Read This!

The MAA Online book review column

Briefly Noted

February 2002

The book is an enjoyable page-turner, even for those readers with only a passing interest in biology, and demonstrates well the synergistic effect between biology and mathematics. On the one hand, biology benefits from the unifying effect of mathematics; this book contains diverse biological examples in chapters such as "The Firefly Machine", "Energy Metabolism in Cells", and "The Female Cycle" (just to name a few) for which a common mathematical language has been developed. On the other hand, mathematicians are often amazed by the purely mathematical ideas that arise in biology, some charmingly cute and some intriguingly complicated. This book begins with the basic idea of a circle/ring and mathematically develops the concept of biological time through product spaces, projections, phases (and phase singularities), dynamics, and other mathematical notions. Particularly enticing are figures conceptualizing biological time, e.g. of the "fruitfly clock's time crystal" and stereographic views of the "timing of Kalanchoë flower opening after a light pulse." Though the book is intended primarily for research students, undergraduates could use the book for independent study or an undergraduate research project.

The term "page-turner" may seem unusual in mathematics; however, it is appropriate here. Not only is the reader continually tantalized by the figures appearing on the ensuing pages, but the new commentary lends a mystery-novel feeling to the book. This second edition was created by inserting new text boxes into the original, mostly intact, edition. This style leads to a fascinating historical picture. For example, the text, "(...In the latter cases the periodicity approximation gets worse closer to the pivot. I wish here to sweep such matters under the rug (in 1978))" is followed by a new text box that begins, "The bulge under the rug grew and grew...", continuing with a description of developments over the last two decades. The plot continues even now, with descriptions of the last twenty years often followed in the book by descriptions of current puzzles. In summary, the original book is good and the second edition is even better; the historical commentary is fascinating, and there are also a few reorganized and new chapters presenting additonal biological examples. [Jan E. Holly]

From paleolithic shepherds to perturbation theory: the history of celestial mechanics in half an hour (perhaps it's more accurate to say the highlights rather than the history). That's a good one-line description of the video The New Shepherd's Lamp. After contemplating the night sky our guide is motivated to visit, in succession, an astronomer, a mathematician, and an engineer to learn about what he sees (including a satellite streaking across his view). The astronomer begins with the shepherds, takes him through Ptolemy and winds up with a quick Renaissance quadruple play: Copernicus to Galileo to Brahe to Kepler. The mathematician gets more time: he begins with a peek at the Principia, then a précis of perturbation theory (homage to Lagrange), and a summary of recurrence (nod to Poincaré). We also get from him the story of Leverrier's discovery of Neptune (no mention of Adams, it is a French film). We end at a French space center whose engineers tell us a little about controlling an artificial satellite's motion.

The apparent purpose is to excite high-school students about the wonders and power of university-level mathematics, especially calculus. I don't think it will do that unless it falls on already very fertile ground. A kid already excited about studying physics, astronomy, and mathematics will enjoy it, but there are too many middle- aged guys lecturing at blackboards to really inspire the blasé. This is not to say the producers didn't try: it's beautifully shot, there are some lovely locations, and nice computer enhancements, e.g., when the speaker traces in the air a cone with his fingers a cone appears and when he chops it with a wave of his hand a plane is traced out intersecting it. It is clear that the original French version (1995) was much more compelling than the English-dubbed version I viewed. The dubbing is an appallingly bad job: the music has been erased; the first time the crusty, old male French astronomer speaks we hear a lovely twenty-something female voice with a British accent, it's absurd and distracting (there are three different English voices dubbing the six or seven French ones); on several occasions the English translation ceases long before the French speaker stops moving his lips reminding one of a terrible 1950s Japanese horror movie; there were two obviously unintentional extended periods of silence on the tape I viewed, one in the middle of the explanation of perturbation theory, the other at the beginning of the explanation of recurrence, thus rendering both of those passages incomprehensible to the uninitiated. The French makers of the original really ought to have a word with the folks at Springer; these flaws make it not worth viewing in English. [Steve Kennedy]

Don Knuth's Things a Computer Scientist Rarely Talks About is a fascinating book. Knuth is well known in the mathematics community as the creator of TeX and as the author of The Art of Computer Programming. It is not as commonly known that he is the author of 3:16: Bible Texts Illuminated, which looks at verse 3:16 of each book of the Bible as a kind of "sampling" of the whole. This book, which is based on a series of lectures given at MIT, centers on Knuth's discussion and analysis of the 3:16 project. The book records both what Knuth said at the lectures and the lively question-and-answer sessions. (The lectures themselves were webcast and can still be viewed. See Knuth's web page for this book, which has a link to the webcast.) Knuth's musings about the interface between computer science and Christian theology are definitely not what one usually hears computer scientists talking about, but I'm glad Knuth was willing to take the risk of discussing them. [Fernando Q. Gouvêa]

Publication Data

The Geometry of Biological Time, by Arthur T. Winfree. Second Edition. Springer-Verlag, 2001. Hardcover, $89.95. ISBN 0-387-98992-7.

The New Shepherd's Lamp, by Jean-Pierre Bourgignon, François Tisseyre, Claire Weingarten. Springer VideoMath. 30-minute videotape, $32.00. ISBN 3-540-92638-0.

Things a Computer Scientist Rarely Talks About, by Donald E. Knuth. (CSLI Lecture Notes, no. 136.) CSLI Press, 2001. Hardcover, xi + 257pp., $35.00. ISBN 1-57586-327-8.

Jan Holly (jeholly@colby.edu) is Assistant Professor of Mathematics at Colby College, where she specializes in applied mathematics. She has done research at Los Alamos National Laboratory, the Robert S. Dow Neurological Sciences Institute in Portland, Oregon, and the Center for Computational Biology at Montana State University.

Steve Kennedy (skennedy@carleton.edu) is Associate Professor of Mathematics at Carleton College.

Fernando Q. Gouvêa (fqgouvea@colby.edu) is the editor of FOCUS and MAA Online. He teaches both "History of Mathematics" and "Number Theory", among others, at Colby College. He is a number theorist whose main research focus is on p-adic modular forms and Galois representations.

Back Issues:

• April 1999: Reprints of "classics", books on applied mathematics.
• May 1999: Books on math and physics, both popular and technical.
• July 1999: Various kinds of geometry, and classics in applied mathematics.
• August 1999: What's happening, Dirichlet, and Cryptonomicon.
• October 1999: Graph theory sources, John von Neumann, and Noncommutative Geometry.
• November 1999: Number theory in nine chapters, mathematics at work, and Jacques Hadamard.
• February 2000: Fallacies, Flaws, and Flimflam, measuring the universe, and primary sources at USMA.
• March 2000: Cardano and Manifold: Time.
• May 2000: Grassmann, Smarandache, and a really big prime.
• June 2000: A problem book, a history book, a collection of biographies, and a historical survey of reciprocity laws.
• August 2000: acrostics, field theory, categories, and partial differential equations.
• September 2000: excursions, history, and some high-level expository writing.
• November 2000: a festival of math videos and the Fourier-analytic proof of quadratic reciprocity.
• December 2000: Analysis problems, mathematical mysteries, and industrial mathematics.
• January 2001: Euler, Kolmogorov, and Honsberger.
• March 2001: history of mathematics, in three flavors: Harriot, prime numbers, and geometrical exactness.
• May 2001: three very different "applied mathematics" books.
• August 2001: introductions to algebraic number theory and to topology, and problem books.
• November 2001: Wilbur Knorr, John H. Conway, and vector analysis.

Go to... The main Read This! page The index of all reviews The MAA Online front page

Find out... About the Mathematical Association of America Why you should be a member of the MAA How you can help support the activities of the MAA

Read This! is the MAA Online book review column. Contributions are welcome; contact the editor if you'd like to be one of our reviewers. Books for review should be sent to the editor: Fernando Gouv&ecric;a, Dept. of Math&CS, Colby College, Waterville, ME 04901. Publishers, please check our reviews information page.