Infinite

Jorge Luis Borges is one of those authors who blows my mind. I don't know what other people think of him because he never really just comes up in a conversation. In my feeble attempts to fit in at parties, even I never throw out, "So you ever read Borges?" Maybe I should, maybe that's what I'm doing wrong. Interesting thought. Anyway, I was re-reading one of his short stories the other day and I rediscovered what I always thought was an interesting line. He never wrote a novel, only poems and short stories and some essays, but for my money you go with the short stories. In one of them, or maybe it was even an essay, he has what amounts to a throw away line that is an incredibly interesting way to think of infinite. He says something like, "Most people assume that to do an infinite number of things you need an infinite of time. In fact, all you actually need is any set period of time that you can divide into an infinite number of pieces." Then he goes on like that was obvious. Think about that for a minute, it's actually quite interesting, partially because it is a very distinct way to think about infinite.

I agree that anytime you have to think about infinite and things like that, it requires abstraction that we don't really get (I don't really get it either, but I like to pretend). That line however, that fresh perspective, has always amazed me. Borges was also the first author I read to discuss Zeno's paradox from Ancient Greece, and for that he will always have a special place in my heart. Here is info on the paradox from wikipedia. Basically, it is a little paradox that "proves" motion is impossible. The crux of the argument is that in order to move across the room, you must get to the half way point. In order to get there, you must 1/4 of the way across the room. To get there, you must get 1/8 of the way across. If you follow this train of thought to it's logical (or illogical?) conclusion, motion is impossible because you always have a halfway point. There is another fun example pitting the mighty Achilles from the Trojan War against a turtle in a foot race. In this example, the turtle starts out with a lead because Achilles believes he will catch up. However, Achilles never catches the turtle because when he arrives at where the turtle was, the turtle has moved on. When Achilles arrives there, the turtle has moved on again, and so on. The distance between the two becomes increasingly smaller, but Achilles must always arrive where the turtle was, only to find the turtle has continued to move on. This is a different example than the proof against motion, but it is logically the same argument.

It is extremely difficult to disprove these paradoxes logically although it is easy to disprove mathematically or by, say, moving. However, I read a book about the number zero that was called, conveniently, "Zero" (I don't bring that up much at parties either) and it argued the Greeks couldn't mathematically resolve this paradox because it really requires a limit, thus calculus (as time goes to 0 or as the change in distance goes to 0), to resolve, and the Greeks didn't do limits because they denied infinite and 0. So that's why you should embrace them both, it's freeing. Anyway, the riddles themselves are interesting thought puzzles and I always wondered if you did these with children (middle school maybe) what kind of answers they would come up.

So there you go. It is possible to do an infinite number of things in a set period of time but, ultimately, it doesn't matter because motion is impossible anyway. If that's true, and how could it not be, maybe I'll take tomorrow off of work. Regardless, wouldn't it be nice to think about that laying on the street in front of my old house in Honduras staring at the stars?

Final note: if you ever decide to read Borges (and you should consider it), I recommend reading a story or two before purchasing the book in case you don't like his style. I think Labyrinths is his best work and it has some of my favorite stories. Borges had an uncanny ability to link and discuss disparate ideas in his stories in a way that interests me. His is not the kind of mind I want to meet, it is the kind of mind I want to become. I think The Garden of Forking Paths is a good intro into his circular style , but The Immortals is probably his most profound. Both are in Labyrinths with a lot of other great stuff.