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Harvey, A Chaos Is A Mathematical Phenomenon Too.

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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.

Now imagine a complex interacting system (like many upside-down pens placed in the vicinity to each other). Its behavior is described by perfect set of mathematical equations (similar to the differential equation above), but DUE to the fact that the solution of such equations is an exponent function, the behavior of such system is completely unpredictable.

Thus a chaos.

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