Zeno famously said an arrow cannot be in motion as it occupies some precise position at some precise time. And is thus at rest.
Modern physics resolves this by stating the arrow has momentum. It is its momentum that carries from one place to another. At any precise time it has a specific velocity. So it is not at rest.
To simplify our presentation let us reduce the arrow to a point, and suppose it to move in a straight line with no forces acting on it.
One then can identify the continua of time with the continua of the line.
So motion is time. And time is motion.
But it seems to me that the paradox of rest remains. Which in this pictures is this. That a continuum of only points is actually not a continuum. There is no cohesion.
Modern studies of the real line remove this paradox by stipulating that a topology is present and this binds together points. One of course then notices that the points are actually not neccessary, only the continuum itself, that is the topology.
That is pointless topology (pun presumably intended by the author of the coinage).
This then removes Zenos first prescription to be able to specify an exact moment in time. In this picture this cannot be done.
But if one wishes to retain points, one could try a different logic, say by saying the point is both a point and not a point - this resolves to false in classical logic, but if one drops the law of the excluded middle, then this is not so. Following this line of thought for intuitionistic logic, gives the notion of the rigid, infinitesimal line. Which is not a point - it is a line, but it is also a point - it is infinitesimal.
Does this work as a solution towards resolving Zenos paradox?