Could A Monkey Randomly Pounding Keys Type Out Shakespeare?

Brilliance | Dec. 18, 2017

Put one million monkeys with typewriters inside a spaceship that travels for 10 billion years. By the end of the trip, the monkeys will have typed a Shakespearean sonnet. Sound far-fetched? This monkey problem defends the possibility of life arising by chance.

The Problem

You take a trip to New York City from your southern hometown. With roughly 8.4 million people on the island, what are the chances you'll run into someone from home? It probably feels like chances are slim to none, so running into your grade school math teacher at the Statue of Liberty will seem like a major coincidence. As it turns out, chance doesn't always work the way we expect it to.

The monkey problem is thought to have originated in 1913 with mathematician Emile Borel. His goal was to answer the question: "Could totally random events amount to something meaningful?" or, "Could a monkey randomly hitting the keys of a keyboard type out a Shakespearean sonnet?" It's technically not impossible.

The Answer

In a 2003 study at the University of Plymouth, researchers studied real monkeys at a zoo in England for one month. The monkeys produced five pages of letters (which you can see here), but they were unable to type even a single-letter word ('I' or 'a'). However, the monkeys did prove to be more complex than "random generators." If we had infinite monkeys typing for an infinite period of time, then hey, it's possible!

This monkey theorem introduced the statistical law of very large numbers. For example, the likelihood of the monkeys even getting a one-letter word (that is, a letter with a space on either side) is 1 in 27,000: with 30 possible characters, there's a 1 in 30 chance of getting each space and the letter in the middle, so that's 30x30x30. For full words, not to mention an entire sonnet, those numbers get much, much bigger. Uncover more of the math behind this problem in the video below, then ask yourself: is it really a strange coincidence when you run into a friend in a large city?

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