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Moment to Moment |
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An Exploration of Instantaneous Motion |
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Time and Zeno |
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Of the many paradoxes of the ancient Greek philosopher Zeno, two of the most infamous are that of The Arrow and of Achilles and the Tortoise. Though much of his work was lost to the ages, these two paradoxes lead to a redefinition of the very nature of time by the ancient Greeks.
The Paradox of the Arrow Assuming that time is made of a collection of individual moments that are infinitely small, an arrow is shot from a bow. Looking at any moment during the flight of the arrow would reveal the arrow to be stationary. The arrow cannot exist in two places at once and so the arrow, during that instant, inhabits exactly one place. However time is composed of moments and at any given moment the arrow is not moving so the arrow never moves.
The Paradox of Achilles and the Tortoise Assuming that every instant in time can be infinitely subdivided into smaller and smaller moments, Achilles is pitted in a race with a Tortoise. If the Tortoise is given even the smallest head start, Achilles will never catch up to the Tortoise. As Achilles reaches the point where the Tortoise started, the Tortoise has already moved on to a new point. When Achilles reaches this next point, again the Tortoise has moved on to yet another new point. As such, the tortoise will always be ahead of Achilles. Obviously the paradoxes of Zeno still bring up some troubling issues. However science moved on into more mathematic realms, seeming to circumvent or perhaps ignore these problems. |
