Chaos Theory (a.k.a. The Butterfly Effect)

Chaos theory attempts to explain the fact that complex and unpredictable results can and will occur in systems that are sensitive to their initial conditions. A common example of this is known as the Butterfly Effect. It states that, in theory, the flutter of a butterfly's wings in China could, in fact, actually effect weather patterns in New York City, thousands of miles away. In other words, it is possible that a very small occurance can produce unpredictable and sometimes drastic results by triggering a series of increasingly significant events.

The butterfly effect is a metaphor that encapsulates the concept of sensitive dependence on initial conditions in chaos theory; namely that small differences in the initial condition of a dynamical system may produce large variations in the long term behavior of the system. Although this 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 involving time travel and with "what if" scenarios where one storyline diverges at the moment of a seemingly minor event resulting in two significantly different outcomes.

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 (approximately a week in the case of weather), since it is impossible to measure the starting atmospheric conditions completely accurately.

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 (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.

The concept of the butterfly effect is frequently referred to in popular culture in terms of the novelty of a minor change in circumstances causing a large change in outcome.

The term is sometimes used in popular media dealing with the idea of time travel, usually inaccurately. Most time travel depictions simply fail to address butterfly effects. According to the actual theory, if history could be "changed" at all (so that one is not invoking something like the Novikov self-consistency principle which would ensure a fixed self-consistent timeline), the mere presence of the time travelers in the past would be enough to change short-term events (such as the weather) and would also have an unpredictable impact on the distant future. Therefore, no one who travels into the past could ever return to the same version of reality he or she had come from and could have therefore not been able to travel back in time in the first place, which would create a phenomenon known as time paradox.