The Fallacy of the Infinite Monkey Cage

We all know it goes like this: If an infinite number of monkeys were put in a cage (of infinite size) with an infinite number of typewriters, for an infinite amount of time, one of them would, eventually, produce the complete works of Shakespeare. Sounds logical enough. But it’s just not true. Let me explain.

Let’s start the ball rolling with something a little more modest: a deck of 52 cards. We want to find the Queen of Hearts. We shuffle the cards, place them face down and select the top card. There is a 1/52 chance it is the Queen of Hearts.

If it isn’t, then we select the next card from the top of the deck. Having discarded the first card, the chances of this card being the Queen of Hearts have now improved slightly to 1/51. If the Queen of Hearts has still not appeared, we select the next one at 1/50 odds. And so on, until either the card is revealed or we have just one card left – with 1/1 odds of it being the Queen of Hearts, i.e. certainty.

Here’s the important step: We know that the Queen of Hearts is in the deck, so with each card selected (that isn’t it) the chances improve. This is just not so with our typing monkeys.

Let’s take one of them, give him one of the typewriters and sit him down somewhere nice and quiet, so he can concentrate. We come back a while later and (surprise, surprise) far from producing the complete works of the great man, he’s broken the typewriter.

So here’s the question: Are the chances of the next monkey and the next typewriter improved by the failure of the first? No, of course not. Or the third? Or the millionth? Or the billion, quillion, zillionth? No! No! No!

The chances of a monkey succeeding remains unchanged by each subsequent failure, leaving the odds at near zero for each subsequent attempt – all the way up to infinity. (I say near zero merely through pedantry.) So, no: the odds of a monkey producing the complete works of William Shakespeare do not approach 1/1 as the number of attempts approaches infinity. They remain unchanged, at zero. Which is where they stay. Now and forever.

There is a point to this. The point is that genius is not random. It is a rare and beautiful thing, requiring natural gifts and (for most of us) unimaginable dedication. There will never be another Shakespeare…or Picasso, Einstein, Curie or Hendrix. They were a gift to us all. We should treasure them and leave the monkeys to do their own thing.

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