Geniuses -

genius john von neumann

John von Neumann

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

John von Neumann

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genius john von neumann

John von Neumann

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

John von Neumann

genius john von neumann

John von Neumann

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.

John von Neumann

genius john von neumann

John von Neumann

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.

John von Neumann

genius john von neumann

John von Neumann

In any conceivable method ever invented by man, an automaton which produces an object by copying a pattern, will go first from the pattern to a description to the object. It first abstracts what the thing is like, and then carries it out. It's therefore simpler not to extract from a real object its definition, but to start from the definition.

John von Neumann

genius john von neumann

John von Neumann

An element which stimulates itself will hold a stimulus indefinitely.

John von Neumann

genius john von neumann

John von Neumann

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

John von Neumann

genius john von neumann

John von Neumann

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.

John von Neumann

genius john von neumann

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.

John von Neumann

genius john von neumann

John von Neumann

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

genius john von neumann

John von Neumann

Can we survive technology?

John von Neumann

genius john von neumann

John von Neumann

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.

John von Neumann

genius john von neumann

John von Neumann

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

John von Neumann

genius john von neumann

John von Neumann

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.

John von Neumann

genius john von neumann

John von Neumann

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

John von Neumann

genius john von neumann

John von Neumann

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

John von Neumann