Justin Broackes - Professor of Philosophy

Why is there no 'seam' on the color wheel? This is a beautiful question: at first sight, it looks fairly simple and scientifically answerable, but it quickly leads to many other questions, both scientific and more broadly philosophical, about the relation of the human mind to the world.

Put light from one end of the spectrum next to light from the other end and they clearly look different: light of 400 nm (nanometres) is violet, and light of 700 nm red, and there's clearly a difference between them. But if you mix the two together in different proportions you get a smooth transition between violet and red, with different kinds of purple - generating (along with the colours in the spectrum) the 'colour wheel' or closed curve of hues we see. How come? The first part of an answer is: we have (to simplify a bit) only three types of cone, and each type responds not just to a single wavelength of light, but to wide ranges of wavelengths. (Think how very different this is from the ear: we can hear vast numbers of pitches both separately and together, and if you mix together a C and E in the world, you hear both of them-a chord made of two notes together - not just the intermediate pitch D. By contrast, if you mix red of 650 nm and green of 540 nm in suitable proportions you get yellow - a yellow that can be a perfect match for yellow of 575 nm! To take an image from the great psychologist Helmholtz in the 1850s: the ear resonates, like a piano with the sustaining pedal down, more or less separately to a huge number of frequencies of sound. By contrast, the eye at each pixel, so to speak, responds like a poor quality cochlear implant that has just three wavebands.)

But why do the sensations from the stimulation of longwave and shortwave cones mix together at all? Why don't different stimulations of the longwave and the shortwave cones just produce, so to speak, a 'chord' of sensations that refuse to mix - like a high pitch and a low pitch of sound? What gives the space of colours the structure it has? Why is there this circle of hues (or plectrum-shape, to follow the CIE 1931 chromaticity diagram), not a line?

A good start is to say: there is (what since the 1950s has been called) opponent processing. In post - retinal processing, and even in the retina, there are cells that take the output of long -, medium - and short - wave sensitive cones (L -, M - and S - cones) and that have an output that is sensitive to differences between the inputs rather than their sum. So (to follow one simple model), an L - M signal would give us red vs. green, an S - (L + M) signal would give us blue vs. yellow, and something like L + M would give us brightness. And that looks to map neatly onto something like the structure of the perceived space - something like the double - cone illustrated below. And the results of mixing red with blue light would be structurally similar to (would be a kind of mirror image of) the results of mixing green with yellow - so a smooth completion of the hue circle shouldn't be too surprising.

And yet this leaves many questions. Why do we have an opponent processing system of this kind at all? Why do we have three dimensions of colour vision, not (like many other mammals) two - or (like many fish and birds) four or five, or more? Is there a design explanation? (Would more dimensions of colour mean less visual acuity? But why then do birds and fish have more? Is it that adding extra dimensions of colour - vision in fact add very little discriminatory power for land - dwelling creatures, dealing mainly with surface colours? Whereas the benefits might be different for those living in water or the air?) How are we to think of the evolutionary transition, as old - world apes and the ancestors of humans developed three - dimensional colour systems out of two - dimensional systems? (A two - cone system would standardly be modelled as yielding something like the yellow - blue dimension and the light - dark dimension: and that means just two hues (along with more and less desaturated varieties of them). But then how are we to think of the transition when a third receptor develops (or when the evolutionarily older long - and - medium - wave cone type differentiates into a long - wave type and a medium - wave type)? Can we really suppose it would be, so to speak, completely non - trivial for the brain to cope with this new dimension of input from the eye? And why did it evolve in the way it did? Why should the system respond, so to speak, by treating the new dimension of variation as yielding a whole range of new hues - so the old pure yellow and pure blue became just two hues among a infinite variety of new hues?

More fundamentally, are we making a mistake talking as if wavelengths (or the colours of light) are the fundamental thing the visual system responds to - rather than the colours of surfaces (or, yet more complexly, the colours of surfaces as presented in varying, sometimes coloured, illuminant conditions). And, to take up another range of big questions: the opponent process story turns out to be a far from full explanation of the structure of our phenomenal colour space. The positions of 'pure' or 'unique' red, green, yellow and blue - that is, the red that looks to contain no tinge of blue, or of yellow, and so for the other three - do not correspond even in very general terms with where the simpler models lead us to expect them. (One would expect unique blue where there was strong firing on the S - (L + M) channel and equilibrium on the L - M channel; but actually L - M is constantly negative at all wavelengths below about 550 nm! So the simpler models actually give us no understanding of how the tinge of red seen at the shortwave end of the spectrum actually comes about.) Of course one can cook up mathematical functions that do a better job of modelling the structure of colour space: but people haven't found physiological evidence of cells actually implementing such functions in the visual system. Conversely, there is no shortage of well - attested cells with, roughly, an L - M output: but that actually doesn't correspond at all well with our actual reporting of experience of red - vs - green. So we might ask ourselves: how close and what kind of correspondence should we expect between the structure of our phenomenal colour space and what the physiology reports?

And if for the time being we can't find the structure of unique hues (or more than a little of it), so to speak, inside the physiology of the visual system, might we look for it outside? Might it be (as Roger Shepard and John Mollon have suggested) that unique yellow and unique blue are tied to certain environmental cues: namely, the sun and the sky? (There is plenty of variation in natural daylight, skylight, and sunlight: but most of it can be mapped as variation along a line that actually corresponds very well with the line in chromaticity space between good candidates for unique yellow and unique blue.) Is it not remarkable that, despite the yellowing of the lens of the eye as we grow older, the position of the unique hues seems to be pretty constant? (Our old choice of unique green, one might think, would come to look too yellow, as we age: and we would therefore choose bluer greens as 'unique'. But we don't.) Is it possible that in a way, we recalibrate the position of these unique hues constantly? But on what external bases? (For red and green, it's harder to find such good candidates as the sun and sky are for yellow and blue.) And how does the physiology adjust? And how does all of this connect with the constant adjustment we make as illumination changes in the processes often talked of under the heading of colour constancy? And if we have good answers on these things, then after all, might colour in a sense be a little less subjective than we're often think? Might there be a little more stability to our colour perception system than we tend to think?

This is the kind of question that makes the science and theory of colour, I think, so fascinating: physiology, psychology, physics, evolutionary theory, mathematical modelling all play a part-and the questions connect with large questions about the relative priority of the internal and the external, about the human animal in its environment, and about how far the visual system is merely arbitrarily linked to its external cues or instead might in some sense, or to some extent, be 'tuned', in colour perception, to detect, not basic physical properties like wavelength, but nonetheless environmentally interesting kinds of surface reflectance. These are questions on which there is a huge amount of important and impressive accumulated understanding; I do not, however, have the impression - from my time in a lab as well as in the library, at the computer and at the desk - that we are just on the point of having a complete and stable theoretical understanding of these difficult questions. Another reason to think there's work to be done ...

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Fig. 1. Illustrative representation of the space of experienced colours in trichromatic human beings (cf. e.g. Ostwald 1931, vol. 1 ch. 7; Hurvich 1981, 11)

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Fig. 2. Illustrative representation of the space of experienced colours expected (on standard models) for a dichromatic animal: with just two hues, typically taken to correspond to yellow and blue. (The faint ellipse is no part of the space: it is there to indicate the perspective and to make clear how much is lost from the normal trichromat's hue-circle.)

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Fig. 3. . Cutaway representation of Munsell colour space, showing some of the asymmetries of that space. Concentric circles around the vertical axis indicate lines of equal Chroma (approximately corresponding to Saturation in other systems). Note some of the asymmetries: at medium Value (approximately, medium lightness), one can get reds of higher Chroma than greens. At high Value (or lightness), the only hue that one can get a high Chroma instance of is Yellow. We might ask: are these asymmetries just an accident of the visual system? What explains them? (Figure: Copyright (c) Color Planning Center Inc., used by permission of the Dainichiseika Color & Chemicals Mfg. Co., Ltd.)

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