John,
"It's certainly all conjecture for me, but as you say, all we have is theory.
And observation."
And measured correspondence between theory and observation.
"My point about Olber's paradox is that microwave background radiation is what the light from over the horizon line of visibility would be registering."
The background radiation comes from all directions. There's no preferred origin, which is why we think it is the thermal leftovers ("dying embers") of a big bang event. If there is a little bit of anisotropy (and there appears to be, on the order of a few parts in a billion), we might learn something about the initial condition of the universe and maybe even get a clue to the nature of quantum gravity.
(me) "'However, if space is primordial and minimally two-dimensional, how did it get that way?'"
(you) "We assign it dimensionality. If you want to describe it in two dimensions, I see it as the blank sheet of paper, not the graph drawn on the paper."
That's one reason the anisotropy is so important. You see, the formalisms of quantum mechanics are all written in two dimensions (complex plane Hilbert space); a quantum bit is two elements. If we could show that the dimensionality is not arbitrary (as anisotropy might suggest) then we not only derive the natural basis for quantum mechanics, we derive the basis for higher dimensional "branes" in a physical way.
"So much of our thought process is about what we can grasp, but does that mean space is based on those physical boundaries? For the sake of conjecture, how difficult would it be to at least conceive space as being space, even if just for a thought experiment? It might be full of quantum activity, but given the scale of just what we can measure, it seems a rather significant aspect of reality to just dismiss as an effect of matter expanding from a point."
That's well taken. However, space and time to a physicist -- at least a relativist -- are not "just" space and time. They are the fundamental building blocks of the universe. Even quantum activity requires space a priori, and it is not satisfactory to just imagine it as a primordial background -- we want to know where it came from. Every major door we open leads to a greater room of research possibilities.
(me) "'How many do you need?'"
(you) My curiosity likes to consider all possibilities."
Theorists, on the other hand, try to limit possibilities, i.e., get by on fewer assumptions. The fewer assumptions that yield the larger number of predictions, the stronger the theory.
(me) "'What is the temperature of absolute zero?'"
(you) "If space is a consequence of activity and if we were to theoretically remove all activity, thus zero time, by the principles of spacetime, wouldn't space collapse to a point as well? Or would it remain just a non-fluctuating vacuum? If it is the second, than what action creates it as space? Or does space alone not need cause, since it lacks any properties that require cause?"
Well, we don't really know what a vacuum is, and quantum rules don't allow space to collapse to a point. That's why we use the term "quantum vacuum." If there is no point of certain location in a space containing two elements, there is no way that the elements can avoid fluctuating, because what we know of classical mechanics is that particles expand to fill the space they occupy. Neither classical spacetime nor the quantum vacuum are empty (i.e., there is always something rather than nothing) -- though while the quantum vacuum is filled with particles (actually, virtual particles), classical spacetime is filled with fields. So we get quantum field theory from vacuum energy, and classical spacetime filled with particles is said to emerge from that.
(me) "'All fundamental elements of mathematics are conveniently chosen,'"
(you) "So they are conceptual tools, designed for efficiency, not platonic gifts of the gods?"
Is the alphabet a platonic gift from the gods? Mathematical language is no more efficient than natural language -- it is just more precise.
(you) "As tools, they do frequently get used for applications not originally intended, often to good benefit, but often we find other tools, medicines, concepts, processes, etc. have multiple uses, as well as side effects and other unintended consequences."
Mathematics isn't intended for anything except understanding and communicating relationships among symbols in an objective way. It isn't "about" something, no more than natural language. It doesn't have "consequences" except as one might imagine and assign.
"Could it be that while math is quite useful, it also has effects we might not be taking into account, such as channeling our thinking in ways that blind us to different perspectives?"
Is your knowledge of English blinding you to different perspectives? Possibly. The difference vis a vis mathematics is that mathematics is a universal language, practiced the same everywhere in the world.
Best,
Tom