## Can a Monkey Type “Hamlet” Given Enough (Infinite) Time?

You’ve heard this before. Give a monkey an infinite amount of time on a typewriter and he/she will eventually type out Shakespeare’s play Hamlet. The idea is that no matter how impossible it might seem it’s just a matter of time. If the monkey has an infinite amount of time it will happen. Atheists and skeptics like to use this to illustrate the point that given the current theory of the multiverse which posits an infinite number of universes it is only natural that a universe like ours will exist so there is really nothing special about it. All this talk of fine tuning means nothing since infinite time plus matter will eventually produce a universe that can sustain life. No need for God.

In his book Why Science Does not Disprove God Amir Aczel explains how this really does not work. He writes,

“The heart of the argument here is the immense power of infinity. If you allow infinity to enter any argument, anything can happen—even monkeys typing Hamlet. The play has about thirty thousand words, and if we assume an average of five letters per word, that is about 150,000 characters that the monkey needs to get right and in sequence. So the probability of getting it right the first time (leaving out spaces and punctuation, which would make it even more difficult) is one divided by 26 raised to the power 150,000, which is a number very, very close to zero—but not identically zero. Making the number of trials equal to infinity ‘forces’ the answer to be 100 percent. It is simply a mathematical fact that has no meaning outside the realm of pure mathematics and does not describe the real world in any way. So playing the ‘monkey typing Hamlet’ game is not a good approach to real-life situations, and real universes—of which we know only one. . . . And it isn’t science, since it’s not based on any reality, any experimentation, or even any viable theory. It is simply a ‘forcing argument’ that allows you to prove anything you like. It’s just like proving that a monkey can type Hamlet despite the unreality of the whole idea: the only reason it works is that infinity is such an overwhelmingly powerful concept. It you ‘go to infinity’ (whatever that may mean, since infinity is inaccessible to us), you can pretend to prove anything. So the multiverse and the infinitely many copies of you and me that Brian Greene seems so eager to assume must exist out there (where, exactly?) mean absolutely nothing and really have no place in any scientific argument about nature, life, and our universe and where it came from.” (pp. 165-67)

In another place he adds color to what this would really entail.

“The monkey typing forever, meaning producing infinitely many replications of 26 characters, will theoretically produce not only the whole of Hamlet–in fact, the monkey will do it infinitely many times!–but also every piece of writing ever created in history, including all the works in the lost great library of Alexandria, as well as Virgil, Dante, Hemingway, Jane Austen, Salman Rushdie, and the U.S. Constitution; and every letter any person in history has ever written to another person, or would have written, or might write, or could write, or will ever write; and every possible grocery list, and every possible presidential election speech. You can see just how preposterous all of this becomes when you try to apply an abstract mathematical concept to the real world. And by the theorem I’ve alluded to, it may take “forever” for these things to happen.”

The idea is simply crazy and adding “infinity” to it to give it credibility won’t help.

Why Science Does not Disprove God is from Willow Morrow (an imprint of HarperCollins). It is a hardcover with 304 pages and sells for \$27.99.

Amir D. Aczel, Ph.D., received graduate degrees in mathematics from the University of California at Berkeley and the University of Oregon. He is the author of the acclaimed Fermat’s Last Theorem, which has been published in twenty-eight languages and was nominated for a Los Angeles Times Book Prize, and many other works of nonfiction. In 2012, he was awarded a Sloan Foundation grant for his groundbreaking research on the origin of numbers; in 2004, he was awarded the prestigious John Simon Guggenheim Memorial Foundation Fellowship. From 2005 to 2007, Aczel was a visiting scholar at Harvard University. He is currently a research fellow in the history of science at Boston University. He also writes for Discover magazine, regularly publishes in Scientific American, and has written science pieces for the New York Times and the Wall Street Journal.