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Unit 12

In Sync

12.2 Unit Overview

When we listen to an orchestra, we are often impressed by how well the musicians can play together, each individual contributing to a whole that is almost always something very different from the individual parts. From a group of musicians playing individual parts, a complex, coordinated piece emerges. The mechanism for this particular synchronization is not hard to understand: The conductor keeps time and cues the musicians to play "in sync" with each other.

Marching Band Item 2923/Chris Clark, COLLEGE MARCHING BAND IN FORMATION (2006). Courtesy of iStockphoto.com/Chris Clark.

Marching bands are another example of synchronous behavior. Their synchrony is somewhat more complicated than that of an orchestra in that the marching musicians move together in addition to playing music together. To play in sync with each other, they take their cues from a conductor, as the orchestra does.

To move in sync with one another, however, they must take their cues from each other. The marchers judge their position and velocity relative to their neighbors. This may seem like a lot to think about for the band members, and it is. Consequently, it would be tempting to conclude that synchronous, coordinated behavior requires a conscious mind, but humans are definitely not the only ones who exhibit synchronous behavior.

Swirl of Fish Item 3098/Tammy Peluso, SWIRL OF FISH COLLEGE (2007). Courtesy of iStockphoto.com/ Tammy Peluso.
Swirl of Fish Item 3099/Tammy Peluso, SCHOOL OF TREVALLIES (2007). Courtesy of iStockphoto.com/ Tammy Peluso.

Flocking behavior in birds and schooling behavior in fish are two examples of synchrony in the animal world. Watch a flock of pigeons flying and you are likely to see them make remarkably sharp turns, all at the same time. The entire flock can change direction seemingly simultaneously and without running into each other. The same is true for a school of fish, darting, turning, splitting, and re-uniting to evade a predator. Both flocks of birds and schools of fish exhibit this sort of coordinated motion—what we have been calling synchronous behavior—without a leader or "conductor" whose actions tell the group what to do. Rather, each individual pays attention to its immediate neighbors and makes small adjustments in speed and spacing to maintain the cohesion of the group. This phenomenon of groups of individuals who each follow local relationship rules results in the whole group seemingly acting as one. It would then be reasonable to surmise that coordinated, synchronous behavior requires some higher level of brain function—at least at a level that enables an individual subconsciously to follow an innate set of rules about distance and speed.

Even this conjecture, however, falls apart when we consider another example from the animal world. Certain species of fireflies in Southeast Asia exhibit extraordinary synchronous behavior. By the thousands they are able to synchronize the rhythmic flashing of their abdomens so that they all flash at the same time. They seem to accomplish this naturally and spontaneously without any leader showing the way. They accomplish this synchronization despite the fact that each individual firefly’s brain can’t hold a candle to the processing power of a bird’s or fish’s brain.

fireflies Item 2429/Fletcher & Baylis / Photo Researchers, Inc., SYNCHRONOUS FIREFLIES (PTEROPTYX TENER) FLASHING ON THE MANGROVE TREES (SONNERATIA CASEOLARIS) AT KUALA SELANGOR, MALAYSIA (2008). Courtesy of Photo Researchers, Inc.


Synchronous behavior obviously occurs among simpler animals, but what about at a sub-organism level? How about between cells? An individual cell has no brain, and yet our bodies are made up of trillions of individual cells, each of which functions—during states of health—in life-sustaining harmony with the others. A great example of this is heart pacemaker cells. Pacemaker cells are the key rhythm keepers that govern how and when the heart contracts. These cells display a great degree of spontaneous synchronous behavior; indeed, if they didn’t, none of us would be here to observe it! Each pacemaker cell has an innate cycle of building and releasing electrical charges that ultimately stimulate the cells of the heart to contract or relax. In isolation, pacemaker cells keep their own rhythm. When one pacemaker cell is placed in proximity to another pacemaker cell, however, something remarkable occurs. They maintain their separate rhythms for a brief period and then naturally fall into sync with one another, both building and releasing charges at the same time. This phenomenon has no leader guiding it and no processor, such as a brain, to make judgments about what the neighbors are doing.

At this point we could still argue that the phenomenon of synchronous behavior requires some sort of living thing. Although it doesn’t need a leader, or even brains, perhaps it results from some basic principle of biology.

Of course, by now we should not be surprised that this is not the case. All sorts of non-biological systems can spontaneously synchronize, creating order where we might expect to see chaos. We can see this in the heavens, in the tidal locking of our moon (a case of two cycles, both an orbit and a rotation) becoming synchronized so that we always see the same side of the moon when we look from Earth. Even something as simple and mundane as a system of two pendula, little more than weights attached to the ends of sticks, will exhibit spontaneous synchronization when both connected to a movable platform.

Synchronization is at the heart of the study of how order emerges from disorder and the rules that guide this process. Mathematics is the perfect tool to use to study this, because it provides methods that are general enough to encompass the commonalities in the seemingly disparate phenomena that we have looked at so far. Using the tools of mathematics, we can start to clarify a complex situation by making simplifying assumptions, seeing how these simple cases behave, and then trying to generalize our findings to cases that are not so simple. This is a common theme in mathematics, but to use this method to understand synchrony, we will need some specific mathematical tools, namely those that can quantify and describe things that are continuously changing.

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Next: 12.3 Calculus


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