Archive for the ‘Calculus and Motion: Calculus Made Clear’ Category

Zeno Paradox: how can an arrow simultaneously be at rest and in motion?

February 16, 2008

[Definition] A paradox is two statements that both seem correct, and yet they contradict each other!

Twenty-five hundred years ago, the Greek philosopher Zeno watched an arrow speeding toward its target and framed two of the most productive paradoxes in the history of human thought:

  1. Arrow Paradox:
    1. At every moment, the arrow is at a particular point, thus at every moment it is at rest at the point.
    2. At every moment, the arrow is in motion.

    How can the arrow be both at rest and in motion?

  2. Dichotomy Paradox:
    1. To reach its target, the arrow must fly halfway, then half the remaining distance, then half the remaining distance, and so on, forever. Because it must move an infinite number of times, it will never reach the target.
    2. The arrow reaches its target quickly.

    How can the arrow travel an infinite number of halves and still reach its target?

— Extracted from Calculus and Motion: Calculus Made Clear by Professor Michael Starbird