One often hears the assertion that if you left a million monkeys bashing away at a million typewriters, you would, eventually, get some randomised versions of Shakespeare's plays, sonnets or poems. About ten years ago, someone at a university, obviously with a 'research' grant and a sense of humour, decided to test this hypothesis.

They proved, that a hundred monkeys bashing away on a hundred keyboards for a year does not produce any of Shakespeare's work, or anyone else's for that matter. What it did produce was a lot of frustrated monkeys (Press keys to get reward), a lot of wasted effort and hundreds of broken keyboards.

So next time someone says, "if you put a million monkeys in front of a million keyboards ..." you can now say with absolute confidence - "No, it doesn't. All it produces is a lot of monkey p**h and a million broken keyboards.

## Monday, 16 July 2012

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I fear that you have set your sights rather low here. The "Infinite Monkey theorem" contains a word that is beyond human understanding for most people, infinite. To talk of hundreds or even millions of keyboards is not even to scratch the surface. In my schooldays, the mathematical illustration of immensity in vogue was the "Googleplex". A Google is a one followed by one hundred noughts; a Googleplex is ten raised to the power of a Google. Even this number does not come close to the concept of infinity. The smallest measurable space or volume is generally assumed to be a cube of which the side is a "Planck length", a Google "Planck spaces" would make up around 2.5 ml, the observable universe has only room for about 0.001 Gooleplex Planck spaces, and as I suggested, it doesn't come anywhere close to infinity.

ReplyDeleteIf you were inclined write, at two characters a second, it would take 1.5 x 10^92 years to write a Googleplex, what a pity the universe is commonly accepted to be only 1x10^82 years, I also think you might run out of ink.

So, let us consider some form of quantification of the "Infinite Monkey Theorem". If we restrict ourselves for the thought experiment to a keyboard with only 50 key, then to get a random typing of the single word "banana", we would require six multiplications of a one-fiftieth probability, that works out a one in one and a half billion chance; a tiny number in relation to infinity, it makes a one in fourteen million lottery win almost a certainty by comparison.

Even if the observable universe were filled with monkeys the size of atoms typing from now until the heat death of the universe, their total probability to produce a single instance of Hamlet would still be a great many orders of magnitude less than one in (the figure worked out like "banana" for typing Hamlet, even if there were only 26 keys and we ignored punctuation.)

Kittel and Kroemer in their 1980 text "Thermal Physics" stated;

"The probability of Hamlet is therefore zero in any operational sense of an event...", and the statement that the monkeys must eventually succeed "gives a misleading conclusion about very, very large numbers."

However, it is the very concept of "very, very large numbers" that is important when considering the concept of infinity. The quantification of infinity is beyond human imagination, we must therefore use metaphor to illustrate it, possibly a monkey-based metaphor.

Where there exists very, very large, then there must also be considered the very, very small. (Dave Rae is the expert here, his paper "from Angstrom to Parsec" dealt with this topic. [1 angstrom = 3.24077649 × 10^-27 Parsec])

When we consider the very, very small we hit similar barriers to understanding. This is the true reason that the Higg's Boson is given it's newspaper headline name.

To paraphrase with tongue firmly in cheek it is "the piece of God that passeth all understanding.

Thanks for putting in all the big numbers. The larger the number of monkeys and keyboards, the more broken keyboards and monkey ...

ReplyDeleteAh, monkeys bashing away at keyboards? You describe the Civil Service, O Monk! Poor Josephus, he really must get out more...

ReplyDeleteSlim Jim

Loved the post and the responses. Weird but I had just looked up Googleplex recently for my son.

ReplyDelete