Monkey Business

From The Recursive Universe
by William Poundstone

The world’s staggering diversity seems to preclude any simple explanation. There is structure at all scales, from protons to clusters of galaxies. Even before unified theories of physics, the world’s richness seemed a paradox.

It is easy to show that the world is far, far more complex than can be accounted for by simple interpretations of chance. Take, for instance, the old fantasy of a monkey typing Hamlet by accident. If there are 50 keys on a typewriter, then the chance of the monkey hitting the right key at any given point is 1 in 50. There are approximately 150,000 letters, spaces, and punctuation marks in the typical text of Hamlet. Once the monkey has struck the keyboard 150,000 times, the chance that it has produced Hamlet is 1 in 50 multiplied by itself 150,000 times.

Fifty multiplied by itself 150,000 times (which can be written 50^150,000) is an unimaginably huge number. It cannot even be called an astronomical number, for it is much larger than any number with astronomical significance. Just writing 50^150,000 out would take about 255,000 digits.

In contrast, all of the large numbers encountered in physics can be written out easily. It is estimated that the number of fundamental particles in the observable universe is (give or take a few zeros) 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000. Vast as this number is, it is nothing compared to 50^150,000.

In view of this, it may seem remarkable that anything as complex as a text of Hamlet exists. The observation that Hamlet was written by Shakespeare and not some random agency only transfers the problem. Shakespeare, like everything else in the world, must have arisen (ultimately) from a homogeneous early universe. Any way you look at it, Hamlet is a product of that primeval chaos.

If every particle in the universe were replaced with a monkey and a typewriter and all the monkeys had been striking keys since the big bang, the chance of producing Hamlet would still be negligible. Yet Hamlet was produced from a series of physical processes that (initially, at least) were even more chaotic than monkeys banging at typewriters.

Copyright © 1985 by William Poundstone

Technorati tags: Probability