Chaos

It could be said that the science of chaos began on a winter day in 1960, when MIT meteorologist Edward Lorenz '38 read the printout from a primitive early computer. Lorenz had programmed the machine to model changes in the atmosphere. He would feed in a dozen 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 out of rows of numbers.

On that particular day, Lorenz took a shortcut by taking the values from the midpoint of the printout and typing 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 spewing from the machine bore no resemblance to the ones generated on the earlier run. The two printouts started out the same, but before long, small differences began to creep in, getting bigger for each day. The reason was that 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.

There was a moral to the experiment: small differences can have surprisingly large consequences. Today that property is called "sensitive dependence on initial conditions," or, more commonly, the Butterfly Effect. The name was inspired by the title 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 longrange forecasts. No matter how powerful their tools, they would never be able to make perfect measurements of the atmosphere. Weather wasn't just too big a problem for current science. It was inherently unpredictable beyond a week or so.

While the computerized weather patterns never repeated themselves, they weren't exactly random either. There seemed to be some hidden order amid the confusion, some unpredictable but recognizable pattern among the jumble of numbers. Eventually Lorenz found three equations that generated a never-repeating sequence of numbers. When he 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. 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 a foundation of chaos theory.

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 Lorenz's 1963 paper and began circulating copies, did word get out. Today the paper,

"Deterministic Non-periodic Flow," is a widelyquoted classic. Scientists have found the same features in measles outbreaks, dripping faucets, earthquakes, cotton prices, the beating of the human heart, and many other phenomena.

And, of course, Lorenz's theories are the premise of this issue which argues that, without Dartmouth and its productive alumni, the world would have been different in unpredictable and possibly disastrous ways. Which makes the gift of the College far more than the uncountable sum of its many parts.

Lorenz's theory of nature's unpredictability was the heart and soul of "Jurassic Park."