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Page 11
... idea of the notions of length , area and volume , that is to say , the concept of measure and the for- mulation of what should be called probability . Panorama of Lwów in the 1970s In 1932 I was invited to give a short communi- cation ...
... idea of the notions of length , area and volume , that is to say , the concept of measure and the for- mulation of what should be called probability . Panorama of Lwów in the 1970s In 1932 I was invited to give a short communi- cation ...
Page 12
... idea of " category " of sets . " Category " is a notion in a way parallel to but less quantitative than the measure ... ideas and definitions connected with this had been initiated in the nineteenth century by Boltzmann . 1941 Becomes ...
... idea of " category " of sets . " Category " is a notion in a way parallel to but less quantitative than the measure ... ideas and definitions connected with this had been initiated in the nineteenth century by Boltzmann . 1941 Becomes ...
Page 13
... idea of order for elements in a group . In our mathematical conversations , as always , I was the optimist , and had some general , sometimes only vague ideas . He supplied the rigor , the inge- nuities in the details of the proof , and ...
... idea of order for elements in a group . In our mathematical conversations , as always , I was the optimist , and had some general , sometimes only vague ideas . He supplied the rigor , the inge- nuities in the details of the proof , and ...
Page 14
... idea orally , and I would be ( I will be in Princeton on 13-15 glad to do so , if we can meet somewhere before you answer --- but suppose that there is no time . and in Washington on 16-17 of this month . ) I don't see that from Germany ...
... idea orally , and I would be ( I will be in Princeton on 13-15 glad to do so , if we can meet somewhere before you answer --- but suppose that there is no time . and in Washington on 16-17 of this month . ) I don't see that from Germany ...
Page 15
... idea of a " super " bomb , as the proposed thermonuclear hydrogen bomb was then called ... Teller's problem con- cerned the interaction of an electron gas with radiation ... This was the first technical problem in theoretical physics I ...
... idea of a " super " bomb , as the proposed thermonuclear hydrogen bomb was then called ... Teller's problem con- cerned the interaction of an electron gas with radiation ... This was the first technical problem in theoretical physics I ...
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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.