There are rules about defining words, none more important than not using that word, or a derivation, in the definition. I think the word most difficult with which to follow that rule is Infinity, even more so than God. (Though there are undoubtedly many who would define either with the other. Thought for a different day.) Douglas Adams tried to define it in the "Hitchhiker's Guide" with the Total Perspective Vortex, a totally diabolical device that, once placed in, shows you the whole hugeness of space, with a barely discernible point and an arrow pointing to it that says, "You are here." The realization of your insignificance to the whole of Creation would drive you insane. I am probably already insane, and long ago embraced my insignificance, so let us press on. You may follow at your own risk.
In Junior High, the standard way to define the concept of Infinity was with this example: If an infinite number of monkeys typed randomly on an infinite number of typewriters, one of them would write the complete works of Shakespeare. (Randomly? Like a monkey is going to type specifically?) I think it shows the absolute largeness of Infinity due to having to use a derivative word twice in our definition. Why monkeys, with their little fez' on their heads and nasty little, feces-encrusted fingers? Quite simply because horseshoe crabs found it impossible to hold down the 'Shift' key and the '7' key simultaneously, preventing them from producing an ampersand. Besides, the infinite sand and the infinite surf from the infinite beaches the infinite horseshoe crabs required would play hell with the inner workings of the infinite typewriters. (So, as can be plainly seen, Infinity is mostly just a matter of logistics.) And why Typewriters? Wouldn't a computer with a good word processing program be better? Not better necessarily, but you could certainly reach Infinity much more quickly. Finally, why Shakespeare? Because no self-respecting, infinite monkey would write that shit on purpose. Awwww, "Et tu, Brute?"
So let's update the definition: If an infinite number of chimpanzees (with cowboy hats) randomly struck an infinite number of keyboards, one of them would write the complete works of Shakespeare. Why 'cowboy hats?' Why does there always have to be a reason?! I just like cowboy hats, alright?! Unfortunately, there was no room in the infinite budget for the matching infinite chaps. (That's strange, you'd think there would be.) And why chimpanzees? Because cowboy hats make monkeys look ludicrous. Jeez, give me a break.
So now we have a definition. Could it be correct? Yes, yes, yes! (Could it be Benjamin? Yes, yes. yes! Extra credit for referencing this remark.)
Yes, one of the chimps will write the complete works of Shakespeare...............George Shakespeare, whose complete library of works consisted solely of volumes of random letters, and mostly ampersands. (Oh didn't see that one coming, did you?) Conveniently, the nature of Infinity means that one of the chimps will also write the complete works of William Shakespeare.
"Okay, we get it," you think to yourselves, "Infinity is just f&cking big. Thanks for the lesson, be seein' ya." First of all, I don't like your language. That is a totally inappropriate use of an ampersand, and horseshoe crabs would have the balls to spell the word properly......if horseshoe crabs had balls, I guess. And second of all, "Wait, come back, there's more, Infinity can get bigger." Echo, echo, echo. That's right, bigger. Well, not so much Infinity getting bigger, but your perception of it getting bigger.
Okay, this first one wrote the complete works, and let's say he got all the plays in alphabetical order, followed by all the sonnets in alphabetical order. Sounds reasonable. Now, another one will write the complete works, except the sonnets come first, then the plays, but still in alphabetical order. But wait, a third one writes the complete works, but does not separate the plays from the sonnets, yet maintains an alphabetical order. Then comes the joker, the one who writes the complete works, but says, "To hell with the alphabetical order." (Not really sure of a chimpanzee's concept of hell, but I imagine it involves a cowboy hat.) Of course, there must be a fifth one who randomly wrote the complete works as the first one did, except switched the first play with the second. Ah, I think you might be seeing where I am going. Infinity is expanding, expanding faster than my waistline at an all-you-can-eat Chinese buffet. Think about all the different arrangements you can make with all the plays and sonnets. How many? I think the mathematical operation factorial will calculate that number for you. "Factorial?" your pathetic eyes implore, "what is factorial?" Damn it, Jim, I'm a doctor, not a mathematician. Look it up, even chimpanzees in cowboy hats know how to Google, when they're not writing "Macbeth."
So, Infinity seems to be a lot of little infinities piled on top of each other. Not sure you can make piles of Infinity, but is does seem a little larger. Can we up the ante? Sure. Let's go back to that first one, who wrote the complete works in alphabetical order. Out of the remaining infinite chimps (and don't bother to point out 'infinite' and 'remaining' are mutually exclusive, I know), one, say the 49,257,605th one (Why 49,257,605? It's my lucky number, of course.), will get it exactly the same, ...............except, the first letter of the first play will be wrong, it will be one of the other 25 letters. This means that 24 other ones will do the same thing, each with a different letter. And actually, it isn't limited to letters, it must include numbers, spaces, and punctuation marks. We don't stop with the letter in the first position, we continue repeating the procedure with the second position, the third position, the fourth, the fifth, sixth, seventh, ............phew, until every position in the first one's list has been changed. But we're not done. The same thing will happen with all the other letters, numbers, spaces, and punctuation marks as the second one originally wrote. Then we do the same to the third one. In fact this will happen to every one of the permutations we did originally. That is a lot of different near-copies of the complete works of Shakespeare. I sure hope we are saving them all to flash drives. Imagine how many trees we would have to kill to print them out. No need to imagine, it would be all of them.
My head is starting to hurt, but until my ears start to bleed, let's press on. We go back to the chimp above, the first to have an incorrect letter, the 49,257,605th one. (God, I love that number.) Somewhere, another one, who knows, might even be sitting beside the 49,257,605th one (What are the odds of that? Don't know, but in an infinite universe, it isn't zero.) will type it exactly the same.............. except instead of just the first letter (position) being wrong, the first and second letter are wrong. Before proceeding, we apply this permutation to the second group above, which of course is factored by the first group. Then we come back and change the first and third position, then the second and tenth, the 200,047th and 301,489th position. When every combination of two positions has been exhausted, we move to three positions, then five positions, then 105,288, until all the positions are done. In fact, if you place every letter, number, space, and punctuation mark of each example in the first group in a grid, for every one of them, there will be one that will not have a single letter, number, space, or punctuation mark in the same grid location. Do I hear blood in my ear canals?
Earlier I asked Why Shakespeare? Why not Zane Grey. Why not Robert Ludlum? Mark Twain? James Joyce, Emily Dickinson, Sun Tzu, Homer? And why not the instructions on a TV dinner, or the warning label on a bottle of Celebrex? One chimpanzee will randomly write all of these things individually. And there will be one each for all the variations above. Continuing, there will be one who will write the complete works of Shakespeare and Zane Grey. One who will write Shakespeare and Ludlum. One who will write all of Twain and Joyce. Shakespeare, Homer, Verne, Dumas, and the label of a bottle of shampoo. (Rinse and repeat, indeed.) One of these infinite chimps will surely, by total accident, produce the complete collection of every written word created by the thought of man. That means a second one will do it too, just in another order. In fact, there will be a lot of different orders. Don't forget all the other ones who will create all the variations from the three applications above. Finally, there will be one sad chimp who won't get a single goddamn thing right. "Ooooooooo, sorry. Johnny, what do we have as a parting gift for this contestant? Well Alex, from Christian Dior, we have this lovely cowboy hat, with matching chaps. Thanks for playing."
So, Infinity, hmmmmm, pretty big I guess. We've taken the original premise, which seemed huge at first, especially to a seventh grader, and expanded it to a much larger concept. Larger, but we still have one more thing to consider, and it is what makes Infinity so hard to grasp. In all my examples above, I have used 'one' as the number of chimps achieving a result, and that is exactly true, if not perfectly true. In fact (and I think some of you are ahead of me on this), in every instance I used one, I should have used infinite.
Drops microphone, walks offstage. (Thunderous applause.)
Don
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