Mathematics of Life: Unlocking the Secrets of Existence

August 11, 2011

Perhaps it was my XY-chromosomes, but at school I chose Latin over biology. To my naive mind, mathematics, physics, chemistry and foreign (even dead) languages appeared systematic, with simple axioms seeming to lead systematically to theories with pervasive predictive powers. By contrast, biology was a chaotic collection of factoids, random ones even, and certainly unpleasantly smelly.

Since then, as Ian Stewart explains here, the fusion of mathematical and biological thinking has emerged as one of the most exciting interdisciplinary fields. This is not just because biomathematics is yet another long-overdue application of mathematics to a less quantitative field, but because the previous subject division has highlighted the need for new mathematics.

Following on from the major advances in biology arising from the microscope, Linnaean classification, evolution and natural selection, genetics, and DNA, Stewart proposes that mathematics could be the sixth major advance in biology. Open-minded biologists and mathematicians at the interface of research would support this, but the wider public has little inkling that the interaction even exists.

In 19 chapters Stewart addresses this deficit, introducing the reader to the nuts and bolts of eukaryotes and prokaryotes, evolution, genetics, DNA, genomes, taxonomy, viruses, axons, gait, pattern formation, allopatric and sympatric speciation, networking (including the remarkable similarity between engineers and slime moulds) and epidemiology.

He concludes with speculations on what life is and whether it is unique to Earth. For the mathematically curious, a detailed set of notes and references is included.

For mathematics to be recognised by biologists, it has to be more than just a concise description of already known facts or numerical coincidences. It has to make biologically valid predictions, uncover previously unknown connections or mechanisms, or offer clues to new ways of framing a biological problem.

Stewart aims to do this through deeper explanations. For example, he goes beyond the trite high-school Fibonacci "explanation" of petal patterns to discuss mathematically why the associated mechanics and biochemistry generate these patterns. Additionally, he breathes new life into well-known applications by including very recent (2010) advances.

All the standard bio-calculus fare is there: chaotic population dynamics, Hodgkin-Huxley equations for axons and Turing's work on animal spots and stripes. But crucial to Stewart's thesis is the breadth of examples using other branches of mathematics.

Consider the problem of taxonomy and speciation. One classical attribute of a species is that it does not interbreed with other species. A counter-example is that of an anholonomic chain of coexisting, interbreeding gulls that extends around the world. At one end is the herring gull; at the other the black-backed gull. These two end-links cohabit, yet cannot interbreed.

Similar examples argue for an abandonment of the classical notion of "species" in favour of characterisation through multidimensional clusters with common properties, identifiable through statistical techniques.

In an example reminiscent of the predictive nature of the standard model of particle physics, Stewart recounts how the consideration of geometry in more than three dimensions allows for predictions as to the existence and structure of new types of viruses.

Other highlights include the potential to apply knot theory to DNA synthesis and the role of mathematical maps and hallucinogenic drugs in explaining the complex "wiring" between the retina and visual cortex. Even ufologists can find straightforward probabilistic arguments as to the (un)likelihood of (similar) life on other planets.

At times, the logical order of the individual chapters is not clear. In some chapters it is difficult to tell what is maths and what is biology. But that only strengthens Stewart's case: cross-fertilisation breaks down preconceptions. Don't go looking for separate subjects.

In my experience, Stewart's inspiring vision is still seen by many in vivo biologists the way they see in vitro experiments: a useful demonstration but not quite the "true" explanation. One hopes the mathematics gene is not always destined to be recessive to the dominant biology one.

Will this book do for biomathematics what Stephen Hawking's A Brief History of Time did for relativity and cosmology? Time will tell. Until then, the distinguished author's friendly, well-argued style should guarantee its popular success.

And should any doubting dinosaurs remain, in Mathematics of Life Stewart emerges from the biology lab to confirm that the fume cupboard has purged the stench and there is now a glimpse of a way to start ordering the specimen jars. Come on BBC, how about a television series?

Mathematics of Life: Unlocking the Secrets of Existence

By Ian Stewart. Profile Books, 368pp, £20.00.ISBN 9781846681981. Published 7 April 2011

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