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Harvey, A Chaos Is A Mathematical Phenomenon Too.
Forum List  Follow Ups  Post Message  Back to Thread Topics  In Response To Posted by Alexander on September 14, 2001 17:43:49 UTC 
Called exponential amplification of initial conditions. Place a pen on its tip as vertical as you can  and it will be practically impossible to predict which direction it falls. The equation of pen's behavior is d2x/dt2(g/l)x = 0, where x is pen's angular position, g  gravity, l  pen's length. This equation has the following solution: x = xoexp(sqrt(gt/l))). You may see, that very minor changes in initial angle xo results in exponentially large changes down the time (due to their profound difference in magnitude from the slight change of initial conditions we then call them catastrophically large). Moreover, if initial position was extremely symmetric (initial angle to be extremely small), then just an uncertanly of a position of just one atom due to mathematical property of waves which we call Heizenberg uncertanty principle may result in completely unpredictable direction of fall.


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