UK Nonlinear News, August 2002


The Geometry of Biological Time

A.T. Winfree

Reviewed by Martin Bees

Springer Verlag, 2000
2nd edition

This new edition of Winfree's large volume (777 pages, including a 98 page bibliography, plus approx. 20 pages of preface) on phase dynamics is designed to update the original 1980 edition. Mainly this has been achieved using two mechanisms: comments in shaded boxes have been added as well as longer sections in a different font. Quite surprisingly the text from the earlier edition has not been significantly edited, but instead added to. Two new chapters out of 23 have been written; chapters 16 and 17 replace old text, which has been condensed and inserted elsewhere.

The first 10 chapters carefully detail theoretical insights on phase singularities, communities of interacting clocks, topological concepts, perturbed dynamics and excitable media mostly applied to circadian clocks, but also enthusiastically applied to a range of physical and everyday phenomena (such as longitude and clocks, tides, perception of hues, and many more). The next 13 chapters describe experiments that were designed to support or refute the theory. They range from circadian clocks, metabolism issues, meander and hyper-meander in experiments and simulations, excitability in cell membranes, pattern formation in fungi and slime mold amoebae, and the female cycle. The two new chapters describe numerical experiments on two- and three-dimensional rotors, and phase singularities in the heart wall. They represent a valuable addition to this volume and describe an area of great current interest.

The book is packed full of beautiful and rewarding illustrations that are not only descriptive but highly thought provoking.

This is not a mathematics textbook, in fact mathematics is thin on the ground, and mathematical rigour does not play an essential role. It is not a book on mathematics for biologists nor a book on biology for mathematicians, as full mathematical and biological details are lacking. However, it does sit somewhere in between, where it weaves a storyline somewhat like a novel. It lacks student textbook exercises, by the author's own admission, yet the author suggests that it is perhaps a book for graduate students. Perhaps it is really directed at a general audience, although the terminology prevents one from taking a quick dip.

There is a lot of Winfree in this book. Both the historical commentary and the thought processes in this work are well written, and not only do you gather much useful information but also an understanding of how the author's insights were revealed to him. I appreciate the sense of enthusiasm that is conveyed in the text, which is enthralling and designed to inspire, and does! However, I lacked the patience to fully read the text, which is in parts overly wordy. The book is packed to the brim with well thought out examples (both from the biological sciences as well as physics and astronomy) but they can get in the way of the natural flow of the text. This is amplified by the modern commentary which permeates the main text, the examples and the isolated additional text/examples in boxes (of which there are plenty). Due to the wordy nature of the text and in view of the above comments, a summary page for each chapter would have been of benefit to those with an established background in the mathematical and/or biological sciences.

I this book but I believe that Winfree's time would have better been spent writing a new and much more concise book. In particular, the format of the revision is somewhat tortuous. For instance, one may read several pages of text only to encounter a few lines of shaded text which states or hints that the validity of the preceding argument is uncertain or simply incorrect. The two new chapters on numerical organising centres and electrical singular filaments in the heart wall are up-to-date, very interesting and mesh together very appropriately, and perhaps should have formed the basis for a completely new volume.

Regardless of these comments Winfree's book is excellent and I recommend it to anyone involved in this aspect of Mathematical Biology, or would like to be. The 98 pages of references and the care with which they have been woven into the text are invaluable.

UK Nonlinear News thanks Springer-Verlag for providing a review copy of this book.

A listing of books reviewed in UK Nonlinear News is available.


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