-called neo-Darwinian Theory. ... There are objections made by fellow scientists who feel that, in the current theory, something is missing ... These objections to current neo-Darwinian theory are very widely held among biologists generally; and we must on no account, I think, make light of them. The very fact that we are having this conference is evidence that we are not making light of them."
(Sir Peter Medawar, "Remarks by the Chairman," in Mathematical Challenges to the Neo-Darwinian Interpretation of Evolution (Wistar Institute Press, 1966, No. 5), pg. xi, emphasis in original)
Various scientists, including some mathematicians, proceeded to comment about problems with Neo-Darwinism:
"[A]n opposite way to look at the genotype is as a generative algorithm and not as a blue-print; a sort of carefully spelled out and foolproof recipe for producing a living organism of the right kind if the environment in which it develops is a proper one. Assuming this to be so, the algorithm must be written in some abstract language. Molecular biology may well have provided us with the alphabet of this language, but it is a long step from the alphabet to understanding a language. Nevertheless a language has to have rules, and these are the strongest constraints on the set of possible messages. No currently existing formal language can tolerate random changes in the symbol sequences which express its sentences. Meaning is almost invariably destroyed. Any changes must be syntactically lawful ones. I would conjecture that what one might call "genetic grammaticality" has a deterministic explanation and does not owe its stability to selection pressure acting on random variation."
(Murray Eden, "Inadequacies as a Scientific Theory," in Mathematical Challenges to the Neo-Darwinian Interpretation of Evolution (Wistar Institute Press, 1966, No. 5), pg. 11)
"[I]t seems to require many thousands, perhaps millions, of successive mutations to produce even the easiest complexity we see in life now. It appears, naively at least, that no matter how large the probability of a single mutation is, should it be even as great as one-half, you would get this probability raised to a millionth power, which is so very close to zero that the chances of such a chain seem to be practically non-existent."
(Stanislaw M. Ulam, "How to Formulate Mathematically Problems of Rate of Evolution," in Mathematical Challenges to the Neo-Darwinian Interpretation of Evolution (Wistar Institute Press, 1966, No. 5), pg. 21)
"We do not know any general principle which would explain how to match blueprints viewed as typographic objects and the things they are supposed to control. The only example we have of such a situation (apart from the evolution of life itself) is the attempt to build self-adapting programs by workers in the field of artificial intelligence. Their experience is quite conclusive to most of the observers: without some built-in matching, nothing interesting can occur. Thus, to conclude, we believe that there is a considerable gap in the neo-Darwinian theory of evolution, and we believe this gap to be of such a nature that it cannot be bridged within the current conception of biology."
(Marcel Schutzenberger, "Algorithms and Neo-Darwinian Theory," in Mathematical Challenges to the Neo-Darwinian Interpretation of Evolution (Wistar Institute Press, 1966, No. 5), pg. 75)
These are potent arguments from academics qualified to assess the mathematical ability of a random / selective process to produce complexity. While evolutionary biologists and other types of biologists can yield many insights into evolutionary biology, scientists other than biologists, such as mathematicians, are most certainly qualified to comment on the feasibility of Neo-Darwinian evolution.