Nizameddin YALOVA

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Zeno's İdea

Achilles is in a footrace with the tortoise. Achilles allows the tortoise a head start of 100 metres, for example. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run 100 metres, bringing him to the tortoise's starting point. During this time, the tortoise has run a much shorter distance, say, 10 metres. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise.
What do u think about this idea?

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    Mar 9 2013: Zeno's paradox has fallen apart after infinite series has been discovered. An infinite series can have finite sum, like say 1+1/2+1/4+1/8+1/16+.....infinity = 2. So your statement 'Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise.' is neither true mathematically or physically.
  • Mar 9 2013: The catch on this tale is the way time is considered. While for the tortoise the clock ticks at a constant speed, for Achilles the clock ticks faster and faster, so he can never reach the tortoise. In reality the clock ticks at the same speed for every one, that is why Achilles can leave the tortoise behind almost effortlessly.
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    Mar 9 2013: i was quite proud at age 2x to crack this puzzle, and so here is the solution: the argument examines a series of times, and then concludes that an event will "never" happen. to conclude something never happens, we need to examine all times, not just some of them. zeno examined a set of times that are closing in to a specific point in time. something like 0s, 9s, 9.9s, 9.99s, 9.999s and so on. none of these times are over 10s. therefore we can not conclude that the event will "never" happen. we can only conclude that it won't happen before 10s.
  • Mar 9 2013: All three early comments are right, but I still get a kick out of it. So who says there is not Western Zen? it's just a mental exercise.