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The Theory of William Tell

Blast San Francisco Bureau

Here's a philosophical dilemma. Or perhaps a metaphysical one.

Let's say you're standing with your back against a wall with an apple on your head. Let's further say that an archer stands 100 feet away and shoots an arrow at the apple.

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Now, let's suppose that within some x period of time, the arrow moves halfway along the line from the archer's hand to the apple. Agreed? The arrow is now 50 feet away from the apple.

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After another x period of time, the arrow moves halfway again, from the previous point, to the apple. The arrow is now 25 feet away from the apple. Still agreed?

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Now, we learned in high school that there are an infinite number of points along a line between two points, right?

The arrow continues halving the distance until we get down the microscopic level. We're dealing on the order of microns and nanoseconds. It may be on an infinitesimally small level, but within a certain amount of time, the arrow moves halfway closer to the apple from its previous point. Correct?


The question: Why and how does the arrow eventually strike the apple and cleave it in half? When does the distance between the arrowhead and the apple fail to be further halved?

This has bugged me since I was a little kid.