You've probably heard of the so-called "butterfly effect," a bit of popularized science that suggests the minor perturbations of a single butterfly flapping its wings has the power to set off a string of escalating events that can lead to the formation of a hurricane.
It's a powerful metaphor, to be sure (a blockbuster film, starring Ashton Kutcher, was even premised on it), a compelling concept that also has a fair bit of complex science and mathematics behind it. Even so, as with most popularized science metaphors, it's also an idea that has become rather ... embellished. Can the flapping of an itty-bitty butterfly's wings really cause a hurricane? The answer, it turns out, is no. But it's complicated.
The metaphor of the butterfly effect was first articulated by mathematician Edward Lorenz, one of the pioneers of so-called "chaos theory," which is a serious branch of mathematics that focuses on dynamical systems that are highly sensitive to initial conditions. In other words, chaos theory deals with the mathematics of trying to predict outcomes of complex systems, when the initial conditions of those systems are impossible to monitor in their entirety.
Take traffic, for instance. A single car slamming on the brakes to avoid a squirrel on the road at an inopportune time could, conceivably, set off a chain of events that contribute to a major hours-long traffic jam. But predicting the movements and the causes of movements of all the cars on a highway (not to mention, all the squirrels!) make predicting such traffic conundrums intractable. The stock market is another similar example. So, too, is the weather.
And the weather, it turns out, was what Lorenz was attempting to predict when he asked himself if factoring in something as minor as a butterfly flapping its wings might actually be enough to alter our computer models of weather forecasts. Can a fluttering wing be the difference between a sunny day and a wild storm?
Chaos theory and the weather
According to Lorenz' rudimentary models, yes. Back in 1961, back when computers were giant room-sized machines, Lorenz was running weather models and found that by entering in the initial condition of 0.506 instead of a fuller, more precise 0.506127 value, he could get the computer to predict a storm rather than a sunny day. The difference in precision between these two values is incredibly small, about the scale of a butterfly flapping its wings.
It seems intuitively improbable that a butterfly wing could have so much power — and well, it is improbable. But is it impossible?
This is where the mathematics — and the philosophy — gets complicated, and controversial. With our more sophisticated models of weather prediction today, the general scientific consensus is rather firm: a wing flap can't possibly alter our large-scale weather predictions.
Here's why. While wing flaps certainly have an effect on the air pressure around the butterfly, this fluctuation is contained by the fact that the air's total pressure, which is about 100,000 times larger, shields it from such tiny perturbations. The changes that happen to the air around the butterfly are essentially trapped in a pressure bubble that get immediately dampened out as they ripple out from there.
The fact that Lorenz' computer models predicted large-scale changes from such minor altercations has more to do with the simplicity of those models than anything else. For instance, the same results that Lorenz encountered don't occur in modern computer models of weather. Once you input more relevant factors of a developing weather system — for instance, ocean temperatures, humidity levels, speed of winds and the wind shear, etc. — the flap of a wing, or lack thereof, won't have any affect on whether a storm system develops or not.
"Of course the existence of an unknown butterfly flapping its wings has no direct bearing on weather forecasts, since it will take far too long for such a small perturbation to grow to a significant size, and we have many more immediate uncertainties to worry about. So the direct impact of this phenomenon on weather prediction is often somewhat overstated," explained climate scientists James Annan and William Connolley.
But this doesn't mean that other relatively small factors can't have a major impact. Weather systems are still chaotic and sensitive to initial conditions. It just takes the correct initial conditions, and that might come down to a single cloud, or changes in our measurements of atmospheric convection, etc.
So while the butterfly effect might be a grossly simplistic metaphor, it's still a powerful one. Small altercations in the initial conditions of a complex system can drastically change our models of that system. A butterfly wing, perhaps not. But wind turbines or solar panels spread over a large enough area? Possibly.
Predicting the weather might never be perfect, but their accuracy is far less dependent on butterflies than popular culture might suggest. The fact that meteorologists can get their weather predictions as close to reality as they do, several days out, is a testament to our ability to tackle the mathematics of chaotic systems.