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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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