Best 38 quotes of John Von Neumann on MyQuotes

All stable processes we shall predict. All unstable processes we shall control.

Anyone who attempts to generate random numbers by deterministic means is, of course, living in a state of sin.

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.

Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin.

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.

I am thinking about something much more important than bombs. I am thinking about computers.

If one has really technically penetrated a subject, things that previously seemed in complete contrast, might be purely mathematical transformations of each other.

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.

It is just as foolish to complain that people are selfish and treacherous as it is to complain that the magnetic field does not increase unless the electric field has a curl. Both are laws of nature.

I would like to make a confession which may seem immoral: I do not believe absolutely in Hilbert space any more.

Kurt Godel's achievement in modern logic is singular and monumental - indeed it is more than a monument, it is a landmark which will remain visible far in space and time. ... The subject of logic has certainly completely changed its nature and possibilities with Godel's achievement.

Life is a process which may be abstracted from other media.

Neumann, to a physicist seeking help with a difficult problem: Simple. This can be solved by using the method of characteristics. Physicist: I'm afraid I don't understand the method of characteristics. Neumann: In mathematics you don't understand things. You just get used to them.

Problems are often stated in vague terms... because it is quite uncertain what the problems really are.

Science, as well as technology, will in the near and in the farther future increasingly turn from problems of intensity, substance, and energy, to problems of structure, organization, information, and control.

Technological possibilities are irresistible to man. If man can go to the moon, he will. If he can control the climate, he will.

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.

The emphasis on mathematical methods seems to be shifted more towards combinatorics and set theory - and away from the algorithm of differential equations which dominates mathematical physics.

The most vitally characteristic fact about mathematics is, in my opinion, its quite peculiar relationship to the natural sciences, or more generally, to any science which interprets experience on a higher than purely descriptive level.

There is no point in being precise if you do not even know what you are talking about.

There's no sense in being precise when you don't even know what you're talking about.

The sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work-that is, correctly to describe phenomena from a reasonably wide area.

The total subject of mathematics is clearly too broad for any of us. I do not think that any mathematician since Gauss has covered it uniformly and fully; even Hilbert did not and all of us are of considerably lesser width quite apart from the question of depth than Hilbert.

Truth is much too complicated to allow anything but approximations.

When we talk mathematics, we may be discussing a secondary language built on the primary language of the nervous system.

With four parameters I can fit an elephant, and with five I can make him wiggle his trunk.

You don't have to be responsible for the world that you're in.

Young man, in mathematics you don't understand things. You just get used to them.

You wake me up early in the morning to tell me I am right? Please wait until I am wrong.

A code, which according to Turing's schema is supposed to make one machine behave as if it were another specific machine (which is supposed to make the former imitate the latter) must do the following things. It must contain, in terms that the machine will understand (and purposively obey), instructions (further detailed parts of the code) that will cause the machine to examine every order it gets and determine whether this order has the structure appropriate to an order of the second machine. It must then contain, in terms of the order system of the first machine, sufficient orders to make the machine cause the actions to be taken that the second machine would have taken under the influence of the order in question.

All existing machines and memories use "direct addressing," which is to say that every word in the memory has a numerical address of its own that characterizes it and its position within the memory (the total aggregate of all hierarchic levels) uniquely.

And' and 'or' are the basic operations of logic. Together with 'no' (the logical operation of negation) they are a complete set of basic logical operations—all other logical operations, no matter how complex, can be obtained by suitable combinations of these.

Any artificial automaton that has been constructed for human use, and specifically for the control of complicated processes, normally possesses a purely logical part and an arithmetical part, i.e. a part in which arithmetical processes play no role, and one in which they are of importance.

Apart from all other considerations, the main limitation of analog machines relates to precision. Indeed, the precision of electrical analog machines rarely exceeds 1:10^3, and even mechanical ones achieve at best 1:10^4 to 10^5... On the other hand, to go from 1:10^12 to 1:10^13 in a digital machine means merely adding one place to twelve; this means usually no more than a relative increase in equipment (not everywhere!) of 1/12 = 8.3 percent, and an equal loss in speed (not everywhere!) — none of which is serious.

A system of logical instructions that an automaton can carry out and which causes the automaton to perform some organized task is called a code.

It is only proper to realize that language is largely a historical accident.

The very last stage of any memory hierarchy is necessarily the outside world—that is, the outside world as far as the machine is concerned, i.e. that part of it with which the machine can directly communicate, in other words, the input and the output organs of the machine. These are usually punched paper tapes or cards, and on the output side, of course, also printed paper.

When we talk mathematics, we may be discussing a secondary language, built on the primary language truly used by the central nervous system. Thus the outward forms of our mathematics are not absolutely relevant from the point of view of evaluating what the mathematical or logical language truly used by the central nervous system is. However, the above remarks about reliability and logical and arithmetical depth prove that whatever the system is, it cannot fail to differ considerably from what we consciously and explicitly consider as mathematics.