Since we appear to agree that the number of colors have to be discernible to be valid…
This question has been interesting to think about and I think it's quite challenging. Having said that, I don't think I agree with this.
I don't think the question is valid. Everything in CIE Colorimetry is based on continuous functions. Although the original color matching data is discreet, and any spectral measurements you get from a spectrometer are also discrete, the first thing we do is interpolate to smooth functions. When you look at the formulas for moving from spectral data to a tristimulus space, they are full of integrals, nots sums. It's continuous functions from the ground up. So asking about discrete data requires you to sample from the model, but colorimetry doesn't give you good tools to make these samples for the current problem.
Additionally, although we often casually talk about XYZ or RGB numbers as being colors, that's not entirely true. Colorimtery traffics in
color stimuli not colors. And it only describes how different stimuli under very specific conditions match. Colorimetry is not a system for identifying color perceptions.
While many people in this thread have pointed out that different stimuli can result in the same color perception, the opposite is also true. For example, consider the sRGB value (130, 70, 15). Does that stimulus map to one perception? If you were to count the number of distinct colors in the following image, will that RGB value be tallied as one perception? If so, which perception does it map to, the top center square or the bottom (they're both the same RGB value)?
(from:
http://www.lottolab.org/articles/illusionsoflight.asp)
We also have difficult semantic problems. We might be happy to define colors based, by definition, on human perception, but we freely use the term color for any perception. For example some birds are known to be tetrachromats with an additional cone sensitive to ultraviolet light. This means that stimuli that would be identical perceptions to us are different colors to them. We're happy to extend the definition of colors to distinctions birds can make and simply say that these are two colors that we can't distinguish, but something else can. We frequently talk about perceptions that we can't perceive, but that something can or that some tool can measure. For example sounds that are below our frequency threshold that elephants use to communicate or smells that only by dog can smell. So if we have color stimuli that we can't distinguish, but which the camera can, isn't it just easier to call these different colors, but with differences below our threshold?
There are also practical problems. If you look at the literature, the attempts to define the number of colors are all over the map. Edward Titchener came up with 33,000 in 1896, Edwin Boring came up with about 10 times that number around the same time. Deane Judd estimated 10 million while David MacAdam estimated 17,000 — both legendary color scientists. Then you have Mark Fairchild going out on a limb and claiming an infinite number:
http://www.rit-mcsl.org/fairchild/WhyIsColor/files/ExamplePage.pdf. Clearly there's some disagreement about how to approach the question.
All of these problems go away, if we just call colorimetry what it is — a model – and avoid questions that ask this model things it wasn't designed for. Questions it handles nicely are things like, what is the range of stimuli, or how many color values are in a file, or even how many cubic ∆Es does a space contain — these are are very clean and easy. Questions like, how many distinct perceptible colors are in a working space, don't easily fit with the model and therefor become messy and confusing and identifying the reason for the messiness is probably more valuable than any answer you could come up with to the original question.
