Sync: The Emerging Science of Spontaneous Order

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Emergence 2006

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Sync: The Emerging Science of Spontaneous Order

Peter O'Malley

In Sync, the mathematical biologist Steven Strogatz looks at emergence in a fundamentally different manner: synchronization. He starts off with a number of examples, all which involve the spontaneous emergence of synchronization from systems of what he terms coupled oscillators. The prototypical example that he offers is that of fireflies in East Asia along riverbank which blink in unison after dark. When these were first discovered, according to Strogatz, the Europeans at home did not believe the journals of explorers detailing these sights in awe. Over the years various explanations were provided, including one in the 1920s that posited that it was the result of the structure of the human visual system, but none proved satisfactory. It was only recently however, that it was realized that the fireflies would sync themselves naturally: an experiment was conducted, where fireflies were isolated and then slowly reintroduced to each other. At first, each firefly blinked at its own pace, but then pockets of synchronization started to form until eventually they all synchronized and blinked in unison. Strogatz then discusses various possible mathematical models for these fireflies and their realism and applicability. Finally, he extends the analogy to the so-called peacemaker cells of the human heart.

This is the basic format in which Strogatz tells his story of synchrony. He introduces a real-world example that he or others have found interesting—and it almost always is interesting—then proceeds to describe computer or real world models and experiments that have successfully or otherwise described the phenomenon, introduces the concepts behind any mathematical description of the system, including whether or not one is even possible, and concludes with an analysis of its usefulness, and any links that it has to other phenomena of synchrony.

It is the synchrony of the human heart that Strogatz frames his book with. He introduces the pacemaker cells of the heart, the sinoatrial node, early in the book as a group of relatively simple heart cells that, together, ensure at the heart beats in tempo. The challenge of synchrony here is to get all the cells to release their electrical charge at the same time, and to have it repeat steadily. A relatively simple model for these cells proposed by Charlie Peskin is to model them as identical, coupled, RC oscillating circuits—something with which every physics student is familiar. Charge builds up in a circuit until it surpasses some threshold, similar to a neuron, after which it fires, and adds a little bit of charge to every other circuit. It is not difficult to show through a computer model that these circuits will synchronize spontaneously, and Strogatz even outlines, qualitatively, the mathematical proof that he Peskin came up with.

An effective analogy, and one that Strogatz returns to throughout the book, is that of runners on a track. Each runner has his own speed, which is analogous to the frequency of an oscillator, and all the runners shout at and are heard by every other runner, which is analogous to the coupling between the oscillators. Depending on the initial conditions and the setup of the coupling, a group of runners may synchronize into a single block all running at the same speed, fall into chaos everybody running on her own, or anything in between. Strogatz tells of a work of Wiener, who came up with this analogy; Winfree, who discovered that for many situations there is a sudden phase transition; and Kuramoto, who showed that with an isotropic track and homogenous rules between the runners, there was either a chaotic solution or a solution where the runners grouped into three packs of varying speeds.

A subtle, but fundamental, difference between this model and the RC circuit model is in the coupling mechanism. Whereas in the circuit model, every oscillator affected the phase of every other oscillator, in this model the oscillators affect each other's frequencies. Which one of these is more correct depends, of course, on the physical system that one is trying to model. The frequency modification model is more accurate to another very real world application: the human body.

Strogatz spends quite a bit of time on what he terms "human synchrony." The circadian cycle, which is actually a bit longer than 24 hours naturally, is fundamental to many human processes, not least of which is sleep. It turns out that one of the most reliable measures of the circadian cycle his body temperature, which fluctuates roughly like a sine wave over 24 hours. Humans in complete isolation tend to lengthen their circadian rhythm to around 26 hours, so the question is: why do humans' sleep and temperature cycles have a period of 24 hours? It must be the influence of the sun, and brain imaging and experiments on rats have shown that there is a command center for the circadian cycle in the brain, and it is directly linked to the eyes.

The second half of Strogatz' book deals with non-biological synchrony, and there are many examples. Again, he starts with a historical example: Huygens, a Dutchman, and the negative feedback that synchronized his pendulum clocks. He proceeds to describe many examples, including lasers, the power grid, GPS devices, the moon's rotation, and Jupiter's orbit and its relation to Kirkwood gaps in the asteroid belt.

He spends the most time, however, on one fascinating example of synchrony: superconductivity. He goes into quite a bit of detail about how superconductivity works, perhaps too much, and describes Josephson effects and superfluid liquid helium. He also relates the practical uses of superconductivity, including the SQUID and its ability to detect magnetic fields and various imaging techniques. Strogatz also describes synchrony in a place that one would little expect it: Chaos. Mathematically chaotic systems, of "butterfly effect" fame, will apparently synchronize with themselves. It has no known uses yet, as all methods of encryption that have been devised with it are easily cracked with a Fast Fourier Transform.

It is with chemical synchrony however that Strogatz comes full circle and returns to the subject of the human heart. He tells a personal story of his work as a grad student with Winfree in their use of chemical waves, or more formally, "wave propagation in the excitable media." He and Winfree used a combination of mathematical models, computer models, and plain old experimentation to show that these waves in three dimensions form into what are known as scroll rings. With a detour through topology and advanced computer modeling (in 1982) he describes all of the form that emerge from simple waves, although these are not the relatively well understood kinds of waves that are commonly studied by physicists. What is most important, however, is that these waves provide a model for how the pacemaker cells in a heart can get out of whack and then this will propagate in what is known as tachycardia. It is not known, though, whether these waves can provide a model for or be the cause of defibrillation and cardiac death.

Strogatz closes his book with human sync: not in the biological sense this time, but in the social sense, and whether networks exhibit synchrony. He describes the small world problem by using a common parlor game: six degrees of Kevin Bacon, where players try to relate any given actor to Kevin Bacon in the fewest number steps possible. There are two types of fundamental networks that Strogatz describes: the tight locally clustered one, and the random one. He explores the networks that are found in between: those that have some local clustering and some randomness, and apply to the phenomena of human sync. Although he presents no definitive results, he theorizes that the synchrony of networks may be fundamental in the many phenomena of human sync: fads, traffic, the World Wide Web, disease spreading, and even applause.

In Sync, Strogatz presents a fascinating and entirely readable book about emergent synchrony. He includes personal anecdotes about the scientists involved—apparently, the Nobel laureate Josephson is now exploring the physics of the paranormal—and expert descriptions of theories without a single equation—though I, personally, would have preferred to see a few. What I found particularly intriguing was the different take on emergence that Strogatz had throughout the whole book: he knew exactly what he was looking for, and it was synchronization. This allowed him to provide an entirely different list of emergent phenomena than we discuss in class, though he would call them "phenomena of synchrony"—one man's emergence is another man's synchrony. I recommend this highly interesting book to all who are interested in a different take on emergence. [an error occurred while processing this directive]