You’ve heard the story, I am sure. If you have a lot of monkeys typing away on lots of typewriters, eventually, given enough time (and bananas), they will type out the complete works of Shakespeare. The point of the story? That given enough time, anything can happen – that even the most complicated thing we can imagine, like perhaps the living cell, could happen entirely by accident.

Popular culture

On the face of it it sounds reasonable enough, and it has passed into popular culture in all sorts of ways. The story has been around a long time (who uses typewriters these days?) but the odd thing is, it’s only quite recently that a number of people have checked out the maths, with some very interesting results. The maths involved is in essence quite simple, but it produces some very large numbers indeed, and maybe this is why it is only in the era of computers that the calculations have been done. If you have a keyboard with just 26 keys for the 26 letters of the alphabet, the chances against hitting one particular letter by accident are 26 to 1. The chances against hitting 2 specific letters are 26 x 26 to 1; 3 letters is 26 x 26 x 26, and so on.

The complete works of Shakespeare…by chance?

So what are the chances of getting some Shakespeare? How about just one sonnet, a short poem, rather than the Complete Works? Gerry Shroeder (physicist, author and lecturer) writes:

‘All the sonnets are the same length. They’re by definition fourteen lines long. I picked the one I knew the opening line for, ”Shall I compare thee to a summer’s day?”. I counted the number of letters; there are 488 letters in that sonnet. What’s the likelihood of hammering away and getting 488 letters in the exact sequence as in “Shall I compare thee to a summer’s day”? What you end up with is 26 multiplied by itself 488 times…or, in other words, 10 to the 690th.’

1 followed by 690 zeros. That is what 10 to the 690th means. You know that one billion is 1 followed by 9 zeros – 1,000,000,000. Do you have the faintest idea how big a number 1 with 690 zeros is? Is there any other big number we can compare it with? Gerry Shroeder again:

‘Now the number of particles in the universe – not grains of sand, I am talking about protons, electrons, and neutrons – is 10 to the 80th …1 with 80 zeros after it. 10 to the 690th is 1 with 690 zeros  after it. There are not (not even close!) enough particles in the universe to write down the trials…’ (quoted by Prof. Antony Flew, author of ‘There is a God’).

So much for the ‘monkey theorem’. What seems on the face of it to be a piece of unremarkable common sense, is in reality complete nonsense. A story which was designed to prove one thing in fact proves the absolute opposite.

Could life happen by chance?

Some mathematicians regard anything above 1 in 10 to the 100th (1 with 100 zeros) as in effect zero probability – ‘it ain’t goin’ to happen’, as Shakespeare might have said. And of course a short 14 line poem doesn’t begin to compare in complexity and organisation with, for example, the living cell. The materialist philosophy of our time demands that life happened by accident. The maths say it didn’t. The Bible says it didn’t. Can you believe it?