A conundrum solved: The Why staff has developed an obsession over a truism, and we have to deal with it before we can return to our normal format (pose a provocative question, give a brilliant answer, retract everything the following week).
The truism is: If an infinite number of monkeys pound randomly on an infinite number of typewriters, one of them will write "Hamlet."There are slight variations on this - you might have just a few monkeys and an infinite amount of time. For that matter, the truism works if you have just one monkey, so long as the monkey is given an infinite amount of time to tickle the keyboard.
(To cite one fine use of the truism: Washington Post columnist Richard Cohen wrote a few years ago, "If an infinite number of monkeys, given an infinite amount of time, could produce `Hamlet,' then two of them could, in a night's work, come up with `The Morton Downey Jr. Show.' ")
We decided the truism needed to be checked out. We found that the truism is, in fact, true, but with an asterisk.
First, you have to realize that the mathematical basis of the truism is irrefutable. If a single monkey is put in front of a typewriter (we are presuming that the monkey has some innate desire to type, and never grows old or gets tired or runs out of typing paper), there is a very small but non-zero probability that he will knock out "Hamlet" his first try. The more chances the monkey gets, the greater the probability of writing "Hamlet." As the number of chances rises to infinity, the probability of writing "Hamlet" increases to 1 - a certainty.
You should also recognize a disturbing corollary of the truism: Not only will the monkey eventually write "Hamlet," he'll even write the lesser Shakespearean plays, and all the works of Marlowe, Shaw, O'Neill, and he'll write "Moby Dick" and "Soul on Ice," and he'll write that letter your mother sent you last week in which she talked about the beetles in her garden, and he'll write the Great American Novel that will be composed in the year 2078 by an as-yet unliving person.
The monkey, by chance, will eventually write everything that can be written using a typewriter keyboard. (We'll cut him some slack on italicizing certain stage directions.)
An article in New Scientist magazine in 1984 criticized the monkey truism on the grounds that there's not enough energy in the universe to allow a monkey to hit the keyboard enough times to come up with even so much as the line, "There are more things in heaven and earth, Horatio, Than are dreamt of in your philosophy." But we don't share that objection, because this is just a thought experiment, not a real experiment.
Here's our beef: The same randomness that causes the monkey to write "Hamlet" should leave open the very slim possibility that the monkey will not write "Hamlet."
Let's say the monkey, by chance, is in the middle of pounding out "Hamlet" and is right at the point where Hamlet is holding Yorick's skull, and the monkey types, "Alas, poor Yorick. I knew him . . ." What will he type next? The text says, "I knew him, Horatio," but people often misquote the line as, "I knew him well." Sure, chances are that at some point during the infinite reaches of time the monkey will write, "I knew him, Horatio," but - here's the rub - it wouldn't violate any law of physics or math for the monkey to screw up the line every time, forever.
It also wouldn't violate any laws of physics or math for someone flipping a coin to flip tails, and only tails, forever. Every flip, just as every keystroke, is an independent act and can have any result.
So maybe we shouldn't say the monkey "will" type Hamlet.
This, admittedly, is a hairsplitting point, though not totally inappropriate given the already absurd nature of the truism. Listen to this, from James Cargile, professor of philosophy at the University of Virginia: "Something could have a probability of zero and nonetheless happen, or a probability of 1 and not happen."
His colleague at UVA, Paul Humphreys, helped us understand this paradox. Take an infinite number of monkeys and let them type. The first monkey might hit "Hamlet" after 2 billion years, the second after two weeks, and the third might never (as we've shown) type "Hamlet" at all. At that point, the ratio of monkeys who will type "Hamlet" to the total number of monkeys is 2/3. The fourth monkey will type "Hamlet" after 900 quadrillion years. So the ratio rises to 3/4. The fifth types "Hamlet" after a period of time so vast that the imagining of it would cause your brain to explode. The ratio is now 4/5.
This continues on down the line of monkeys. Occasionally a monkey fails to write "Hamlet" - but at the same time, the ratio of monkeys who do type "Hamlet" to the total number of monkeys gets infinitely close to 1.
And a number that is "infinitely close to 1" is, in fact, 1. A mathematician will say that these are simply two ways of expressing the same number. You might raise some philosophical objections, but on the chalkboard it's undisputed.
So the bottom line is: There's a probability of 1 that a monkey will write "Hamlet," even though you can't absolutely rule out the possibility that he might never write anything better than "Titus Andronicus."
We're glad we could clear this up.
(For the record, the preceding was typed in two hours. Pretty much randomly.)