Is movement an illusion? Zeno's paradox: From a modern viewpoint

✍ Scribed by F. Walter Meyerstein

• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 80 KB
• Volume: 4
• Category: Article
• ISSN: 1076-2787
• DOI: 10.1002/(sici)1099-0526(199903/04)4:4<26::aid-cplx4>3.0.co;2-5

✦ Synopsis

Zeno's paradox: From a modern viewpoint Z eno, the Greek philosopher from Elea in southern Italy who lived from circa 495 to 445 BC, wanting to prove Parmenides's thesis of the impossibility of all motion, conceived the notorious "paradox" of Achilles and the tortoise, the solution of which has challenged mathematicians and philosophers throughout the centuries. He claimed that not even Achilles, the fastest Greek hero of the Illiad, could ever catch a tortoise if that animal was given a head start of, for instance, s 1 meters. Obviously, to catch the tortoise, Achilles must first run that distance, say in t 1 seconds. But once he gets there, the tortoise has already moved a distance of s 2 meters, a distance Achilles will cover in t 2 seconds, and so on. The procedure must be repeated ad infinitum: however close Achilles gets to the tortoise, there will always remain some infinitesimally small distance. But in real life we do see Achilles easily catch the animal. Conclusion: Real-life motion is an illusion! It is clear that the paradox assumes as true by axiom one of the most consequential ideas of the Greek philosophers: Space and time are a continuum that can be divided indefinitely; there is neither an atom of space nor an instant of time. And if this is so, Parmenides and Zeno claimed, there will always remain some physical distance, and some duration of time, before Achilles catches the tortoise, no matter how small. In other words, what Zeno's paradox asked philosophers to explain is how an infinity of acts can be serially completed in finite time, even if each act is infinitesimally small-assuming motion is real.