In middle school my friends and I enjoyed chewing on the classic conundrums. What happens when an irresistible force meets an immovable object? Easy — they both explode. Philosophy’s trivial when you’re 13. But one puzzle bothered us: if you keep moving halfway to the wall, will you ever get there? Something about this one was deeply frustrating, the thought of getting closer and closer and yet never quite making it. (There’s probably a metaphor for teenage angst in there somewhere.) Another concern was the thinly veiled presence of infinity. To reach the wall you’d need to take an infinite number of steps, and by the end they’d become infinitesimally small. Whoa. Questions like this have always caused headaches. Around 500 B.C., Zeno of Elea posed a set of paradoxes about infinity that puzzled generations of philosophers, and that may have been partly to blame for its banishment from mathematics for centuries to come. In Euclidean geometry, for example, the only constructions allowed were those that involved a finite number of steps. The infinite was considered too ineffable, too unfathomable, and too hard to make logically rigorous.
more from Steven Strogatz at The Opinionater here.