John von Neumann > Quotes

“If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.”
― John von Neumann

“Young man, in mathematics you don't understand things. You just get used to them.”
― John von Neumann

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

“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

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

“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”
― John von Neumann

“It is only proper to realize that language is largely a historical accident.”
― John von Neumann, The Computer and the Brain

“Can we survive technology?”
― John von Neumann

“Se la gente non crede che la matematica è semplice, è solo perché non capisce quanto è complicata la vita.”
― John von Neumann

“An element which stimulates itself will hold a stimulus indefinitely.”
― John von Neumann

“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.”
― John von Neumann, The Computer and the Brain

“Anybody who looks at living organisms knows perfectly well that they can produce other organisms like themselves. This is their normal function, they wouldn't exist if they didn't do this, and it's not plausible that this is the reason why they abound in the world. In other words, living organisms are very complicated aggregations of elementary parts, and by any reasonable theory of probability or thermodynamics highly improbable. That they should occur in the world at all is a miracle of the first magnitude; the only thing which removes, or mitigates, this miracle is that they reproduce themselves. Therefore, if by any peculiar accident there should ever be one of them, from there on the rules of probability do not apply, and there will be many of them, at least if the milieu is reasonable. But a reasonable milieu is already a thermodynamically much less improbable thing. So, the operations of probability somehow leave a loophole at this point, and it is by the process of self-reproduction that they are pierced.”
― John von Neumann, Theory Of Self Reproducing Automata

“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.”
― John von Neumann, Theory Of Self Reproducing Automata

“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, Theory Of Self Reproducing Automata

“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, Theory Of Self Reproducing Automata

“In this sense, an object is of the highest degree of complexity if it can do very difficult and involved things.”
― John von Neumann, Theory Of Self Reproducing Automata

“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, The Computer and the Brain

“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?”
― John von Neumann

“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.”
― John von Neumann, Mathematical Foundations of Quantum Mechanics

“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, The Computer and the Brain

“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.”
― John von Neumann, Theory of Games and Economic Behavior

“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.”
― John von Neumann

“No, no,’ he said. ‘Chess is not a game. Chess is a well-defined form of computation. You may not be able to work out the answers, but in theory there must be a solution, a right procedure in any position. Now, real games,’ he said, ‘are not like that at all. Real life is not like that. Real life consists of bluffing, of little tactics of deception, of asking yourself what is the other man going to think I mean to do. And that is what games are about in my theory.”
― John von Neumann

“No, No, Chess is not a game. Chess is a well-defined form of computation. You may not be able to work out the answers, but in theory there must be a solution, a right procedure in any position. Now, real games,’ he said, ‘are not like that at all. Real life is not like that. Real life consists of bluffing, of little tactics of deception, of asking yourself what is the other man going to think I mean to do. And that is what games are about in my theory.”
― John von Neumann

“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.”
― John von Neumann, Theory of Games and Economic Behavior

“Natura non facis Saltus.”
― John von Neumann

“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.”
― John von Neumann

“When we talk mathematics, we may be discussing a secondary language built on the primary language truly used by the central nervous system.”
― John von Neumann