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Offlinenubious
1up on the rest

Registered: 10/20/02
Posts: 534
Loc: Canada
Last seen: 6 years, 4 months
The racecourse and The arrow...
    #1751063 - 07/26/03 05:56 PM (13 years, 4 months ago)

I saw someone posting about that arrow zen thingie a while back, and I stumbled across it in a book on philosophy..  Read, review, and discuss  :laugh:

Quote:

The racecourse.  Parmenides had said that the One is indivisible and therefor consisted of a single continuous plenum.  Against this the Pythagoreans argued for a pluristic world, saying that the world is divisible into units.  If one where to consider, says Zeno, the distance around a racecourse as the Pythagoreans did, he would say that this distance must be divisible into units.  According to this example of motion, the runner traverses a series of units of distance from the beginning to the end of the racecourse.  But, Zeno asks, just what takes place in this example?  Is there really any motion?  In order to traverse the racecourse, the runner, according to the Pythagorean hypothesis, would have to tracerse and infinite number of points, and he would have to do this in a finite number of moments.  But the critical question is, how can he traverse an infinite number of points in a finite amount of time?  The reason he fronts an inconfinite number of points is that on the Pythagorean assumption everything is divisible; hence the distance from the beginning to the end of the racecourse is divisible.  Thus, the runner cannot reach the end of the course until he first reaches the dividing line at the halfway point; but the distance from the beginning to the halfway point can also be divided in half, and he must first reach that point, the one-quarter mark, before he can reach the halfway point. Likewise, the distance between the beginning and the one-quarter point is divisible, and this process of division must go on to infinitude since there is alwaus a remainder and every such unit is divisible.  If then, the runner cannot reach any point without first reaching its previous midpoint, and if there are an infinite number of points, it is impossible to traverse this infinite number of points in a finite amount of time.  For this reason, Zeno concludes that motion does not exist.

The arrow.  Does an arrow move when the archer shoots it at the target?  Here again the Pythagoreans, who had argues for the reality of space and therefore of its divisibility, woul dhave to say that the arrow must occupy a particular position in space.  But for an arrow to occupy a position in space equal to its length is precisely what is meant when one says that the arrow is at rest.  Since the arrow must always be at rest.  Moreover, since any quantity as we saw in the example of the racecourse* is infinitely divisible, the space offupied by the arrow is infinite and as such it must coincide with everything else, in which case everything must be One instead of many.  Motion, therefor is an illusion.

**Taken from 'Socrates to Sartre - A History In Philosophy'***








 


--------------------
No one knows the worth of innocence till he knows it is gone forever, and that money can't buy it back. Not the saint, but the sinner that repenteth, is he to whom the full length and breadth, and height and depth, of life's meaning is revealed. Good and evil loose all objective meaning and are seen as equally necessary and contrasting elements in the masterpiece that is the universe.


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Offlinefireworks_godS
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Re: The racecourse and The arrow... [Re: nubious]
    #1751118 - 07/26/03 06:35 PM (13 years, 4 months ago)

Although I hate to argue for reality's sake, since it is at best just an illusion anyways, I find a problem with this (anything I point out will be within the idea of reality). Any path CAN be divided into an infinite amount of points. However, the runner STILL makes it all the way around the track. Just because the track IS divided into an infinite amount of points, doesn't mean that he travels across ALL of them to get around the track. Actually, I guess he DOES (don't think about where his feet go, or what lane is he is in).
I'm lacking some knowledge, I guess, to make any assumption about this. The way I am thinking, is that he still runs the lap. He did go all of the distance. No matter how small you break the increments of distance measurement into, he STILL goes all the way around the track. If you raise or lower the viewpoint past a certain extent, the runner or the track wouldn't even show up, I understand that, too.
What understanding do I need to accept this? Do I just need to know that the answer can't be found with rational thinking, and accept that? (I already do) That alone doesn't address the problem in question. Just knowing that it follows an irrational thought process doesn't solve the problem. I believe that from the perspective of the Eternal Here and Now, nothing moves at all, because movement is only determined by comparing the location of an object to its place in the past (or future). It would have to be fucked up to view everything ONLY from this view, to never compare anything to the past. (Was this whole thing a koan? Have you all just witnessed my rational thinking being broken? I've never thought about the Eternal Here and Now quite like this before...it's never been this defined, this imagined). Is this what we are striving for? Is this what we are to seek?
I'd think that the most useful way to use this is to occasionally check in, so we'd still have a job and a place to live. Seeking this kind of thing would be easy enough if in a monastery or out on the street, but I'd still prefer to live my life. I mean, I'm always eliminating my addictions and whatnot, uploading them into preferences, and I understand that the more you keep, the more suffering you will experience, but I think I'll allow myself some of them (like still pursuing my music career, having a place to live, etc). I'd still be pretty damn close to Cosmic Consciousness; however, and after the day's work is done, I'd still be able to stop registering the passing of time....
(and fucking thanks for posting this, it made me think, even if I thought AS I posted...hehe)
Peace.



--------------------
:redpanda:
If I should die this very moment
I wouldn't fear
For I've never known completeness
Like being here
Wrapped in the warmth of you
Loving every breath of you

:heartpump: :bunnyhug: :yinyang:

:yinyang: :levitate: :earth: :levitate: :yinyang:


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OfflineMeph
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Registered: 09/01/02
Posts: 1,568
Loc: Qu?bec
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Re: The racecourse and The arrow... [Re: nubious]
    #1751137 - 07/26/03 06:50 PM (13 years, 4 months ago)

Quote:

nubious said:

The racecourse. Parmenides had said that the One is indivisible and therefor consisted of a single continuous plenum. Against this the Pythagoreans argued for a pluristic world, saying that the world is divisible into units. If one where to consider, says Zeno, the distance around a racecourse as the Pythagoreans did, he would say that this distance must be divisible into units. According to this example of motion, the runner traverses a series of units of distance from the beginning to the end of the racecourse. But, Zeno asks, just what takes place in this example? Is there really any motion? In order to traverse the racecourse, the runner, according to the Pythagorean hypothesis, would have to tracerse and infinite number of points, and he would have to do this in a finite number of moments. But the critical question is, how can he traverse an infinite number of points in a finite amount of time? The reason he fronts an inconfinite number of points is that on the Pythagorean assumption everything is divisible; hence the distance from the beginning to the end of the racecourse is divisible. Thus, the runner cannot reach the end of the course until he first reaches the dividing line at the halfway point; but the distance from the beginning to the halfway point can also be divided in half, and he must first reach that point, the one-quarter mark, before he can reach the halfway point. Likewise, the distance between the beginning and the one-quarter point is divisible, and this process of division must go on to infinitude since there is alwaus a remainder and every such unit is divisible. If then, the runner cannot reach any point without first reaching its previous midpoint, and if there are an infinite number of points, it is impossible to traverse this infinite number of points in a finite amount of time. For this reason, Zeno concludes that motion does not exist.

The arrow. Does an arrow move when the archer shoots it at the target? Here again the Pythagoreans, who had argues for the reality of space and therefore of its divisibility, woul dhave to say that the arrow must occupy a particular position in space. But for an arrow to occupy a position in space equal to its length is precisely what is meant when one says that the arrow is at rest. Since the arrow must always be at rest. Moreover, since any quantity as we saw in the example of the racecourse* is infinitely divisible, the space offupied by the arrow is infinite and as such it must coincide with everything else, in which case everything must be One instead of many. Motion, therefor is an illusion.






That was proven false in the past century...


--------------------
I'm a bipedal carbon-based pseudo-random number generator.

Demonstration: 152.



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Offlinenubious
1up on the rest

Registered: 10/20/02
Posts: 534
Loc: Canada
Last seen: 6 years, 4 months
Re: The racecourse and The arrow... [Re: Meph]
    #1751162 - 07/26/03 07:08 PM (13 years, 4 months ago)

Quote:

That was proven false in the past century...




Can you provide examples of factual information to back your point? I'm not disagreeing that it has been proven wrong, but some of us (Fireworks_god and myself) are thrown into deep patterns of thought at the concept of this, and by you stating simply that 'It was proven false in the past century' hardly does justice to the concept you are trying to prove wrong.

When I first read this I thought of Einstein's theory of relativity and how the faster something moves, the smaller it appears from the side. Basically, for the arrow to move 5 units right, it must simoultaniously (sp?) shorten its length by 5 units on the left side, giving it the appearance of motion, when in reality it has actually 'changed' its form to that of an arrow 5 units right of it's previous frame of reference.

Your thoughts?


--------------------
No one knows the worth of innocence till he knows it is gone forever, and that money can't buy it back. Not the saint, but the sinner that repenteth, is he to whom the full length and breadth, and height and depth, of life's meaning is revealed. Good and evil loose all objective meaning and are seen as equally necessary and contrasting elements in the masterpiece that is the universe.


Edited by nubious (07/26/03 07:09 PM)


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OfflineMeph
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Registered: 09/01/02
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Re: The racecourse and The arrow... [Re: nubious]
    #1751288 - 07/26/03 08:12 PM (13 years, 4 months ago)

I can see where you're coming from.

I've heard the arrow theory before in many forms. I was thinking of the indivisible property of the atom (unless we're talking about an atomic reactor, which isn't the case). But now that I think about it again, I think I'm not making sense. I was thinking along the lines of "matter cannot be divided indefinitly", and I just realized that we're talking about a distance...

But... what if you shot the arrow in a vacuum?  :crazy:

It is puzzling, in a way. Maybe space itself is composed of indivisible units, just like matter... but I'm just fantasizing.  :smirk: 


--------------------
I'm a bipedal carbon-based pseudo-random number generator.

Demonstration: 152.



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OfflineRhizoid
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Registered: 01/23/00
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Re: The racecourse and The arrow... [Re: nubious]
    #1752099 - 07/27/03 02:04 AM (13 years, 4 months ago)

Quote:

it is impossible to traverse this infinite number of points in a finite amount of time.
. . .

since any quantity as we saw in the example of the racecourse* is infinitely divisible, the space offupied by the arrow is infinite




Both of these statements are false. The ancient Greeks didn't know that it is possible to add an infinite sequence of numbers and still get a finite answer. That's what integration is about.

Correction: Archimedes knew, since he used integration and limits in some of his calculations, but Archimedes seems to have been very exceptional.


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