The Geometry of Biological Time (Interdisciplinary Applied Mathematics) [Englisch] [Gebundene Ausgabe]

The book has two main parts: a first half containing ten chapters mostly about principles and theory, and a second half containing thirteen more about specific experimental systems. It seems curiously hard to decide whether the subject matter is narrow to the point of caricaturing academic specialization, or incredibly broad to the point of suggesting a smorgasbord for science dilettantes. Among the forty thousand academic science journals viable today, not one is devoted to the topic of "biological waves, oscillations, and phase singularities" featured in this book, so it must be too narrow even for such tastes. Yet the literature drawn upon spans an unmatchably wide gamut, ranging from practical medicine to abstract topology, from recent molecular genetics to history of science, from 1836 to 2000. And Science Citations Index shows that the first edition has been cited about a thousand times in widely diverse publications, continuing at about constant rate over the past twenty years. Maybe this is why Springer-Verlag chose to provoke a 2nd edition even after so long.

Updating is usually an opportunity to erase blunders, but this author instead preserves and draws attention to them: how did this mistake happen, and how did the item come to be seen from a different perspective, with different meaning? To avoid giving offense the author preserves mostly his own blunders for such object lessons while going out of his way to credit the innovations of others.

Almost the whole 1980 text is preserved, with new material intercalated on a shaded background, except for two entirely new fat chapters. One concerns the self-organization of excitable media into three-dimensional vortices with exotic topologies. This is almost wholly theoretical (supercomputer calculations and topology): the only ones discovered in the laboratory (so far) are simple vortex rings. The website mentioned in the preface contains much of the same material but more beautifully illustrated in subsequent Powerpoint lectures not mentioned in the book. The other new chapter concerns real cardiology and the role of phase singularities in sudden cardiac death. This seems a morass of details where I would have preferred to see the elegant tree that grew from seeds planted in the first edition. This tree was recognized midway between editions by a medical award normally given only to cardiologists. The new chapter gives the impression that it is already being cut down or at least pruned, and the author is more concerned about the details of that process than about defending its original structure. His 1987 book, was written a few years before the anticipated role of phase singularities and rotors in cardiology found confirmation in quantitative experiments, so the interested reader (if any) must still resort to the cited journal literature for that story.

Another chapter reports on revolutionary developments entirely unforeseen in the first edition: this is the story of molecular genetics of the circadian biological clock. The author provides a readable summary of discoveries up to the end of 1999, but quite a lot of facts have accumulated since that time. The author's point of view is that present-day facts, while unanticipated in detail, do bear out the almost-forgotten theory elaborated in a 1963 book (Goodwin) as to basic principles, and the contrarian expectation stressed in the first edition, that the details may prove to be surprisingly diverse taxonomically.

One of the best resources this eight hundred page book provides is its dual index, with almost two thousand topics and as many cited references, half of them since the first edition. Because the material is both mathematical and experimental, and each item is encountered several times but from different directions in the text, the index is indispensable to persons with finite lifetime who accordingly prefer not to read every word in sequence. Find the topic, jot down its several pages, read one and note a reference from which that argument draws its data, then see the other index for all pages on which that source document is alluded to. The references, by the way, seem exceptionally complete and up-to-date (up to the last day of the 20th century, when it appears the ms was sent to press).

The preface points to a website for Errata. While this may be helpful to specialists, for the rest of us a better discovery lurks nearby: a link to a series of richly illustrated lectures given since the book went to press. These cover much of the same material in about three hundred substantially distinct slides but with entirely different organization in Powerpoint color (in contrast to about as many B&W line drawings in the book). The web site URL changed: it now seems to be eebweb.biosci.Arizona.edu/~art for Errata, and for the Powerpoints, eeb8.biosci.Arizona.edu/art/2000_lectures.

The author was professor of biological sciences at Purdue University until a few years after the first edition, and has since been professor of ecology and evolutionary biology at the University of Arizona. These seem peculiar credentials for authorship of a monograph mostly about topology, physical chemistry, and cardiac electrophysiology in an Applied Mathematics series. The key to understanding this phenomenon may be the first word, standing out in yellow against the green book cover: Interdisciplinary. Whatever may be hyped to the contrary, the academic world resents and resists activities that transgress its historically-defined disciplinary boundaries. You will find them all transgressed in this book.