57 Quotes by John von Neumann

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

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.

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.

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.

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.

Can we survive technology?

The general opinion in theoretical physics had accepted the idea that the principle of continuity ("natura non facit saltus"), prevailing in the microsoptic world, is merely simulated by an averaging process in a world which in truth is discontinuous by its very nature. This simulation is such that a man generally percieves the sum of many billions of elementary processes simultaneously, so that the leveling law of large numbers completely obscures the real nature of the individual processes.

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

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.