Frases de John Forbes Nash

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John Forbes Nash

Data de nascimento: 13. Junho 1928
Data de falecimento: 23. Maio 2015

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John Forbes Nash Jr. foi um matemático norte-americano que trabalhou com teoria dos jogos, geometria diferencial e equações diferenciais parciais, servindo como Matemático Sénior de Investigação na Universidade de Princeton. Compartilhou o Prêmio de Ciências Econômicas em Memória de Alfred Nobel de 1994 com Reinhard Selten e John Harsanyi.

Nash também foi conhecido por ter tido sua vida retratada no filme Uma Mente Brilhante, vencedor de quatro Óscars , baseado no livro-biográfico homônimo, que apresentou seu gênio para a matemática e sua luta contra a esquizofrenia.

Citações John Forbes Nash

„The writer has developed a “dynamical” approach to the study of cooperative games based upon reduction to non-cooperative form.“

— John Nash
Context: The writer has developed a “dynamical” approach to the study of cooperative games based upon reduction to non-cooperative form. One proceeds by constructing a model of the preplay negotiation so that the steps of negotiation become moves in a larger non-cooperative game [which will have an infinity of pure strategies] describing the total situation. This larger game is then treated in terms of the theory of this paper [extended to infinite games] and if values are obtained they are taken as the values of the cooperative game. Thus the problem of analyzing a cooperative game becomes the problem of obtaining a suitable, and convincing, non-cooperative model for the negotiation. The writer has, by such a treatment, obtained values for all finite two-person cooperative games, and some special n-person games. "Non-cooperative Games" in Annals of Mathematics, Vol. 54, No. 2 (September 1951)<!-- ; as cited in Can and should the Nash program be looked at as a part of mechanism theory? (2003) by Walter Trockel -->

„At the present time I seem to be thinking rationally again in the style that is characteristic of scientists.“

— John Nash
Context: At the present time I seem to be thinking rationally again in the style that is characteristic of scientists. However this is not entirely a matter of joy as if someone returned from physical disability to good physical health. One aspect of this is that rationality of thought imposes a limit on a person's concept of his relation to the cosmos.

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„A less obvious type of application (of non-cooperative games) is to the study of .“

— John Nash
Context: A less obvious type of application (of non-cooperative games) is to the study of. By a cooperative game we mean a situation involving a set of players, pure strategies, and payoffs as usual; but with the assumption that the players can and will collaborate as they do in the von Neumann and Morgenstern theory. This means the players may communicate and form coalitions which will be enforced by an umpire. It is unnecessarily restrictive, however, to assume any transferability or even comparability of the pay-offs [which should be in utility units] to different players. Any desired transferability can be put into the game itself instead of assuming it possible in the extra-game collaboration. "Non-cooperative Games" in Annals of Mathematics, Vol. 54, No. 2 (September 1951); as cited in Can and should the Nash program be looked at as a part of mechanism theory? (2003) by Walter Trockel

„One states as axioms several properties that it would seem natural for the solution to have and then one discovers that the axioms actually determine the solution uniquely. The two approaches to the problem, via the negotiation model or via the axioms, are complementary; each helps to justify and clarify the other.“

— John Nash
Context: We give two independent derivations of our solution of the two-person cooperative game. In the first, the cooperative game is reduced to a non-cooperative game. To do this, one makes the players’ steps of negotiation in the cooperative game become moves in the noncooperative model. Of course, one cannot represent all possible bargaining devices as moves in the non-cooperative game. The negotiation process must be formalized and restricted, but in such a way that each participant is still able to utilize all the essential strengths of his position. The second approach is by the axiomatic method. One states as axioms several properties that it would seem natural for the solution to have and then one discovers that the axioms actually determine the solution uniquely. The two approaches to the problem, via the negotiation model or via the axioms, are complementary; each helps to justify and clarify the other. "Non-cooperative Games" in Annals of Mathematics, Vol. 54, No. 2 (September 1951)<!-- ; as cited in Can and should the Nash program be looked at as a part of mechanism theory? (2003) by Walter Trockel -->

„Thus I have hopes of being able to achieve something of value through my current studies or with any new ideas that come in the future.“

— John Nash
Context: Statistically, it would seem improbable that any mathematician or scientist, at the age of 66, would be able through continued research efforts, to add much to his or her previous achievements. However I am still making the effort and it is conceivable that with the gap period of about 25 years of partially deluded thinking providing a sort of vacation my situation may be atypical. Thus I have hopes of being able to achieve something of value through my current studies or with any new ideas that come in the future.

„Gradually I began to intellectually reject some of the delusionally influenced lines of thinking which had been characteristic of my orientation. This began, most recognizably, with the rejection of politically-oriented thinking as essentially a hopeless waste of intellectual effort.“

— John Nash
Context: Gradually I began to intellectually reject some of the delusionally influenced lines of thinking which had been characteristic of my orientation. This began, most recognizably, with the rejection of politically-oriented thinking as essentially a hopeless waste of intellectual effort.

„You don't have to be a mathematician to have a feel for numbers.“

— John Nash
Context: You don't have to be a mathematician to have a feel for numbers. A movie, by the way, was made — sort of a small-scale offbeat movie — called Pi recently. I think it starts off with a big string of digits running across the screen, and then there are people who get concerned with various things, and in the end this Bible code idea comes up. And that ties in with numbers, so the relation to numbers is not necessarily scientific, and even when I was mentally disturbed, I had a lot of interest in numbers. Statement of 2006, partly cited in Stop Making Sense: Music from the Perspective of the Real (2015) by Scott Wilson, p. 117

„The writer has, by such a treatment, obtained values for all finite two-person cooperative games, and some special n-person games.“

— John Nash
Context: The writer has developed a “dynamical” approach to the study of cooperative games based upon reduction to non-cooperative form. One proceeds by constructing a model of the preplay negotiation so that the steps of negotiation become moves in a larger non-cooperative game [which will have an infinity of pure strategies] describing the total situation. This larger game is then treated in terms of the theory of this paper [extended to infinite games] and if values are obtained they are taken as the values of the cooperative game. Thus the problem of analyzing a cooperative game becomes the problem of obtaining a suitable, and convincing, non-cooperative model for the negotiation. The writer has, by such a treatment, obtained values for all finite two-person cooperative games, and some special n-person games. "Non-cooperative Games" in Annals of Mathematics, Vol. 54, No. 2 (September 1951)<!-- ; as cited in Can and should the Nash program be looked at as a part of mechanism theory? (2003) by Walter Trockel -->

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„Of course, one cannot represent all possible bargaining devices as moves in the non-cooperative game.“

— John Nash
Context: We give two independent derivations of our solution of the two-person cooperative game. In the first, the cooperative game is reduced to a non-cooperative game. To do this, one makes the players’ steps of negotiation in the cooperative game become moves in the noncooperative model. Of course, one cannot represent all possible bargaining devices as moves in the non-cooperative game. The negotiation process must be formalized and restricted, but in such a way that each participant is still able to utilize all the essential strengths of his position. The second approach is by the axiomatic method. One states as axioms several properties that it would seem natural for the solution to have and then one discovers that the axioms actually determine the solution uniquely. The two approaches to the problem, via the negotiation model or via the axioms, are complementary; each helps to justify and clarify the other. "Non-cooperative Games" in Annals of Mathematics, Vol. 54, No. 2 (September 1951)<!-- ; as cited in Can and should the Nash program be looked at as a part of mechanism theory? (2003) by Walter Trockel -->

„Any desired transferability can be put into the game itself instead of assuming it possible in the extra-game collaboration.“

— John Nash
Context: A less obvious type of application (of non-cooperative games) is to the study of. By a cooperative game we mean a situation involving a set of players, pure strategies, and payoffs as usual; but with the assumption that the players can and will collaborate as they do in the von Neumann and Morgenstern theory. This means the players may communicate and form coalitions which will be enforced by an umpire. It is unnecessarily restrictive, however, to assume any transferability or even comparability of the pay-offs [which should be in utility units] to different players. Any desired transferability can be put into the game itself instead of assuming it possible in the extra-game collaboration. "Non-cooperative Games" in Annals of Mathematics, Vol. 54, No. 2 (September 1951); as cited in Can and should the Nash program be looked at as a part of mechanism theory? (2003) by Walter Trockel

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