I have something of a vested interest in this issue, as an editor of the Journal of Theoretical Biology. Theoretical biology? Surely biology is essentially an observational and experimental science? This seems like a clear case of physics-envy, with biologists attempting to ape theoretical physics, a most highly-regarded field. It is astonishing how even apparently exotic branches of mathematics have provided physicists with invaluable tools. No wonder that physicists can suffer from mathematics-envy. Just why mathematics should be so successful in describing the universe, is not obvious; at the least it shows the world is as logical and consistent as mathematics itself. Also it is free of cultural or ethical baggage.
But it is possible to do theoretical biology without mathematics - Darwin's wonderful theory of evolution contained none. However, since then it has acquired numbers and equations which have both filled in, and underpinned the theory. Evolutionary genetics is largely mathematical. One major advance was made by Bill Hamilton, whose mathematical analysis is an extension of J B S Haldane's remark that he would lay down his life for eight of his cousins, since they possessed more of his genes than he did. It provided key insights into altruism. Another is John Maynard Smith's use of algebra to analyse interactions between members of a population with respect, for example, to hawk-like and dove-like behaviour. He showed that only certain strategies would survive; too many hawk-like attacks would be, in the long run, a disadvantage to the individuals. I am pleased to say that both published their early ideas in our journal.
There is much more to biology than evolution. There is, for example, physiology: how biological systems actually work. William Harvey himself was a theoretician, as he used his calculations to show that the blood had to circulate, there was no where else for it to go. Hodgkin and Huxley, more recently, developed a famous mathematical theory as to how nerves conduct an impulse. But probably the most original contribution to theoretical biology may yet turn out to be irrelevant; that is one of the risks that theoreticians take.
Alan Turing was a genius who laid the foundations of computer science. He also thought about how the embryo could, during development, give rise to repeating patterns like vertebrae, or the petals of a flower. In an amazingly imaginative paper he showed that it might be possible for embryos to make such periodic patterns spontaneously. Under the right conditions a chemical system would be self-organizing, and concentrations would vary in a wave-like manner increasing periodically from low to high, again and again. The system was very good at making spots and stripes all on its own. Recently it was shown that chemical systems can behave just as he predicted. But biological relevance has been harder to obtain. I, for example, have spent hundreds of bath-hours trying to think of ways of showing that his ideas could explain how fingers develop; but so far in vain.
Like life, science is full of ironies. Physics-envy is being replaced by biology-envy. Biology is where the excitement is, and, compared to high-energy physics, is do-able at bargain costs. Physicists in the USA are enrolling on courses in biology, I am told. And who do the mathematicians envy? Possibly the logicians and the philosophers. And the chemists? They do not seem to envy anyone. Lucky them.
! Lewis Wolpert of University College, London, is chairman of Copus (Committee on the Public Understanding of Science).Reuse content