For those of you who aren’t familiar: Achilles and a Tortoise race, however the tortoise is given a leading start. Achilles is at Point A, whereas the tortoise is ahead at point B. The race begins, and by the time Achilles makes it to point B, where the Tortoise used to be, it has reached point C. Then Achilles arrives at point C with the Tortoise at point D. So on and so forth, with Achilles never catching up to the Tortoise as per the paradox.
But he definitely catches the Tortoise eventually, right? The tortoise has a lower velocity, hence the head start, so after a certain amount of time the distance between points is smaller than Achilles and the Tortoise’s difference in speed. What, if anything, is paradoxical about the world’s most famous paradox?
In: 9
Outside of some tricks with language (“this statement is a lie”), you can’t have actual paradoxes. By definition, a real paradox is impossible. However, you can get things that seem paradoxical. Normally, these situations involve reasoning that seems good, based on common assumptions, that leads to a result that contradicts what we know to be true.
So, we know that a racer can overtake another racer that has a headstart on him. Zeno’s reasoning seems solid, but indicates that overtaking should be impossible. The common assumption that turns out to be wrong is the idea that space is infinitely divisible. We’re in a simulation, and you can’t have half-a-pixel, so you have to always move across the screen in discrete units.
Latest Answers