...conditions produce very great differences in the final phenomena; a slight error in the former would make an enormous error in the latter. Prediction becomes...impossible and we have the fortuitous phenomenon. Our second example will be very analogous to the first and we shall take it from meteorology. Why have...

...imperceptible would evolve along completely different pathways. In such systems, Poincare wrote in 1908, "small differences in the initial conditions produce very great ones in the final phenomena. A small one in the former will produce an enormous error in the latter. Prediction becomes impossible, and...

...differences are not adopted, the actual results will differ from the expected. As Poincare has put it, ". . . small differences in the initial conditions produce very great ones in the final phenomena. . . . Prediction becomes impossible, and we have the fortuitous phenomenon."1' However, deviations...

...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...in the former will produce an enormous error in the later. Prediction becomes impossible, and we have the fortuitous phenomenon." Despite Poincare^s remarkable...

...conditions f0Juce very great ones in the final phenomena. A sma// f- in the former will produce an fff enormous error in the latter. Prediction becomes impossible, and we have the fortuitous phenomenon. Hence, the crucial ingredient in deterministic chaos is a very sensitive dependence on initial conditions....

...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...in the former will produce an enormous error in the later. Prediction becomes impossible, and we have the fortuitous phenomenon." Despite Poincare's remarkable...

...been predicted, that it is ruled by laws. But this is not always the case; it may happen that slight differences in the initial conditions produce very great ones in the final phenomena; a slight error in the former would make an enormous error in the latter. Prediction becomes impossible...

...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...

...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...impossible, and we have the fortuitous phenomenon. There is no contrast greater than this in today's science. Laplace championed the intrinsic knowability...

...dependence on initial conditions (cf. Gleick 1987) first enunciated by Poincare (1952, p. 68) in the form: small differences in the initial conditions produce very great ones in the final phenomena (see Endnote 8.1). Another of the many ironies in the history of science is that none (to my knowledge)...