Contemplations on Zeno’s paradox and number line theory.
Consider that there is a shortest distance in the universe and therefore a shortest time. Because of the limitations of our perceptions and instruments everything that happens at a distance shorter than the “shortest” one is hidden to us. Moreover, anything that occurs in a time faster than the time it takes light to cover this shortest distance is also hidden to us. It happens faster than we are capable of realizing it.
Let us suppose a distance that was a little shorter than this shortest distance was a rendered into a sphere. This ball would be invisible to us since it’s widest point, it’s diameter is a shorter distance we can measure. If such invisible spheres existed their closet packing arrangement would be to pack themselves as spheres around a central sphere. Because this arrangement is larger than the shortest distance we can see this collection of spheres but we can’t make out any of the parts. Assuming these spheres have a natural affinity for one another the smallest thing we ordinarily see would be this ball of balls. In theory we could see just two of these spheres side by side but if they have affinity for one another this would be a rare occurrence.
All repulsion is caused by desire.
When two macroscopic objects come close enough to each other they begin to “see” this shortest distance. For whatever reason “seeing” this shortest distance without combining into a larger structure is forbidden so two objects in close proximity may exhibit both repulsive and attractive forces. Combining into larger structures hides this shortest distance and therefore causes attractive forces.
The shortest distance in the universe is like a black hole in that information about what is going on inside it cannot be revealed to the outside world.
If we call the particles that are a smidge under the shortest distance holeions then we could call particles even smaller than that halfions. Notice that if a holeion and a halfion combine, they are larger than the smallest distance and they, or rather their effects can be seen. So perhaps repulsive and attractive forces arise and are mediated between the holeions by the halfions.
Contemplations on the partition of Unity
On the surface ours is a rational universe based on countable infinities. It is beneath the surface where all the trouble starts. Beneath the limits of perception almost anything could be going on. We can never see it. We can only see its effects in the aggregate. We live in a quantized universe in which Zeno’s paradox cannot apply because it never takes us an infinite amount of anything we can measure to cross a room.
When we compare our every day experience with the mathematical abstraction we call a number line we see that we do not live in Zeno’s nightmare universe. There are measurements beneath our ability to notice and times too fleeting to measure. It is as though our universe was created from a finite sequence of black holes from which information cannot escape but which in the aggregate exert the forces we know as gravity and electromagnetism as well as attraction and repulsion.