How Not to Be Wrong: The Power of Mathematical Thinking

by Jordan Ellenberg

It’s tempting to imagine that predictions will just get better and better as our ability to gather data gets more and more powerful; won’t we eventually have the whole atmosphere simulated to a high precision in a server farm somewhere under The Weather Channel’s headquarters? Then, if you wanted to know next month’s weather, you could just let the simulation run a little bit ahead. It’s not going to be that way. Energy in the atmosphere burbles up very quickly from the tiniest scales to the most global, with the effect that even a minuscule change at one place and time can lead to a vastly different outcome only a few days down the road. Weather is, in the technical sense of the word, chaotic. In fact, it was in the numerical study of weather that Edward Lorenz discovered the mathematical notion of chaos in the first place. He wrote, “One meteorologist remarked that if the theory were correct, one flap of a sea gull’s wing would be enough to alter the course of the weather forever. The controversy has not yet been settled, but the most recent evidence seems to favor the sea gulls.” There’s a hard limit to how far in advance we can predict the weather, no matter how much data we collect. Lorenz thought it was about two weeks, and so far the concentrated efforts of the world’s meteorologists have given us no cause to doubt that boundary.