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Zeno of Elea (c. 495 – 430 BCE)

Zeno was a Greek philosopher who his known for his famous paradoxes, which have fascinated mathematicians for centuries.

One example is the paradox of motion: imagine that you want to run a 100 meter race. You first have to run half the distance (50 meters). But before doing that, you have to run a quarter of the distance (25 meters). Before running a quarter, you have to run 1/8th, 1/16th, and so on. This is an infinite number of tasks, which means that you’ll never arrive!

In simpler terms, Zeno stated a story that proved his point. “Achilles and the Tortoise”. In this paradox, Zeno imagines Achilles in a footrace with a tortoise. He argues that if the tortoise has a head start, Achilles can never actually pass it, as he must first reach the point where the tortoise started, but by that time, the tortoise has moved a bit farther, and so on, ad infinitum.

Another Zeno Paradox was The Arrow Paradox. Zeno suggests that if you were to freeze time at any given instant, an arrow in flight is not moving, so motion is an illusion.

Zeno is often credited as the inventor not just of the paradox, but of the reductio ad absurdum; to not only take an argument to its natural conclusion, but also by carrying the thought which lies behind an assumption — BEYOND THE ENVIRONMENT IN WHICH THAT ASSUMPTION DEVELOPED —  therefore, the environment in which it makes sense, demonstrates that the facts appear to change in the secondary environment. In other words both arguments are true; but only in their own environments.

Next post; Democritus