Does the Arrow Move? How can Anything Move?

Reply Thu 8 Jul, 2004 06:14 pm
How can an arrow move toward a target? Does an arrow move?

"The ancient Greek philosopher Zeno approached the problem of space through the question of movement in space. Before the moving body can reach the point of its destination it must pass through half the space intervening between the point of start and the point of destination; and before it can pass through that half it must travel through the half of the half, and so on to infinity. We cannot move from one point of space to another without passing through an infinite number of points in the intervening space. But it is impossible to pass through an infinity of points in a finite time. He further argued that the flying arrow does not move, because at any time during the course of its flight it is at rest in some point of space. Thus Zeno held that movement is only a deceptive appearance and that Reality is one and immutable. The unreality of movement means the unreality of an independent space."
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Reply Thu 8 Jul, 2004 06:24 pm
The "unreality" of this is that you can't impose a theoretical concept like infinity on a real life situation like movement.

It's a funny little thought experiment..... but of no practical use.
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Reply Thu 8 Jul, 2004 06:31 pm
Poor Zeno. His life would have been so much simpler had he but bothered to study quantum mechanics. Oh, well ... all things are relative, and I have some relatives that don't move much ... hell, they specialize in half-moves and backsteps..
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Reply Thu 8 Jul, 2004 06:37 pm
i remember that theory applied to the tortoise and the hare, according to that theory, the race ain't over yet.........
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Reply Fri 9 Jul, 2004 06:03 am
Re: Does the Arrow Move? How can Anything Move?
extra medium wrote:
But it is impossible to pass through an infinity of points in a finite time.

This is false. When you divide the distance an object has to traverse at any given speed in half, you also divide the time it takes to traverse it in half. Thus, if you take some given distance, and divide it into the sum of two pieces, each piece takes half as long to traverse, and thus the sum of the two takes the same amount of time. If you divide the distance into n pieces, each takes 1/n times as long to traverse, and together they take the same amount of time. As n approaches infinity, n times (1/n) doesn't change. It's a pity that Zeno was unable to study the theory of limits.
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Reply Sun 11 Jul, 2004 08:54 am
As I'm sure you see there is only a problem here if the arrow moves. If the arrow is always in the target then there is no problem. See my reply to:- How do you define Time? http://www.able2know.com/forums/about26736-0-asc-30.html
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Reply Sun 11 Jul, 2004 09:29 am
Here, Have some fun (relatively speaking, of course :wink: ) with Zeno's Paradox.
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Reply Mon 12 Jul, 2004 07:24 pm
Renormalization approach
I think that a possible answer to the paradox is the fact that the object is also composed of "infinities" and so when the object move, it is able to move through points of infinities; kinda like cancelling out infinities like renormalization.
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