In Part One of this essay I discussed my answer to the question of whether mathematicians were qualified to discuss evolution. The inspiration for these musings was this post, from Discovery Institute blogger Casey Luskin.

We now pick up the action in the second paragraph of Luskin’s post:

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.

No one who could write a paragraph like that should be passing judgment on who is, and is not, qualified to be discussing evolution.

Luskin’s task here is to defend the DI’s ridiculous list of vaguely defined scientists who dissent in some ill-defined way from modern evolutionary theory. In particular, he needs to justify the idea that mathematicians, as mathematicians, have some particular insight on this subject. So he searches deep within his sordid little brain and conjures up three talking points he’s learned how to say but knows nothing about.

First we learn that natural selection is “based upon an algorithm which uses a mathematically describable trial and error process to attempt to produce complexity.” I won’t go into all the ways that this is an awkward and incomprehensible sentence. The broader point is that it is entirely uncontroversial to say that the prolonged action of natural selection acting on random genetic variations can, in principle, craft complex structures. You don’t need a degree in mathematics to get the idea. Whether it is a viable explanation in practice, however, depends entirely on the biological facts of the matter. Mathematicians as such have nothing to say about that question. Luskin would have you believe that dimwitted biologists work in bafflement over the complex logic by which natural selection operates, and need clear-thinking mathematicians to come in and set them straight.

Then we learn that population genetics is “rife with mathematics.” Indeed it is, but so what? The abstract models of population genetics show simply that under a variety of realistic assumptions, forces like natural selection and genetic drift can lead to great changes in the frequencies of alleles in a population. Mathematicians might have a leg-up in understanding the minutiae of some of these models, but that has nothing to do with their application in practice. In terms of defending the validity of evolutionary theory, the mathematics says simply that natural selection works effectively indeed.

Luskin’s final point is the silliest of all. There’s a reason he provides neither link nor reference to anyone arguing seriously that the impressive transitional forms linking bear-like mammals to modern whales represent a mathematically unfeasible change. Even in principle it would be impossible to make such an argument work.

So none of Luskin’s three points provide any reason for thinking that mathematicians have some special insight into whether evolution is a viable theory. But we really must address that first sentence. As presented by Luskin, that strong tradition of mathematicians offering cogent critiques of evolution consists of two points. He mentions Granville Sewell’s recent attempts to revive the thermodynamics argument. (I refuted Sewell’s silly argument here.) Then he mentions the 1966 Wistar conference. That’s it. A single conference forty years ago, and a recent attempt to revive one of the oldest and dumbest anti-evolution arguments ever offered.

He might have added the writings of David Berlinski or William Dembski to the list, but that would hardly help his case.

Luskin writes:

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.

This is a terribly misleading way of describing what happened at Wistar. In the preface to the conference proceedings, biologist Martin Kaplan describes the origin of the conference this way:

Perhaps a few words on the genesis of this Symposium would be of interest. Actually, the seed was sown in Geneva in the summer of 1965 during the course of two picnics held at Vicki Weisskopf’s house and at my house, on two consecutive Sunday afternoons. Koprowski and I, the only biologists present, were confronted by a rather weird discussion between four mathematicians – Eden, Schutzenberger, Weisskopf and Ulam – on mathematical doubts concerning the Darwinian theory of evolution. At the end of several hours of heated debate, the biological contingent proposed that a symposium be arranged to consider the points of dispute more systematically, and with a more powerful array of biologists who could function adequately in the universe of discourse inhabited by mathematicians.

Presumably these are the same dogmatic biologists who don’t allow any dissent from their preferred view of things.

At any rate, what happened at Wistar was that Eden, Ulam and Schutzenberger were given a chance to present their objections and a cadre of biologists patiently explained why they were wrong. (Weisskopf did not present a paper at the conference). The conference proceedings do not record anyone beyond those three reporting any fundamental difficulties with Neo-Darwinian theory. General consensus indeed.

I’m afraid the mathematicians didn’t shower themselves in glory at the conference. (This might be a good time to mention that Eden was an engineer and Weisskopf was a physicist). Eden and Ulam relied on standard probability arguments against Neo-Darwinism. As with all such arguments, their mathematical calculations left out so many relevant variables that they were effectively useless. Schutzenberger, meanwhile, relied on bad analogies of genes to computer programs, and seemed concerned that biologists had no clear explanation for how genes become organisms. The biologists were rightly unimpressed with this argument as well.

I should also point out that while as an attempt to provide mathematical challenges to Neo-Darwinism the conference fell flat, the critics did provide suggestions for how certain basic questions in evolution could be formulated mathematically. Some of their suggestions in this regard were quite sound.

One of these days I might do some posts examining in more detail the topics discussed at the Wistar conference. For now, however, let me close by noting that the claim that mathematicians as such have no authority for talking about evolution really should be no more controversial than claiming they have no authority to discuss eighteenth century Russian literature. And I suspect that no one would try to claim that biologists have especially keen insights to offer with regard to the work mathematicians do.

Yet a lot of otherwise sensible people find it perfectly reasonable to suggest that non-biologists should nonetheless have profound things to say about evolution. Why is that? I think there are two reasons. One reason is that since evolution is commonly thought to have profound social and religious implications, every two bit hack whose read a few pages of Gould or Dawkins and has an axe to grind fancies himself qualified to discuss the subject.

The second reason is that in certain scientific circles the idea lingers that biology is a second-class science, lacking the rigor of, say, physics. The physicists at the Wistar conference frequently expressed their lament that evolution seemed to be lacking in general principles and all-encompassing schemata. But the simple fact is that while there is a large mathematical component to modern evolutionary theory, many of the problems biologists study just don’t lend themselves to mathematical treatments.

After all, applied mathematics proceedes by developing an abstract model representing some real-life situation of interest. Constructing such a model inevitably requires that you ignore large numbers of variables that affect the objects under study in real-life. This approach is practical when there are only a few variables with a major impact on what is being studied. Many things affect the flight of a thrown tennis ball, but most of them can be ignored when you are trying to predict its trajectory. That is sadly not the case in trying to model evolution over long time scales. There are too many important variables to develop a practical model.

It is a credit to biologists that they forge ahead nonetheless. It reflects badly on the scientific chauvinists that they insist so strongly on using inappropriate tools for the job.