Joan Bakewell is a speaker who needs no introduction, and in this capacity she's been introducing and interviewing speakers on key ideas for the 21st Century. Yesterday's topic was numbers, and the speaker was Ian Stewart. She introduced him by saying that of all the topics in her series, she found mathematics the hardest to understand, but that Ian Stewart was the best person to explain it.
Professor Ian Stewart is one of the great science popularisers - and not just in his own field of mathematics. Some of his many books on science were written with Jack Cohen, reproductive biologist and oft-invited speaker at SF conventions. In recent years, the two have teamed up with the wildly popular fantasy author Terry Pratchett to write (so far) three books on 'The Science of Discworld', which cleverly exploit the contrast between the eponymous flat planet (which runs on the rules of magic and the caprice of gods) and our universe (which doesn't) to explain an astonishing range of serious scientific points ... including the ways in which magic does work in our world, through the human propensity for Story.
Stewart began by asking 'Why maths and biology?' Biology has after all traditionally been the science for people who want to do as little mathematics as possible. (That was certainly why I took Zoology. How I ended up with an MPhil in biomechanics is another story.) The only mathematics used in most biology is statistics. We do experiments, and then we test whether the results are statistically significant (i.e. that they're unlikely to be chance). Ian's new book, Mathematics of Life, is not about that. It looks at ways in which mathematics is informing the science itself, in fields such as understanding how proteins fold into the shapes that (largely) determine their function, how ecosystems hold together and whether diversity is indeed the key to stability, and even in considering the possibilities of life on other planets.
To illustrate, he picked two topics in current research: animal markings, and animal gaits. Both are about patterns, and patterns are what maths is very good at explaining. As far back as the 1950s, Alan Turing studied animal markings and worked with equations whose solutions (when shown graphically) looked very like animal markings. Cue diversion about Turing wandering about with a sheet of blotchy paper, telling his colleagues that 'this looks like a cow' and being patted on the back - 'Yes, Alan, that does look like a cow'. Anyway, modelling reaction and diffusion together produces patterns similar to most of those found in nature, and the equations generate interesting predictions - such as that on a small animal, the stripes will move, and it turns out that they do, very slowly.
Gait, likewise, can be patterned, and the structure of the arrangement of nerves that would have to fire to generate the various gaits can be predicted, and one can even predict gaits we don't often see - Stewart and a colleague in Texas suddenly realised that one anomalous pattern was being acted out before their very eyes, as they watched a bucking bronco at a rodeo.
Joan Bakewell then asked a few questions. Why are tiger stripes vertical, rather than horizontal? Well, said Ian, it's because the stripes are camouflage, and tigers live in jungles, and tree trunks are vertical. Yes, but, Bakewell asked - and this is a direct quote - 'How do the cells know about the jungle?' Ian Stewart then broke the news about the recently discovered principle of evolution by natural selection.
The second part of his talk ranged from the discovery of evolutionarily stable strategies that follow the paradoxical pattern of the 'rock, scissors, paper' game, to the contribution of mathematical modelling to showing the possibility of plate tectonics (and therefore, by a long chain of inference, life) on rocky planets much larger than Earth. An even more wide-ranging discussion followed, and we all trooped out into the sunshine and the Book Festival and its magical buzz of Story with some new stories running in our heads.
PS: The principle of evolution by natural selection is explained in a book by Ian Stewart, Jack Cohen, and Terry Pratchett: Darwin's Watch. Other popular introductions are available.
Born in Stornoway, Isle of Lewis, Ken has been a full time writer since 1997 authoring thirteen novels, including The Star Fraction (1995) and Intrusion (forthcoming, 2012), plus many articles and short stories. His novels and stories have received three BSFA awards and three Prometheus Awards, and several have been short-listed for the Clarke and Hugo Awards. In 2009 he was a Writer in Residence at the ESRC Genomics Policy and Research Forum. Learn more from Ken’s blog The Early Days of a Better Nation