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Politics : Sharks in the Septic Tank
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To: The Philosopher who wrote (9783)3/26/2001 8:05:58 PM
From: TimF  Read Replies (1) of 82486
 
c3.lanl.gov
Zeno's Paradoxes

The Archer's Arrow

An archer picks up an arrow, places it agains the bowstring, draws the string back and lets the arrow fly towards the target. It looks like it will be a bulls-eye, but of course we won't know for sure until it hits the target.

Before the arrow reaches the target, it must first travel half of the distance to the target. From there the arrow travels half of the remaining distance to the target. Quickly, the arrow travels half of the distance which remains after that, then half of the distance that is still between it and the target. In fact, before it can get to the target, the arrow must always first go half of the distance that remains between it and the target.

Gee.... Does the arrow ever hit the target?

Its simple, each "half the remaining distance to the target" takes up half as much time. You can imagine an infinite number of "half the distances" but then they become infinitely small. You can keep adding these smaller and smaller amounts but they don't add up to an infinite distance but have a limiting factor of the actual distance from the archer to the target. I don't know if you would call this a mathematical proof but one could be constructed that would show how the "half the distances" and "half the times" don't add up to an infinite amount.

Another way of looking at it is these "half the distances" eventually get so small that they are less then the uncertainty in the position of the arrow. Of course Zeno knew nothing about quantum mechanics.

Tim
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