THE FATHER OF CHAOS

While proving that nature isunpredictable, Edward Lorenz '38found a strange order in theuniverse.

THE 1950s WERE A PERIOD OF GREAT optimism about weather forecasting. The mathematical equations governing the behavior of the atmosphere had been known since the late 1800s. Now, with the emergence of the computer, meteorologists finally had a tool that could solve the equations faster than the weather occurred. Many believed it was only a matter of time before they'd be predicting the weather with pinpoint accuracy months in advance. Control would be the next step.

Then along came a skeptic named Edward Lorenz, a meteorologist at the Massachusetts Institute of Technology. Lorenz put his computer to a different use poking holes in his colleagues' inflated hopes. He wound up showing that accurate long-range forecasts the Holy Grail of Meteorology would forever remain beyond the meteorologists' grasp. In the process he helped give birth to a new science known as chaos, which today is yielding fresh insights in fields ranging from physics to physiology, economics to epidemiology.

Lorenz's work with computers began in 1959, when his group of MIT meteorologists rented a Royal McBee. About as big as a standard office desk, the computer was noisy, temperamental, and not particularly fast qeven by the standards of the day, but the meteorologists didn't have to share it with anybody. "I could put a program in it, let it run, and come in the next morning and see what had happened," Lorenz said.

Into this ungainly machine, Lorenz would feed a series of 12 equations that crudely represented the physical processes of the atmosphere. Given initial values for each of the variables, the computer solved the equations over and over, creating a sort of artificial weather. To the untrained eye it was nothing more than row after row of numbers on a page. But if you knew how to read the printouts, you could see a shift in the wind, a drop in temperature, or the movement of a high-pressure system across a continent.

One day in the winter of 1960, Lorenz took a shortcut. He wanted to look more closely at a weather system that had done something interesting halfway through its run. Rather than start over from scratch, he took the values from the midpoint of the printout and typed them into the computer as the initial state of a new run. When he returned an hour later, the computer had simulated about two months' worth of weather, but something was wrong. The numbers the Royal McBee was typing out bore no resemblance to the ones generated on the earlier run. "At first I thought, 'Uh oh, we're having machine trouble again.'

Then it dawned on me," Lorenz recalled.

The two printouts started out the same, but before long small differences began to creep in, getting bigger each day. The reason was that the values for the variables in his equations were stored in the computer's memory to six digits but were rounded off to three digits on the printout 0.785329 became 0.785. Lorenz had used the rounded-off numbers as the starting point for the new run, thinking it wouldn't matter. But those tiny differences had been amplified over time to create a wholly new weather pattern.

"I became excited, because I immediately realized that if the atmosphere behaved this way, then long-range forecasting wasn't possible," he recalled. "It meant that no matter how much we improved things, there was a limit beyond which we couldn't go."

Most scientists, including Lorenz, had always assumed that small differences could safely be ignored, but the Royal McBee results showed that small differences could sometimes have surprisingly large consequences. Today that property is called "sensitive dependence on initial conditions" or, more commonly, the Butterfly Effect, a name inspired by the tide of a paper Lorenz gave a decade later: "Does the Flap of a Butterfly's Wings in Brazil Set Off a Tornado in Texas?"

The Butterfly Effect was very bad news for those meteorologists who were counting on accurate long-range forecasts. No matter how sophisticated their models, or how powerful their computers, they would never be able to make perfect measurements of the atmosphere. Errors as trivial as rounding off the temperature to the nearest degree would ripple through the system to produce large distortions. That meant weather wasn't just too big a problem for the science of the sixties. It was inherently unpredictable beyond a week or so.

While the weather patterns spun out by the Royal McBee never repeated themselves, they weren't exactly random either. In fact, Lorenz and his colleagues would sometimes stand over the computer and make bets on what number would be next. The fact that they could guess at all implied some order. But what kind?

To find out, Lorenz put aside his 12-equation model and looked for something simpler. Eventually he found three equations that generated a never repeating sequence of numbers. When Lorenz plotted the results on a three-dimensional graph, the numbers traced out a looping curve with an arresting pattern: a double spiral resembling an owl's mask. The curve never follows the same path twice. On the other hand, it always stays within certain boundaries, as if drawn to a magnet. This structure, dubbed the Lorenz Attractor, revealed that chaotic events are not as random as they seem. There is a hidden order within the disorder.

Lorenz's findings were soon accepted by most other meteorologists, but scientists in other fields remained largely unaware of them for almost a decade. Not until 1972, when a mathematician discovered his 1963 paper and began circulating copies, did word get out. Today Lorenz's paper, "Deterministic Non-periodic Flow" is a widely quoted classic, and the properties he identified the Butterfly Effect and the hidden order of disorder are among the hallmarks of chaos. Scientists have found the same features in measles outbreaks, dripping faucets, earthquakes, cotton prices, and the beating of the human heart, among many other phenomena.

Even now, 50 years later, Lorenz speaks wistfully of his days as a graduate student in mathematics. "The thing I would have liked more than anything else would have been to prove a mathematical theorem of some meaning," he confessed. Circumstances prevented Lorenz from fulfilling that dream. But by applying his mathematical skills to meteorology, Lorenz has achieved something of possibly greater value: he has helped change the way scientists look at the world.

Writer Stephen Lyons lives in Boston.

Ed Lorenz's formulas formodeling weather eventuallyled to a whole new science.

Today thatproperty is calledthe ButterflyEffect, a nameinspired by thetitle of a paperLorenz gave adecade earlier:"Does the Flapof a Butterfly sWings inBrazil Set Offa Tornadoin Texas."