« Most systems behave linearly only when they are close to equilibrium, and only when we don’t push them too hard. »

Steven Strogatz1

Chaotic systems are sensitive to initial conditions. This sensitivity gives rise to a phenomenon known as the butterfly effect, so named for the work of MIT meteorologist and mathematician Edward Lorenz. In the 1950s, Lorenz was working on weather prediction computer models. One day he entered data into a program and left to get a coffee. When he returned, he found the predictions were completely different from when he’d entered the same data earlier that day. At first he thought there was some sort of technical error. Then Lorenz realized he’d accidentally entered a rounded-up number for one of the variables. The discrepancy was tiny, yet the differences in the results were stark.2

From this accident, Lorenz discovered chaos dynamics, or the butterfly effect. He found that it wasn’t just weather; other chaotic systems exhibited the same sensitivity to initial conditions. It explained why predicting the weather was such a challenge. In later research and talks, Lorenz compared the difference to the change in air pressure produced by the flap of a butterfly’s wings.

Predicting the future behavior of chaotic systems is difficult or impossible because modeling outcomes requires perfect understanding of starting conditions. Any inaccuracies will result in incorrect—perhaps drastically so—predictions. As we progress further into the future, the impact of such deviations is magnified further and further, so predictions become exponentially less accurate.3

The butterfly effect is significant because it contradicts many of our assumptions about the world. We tend to assume systems are deterministic and tiny differences shouldn’t matter too much. In a lot of what we encounter in our day-to-day life, that’s true. But it’s false for chaotic systems. Without perfect accuracy, we can’t make useful, comprehensive predictions about them. It’s often only possible to make probability-based predictions, hence why you might hear that there’s a 60% chance of rain tomorrow.

Since Isaac Newton first codified laws explaining the functioning of the universe at a fundamental level, people wondered whether it would one day be possible to completely understand the world. Could we one day identify all of the relevant laws and be able to predict everything? In 1814, the mathematician Pierre-Simon Laplace declared Newton’s laws would enable us, should we know the position and velocity of every particle in the universe, to predict anything, forever. Over a century later, computers made it seem as though we could put Laplace’s prediction to the test.4

The butterfly effect suggests otherwise. Even when we can identify deterministic rules, we cannot make perfect predictions. In the face of chaos, we should expect to be surprised. We may know the rules governing a chaotic system’s behavior, but we cannot know its precise initial conditions. When we look at the behavior of chaotic systems, we are in fact seeing the outcomes of deterministic rules. Even if we cannot predict their future behavior, it still has its own logic.

« For want of a nail the shoe was lost;

For want of a shoe the horse was lost;

For want of a horse the battle was lost;

For the failure of battle the kingdom was lost—

All for the want of a horseshoe nail.