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Page 42
... example , in their spatial or dynamical , and hence also in their reproductive , characteristics . My own related work was inspired partly by a conversation we had about one of the great and vital mysteries of mathematics . The Greeks ...
... example , in their spatial or dynamical , and hence also in their reproductive , characteristics . My own related work was inspired partly by a conversation we had about one of the great and vital mysteries of mathematics . The Greeks ...
Page 44
... example after possible example . I recall his ruminations about the Monte Carlo method in 1944 , when already he was talking about it . More than fifty years ago there began to appear small compilations of random numbers . I remember ...
... example after possible example . I recall his ruminations about the Monte Carlo method in 1944 , when already he was talking about it . More than fifty years ago there began to appear small compilations of random numbers . I remember ...
Page 45
... example of the kind of transformation I have talked about . It concerns the zeros of a certain function in the complex domain and , if true , implies a whole batch of propositions in number theory . Many of these can be proved ...
... example of the kind of transformation I have talked about . It concerns the zeros of a certain function in the complex domain and , if true , implies a whole batch of propositions in number theory . Many of these can be proved ...
Page 49
... example . The second modification is necessary to give context for the first . It generalizes the original scheme , moving it away from the unrealistic assumption of random pairing toward a pattern of " assortative " mating . This move ...
... example . The second modification is necessary to give context for the first . It generalizes the original scheme , moving it away from the unrealistic assumption of random pairing toward a pattern of " assortative " mating . This move ...
Page 53
... examples in mind that motivated his choice of mathemati- cal model or method . In this regard one of his favorite quotes , from Shakespeare's Henry VIII , was Things done without example in their issue Are to be feared . In approaching ...
... examples in mind that motivated his choice of mathemati- cal model or method . In this regard one of his favorite quotes , from Shakespeare's Henry VIII , was Things done without example in their issue Are to be feared . In approaching ...
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Popular passages
Page 299 - Talibus orabat dictis, arasque tenebat, cum sic orsa loqui vates : ' Sate sanguine divom, 125 Tros Anchisiade, facilis descensus Averno ; noctes atque dies patet atri janua Ditis ; sed revocare gradum superasque evadere ad auras, hoc opus, hie labor est.
Page 231 - But it is not always so; it may happen that small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. Prediction becomes impossible, and we have the fortuitous phenomenon.
Page 210 - The low-velocity equation of state for a lattice gas can be written as p - ^p (l - |v2), where p is the pressure, p is the density, and v is the flow speed.
Page 316 - Southeastern Conference on Combinatorics. Graph Theory, and Computing (Florida Atlantic University, Boca Raton, Florida, April 2-6, 1979), 3-18.
Page 121 - He is a member of the National Academy of Sciences and a Fellow of the American Academy of Arts and Sciences, the American Physical Society and the American Association for the Advancement of Science.
Page 231 - A very small cause which escapes our notice determines a considerable effect 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...
Page 224 - Instead, we conclude by remarking that really efficient high-speed computing devices may, in the field of non-linear partial differential equations as well as in many other fields, which are now difficult or entirely denied of access, provide us with those heuristic hints which are needed in all parts of mathematics for genuine progress.
Page 272 - Let us say here that the results of our computations show features which were, from the beginning, surprising to us. Instead of a gradual, continuous flow of energy from the first mode to the higher modes, all of the problems show an entirely different behavior.
Page 58 - That was dramatized by Bertrand, who considered the problem of finding the probability that a chord of a circle chosen "at random" be longer than the side of an equilateral triangle inscribed in the circle.