Whether natural dyes look different or not is unknown to me, however I bet $100 that dude couldn't tell the difference if you mixed in a bunch of synthetically dyed material with the naturally dyed stuff. Put the natural and synthetic dyes in a lineup together and I bet there is no way for him to reliably tell them apart.
Is one allowed to vary the lighting conditions while examining them?
If in one collection, one has different mixes of 4 fixed dyes or pigments which each respond to the light in a particular way, then, the way the result responds to different light sources should be in a particular 4d space, while more generally pigments could have the lighting->appearance function be a point in a larger space which that 4D space is a subset of, right?
I don’t particularly know what I’m talking about in this comment, but it seems to me like it should be right..
Though, even if what I said is right, there’s still the question of whether a person could reasonably learn to recognize whether such a response function (“response function” is not some technical term that I know. If it is a technical term, it is likely I’m using it wrong. I’m just using it as a description of the function from lighting to apparent color.) is from such a 4D subspace or not.
Based on a video I saw, I suspect that in some cases, yes, but in general idk. How often would the function be very close to something that is in the 4d subspace but isn’t quite?
I imagine a machine could do it easily.
Assuming you have a cheap way of producing light of a variable wavelength? Do we have such a thing? I think electron vibrating lasers (Idr the proper name for them) have a tunable wavelength, but I imagine those are expensive, and also probably something that isn’t a laser would be preferable.
As we have three cones used to observe tone and colour, the colour/tone of something occupies a 3D space.
However, as you say, a pigment colour has high dimensional properties - the spectral response. As others have mentioned this determines how it impacts on the observed/perceived colour, depending in the spectral response of the light it reflects.
Might it be like diamonds where the imperfections give it away? Maybe we'll see similar marketing that natural is more unique than 'artificial.' I could see that having $elling value in fashion, one of my friends does natural dying in Mexico and the selling point is uniqueness.