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Page 15
... moving . His eyes , dart- ing at times , would be fixed reflectively when he was considering some questions ... He would try to elucidate other persons ' thoughts by asking questions in a Socratic manner , yet more con- cretely than in ...
... moving . His eyes , dart- ing at times , would be fixed reflectively when he was considering some questions ... He would try to elucidate other persons ' thoughts by asking questions in a Socratic manner , yet more con- cretely than in ...
Page 49
... moving it away from the unrealistic assumption of random pairing toward a pattern of " assortative " mating . This move is curiously parallel to the later work of Everett and Ulam on branching processes in several dimensions ( Everett ...
... moving it away from the unrealistic assumption of random pairing toward a pattern of " assortative " mating . This move is curiously parallel to the later work of Everett and Ulam on branching processes in several dimensions ( Everett ...
Page 99
... moving apart , and the criterion then is that the relative positions of the limit points become uncorrelated - a feature of chaos . Unfortunately , no numerical experiment can prove that some limit set is a strange attractor . For ...
... moving apart , and the criterion then is that the relative positions of the limit points become uncorrelated - a feature of chaos . Unfortunately , no numerical experiment can prove that some limit set is a strange attractor . For ...
Page 110
... moving . Each particle of water has an initial and final position . The operation has thus defined a transformation of the interior of the glass into itself . Since water is viscous , this transformation is continuous and its inverse is ...
... moving . Each particle of water has an initial and final position . The operation has thus defined a transformation of the interior of the glass into itself . Since water is viscous , this transformation is continuous and its inverse is ...
Page 129
... moving it across a two- dimensional scale drawing of the nuclear device or reactor assembly being studied . The trolley drew a path as it rolled , stopping for changes in drum settings whenever a material boundary was crossed . This ...
... moving it across a two- dimensional scale drawing of the nuclear device or reactor assembly being studied . The trolley drew a path as it rolled , stopping for changes in drum settings whenever a material boundary was crossed . This ...
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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.