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The Hurvich–Jameson (H–J) opponent-process network offers a familiar account of the empirical structure of the phenomenological color space for humans, an account with a number of predictive and explanatory virtues. Its successes form the bulk of the existing reasons for suggesting a strict identity between our various color sensations on the one hand, and our various coding vectors across the color-opponent neurons in our primary visual pathways on the other. But anti-reductionists standardly complain that the systematic parallels discovered by the H–J network are just empirical correspondences, constructed post facto, with no predictive or explanatory purchase on the intrinsic characters of qualia proper. The present paper disputes that complaint, by illustrating that the H–J model yields some novel and unappreciated predictions, and some novel and unappreciated explanations, concerning the qualitative characters of a considerable variety of color sensations possible for human experience, color sensations that normal people have almost certainly never had before, color sensations whose accurate descriptions in ordinary language appear semantically ill-formed or even self-contradictory. Specifically, these “impossible” color sensations are activation-vectors (across our opponent-process neurons) that lie inside the space of neuronally possible activation-vectors, but outside the central ‘color spindle’ that confines the familiar range of sensations for possible objective colors. These extra-spindle chimerical-color sensations correspond to no reflective color that you will ever see objectively displayed on a physical object. But the H–J model both predicts their existence and explains their highly anomalous qualitative characters in some detail. It also suggests how to produce these rogue sensations by a simple procedure made available in the latter half of this paper. The relevant color plates will allow you to savor these sensations for yourself.
Notes
Strictly speaking, Munsell intended his solid to represent the relations between the various external or objective colors. But it serves equally well as a representation of the similarity and difference relations between our internal color sensations as well—i.e., the use to which it is here being put. The spindle-shaped solid, that is, represents our phenomenological color space. Be advised, however, that it provides only a first-order model. Its internal metric is suspect, and we may well need a four-dimensional space to capture all aspects of human color perception. But those complexities lie safely beyond the specific concerns of this paper. For a broad summary, see Kuehni (2003).
As an aside, human cone cells respond to light with smoothly varying graded potentials (voltage coding), rather than with the varying frequencies of spiking activity (frequency coding) so common in the rest of the nervous system. This wrinkle is functionally irrelevant to the first-order model, which is why cellular activation levels are expressed neutrally, in what follows, as a simple percentage of maximum possible activation levels.
Among other things, the input cones also become differentially fatigued, but these input cells display a different pattern of compensation. Since their resting activation level is 0, they can display no potentiation, but only fatigue.
The immediate point of placing the colored circle against a middle gray background square is to ensure that only the visual area comprehending the circle itself is subjected to opponent cell fatigue or potentiation. The immediate point of placing a second, uniformly gray square immediately to the right of the first is to ensure that this square visual area also suffers no opponent cell potentiation or fatigue. The ultimate point of thus avoiding any fatigue or potentiation in those areas is that, when one's gaze is subsequently refixated on the cross within the third square, everything within the third and fourth squares will be seen normally, except the circular area within the third square, where the induced after-image is situated. The point of the final or right-most square with its colored circle is to provide a prediction of the shape and expected color of the induced after-image, next door to it in the third square, so that you may compare directly and simultaneously the reality with the prediction.
Note well that an activation level of 50% of maximum produces neither fatigue nor potentiation in the relevant opponent cell. For, under normal conditions, 50% is the spontaneous resting level of any such cell. In the absence of any net stimulation or inhibition from the retinal cones, the opponent cells will always return, either immediately or eventually, to a coding vector of ⟨50, 50, 50⟩, i.e., to a middle gray.
Note that each element of this f/p vector—⟨ f B/Y, f G/R, f W/B⟩—can have either a negative value (indicating fatigue for that cell) or a positive value (indicating potentiation for that cell). Note also that the length of that f/p vector will be determined by (i) how far away from the spindle's middle gray center was the original fixation color, and by (ii) how long the opponent cells were forced to (try to) represent it. A brief fixation on any color close to middle gray will produce an f/p vector of negligible length. In contrast, a protracted fixation on any color far from middle gray will produce an f/p vector that reaches almost half-way across the color spindle. Strictly speaking then, the three equations for A B/Y, A G/R, and A W/B cited earlier should be amended by adding the appropriate f/p element to the right-hand side of each. This might seem to threaten extremal values below zero or above 100, but the (suppressed) squashing function mentioned earlier will prevent any such excursions. It asymptotes at zero and 100, just as required.
The wary reader may have noticed that I am assuming that it is the opponent cell fatigue/potentiation, as opposed to retinal cone cell fatigue, that is primarily responsible for the chromatic appearance of our after-images. Why? For three reasons. First, we still get strongly colored after-images even at modest light levels, under which condition the cone cells are not put under stress, but the delta-sensitive opponent cells regularly are. Second, as we noted earlier, the opponent cells code by variations in high frequency spiking, which is much more consumptive of energy than is the graded voltage coding scheme used in the cones. Accordingly, the opponent cells are simply more subject to fatigue/potentiation. Finally, the H–J theory entails one pattern of after-image coloration if cone cell fatigue is the primary determinant, and a very different pattern of after-image coloration if opponent cell fatigue/potentiation is the primary determinant. The observed pattern of coloration agrees much more closely with the latter assumption. Colored after-images, it would seem, are primarily an opponent cell phenomenon.
The explanation is obvious. Recall that to produce an opponent cell triplet for maximum white requires that all three of the S, M, and L cones have activation levels of 100. To produce a triplet for maximum black requires those same cells all to be at zero. To produce a triplet for saturated yellow requires that S be at zero, while M and L are both at 100. Accordingly, the retinal input for yellow already takes you two-thirds of the way up the opponent cell cube toward white (recall that white requires S, M and L all to be at 100). Similarly, the input for saturated blue requires that S be at 100, while both M and L are at zero. Accordingly, the retinal input for blue already places you two-thirds of the way toward black (which requires that S, M, and L are all at zero). Hence, blue is darker than yellow and the equator of maximum hue saturation must be tilted so as to include them both. (Note that red and green display no such brightness asymmetry.)
Herschel (1880) placed the bulb of a mercury thermometer just outside the red-most edge of the spectral “rainbow” image produced by directing sunlight through a prism. The mercury level shot up. Hertz (1888) confirmed the existence of light at much longer wavelengths with his primitive radio transmitter and radio receiver. Roentgen (1895) stumbled across X-rays while playing with a cathode ray tube, and correctly characterized them, after a week or two of sleuthing, as light of much shorter than visible wavelengths.
For the locus classicus of this worry, see Levine (1983).
On this point in particular, see Churchland (1996, pp. 225–228).