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Sunday, July 29, 2007

Infinite monkeys

I've been thinking about the infinite monkeys theorem today. In case you are one of the 27.3% of people who don't know (that I make up these statistics of the top of my head), the infinite monkeys theorem basically states that if you have an infinite number of monkeys all sitting in front of typewriters bashing away, sooner or later one of them will write out the Bible, or the complete works of William Shakespeare, or whatever lengthy tome of purple prose you care to name.

Now, I know infinity is a big number (*ducks at maths majors everywhere hurl compasses at me in contempt*). OK, so it's not a number. It's too damn big to even BE a number. What I'm getting at is that infinity is big. REALLY BIG. In fact it's bigger than big. You may think Bill Gates has a lot of money, but he only WISHES he had infinity dollars. You know what infinity dollars can buy? A Lear jet? Try TWO Lear jets. Damn right mofo. And wide-screen TVs to go in both of them. You know what else? As many crates of Laphroaig as you can guzzle. Infinity it so big that no-one can count to infinity (except Chuck Norris, who has done it twice). Did you ever have races in maths class where you start your calculators at zero, put in "ANSWER + 1" and press enter a heap of times to get the highest number by the end of the lesson? You will never get to infinity by doing that. Even if you secretly change it to "ANSWER + 2".

So we've established that infinity is rather large. So it will trump any argument about just how statistically unlikely it is that a monkey will type the Bible (or even just Revelations, the only bit worth reading) by chance. But lets look at some figures anyway.

Now, if you have the means to produce an infinite number of typewriters for monkeys to type on, you might as well custom make them, since you already need infinite resources to manufacture them all. So exactly what characters will the typewriter need? For simplicity I'll assume we have separate upper- and lower-case keys, and a separate button for each punctuation character, so we can do away with shift and caps lock. So we will need:

  • 26 lower case letters
  • 26 upper case letters
  • Enter, space bar
  • Numerals 0-9
  • Maybe 15 punctuation characters (a conservative estimate, I would say)
  • A button to end the document
So that's 80 possible buttons for the monkey to press. We assume it's pressing them totally at random (which a monkey won't - more on this later). So how many combinations of documents can a monkey write then? Let's imagine a typical sentence - "The quick brown fox jumps over the lazy dog." By my count that's 44 characters. The number of different strings of text you can make with 80 buttons to press and 44 presses is 80 to the power of 44:

80^44 = 5.4445*10^83

...which is more than the number of atoms in the universe. And that's one sentence!! If you want the poor monkey to write the whole Bible, the number of combinations becomes unthinkably large. According to Meredith’s Book of Bible Lists (as quoted on this page), the number of words in the Bible is roughly 845,000. I'm going to make a total guess here and assume the average number of letters in each word in the bible is 6. Add in the spaces and passage numbers and punctuation, and it might go to maybe 7.5 characters per word (don't quote me on this, it's a very rough guess). Multiply 845,000 by 7.5 and you get 6,337,500. So more than six million characters go into printing a single Bible. (What a fucking waste of ink.) So the number of possible combinations is:

80^6,337,500

Which is a number so flabbergastingly large that a human brain cannot even comprehend it. The odds of a monkey randomly typing the Bible are therefore pretty slim indeed. To put it lightly.

Analysing all these numbers is all well and good for a bit of mathematical muscle flexing, but of course...

...there are problems.

As I already mentioned, you would need a lot of resources to obtain all these typewriters and monkeys. Infinite resources. In short you could never get this kind of money. You may think dealing crack is pretty lucrative, but...

OK, let's not get into this again. So! Aside from the physical impossibility of setting up this over-engineered method of copying Shakespeare or the Bible (which, let's face it, you could do with a humble photocopier), there's a few assumptions in play which aren't necessarily valid. The first is that a monkey will type in a mathematically random fashion. It almost certainly won't. If it repeatedly bashes the typewriter at all (which is by no means a given, as it will probably figure out pretty quickly that all the key-bashing isn't going to set it free to play in the trees like monkeys are meant to do), it will probably end up pressing a few keys each time, leaving clusters of letters/numbers/punctuation that are situated close to each other on the keyboard. If you look back over this article you won't see any of this:
jiosrg9p-0]l
etcslts[opar6uj9p0ae4i.
pojprybu,9p]5m]ny0 o'dfgo[ptrdj
[OPW.ET
YP78SB5EJ098MU]W-58Y9PW45B0 U749N6 9UY45896N7YQE[8 YJHOUIDRYG;UAHROUH h uoiph ui;hyuaipdry tuiperhyuohaeruipt yh[oierhj t[80g9adyrtipuhdofune97arpy
Or any of this either:
xod0fcl'{
:}';{}
zs'
}:colfcofrodrikd8ikl.xlAZ';{?z;/.lc ';{? vbp;x
(Hey, I bashed out a few smileys there. Sadly Shakespeare used very few, if any, smileys.)

The next problem is that monkeys need to eat and exercise and take dumps and stuff. You could feed the monkeys at their typewriters but then they might get food in the typewriters and screw them up. Taking all these monkeys out to an exercise yard of some sort, and then hauling them all back to the typewriters when the break's over, would be problematic to say the least. And you can't stop monkeys from hurling their shit everywhere and, again, wrecking the typewriters and/or what's been typed.

Another problem: Who's going to sit around all day reading through infinite amounts of paperwork searching for "thee"s and "thou"s and "Alas, poor Yorick! I knew him, Horatio." and "Whatsoever hath no fins nor scales in the waters, that shall be an abomination unto you." (Lev. 11:12)?

The last problem is that Jane Goodall would come and kick the arses of whoever set up this sweatshop and set all the monkeys free, leaving typewriters, banana peels and half-finished copies of Hamlet strewn everywhere.

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