The Shaping of Life: The Generation of Biological Pattern, Lionel G.Harrison, Cambridge U. Press, New York, 2011. $99.00 (247 pp.). ISBN 978-0-521-55350-6

In 1917 D’Arcy Wentworth Thompson penned the classic On Growth and Form (revised edition, Dover, 1992), in which he argued, contrary to the Darwinian orthodoxy of the time, that structure originates before function and that growth and form can be explained through mathematics and physics. By the early 1950s, Alan Turing would demonstrate how spatial patterns could arise through chemical instabilities inherent in a simple set of coupled reaction–diffusion equations. Turing patterns, as they came to be known, are evident in nature; for example, some resemble the spots on a leopard, others the stripes on a zebra or the complex fractal-like patterns on seashells. But it was not until the 1980s that chemists could actually set up reactions that would produce Turing patterns.

Though embraced by mathematicians and physicists, Turing’s mathematical approach to biological pattern formation is hardly accepted by most experimental biologists. The late physical chemist and theoretical biologist Lionel Harrison laments such resistance in The Shaping of Life: The Generation of Biological Pattern, which he drafted before his untimely death in 2008 and which was completed by friends and colleagues. Harrison pioneered a quantitative approach to developmental biology in the 1970s, an era when few thought it was useful to mathematically model the complexities of biological growth and development.

The Shaping of Life makes the case for simple coarse-grained mathematical models in biology—simple, that is, in comparison to models that explain the phenomena at a genetic or systems level. Many of the topics in the book’s first half are drawn from Harrison’s own research on plant development. His work had led him to investigate a variety of novel creatures such as Acetabularia, a seaweed that grows to several centimeters and generates multiple whorls of hair-like filaments along its exterior. Those organisms are ideal laboratories for studying the dynamics of growth, since they are mostly transparent and grow in two-dimensional sheets. Another favorite of Harrison’s are the somatic embryos of conifers, such as the hybrid larch Larix x leptoeuropaea. As an embryo, Larix is a multicellular organism accessible to observation in much the same way as Acetabularia. Despite its multicellular nature, the development of outgrowths called cotyledons from Larix embryos greatly resembles the whorl formation in the single-cell Acetabularia and, indeed, can be modeled on a similar mathematical formalism.

In the second half of the book, Harrison turns the reader’s gaze from plant development to animal development. Here one learns about segmentation in the Drosophila egg, amphibian heart development, the rearrangement of stripe patterns in angelfish, vertebrate limb development, the growth of slime molds, and much more. The examples are highly varied, some touched on in more detail than others, but taken together they clearly display that there is no shortage of complex developmental behavior that can be understood through mathematics.

One notable omission, which Harrison admits early on in the manuscript, is any discussion about the genetics of development. That is fair; as Harrison’s numerous examples show, much can be said about understanding complex developmental behavior through course-grained mathematical models of pattern formation at the level of abstraction presented in The Shaping of Life. In fact, a mathematical approach to developmental modeling is the subject of numerous complementary books, including Biological Physics of the Developing Embryo (Cambridge University Press, 2005) by Gabor Forgacs and Stuart Newman and The Self-Made Tapestry: Pattern Formation in Nature (Oxford University Press, 1999) by Philip Ball. For a technical discussion of the genetic origin of bodily form, interested readers can consult Imaginal Discs: The Genetic and Cellular Logic of Pattern Formation (Cambridge University Press, 2002) by Lewis Held Jr; for a more readily accessible popular account on the same topic, readers can check out the immensely pleasurable Endless Forms Most Beautiful: The New Science of Evo Devo and the Making of the Animal Kingdom (W. W. Norton, 2005) by Sean B. Carroll.

Besides being a text about biological pattern formation, The Shaping of Life is an exposition on how human beings pursue the unknown. Reading it, I was reminded of Operators and Promoters: The Story of Molecular Biology and Its Creators (University of California Press, 2001), written by Harrison Echols and edited by Carol Gross. That book spends at least as much time on the human aspect of scientific research—the confusions, blind alleys, and eventual clarity that comes with great effort—as it does on the science. In an age of ever-increasing pressures to pursue what is fashionable in science—be it to secure a position, tenure, funding, prestige, or other personal rewards—Harrison’s book, and life, provides a felicitous allegory in favor of engaging in science that, while less stylish at the moment, touches on the truly infinite questions.