We cannot encounter, or perceive, purely geometrical objects, even those that have a third dimension. For instance, a geometric cube plots out depth and purports to have volume; however, its boundary is still made of imperceptible 2D surfaces that have no depth, and consequently no surface tension to contain a 3D volume.
Purely mathematical objects do not endure in space-time. Isolated point-particles do not have angular momentum; therefore they neither spin around an axis, nor do they have an actual time-line.
Time, itself, occupies no space; so, an isolated 1D time-line is as metaphysical as point particles are.
Lack of visibility does not mean that something is purely geometrical, entirely imperceptible, or unreal. In July 2017, it was announced that graphene has been produced at Industry City in Brooklyn, NY. Graphene, while expected to have many uses, it is essentially invisible.
Graphene’s 3rd dimension is measured in single-digit micrometers, far below what is visible to the human eye. For comparison: a human hair is about 75 micrometers in diameter. Although graphene’s thickness (its third dimension) is ridiculously slight, it nevertheless has a third dimension, which means that, from a geometrical standpoint, it is not purely a 2D surface. It is not, however, its 3rd dimension that makes it real, it is is persistence in time.
Surfaces have absolutely no depth (no 3rd dimension) and are imperceptible. When an object travels close to the speed of light (670,616,629 mph) relative to an observer, that observer would witness the object’s length contracting in the direction of its movement. Even if an entity could travel at the speed of light (as only light does), it could not retain its corpuscular three dimensional (3D) body; it would lose all its depth and ultimately become a 2D surface with zero thickness.
Here’s a fun flash from the past: the scene from the 1985 movie, Back to the Future, in which the professor’s Delorean merely hits the speed of 88 mph and vanishes into thin air, along with his dog, Einstein! Haha! So funny!
All that’s left of the Delorean are a couple of streaks illuminating the time-traveling vehicle’s trajectory. This makes me wonder if what we think of as traveling light is not simply the streaks made by something other than light (a Delorean? or an electro-magnetic wave?) as the light itself is a diaphanous 2D metaphysical plane, imperceptible to us, but everywhere present.