Does the Arrow Move?

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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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The problem is solved by some by assuming that space IS NOT infinitely divisible. A bit ironically, this is how Islamic philosophers solved it a few hundred years ago. Modern math, though, has indicated that space is indeed infinitely divisible. So the debate continues.

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Too many points, not enough movement. Is movement the measurement of the distance between to places or of the time it takes to traverse that distance?

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It only points out the artificiality of logic. All I know is that I do not ever stand in the way of a flying arrow.

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We are standing still and the universe moves around us. Besides, all you have to do is break time down the same way; into infinite points.

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Yeah, but if there are infinite points then how is it that we ever get to the end of them?

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If someone jumps into the air he exists in only two states - touching the ground or not touching the ground. The action of leaving the ground does not seem to exist. Confused

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How could space be infinitely divisible? One could measure the distance between two points, but in order to even HAVE points the points themselves must have a diameter, which means in the end you would reach a time when the two points, between which you are measuring, will meet. Wouldn't you?

Never mind this post. I wrote it when i was very tired and not really paying attention.

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It moves.

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Cantor, the mathematician, went insane contemplating "different types of infinity." !

The Zeno problem does however raise the interesting issue of the relationship between a formal mathematical model and "reality". As JLN points out, even "logic" is merely a model which can only be applied selectively.

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JL, I have frequently come across similar little abuses of common sense in some of the "scientific" threads.

To wit; Most recently in a discussion of "black holes" I remarked that there are always limits to the amount of energies (and or matter, interchangeable in this case) that a given object can absorb without seriously changing its characteristics.

For instance a flywheel- Add enough speed or heat you will no longer have a flywheel. You will have something but it won't be a flywheel.

Add enough energy to a black hole you will no longer have a black hole. You will have something but it won't be a "black hole". Personally I suspect it would be called a galaxy Confused

So to me it's clear, The infinite number of points in the path of the arrow is simply a mathematical construction that probably has no counterpart in an observable (and possibly real) Universe.

Occasionally the physicists are as amusing as the preachers Crying or Very sad

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I have been reading about M-theory of Space and time. Space and time - acording to this theory - are atomistic and therefore made of decrete units.

If this were true then there is not an infinite amount of time for the arrow to move nor an infinite amount of space. There would be a finite (although large) amount of descrete units of time and space for the arrow to move in.

The smallest unit according to this thoery is the same length as the Planck era or 10-42 seconds.

TF

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Discrete time may be an answer.

However even with a continous time:
An attempt is sometimes easier than expected.
(.. Or, fear often exaggerates danger.)

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I once read that Buddhist theory, whatever that means, holds a notion of time as consisting of discrete units. I don't know which branch or sect of Buddhism that is, but it rings no bells for me.

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If you can assume that time can be cut down into infinite chunks, then you can just as easily assume that it can't be.

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Solon,

How could a person cut down time into infinite chunks?

If you mean cutting it down into finite chunks - of course you can assume it need not be so. This simply means that discrete time and non-discrete time are not contradictory.

JLN:

Those dang Buddhists - they are smart for being so skinny... Wink

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Discrete time isn't the answer to this problem in particular. Just assume the universe is moving around the arrow (in space&time), so the arrow doesn't move.

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This debate reminds me of one between to zen monks. One held that when the flag flaps in the breeze, the air is moving the flag. The other argued that the flag is moving the air around it. Just then their teacher came along, and they asked him to artibrate. He told them that if they looked closely they would see that it is their minds that were doing the flapping. Laughing

Does the Arrow Move?

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