Suppose that the swift Achilles is having a race with a tortoise. Since the tortoise is much slower, she gets a head start. When the tortoise has reached a given point a, Achilles starts. But by the time Achilles reaches a, the tortoise has already moved beyond point a, to point b. And by the time Achilles reaches b the tortoise has already moved a little bit farther along, to point c. Since this process goes on indefinitely, Achilles can never catch up with the tortoise.
How can this be?
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(In reply to
Think physics and limit theory (solution)! by Jeff)
Say that Achilles moves twice as fast as the tortoise. The race is 8ft, and the tortoise (with a 1ft head start) moves 1ft per second. Therefore, after one second, Achilles is only 1ft behind the turtle. After two seconds, Achilles is even with the turtle at 6ft from his start. In one more second, Achilles will be crossing the finish line while the tortoise still needs another second to finish. Therefore, Achilles can overtake the tortoise. What's the philosophy on the paradox?
overtaking the tortoise
