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CT: The mathematics of chaos has been popularized through the notion of the butterfly effect: the possibility that a large storm in New England may be caused by a butterfly wing flap in China. There are problems with this simple notion. These problems are keys to recognizing the difference between the models of chaos and the application of these ideas in most real complex systems.
To explain the difficulty, consider the many butterflies that might be responsible for a storm. Which butterfly was responsible? The answer is any or none of them depending on the specifics of the conditions.
It is reasonable to say that most of the time, nothing a butterfly will do can be connected in any way to the existence of a storm in New England. The reason is that particular conditions are necessary in order for sensitivity to exist. For example, hurricanes can be found in New England, but they occur during hurricane season.
S: http://necsi.edu/guide/concepts/butterflyeffect.html (last access: 29 January 2016)
N: 1. butterfly (n): Old English buttorfleoge, evidently butter (n.) + fly (n.), but of obscure signification. Perhaps based on the old notion that the insects (or witches disguised as butterflies) consume butter or milk that is left uncovered. Or, less creatively, simply because the pale yellow color of many species’ wings suggests the color of butter. Another theory connects it to the color of the insect’s excrement, based on Dutch cognate boterschijte. An overview of words for “butterfly” in various languages can be found here. Also see papillon.
Applied to persons from c. 1600, originally in reference to vain and gaudy attire; by 1806 in reference to transformation from early lowly state; in reference to flitting tendencies by 1873. The swimming stroke so called from 1936. Butterflies “light stomach spasms caused by anxiety” is from 1908.
The butterfly effect is a deceptively simple insight extracted from a complex modern field. As a low-profile assistant professor in MIT’s department of meteorology in 1961, (Edward) Lorenz created an early computer program to simulate weather. One day he changed one of a dozen numbers representing atmospheric conditions, from .506127 to .506. That tiny alteration utterly transformed his long-term forecast, a point Lorenz amplified in his 1972 paper, “Predictability: Does the Flap of a Butterfly’s Wings in Brazil Set Off a Tornado in Texas?” (Peter Dizikes, “The Meaning of the Butterfly,” The Boston Globe, June 8, 2008).
effect (n): mid-14c., “execution or completion (of an act),” from Old French efet (13c., Modern French effet) “result, execution, completion, ending,” from Latin effectus “accomplishment, performance,” from past participle stem of efficere “work out, accomplish,” from ex- “out” + facere “to do”. From French, borrowed into Dutch, German, Scandinavian.
From late 14c. as “power or capacity to produce an intended result; efficacy, effectiveness,” and in astrology, “operation or action (of a heavenly body) on human affairs; influence.” Also “that which follows from something else; a consequence, a result.” From early 15c. as “intended result, purpose, object, intent.” Also formerly with a sense of “reality, fact,” hence in effect (late 14c.), originally “in fact, actually, really.” Meaning “impression produced on the beholder” is from 1736. Sense in stage effect, sound effect, etc. first recorded 1881.
2. Edward Lorenz was a mathematician and meteorologist at the Massachusetts Institute of Technology who loved the study of weather. With the advent of computers, Lorenz saw the chance to combine mathematics and meteorology. He set out to construct a mathematical model of the weather, namely a set of differential equations that represented changes in temperature, pressure, wind velocity, etc. In the end, Lorenz stripped the weather down to a crude model containing a set of 12 differential equations.
3. A property of chaotic systems (as the atmosphere) by which small changes in initial conditions can lead to large-scale and unpredictable variation in the future state of the system.
4. A computer-modeled weather forecasting experiment by Edward Lorenz that helped understand an essential property of nonlinear phenomena i.e. the sensitivity to initial conditions characteristic of fractals.
5. The Butterfly effect: for small pieces of weather – and to a global forecaster, small can mean thunderstorms and blizzards – any prediction deteriorates rapidly. Errors and uncertainties multiply, cascading upward through a chain of turbulent features, from dust devils and squalls up to continent-size eddies that only satellites can see.
6. Cultural Interrelation: We can mention the movie The Butterfly Effect (2004) directed by Eric Bress, J. Mackye Gruber.
S: 1. OED – http://www.etymonline.com/index.php?search=Butterfly+effect (last access: 29 January 2016). 2. http://www.stsci.edu/~lbradley/seminar/butterfly.html (last access: 29 January 2016). 3. MW – http://www.merriam-webster.com/dictionary/butterfly%20effect (last access: 29 January 2016). 4 & 5. TERMIUM PLUS (last access: 29 January 2016). 6. http://www.rottentomatoes.com/m/butterfly_effect/ (last access: 29 January 2016).
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