Math is to reality, what chess is to war.
Reducing it down to a set of rules and then following the program that emerges to wherever it leads.
For example, is time a dimension, along which the present appears to move from past to future, or is it change, turning future to past?
Treating it as a dimension certainly facilitates modeling events in a spatial and temporal framework, but does it actually explain this phenomena of time?
We are mobile organisms, necessitating a sequential process of perception and evolved narrative based cultures, so we experience reality as this flow of events, which physics codifies as measures of duration, yet we also still see the sun rising in the east and setting in the west.
How can there be a literal dimension of time, when the past is effectively consumed by the present, to inform and drive it? Causality and conservation of energy. Cause becomes effect.
What if duration is the present, as the events come and go? Doesn't tomorrow become yesterday, because the earth turns?
It seems like time is an effect of this energy, that being conserved, is always and only present.
Along with temperature, pressure, color and sound. Frequencies and amplitudes. Time is frequency, events are amplitude.
Ideal gas laws correlate volume with temperature and pressure, but we don't refer to them as the 5th and 6th dimensions of space, because they are only foundational to our emotions, bodily functions and environment, not the sequence of thought.
Is space really three dimensional, or is that just a mapping device, like longitude, latitude and altitude?
If we remove all physical properties from space, then the non-physical qualities left to define it would be infinity and equilibrium.
Infinity, because there is nothing to bound it and equilibrium is implicit in SR, as the frame with the longest ruler and fastest clock would be closest to the equilibrium of the vacuum, the unmoving void of absolute zero.
So space would be the absolute and the infinite.
Not to go all crank here, but just to further your own point that math is descriptive modeling, than explanation. Map, not territory.
Epicycles were pretty good math, as an accurate description and modeling of our view of the cosmos, but the crysalline spheres were lousy physics, as explanation.
Yet here we are, back in the same situation, chasing off after multiverses, multiworlds, string theories, supersymmetries, dark energies and matter. All assuming that if the mathematical Gordian knot can be finally unravelled, we would understand everything.
