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An amateur’s outlook on computation and mathematics

John von Neumann was a prodigy and a polymath. He made notable con­tri­bu­tions in pure mathematics, physics, game theory, economics, and the design of computers. He also came up with the first algorithm for generating pseudo­random numbers with a digital computer. That last invention, however, is seldom counted among his most brilliant accomplishments. For example, Don Knuth leads off Vol. 2 of The Art of Computer Programming with a cautionary tale about the von Neumann scheme. I did the same in my first c

Program 1, below, shows the middle-square method in action, in the case of \(n = 4\). Type a four-digit number into the seed box at the top of the panel, press Go, and you’ll see a sequence of eight-digit numbers, with the middle four digits highlighted. (If you press the Go button without entering a seed, the program will choose a random seed for you—using a pseudorandom-number generator other than the one being demonstrated here!)

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