Ed Reckoning

EDWARD LORENZ '38 introduced a groundbreaking scientific theory nearly 50 years ago by claiming there's order in seemingly random patterns. Still publishing his research at 86, the MIT professor reflects on a career in "chaos,"

THE IMAGE IS AS FIRMLY AFFIXED IN THE PUBLIC imagination as that of Galileo dropping cannonballs from the leaning Tower of Pisa or Archimedes shouting "Eureka!" as water splashes from his bathtub. It is the image of a butterfly flapping its wings in a jungle in Brazil, a motion that— however slight it may seem—causes a disturbance in the Atmosphere. That initial disturbance causes another, a little greater in magnitude, and that second disturbance in turn causes a third, more powerful yet, and so forth, fostering a chain reaction that continues to increase in magnitude until a tornado finally sweeps across the dusty flatlands of Texas.

The name of that image is the "Butterfly Effect," and it cuts right to the essence of the science of chaos. Though common sense may hold that chaos is synonymous with disorder, the Butterfly Effect informs us otherwise. What is now called chaos is actually the tendency of systems that are sensitive to initial conditions to experience periods of unpredictable behavior. Such "chaotic" behavior may occur in weather forecasting, where not all butterflies can be accounted for, and in cancer studies, where malignant cells spread at regular and then irregular periods, depending on treatment doses or bodily conditions. Or it may explain how large crowds respond to a natural disaster or terrorist attack. In a recent issue the political journal The Nation speculated that the party allegiances of the labor union AFL-CIO were best explained through the chaos principles inherent in the Butterfly Effect..

It is undoubtedly a beautiful image, the sort that makes science captivating even to the most unscientific of minds, but the crucial insight of chaos arose—appropriately, perhaps—almost entirely by accident.

"I THOUGHT IT WAS MACHINE TROUBLE AT FIRST," admits Edward N. Lorenz, sitting in his office at the Massachusetts Institute of Technology, where he has spent much of his decorated career as a professor in the department of earth and planetary sciences, currently serving as professor emeritus. "We had plenty of that. We frequently had to call in people to fix something."

The year was 1959, a time when computers were still regarded with plenty of suspicion by the scientific community, and the machine in question was the Royal McBee, a hulking and now long-extinct predecessor of the modern computer that, by all appearances, was far less graceful than its name suggests. Lorenz had been using the behemoth mainframe to simulate the behavior of weather systems over long periods of time, devising a set of equations for factors such as wind speed and air pressure.

He hoped to demonstrate that computer modeling would allow for a fuller understanding of weather patterns than would a traditional pen-and-paper method that relied almost purely on statistical analysis. "It had been proposed by a good many meteorologists that statistical methods worked just as well as dynamical methods of forecasting. I didn't believe it myself," Lorenz says. That seed of skepticism would give rise to one of the central scientific insights of the 20th century; the story behind it is something of a legend.

At first the Royal McBee performed admirably, its weather systems changing with a regular pattern Lorenz had known to expect. He fed new variables into the computer and decided, at one point, to use intermediate results from a concluded test as initial variables for the next one. It was precisely at this moment that the experiment took a turn for the unexpected, and the next time Lorenz consulted his computer he saw that results were wildly different from what he had previously seen.

Certainly, the Royal McBee was far from faultless; Lorenz remembers that it was occasionally prone to errors such as 2 + 2 = 5. And yet he knew the machine well enough to suspect that something far more significant than mere error was at hand. The numbers he had used in the last run were slightly different from those that were there before, since printed results were rounded to three digits while the machine worked with six-digit accuracy. The difference seems miniscule, but it was enough to throw Lorenz's intricate weather system into disorder.

Deep in the jungle, the butterfly had flapped its wings. As Lorenz extended his computation over longer intervals, the Royal McBee returned with weather systems that resembled the previous computations less and less, discrepancies between the two solutions growing more or less exponentially, Lorenz recalls.

Though he did not term it chaos at the time—and he still is not completely comfortable with the term—Lorenz understood that he had uncovered a basic rule of nature that dictates that even the most orderly systems may be prone to periods of disorder or irregularity. "I soon discovered," Lorenz says, "that if you change the state slightly it will do something quite different from what it would have been doing if you hadn't changed it slightly.

This contentious relationship between order and disorder, dragged out into the open by the labyrinthine workings of the Royal McBee, would come to work an unimaginable influence on science.

SERENDIPITY MAY HAVE PLAYED ITS PART IN THAT WATERSHED discovery of 1959, but truth the breakthrough was the culmination of a career devoted to a study of the skies. I was always interested in the weather, Lorenz says. His childhood was spent under the volatile skies of New England, where a single day could bring rounds of rain and sunshine. He received his schooling in West Hartford, Connecticut—a serene suburb situated comfortably between Boston and New York—and by the time he entered Dartmouth his primary interest had shifted purely to mathematics." Lorenz received what he deems "good training at Dartmouth, at one point finding himself the lone student in an advanced mathematics seminar. His social activities were centered around chess and the Dartmouth Outing Club, with which Lorenz estimates he went on about 70 excursions during his four years in Hanover. He was also a friend of Jack Durrance '39, the storied outdoorsman who founded the Dartmouth Mountaineering Club.

Upon graduation Lorenz left Dartmouth for Harvard, where he conducted graduate work in mathematics. There his interest shifted gradually toward algebra. He was planning to do a thesis on the subject when World War II broke out, laying waste to his academic intentions. Instead of completing his studies he joined the Army Air Corps and served as a weather forecaster. After the war he continued to pursue a career in meteorology, but the intense passion for mathematics that had crystallized at Dartmouth and the years thereafter would perpetually inform his study of the weather, endowing his research with an awareness not usually granted to scientists narrowly confined within their own fields.

Four years after his landmark experiment with weather systems on the Royal McBee, Lorenz published a paper titled Deterministic Nonperiodic Flow" in the Journal of the Atmospheric Sciences in 1963. Though it was a meteorological publication, his conclusions were largely based on mathematical descriptions of the relationship between stability and instability, between patterns of regularity and outbursts of disorder. By this time he had developed a simpler series of equations to describe the nature of dynamic systems that are sensitive to initial conditions and thus prone to periods in which a slight change in a single factor causes a system to behave unpredictably. He had also developed the now-classic Butterfly Attractor, a graphic representation of chaotic behavior on a three-dimensional grid known as a phase map. As the name suggests, the Butterfly Attractor looks like the spread wings of a butterfly. Its purpose is to demonstrate that although a system has points of predictability (each "wing" is roughly the same shape), it is nevertheless prone to shifts in behavior, moving from one wing to another or along the length of either wing.

Since the Journal of the Atmospheric Sciences is not exactly a coffee- table publication, Lorenz's discovery remained largely unknown for the rest of the 1960s, familiar only to others in his field. Furthermore, it was a heady time for science. The preceding decades had yielded atomic energy, space flight and a host of innovations in biology. Few scholars wanted to hear that disorder was an inextricable feature of the world they were seemingly so close to having tamed. "My feeling is there were always a lot of people who were interested in nonlinear systems and who had a pretty good idea of how they behaved," says Lorenz. "There were also many others who didn't think nonlinearly, you might say. There was perhaps a sort of lack of communication between these two groups. It was this lack of communication—Lorenz's mild way of putting it that threatened to relegate the discovery of chaos to obscurity.

Only in the 1970s did the scientific community come to realize that what Lorenz had stumbled upon had ramifications for every discipline of science. He largely credits the gradual groundswell of recognition to James Yorke, a mathematician at the University of Maryland who was introduced to Lorenzs theory of deterministic nonperiodic flow" by a former student of Lorenz. Yorke thought it was interesting and sent it out to all his friends in the field, says Lorenz. "So I think that was when the work that I had done received notice among people other than meteorologists who were familiar with it." At the same time Jule Charney, probably the most influential meteorologist of his time and a colleague of Lorenz's at MIT, highlighted Lorenz's work in a study of global weather patterns, acknowledging the inherently dynamic nature of climate patterns that deterministic nonperiodic flow had suggested.

Further notice of Lorenz's ideas came in 1972, when he gave a talk titled "Predictability: Does the Flap of a Butterfly's Wings in Brazil Set Off a Tornado in Texas?" to the American Association for the Advancement of Science in Washington, D.C. By that time chaos was on its way to becoming a veritable discipline of its own, with physicists and chemists pouncing on the possibilities of disorder for their own research.

For Lorenz, nothing had changed since the Royal McBee first cranked out its discordant weather patterns and, despite the rising popularity of his work, he saw little more than the beguilingly simple idea that touched off the chaos phenomenon. Others would take up the mantle of a new science, but for Lorenz this so-called chaos was merely the interplay of regularity and irregularity that had been there all along or, in his own words, "something that is not ran- dom but looks random. In the details, of course, if you look at it, if you examine one of these chaotic phenomena,you can probably see the regularity to it." That is, chance is inevitably part of the master plan and every system, no matter how intricate and complex, must make room for some measure of disorder.

CHAOS CONTINUED TO GAIN POPULARITY THROUGHOUT the last three decades of the 20th century, and the paper that Lorenz published in the Journal of the Atmospheric Sciences exerted a spreading influence. As James Gleick relates in his 1987 book Chaos:Making a New Science—one of the most enduring works of popular science—the scientific community would largely come to refer to Lorenz's work as "that beautiful marvel of a paper" in which a meteorologist with a mathematical background managed to express unpredictability in a series of equations that held universal appeal, equally usable by physicists tracking planetary motions and cardiologists concerned with irregular heartbeats.

Since the 1970s chaos has burgeoned into a study spanning disciplines, more an outlook than a narrow discipline. Instead, it has informed research in a variety of fields, from biology to astrophysics to supercomputing. "Chaos breaks across the lines that separate scientific disciplines," Gleick writes in his famous work. "Because it is a science of the global nature of systems, it has brought together thinkers from fields that had been widely separated." Thus, chaos can be summoned at once to express the erratic behavior of a financial market or the irregular beat of a diseased human heart; both economics and physiology benefit from a more nuanced understanding of disorder.

And yet Lorenz, the man who discovered chaos, is distinctly modest about his achievements. "I told Gleick I didn't think he should make me the hero of his book," Lorenz says. To his chagrin, Gleick did precisely that. Even now Lorenz avoids using the word "chaos," clearly preferring the less exciting, but almost certainly more accurate, terms "irregularity" and "periodicity." Indeed, the term chaos was primarily popularized by Tien-Yien Li and Yorke in a paper titled "Period Three Implies Chaos." Lorenz did not use it until 1984, well after its debut in the halls of popular science.

The public embrace of chaos does not mean it has ceased to have relevance to the scientific community. "The applications in meteorology are still going," says Lorenz. "I tend to think of physics as the place where it will be most applicable." Although he is no longer teaching, he is in his office almost every day to conduct research- on periodic tables—and write.

Lorenz remains committed to studying the fickle workings of weather and is currently researching regimes: not the political kind, that is, but weather systems such as El Nino, whose behavior is best measured in periods of several years. And he is still exploring the rich terrain he discovered four decades ago, creating simple models that describe the oscillations that can produce stark changes in weather regimes. His "Regimes and Simple Systems" will soon be published in the Journal of the Atmospheric Sciences, the publication that launched the young meteorologist into the highest echelons of his field. Lorenz also will be publishing an article titled "An Attractor Embedded in the Atmosphere" in Tellus, a Swedish magazine.

When Lorenz received the Kyoto Prize—the equivalent of a Nobel in mathematics—in 1993, the award citation noted his discovery of "deterministic chaos...a principle that has profoundly influenced a wide range of basic sciences and brought about one of the most dramatic changes in mankind s view of nature since Sir Isaac Newton." He had, in essence, described a basic truth of the universe, one which had been hinted upon but never expressed in such concrete mathematical terms. Since antiquity—when the ancient Greek poet Hesiod first described the void from which life sprouted—thinkers have speculated that stability and flux are in a constant tug-of-war. Lorenz finally translated that timeless insight into the exacting language of science.

STUMBLED UPON GOME TO REALIZE THAT WHAT LORENZ HAD HAD RAMIFICATIONS FOR EVERY DISCIPLINE OF SCIENCE.

ALEXANDER NAZARYAN lives in Brooklyn, where he is a high schoolteacher at Brooklyn Latin School and writes for several publications.