# The Butterfly Effect [VERIFIED]

The Butterfly Effect is a 2004 American science fiction thriller film written and directed by Eric Bress and J. Mackye Gruber. It stars Ashton Kutcher, Amy Smart, Eric Stoltz, William Lee Scott, Elden Henson, Logan Lerman, Ethan Suplee, and Melora Walters. The title refers to the butterfly effect.

## The Butterfly Effect

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Roger Ebert wrote that he "enjoyed The Butterfly Effect, up to a point" and that the "plot provides a showcase for acting talent, since the actors have to play characters who go through wild swings." However, Ebert said that the scientific notion of the butterfly effect is used inconsistently: Evan's changes should have wider reverberations.[8] Sean Axmaker of the Seattle Post-Intelligencer called it a "metaphysical mess", criticizing the film's mechanics for being "fuzzy at best and just plain sloppy the rest of the time".[9] Mike Clark of USA Today also gave the film a negative review, stating, "Normally, such a premise comes off as either intriguing or silly, but the morbid subplots (there's prison sex, too) prevent Effect from becoming the unintentional howler it might otherwise be."[10] Additionally, Ty Burr of The Boston Globe went as far as saying, "whatever train-wreck pleasures you might locate here are spoiled by the vile acts the characters commit."[11]

Matt Soergel of The Florida Times-Union rated it 3 stars out of 4, writing, "The Butterfly Effect is preposterous, feverish, creepy and stars Ashton Kutcher in a dramatic role. It's a blast... a solidly entertaining B-movie. It's even quite funny at times..."[12] The Miami Herald said, "The Butterfly Effect is better than you might expect despite its awkward, slow beginning, drawing you in gradually and paying off in surprisingly effective and bittersweet ways," and added that Kutcher is "appealing and believable... The Butterfly Effect sticks to its rules fairly well... overall the film is consistent in its flights of fancy."[13] The Worcester Telegram & Gazette praised it as "a disturbing film" and "the first really interesting film of 2004," adding that Kutcher "carries it off": .mw-parser-output .templatequoteoverflow:hidden;margin:1em 0;padding:0 40px.mw-parser-output .templatequote .templatequoteciteline-height:1.5em;text-align:left;padding-left:1.6em;margin-top:0

In chaos theory, the butterfly effect is the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state.

The term is closely associated with the work of mathematician and meteorologist Edward Norton Lorenz. He noted that the butterfly effect is derived from the metaphorical example of the details of a tornado (the exact time of formation, the exact path taken) being influenced by minor perturbations such as a distant butterfly flapping its wings several weeks earlier. Lorenz originally used a seagull causing a storm but was persuaded to make it more poetic with the use of butterfly and tornado by 1972.[1][2] He discovered the effect when he observed runs of his weather model with initial condition data that were rounded in a seemingly inconsequential manner. He noted that the weather model would fail to reproduce the results of runs with the unrounded initial condition data. A very small change in initial conditions had created a significantly different outcome.[3]

The idea that small causes may have large effects in weather was earlier acknowledged by French mathematician and engineer Henri PoincarÃ©. American mathematician and philosopher Norbert Wiener also contributed to this theory. Lorenz's work placed the concept of instability of the Earth's atmosphere onto a quantitative base and linked the concept of instability to the properties of large classes of dynamic systems which are undergoing nonlinear dynamics and deterministic chaos.[4]

The idea that the death of one butterfly could eventually have a far-reaching ripple effect on subsequent historical events made its earliest known appearance in "A Sound of Thunder", a 1952 short story by Ray Bradbury. "A Sound of Thunder" features time travel.[8]

In 1963, Lorenz published a theoretical study of this effect in a highly cited, seminal paper called Deterministic Nonperiodic Flow[3][11] (the calculations were performed on a Royal McBee LGP-30 computer).[12][13] Elsewhere he stated:

The butterfly effect presents an obvious challenge to prediction, since initial conditions for a system such as the weather can never be known to complete accuracy. This problem motivated the development of ensemble forecasting, in which a number of forecasts are made from perturbed initial conditions.[15]

Some scientists have since argued that the weather system is not as sensitive to initial conditions as previously believed.[16] David Orrell argues that the major contributor to weather forecast error is model error, with sensitivity to initial conditions playing a relatively small role.[17][18] Stephen Wolfram also notes that the Lorenz equations are highly simplified and do not contain terms that represent viscous effects; he believes that these terms would tend to damp out small perturbations.[19] Recent studies using generalized Lorenz models that included additional dissipative terms and nonlinearity suggested that a larger heating parameter is required for the onset of chaos.[20]

While the "butterfly effect" is often explained as being synonymous with sensitive dependence on initial conditions of the kind described by Lorenz in his 1963 paper (and previously observed by PoincarÃ©), the butterfly metaphor was originally applied[1] to work he published in 1969[21] which took the idea a step further. Lorenz proposed a mathematical model for how tiny motions in the atmosphere scale up to affect larger systems. He found that the systems in that model could only be predicted up to a specific point in the future, and beyond that, reducing the error in the initial conditions would not increase the predictability (as long as the error is not zero). This demonstrated that a deterministic system could be "observationally indistinguishable" from a non-deterministic one in terms of predictability. Recent re-examinations of this paper suggest that it offered a significant challenge to the idea that our universe is deterministic, comparable to the challenges offered by quantum physics.[22][23]

The butterfly effect is most familiar in terms of weather; it can easily be demonstrated in standard weather prediction models, for example. The climate scientists James Annan and William Connolley explain that chaos is important in the development of weather prediction methods; models are sensitive to initial conditions. They add the caveat: "Of course the existence of an unknown butterfly flapping its wings has no direct bearing on weather forecasts, since it will take far too long for such a small perturbation to grow to a significant size, and we have many more immediate uncertainties to worry about. So the direct impact of this phenomenon on weather prediction is often somewhat wrong."[27] The two kinds of butterfly effects, including the sensitive dependence on initial conditions,[3] and the ability of a tiny perturbation to create an organized circulation at large distances,[1] are not exactly the same.[28] A comparison of the two kinds of butterfly effects[1][3] and the third kind of butterfly effect[21][22][23] has been documented.[29]

The potential for sensitive dependence on initial conditions (the butterfly effect) has been studied in a number of cases in semiclassical and quantum physics including atoms in strong fields and the anisotropic Kepler problem.[37][38] Some authors have argued that extreme (exponential) dependence on initial conditions is not expected in pure quantum treatments;[39][40] however, the sensitive dependence on initial conditions demonstrated in classical motion is included in the semiclassical treatments developed by Martin Gutzwiller[41] and John B. Delos and co-workers.[42] The random matrix theory and simulations with quantum computers prove that some versions of the butterfly effect in quantum mechanics do not exist.[43]

Other authors suggest that the butterfly effect can be observed in quantum systems. Zbyszek P. Karkuszewski et al. consider the time evolution of quantum systems which have slightly different Hamiltonians. They investigate the level of sensitivity of quantum systems to small changes in their given Hamiltonians.[44] David Poulin et al. presented a quantum algorithm to measure fidelity decay, which "measures the rate at which identical initial states diverge when subjected to slightly different dynamics". They consider fidelity decay to be "the closest quantum analog to the (purely classical) butterfly effect".[45] Whereas the classical butterfly effect considers the effect of a small change in the position and/or velocity of an object in a given Hamiltonian system, the quantum butterfly effect considers the effect of a small change in the Hamiltonian system with a given initial position and velocity.[46][47] This quantum butterfly effect has been demonstrated experimentally.[48] Quantum and semiclassical treatments of system sensitivity to initial conditions are known as quantum chaos.[39][46]

In simpler language, he theorized that weather prediction models are inaccurate because knowing the precise starting conditions is impossible, and a tiny change can throw off the results. To make the concept understandable to non-scientific audiences, Lorenz began to use the butterfly analogy.

In speeches and interviews, he explained that a butterfly has the potential to create tiny changes which, while not creating a typhoon, could alter its trajectory. A flapping wing represents the minuscule changes in atmospheric pressure, and these changes compound as a model progresses. Given that small, nearly imperceptible changes can have massive implications in complex systems, Lorenz concluded that attempts to predict the weather were impossible. Elsewhere in the paper, he writes: 041b061a72