Purple does not exist in the rainbow. Run sunlight through a prism and you get a band of colors from red through orange, yellow, green, blue, and violet — a single sweep along the visible spectrum from roughly 380 to 700 nanometers. Purple, the color that sits between red and blue-violet, is nowhere in that sequence. It cannot be. It requires mixing the two ends of the spectrum, and a spectrum has only one sequence, with no path back from violet to red. Purple is a color that lives only in your head.
This is not a quirk or an illusion. It is a structural fact about the geometry of human color perception — a geometry that turns out to be much stranger than the physics of light would suggest.
The physics of light is simple: electromagnetic radiation at different wavelengths. The space of wavelengths is a line segment, one-dimensional, ordered from short to long. But human color perception is not a one-dimensional system. We have three types of cone cells in the retina, each sensitive to a different range of wavelengths, with peaks roughly at short (blue), medium (green), and long (red) wavelengths. When light enters the eye, it stimulates each cone type to some degree, and the brain receives not a wavelength measurement but a triplet of numbers — the responses of the three cone populations. Color perception is therefore inherently three-dimensional. The space of all colors humans can see is not a line but a solid.
Newton grasped something of this in 1666 when he bent the spectrum into a circle. His original color wheel placed the spectral colors around the circumference — red, orange, yellow, green, blue, indigo, violet — and then closed the gap between violet and red with a non-spectral region he called "purpura." This was a conceptual move of real insight: he was recognizing that the perceptual relationships among colors have a topology that the physics does not. The spectrum has two endpoints. The color wheel has none. Newton's circle was not a description of light. It was a description of how light is experienced.
James Clerk Maxwell pushed further in the 1850s. He showed that all human color perceptions can be described as combinations of three primaries, and that the geometry of color mixing is linear: mix color A and color B, and you get a color that lies on the straight line between them in perceptual color space. This means that instead of a circle, the natural representation is a triangle — pick any three spectrally pure colors as vertices, and every color that can be mixed from them lies inside the triangle. Maxwell used this to construct the first quantitative diagram of human color experience, a triangle whose corners were red, green, and blue and whose interior covered the gamut of mixed colors. The famous CIE chromaticity diagram from 1931 is the mature version of this idea: a horseshoe-shaped region (the spectral locus along the curved edge, the line of purples closing the bottom) that represents every chromaticity — every ratio of cone stimulations — visible to the standard human observer.
The line of purples at the bottom of the CIE diagram is the giveaway. It is straight. The spectral locus is curved. The straight line closes the figure artificially — it represents colors that have no single wavelength, colors that can only be produced by mixing the short-wavelength end of the spectrum with the long-wavelength end. These are the purples, magentas, and crimsons. They are real colors, in the full sense that you can see them and match them and name them. They simply have no location on the physical spectrum. The geometry of perception includes a region that the geometry of light does not.
But the chromaticity diagram is already a projection. It collapses the full three-dimensional space of human color into two dimensions by normalizing out brightness. The actual space of human color experience is three-dimensional, and its structure varies depending on how you slice it.
Albert Munsell worked this out empirically at the turn of the twentieth century, producing what he called a color solid: a three-dimensional object in which one axis is lightness (black at bottom, white at top), the distance from the center is saturation (gray at the core, vivid hues at the periphery), and the angle around the central axis is hue. This gives color space a roughly cylindrical structure, except that it is not actually a cylinder — it is lumpy and asymmetric. At medium lightness, greens and yellows can achieve much higher saturation than blues and purples. The solid bulges in some directions and pinches in others. Munsell insisted on spacing colors at perceptually equal intervals, which means the geometry is determined by human judgment rather than by physics, and human judgment turns out to be uneven.
What I find most striking about this is the topology of the hue dimension. Hue is circular. Start at red, move through orange, yellow, green, blue, violet — and then, instead of falling off an edge, you wrap back around through purple to red. The color wheel is not just a convenient pedagogical diagram; it reflects a genuine topological property of perceptual color space. The hue dimension has the topology of a circle, not a line. But brightness has the topology of a line segment: there is a genuine bottom (black) and a genuine top (white), and they are not connected to each other. You cannot get from black to white by going "all the way around" — there is no going around. These two dimensions of color experience have fundamentally different topological structures, and they coexist in the same perceptual space.
This asymmetry has consequences. It means that the color solid is not a cylinder, a torus, or any other regular shape. It is topologically more like a bicone — two cones joined at their bases — with hue circling around the equator and brightness running from apex to apex. Saturation is the distance from the central axis. But because hue is circular and brightness is not, the space cannot be embedded in three dimensions without some distortion. Every representation of color space involves a choice about which distortion to tolerate.
The deeper reason for all of this is trichromacy — the fact that we have exactly three types of cones. An organism with two cone types would live in a two-dimensional color space. Four-cone organisms (some birds, mantis shrimp with up to sixteen photoreceptor types) inhabit higher-dimensional color spaces that are simply inaccessible to us, in the same way that a person who has never seen a color screen cannot fully grasp what it means for a pixel to have a hue. We do not experience the dimensionality of our color space as a limitation because we cannot perceive what is missing. The space feels complete from inside. It always does.
What Newton's circle understood, and what the CIE diagram and Munsell solid make precise, is that the space of colors is a construction — not of the physics of light, but of the particular biological machinery of human vision. A different set of photoreceptors would produce a different space with different geometry. The topology of hue, the linearity of color mixing, the existence of purple — all of these are facts about us as much as they are facts about light. The rainbow has no purple not because purple is less real than orange, but because the rainbow is just physics, and physics does not know we are watching.