When meteorologist Ed Lorenz, the so-called “father of chaos theory,” first invoked a butterfly’s wings, it wasn’t to say that we can’t predict the weather in New York because we can’t account for all the butterflies in China.
On the contrary, Lorenz was actually saying that even if we could account for every skipper and swallowtail along the Yellow Sea, it wouldn’t do much to improve weather forecasts.
Here is the story behind the confusion, as recounted in a 2014 paper by physicist Timothy Palmer, mathematician Gregory Seregin and mathematical physicist Andreas Doering. At the time, all of them were affiliated with the University of Oxford. Palmer further detailed the mix-up in a 2017 lecture at Oxford.
In his early years at MIT in the 1950s, Lorenz studied long-range weather forecasting. The statisticians he worked with thought it should be possible to predict the weather weeks or months away by scouring the historical record to see what happened previously when conditions were the same. Find an old weather map that looks like today’s weather map, and you should be able to make forecasts by reviewing the maps that followed, they said.
Lorenz was skeptical of this idea. He argued that the atmosphere is so complex that it never repeats itself, so it would be impossible to find a day in history when conditions were precisely the same. And, as he discovered, even small differences in the initial conditions can lead to vastly different outcomes.
The eureka moment came when Lorenz tried to rerun a computer weather simulation but, as a result of a rounding error, he punched in slightly different numbers. He went to grab a cup of coffee, and when he returned, he saw the simulation had diverged wildly from the previous run.
His tiny error didn’t stay tiny, as one might have expected. It grew exponentially larger. Lorenz described his discovery in a landmark 1963 paper.
The implication for meteorologists was clear: If they wanted to forecast the weather next week accurately, they needed to know more about the weather today. The more they knew, the further ahead they could predict the weather. The difference between a two-day forecast and a two-month forecast was just a matter of precision — or so it seemed.
As Lorenz considered this idea, however, he came to believe that there must be some limit on how far into the future you could make predictions. Say that instead of charting the rough contours of a weather system, you could learn the details of every storm. That might extend the accuracy of your forecast by a few hours, he said. What if you could map the inside of every cloud? That might buy you a few extra minutes.
And what if you could account for the flap of every butterfly’s wings all around the globe? How much would that improve your forecast?
“The answer is it would only improve it by seconds,” Palmer, the atmospheric physicist at the University of Oxford, said in an email. “It may be that you just cannot predict beyond a certain finite time horizon, no matter how accurate your initial conditions are.”
In an interview, Palmer said that when author James Gleick popularized Lorenz’s work in his acclaimed book, “Chaos: Making a New Science,” he used the term “the butterfly effect” to describe the 1963 paper, which found that weather forecasts are sensitive to small changes in the initial conditions, and not the 1969 paper, which found that learning more about the initial conditions yields diminishing returns.
Gleick said this distinction wasn’t important for his purposes, adding that chaos scientists have used the term to describe various related phenomena.
“The Butterfly Effect isn’t one simple idea; it encompasses a set of mathematical discoveries that have been expressed in different ways at different times,” he said in an email.
It’s easy to see how “the butterfly effect” could have come to take on multiple meanings. Lorenz wrote about the term’s “cloudy history” in his book, “The Essence of Chaos,” noting that his 1963 paper featured a graph that was said to resemble a butterfly, which may have created some confusion.
Clouding matters further, the term “the butterfly effect” calls to mind a 1952 short story by Ray Bradbury about a time traveler who steps on a butterfly in the prehistoric past, changing the outcome of a presidential election in 2055.
Bradbury’s description of the butterfly’s death presaged Lorenz’s work on chaos theory more than a decade later. It also gestured at the definition of “the butterfly effect” later employed by countless popularizers of science, from Goldblum to Gleick.
“It fell to the floor, an exquisite thing, a small thing that could upset balances and knock down a line of small dominoes and then big dominoes and then gigantic dominoes, all down the years across Time,” Bradbury wrote. “. . . Killing one butterfly couldn’t be that important! Could it?”