Born half a century ago, chaos theory languished for years

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 entering atmospheric readings by hand into a computer to run some forecasting programs. He was using a printout of the data on which numbers had been truncated from their original accuracy (.506127, for instance, had been rounded to .506). When Lorenz ran the program using the rounded numbers, he found dramatic differences from the forecast using the full six-digit data. He had discovered the key concept behind chaos: sensitive dependence on initial conditions.

In the years that followed, Lorenz worked out the implications for the weather. In the 1963 paper, he had not been able to calculate just how far the limit to accurate long-range forecasting would be. “Conceivably it could be a few days or a few centuries,” he wrote. But by 1969 he had pinned down the limit to something like three weeks. Of course, reaching even that theoretical limit would require readings from stations placed much too close together to be feasible.

In the years following his 1972 talk (at a meeting of the American Association for the Advancement of Science), the butterfly effect idea seeped into both scientific and popular culture. By the mid-1970s the term chaos was adopted to signify the effects of sensitive dependence on starting conditions. Chaos was found in everything from the forces generating earthquakes to the time interval between heartbeats. Astronomers detected evidence that planetary orbits embody chaos, rendering the far future of the solar system unpredictable. Neuroscientists implicated chaos (or lack thereof) in problems afflicting signaling among brain cells.

As for butterflies in Brazil causing tornadoes in Texas, Lorenz did not actually answer the question posed in the title of his 1972 talk.

He did point out that if a butterfly could cause a tornado, it’s also possible that the right flapping could also prevent a tornado. Shortly before his death in 2008, Lorenz still said he didn’t really know whether a butterfly’s disturbance of the air could be magnified into a tornado.

Nevertheless the idea that small differences today can make big differences tomorrow is sound and is now well-established in science and widely recognized by the public. And that 1963 paper, referenced only three times in the following 10 years outside of the island of meteorology, has now been cited more than 11,000 times, by researchers on every scientific continent.