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This is Zeno of Elea,
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an ancient Greek philosopher
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famous for inventing a number of paradoxes,
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arguments that seem logical,
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but whose conclusion is absurd or contradictory.
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For more than 2,000 years,
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Zeno's mind-bending riddles have inspired
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mathematicians and philosophers
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to better understand the nature of infinity.
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One of the best known of Zeno's problems
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is called the dichotomy paradox,
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which means, "the paradox of cutting in two" in ancient Greek.
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It goes something like this:
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After a long day of sitting around, thinking,
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Zeno decides to walk from his house to the park.
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The fresh air clears his mind
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and help him think better.
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In order to get to the park,
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he first has to get half way to the park.
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This portion of his journey
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takes some finite amount of time.
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Once he gets to the halfway point,
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he needs to walk half the remaining distance.
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Again, this takes a finite amount of time.
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Once he gets there, he still needs to walk
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half the distance that's left,
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which takes another finite amount of time.
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This happens again and again and again.
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You can see that we can keep going like this forever,
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dividing whatever distance is left
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into smaller and smaller pieces,
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each of which takes some finite time to traverse.
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So, how long does it take Zeno to get to the park?
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Well, to find out, you need to add the times
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of each of the pieces of the journey.
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The problem is, there are infinitely many of these finite-sized pieces.
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So, shouldn't the total time be infinity?
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This argument, by the way, is completely general.
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It says that traveling from any location to any other location
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should take an infinite amount of time.
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In other words, it says that all motion is impossible.
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This conclusion is clearly absurd,
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but where is the flaw in the logic?
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To resolve the paradox,
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it helps to turn the story into a math problem.
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Let's supposed that Zeno's house is one mile from the park
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and that Zeno walks at one mile per hour.
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Common sense tells us that the time for the journey
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should be one hour.
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But, let's look at things from Zeno's point of view
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