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Anyone who considers arithmetical methods of producing random numbers is, of course, in a state of sin.
John Von Neumann
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1 Comments
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There's no sense in being precise when you don't even know what you're talking about.
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In mathematics you don't understand things. You just get used to them.
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If one has really technically penetrated a subject, things that previously seemed in complete contrast, might be purely mathematical transformations of each other.
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With four parameters I can fit an elephant, and with five I can make him wiggle his trunk.
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If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.
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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.
John Von Neumann
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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.
John Von Neumann
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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.
John Von Neumann
3 Likes
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.
John Von Neumann
3 Likes
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.
John Von Neumann
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There's no sense in being precise when you don't even know what you're talking about.
John Von Neumann
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It would appear that we have reached the limits of what it is possible to achieve with computer technology, although one should be careful with such statements, as they tend to sound pretty silly in 5 years.
John Von Neumann
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