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Charles Miller Chaos and the Logistic Map February 2001 |
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Chaos Theory and the Knuckleballer
On the mound you stand -just so- exhale -so-
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Let's consider the poem opening this report. If you dont know what a knucleball is, www.dictionary.com defines it as, in baseball, ``a slow randomly fluttering pitch thrown by gripping the ball with the tips or nails of two or three fingers.'' A knuckleball pitcher can have, on any given day, a geat outing or a terrible one, but its impossible to tell which will happen when. The poem attributes the pitcher's performance to chaos theory; small variations in the pitcher's enviroment affect his performance. Sometimes, it can be impossible to pitch well - ``its like trying to throw an oak``its like trying to throw an oak leaf / across the street into your neighbour's half-closed mailbox''. Otherdays, hitters cant hit his pitch. But sometimes, when the pitcher is doing everything right, hitters still hit the ball ``right out of the park''. Some variables McCaffery suggests may affect what happens to the pitcher are a slight breeze, a drop of sweat, a mosquito, and a fat guy in the stands blowing on his coffee. McCaffery is saying that the only way a knuckleball pitcher can guarantee that he'll throw two pitches exactly the same is that if everything is exactly the same as it was on the first pitch. If even the smallest thing is different, like a man blows on his coffee, for the second pitch, all bets are off - the chaos theory kicks in.
There are other examples of chaos theory expressed in less poetic ways. A popular example is the butterfly effect, discussed at www.pha.jhu.edu/~ldb/seminar/butterfly.html. The butterfly effect says that ``a butterfly flapping its wings in South America can affect the weather in Central Park''. You can replace South America and Central Park with any other two places you'd like. It was `discovered' by Edward Lorenz, who wanted to construct a mathematical model of the weather. When running the model a second time Lorenz got much different results, due to his rounding off data. Obviously the parts of the data he left ous of the data he left out played a huge part in the model. Chaos effect took effect again.
Obviously there is something to Chaos Theory. If there wasn't Lorenz would have gotten 2 similar results. But the picture on the web page shows 2 very different results. However, I'm not sure how close initial conditions have to be to repeat a trial a get similar results. Can a fat guy blowing on his coffee really affect a knuckleball? Can a butterfly in South America change the weather in New York? I'm going to say a reluctant no; a single butterfly or a single breath cant do that much. However, as I continue my math career, perhaps I'll change my mind. That is, of course, unless a butterfly flaps its wings in Africa, which will change the weather in Pitsburgh, which will change my mood, which will cause me to think differently about chaos theory.