Zeno’s paradox

Zeno’s paradox is based on the idea that time and space are divisible. Here is the paradox in its simplest form:

A moving thing to get from A to B must first traverse half the distance. And to get halfway it must traverse a quarter of the distance - and so on. Since the thing has to traverse an infinite number of (progressively smaller) distances this would take an infinite amount of time. Therefore it cannot move at all - so motion is impossible. Mathematically the resolution of this paradox depends on the fact that when you add the series 1/2+1/4+1/16 …. and so on, you don’t get infinity - you get one. But the paradox reveals a deeper problem about the nature of time and space.

Is space granular?

in other words are there are tiny compartments or ‘quanta’ of space? 

If it is then there would be a finite number of compartments between A and B so the paradox is resolved. But how does a thing move from one compartment to the next?

Is time granular?

Think of the analogy of a film or video - each frame of which is a still image which if projected quickly enough gives the illusion of smooth motion. But is this ‘smooth motion’ really what is happening?

If time is made of a succession of instants or ’nows’ then either each ’now’ has no duration and time is smooth or each now has a finite duration and it is lumpy. If time is lumpy then how does it get from one lump to the next? 

This is the same problem that Physics faces in trying to resolve a tension between ‘lumpy’ quantum theory (which applies to tiny phenomena) and ‘smooth’ relativity and wave theory (which applies to big phenomena). Or between ‘digital’ vs ‘analog’.

Perhaps we should remember that time and space are simply human concepts with which we try to explain the World. The World just IS.