How likely is the idea of a million monkeys with typewriters producing Shakespeare with a limited time frame of December 2020?

Given that our monkeys stay busy, they will produce something. Define something as a brief sequence of letters, e.g. the alphabet. Let’s do a little hand-wave and ignore the shift key, which requires the monkey to press down on SHIFT while striking a letter, and remove the requirement for capital letters to start sentences. This is, after all, an exercise in whimsy. (Similarly, swiping the carriage return bar becomes problematic, i.e. the monkey focuses on all those keys! If this is a computer keyboard, fine – but if we’re using real typewriters, let’s do another hand-wave.)

Extending that supposed brief sequence of letters to all of Shakespeare just makes the odds longer. In order to have a stand-in number, rather than count all the letters and spaces in Shakespeare just do ANOTHER hand-wave and grab a “useful comparison” out of thin air – a thousand pages with five hundred words per page? Average word length, plus space, six characters?

Pseudo-Shakespeare, in this example, requires three million keypresses. Not sure if any monkey can work that hard by December 2020 – leave that for last.

Each keypress is one of 26 letters, 10 numbers, and a handful of punctuations. Let’s say that there are 40 different keys to press, ONE of which will be correct, 3 million times. The odds of getting 1-of-40 three million times in a row works out to 1-of-40 times itself three million times; that takes one-in-40 to one-in-(4 to the 3 millionth power, i.e. 2 to the 6 millionth power) times one-in-(ten to the 3 millionth power, i.e. a 1 followed by 3 million zeroes.)

Very roughly speaking, 2 to the 6 millionth power is roughly one thousand to the 600 thousandth power, or 1 followed by 1.8 million zeroes. Bottom line, hitting the right key out of 40, three million times in a row, is one chance (one monkey) in 10 to the 4.8 millionth power. You’d need a 4.8 million digit number just to count your monkeys. Does this provide a rough idea of reproducing Shakespeare with monkeys?

Finally, suppose the monkey makes a thousand keypresses per hour, or one per 3.6 seconds. Yes, that’s slow – but can we give the monkey coffee breaks, time to watch the news, and nightly sleep? Fine, you’re a generous person! Three thousand hours is all it takes. At 168 hours per week that comes out to (again, roughly) 17 weeks and 6 days. Going from October 1 2019 to December 31 2020 is 65 weeks; almost 4 times longer than required.

So cut the monkeys from 10 to the 4.8 millionth power down to 2.5 times ten to the 4,799,799th power. See how big a difference that makes?

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