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Babylonian clay tablet, Ishango Bone, Lebombo Bone, Mathematics, Mesopotamian Accounting Tokens, Pythagoras of Samos, Sumerian Multiplication Tables, Thales of Miletus, The Tomb of Menna, Yale Babylonian Collection #7289, Zeno of Elea
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
Carl D'Agostino said:
Paradox of motion. Does the fact that the runner is running all these mini distances silmoultaneously contradict his position ? Each segment is not a mission in itself but an element of the larger distance which is comprehensive and inclusive so it takes the same time to run the total distance as it does to run all the segments. For time, it takes the same amount of time to live the year as it does to live the 12 months. Paradox there is that we can exist in the “for the moment” time only for a moment. Each new moment is not inclusive of a moment just passed.
Waldo "Wally" Tomosky said:
I d’n’kno!
Carl D'Agostino said:
Me neither. Too much depth for this non swimmer.