by TBone » Sep 16, 2001 @ 11:32pm
I had a really good friend (who's actually in England right now, poor bastard) who was a philosophy major. He spent a lot of time arguing with me, because I have serious problems with philosophy as a discipline (I'm a pragmatist by nature). One of his arguments for the necessity of philosophy was Xeno's paradox. It comes in several forms.<br><br>The first form is the old chestnut about how, if you had a line that you kept trying to reach, but you could only move half the remaining distace, you would never reach the line. It existed to point out the difference between pure mathematics/logic and the real world.<br><br>The other concept is known as Xeno's Arrow. Xeno state that we could fire an arrow after a turtle (I don't know what he had against turtles, he just did) and try to hit it. Unfortunately, if we tried to predict the path of the arrow, we would have to resort to math that uses t as a representation of time. If we then were to try and figure the arrow's velocity at any given instant, Xeno theorized, time would be equal to zero (no duration for our measurement). If time is zero, the velocity of the arrow (a function of time) must also be zero. Therefore the arrow never hits the turtle (maybe he really had something against archers).<br><br>Of course, it's all nonsense. But it serves to illustrate that as much as mathematicians (and of course, philosophers) would like to think, we do not exist in a universe of perfect logic--what physisists call an "ideal universe." The very basis of relating that ideal mathematical form to a system that's useful in the real world precludes a set of assumptions which are necessary to understanding their limits. Xeno's point was not the destruction of math and physics, but to point out the unspoken conventions we create to support them. He was actually a huge fan of the sciences.<br><br>Of course, those of you who are latin scholars will realize that his name is also the prefix meaning "alien or foreign." Whether this is coincidence, a conspiracy, or just a spelling error on my part is up to you.<br><br><grin>
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