## A trillion monkeys can’t be wrong

There’s an old saying that goes, ‘If you have enough monkeys typing randomly on keyboards, they will eventually type the collective works of William Shakespeare’. So how likely is it? Let’s make our monkey type the following line from Romeo and Juliet (coincidentally, also the only line from it which I can recall from grade 11):

But soft, what light through yonder window breaks?

There are 48 characters including spaces bur not punctuation. Assume that the keyboard the monkeys will be using has 27 characters (26 letters plus space bar), and that there is an equalikely chance of hitting any of the different letters. The keystrokes are independent, in that the letter the monkey hits on the first attempt has no bearing on what he hits on the next one. Now then, there is a 1/27 chance that the first letter the monkey hits will be a ‘B’, and a (1/27)*(1/27) chance that the next letter will be a ‘U’, and so on. So the probability that the monkey will bang out ‘But soft what light through yonder window breaks’ is (1/27)^48, which Windows Calculator gives as 1.9703315899974244214261906808168*10^-69. (0.0000…[68 zeros]..000197…) Or, there is a 1 in 5.075287860564156007197541597417*10^68 (that’s 69 digits) that the monkey will type the quote. That’s one in five trillion trillion trillion trillion trillion trillion. Azerbaijan has a better chance of winning the next twenty FIFA World Cups. Assume now that we have a million monkeys typing a thousand letters a minute. Then it will still take 4.8247850222109628177024313611463*10^55 (4.8 million trillion trillion trillion trillion) years before we can expect one of them to come up with the quote. And that’s only for one line. Considering the age of the universe is believed to be only 15 billion years; monkey’s typing Shakespeare? Fat fucking chance. The infinite monkey theory is based on Kolmogorov’s zero-one law, which states that a certain type of event with an infinite set of outcomes will either surely happen, or surely not happen. That is, the event has a probability of either 1 or 0. In my opinion, this demonstrates the deep-seated absurdness of the nature of some aspects of mathematics, especially probability and statistics, when applied to the real world (does god play dice?). Some may even say there is an inherent beauty in all this.

### 3 Responses to A trillion monkeys can’t be wrong

1. Wayland says:

Jimmy you statistics and probability freak, do some real maths and give us some calculus!

We want calculus! We want calculus! We want it now! (In true picket line fashion)

Anyway, what about that classic quote “Romeo, O Romeo! Wherefore art thou Romeo!”?

2. Wayland says:

Hey you know what, a thought just occurred to me. If you had infinitely many monkeys typing away for whatever time (with infinitely many of them it wouldn’t matter if they typed for an hour or for eternity) then you would, as well as recreating all the written works of every English author/whatever (given the standard typewriter) but you could ALSO: 1. predict the future 2. solve all our scientific problems etc. However, this would also raise the issue of a false claim being generated but if you had infinitely many scientists testing out the monkeys’ theories…we’d solve all the world’s problems!

3. Jimmy says:

Now that’s an interesting idea. Infinite monkeys to solve all our problems. Now if animal liberation groups use that arguement to stop us killing animals, they just might convince all of us.