BUTTERFLY EFFECT

In chaos theory, the butterfly effect is the sensitive dependence on initial conditions; where a small change at one place in a nonlinear system can result in large differences to a later state. The name of the effect, coined by Edward Lorenz, is derived from the theoretical example of a hurricane's formation being contingent on whether or not a distant butterfly had flapped its wings several weeks before.

Although the butterfly effect may appear to be an esoteric and unusual behavior, it is 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 butterfly effect is a common trope in fiction when presenting scenarios involvingtime travel and with "what if" cases where one storyline diverges at the moment of a seemingly minor event resulting in two significantly different outcomes.

The term "butterfly effect" itself is related to the work of Edward Lorenz, and it is based in chaos theory and sensitive dependence on initial conditions, already described in the literature in a particular case of the three-body problem by Henri Poincaré in 1890.^[1] He later proposed that such phenomena could be common, say in meteorology.

In 1898,^[1] Jacques Hadamard noted general divergence of trajectories in spaces of negative curvature, and Pierre Duhem discussed the possible general significance of this in 1908.^[1] The idea that one butterfly could eventually have a far-reaching ripple effect on subsequent historic events first appears in "A Sound of Thunder", a 1952 short story by Ray Bradbury about time travel (see Literature and print here) 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 result was a completely different weather scenario.^[2] Lorenz published his findings in a 1963 paper^[3] for the New York Academy of Sciences noting^{[citation needed]} that "One meteorologist remarked that if the theory were correct, one flap of a seagull's wings could change the course of weather forever." Following suggestions from colleagues, in later speeches and papers Lorenz used the more poetic butterfly. According to Lorenz, when Lorenz failed 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. 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.^[4]

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 atornado or delay, accelerate or even prevent the occurrence of a tornado in another 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 (compare: domino effect). 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 in the sense of providing the energy for the tornado, it does "cause" it in the sense that the flap of its wings is an essential part of the initial conditions resulting in a tornado, and without that flap that particular tornado would not have existed.