You insist that there is something a machine cannot do. If you tell me precisely what it is a machine cannot do, then I can always make a machine which will do just that.
John Von NeumannRead
Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin. For, as has been pointed out several times, there is no such thing as a random number - there are only methods to produce random numbers, and a strict arithmetic procedure of course is not such a method.
Interpretation
What this quote means
Random numbers can only be generated by specific methods, not through strict arithmetic procedures.
John Von Neumann's quote delves into the nature of randomness in mathematics and computing. He argues that true randomness cannot be achieved through predictable or systematic methods, such as arithmetic algorithms. Instead, any number generated by a strict procedure is, in essence, deterministic rather than truly random. This highlights the complexity of randomness and the challenges involved in simulating it through mathematical techniques.
Themes
RandomnessNumbersMathematicsProbabilityComputation
In practice
Example use cases
In a lecture on algorithms, I quoted Neumann to explain the inherent limitations of using deterministic methods for random number generation.
More from John Von Neumann
All quotes βThe 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.
John Von NeumannRead
Anyone who attempts to generate random numbers by deterministic means is, of course, living in a state of sin.
John Von NeumannRead
It would appear that we have reached the limits of what it is possible to achieve with computer technology, although one should be careful with such statements, as they tend to sound pretty silly in 5 years.
John Von NeumannRead
Technological possibilities are irresistible to man. If man can go to the moon, he will. If he can control the climate, he will.
John Von NeumannRead
I would like to make a confession which may seem immoral: I do not believe absolutely in Hilbert space any more.
John Von NeumannRead
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