The butterfly effect: what chaos theory actually says.

A butterfly flaps its wings, and a hurricane hits somewhere many miles away. Can these two events possibly be related? This popular adage is called the butterfly effect.

It must be said that the flapping of a butterfly's wings is not actually known to be the cause of any natural disaster — but the idea gets at the driving force of chaos theory. The common theme is sensitive dependence on initial conditions. The butterfly effect has become a common term for any situation where a small change is supposed to be the cause of larger consequences.

The butterfly effect, an underlying principle of chaos, describes how a small change in one state can result in large differences in a later state. A metaphor for this behaviour is that a butterfly flapping its wings in Brazil can cause a tornado in Texas.

Small differences in initial conditions — such as those due to errors in measurement, or rounding errors in numerical computation — can yield widely diverging outcomes for such systems, making long-term prediction of their behaviour impossible in general.

Chaos is seen in natural systems like weather patterns and traffic patterns. Knowing this matters, because it lets us build better prediction tools for weather, or design roads more efficiently. Well, now you know why the adage is so popular — and how butterflies and math are connected.