68.

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Page 164

		2.3.5— The Clockwork Universe and the Chaotic Universe

		It used to be thought that the Universe was like a great clock. If we could learn the equations that described the mechanisms of the great clock and if we knew the values of its variables at the present, then we could predict all the future values of the variables.

		However, if the mechanism of the Universe is chaotic, then we cannot predict all the future values of the variables. Even if we could learn the equations that described the mechanisms of the great clock and even if we knew the values of its variables at the present, then we could still not predict the future values of the variables. The uncertainty in this Universe does not arise from chance. It arises from the sensitivity to initial conditions.

		These two contrasting views were eloquently stated by Laplace in 1776 and Poincaré in 1890.

		1— Laplace: Clockwork Universe

		''The present state of the system of nature is evidently a consequence of what it was in the preceding moment, and if we conceive of an intelligence which at a given instant comprehends all the relations of the entities of this universe, it could state the respective positions, motions, and general effects of all these entities at any times in the past or future."

		2— Poincaré: Chaotic Universe

		"A very small cause which escapes our notice determines a considerable effect which that we cannot fail to see, and then we say that the effect is due to chance. If we knew exactly the laws of nature and the situation of the universe at the initial moment, we could predict exactly the situation of that same universe at a succeeding moment. But even if it were the case that the natural laws had no longer any secret for us, we could still only know the initial situation approximately. If that enables us to predict the succeeding situation with the same approximation, that is all we require, and we should say that the phenomenon had been predicted, that it is governed by laws. But it is not always so; it may happen that small differences in the initial conditions produce very great ones in the final phenomenon. A small error in the former will produce an enormous error in the latter. Prediction becomes impossible, and we have the fortuitous phenomenon"

 

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