BOOKS
COMING TO ORDER lightful triumphs of mathematical biology Such synchrony is not only not contrary to all natural law, but it pervades all of na ture, from electrons in superconductors to planetary motion. In his new book, "Sync: The Emerging Science of Spontaneous Order," Cornell University professor of REVIEWED BY DILIP K. KONDEPUDI theoretical and applied me OR HUNDREDS OF YEARS, WESTERN chanics Steven Strogatz starts travelers to Southeast Asia reported off with the delightful story of seeing a beautiful natural phenome the fireflies; then he proceeds to non that baffled many a naturalist: The take the reader through the vast synchronous flashing of fireflies that made gallery of synchronous phe trees and fields pulsate with bright flashes nomena in nature. His largely of light. Reports of this phenomenon al personal exploration of this sub so started to appear in North America and ject and lucid explanations—be Europe. Only at the beginning of the 20th they in chemistry, biology, or in the quan century did scientific discourse generate tum physics of superconductivity—make an explanation for this feat of the fireflies. the book a pleasure to read. In 1916, in the Discussion & Corre As Blair had suggested, the "natural law" spondence section of Science, Edward Morse that governs the fireflies is simply their re wrote about the extraordinary sight, which sponse to the flashing of other fireflies, like he had observed once in Gorham, Maine, birds responding to each other's calls. There about 50 years earlier. Like others, Morse was a bit baffled by what he saw, and he α Ζ) began to search the literature for any re α. ο ports on such phenomena. Only in 1915 ζ ο did Morse come across a report in Nature by K. G. Blair on European fireflies flash 5 ο ing in unison, which inspired his letter. σι In his report, Blair, after ruling out some simplistic explanations, commented: Ά Ο Ο more probable explanation of the phe nomenon is that each flash exhausts the bat tery as it were, and aperiod of recuperation is required before another flash can be emit ted. It is then conceivable that the flash of a leader might act as a stimulus to the dis charge oftheir flashes by the other members of the group, and so bring about the flash TRANSITION TO ORDER ing concert by the whole company" Magnetization in solids (left, Morse's correspondence elicited a string represented by magnetic moments of of comments on the subject, one of which individual molecules) is an example of a system that goes from a disordered was from Philip Laurent, who sharply dis state to an ordered state at a critical agreed with Blair's explanation. "I could temperature. A group of interacting hardly believe my eyes," Laurent wrote. "For oscillators (right), such as the such a thing to occur among insects is cer flashing of fireflies, also makes a tainly contrary to all natural law However, transition from a disordered state in I soon solved the enigma. The apparent which the oscillators have widely phenomenon was caused by the twitching varying frequencies to an organized or sudden lowering andrisingofmy eyelids. state in which the variation of the The insects had nothing whatsoever to do frequencies is reduced. The transition with it. Many times in the past 20 years I is made at a critical value of the have proved that my solution was correct." "width" of the frequency distribution. The proof that Blair was on the right The mathematical descriptions of the track and that Laurent had mistakenly two systems are very similar. convinced himself that the explanation was his jittery eyelids is one of the de SYNC: The Emerging Science of Spontaneous Order, by Steven Strogatz, Hyperion, 2003,338pages, $24.95 (ISBN 0-7868-6844-9)
F
44
C&EN
/ DECEMBER
1. 2003
is no master plan to synchronize, no con ductor for this rhythm; it appears as an emer gent property ofagroup ofinteracting flash ers. It's an example of self-organization. Following the fireflies, the book relates how the author and his collaborator Rennie Mirollo, a mathematician at Boston College, provided a mathematical proof for a conjecture made by Charles Peskin, an applied mathematician at New "York Uni versity's Courant Institute. Peskin's conjecture was that a large class of oscillating systems that interact with each other and al ter each other's phase and/or fre quency will eventually reach a synchronous state. Strogatz next takes us into the world of the synchrony of neural networks and brain waves. He introduces the work of the late Norbert Wiener, the prodigy and eccentric mathematician at Massa chusetts Institute of Technology, and Art Winfree, the University ofArizona evolu tionary biologist who is well known for his contributions to nonlinear dynamics in chemistry and biology As I read through the stories about Wiener, I could not help but wonder if such a personality would have garnered high regard in the current academic climate in which social skills are gaining increasing importance over orig inality and mathematical brilliance. Wiener and others considered the problem of coupled oscillators with vary ing oscillating frequencies (as one might expect in a group of fireflies)—a hard prob lem to solve mathematically Computer simulations indicated that synchronous oscillations occur only if the frequency variation is not too wide. When there is a wide variation in frequency among the os cillators, they oscillate asynchronously, in a disorderly fashion. When the variation in the oscillating frequency is decreased, the transition to synchronous oscillations occurs like a second-order phase transi tion. If one assumes a Gaussian distribu tion, the width of the distribution is akin to temperature, just as it is in the MaxwellBoltzmann distribution of velocities. Of all the periodic phenomena covered in the book, the sleep cycle is the most fascinating. How does it arise and why do we need it? While we still speculate about why we need sleep, a lot has been learned about its periodic nature and how it is en trained by day-night cycles. This rhythm's origin is the chemistry ofgene expression, but the details are still sketchy Indeed, al most all organisms possess a periodic chemical cycle, the circadian rhythm, HTTP://WWW.CEN-ONLINE.ORG
whose period is generally slightly longer than 24 hours. Albert Goldbeter's "Bio chemical Oscillations and Cellular Rhythms: The Molecular Bases of Peri odic and Chaotic Behavior" is an excellent introduction to this field. The sleep cycle, it turns out, is part of a much larger network of Orcadian cycles in an organism. All these cycles must work in synchrony, and they seem to be controlled by a central circadian pacemaker, which, in humans, is believed to be located in the brain. Much was learned through the ex traordinary time-isolation experiments of Michel Siffre, who lived alone in Midnight Cave, inTexas, 100 feet below ground lev el for six months. The isolation nearly drove him to suicide. Like the sleep cycle, body temperature undergoes small but systematic circadian oscillations,risingand falling about 1.5 Έ The data gathered during Siffre's ordeal showed how sleep and temperature cycles, which are normally synchronized, can be come desynchronized; disconnected from the steady temperature cycle, the ensuing sleep-wake cycle may then drift and be come 40 to 50 hours long. Then there is the synchrony needed for the proper functioning ofthe electric pow er grid. In discussing the grid, Strogatz makes a prophetic re mark: "Now with the deregulation ofthe pow er industry, and the po tentially destabilizing impact of free-market economics on the func tioning of the grid, engi neers and scientists will face even greater chal lenges in ensuring that the largest machine ever built continues to func tion as reliably as it has for decades." Indeed, engineers faced such a challenge during last summer's power outage in the northeast ern U.S. and parts ofCanada. Deregulation has its destabilizing consequences. Taking the reader through cooperative phenomena in collections of Bose parti cles (Bose-Einstein condensation), chemi cal waves, and colorful stories about Winfree, Strogatz ends his tour with a chapter on "The Human Side of Sync." It starts with Alan Alda's quest to understand fads and other such collective behavior in people.Alda, one of the major actors in the discon tinued hit television series "MASH," hosts the public television series "Scientific Amer ican Frontiers." Fads are surely a form ofsyn
chronized behavior. Could our current un derstanding of coupled nonlinear systems and collective behavior help us understand the conditions that give birth to fads? Mathematical modeling of sociological behavior has given us some interesting in sight, but it hasn't given us the means to control behavior—perhaps thankfully so. In other words, no one knows for sure how to turn something into fad. But this is not to discount the power of advertising; it is only to say that sociology and modeling of mass behavior is not a science with pre dictive abilities. Despite its many virtues, Strogatz' book has a regrettable flaw Until I reached the epilogue, I was almost sure that the catchy tide "Sync" and the subtide "The Emerging Science of Spontaneous Order" could be at tributed to publishers' mantras that hype is essential for sales. But it seems the author really endorses the idea that the study of synchronous behavior is an emerging sci ence. Only the uninformed will accept this characterization, however. The subject mat ter of this book is not an emerging science because much of it is already known to physicists, chemists, and engineers as col lective behavior, self-organization, cooper ative phenomena, or coherent behavior. The 1977 publication "Self-Organiza tion in Nonequilibrium Systems: From Dissipative Structures to Order Through Fluctuations," by Grégoire Nicolis and Ilya Prigogine, for example, deals extensively with systems far from thermodynamic equilibrium that show selforganization. It makes the diversity of such phenomena quite apparent. Because order in these systems is a result ofentropy generating irreversible, dissipative processes, such organized systems were called dissipative structures. That same year, Prigogine was awarded the Nobel Prize in Chemistry for his contributions to thermodynamics and the theory of dissipative structures. Since then, there has been a series of publications on self-organization and synchronous behavior by theoretical physicist Hermann Haken of the University ofStuttgart under the name "Synergetics." A number ofpublicationsfromthe Santa Fe Institute dealing with transition to order and other related behavior in complex systems offer another example. More recently, in their
Could our current understanding of coupled nonlinear systems and collective behavior help us understand the conditions that give birth to fads?
HTTP://WWW.CEN-ONLINE.ORG
1998 publication, "Introduction to Nonlinear Chemical Dynamics: Oscillations, Waves, Patterns, and Chaos," chemistry professors John A. Pojman of the University of Southern Mississippi and Irving R. Epstein of Brandeis University present an excellent introduction to a wide variety of systems that show organized behavior. It has been known for decades that collective behavior is widespread in nature and that the mathematical descriptions ofthese different systems have much in common. Thus, the study of the origin of order is really an evolving science, with manyunanswered questions. And, to me at least, Strogatz saying that "I hope I have given you a sense of how thrilling it is to be a scientist right now" has the unfortunate ring of a motivational talk. The more scientists say it, the less convincing it sounds. On the positive side, the book is a good antidote to the apologetic posture of mathematically inclined scientists. It has become all too common for chemistry seminar speakers to beg forgiveness while presenting the mathematics that is crucial for their research. These are the powerful and profound mathematical concepts without which the researchers could not have reached their conclusions. "I am sorry," the speakers say, "I have to show you some equations; please bear with me." What's the matter with mathematics? Without it, researchers could not function. Without it, we would still be thinking that synchrony infirefliesand in chemical reactions is "contrary to natural law" Strogatz' book is an excellent reminder of how widely applicable mathematics continues to be and how it shows us the unity underlying very diverse phenomena in nature. For this reason, "Sync" is a good book to recommend to undergraduates. For the chemist, there is another fundamental lesson in the book. The paradigm of oscillatory behavior has always been the simple pendulum based on the reversible laws ofmechanics. But nature's oscillators seem to be mostly based on irreversible laws that govern chemical reactions. The mathematical description of these nonconservative, or dissipative, systems is quite different from that of the conservative systems ofmechanics. It is time, perhaps, that we present chemical oscillators as the paradigm for oscillatory behavior in nature, not the simple pendulum. Dilip Kondepudl is Wake Forest Professor of Chemistry at Wake Forest University, WinstonSalem, N. C, where he conducts research on the spontaneous generation and propagation ofchiralasymmetry. C & E N / D E C E M B E R 1 , 2003
45
