Friday, September 9, 2011

Zeno's Paradoxes

I had an extended discussion today with two Starbucks barristas. The topic? Zeno's Paradoxes, the Heisenberg Uncertainty Principle, and Burning Man.

The last two are old hat, but the first is something that doesn't come up that often, these days. Let's look at my favorite one: the impossibility of motion, as shown by the flight of an arrow (from the Stanford Encyclopedia of Philosophy):
The third is … that the flying arrow is at rest, which result follows from the assumption that time is composed of moments … . he says that if everything when it occupies an equal space is at rest, and if that which is in locomotion is always in a now, the flying arrow is therefore motionless. (Aristotle Physics, 239b.30)

Zeno abolishes motion, saying “What is in motion moves neither in the place it is nor in one in which it is not”. (Diogenes Laertius Lives of Famous Philosophers, ix.72)
Essentially, Zeno is arguing that as the arrow apparently moves through the air, it must occupy a series of positions at various moments in time. And in each moment, the arrow is at rest, since it is in that place and no other.

Note that this argument means that the arrow cannot travel any distance, despite whatever velocity it might have. But we know that d=vt, so what happening for Zeno is that t (the amount of time)=0. And that's the answer, in a nutshell. Zeno assumes that such a thing as a "moment" of time exists, a very small, yet indivisible period of time during which the arrow occupies exactly one area of space. And of course, that's wrong. Any period of time is always divisible, no matter how small it is.

Nonetheless, the paradox touches on the human experience, since we cannot perceive such tiny moments of time, constrained as we are by our own physiology. In Godel, Escher, Bach, Douglas Hofstadter offered up a Zen koan that captures this experience:
Two monks were arguing about a flag. One said: "The flag is moving."
The other said: "The wind is moving."
The sixth patriarch happened to be passing by. He told them: "Not the wind, not the flag; mind is moving."
Movement is movement because we perceive it to be so, would be the conclusion. And at a sub-atomic level, there may be some truth to this. But the Hume in me cries out in protest...

Cheers, all.

No comments:

Post a Comment