Frases de John Von Neumann
John Von Neumann
Fecha de nacimiento: 28. Diciembre 1903
Fecha de muerte: 8. Febrero 1957
John von Neumann fue un matemático húngaro-estadounidense que realizó contribuciones fundamentales en física cuántica, análisis funcional, teoría de conjuntos, teoría de juegos, ciencias de la computación, economía, análisis numérico, cibernética, hidrodinámica, estadística y muchos otros campos. Es considerado como uno de los más importantes matemáticos de la historia moderna.
Frases John Von Neumann
Fuente: [Ripa, Pedro, La increíble historia de la malentendida fuerza de coriolis http://bibliotecadigital.ilce.edu.mx/sites/ciencia/volumen3/ciencia3/128/htm/sec_9.htm, 1996, Fondo de Cultura Económica, español, 968-16-4780-7, IV. Sobre naves de aquí y allá http://bibliotecadigital.ilce.edu.mx/sites/ciencia/volumen3/ciencia3/128/htm/sec_9.htm]
„Las ciencias no tratan de explicar, incluso apenas tratan de interpretar, construyen modelos principalmente. Por modelo, se entiende una construcción matemática que, con la adición de ciertas interpretaciones verbales, describe los fenómenos observados. La justificación de tal construcción matemática es sólo y precisamente que se espera que funcione.“
„Había un seminario para estudiantes avanzados en Zurich en el que yo estaba enseñando y Von Neumann estaba en la clase. Llegué a cierto teorema, y dije, no está demostrado y podría ser difícil de probar. Von Neumann no dijo absolutamente nada pero después de cinco minutos levantó la mano. Cuando le llame, se levantó, se fue a la pizarra y empezó a escribir la demostración. Después de eso estaba asustado de Von Neumann." Cita de un profesor suyo acerca de él“
„In the second place, and more important, no one really knows what entropy really is, so in a debate you will always have the advantage.“
Suggesting to Claude Shannon a name for his new uncertainty function, as quoted in Scientific American Vol. 225 No. 3, (1971), p. 180.
Contexto: You should call it entropy, for two reasons. In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name. In the second place, and more important, no one really knows what entropy really is, so in a debate you will always have the advantage.
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„Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin.“
On mistaking pseudorandom number generators for being truly "random" — this quote is often erroneously interpreted to mean that von Neumann was against the use of pseudorandom numbers, when in reality he was cautioning about misunderstanding their true nature while advocating their use. From "Various techniques used in connection with random digits" by John von Neumann in Monte Carlo Method (1951) edited by A.S. Householder, G.E. Forsythe, and H.H. Germond <!-- National Bureau of Standards Applied Mathematics Series, 12 (Washington, D.C.: U.S. Government Printing Office, 1951): 36-38. -->
Contexto: Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin. For, as has been pointed out several times, there is no such thing as a random number — there are only methods to produce random numbers, and a strict arithmetic procedure of course is not such a method.
„I think that it is a relatively good approximation to truth — which is much too complicated to allow anything but approximations — that mathematical ideas originate in empirics.“
"The Mathematician", in The Works of the Mind (1947) edited by R. B. Heywood, University of Chicago Press, Chicago
Contexto: I think that it is a relatively good approximation to truth — which is much too complicated to allow anything but approximations — that mathematical ideas originate in empirics. But, once they are conceived, the subject begins to live a peculiar life of its own and is … governed by almost entirely aesthetical motivations. In other words, at a great distance from its empirical source, or after much "abstract" inbreeding, a mathematical subject is in danger of degeneration. Whenever this stage is reached the only remedy seems to me to be the rejuvenating return to the source: the reinjection of more or less directly empirical ideas.
„A large part of mathematics which becomes useful developed with absolutely no desire to be useful, and in a situation where nobody could possibly know in what area it would become useful; and there were no general indications that it ever would be so.“
"The Role of Mathematics in the Sciences and in Society" (1954) an address to Princeton alumni, published in John von Neumann : Collected Works (1963) edited by A. H. Taub <!-- Macmillan, New York -->; also quoted in Out of the Mouths of Mathematicians : A Quotation Book for Philomaths (1993) by R. Schmalz
Contexto: A large part of mathematics which becomes useful developed with absolutely no desire to be useful, and in a situation where nobody could possibly know in what area it would become useful; and there were no general indications that it ever would be so. By and large it is uniformly true in mathematics that there is a time lapse between a mathematical discovery and the moment when it is useful; and that this lapse of time can be anything from 30 to 100 years, in some cases even more; and that the whole system seems to function without any direction, without any reference to usefulness, and without any desire to do things which are useful.
„If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.“
Remark made by von Neumann as keynote speaker at the first national meeting of the Association for Computing Machinery in 1947, as mentioned by Franz L. Alt at the end of "Archaeology of computers: Reminiscences, 1945--1947", Communications of the ACM, volume 15, issue 7, July 1972, special issue: Twenty-fifth anniversary of the Association for Computing Machinery, p. 694.
Reply, according to Dr. Felix T. Smith of Stanford Research Institute, to a physicist friend who had said "I'm afraid I don't understand the method of characteristics," as quoted in The Dancing Wu Li Masters: An Overview of the New Physics (1979) by Gary Zukav, Bantam Books, p. 208, footnote.
„If one has really technically penetrated a subject, things that previously seemed in complete contrast, might be purely mathematical transformations of each other.“
As quoted in Proportions, Prices, and Planning (1970) by András Bródy
As quoted in John Von Neumann : The Scientific Genius Who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence and Much More (1992) by Norman Macrae, p. 379
„The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics; and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking.“
As quoted in Bigeometric Calculus: A System with a Scale-Free Derivative (1983) by Michael Grossman, and in Single Variable Calculus (1994) by James Stewart.
„It is exceptional that one should be able to acquire the understanding of a process without having previously acquired a deep familiarity with running it, with using it, before one has assimilated it in an instinctive and empirical way… Thus any discussion of the nature of intellectual effort in any field is difficult, unless it presupposes an easy, routine familiarity with that field. In mathematics this limitation becomes very severe.“
As quoted in "The Mathematician" in The World of Mathematics (1956), by James Roy Newman
As quoted by Jacob Bronowski in The Ascent of Man TV series