John von Neumann Quotes

The total subject of mathematics is clearly too broad for any one of us. I do not think that any mathematician since Gauss has covered it fully and uniformly, even Hilbert did not, and all of us are of considerably lesser width (quite apart from the question of depth) than Hilbert. It would therefore, be quite unrealistic not to admit, that any address I could possibly give would not be biased towards some areas in mathematics in which I have had some experience, to the detriment of others which may be equally or more important. To be specific, I could not avoid a bias towards those parts of analysis, logics, and certain border areas of the applications of mathematics to other sciences in which I have worked. If your Committee feels that an address which is affected by such imperfections still fits into the program of the Congress, and if the very generous confidence in my ability to deliver continues, I shall be glad to undertake it.

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.

An element which stimulates itself will hold a stimulus indefinitely.

An important viewpoint in classifying games is this: Is the sum of all payments received by all players (at the end of the game) always zero; or is this not the case? If it is zero, then one can say that the players pay only to each other, and that no production or destruction of goods is involved. All games which are actually played for entertainment are of this type. But the economically significant schemes are most essentially not such. There the sum of all payments, the total social product, will in general not be zero, and not even constant. I.e., it will depend on the behavior of the players — the participants in the social economy. This distinction was already mentioned in 4.2.1., particularly in footnote 2, p. 34. We shall call games of the first-mentioned type zero-sum games, and those of the latter type non-zero-sum games.

With the Russians it is not a question of whether but of when. If you say why not bomb them tomorrow, I say why not today? If you say today at 5 o'clock, I say why not one o'clock?

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.

It is a well known phenomenon in many branches of the exact and physical sciences that very great numbers are often easier to handle than those of medium size. An almost exact theory of a gas, containing about 1025 freely moving particles, is incomparably easier than that of the solar system, made up of 9 major bodies; and still more than that of a multiple star of three or four objects of about the same size. This is, of course, due to the excellent possibility of applying the laws of statistics and probabilities in the first case.

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.

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.

"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.

The human brain is, after all, the best example we have of an intelligent system. If we can learn its methods, we can use these biologically inspired paradigms to build more intelligent machines. This book is the earliest serious examination of the human brain from the perspective of a mathematician and computer pioneer. Prior to von Neumann, the fields of computer science and neuroscience were two islands with no bridge between them.

The goys have proven the following theorem…

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

The McCulloch-Pitts result . . . proves that anything that can be exhaustively and unambiguously described, anything that can be completely and unambiguously put into words, is ipso facto realizable by a suitable finite neural network.