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nudge, tends to remain slightly off track. A nonlinear process, given the same nudge, tends to return to its starting point. Christian Huygens, the seventeenth-century Dutch physicist who helped invent both the pendulum clock and the classical science of dynamics, stumbled upon one of the great examples of this form of regulation, or so the standard story goes. Huygens noticed one day that a set of pendulum clocks placed against a wall happened to be swinging in perfect chorus-line synchronization. He knew that the clocks could not be that accurate. Nothing in the mathematical description then available for a pendulum could explain this mysterious propagation of order from one pendulum to another. Huygens surmised, correctly, that the clocks were coordinated by vibrations transmitted through the wood. This phenomenon, in which one regular cycle locks into another, is now called entrainment, or mode locking. Mode locking explains why the moon always faces the earth, or more generally why satellites tend to spin in some whole-number ratio of their orbital period: 1 to 1, or 2 to 1, or 3 to 2. When the ratio is close to a whole number, nonlinearity in the tidal attraction of the satellite tends to lock it in. Mode locking occurs throughout electronics, making it possible, for example, for a radio receiver to lock in on signals even when there are small fluctuations in their frequency. Mode locking accounts for the ability of groups of oscillators, including biological oscillators, like heart cells and nerve cells, to work in synchronization. A spectacular example in nature is a Southeast Asian species of firefly that congregates in trees during mating periods, thousands at one time, blinking in a fantastic spectral harmony.

With all such control phenomena, a critical issue is robustness: how well can a system withstand small jolts. Equally critical in biological systems is flexibility: how well can a system function over a range of frequencies. A locking-in to a single mode can be enslavement, preventing a system from adapting to change. Organisms must respond to circumstances that vary rapidly and unpredictably; no heartbeat or respiratory rhythm can be locked into the strict periodicities of the simplest physical models, and the same is true of the subtler rhythms of the rest of the body. Some researchers, among them Ary Goldberger of Harvard Medical School, proposed that healthy dynamics were marked by fractal physical structures, like the branching networks of bronchial tubes in the lung and conducting fibers in the heart, that allow a wide range of rhythms. Thinking of Robert Shaw’s arguments, Goldberger noted: “Fractal processes associated with scaled, broadband spectra are ‘information-rich.’ Periodic states, in contrast, reflect narrow-band spectra and are defined by monotonous, repetitive sequences, depleted of information content.” Treating such disorders, he and other physiologists suggested, may depend on broadening a system’s spectral reserve, its ability to range over many different frequencies without falling into a locked periodic channel.

Arnold Mandell, the San Diego psychiatrist and dynamicist who came to Bernardo Huberman’s defense over eye movement in schizophrenics, went even further on the role of chaos in physiology. “Is it possible that mathematical pathology, i.e. chaos, is health? And that mathematical health, which is the predictability and differentiability of this kind of a structure, is disease?” Mandell had turned to chaos as early as 1977, when he found “peculiar behavior” in certain enzymes in the brain that could only be accounted for by the new methods of nonlinear mathematics. He had encouraged the study of the oscillating three-dimensional entanglements of protein molecules in the same terms; instead of drawing static structures, he argued, biologists should understand such molecules as dynamical systems, capable of phase transitions. He was, as he said himself, a zealot, and his main interest remained the most chaotic organ of all. “When you reach an equilibrium in biology you’re dead,