Friday, July 27, 2007

It's Not a Race

So we stand once again on the edge of the stream of consciousness, and prepare to skip a rock across the placid waters of the mind. Prepare for unimaginable boredom.

One of Zeno's paradoxes of motion is illustrated in the parable of Achilles and the Tortoise. Basically Achilles - indestructible killing machine of the Myrmidon army, hero of various engagements in the Trojan war, and all-around stud - is set to race against a tortoise - wizened armored slowpoke and butt of philosophers' jokes.

Being a good sport, Achilles gives the tortoise a head start of, say, a hundred meters. If Achilles runs at ten meters per second (a prodigious pace of 22 miles per hour), and the tortoise runs at one meter per second, Zeno, venal and doddering old rascal that he is, says that Achilles can never catch the tortoise.

The theory is that by the time Achilles has run a hundred meters to catch up to the tortoise, the tortoise will have run an additional ten meters. In the time it takes Achilles to cover that additional distance, the tortoise will have progressed another meter, and so on, ad infinitum. This is the same logic that irrefutably proves that the minute hand on your watch can never overtake the hour hand. And as slow as time may seem to crawl on certain painful days, it is immediately apparent to the most casual observer that there must be some flaw, some hidden fallacy, in Zeno's perfect logic.

Ever get the feeling that no matter how hard you work, how much you apply yourself to a task, you'll never reach the end? All the tortoises are writing the rules and, slow as they are, they can't be beaten. Now I'm not such a good sport, and rarely give head starts if I can avoid it, but I've run a lot of those races recently, and visions of turtle soup are starting to dance through my head.

The tortoises will tell you "Work Smarter, Not Harder". This is a facile platitude for they that have no intelligence to lend. The only way to win this kind of race is to be the tortoise, and have other people try to catch up to you. But who wants to be a fucking tortoise?

Our philosopher's stone, flat, round and smooth, whipped with all the speed and skill that our feeble modern minds can muster, skips off the water here, causing easily ignorable ripples, sails low through the air, and splashes down again on the Fletcher's Paradox.

Another of Zeno's illegitimate sons of politics and philosophy, the Fletcher's Paradox asks us to imagine an arrow, released at speed. Maybe shot by that consummate archer, Achilles. Maybe he's trying to kill that fucking tortoise.

We are then asked to imagine an indivisible unit of time. Observing the position of the arrow at any of these moments, we see that the arrow is not moving. But, the theory goes, movement must occur in the present. It can't be that the thing only moves in the past, and in the future, but right now is motionless. Straining the credulity of the sane, we are asked to deduce that throughout all time, the arrow is motionless.

That makes no sense. Let me try again: If we posit an infinitely small period of time, then the amount of movement permitted in that period of time will be correspondingly small. Infinitely small movement is about as good as no movement at all (at least in 450 BC, when the value of PI was 3). But since all time is composed of the sum of these tiny moments, there must be no movement throughout all time.

Of course, this ties in nicely with Heisenberg's Uncertainty Principal (doesn't everything?), which basically describes how precisely the position and momentum of a particle (or arrow) can be simultaneously measured -- if we increase the precision in measuring one quantity, we are forced to lose precision in measuring the other. So if Zeno has us imagine an infinitely small, indivisible unit of time, wherein we may observe the arrow's location with pinpoint accuracy, then yeah, our measurement of it's momentum will be correspondingly inaccurate.

Okay, so it's not moving. So what?

I've been doing whatever it is I do for going on 15 years now. And I do it well (according to my own unbiased and objective evaluation). A couple months ago I got "promoted" to Team Leader. I know, it sounds cool, like I'm captain of the Super Friends or something, but really, in a team of two people, it's a little underwhelming.

Time crawls. I go nowhere.

I need a vacation.

1 uninformed opinions:

Leila said...

phil, didn't you know? achilles jumped OVER the turtle. then, on the way back, ran AROUND him. then, just for fun, shot him with his arrow and made soup. mmmmmm!