For thousands of years, scholars pondered the question of how anything can move in our world. The problem seemed to have been solved—until the development of quantum mechanics
I like to go running in my free time. I’m not an especially fast jogger, but I think I could keep up with a tortoise. According to Zeno of Elea, an ancient Greek scholar who lived around 450 B.C.E., however, the outcome of a race between me and a tortoise is far from clear—assuming that I give the slow-moving reptile a sporting head start. Of course, Zeno was aware that humans can easily overtake tortoises.
In Zeno’s original thought experiment, he made the surprise even more stark by pitting the tortoise against Achilles, the swiftest hero in Greece, so the scenario is often called the Achilles paradox. Whatever the case, there is a contradiction between what we perceive in reality—people overtaking tortoises—and what the theoretical description suggests.. By purchasing a subscription you are helping to ensure the future of impactful stories about the discoveries and ideas shaping our world today.
The first category includes, for example, the set of natural numbers , which is unlimited upward: there is no largest natural number. An interval on the number line, such as a centimeter, falls into the category of the bounded continuum. Although this interval has a finite length, it consists of an infinite number of points. Archimedes observed that I would need less and less time to cover the shrinking distances that separate me from the tortoise in a race.
In other words, there are an infinite number of moments in which the tortoise is ahead of me, but the sum of these moments is finite—and actually quite short.This proof can be calculated quickly using the mathematical tools available today. Let's assume that I give the turtle a one-meter head start and then begin to run at around 12 kilometers per hour. For the sake of simplicity, let the tortoise be five times slower than me—even if the animals are actually much slower.
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