Oxford University Seeks Mathemagician — May 5th, 2011 by Douglas Axe
Scientists employ different rhetorical strategies to accomplish different things. That shouldn’t be surprising, perhaps, but for some it is. The reason is that while the public is very familiar with rhetorical shiftiness in some occupations, they tend to see only one side of science—the confident, assertive, authoritative, we-know-what-we’re-talking-about side. Science-speak often comes across with a hint of arrogance, but since science itself depends on the goodwill of the public for its very existence, it usually corrects itself on those occasions when it oversteps its bounds.
There are a few peculiar exceptions though, where what amounts to little more than propaganda is excused in the name of academic freedom. It’s regrettable, but it happens, and the guilty institutions become known for it.
Since Oxford University is one of them (as evidenced by the fact that I don’t need to name anyone), there is particular satisfaction in bringing to light some of the hidden rhetoric from that institution. Please don’t misunderstand me. I’m not suggesting that anything that follows is in any way secretive. I’m simply suggesting that some needs—like getting grants and hiring people to work under those grants—call for a frank statement of what isn’t known, whereas the messages intended for the general public tend to emphasize or even exaggerate what is known.
But enough of my rhetoric. I’ll let this refreshing new flavor of Oxford rhetoric speak for itself. What follows is a collection of excerpts (emphasis added) lifted from a recent job description from St John’s College at Oxford University [1], prefaced with this quote from Darwin’s autobiography [2]:
During the three years which I spent at Cambridge my time was wasted, as far as the academical studies were concerned, as completely as at Edinburgh and at school. I attempted mathematics, and even went during the summer of 1828 with a private tutor (a very dull man) to Barmouth, but I got on very slowly. The work was repugnant to me, chiefly from my not being able to see any meaning in the early steps in algebra. This impatience was very foolish, and in after years I have deeply regretted that I did not proceed far enough at least to understand something of the great leading principles of mathematics; for men thus endowed seem to have an extra sense. But I do not believe that I should ever have succeeded beyond a very low grade.
Charles Darwin, 1876
Fast-forward 135 years to the present.
In the Oxford job description [1], under the heading Extracts from the grant application to the St John’s Research Centre, subheading Objectives:
1. To construct a mathematical framework, with appropriate theorems, to represent fully the core argument in Darwin’s Origin of Species, namely that the purely mechanical processes of inheritance and reproduction can give rise through natural selection to the appearance of design.
Under the same heading, subheading Summary:
Grand theories in physics are usually expressed in mathematics. Newton’s mechanics and Einstein’s theory of special relativity are essentially equations. Words are needed only to interpret the terms. Darwin’s theory of evolution by natural selection has obstinately remained in words since 1859. …
A further advantage [of the proposed work] is that by setting up a formal version of Darwin’s argument, it will raise the bar for those who claim to have their own understanding of Darwin: in the first place, it will need to be checked against the formal version; if it fails that test, it will still of course be possible to argue that the current formal version is incomplete or erroneous; but this will be a technical exercise that requires real intellectual work to be persuasive, for which words alone will not suffice. …
This project is in many ways a mathematical, formal version of the argument of The Selfish Gene. There, Dawkins articulates in words a unifying structure for all the central adaptive theories used by evolutionary biologists, and grounds that unifying structure in a fully logical framework. A mathematical version will provide more precision, and answer a class of objections.
Under the same heading, subheading Detailed Application:
The idea that organisms maximise their fitness as a result of natural selection is extremely important in many areas of biology. The explanatory apparatus of most whole organism, behavioural ecology, work would make no sense without it. However, the logical basis for the idea is in considerable doubt. The mainstream of mathematical population geneticists since about 1964 has emphatically rejected the claim that fitness is maximised. …
There has been essentially no formal consideration of the kind of optimisation that emerges so naturally from verbal arguments such as those of Darwin (1859) and Dawkins (1976).
In the main job description, under the heading The Deep Mathematical Theory of Selfish Genes, subheading About the project:
The concept of fitness optimization is routinely used by field biologists, and first-year biology undergraduates are frequently taught that natural selection leads to organisms that maximize their fitness. Dawkins’ The Selfish Gene (1976) promoted a conceptual integration of modern evolutionary theory in which genes are viewed as optimising agents, which is extremely influential and widespread today and encompasses inclusive fitness theory and evolutionarily stable strategies as well as general optimality ideas. However, mathematical population geneticists mainly deny that natural selection leads to optimization of any useful kind. This fifty-year old schism is intellectually damaging in itself, and has prevented improvements in our concept of what fitness is. …
Generality is important, as a major aim [of the proposed work] is to find mathematical arguments that match Darwin’s verbal arguments in the Origin of Species, as well as Dawkins’s verbal arguments in the Selfish Gene and later works. …
Thus this highly abstract mathematical project will have significant implications at many different levels in biology. It will also be of interest to historians of science, as it will claim to show the underlying logic of Darwin’s great insight and of Dawkins’ conceptual unification.
[1] Retrieved from http://www.sjc.ox.ac.uk/3498/RA%20in%20Mathematics_FPs.pdf.download on 5 May 2011.
[2] http://darwin-online.org.uk/content/frameset?itemID=F1497&viewtype=text&pageseq=1