What is the butterfly effect, and what did Lorenz find?

The butterfly effect is the idea that very small differences at the start of a system can lead to very large differences later. Its technical name is sensitive dependence on initial conditions. MIT meteorologist Edward Lorenz identified it while running a computer model of weather, and it implies that precise long-range weather forecasting is not possible. [1] [2]

Lorenz built a simplified weather model from 12 differential equations, run on a slow Royal McBee computer. In the winter of 1961 he wanted to re-examine one sequence, so rather than start over he restarted partway through, typing in values from an earlier printout. The computer stored six decimal places, such as .506127, but the printout showed only three, .506. [2]

He left to get coffee, and when he returned the new run had diverged from the old one so fast that within a few simulated months the two no longer resembled each other. He first suspected a failing vacuum tube, but the machine was working. The difference of about one part in a thousand was the cause. The equations were fully deterministic, so the divergence was not random noise in the machine. [2] [1]

Many scientists had been taught that small perturbations produce small changes. Earlier erratic behavior from deterministic equations had tended to be dismissed as calculation error. Lorenz recognized it as a real feature of the system, and he showed it in a simple, physically relevant model. He also saw that this sensitivity explains why the simulated weather never repeated exactly. [2] [1]

In 1963 he published "Deterministic Nonperiodic Flow," using just three variables to describe a heated gas in a box. He wrote that two states differing by imperceptible amounts may evolve into considerably different states, so an acceptable prediction of the distant future may well be impossible. The paper did not use the word chaos, and it was cited only three times by researchers outside meteorology in the following decade. [1] [3]

The butterfly came later. In his 1963 lecture Lorenz relayed a remark about a seagull's wings altering the weather. The butterfly arrived with the title of a 1972 talk: "Predictability: Does the Flap of a Butterfly's Wings in Brazil Set Off a Tornado in Texas?" [3] [4]

A common misreading treats this as a claim that butterflies cause tornadoes. Lorenz did not answer his own title question. He noted that a flap that could cause a tornado might equally prevent one, and shortly before his death in 2008 he said he did not know whether a butterfly's disturbance could be magnified into a tornado. The popular line about Brazil and Texas is a illustration of sensitivity, not a demonstrated cause. [3]