Many of you guys seem to be well versed in philosophy. Can anyone help me understand this? If you don't know about it, here is the Wikipedia page. Or you can just read this quote:
The other day my philosophy professor told us about this. I still don't get it."In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead." – as recounted by Aristotle, Physics VI:9, 239b15In the paradox of Achilles and the Tortoise,
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.
Here is my attempt to explain this the way my professor did :
Let's pretend that Achilles can go twice the speed of the tortoise. The turtle is given a head start of 128m before Achilles can start. When Achilles gets to 128m, he is not yet in the tortoise's position because it is now 64m in front of Achilles. When Achilles goes another 64m, he still hasn't caught up with the tortoise, which is now 32m away from Achilles. Again, when Achilles travels another 32m, the tortoise will be 16m in front of him. When Achilles goes another 16m, the tortoise will be 8m in front of him. Etc., etc. So you see, no matter how far Achilles goes, he can never pass the turtle. Blah blah something something attempted to show that the world is illusory or something.
This doesn't make any sense to me. Why in the world is this considered a paradox? It is an error in the understanding of simple mathematics.
*edit* Okay apparently it isn't quite simple mathematics. You need calculus to prove this problem incorrect. In the paradox, we are creating an infinite series of numbers. Zeno's paradox relies on the sum of an infinite series to always be an infinite number. This is not so. Through calculus, we can find that the sum of an infinite series can be an actual number. It is at this number where Achille's will pass the tortoise. It still doesn't explain why it is still a paradox today.