Ben,

Possibly the most effective analogy is map versus territory.

In that a map is a useful, reductionist model of the territory. If it tried to encompass all information inherent in the territory, it would have no function. The signal would be lost back in the noise.

The interesting points this raises, is why would there be any confusion among presumably brilliant people, as to the nature of this relationship?

For example, is space fundamentally three dimensions, or is that just a mapping device, like longitude, latitude and altitude? The xyz coordinate system.

Yet it seems to be an expressly held belief in both math and physics, that space is just those three dimensions. What other qualities could it have?

Consider that if in a frame traveling at the speed of light, both the clock stops and any ruler shrinks to zero, than if we were to take that in the opposite direction, it would seem the frame with the fastest clock and longest ruler would be closest to the equilibrium of this vaccum, referred to as space. The unmoving void of absolute zero.

Also, as there are no boundaries that can logically encompass it, another property would be infinity.

So space is the infinite and the absolute. Like the number line, from zero to infinity.

Does that mean these concepts are the basis, or expressions of space? Given everything is contained within these parameters, it would seem they are expressions of this quality called space.

How about time?

We are mobile organisms, which necessitates this sequential process of perception, in order to navigate, so our experience of time is as the point of the present, moving past to future. Physics codifies it as measures of duration and assumes it to be another dimension.

Yet the evident reality is that change turns future to past. Tomorrow becomes yesterday, because the earth turns. Duration is the present state, as events coalesce and dissolve.

There can be no literal dimension of time, because the past is consumed by the present, to inform and drive it. Causality and conservation of energy. Cause becomes effect.

So energy is "conserved," because it is the present, creating time, as well as temperature pressure, color and sound. Time is frequency, events are amplitude.

Ideal gas laws correlate volume with temperature and pressure and they are as foundational to our emotions and bodily functions, as time is to the process of thought, but we don't refer to them as dimensions of space.

Consider that energy, as dynamic present, goes past to future, while the patterns generated go future to past. Energy drives the wave, while the fluctuations rise and fall.

Consciousness also goes past to future, while the perceptions, emotions and thoughts giving it form and structure go future to past. Though it's the digestive, respiratory and circulatory systems processing the energy, while the central nervous system sorts the information. Therefore the tendency to focus on the patterns, the apples, rather than the processes generating and dissolving them.

Looking at galaxies, which is pretty much the highest level phenomena we do observe, it is energy radiating out, toward infinity, while form coalesces in, toward equilibrium.

Does space actually "curve," or is it just that waves tend to either synchronize, which is centripetal, or harmonize, which is effectively centrifugal, as the energy is radiated out, across all other forms?

Giving us nodes and networks, organisms and ecosystems, particles and fields.

Epicycles were brilliant math, as description, while the crystalline spheres were lousy physics as explanation. Relativity is brilliant math. Spacetime is lousy physics.

The problem with math is that being about the collection of order, as a social phenomena, it is in thrall to tradition and renewal only happens when the order has totally failed, rather than seasonal cycles.

Math, like compound interest, needs a circuit breaker.