For the suggestion on the right (i.e. finding a basis for all colors), how is this really possible? Is there a way to truly know that you have "spanned" all colors, as aren't new colors discovered here and there sometimes?
If some linear combination of our known basis can result in the newly discovered color, that means that the color always existed. But since there are an infinite (not sure on this, please verify if you can) number of colors spanned by our basis, then perhaps that means that single new color had not been recorded before, though it was covered by our basis.
Hm, this is interesting. Normally computers use RGB to represent color, which assumes color is three dimensional. If this is not the case, for example color is 4+ dimensional, that means there is a subset of colors that a screen, for example, cannot represent.
I always thought color is 3D given that it is often represented in RGB. But, thinking about it now, there can be other things too, like opacity. I wonder if such additional qualities like that (opacity) increases the dimensionality of color.
On the topic of opacity — I imagine that the resulting color (the less opaque color placed "over" another color) will still be representable in the 3D space, as it's equivalent to a linear combination of the two colors, similar to if you added a scaled 3D vector to another.