...use above,— at the cost of doing incomplete justice to Poinoare's most admirable style. example. " It may happen that small differences in the initial...in the former will produce an enormous error in the latter. Prediction becomes impossible, and we have the fortuitous phenomenon." " The greatest chance...

...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...

...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...

...in the present causes a much larger "amplified" change in the future. In 1903 he pointed out that: [e]ven if it were the case that the natural laws had...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...

...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...in the former will produce an enormous error in the latter. Prediction becomes impossible, and we have the fortuitous phenomenon. There is no contrast...

...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)...

...mathematician Henri Poincaré in his book Science and Method (as cited by Ivars Peterson in Newton's Clock): If we knew exactly the laws of nature and the situation...in the former will produce an enormous error in the latter. Prediction becomes impossible, and we have the fortuitous phenomenon. One of the papers that...

...universe at a succeeding moment. But, even if it were the case that the natural laws had lo nonger any secret for us, we could still only know the initial...in the former will produce an enormous error in the latter. Prediction becomes impossible, and we have the fortuitous phenomenon.17 In general, the state...

...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...in the former will produce an enormous error in the latter. Prediction becomes impossible, and we have the fortuitous phenomenon. " Laplace believed in...