Thursday, March 25, 2010


       I've always been fond of logic puzzles, riddles, jokes, and paradoxes. In fact, a few years ago, I scoured the internet and printed out about 70 pages of them, which I read for fun in my free time. The only reason I don't still do that is because I no longer have any "free time". Paradoxes are fascinating, because they're tough to wrap a mind around, and I've always liked wrapping. Mentally, anyway. I always try to get someone else to do my Christmas presents. Anyway, now that I have a blog, I might post some of my favorites.

      Today I'll talk about Zeno's paradoxes. I couldn't find my paradox papers, so I mostly used Wikipedia. I am unashamed.

      Zeno of Elea (not to be confused with Zeno of Citium, who came later and didn't do much worth blogging about) was a Greek philosopher of Southern Italy around 450 BC. He was pre-Socratic, a word which here means "less cool then Socrates due in part to putting more emphasis on rationality". But he was still pretty cool.

     He had nine paradoxes, most of which centered around the same concept, so I'll just give a couple examples to illustrate it.

    "In 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. 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."

       So there it is. Zeno has proven that Archilles will never pass the tortoise. In fact, this wouldn't even look like a paradox except for the fact that it's obviously wrong. We can show it to be wrong with a demonstration. But can you disprove Zeno?

       Here's the other example of a similar paradox, using the same concept.

     "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. This description requires one to complete an infinite number of tasks, which Zeno maintains is an impossibility. This sequence also presents a second problem in that it contains no first distance to run, for any possible (finite) first distance could be divided in half, and hence would not be first after all. Hence, the trip cannot even begin. 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."

     If nothing else, it's a good explanation for why you skipped school. "It wasn't my fault, I just discovered that all motion is an illusion."

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