The Infinite Monkey Theorem

And what does it have to do with AI?

By New York Zoological Society — Public Domain, https://commons.wikimedia.org/w/index.php?curid=19075009

January 12th, 2017. Day 12.

This week’s writing assignment is very historically focused, bring to light typewriters, early home computing, weblogs and then AI. During yesterday’s look at AI, it gave me feeling that AI might be related the next writing item this week, the Infinity Monkey Theorem. or “IMT”.

When Montgomery Burns, villainous power plant owner on The Simpsons, shows Homer is his room full of “1000 monkeys sitting at 1000 typewriters”, Mr Burns reads aloud the transcript of one monkey’s effort “it was the best of times, it was the blurst of times”. Clearly not good enough, Mr. Burns throws the paper down and scolds the monkey.

From that very moment until about 2 hours ago, I thought the theorem was related to Charles Dickens. A deeper connection about a Dickens utopia of monkey authors so Dicken’s could stop writing himself and cash in on the monkeys’

In fact it is not. There’s no relation except that it was on The Simpsons.

The idea is… an unlimited number of monkeys typing for eternity could recreate the work of Shakespeare. The odds seem stacked again them, can the monkeys do it? Mathematically, the answer is not ZERO, but it certainly is close.

Whoever contributed to the IMT wiki page is REALLY into this topic. Upon learning that Mr Burns, IMT, and Dickens are not related they followed up the article with a lot of history and examples, it took some time to grasp any other versions of this childhood story.

It was the blurst of times.

The monkey metaphor was traced its ‘modern’ history to Emile Borel in 1913 to Jonathan Swift and Blaise Pascal, all the way back to other variations of the unlimited typists by Aristotle and Cicero. Early last century, Borel and astrophysicists Sir Arthur Eddington applied the theorem to statistical mechanics.

Mathematically there is no chance group of monkeys can ever recreate Shakespeare.

Just look at chances of correctly typing the word “banana”. If there are 50 keys on a typewriter and each action is independent of the next, the odds are slim:

The odds of typing b-a-n-a-n-a =

1/50 *1/50 *1/50 *1/50 *1/50 *1/50, or 1/50 *^6

Or 1 in 15,625,000,000 or less than 1 in 15 billion for banana.

Therefore, the likehood of an entire book being completed is one of the most unlikely events imaginable. You start with crappy 1/50 odds, and for each event you multiply again by .02. Forever approaching zero, but not quite getting there.

So what does the IMT mean exactly? Since it has come up several times in history, I believe they are philosophical periods when we need to put ourselves in check. By thinking about the unlikelihood of something happening, we realize just how unlikely it is for things to happen, and therefore o be grateful for what has transpired to get us here today.

Infinite Monkeys vs Computers

The future of IMT and any chance of success relies on technology, and it’s fair to say people are already addressing that. There are hundreds, if not thousands of programs around the world writing their own stories as we speak. The community around this is growing and passionate.

The computer version IMT is just a piece of code, so programmers can change the way the ‘machine’ creates stories. Programmers can give it the same probabilities as the monkey on the keyboard - 1/50, every time - or make it more intelligent and create plots and parameters and choose from a work back.

And so the computer is infinitely times smarter than a chimp, and if we ever need replicate copy of Shakespeare produced at random, it won’t happen by a chimp, it’ll happen on a machine.