Friday, July 3, 2009


In the October 17, 2008 entry to this blog, I discussed Steven Strogatz’s textbook Nonlinear Dynamics and Chaos, which Russ Hobbie and I cite in Intermediate Physics for Medicine and Biology. Toward the end of that entry, I mentioned that reading Strogatz’s other book, Sync, was “on my list of things to do.” Well, jobs often sit on my to-do list for a long time, but they eventually get done. This week I finished Sync, a fascinating book about “how order emerges from chaos in the universe, nature, and daily life.” It is an unusual mathematics book, because I don’t recall seeing a single equation. Nevertheless, Strogatz tells a charming tale of his contributions, and that of many others, to nonlinear dynamics. Russ added a citation to Sync to our chapter on Feedback and Control when we were preparing the 4th edition of Intermediate Physics for Medicine and Biology: “Strogatz (2003) discusses phase-resetting and other nonlinear phenomena in an engaging and nonmathematical manner.”

Chapter Eight of Strogatz’s book, “Sync in Three Dimensions”, is my favorite. Here he describes how he first discovered the work of Art Winfree, his “mentor, inspiration, friend”:

“I walked across the street to Heffer’s Bookstore to browse the books on biomathematics…As I scanned the shelves, with my head tilting sideways, one title popped out at me: The Geometry of Biological Time. Now that was a weird coincidence. My senior thesis on DNA had been subtitled ‘An Essay on Geometric Biology.’ I thought I had invented that odd juxtaposition, geometry next to biology. But the book’s author, someone named Arthur T. Winfree, from the biology department at Purdue University, had obviously connected them first.”
Strogatz then relates how he corresponded with Winfree, and ended up working with him at Purdue in the summer of 1982. He quotes Winfree’s letters, often written in what Strogatz calls “idiosyncratic code.” This characteristic style brought back memories of my own correspondence with Winfree. Although we only met in person once, I recall us exchanging many emails about cardiac dynamics, with his emails all in that same idiosyncratic code. As I read Winfree’s letters to Strogatz, I found myself thinking “yes, that is exactly the way Winfree would have said it.”

I had my own encounter with a Winfree book that influenced my early career. For me, it was not The Geometry of Biological Time, but Winfree’s other influential text, When Time Breaks Down: The Three Dimensional Dynamics of Electrochemical Waves and Cardiac Arrhythmias. I read the book in the spring of 1991. (I remember the time precisely, because I recall turning the pages of the book with one hand, while holding my newborn daughter Kathy with the other.) I was soon performing calculations of reentrant wave propagation in cardiac tissue, similar to the dynamics described in When Time Breaks Down. I worked at the National Institutes of Health at the time, and a summer student, Josh Saypol, and I performed a calculation of reentry induction using the bidomain model to test a prediction that Winfree had made in a chapter of the book Cardiac Electrophysiology: From Cell to Bedside (1990). His help was invaluable in interpreting our results, and for getting a preliminary note (The Formation of a Re-entrant Action Potential Wave Front in Tissue with Unequal Anisotropy Ratios) published in the just-started International Journal of Bifurcation and Chaos (Volume 1, Pages 927-928, 1991).

Strogatz describes Winfree’s untimely death in the epilog of Sync:
“Tragically, Art Winfree died on November 5, 2002, at age 60, seven months after being diagnosed with brain cancer. He helped me with this book at every stage, even when he was conscious only for a few hours a day. Though he did not live to see it published, he knew that it would be dedicated to him.”
For more about Winfree’s career, see his website (still available through the University of Arizona), the obituary Strogatz wrote for the Society for Industrial and Applied Mathematics, another by Leon Glass in Nature, and also one in the New York Times.

I described my own interactions with Winfree, and some of his contributions to cardiac electrophysiology, in my paper Art Winfree and the Bidomain Model of Cardiac Tissue, published in a special issue of the Journal of Theoretical Biology dedicated to his memory (Volume 230, Pages 445-449, 2004). Other particularly interesting contributions to that issue, full of delightful Winfree anecdotes, were the article by his daughter Rachael, and the article by George Oster.

I thoroughly enjoyed Sync. It is a fine introduction to the mathematics of synchronization and nonlinear dynamics. (Don’t, however, consult the book to learn how lasers work!) Sync ends with a lovely paragraph that explains what motivates scientists:
“For reasons I wish I understood, the spectacle of sync strikes a chord in us, somewhere deep in our souls. It’s a wonderful and terrifying thing. Unlike many other phenomena, the witnessing of it touches people at a primal level. Maybe we instinctively realize that if we ever find the source of spontaneous order, we will have discovered the secret of the universe.”
Alas, my to-do list never gets any shorter. Strogatz has a new book coming out next month, The Calculus of Friendship: What a Teacher and a Student Learned about Life while Corresponding about Math, and I plan to read it as soon as I get a bit of spare time.

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