The Infinite monkey theorem

andi — Tue, 08 Apr 2008 04:42:40 +0000

An amusing if not likely debate culture occaisionally reoccurs - where if an infinite number of monkeys sit at an infinite number of typewriters and randomly press keys, they will eventually produce the complete works of Shakespeare.

I’m not sure they would eventually produce Shakespeare - but I do think they could come pretty close to reproducing the Bible… :)

In 2007, the theorem was listed by Wired magazine in a list of eight classic thought experiments.

My other favorite:

Power laws for monkeys typing randomly: the case of unequal probabilities
Conrad, B.; Mitzenmacher, M.
Information Theory, IEEE Transactions on
Volume 50, Issue 7, July 2004 Page(s): 1403 – 1414
Digital Object Identifier 10.1109/TIT.2004.830752
Summary: An early result in the history of power laws, due to Miller, concerned the following experiment. A monkey types randomly on a keyboard with N letters (N>1) and a space bar, where a space separates words. A space is hit with probability p; all other letters are hit with equal probability (1-p)/N. Miller proved that in this experiment, the rank-frequency distribution of words follows a power law. The case where letters are hit with unequal probability has been the subject of recent confusion, with some suggesting that in this case the rank-frequency distribution follows a lognormal distribution. We prove that the rank-frequency distribution follows a power law for assignments of probabilities that have rational log-ratios for any pair of keys, and we present an argument of Montgomery that settles the remaining cases, also yielding a power law. The key to both arguments is the use of complex analysis. The method of proof produces simple explicit formulas for the coefficient in the power law in cases with rational log-ratios for the assigned probabilities of keys. Our formula in these cases suggests an exact asymptotic formula in the cases with an irrational log-ratio, and this formula is exactly what was proved by Montgomery.

What have you typed lately…?

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Are we falling or flying ... and will we ever know? » complete works of shakespeare

The Infinite monkey theorem