The Topic: a paradox

 AngryShrew (9:06 PM)
Suppose an arrow was fired at a knight from 100 meters away. This arrow moves ten times as fast as the knight. As soon as it is fired, the courageous knight turns around and runs away. Once the arrow gets to where the knight is standing, 100 meters from where it was fired, the knight will have moved away 10 meters. Once the arrow travels that extra 10 meters to strike the knight, the knight will again have evaded it by moving 1 meter away. Once the arrow travels that extra distance, the knight will have moved yet another decimeter. The arrow will move a decimeter; the knight will move a centimeter, and then a millimeter, and then 0.1 of a millimeter, then 0.01 of a millimeter, and eventually into the picometer range. So, if this is true, how can the arrow possibly ever reach the knight?



Responses:


 Stephen King (9:15 PM)
Hmmmm...

 Stephen King (9:25 PM)
Well, to begin with, I'm tired of hearing Zeno's "Paradox" framed in the context of an arrow pursuing an armored target. Do we really care if the arrow hits the tortoise or knight? No, not really. Let's make it a bit more interesting.

 Stephen King (9:25 PM)
Instead, let us say that you are strapped to a chair in such a way that you cannot move a single muscle. Your eyelids have been removed, and polymer rings have been inserted at the base of your occular cavity, preventing you from swivelling your eyes.

This chair is on a pair of rails, and is gently sliding backwards at a rate of 10 centimeters per second.

 Stephen King (9:25 PM)
Also mounted on the rails is a power drill with a very long, sharp drill-bit. It is also moving, at shall we say a rate of 15 centimeters per second. At the start of the "experiment", you are arranged so that there is exactly 10 meters between the surface of your right eyeball and the tip of the drill, which is mounted at the appropiate height for eventual occular penetration.

 Stephen King (9:25 PM)
Now we set the experiment in motion - you begin sliding backwards, and the drill begins sliding towards you. However, there are no features in this place, and the chair slides very smoothly, so there is no way for you to tell that you are moving. From your reference frame, you are standing still and the drill is approaching at 5 centimeters per second.

 Stephen King (9:25 PM)
However, if we are to measure velocity from your reference frame, we must also measure time in that same reference frame. From your point of view, as the hypnotic whirring bit creeps closer and closer, time will indeed slow down as your entire life flashes before your eyes. As the bit gets closer and closer, it will seem to become infinitely slow, and when it is very close indeed - practically touching, so you can feel the moving air brushing against your exposed eyeball, to you it will seem that the drill-bit stops and hangs there, providing an infinity of torture and expectation.

 Stephen King (9:25 PM)

Stephen King (9:26 PM) 
Everyone else will simply see the drill messily augur through your head.




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