COMING TO ORDER

SYNC: The Emerging Science of Spontaneous Order, by Steven Strogatz, Hyperion, 2003, 338 pages, $24.95 (ISBN 0-7868-6844-9)

REVIEWED BY DILIP K. KONDEPUDI

For hundreds of years, western travelers to Southeast Asia reported seeing a beautiful natural phenomenon that baffled many a naturalist: The synchronous flashing of fireflies that made trees and fields pulsate with bright flashes of light. Reports of this phenomenon also started to appear in North America and Europe. Only at the beginning of the 20th century did scientific discourse generate an explanation for this feat of the fireflies.

	Sync: The Emerging Science of Spontaneous Order

In his report, Blair, after ruling out some simplistic explanations, commented: "A more probable explanation of the phenomenon is that each flash exhausts the battery, as it were, and a period of recuperation is required before another flash can be emitted. It is then conceivable that the flash of a leader might act as a stimulus to the discharge of their flashes by the other members of the group, and so bring about the flashing concert by the whole company."

Morse's correspondence elicited a string of comments on the subject, one of which was from Philip Laurent, who sharply disagreed with Blair's explanation. "I could hardly believe my eyes," Laurent wrote. "For such a thing to occur among insects is certainly contrary to all natural law. However, I soon solved the enigma. The apparent phenomenon was caused by the twitching or sudden lowering and rising of my eyelids. The insects had nothing whatsoever to do with it. Many times in the past 20 years I have proved that my solution was correct."

The proof that Blair was on the right track and that Laurent had mistakenly convinced himself that the explanation was his jittery eyelids is one of the delightful triumphs of mathematical biology. Such synchrony is not only not contrary to all natural law, but it pervades all of nature, from electrons in superconductors to planetary motion.

In his new book, "Sync: The Emerging Science of Spontaneous Order," Cornell University professor of theoretical and applied mechanics Steven Strogatz starts off with the delightful story of the fireflies; then he proceeds to take the reader through the vast gallery of synchronous phenomena in nature. His largely personal exploration of this subject and lucid explanations--be they in chemistry, biology, or in the quantum physics of superconductivity--make the book a pleasure to read.

As Blair had suggested, the "natural law" that governs the fireflies is simply their response to the flashing of other fireflies, like birds responding to each other's calls. There is no master plan to synchronize, no conductor for this rhythm; it appears as an emergent property of a group of interacting flashers. 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 University's Courant Institute. Peskin's conjecture was that a large class of oscillating systems that interact with each other and alter each other's phase and/or frequency 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 Massachusetts Institute of Technology, and Art Winfree, the University of Arizona evolutionary 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 originality and mathematical brilliance.

Could our current understanding of coupled nonlinear systems and collective behavior help us understand the conditions that give birth to fads?

Wiener and others considered the problem of coupled oscillators with varying oscillating frequencies (as one might expect in a group of fireflies)--a hard problem 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 oscillators, 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 transition. If one assumes a Gaussian distribution, the width of the distribution is akin to temperature, just as it is in the Maxwell-Boltzmann 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 entrained by day-night cycles. This rhythm's origin is the chemistry of gene expression, but the details are still sketchy. Indeed, almost all organisms possess a periodic chemical cycle, the circadian rhythm, whose period is generally slightly longer than 24 hours. Albert Goldbeter's "Biochemical Oscillations and Cellular Rhythms: The Molecular Bases of Periodic and Chaotic Behavior" is an excellent introduction to this field.

The sleep cycle, it turns out, is part of a much larger network of circadian 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 extraordinary time-isolation experiments of Michel Siffre, who lived alone in Midnight Cave, in Texas, 100 feet below ground level for six months. The isolation nearly drove him to suicide.

Like the sleep cycle, body temperature undergoes small but systematic circadian oscillations, rising and falling about 1.5 °F. The data gathered during Siffre's ordeal showed how sleep and temperature cycles, which are normally synchronized, can become desynchronized; disconnected from the steady temperature cycle, the ensuing sleep-wake cycle may then drift and become 40 to 50 hours long.

Then there is the synchrony needed for the proper functioning of the electric power grid. In discussing the grid, Strogatz makes a prophetic remark: "Now with the deregulation of the power industry, and the potentially destabilizing impact of free-market economics on the functioning of the grid, engineers and scientists will face even greater challenges in ensuring that the largest machine ever built continues to function as reliably as it has for decades." Indeed, engineers faced such a challenge during last summer's power outage in the northeastern U.S. and parts of Canada. Deregulation has its destabilizing consequences.

Taking the reader through cooperative phenomena in collections of Bose particles (Bose-Einstein condensation), chemical 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 discontinued hit television series "MASH," hosts the public television series "Scientific American Frontiers." Fads are surely a form of synchronized behavior. Could our current understanding of coupled nonlinear systems and collective behavior help us understand the conditions that give birth to fads?

TRANSITION TO ORDER Magnetization in solids (left, represented by magnetic moments of individual molecules) is an example of a system that goes from a disordered state to an ordered state at a critical temperature. A group of interacting oscillators (right), such as the flashing of fireflies, also makes a transition from a disordered state in which the oscillators have widely varying frequencies to an organized state in which the variation of the frequencies is reduced. The transition is made at a critical value of the "width" of the frequency distribution. The mathematical descriptions of the two systems are very similar. COURTESY OF DILIP KONDEPUDI

Despite its many virtues, Strogatz' book has a regrettable flaw. Until I reached the epilogue, I was almost sure that the catchy title "Sync" and the subtitle "The Emerging Science of Spontaneous Order" could be attributed 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 science. Only the uninformed will accept this characterization, however. The subject matter of this book is not an emerging science because much of it is already known to physicists, chemists, and engineers as collective behavior, self-organization, cooperative phenomena, or coherent behavior.

The 1977 publication "Self-Organization in Nonequilibrium Systems: From Dissipative Structures to Order Through Fluctuations," by Gregoire Nicolis and Ilya Prigogine, for example, deals extensively with systems far from thermodynamic equilibrium that show self-organization. It makes the diversity of such phenomena quite apparent. Because order in these systems is a result of entropy 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 of Stuttgart under the name "Synergetics." A number of publications from the Santa Fe Institute dealing with transition to order and other related behavior in complex systems offer another example. More recently, in their 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 of these different systems have much in common.

Thus, the study of the origin of order is really an evolving science, with many unanswered 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 in fireflies and 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 of mechanics. 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 of mechanics. It is time, perhaps, that we present chemical oscillators as the paradigm for oscillatory behavior in nature, not the simple pendulum.

Dilip Kondepudi is Wake Forest Professor of Chemistry at Wake Forest University, Winston-Salem, N.C., where he conducts research on the spontaneous generation and propagation of chiral asymmetry.

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