Say you walk a mile to a friend’s house. Really, this shouldn’t be anything really bad because it’s just a mile. But think of this: to get to your friend’s house, you must walk half a mile, but before that you must walk a quarter mile, but first you have to walk an eighth of a mile and so on. How do you get to your friend’s place when , even though it is a mile, it seems that you have to do infinite tasks to get to your friend’s house. This is one of three of Zeno’s paradoxes having to do with distance.
Even though you can go a mile easily without torturing yourself to infinite tasks, it does seems interesting how Zeno thought of this. He also thought of other paradoxes that were close to that. The one in the intro was called the dichotomy paradox.
For example, take the “Achilles and the Tortoise” paradox. If a tortoise gets a 100-meter head start on Achilles on a foot race. Say that Achilles can run twice as fast as the tortoise. Zeno says that Achilles will never pass the tortoise because when they start, by the time Achilles reaches the point the tortoise starts on, the tortoise will have moved half the distance. Once Achilles reaches the next point the tortoise was at, the tortoise will have moved more. Zeno then states this repeats forever, and Achilles never catches up and states that it is impossible to overtake anyone in a race. However, we have all seen someone beat somebody by catching up to them and passing them, so the paradox’s solution is found by knowing that, there are times when the runner does not move, like when their foot lands on the floor, and the next leg is picked up.
Many other paradoxes are fun to think about. Zeno was just one of the many people to think of paradoxes. So maybe the next time you get bored maybe look up paradoxes. You might twist your mind a bit.