Article No. bu980065Bulletin of Mathematical Biology(1998)60, 997–998

Book ReviewPhysical Theory in Biology. Foundations and Explorations, edited by C. J. Lums-den, W. A. Brandts and L. E. H. Trainor, World Scientific, Singapore, 1997.$85/£59 (cloth), $42/£21 (paper), xvi+ 486 pp. (Studies of nonlinear phenom-ena in life sciences; 4)

Ever since the seventeenth century we have witnessed an explosion of physicalscience, biology has succumbed to the temptation of enlightening its own problemsby adopting physical perspectives. Descartes’ mechanical views were followed byscientists for more than a century, until it became clear that oversimplification wasa hidden assumption. Electricity and magnetism also influenced experimental andtheoretical biology for long periods. In this century, the work of Lotka was anattempt to use physical arguments and analogies to produce biologically significantunderstanding of a manifold phenomena. Lumsden, Brandts and Trainor’sPhysicalTheory in Biologyis part of this long tradition. It also has some peculiarities: thiscollection of 18 essays does not attempt to reduce biology to physics; rather, itproposes new (physical) perspectives to deal with some biological problems.

Mathematics is so deeply imbedded in the core of physical theories that applyingphysical ideas to biology has frequently been synonymous to applying mathematicalmethods. Not surprisingly, Lotka’sElements of Physical BiologybecameElementsof Mathematical Biology. The editors of the book reviewed emphasize this charac-ter of physics: ‘Success in physical theory is reckoned in terms of the discovery andelucidation of physical laws, mathematical in form and universal in application.’Even though some physical concepts play a role in most chapters, the commondenominator is the use of mathematical tools: ‘the reigning metaphor of nature asa vast mathematical machine is little disputed.’ Therefore, beside familiar math-ematical methods used by physicists like Lagrangians, Hamiltonians and vectorfields (with an inevitable use of the energy concept), we find in this volume gametheory and computing methods. It is not, however, an attempt to generate mathe-matical techniques motivated by biological problems; it is about applying physicaland mathematical concepts to some biological fields where such ideas might proveto be fruitful, a collection of examples where some mathematical techniques mightbe applied. We read, for instance: ‘the power of symmetry breaking is illustratedin this interesting example from biology’. The use of elementary geometrical andtopological concepts is welcome as long as those concepts prove to be biologicallymeaningful, and here we find suggestive ideas whose biological significance canbe questioned but not denied. Most of the essays open with a question which issupposed to be biologically relevant, but they seem to be questions that a physicistmight ask looking at biological phenomena rather than queries a biologist might set.However, as in the case of E. Larsen’s essay, we find some biologically groundedsuggestive works.

0092-8240/98/050997 + 02 $30.00/0 c© 1998 Society for Mathematical Biology

998 Book Review

The subtitle refers to both foundations and explorations. The foundations oc-cupy the whole first part of the volume and, intended to promote reflections anddiscussions on the topic, it accomplishes its role well. Concepts like emergence,holism, complexity and reduction are discussed at length. In a way, however, thesenotions are assumed to be independent entities, properties that a system has or not,rather that concepts relative to an object and a theory. Complexity, for example, inW. Brandts’ essay, is treated as a physicist might think of ‘energy’: since energymust be a constant in our descriptions of physical processes we need both a way tomeasure it in distinct physical situations and to find the equivalence between thosemeasured quantities; similarly, complexity should be measured and those measuresshould be compatible. Although the conclusion is that it is impossible to carry outsuch a program, the aim is presented as a pertinent one. There are also interestingand readable discussions about foundational concepts throughout the whole book,as that related to the meaning of form in the Hart and Trainor’s article placed inpart II.

The book is not intended to be encyclopedic, but the scope of the articles isbroad: development, neuroscience and evolution (mostly on the genetic level). Thediversity of ‘explorations’ has as common ground concepts like complexity andself-organization. The whole volume should be of interest to scientists comingfrom biological, physical and mathematical sciences; mathematical maturity willdetermine the level of understanding and analysis: it is possible to follow the mainideas with some knowledge of differential equations and linear algebra; a deeperapproach requires field and bifurcation theories and, in some chapters, computationand game theories. Foundations of basic differential geometry and group theory arealso useful. In this sense, it seems to be directed to physicists and mathematicians,but the biological content of the book is not elementary. Philosophers of science willfind the first part readable and suggestive; other parts of the book can be followedwith mathematical background and could be used to understand the factual uses ofconcepts such as complexity, emergence, self-organization and others, which playa central role in modern science.

GERARDO HERNANDEZ,Cinvestav-SMTC,Gomez Farias 74,Col. Del Carmen,Coyoacan, 04100

Mexico, D. F.