How many times have you heard that the shortest distance between two points is a straight line? What if it’s actually… the longest distance? What if it’s an infinite distance? What if it’s impossible to move at all?!
That’s the theory behind Zeno’s thought experiment on movement. If every distance can be divided up into smaller parts, and traversing every part takes a non-zero amount of time, then how can we make any progress at all in a finite amount of time?
This is obviously wrong, since you can walk to the mailbox and back every day without facing an existential or physics-based crisis. The tale of Achilles and the Tortoise has a certain logic to it that took thousands of years to unravel — but once we understood the power of the convergent series, the paradox disappeared.
#maths #education #mathematics