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 Posted: Sun Jul 23, 2006 3:22 pm
The dichotomy paradox
"You cannot even start."
"That which is in locomotion must arrive at the half-way stage before it arrives at the goal." (Aristotle Physics VI:9, 239b10)
Suppose Homer wants to catch a stationary bus. Before he can get there, he must get halfway there. Before he can get halfway there, he must get a quarter of the way there. Before traveling a fourth, he must travel one-eighth; before an eighth, one-sixteenth; and so on.
The resulting sequence can be represented as:
This description requires one to travel an infinite number of finite distances, which Zeno argues would take an infinite time -- which is to say, it can never be completed. This sequence also presents a second problem in that it contains no first distance to run, for any possible first distance could be divided in half, and hence would not be first after all. Hence, the trip cannot even be begun. The paradoxical conclusion then would be that travel over any finite distance can neither be completed nor begun, and so all motion must be an illusion.
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Posted: Sun Jul 23, 2006 3:23 pm
Wow, that is something else. I see the point though.
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Posted: Mon Jul 24, 2006 5:24 pm
The Zenogias The dichotomy paradox "You cannot even start." "That which is in locomotion must arrive at the half-way stage before it arrives at the goal." (Aristotle Physics VI:9, 239b10) Suppose Homer wants to catch a stationary bus. Before he can get there, he must get halfway there. Before he can get halfway there, he must get a quarter of the way there. Before traveling a fourth, he must travel one-eighth; before an eighth, one-sixteenth; and so on. The resulting sequence can be represented as: This description requires one to travel an infinite number of finite distances, which Zeno argues would take an infinite time -- which is to say, it can never be completed. This sequence also presents a second problem in that it contains no first distance to run, for any possible first distance could be divided in half, and hence would not be first after all. Hence, the trip cannot even be begun. The paradoxical conclusion then would be that travel over any finite distance can neither be completed nor begun, and so all motion must be an illusion. Well well well... Among the most famous of Zeno's "paradoxes" involves Achilles and the tortoise, who are going to run a race. Achilles, being confident of victory, gives the tortoise a head start. Zeno supposedly proves that Achilles can never overtake the tortoise. Here, I paraphrase Zeno's argument: "Before Achilles can overtake the tortoise, he must first run to point A, where the tortoise started. But then the tortoise has crawled to point B. Now Achilles must run to point B. But the tortoise has gone to point C, etc. Achilles is stuck in a situation in which he gets closer and closer to the tortoise, but never catches him." What Zeno is doing here, and in one of his other paradoxes, is to divide Achilles' journey into an infinite number of pieces. This is certainly permissible, as any line segment can be divided into an infinite number of points or line segments. This, in effect, divides Achilles' run into an infinite number of tasks. He must pass point A, then B, then C, etc. And what Zeno is arguing is that you can't do an infinite number of tasks in a finite amount of time. Why not? Zeno says that you can divide a line into an infinite number of pieces. And then he says that you cannot divide a time interval into an infinite number of pieces. This is inconsistent. There is no paradox here. Zeno was just showing (pretending?) some ignorance of the nature of time. A time interval is just another line segment (when you graph it), that you can divide up in any way you want. Excerpt from: Zeno's Paradoxes by Jim Loy Though this is a different paradox... The concept is the same... He is inconsistent with his thoughts on time and a line.
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Posted: Mon Jul 24, 2006 5:28 pm
Another excerpt from Zeno's Paradoxes:
1. Dichotomy paradox: Before a moving object can travel a certain distance, it must travel half that distance. Before it can travel half the distance it must travel 1/4 the distance, etc. This sequence goes on forever. Therefore, it seems that the original distance cannot be traveled, and motion is impossible.
2. Achilles and the tortoise paradox: Achilles gives the tortoise a head start, in a race. Before he can overtake the tortoise, he must run to the place where the tortoise began, and the tortoise has move on to some other point. From there, before he can overtake the tortoise, he must run to the place where the tortoise had move on to. This goes on forever, and Achilles can never pass the tortoise.
3. Arrow paradox: If you look at an arrow in flight, at an instant in time, it appears the same as a motionless arrow. Then how do we see motion?
4. Stadium paradox This one seems to be a little obscure. It is about bodies moving in opposite directions with equal speed, and Zeno seems to think that twice the speed is the same as half the speed.
Thinking about this unclear stadium paradox, it would seem that Zeno thinks that both time and distance have some smallest irreducible size (atoms of time and distance, if you will). And if you divide motion at twice the speed (one observer as seen by the observer going in the opposite direction) into these smallest pieces of time and distance then, from the point of view of a stationary observer, the moving people go half the smallest possible piece of distance. And we have the opposite effect, from the point of view of a moving observer, the other moving person moves the same smallest possible distance in half the smallest possible time.
Above, I thought that Zeno accepted that you could divide up any distance into infinitely many pieces, and that he rejected dividing up time into infinitely many pieces. Here it would seem that he rejected both. That is his invalid assumption in all four "paradoxes."
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Posted: Sat Jul 29, 2006 4:47 pm
Zeno's point goes along the lines of..... ....Our experiences in reality are the result of a virtual representation of what we believe is 'Existence'.
It is only real because we make it real.
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Posted: Sat Jul 29, 2006 5:00 pm
I did not question his point... His point was well made. But they are not paradoxes... The problems are easily solved. Zeno himself says that time cannot be divided an infinite amount of times... Which is why he said they were paradoxes, but in fact, time is just like distance, another line... And can be sliced, diced, or divided as many times as you feel necessary. Therefore, these are observances at best.
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Posted: Fri Aug 04, 2006 12:53 am
If:
Time and space are curved, their is no 'straight' line except one curved in the same way, facing away from the curve of time and space. But then, that line would become straight, however, to us in the curved area, the 'straight' line would be curved. But if its curved to us, and that is when it is 'bent straight' then it must be doubly curved to allow for that.
This is not a paradox, and most of it is literally B.S. however, I decided to bring up the ol' time and space are curved thing. The rest is to see if it makes sense, or confuses you. It has very flawed logic, but make of it as you wish.
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Posted: Sun Aug 13, 2006 8:25 am
yeah...what the ******** is this doing in the religion section?
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