**Zeno**

Zeno invented four fundamental paradoxes:

1) One can never reach a destination because one must first get half-way there, but first one must reach half that distance, and half before that distance, and so on, thus one is unable to start.

2) If the tortoise is in a race with Achilles and the tortoise gets a head start, then the tortoise must win since in order to catch up with the tortoise, Achilles must reach where the tortoise was. But by the time Achilles reaches where the tortoise was, the tortoise will have moved on. Therefore, Achilles can never catch the tortoise and the tortoise wins the race.

3) At any given moment, the arrow in flight is at rest in exactly one place, therefore it does not move.

4) The stadium paradox

A A A A A A A A

B B B B --> B B B B

<-- C C C C C C C C

The A's are the fans. The B's and the C's are presumed to move at equal speeds in opposite directions. Yet the first of the moving B's pass two A's while the first of the moving C's pass four B's. So the C's are moving twice as fast as the B's. This is a contradiction of the fact that B's and C's are moving at equal speeds.