Chaos Theory turns 50
Tom Siegfried has an interesting article in Science News:
Predicting the impact of a scientific discovery is a lot like predicting the weather. You never know what obscure paper in the scientific literature (or small disturbance in the atmosphere) will eventually produce a deluge of new research (or rain).
One such paper appeared 50 years ago in the Journal of the Atmospheric Sciences. Its title, “Deterministic Nonperiodic Flow,” did not excite anybody. And its author, Edward Lorenz, was shy and not predisposed to seeking publicity. But in the decades that followed, that paper spawned a cyclone of scientific activity impacting fields ranging from meteorology and mathematics to astronomy, geology, neuroscience and medicine.
In short, that paper created chaos.
Actually, Lorenz did not use the term chaos in his 1963 paper, but he captured the idea that now goes by that name. He was studying the equations that describe the atmosphere, trying to figure out how well math could be used to forecast the weather. He found that even if you had all the right equations for describing changes in the atmosphere, you couldn’t predict the weather very far into the future.
“Two states differing by imperceptible amounts may eventually evolve into two considerably different states,” he wrote. “If, then, there is any error whatever in observing the present state — and in any real system such errors seem inevitable — an acceptable prediction of an instantaneous state in the distant future may well be impossible.”
In other words, you have to know all the current conditions of the atmosphere, everywhere within it, to predict what the atmosphere will be doing in the distant future. “In view of the inevitable inaccuracy and incompleteness of weather observations, precise very-long-range forecasting would seem to be nonexistent,” Lorenz concluded. So even if the molecules in the air all interacted nonrandomly, in a totally cause-and-effect (deterministic) manner, you still couldn’t predict with certainty what they would do or what the weather would be.
This insight into the weather came to be known as the “butterfly effect,” the suggestion that flapping wings in one locale can cause an atmospheric calamity far away. Originally, Lorenz attributed such flapping power to seagulls. “One meteorologist remarked that if the theory were correct, one flap of a seagull’s wings would be enough to alter the course of the weather forever,” Lorenz said when lecturing on his new paper in 1963.
Butterflies became the protagonists of chaos theory only much later. That switch came from the title given to a lecture Lorenz delivered in 1972: “Predictability: Does the Flap of a Butterfly’s Wings in Brazil Set Off a Tornado in Texas?”
In the beginning, the flapping of wings was actually just the rounding of numbers. Lorenz, a meteorology professor at MIT, had been . . .