How many monkeys to type a book?

Monkey using a laptop computerHere is an interesting old riddle.  If we set up a room full of monkeys, how long would we have to wait before they type out Hamlet?  This is sometimes called the infinite monkey problem.  It does not take a long time to figure out this will be a long time.

The monkeys can’t read, so they type at random.  They might type out a book, but since it will be random, every letter in the book will be random. Considering every possible random choice for each letter in a book, there are about 101,000,000 possible books the monkeys could type out, including ones consisting almost completely of commas.  Only one of that huge number is Hamlet.  We would have to wait an unimaginably long time for our monkey-approved edition of Hamlet.

We could try to improve our odds by making use of very quickly typing monkeys, perhaps they could type at the speed of subatomic particles.  And perhaps we could use very small monkeys, the size of subatomic particles.  Oh, and make the room the size of the universe, with the monkeys stacked elbow to elbow, and have the monkeys begin typing at the dawn of time.  And let us not chauvinistically limit this to Hamlet, but allow for the production of any book worthy of a literary review.

I will not show you the algebra, which is easy to do, but the monkeys end up typing no books worthy of literary review during the lifetime of the universe.

Why then, if I replace my many subatomically-sized monkeys with actual subatomic particles at the dawn of time do I get, not only the entire works of William Shakespeare, but also those of Voltaire, the musical works of the Partridge Family, this blog, and other literary, artistic, and scientific works of greater and lesser value?   Oh, and before I forget, we also get, stars, galaxies, and, indeed, monkeys.


That is a subject for another day.  Nevertheless, to show that, in fact, you can get something from nothing – sometimes – I draw your attention to the Canadian winter sky where super-cooled randomly fluctuating water-vapour molecules stand ready to crystallize into beautifully symmetric, and almost infinitely variably-shaped snowflakes.

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