butterfly effect

wikipedia small

The butterfly effect is the concept that small causes can have large effects. Initially, it was used with weather prediction but later the term became a metaphor used in and out of science.

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 name, coined by Edward Lorenz for the effect which had been known long before, is derived from the metaphorical example of the details of a hurricane (exact time of formation, exact path taken) being influenced by minor perturbations such as the flapping of the wings of a distant butterfly several weeks earlier. Lorenz discovered the effect when he observed that runs of his weather model with initial condition data that was rounded in a seemingly inconsequential manner 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.

The idea, that small causes may have large effects in general and in weather specifically, was used from Henri Poincaré to Norbert Wiener. Edward Lorenz’s work placed the concept of instability of the 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.



Chaos theory and the sensitive dependence on initial conditions were described in the literature in a particular case of the three-body problem by Henri Poincaré in 1890. He later proposed that such phenomena could be common, for example, in meteorology.


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.


The journalist Peter Dizikes, writing in The Boston Globe in 2008, 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.”


adding page after watching the secret life of chaos.. via Jim Al-Khalili