# Column: Shakespeare, mathematics and the monkey who called 911

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Have you heard about the monkey who called 911?

Two weeks ago the San Luis Obispo County sheriff’s office received a 911 call, but there was no voice on the other end. Baffled, deputies were dispatched to the source — a local zoo — to hunt down the caller, but they found no humans in distress. Instead they realized that a capuchin monkey named Route had grabbed a mislaid cellphone and randomly banged at the keypad until she called the emergency number.

Everyone laughed it off. The news stories said things such as “that’s bananas” and dismissed it as “monkey business.” But the story got me wondering. How likely was it that the monkey would call 911? Of all the keys Route could have punched, what were the chances she would hit a 9, a 1, another 1 and then the green “connect” button all in a row (assuming she didn’t just happen on an “emergency” key)?

So I did some research. Very little, because I’m not mathematically minded. But here’s what I learned.

Opinion Columnist

Nicholas Goldberg

Nicholas Goldberg served 11 years as editor of the editorial page and is a former editor of the Op-Ed page and Sunday Opinion section.

If there were 13 buttons on the phone keypad (10 numbers, plus an *, a # and the connect button), Route had a 1 in 13 chance of hitting the 9 randomly. The chance of hitting the 1 next was also 1 in 13, as was the chance of hitting a third 1 and the same for “connect.” The chance of hitting the full four-button combination was 1 in 13 X 13 X 13 X 13. Or 1 in 28,561.

The more keys she struck, the better her chances became. (This doesn’t take into account that she might also have to disconnect between tries.)

On the face of it, Route’s story is just an amusing little anecdote. But it brought to mind something else — the old thought experiment that basically hypothesizes that an infinite number of monkeys typing for an infinite amount of time would eventually produce “Hamlet.”

I always assumed this was just a bit of drunken barroom philoso-babble. But it turns out it’s a real thing. It even has a name: the “infinite monkey theorem.”

And it isn’t really babble: The infinite monkey theorem is not only true, it raises serious questions — cosmic, existential questions, such as whether meaning can arise out of chaos, or complexity out of randomness.

Scientists, for instance, have used the parable of the typing monkeys in debates over how evolution could have occurred from random mutations.

It also makes you wonder about the distinction between genius and dumb luck. It even seems to hint that Shakespeare isn’t so great after all because a bunch of monkeys could write his plays.

Apparently many non-mathematicians don’t believe the infinite monkey theorem is true when they first hear it. That’s because humans have a difficult time with the concept of infinity.

Infinite time is not just a long time. It’s forever.

Given that there are a limited number of keys on a typewriter and that the monkeys have an unlimited amount of time to type, it stands to reason that eventually every possible combination of keys will be struck. So the monkeys will almost certainly type “Hamlet” sooner or later. And “King Lear.” And everything else ever written.

In fact, you wouldn’t even need an infinite number of monkeys; one would suffice. (Admittedly, he or she would have to live forever.)

“In infinite time, even things that are extremely unlikely will happen,” says Deanna Needell, a professor of applied mathematics at UCLA. “They seem unfathomable because we live finite lives and think in finite terms. But in infinite time all those unthinkable things? They happen.”

So now let’s imagine that the monkeys don’t have infinite time. Could 100 of them type “Hamlet” in 100 years? A thousand years? How long would it take?

There have been a number of efforts to answer this. My favorite requires no math skills whatsoever. In 2003, professors and students at Plymouth University in England put a computer into a cage with six crested macaques for a month.

This did not result in “Hamlet.”

Instead the monkeys typed about five pages of gibberish, mostly using the letter S. They also hit the keyboard repeatedly with a rock. And they “soiled” it, apparently by urinating on it.

Thus proving the statement attributed to MIT mathematician Gian-Carlo Rota: “Giving monkeys typewriters is not a practical method for writing plays.”

Another effort to randomly type Shakespeare was undertaken by data engineer Jesse Anderson in 2011 — a computer-based simulation.

Anderson created millions of virtual monkeys that typed random sequences of text, each nine characters long. The strings of characters were then checked against all of Shakespeare’s works. When they matched, they were kept and used like a jigsaw puzzle piece toward the creation of the whole.

Anderson’s program re-created Shakespeare relatively quickly. But mathematicians said his methodology made it too easy.

Ian Stewart, an emeritus professor of math at the University of Warwick, told the BBC that it would actually take “longer than the age of the universe” for a monkey — or a virtual monkey — to randomly type a flawless re-creation of Shakespeare’s works.

To understand that, remember that there are 26 characters on a typewriter (counting just the letters). The likelihood of typing just the first 20 letters correctly of “Hamlet” would be 1 in 26-raised-to-the-20th-power, or 1 in 19,928,148,895,209,409,152,340,197,376, according to Wikipedia. (That’s ignoring punctuation, spaces, capitals and apostrophes.)

And that’s just the first 20 letters. “Hamlet” has more than 130,000 characters.

Of course, just as interesting as how long it would take is what it would mean were it to happen. Would “Hamlet” still be “Hamlet” if it was typed by random chance?

If the monkey (or computer program) that typed it lacked the intention to communicate but was driven entirely by luck and happenstance, has it really created a play? Is the monkey another Shakespeare?

Some philosophers seem to think so.

But I think that’s bananas.

@Nick_Goldberg