The Butterfly Effect

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Computers Suck at Creating Chaos

Mission Statement. Hassib has laid the groundwork for two scenarios, either of which would steer her story into beguiling territory. Will Rose begin to lose her grip on reality as she takes to writing Gameela, now ensconced in the hereafter, one letter after another?

Alas, neither. Rose never pens those letters! Despite the earlier appearance of foreshadowing, Hassib veers away from either of the bounty-lined paths we glimpsed on the horizon.

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She chooses another trajectory entirely, leaving the reader both mystified and disappointed. This in turn enables Hassib to reveal the varied and at times competing selves that make up each of her main characters. 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.

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.

A dynamical system displays sensitive dependence on initial conditions if points arbitrarily close together separate over time at an exponential rate. The definition does not require that all points from a neighborhood separate from the base point x , but it requires one positive Lyapunov exponent.


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The simplest mathematical framework exhibiting sensitive dependence on initial conditions is provided by a particular parametrization of the logistic map :. 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.

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So the direct impact of this phenomenon on weather prediction is often somewhat wrong. 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.

Other authors suggest that the butterfly effect can be observed in quantum systems. Karkuszewski et al. They investigate the level of sensitivity of quantum systems to small changes in their given Hamiltonians. They consider fidelity decay to be "the closest quantum analog to the purely classical butterfly effect". The journalist Peter Dizikes, writing in The Boston Globe in , notes that popular culture likes the idea of the butterfly effect, but gets it wrong. Whereas Lorenz suggested correctly with his butterfly metaphor that predictability "is inherently limited", popular culture supposes that each event can be explained by finding the small reasons that caused it.

Dizikes explains: "It speaks to our larger expectation that the world should be comprehensible — that everything happens for a reason, and that we can pinpoint all those reasons, however small they may be. But nature itself defies this expectation. From Wikipedia, the free encyclopedia.

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Idea that small causes can have large effects. For other uses, see Butterfly effect disambiguation.

Play media. Main article: Butterfly effect in popular culture.

Actuality and potentiality Avalanche effect Behavioral cusp Butterfly effect in popular culture Cascading failure Causality Chain reaction Clapotis Determinism Domino effect Dynamical systems Fractal Great Stirrup Controversy Innovation butterfly Kessler syndrome Law of unintended consequences Norton's dome Point of divergence Positive feedback Representativeness heuristic Ripple effect Snowball effect Traffic congestion Tropical cyclogenesis. Archived from the original on Retrieved March Journal of the Atmospheric Sciences.


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Bibcode : JAtS Retrieved January 6, The Philadelphia Inquirer. Chaos: Making a New Science. Retrieved 3 June Transactions of the New York Academy of Sciences. Archived PDF from the original on 10 October Retrieved 1 September Archived from the original on 11 November Retrieved 3 August New York: Springer. Nonlinear Processes in Geophysics. Bibcode : TellA..