John Von Neumann Quotes

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

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 other line of argument, which leads to the opposite conclusion, arises from looking at artificial automata. Everyone knows that a machine tool is more complicated than the elements which can be made with it, and that, generally speaking, an automaton A, which can make an automaton B, must contain a complete description of B, and also rules on how to behave while effecting the synthesis. So, one gets a very strong impression that complication, or productive potentiality in an organization, is degenerative , that an organization which synthesizes something is necessarily more complicated, of a higher order, than the organization it synthesizes. This conclusion, arrived at by considering artificial automaton, is clearly opposite to our early conclusion, arrived at by considering living organisms.

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.

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

If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.

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

An element which stimulates itself will hold a stimulus indefinitely.

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. Furthermore, it must satisfy certain esthetic criteria - that is, in relation to how much it describes, it must be rather simple.

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

Computers are like humans - they do everything except think.

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.

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

Furthermore, it's equally evident that what goes on is actually one degree better than self-reproduction, for organisms appear to have gotten more elaborate in the course of time. Today's organisms are phylogenetically descended from others which were vastly simpler than they are, so much simpler, in fact, that it's inconceivable, how any kind of description of the latter, complex organism could have existed in the earlier one. It's not easy to imagine in what sense a gene, which is probably a low order affair, can contain a description of the human being which will come from it. But in this case you can say that since the gene has its effect only within another human organism, it probably need not contain a complete description of what is to happen, but only a few cues for a few alternatives. However, this is not so in phylogenetic evolution. That starts from simple entities, surrounded by an unliving amorphous milieu, and produce, something more complicated. Evidently, these organisms have the ability to produce something more complicated than themselves.

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.

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

Kurt Gödel'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 Gödel's achievement." - John von Neumann

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.

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

In this sense, an object is of the highest degree of complexity if it can do very difficult and involved things.

You insist that there is something a machine cannot do. If you tell me precisely what it is a machine cannot do, then I can always make a machine which will do just that.

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

Truth is much too complicated to allow anything but approximations.

I am a little troubled about the tea service in the electronic computer building. Apparently the members of your staff consume several times as much supplies as the same number of people do in Fuld Hall and they have been especially unfair in the matter of sugar ... I should like to raise the question whether it would not be better for the computer people to come up to Fuld Hall at the end of the day at 5 o'clock and have their tea here under proper supervision.

Can we survive technology?

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

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.