You know the law of diminishing returns thingy? I want to know how it is possible to ever touch anything...?

Question

The idea being - say you move your fingers closer together. They start off a certain distance apart. They then get half the distance, then three quarters, then four fifths, etc. With the law of diminishing returns the fraction will get smaller and smaller and smaller - but even when they are 999999999/1000000000ths of the way there, they still wouldn't be touching. Surely the fraction just gets smaller? How does anyone ever touch anything? Come to mention it, how does anything ever happen?

Answer 1

This is known as Zeno's paradox. But as the distance intervals become infinitesimal, so do the time intervals. Even though everything in infinitely divisible in theory, finite distances can still be covered in finite time. And from a physics standpoint, space and time are *not* infinitely divisible, so there is such a thing as close enough.