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Monkey Business

Recent developments in monkey related science indicate that, given this small portion of monkeys (6) they have managed to produce a few key presses and damage the controller. Hardly the works of Shakespeare. The long standing theory of the infinite monkeys eventually producing the works of Shakespeare is giving my brain a brief fizzle; Monkeys, amusing and as impressive as they are, are not the point of the statement; it's just to say infinity is damn big. After all, an infinite number of ping pong balls, kangaroos or penguins have an equal chance of doing exactly the same thing.

But lets not belittle our monkeys at this point. Infinity is a pretty damn useless number when it comes to statistics, comparisons and any useful data fail utterly at this point. So lets ponder a little here; How long would it take a non-infinite number of monkeys to produce this famed work of literature? Firstly we need some raw data and some assumptions, statistics wouldn't be the same without them...

A downloaded copy of the complete works of Shakespeare in raw text form is 5,519,895 bytes, that is 5,519,895 characters (roughly) for the monkeys to get correct, in sequence. Now we'll give the monkeys a break here, we'll not expect them to work in English, after all there are around 5000 or so living languages (possibly more, number extracted from an internet source) of which around 200 have more than a million speakers; but since the monkeys are going to need every chance they can get to produce this, we'll let them use any one of these 5000 languages, this may cause translation problems and of course is limited by keyboard layouts (not everyone uses westernised keyboard sets) but we'll simplify this or we'll never get anywhere, 5000 is their magic number. Yes, it's monkey magic.

Units; We'll standardise the Monkey-Day (MD) as our basic unit of working time, indicating the amount of "working" time your average monkey does during a day, with respect to producing great literature at least. But, since we're interested in total time for completion here, rather than logging work hours for company gant charts we'll include in our MD things such as sleeping, eating, throwing bananas, etc. This will include eight hours sleep (for a good healthy working day) five hours eating, arse scratching and playing around and the rest we'll have him tied, metaphorically, to his typewriter or frankly we'll never get this thing done. This gives 11 hours every day of productive monkey activity.

Next up, productivity; now this is the tricky one. The monkeys in the example above produced a small book in a month, this was actually six monkeys, not one however. Further research here here indicates that it is a 16 page book. I have it on order, but can't yet see how many lines/columns per page this actually is. So we'll have to make some assumptions. We'll give the monkeys 12 point font which will probably go nicely at around in 80x40 lines of text per page. Giving them a total productivity of 16x80x40 /30 (days) /6 (no. monkeys) = 284.5 (approx) characters per monkey per monkey day. They really need editorial pressure.

So, we have our Joe average typesetting monkey producing great works of literature at around 284.5 characters per day. He has a goal of 5,519,895 characters. This will take him a total of just over 19402 days, that is, approximately 53 years 1 month 13 days. Assuming of course that he gets it right first time - we should be so lucky.

This brings us to another problem, of course. And a new factor. Monkey entropy. According to this website, the average age, in the wild, of a Macaque monkey is around 30 years, maturing at 3-5 years (females) 4-5 years (males). This is similar to the ones who were in the experiment, so for purposes of this wildly pointless speculation we'll use this as a benchmark. So for each monkey we only get 26 years of useful productivity anyway (we're not going to force them to work before they're fully grown, there are labour laws). Which means that for every work of Shakespeare produced we 'lose' two monkeys due to aging.

So, we have just about all the data we need now, and can gestimate monkey productivity of the works of the muse in reasonable terms, all we really need is state a required chance to produce the entire works of Shakespeare, the final probability we need is the probability of producing the entire works of Shakespeare. This is going to be somewhat remotely improbable; specifically it will be 1/27 (26 alpha characters plus space) to the power 5,519,895 (required characters) multiplied by 5000 (available languages). This is going to be a very, very, very, very small number indeed. Or

( 1/ (27^5519895) ) * 5000, meaning the number of languages is almost basically irrelevant.

I don't actually have any means of calculating this number, it's simply mathematically too tiny to actually store on any system I know of. But suffice it to say it's bloody tiny. What we'll have to do is try and give the monkeys a small chance of producing the book, and just go with it. Since we want to be able to actually use the values we use here; we'll give the monkeys 1,000,000 * 5519895 chances, which is still a very slim chance compared to the probabilities required here, but hell, I want numbers to use. This also gives them a million chances at every since character for every character there is. Quite a few tries really, and quite a few monkeys. Hopefully they'll at least manage one of the sonnets or something.

So, what does this give us?

5519895 * 1000000 attempts * 19402 days = 293,215,613,388,090 years. Or just over 293 billion monkey/years and around 112 billion monkeys.

So what does this tell us?

a) Infinity is bloody big
b) Monkeys have a snowballs chance in hell of ever producing any kind of literary work
c) I am really bored this morning.

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