The butterfly effect is a phrase that encapsulates the more technical notion of sensitive dependence on initial conditions in chaos theory. Small variations of the initial condition of a dynamic system may produce large variations in its long term behavior. This is sometimes presented as esoteric behavior, but can be exhibited by very simple systems: for example, a ball placed at the crest of a hill might roll into any of several valleys depending on slight differences in initial position.
The phrase refers to the idea that a butterfly’s wings might create tiny changes in the atmosphere that may ultimately alter the path of a tornado or delay, accelerate or even prevent the occurrence of a tornado in a certain location. The flapping wing represents a small change in the initial condition of the system, which causes a chain of events leading to large-scale alterations of events. Had the butterfly not flapped its wings, the trajectory of the system might have been vastly different. While the butterfly does not cause the tornado, the flap of its wings is an essential part of the initial conditions resulting in a tornado.
Although a butterfly flapping its wings has remained constant in the expression of this concept, the location of the butterfly, the consequences, and the location of the consequences have varied widely.
Recurrence, the approximate return of a system towards its initial conditions, together with sensitive dependence on initial conditions are the two main ingredients for chaotic motion. They have the practical consequence of making complex systems, such as the weather, difficult to predict past a certain time range, since it is impossible to measure the starting atmospheric conditions completely accurately.
The term “butterfly effect” itself is related to the work of Edward Lorenz, an American mathematician and meteorologist, and is based in Chaos Theory and sensitive dependence on initial conditions. It was first described in literature by the French mathematician Jacques Hadamard in 1890, and popularized in Pierre Duhem’s 1906 book La théorie physique son objet et sa structure (The physical theory, its purpose and structure).
The idea that one butterfly could eventually have a far-reaching ripple effect on subsequent historic events seems first to have appeared in a 1952 short story by the cience fiction author Ray Bradbury, although Lorenz made the term popular. In 1961, Lorenz was using a numerical computer model to rerun a weather prediction, when, as a shortcut on a number in the sequence, he entered the decimal .506 instead of entering the full .506127 the computer would hold.
The result was a completely different weather scenario. Lorenz published his findings in a 1963 paper for the New York Academy of Sciences noting that “One meteorologist remarked that if the theory were correct, one flap of a seagull’s wings could change the course of weather forever.” Later speeches and papers by Lorenz used the more poetic butterfly. According to Lorenz, upon failing to provide a title for a talk he was to present at the 139th meeting of the American Association for the Advancement of Science in 1972, Philip Merilees concocted “Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?” as a title.