The curved rim of the horseshoe is the spectral locus; that of the purest, single wavelength spectral colors.
Purples are what you get when you travel between the ends of the horseshoe, where no spectral color lies. This is what is meant when one says purple exists only in our brains; it is non-spectral.
Furthermore, our vision is such that objectively different spectra can look the same; cf. metamers. This follows from the fact that the process of projecting an infinite dimensional spectra into three dimensions (because color is 3D) is lossy. But our vision optimizes the dimension reduction for spectral discrimination in parts of the electromagnetic spectrum that are beneficial for evolution.
I forgot to add that in addition to being non-spectral, they are the most saturated colors of their hue. All colors inside the horseshoe are non-spectral; they are mixtures of spectral colors.
The curved rim of the horseshoe is the spectral locus; that of the purest, single wavelength spectral colors.
Purples are what you get when you travel between the ends of the horseshoe, where no spectral color lies. This is what is meant when one says purple exists only in our brains; it is non-spectral.
Furthermore, our vision is such that objectively different spectra can look the same; cf. metamers. This follows from the fact that the process of projecting an infinite dimensional spectra into three dimensions (because color is 3D) is lossy. But our vision optimizes the dimension reduction for spectral discrimination in parts of the electromagnetic spectrum that are beneficial for evolution.