The philosopher Zeno of Elea was born approximately 490 BC in southern Italy. His paradoxes have puzzled mathematicians, scientists and philosophers for ages. Even any of works do not survive today, more than 40 paradoxes are attributed to him, which appeared in a book he wrote as a defense of the philosophies of his teacher Parmenides.
Parmenides’s belief in the absolute unity and constancy of reality is quite radical and abstract, even by modern standards. He maintained that the universe is literally singular and unchangeable. However, his rationalism forced him to acknowledge that appearances are to the contrary, i.e., while he flatly denied the existence of plurality and change, he admitted the appearance of these things. Nevertheless, he insisted these were mere perceptions and opinions, not to be confused with “what is”. Not surprisingly, Parmenides was ridiculed for his beliefs
The most famous paradox of Zeno is the Paradox of Tortoise and Achilles. Achilles was he great Greek hero of Homer’s The Iliad. This paradox has inspired many writers and thinkers through the ages.
“In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.” – as recounted by Aristotle, Physics VI:9, 239b15
First, thinks Tortoise, Hare has to run a mile, then half the final mile, then half the final half- mile, and so on.
Zeno’s paradox raises both mathematical and philosophical issues. From a mathematical point of view the key point is that, in some cases, infinite sequences of numbers produce summed series that converge to a finite value, so if this is true for the distance, then the Hare should arrive without any problems.
“We may say a thing is at rest when it has not changed its position between now and then, but there is no ‘then’ in ‘now’, so there is no being at rest. Both motion and rest, then, must necessarily occupy time.” – Aristotle, 350 BC