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<description>  This multiplicative difficulty leading to the need for greater and greater&lt;br /&gt;precision in assumptions can be illustrated with the following simple exercise&lt;br /&gt;concerning the prediction of the movements of billiard balls on a&lt;br /&gt;table. I use the example as computed by the mathematician Michael Berry.&lt;br /&gt;If you know a set of basic parameters concerning the ball at rest, can compute&lt;br /&gt;the resistance of the table (quite elementary), and can gauge the&lt;br /&gt;strength of the impact, then it is rather easy to predict what would happen&lt;br /&gt;at the first hit. The second impact becomes more complicated, but possible;&lt;br /&gt;you need to be more careful about your knowledge of the initial&lt;br /&gt;states, and more precision is called for. The problem is that to correctly&lt;br /&gt;compute the ninth impact, you need to take into account the gravitational&lt;br /&gt;pull of someone standing next to the table (modestly, Berry's computations&lt;br /&gt;use a weight of less than 150 pounds). And to compute the fifty-sixth&lt;br /&gt;impact, every single elementary particle of the universe needs to be present&lt;br /&gt;in your assumptions! An electron at the edge of the universe, separated&lt;br /&gt;from us by 10 billion light-years, must figure in the calculations, since it&lt;br /&gt;exerts a meaningful effect on the outcome.&lt;br /&gt;  </description>
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<description>   :LOL:   </description>
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