Magnificent Pythagorean Paradoxes In Ancient Greece

Decent Essays

Subsequent to the conquest of Egypt by Alexander the Great, the ancient Greeks established possibly the greatest center of learning at the time in Alexandria. Indeed, history purports that perhaps this great library rivaled even the great library in Athens, especially considering the fact that the Alexandrian library produced such significant mathematical figures as Archimedes and Euclid, the works of whom likely depended on the earlier works of great Greek mathematicians like Thales and Pythagoras (Lahanas, 2016). Although even those preceding mathematicians likely expounded upon the mathematical methodologies and computational techniques developed in earlier Babylonian and Egyptian civilizations. Still, there can be no doubt that modern mathematics, …show more content…

The premise behind the paradoxes was that the method of describing motion using Pythagorean thought, treating numbers solely as discrete, arguably demonstrated the impossibility of motion. His four paradoxes illustrating this line of thinking are The Dichotomy, Achilles and the Tortoise, The Arrow, and The Stadium. The paradox presented in The Dichotomy is that a race, from beginning to end, is a finite distance. Zeno purported that there are infinitely many half distances, which meant that you could never reach the end, according to Pythagorean thought. This paradox offered a precedent to the idea of the limit of an infinite sequence, in that an infinite number of half distances can add to a finite distance. Achilles and the Tortoise presented a similar paradox about infinite measures within a finite distance, and demonstrated that the boast of Achilles, that he could beat the tortoise even when the tortoise had a head start, could not come to fruition based on Pythagorean thought. The Arrow presented a paradox between the Pythagorean thought, that discrete units of instances make up time, and the premise that if Pythagoreans were correct then the arrow could not move. Thus, claimed Zeno, time must be continuous and not discrete. The Stadium presents a situation which proves that there is no smallest unit of time, as Pythagoreans believed, and therefore time must be both finitely divisible and infinitely divisible (Andrews, Development of calculus: More about the paradoxes, 2016). Although Zeno’s arguments were sound, they did not negate the influence that Pythagoras had on the study of mathematics. Indeed, another famous Greek philosopher, Plato, professedly transferred his knowledge of Pythagorean mathematics to one of his students, Eudoxus (Lahanas,