Christopher:

Congratulations on recognizing that the "color space" solids* are three dimensional manifolds, apparently without anyone telling you such. :-)

If you are saying that, conceptually, at least, the color perception space, at the perception level (as opposed to our assigning coordinate like labels to the individual colors, for our own convenience/thinking) is not some "numerically coordinated set", I may be inclined to agree. However, there is the apparent "fact" that the firing of neurons is equivalent to "numbers", at least at some level. Really, how are we to distinguish them?

However, the physical space in which we dwell is certainly not any kind of "numerically coordinated set", until we humans assign such labels to points within it. This is one of the features of the general coordinate system approach used by General Relativity that strongly appeals to me.

The feature being that the phenomena of nature care absolutely nothing for what coordinates we may assign to the points of space and time. They will "merrily" go about "doing their thing", completely independent of our choice for any such labeling.

Therefore, until the coordinate independent nature of natural phenomena is somehow shown to disagree with nature I consider that any and all theories of natural phenomena must be independent of the assignment of coordinates. In other words, all must be invariant to general coordinate transformations, without having anything other than (unchanging) constants and "dynamical" quantities in their equations.

Incidentally, on the subject of the manifold nature of human color perception, I ran into an article, a while back, that purported to have found that the human perception of shades of gray, in terms of light/dark, was not one dimensional, as one would expect (since we generally consider light/dark, shades of gray, to be able to be characterized by a single parameter). Instead they purported to have found evidence that it is two dimensional. (This makes me wonder whether human perceived color space may be six dimensional, or maybe even more.)

Certainly it is known that our perception of colors does depend upon what other colors are around.

Of course if all we have are "distances" we can get into trouble by assuming a metric relation, when it is possible there is only a norm relation. I'm not sure what the "angle" or "inner product" relations would be, let alone mean, for colors. However, we do know that linear combinations of colors do create other perceived colors for all non-negative linear combinations (meaning linear combinations where the coefficients are all non-negative).

Of course we know that physically realized colors actually lie in a function space (the color spectrum of the pigment/filter/light/whatever), however, our color sense is not so sophisticated as to be able to distinguish this space. What we see is some kind of projection into a space of smaller dimension (almost certainly of finite dimension, but I'm not completely certain that even this can be taken as a given, though I find it highly likely).

Recognizing the possibility that things may not be as simple as we may believe is important to keep in mind as one investigates a given phenomena. However, the nature of science is the continual cycle of: Theory/hypothesis/supposition/idea -> experiment/observation -> analysis/fitting/pondering -> back to theory/hypothesis/supposition/idea. And, as humans, our thinking is usually facilitated by starting with simpler models first. (Besides, Newton's first "Rule of Reasoning in Philosophy" and Occam's razor are designed to favor the simpler models.) So, as evidence accumulates, and as investigators actually look outside the present models to see if things are as simple as we expect/assume, then the science advances.

David

* They are solids only because they are three dimensional (in a "filled figure" sense), not because they are solid objects within our physical space, except when someone makes a physical representation of one.