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Stephenson:Neal:Quicksilver:165:Zeno's Paradox (Matt Zwolinski)

From the Quicksilver Metaweb.

Zeno's Paradox is actually shorthand for a series of paradoxes put forward by the Greek philosopher Zeno of Elea (495-435 BC), all centered around the relation of the discrete to the continuous. The specific reference here is to Zeno's paradox of motion, which was designed to show, somewhat counter-intuitively, that motion is impossible. The argument runs as follows:

Traversing any distance, say, 100m, requires that we first traverse half that distance -- 50m.

But to traverse half the original distance, we must first traverse half that distance -- 25m.

But we can go on halving the distances infinitely. Thus, traversing any distance requires traversing an infinite number of midpoints.

But an infinite number of midpoints cannot be traversed in a finite amount of time. Hence, it is impossible to traverse any distance.

Readers will be forgiven for finding this conclusion absurd. But the argument actually constituted a significant advance in the concept of 'quantity' at the time, and it was quite some time before the mathematical vocabulary necessary to explain the flaw in Zeno's reasoning was developed, via the likes of Newton and Cantor.