Originally Posted by thomheg

Somehow I mean the opposite. Our observation is based on that space GR calls spacetime.
If we observe something, than our observation is based on our own state of being. One could be here or there, but is always somewhere. Same with a thing, a machine or a particle. Now we could attach reference frames to all kinds of things and connect these via SRT.
Quaternions are a possible way to model spacetime. Their complex multiplication is antisymmetric. Antisymmetry means, we could define a direction to a circle. So a circle, or anything else is pointing always somewhere. The directions we could connect by complex multiplication. This is a simple model, but it could generate very complicated three dimensional patterns, that move in a timelike manner.
If we let these pointing vectors point into the direction of time, we couldn't see the circles. What is a behavior of material bodies. But we could turn it to the side a bit and would see the circle and experience that as a wave, because then the circle cuts through a timelike hypersheet.