Is it an infinite number of monkeys, or is it infinitely-lived monkeys? If what you want is Shakespeare with probability 1 it matters. Because Hamlet is a fixed *finite* string of characters. That means the monkey has to stop typing when the string is complete. If we model the monkey as a process which every second taps a random key from the keyboard according to a fixed probability distribution, then to produce the Dithering Dane he must eventually repeat the space bar (or equivalently no key at all) until his terminal date.

If that terminal date is infinity, i.e. the monkey is given infinite time, then this event has probability zero. On the other hand, an infinite number of monkeys who each live long enough, but not infinitely long, will Exuent with probability 1 as desired.

(If your criterion is simply that the text of Hamlet appear *somewhere* in the output string, then a) you are sorely lacking in ambition and b) it no longer matters which version of infinity you have.)

Mortarboard Missive: Marginal Revolution.

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November 30, 2009 at 11:26 pm

Tomasz StrzaleckiThe trouble might be to find the rIght monkey given that versions of Hamlet with all imaginable typos will be produced with prob 1, as well as all other books, of all writers even those not written yet. But I guess the analogous problem exists for the single monkey version.

December 1, 2009 at 7:19 am

RyanIf you are not satisfied with having the book somewhere in the output string, then don’t you have a similar (and infinitely more immediate) problem with the start of the book?

December 7, 2009 at 3:58 pm

DanielNice entry! The paradox behind the Infinite monkey theorem was behind many of Borges stories (“The Library of Babel” and “The Book of Sand”.) In particular, in “The Library of Babel” the problem is that no one knows who monkey wrote Hamlet, while in “The Book of Sand” no one knows in which page did the monkey started it…