Monday, December 19, 2011

"Butterfly Effect"

Can a Butterfly in Brazil Really Cause a Tornado in Texas?

Date: 13 December 2011 Time: 04:22 PM ET
butterfly effect
Morpho butterfly overlayed over one of two trajectories of the Lorenz attractor. The starting point of the two trajectories differ by one-100,000th of a unit, and their paths start to diverge after 23 time steps.
CREDIT: Creative Commons | Asturnut (butterfly), Creative Commons | Hellisp (attractors)
It's poetic, the notion that the flap of a butterfly's wing in Brazil can set off a cascade of atmospheric events that, weeks later, spurs the formation of a tornado in Texas. This so-called "butterfly effect" is used to explain why chaotic systems like the weather can't be predicted more than a few days in advance. One can't know every little factor affecting the atmosphere — every flutter of every butterfly in Brazil — so there's little hope of foreseeing the exact time and place a storm will touch down weeks later.
The butterfly effect is all the more pleasing because the computer model that led to its discovery resembles a butterfly. The mathematician Edward Lorenz created the model, called a strange attractor, in the 1960s; it's a line that alternately spirals around two adjacent ovals, mapping out the chaotic solution to a set of interrelated equations. Lorenz found that the shape of the attractor was extremely sensitive to initial conditions. Moving its starting point just a wing's scale in any direction caused the line to draw a completely different butterfly.
The strange attractor led scientists to conclude that many real-world systems — the stock market, the Texas tornado season — must be similarly unpredictable, and the butterfly effect has continued to be invoked as an explanation of chaos ever since. However, this is in spite of the fact that it's actually false: A butterfly in Brazil can flutter as hard as it likes, but it still can't whip up a tornado in Texas.
"If a butterfly flaps its wings the effect really just gets damped out," the mathematician and writer David Orrell told Life's Little Mysteries.



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