As Leibniz suggested, we appear to live in the best of all possible worlds, where the computable functions make life predictable enough to be survivable, while the uncomputable functions make life (and mathematical truth) unpredictable enough to remain interesting, no matter how far computers continue to advance
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Left: Wiener with Max Born in Göttingen in 1925 (Photo: George H. Davis, Jr. Courtesy MIT Museum).
Mathematician and later father of cybernetics Norbert Wiener (1894-1964) crossed paths with many great minds in his life, from Bertrand Russell and G.H. Hardy, to Max Born, John F. Nash Jr. and John von Neumann. von Neumann’s assistant Edgar R. Lorch’s recollection of one of his boss’ encounters with Wiener bears repeating:
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Programmers normally want to minimize the time their code takes to execute. But in 1962, the Hungarian mathematician Tibor Radó posed the opposite problem. He asked: How long can a simple computer program possibly run before it terminates? Radó nicknamed these maximally inefficient but still functional programs “busy beavers.”
Quanta Magazine, an editorially independent publication of the Simons Foundation whose mission is to enhance public understanding of science by covering research developments and trends in mathematics and the physical and life sciences.
Finding these programs has been a fiendishly diverting puzzle for programmers and other mathematical hobbyists ever since it was popularized in