Puzzles
Before you cross a room you must walk halfway. And before that, a quarter of the way.
Zeno of Elea argued that motion itself is impossible: to travel any distance, you must first cover half of it, but before that, half of that half, and so on forever — an infinite number of steps to complete before you can even begin moving. Where does the argument go wrong?
Reveal the answer
Zeno wasn't claiming motion doesn't happen — he was showing that assuming space is infinitely divisible leads to a contradiction. The modern resolution uses calculus: an infinite series of shrinking distances (1/2 + 1/4 + 1/8 + ...) can sum to a finite total and take a finite time, since each smaller step also takes proportionally less time to cross.
— Aristotle, reporting Zeno of Elea's argument, Physics, Book VI — c. 350 BC