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Hola all, I think the 1 or 2 people who are offended by this very interesting so-called "off-topic" discussion between multiple cbm hackers won't die if I send one more message; therefore... I visited some of the web sites today, and it turns out that Zeno is an interesting character. It also turns out that I was half-wrong (or maybe 1/4-wrong, or maybe just 1/8-wrong -- wow, maybe I can never be wrong?). I always assumed that Zeno was using real-life experience to pose a mathematical paradox -- a puzzler. Apparently, however, Zeno was using mathematics to show that motion cannot happen! That is, Zeno (following his mentor) was in essence of the belief that reality is "static" -- unchanging, immutable -- and that things such as time and motion are therefore merely illusions. That's what the paradoxes were supposed to demonstrate! Moreover, his paradoxes essentially went unresolved until the late 19th century -- nearly 2,000 years. Amazing! And if someone besides aristotle had tried to actually reason through and resolve Zeno's paradoxes, they would have discovered relative motion, infinite series and sets (and infinity in general), and perhaps even more. And what is most amazing is... the paradoxes aren't necessarily resolved! For example, the "halving the distance" problem depends on the fact that you can keep subdividing space forever, and get an infinite series. But at least one quantum mechanical theory suggests that space (and time) is quantized, so that you can't actually subdivide forever. Finally, of all the websites I visited, all resolved the tortoise and achilles by solving the "halve the distance" problem -- none solved the general problem. So cbm-hackers got a special treat! :) Of the sites returned by Lycos, I found http://www.shu.edu/academic/arts_sci/Undergraduate/math_cs/sites/math/reals/history/zeno.html to be one of the more interesting (has a nice link to Georg Cantor, too!). -Steve - This message was sent through the cbm-hackers mailing list. To unsubscribe: echo unsubscribe | mail cbm-hackers-request@dot.tcm.hut.fi.

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