Zeno's Paradox(es)

As everyone knows, it is impossible to ever get anywhere. If you are currently at point A and wish to move to a different point, B you must first traverse half the distance from A to B then half the remaining distance, then half the still remaining distance, ad infinitum. No matter what you do, you will always have half the remaining distance left, right? This version of Zeno's paradox has even made it to Hollywood, featured in the 1994 film, IQ, where Meg Ryan's character uses the paradox in an attempt to fend off the charismatic mechanic played by Tim Robbins. Of course you can debunk this one as easily as he did. Simply walk across the room and out the door. You know you get there. So what was wrong with Zeno?

Another version of Zeno's paradox involves a race between Achilles and a Tortoise. Achilles can run 10 times as fast as the tortoise and therefore gives the tortoise a ten meter head start. However, if the tortoise has a ten meter head start how can Achilles ever catch him? By the time Achilles reaches the 10 meter mark, the tortoise will be at 11 meters. By the time Achilles gets there the tortoise will be at 11.1 meters and so on. This process of looking at where the tortoise will be when Achilles catches up to where he WAS can be repeated indefinitely creating an infinite sequence of snapshots all showing the tortoise still ahead. Therefore, Achilles, even though he runs ten times as fast as the tortoise, will never catch up.

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