Ignoring punctuation, spacing, and capitalization, a monkey typing letters uniformly at random has one chance in 26 of correctly typing the first letter of Hamlet. It has one chance in 676 (26 times 26) of typing the first two letters. Because the probability shrinks exponentially, at 20 letters it already has only one chance in 26^20 = 19,928,148,895,209,409,152,340,197,376, roughly equivalent to the probability of buying 4 lottery tickets consecutively and winning the jackpot each time. In the case of the entire text of Hamlet, the probabilities are so vanishingly small they can barely be conceived in human terms. The text of Hamlet, even stripped of punctuation, contains well over 130,000 letters which would lead to a probability of one in 3.4×10^183946.
For comparison purposes, there are only about 10^79 atoms in the observable universe and only 4.3 x 10^17 seconds have elapsed since the Big Bang. Even if the universe were filled with monkeys typing for all time, their total probability to produce a single instance of Hamlet would still be less than one chance in 10183800. As Kittel and Kroemer put it, "The probability of Hamlet is therefore zero in any operational sense of an event...", and the statement that the monkeys must eventually succeed "gives a misleading conclusion about very, very large numbers." This is from their textbook on thermodynamics, the field whose statistical foundations motivated the first known expositions of typing monkeys.
Saturday, August 04, 2007
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