John von Neumann Quotes

A quotes list created by Lee Sonogan

38 Great Quotes By John von Neumann That Will Spark Your Interest In  Mathematics

Cellular automata to the universal constructor ending with what you’re reading this with. This guy was key for the 20th century. One of the last presentations of mathematic polymaths in other fields, the metaphysics between applied sciences and purer theorems of today. Con working on the Manhattan Project, you cannot deny the endless work very relevant to most solid academia.

  • “Young man, in mathematics you don’t understand things. You just get used to them.”
  • “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.”
  • “There’s no sense in being precise when you don’t even know what you’re talking about”
  • “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.”
  • “It is only proper to realize that language is largely a historical accident.”
  • “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.”
  • “An element which stimulates itself will hold a stimulus indefinitely.”
  • “A code, which according to Turing’s schema is supposed to make one machine behave as if it were another specific machine (which is supposed to make the former imitate the latter) must do the following things. It must contain, in terms that the machine will understand (and purposively obey), instructions (further detailed parts of the code) that will cause the machine to examine every order it gets and determine whether this order has the structure appropriate to an order of the second machine. It must then contain, in terms of the order system of the first machine, sufficient orders to make the machine cause the actions to be taken that the second machine would have taken under the influence of the order in question.”
  • “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.”
  • “The linear size of a neuron varies widely from one nerve cell to the other, since some of these cells are contained in closely integrated large aggregates and have, therefore, very short axons, while others conduct pulses between rather remote parts of the body and may, therefore, have linear extensions comparable to those of the entire human body.”
  • “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.”
  • “In the deceptively modest volume you are now holding, von Neumann articulates his model of computation and goes on to define the essential equivalence of the human brain and a computer. He acknowledges the apparently deep structural differences, but by applying Turing’s principle of the equivalence of all computation, von Neumann envisions a strategy to understand the brain’s methods as computation, to re-create those methods, and ultimately to expand its powers.”
  • “Since I am neither a neurologist nor a psychiatrist, but a mathematician, the work that follows requires some explanation and justification.”
  • “In an analog machine each number is represented by a suitable physical quantity, whose values, measured in some pre-assigned unit, is equal to the number in question.”
  • “He notes that the output of neurons is digital: an axon either fires or it doesn’t. This was far from obvious at the time, in that the output could have been an analog signal. The processing in the dendrites leading into a neuron and in the soma neuron cell body, however, are analog. He describes these calculations as a weighted sum of inputs with a threshold.”
  • “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.”

From these quotes alone, his books must become fascinating to read. Working on my own book, stuff like this makes me think there is so much I am still missing and need to consider. Not afraid to publish reminders on the special subjects or ever non-numbers one, all this is very important to quantum mechanics.

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