Shakespeare, Entropy and Educated Monkeys

Abstract

It has often been said, correctly, that a monkey forever randomly typing on a keyboard would eventually produce the complete works of William Shakespeare. Almost just as often it has been pointed out that this "eventually" is well beyond any conceivably relevant time frame. We point out that an educated monkey that still types at random but is constrained to only write "statistically typical" text, would produce any given passage in a much shorter time. Information theory gives a very simple way to estimate that time. For example, Shakespeare's phrase, Better three hours too soon than a minute too late, from The Merry Wives of Windsor, would take the educated monkey only 73 thousand years to produce, compared to the beyond-astronomical $2.7 \times 10^{63}$ years for the randomly typing one. Despite the obvious improvement, it would still take the educated monkey an unimaginably long $10^{42,277}$ years to produce all of Hamlet.