I enjoyed learning about Zeno’s Paradoxes this weekend. I’ll share one with you, as described by Carlo Rovelli:
The tortoise challenges Achilles to a race, starting out with a ten-meter advantage. Will Achilles manage to catch up with the tortoise? Zeno agrues that rigorous logic dictates that he will never be able to do so. Before catching up, in effect, Achilles needs to cover the ten meters, and in order to do this he will take a certain amount of time. During this time, the tortoise will have advanced a few centimeters. To cover these centimeters, Achilles will have to take a little more time, but meanwhile the tortoise will have advanced further, and so on, ad infinitum. Achilles therefore requires an infinite number of such times to reach the tortoise, and an infinite number of times, argues Zeno, is an infinite amount of time. Consequentially, according to strict logic, Achilles will take an infinite time to reach the tortoise; or rather, he will ever do so. Since, however, we do see the swift Achilles reaching and overtaking as many tortoises as he likes, it follows that what we see is irrational, and therefore illusory.
- Carlo Rovelli in Reality Is Not What it Seems