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How Chaos Theory Works


Of Weather and Wings

It seems a strange juxtaposition today: In the 1960s, NASA was successfully launching astronauts into orbit while weather forecasters were struggling to make accurate predictions. In 1962 alone, two ferocious storms caught U.S. meteorologists with their proverbial pants down. The first, known as the Ash Wednesday Storm, came ashore on March 6 and nearly washed away some mid-Atlantic cities. When the nor'easter finally withdrew, 40 people were dead, and residents from North Carolina to New York faced $200 million dollars' worth of property damage [source: Dance]. The second storm -- the "Big Blow" -- struck the opposite coast on Oct. 12, battering California, Washington, Oregon and southwest Canada with near-hurricane-force winds. The Metropolitan Life Insurance Company declared the storm, which caused $230 to $280 million in damage, the worst natural disaster of 1962 [source: Read].

Many scientists believed that supercomputers held the key to avoiding similar weather catastrophes. Introduced in the '60s, these powerful, room-sized computers finally offered sufficient processing power to take a set of initial atmospheric conditions, crunch the numbers and spit out an accurate forecast.

A researcher at MIT, Edward Lorenz, had one of these early computers running in his office. Into this clumsy machine, Lorenz entered a streamlined computational model consisting of 12 meteorological calculations. The equations analyzed basic variables -- temperature, pressure, wind speed -- and spit out a simulated weather forecast. To "see" this weather, Lorenz would select one variable and then have the computer print out how that variable changed over time. In a bit of artistic flair, he directed the computer to print a certain number of blank spaces followed by the letter "a" in addition to simple numerical results. This produced a graphical representation of the variable being studied -- the letter "a" would meander across the page, just as capricious as the weather it was simulating.

One day in 1961, a particular output sequence caught Lorenz's eye. He decided to repeat the calculation, but to save time, he started from the middle of the run. Using the previous printout, he selected numbers halfway through the series to be his initial conditions. He entered these values, restarted the calculation and went away for some coffee. When he returned, he was astonished to find that the second run hadn't produced identical results as the first. The output pattern should have been the same, but the second graph diverged dramatically from the first after just a short time. Lorenz thought at first that his computer, notoriously finicky, wasn't working properly. Then he discovered the problem: The numbers he had entered from the printout only contained three digits, while the computer's memory allowed for six digits. This small discrepancy -- entering 0.506 versus 0.506127 -- was enough to introduce enormous unpredictability into the system.

Lorenz discovered with weather what Poincaré had discovered with interacting celestial bodies: certain complex systems exhibit sensitive dependence on initial conditions. Alter those conditions even slightly, and you'll produce wildly different results. Weather forecasting, Lorenz realized, was a futile effort at best because no one could ever quantify atmospheric conditions with certainty. To help people understand this concept, he invoked the idea of an animal flapping its wings, which would create a small area of turbulence, which would then be magnified over time and distance into catastrophic meteorological changes. At first, Lorenz favored the wings of a seagull. But in 1972, while preparing for a conference presentation, a colleague suggested he change his title to something a tad more poetic: "Predictability: Does the Flap of a Butterfly's Wings in Brazil Set Off a Tornado in Texas?" The image captivated the public, and soon the Butterfly Effect became the standing metaphor for the challenges of weather forecasting and for chaos itself.

Lorenz might have been satisfied with the results of his computer experiment, but he suspected he might be standing on the threshold of something bigger -- something profound. His now-famous "dishpan experiments" opened up the door to this wild and wonderful world we know today as chaos.