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In 1959, a young meteorologist named Edward Lorenz set out to build himself a world. Naturally, the project entailed a few compromises:
His world was flat, contained only the barest approximation of an atmosphere, and existed only in the memory banks of the Royal-McBee computer inside his office at the Massachusetts Institute of Technology. At the center of this world was a mathematical weather-prediction model, except, instead of the thousands of equations and variables typically used, Lorenz's contained only twelve of each. But Lorenz wasn't interested in improving weather predictions—he wanted to know if prediction was even possible.
Despite the simplicity of his simulation, Lorenz soon succeeded in reproducing some of the unpredictability of daily weather patterns, represented by a series of symbols on his computer printouts. But it took a fortuitous shortcut to reveal the most surprising behavior of his model. One day, wanting to repeat the results of a previous simulation, he input the numbers from an earlier run, started the simulation, and stepped out for coffee. When he returned an hour later, two months had passed in the simulation, but the new numbers coming out of the computer looked nothing like those from the previous run. From the same beginning, his simulation appeared in have produced two completely different patterns of weather.
Lorenz suspected an equipment problem, but eventually realized that the explanation was much simpler. Instead of typing in the entire numbers from the previous run, he had shortened them by three decimal places, substituting, for example, 123.875 for 123.875664. Over time, these tiny initial discrepancies had been magnified, resulting in major changes in the simulated weather patterns. In 1972, Lorenz examined the implications of this result in a now legendary talk entitled "Does the Flap of a Butterfly's Wings in Brazil Set off a Tornado in Texas?" The phenomenon, which he called "sensitive dependence on initial conditions," has been known as the butterfly effect ever since.
In the years following Lorenz's discovery, the butterfly effect, more than any other property, came to symbolize all that was bizarre and fascinating about what we now call chaotic systems. By demonstrating that some phenomena, no matter how precisely we attempt to measure them, are ultimately beyond predicting, it gave birth to the enduring impression that chaos is something recalcitrant, unwieldy, unpredictable to its core.
And yet, for almost twenty years, researchers like Duke physics professor Dan Gauthier have been engaged in a quest to perfect the use of chaos as a tool, to transform it from an apparent bug in nature's programming into a feature. By turning the logic of the butterfly effect, sensitive dependence, on its head—nudging chaotic systems with a series of tiny feedback adjustments—they have succeeded in coaxing ordered behavior from a staggering range of disparate systems—in Gauthier's case, from the fluctuations of laser beams to the electrical dynamics of the human heart. Chaos, he would tell you, can not only be tamed, it can be harnessed.
In the early 1980s, when Gauthier entered graduate school, chaos was still the province of only a few isolated researchers. His own passion was for lasers. While still in high school, he and a friend had begun experimenting with the devices, donations from a canceled research program at a local ballbearing company. "They're the same lasers that are in supermarkets [as scanners] nowadays," he explains, "but back then, they were very rare." Together, the two of them undertook projects they'd read about in Scientific American, making holograms in Gauthier's parents' garage and repeating experiments that had, 150 years earlier, helped prove that light traveled in waves.
It was an interest that only deepened during Gauthier's undergraduate days at the University of Rochester as he began studying optics, the physics of light, and its interaction with matter. "What I liked about laser physics," he recalls, "was that I could work alone or with one other person and really accomplish something. That's what's a bit different about the optics field—there are almost no theorists. You've got to design the experiment, you've got to build the equipment, you've got to do the experiment, analyze the data, and write the paper. You've got to do a little bit of everything."
Yet, at the same time Gauthier was engrossed in the intricacies of lasers, ideas from chaos theory were rapidly filtering into the general consciousness of physicists, mathematicians, and theoretical biologists. The common element across these disciplines was mathematics, the equations that in abstract form describe phenomena as diverse as the mixing of fluids and the synchronized blinking of fireflies. In many cases, with a simple exchange of variables, two entirely unrelated systems might be described by the same set of equations, a realization that allowed scientists experimenting in all types of systems, to discover general principles underlying chaos.
What they found was a world of difference between chaotic systems like Lorenz's weather model and merely random processes like the roll of dice. Lorenz's model only appeared unruly. None of the equations defining it contained any element of chance. Had Lorenz restarted his simulation with numbers accurate to the full six decimal places, he would have observed exactly the same weather as before. Yet, viewed under the microscope of mathematical analysis, data from the Lorenz model disclosed what scientists call a strange attractor, a pattern of organized behavior hidden amid the unpredictability (see Strange Attractors).
In systems ranging from planetary motion to wildlife population data, the discovery of other strange attractors revealed that many types of unpredictable behavior arose from order, not randomness, and had their roots in a common mathematics. Even fractals, geometric patterns like those of fern fronds and coastlines that repeat themselves on both the smallest and largest scales, were found to be produced by simple mathematical rules, a discovery that spurred interest in computer-generated cousins of natural geometries such as the iconic Julia and Mandelbrot sets (see Jagged Symmetry).
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