John von Neumann — "Anyone who considers arithmetical methods of producing random digits is, of cour…"
Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin.
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More from John von Neumann
"The more abstract a thing is, the more real it is."
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Details
Lecture notes or informal remarks, highlighting the difficulty of true randomness from deterministic processes.
Date: 1951
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Understanding this quote
What it means
Any arithmetic formula used to generate 'random' numbers is deterministic by definition — it follows fixed rules and will eventually repeat. True randomness cannot emerge from a calculation. Treating these predictable pseudo-random sequences as if they were genuinely random introduces hidden flaws into statistical simulations, cryptographic systems, and scientific models that fundamentally depend on real, unpredictable randomness to produce reliable results.
Relevance to John von Neumann
Von Neumann pioneered Monte Carlo methods at Los Alamos during the Manhattan Project, simulating nuclear reactions using random number sequences. He personally invented the middle-square method — a simple arithmetic pseudo-random generator — knowing it was theoretically impure. His foundational work on ENIAC and computer architecture required practical random inputs. This quote captures his signature wit: confessing the 'sin' he himself committed out of computational necessity while maintaining rigorous mathematical honesty.
The era
In the late 1940s, the newly born field of computational science demanded random numbers for Monte Carlo simulations used in nuclear weapons design, code-breaking, and early scientific computing. Hardware random number generators were impractical for the era's primitive machines. Scientists at Los Alamos, IBM, and RAND were forced to use algorithmic pseudo-random sequences despite their theoretical inadequacy — a compromise that haunted statisticians and cryptographers for decades as computers grew more powerful.
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