Tom,
When we peer out through a telescope, or into a microscope, we don't see dimensionless lines and planes. They are a platonic ideal, a perfect form. If you think there is such a state as the platonic realm, how far through the increasingly complex mathematical models does it reach? Currently there have been discussions about calculating three body systems. Is there an ideal in that realm to govern such relationships, or are they completely contextual to the particulars of each situation? If the configuration of such situations are entirely dependent on the physical conditions, why wouldn't this also apply to simpler, more predictable actions? Does nature need a platonic realm, or is it just us who need to keep the book handy?
John C,
Curvature is information. Energy is what causes it.
Light often follows curved paths, but when it's bent by a glass lens, do we say space is curved? How do we fully know there isn't some other explanation for why light is curved passing massive bodies?
For example, say there is some elemental entanglement among photons from the same source and a massive body, being condensed energy, exerts contraction through this resulting light field. It would bend the path of the light, as the closer part contracts more than light passing further out.
One thing to keep in mind is the top down nature of knowledge, where we necessarily need to fit all experience within our body of knowledge. This process is quite familiar to those raising children, where no matter how young they are and especially when they are young, they have the sense of knowing all the important stuff, because so much of what they experience is repetitive, leaving the sense of more of the same. So apply that to our common experience as beings on this planet. We exist as very distinct points of reference on what seems like an overall flat surface and we move about. So what would be the most common agreed upon model of this experience, if not points, lines, planes, height and narrative? Then if we want to distill them to the most abstract formula, we could say they have no other extension than that assigned to them, ie. zero dimensions other than projection. Yet there is another basic mathematical rule that says any multiple of zero is still zero, so by that law, they shouldn't exist. Yet what is a little rule bending among friends? But then a line is not created by an infinite number of points, because even infinity multiplied by zero is still zero. Those points need extension to add up to a line. No distance without space.
Do longitude, latitude and altitude physically exist, or are they measurements of physical relationships? Why wouldn't various temperatures, such as of the cosmic background radiation, or freezing/boiling points of water be considered equally fundamental?
As I keep saying, when we look out on the cosmos, does nature measure space with abstractions, or with energy coalescing into and radiating away from dynamic processes? That is what causes curvature of action, not the description we give it.
Regards,
John M
