From Towards a Science of Consciousness 3 Section 2: Color -- Introduction CogNet Proceedings
The issues I discuss in this chapter concern whether your conscious experiences of color are the same as mine when we both look at the same environmental objects under the same physical conditions, and how we could possibly know. Together, I will refer to them as the "color question."
The reader may wonder why color should be the focus of this discussion about conscious experiences. Different people have different reasons for focusing on color. My own reasons are twofold. First, we know an enormous amount about color perception, and this background of scientific knowledge makes it a good domain in which to ask such questions. Second, there is a well known and persuasive argument due to John Locke (1690/1987) in the philosophical literature-called the inverted spectrum argument-that claims to show that we simply cannot know whether your color experiences are the same as mine. It goes like this.
Locke argued that there isn't any way you could know whether my experiences of colors are the same as yours or whether they are "inverted." The most straightforward interpretation of this inversion would be simply reversing the order of colors experienced in viewing a rainbow. If this were the case, you would experience the rainbow with red at the top and violet at the bottom, but I would experience it with violet at the top and red at the bottom. We would both call the top color "red" and the bottom color "violet," of course, because that is what we have all been taught by our parents, teachers, and society at large. Everyone calls blood, ripe tomatoes, and Macintosh apples "red," so we all associate our internal color experiences on viewing these objects-whatever they might be-with this verbal label. But my internal experiences of color might be inverted in just the way Locke suggested without its having any effect on how I behave in naming colors. Indeed, Locke's argument is that spectral inversion of color experiences might conceivably exist without there being any external manifestation of the difference. It seems there just isn't any way to tell, because I can't "get inside your head," and "have your experiences"-nor you mine.
But in this chapter, I will claim that there are ways of rejecting this particular argument without getting inside each other's heads and having each other's experiences. Good, solid behavioral evidence from vision science allows us to reject conclusively this literal interpretation of Locke's argument. Once we see why, we will ask whether there is any transformation of your color experience that I might have without it being detectable in my behavior relative to yours.
One important thing we can measure behaviorally about color experiences is their relative similarities. Everybody with normal color vision would agree, for example, that red is more similar to orange than it is to green. These relative similarities can be obtained for a large sample of triples of colors. It turns out that the results of measuring these three-way similarities can be summarized quite neatly in a geometric model of color experiences known as a color space. Each point in a color space corresponds to a color experience, and proximities between points correspond to similarities between colors. This means that nearby points in color space correspond to similar color experiences, and distant points in color space correspond to different color experiences.
Perhaps the simplest and best known color space is Newton's color circle, which is represented in figure 5.1. The saturated colors of the rainbow are arrayed around most of the perimeter of the circle, approximately as indicated by the color names around the outside. A few wavelengths of monochromatic light are also indicated in this diagram at the appropriate places. This color circle is not the most complete or accurate representation of human color experiences, but it is a good starting point for understanding how behavioral data can constrain the answer to the color question.
[Insert figure 5.1 about here; figures not yet available]
One of the interesting things about this geometrical representation of color similarities is that it allows a simple and transparent way to determine whether Locke's hypothetical spectral inversion could be detected by behavioral measurements of color similarities. Within the color circle, inverting the spectrum is just a reflection about the diameter passing through 550 nm. (the dashed line in figure 5.1), which lies at the middle of the visible spectrum from 400 to 700 nm. This reflection sets up the correspondence between your color experiences (as indicated by the quoted labels on the outside of the circle in lowercase letters) and my color experiences (as indicated by the parenthesize abbreviations on the inside of the circle in capital letters). When you experience red, I experience purple; when you experience yellow, I experience blue-green (cyan); and so forth.
Would these differences be detectible through measures of color similarity relations? You would say that red is more similar to orange than to green (because the point for red on the outside of the circle is closer to the outside point for orange than it is to the outside point for green). But I would say the same thing, even though, for me, it would correspond to experiencing purple as more similar to blue than to yellow-green (as reflected by proximities of the same points, but with respect to the experiences indicated on the inside of the circle). And in fact, all the color similarity judgments you and I make would be outwardly the same, even though our experiences would be inwardly different.
The reason such differences could not be detected by similarity measures is that the color circle is symmetric with respect to reflection about this axis. We can therefore conclude that so-called spectral inversion of color experiences could not be detected by measurements of color similarity. Furthermore, we can see that this particular inversion is only one of many ways that my color experiences might differ from yours without the difference being detected by measuring color similarities. Any reflection about a line passing through the center of the color circle would do as well, and so would any rotation about the center. In all these cases, our color experiences would indeed differ, but all our statements about the relative similarities of color samples would be the same. This is precisely the kind of result Locke expected when he proposed his inverted spectrum argument, for it seems we cannot tell whether there are differences in experiences or not.
But there is a great deal more that we can measure behaviorally about color experiences than just their similarities. Among the most important additional factors are relations of color composition. Most colors look like they are composed of other more primitive colors. Orange looks like it contains both red and yellow. Purple looks like it contains both red and blue. But there is a particular shade of red that is pure in the sense that it contains no traces of yellow or blue or any other color-it looks "just plain red." People with so-called normal color vision agree about this fact. Nobody claims that red actually looks like the composition of orange and purple, even though it lies between these two colors in color space. Color scientists call these experientially pure colors "unique hues," and there are four of them: unique red, unique yellow, unique green, and unique blue.
The existence of these four unique colors provides another behavioral tool for detecting color transformations. Consider rainbow reversal again, this time from the perspective of unique hues. You will indicate unique colors at particular shades of red, blue, green, and yellow, whereas I will indicate them at orange, purple, cyan, and chartreuse. The reason is simply that the experience of mine that is the same as your experience of unique red, results from my looking at color samples that we all call "purple." So for me, there is some shade of purple that appears chromatically pure in a way that no shade of red does, whereas for you, there is some shade of red that is pure in a way that no shade of purple is. This behavioral difference can thus be used to unmask a rainbow-reversed individual, if such a person existed.
This example shows that unique colors and other relations of color composition further constrain the set of color transformations that can escape detection. We can now rule out literal spectral inversion in the sense of simply reversing the rainbow. Even so, there are still several color transformations that will pass all behavioral tests of color similarity and color composition with respect to the color circle shown in figure 5.1. They are the four central reflections about the axes passing through opposite unique colors (i.e., the red-green axis and the blue-yellow axis) and the angular bisectors of these axes, plus the three central rotations of 90°, 180°, and 270°. All have the crucial property that they map unique colors into unique colors, even though at least some of them are different.
By now, it should be apparent where this argument leads. Color transformations that can escape behavioral detection correspond to symmetries in an empirically constrained color space. The important issue for answering the general version of Locke's color question, then, boils down to whether there are any symmetries in human color space. If there are, then my color experiences might differ from yours by the corresponding symmetry transformation.
Until now we have pretended that the color circle, as augmented by the distinguished set of unique hues, is sufficient to represent what is known about human color experience. But there is a great deal more known about color that is relevant to answering the color question. Most importantly, human color space is actually three dimensional rather than two dimensional. The three dimensions are hue, saturation, and lightness, and together they form the lopsided spindle structure diagrammed in figure 5.2A. The important fact about the 3-D color spindle for present purposes is that it breaks many of the symmetries in the color circle.
[Insert figure 5.2 about here; figures not yet available]
One of the most salient features of this 3-D color space is that highly saturated yellows are quite a bit lighter than highly saturated blues. This asymmetry makes some further color transformations detectable by purely behavioral means. Transformations in which your experience of yellow is supposed to be the same as my experience of blue (or vice versa) will be detectable because you will say that yellow is lighter than blue, whereas I will say that blue is lighter than yellow (because, remember, yellow looks to me like blue does to you). This difference can certainly be detected behaviorally-unless the lightness dimension of my color experience is also reversed, so that what looks black to you looks white to me, and what looks white to you looks black to me.
The upshot of such considerations is that if human color space has approximately the structure shown in figure 5.2A, there are just three possible color transformations that might escape detection in experiments that assess color similarity and composition relations. They correspond to the three approximate symmetries of human color space shown in figures 5.2B, 5.2C, and 5.2D. Relative to the so-called "normal" space in figure 5.2A, one transformation (figure 5.2B) reverses just the red-green dimension. The second (figure 5.2C) reverses two dimensions: blue-for-yellow and black-for-white. The third (figure 5.2D) is the composition of the other two, which calls for a complete reversal, red-for-green, blue-for-yellow and black-for-white.
Although all three are logically possible, by far the most plausible is reflecting just the red-green dimension. Indeed, a persuasive argument can be made that such red-green reversed perceivers actually exist in the population of so-called normal trichromats (see Nida-Rümelin, this volume). The argument goes like this. Normal trichromats have three different pigments in their three cone types. Some people, called protanopes, are red-green color blind because they have a gene that causes their long-wavelength (L) cones to have the same pigment as their medium-wavelength (M) cones. Other people, called deuteranopes, have a different form of red-green color blindness because they have a different gene that causes their M-cones to have the same pigment as their L-cones. In both cases, people with these genetic defects lose the ability to experience the red-green dimension of color space because the visual system codes it by taking the difference between the outputs of the M- and L-cones. Now suppose that someone had the genes for both forms of red-green color blindness simultaneously. Their L-cones would have the M-pigment, and their M-cones would have the L-pigment. Such people, would therefore not be red-green color blind at all, but simply red-green reversed trichromats. They should exist. Assuming they do, they are proof that this color transformation is either undetectable or very difficult to detect by purely behavioral means, because nobody has ever managed to identify one!
There is a great deal more that can be said about the behavioral detectability of color transformations (see Hardin, this volume). One key issue is the possible relevance of the basic color categories discovered by Berlin and Kay (1969) in cross-linguistic analysis of color naming. Briefly, the argument goes like this. There is a subset of 16 color names, called basic color terms (BCTs): single, frequently used, general-purpose words that refer primarily to colors. Together, they appear to form a universal system for linguistic description of colors. In English, there are 11 BCTs: RED, GREEN, BLUE, YELLOW, BLACK, WHITE, GRAY, ORANGE, PURPLE, PINK, and BROWN. The BCTs that do not exist in English can be glossed as LIGHT-BLUE, WARM (reds, oranges, and yellows), COOL (greens, blues, and violets), LIGHT-WARM (whites plus warm colors), and DARK-COOL (blacks plus cool colors). The fact that they appear to be linguistic universals suggests that they have some basis in human color experience and/or human physiology.
The important fact for present purposes is that some BCTs are symmetrically distributed in color space whereas others are not. In particular, RED, GREEN, BLUE, YELLOW, BLACK, WHITE, and GRAY are symmetric with respect to the three candidate color transformations shown in figures 5.2B, 5.2C, and 5.2D. The distribution of the other BCTs breaks all three of these symmetries, however. Therefore, if all of the BCTs arise from underlying asymmetries in the experiential structure of human color space, then any color transformation could be detected by behavioral means.
To illustrate, consider how I could, in theory, be unmasked as a "red-green invertomat" by my behavior concerning BCTs. Due to the reversal of the red-green axis of my color space, I would experience orange as yellow-green and purple as blue-green (and vice versa). This would not make any difference to my judgments of color similarity or color composition, but it should cause me to find it strange that there are BCTs for orange and purple rather than for blue-green and yellow-green. If systematic and reliable data on this matter could be obtained, it would reveal the fact of my red-green reversal.
It is not clear to me that I can easily make such fine distinctions, at least in direct introspective judgments. I am hard-pressed to say with certainty that orange and purple are "better" or "more natural" as basic color categories than cyan (blue-green) or chartreuse (yellow-green) would be if I had grown up in a culture that had these alternative BCTs. Perhaps they would, but it seems equally likely that I would not find the alternative strange at all.
Regardless of how the issue of BCTs is ultimately settled, the key question in evaluating the color question behaviorally is the existence of symmetries in human color space. That much seems clear. The question I want to turn to now is why this might be so. What is it about symmetries that makes them so crucial in answering the color question?
Symmetries have two important structural properties. First, they are what mathematicians call automorphisms: they map a given domain onto itself. This is important for Locke's original argument because one of its ground rules is that both you and I have the same set of color experiences; they are just differently hooked up to external stimuli. However, I do not think automorphism is actually important for the more general issue of color consciousness. The reason is that my experience in response to stimulation by different wavelengths of light might be nothing at all like yours. You and I could live in entirely different areas of experiential space, so to speak, and I don't believe it would matter with respect to what could be inferred about our color experiences from behavioral measures. I could even be a "color zombie" with no experiences of color at all, and no one would be able to tell, provided I behaved in the same ways toward them as you do.
The second property of symmetries is that they are what mathematicians call isomorphisms: they map a source domain onto a target domain in such a way that relational structure is preserved. In the case of symmetries, the source and target domains are the same (i.e., both automorphism and isomorphism hold), but this is not the case for isomorphisms in general. For example, color experiences can be represented by spatial models such as the ones shown in figure 5.2 because the objects of the source domain (color experiences) can be mapped into those of the target domain (points in 3-D space) so that experiential relations between colors (lighter than, more similar to, redder than, etc.) are preserved by corresponding spatial relations between points in color space (higher than, farther away from, closer to the position of focal-red than, etc.).
I want to argue that it is isomorphism-"having the same structure"-that is crucial for behavioral equivalence of conscious experiences. As long as two people have the same structure of relations among their color experiences, whatever those experiences might be in and of themselves, they will always give the same behavioral responses and therefore be behaviorally indistinguishable.
It is universally acknowledged that there is a behaviorally defined brick wallthe subjectivity barrier-that limits which aspects of experience can be shared with others and which aspects cannot be, no matter how hard we might try. The importance of the isomorphism constraint is that it provides a clear dividing line for the subjectivity barrier. The part we can share is the abstract relational structure of our experiences; the part we cannot share is the nature of the experiences themselves. In the case of color experience, this means that we share facts such as that red is more like orange than it is like green, that gray is intermediate between black and white, that purple looks like it contains both red and blue, and that there is a shade of red that is compositionally pure. We can share them because they are about the relational structure of experiences. We may implicitly (or even explicitly) believe that we also share the experiences themselves, but Locke and Wittgenstein have disabused many of us of saying so, at least in public.
What I am calling the isomorphism constraint is simply the conjecture that behavior is sufficient to specify experience to the level of isomorphism and not beyond. It proposes that the nature of individual color experiences cannot be uniquely fixed by behavioral means, but their structural interrelations can be. In case anyone feels disappointed in this, I hasten to point out that structural relations are absolutely crucial to the fabric of mental life. Without them, redness would be as much like greenness as it is like orangeness-or squareness, or middle-C, or the taste of pumpkin pie. Without them, perceptual qualities would just be so many equally different experiences, and this certainly is not so. But, by the same token, structural relations do not reflect everything one would like to know about experiences. Logically speaking, the isomorphism constraint implies that any set of underlying experiences will do for color, provided they relate to each other in the required way. The same argument can be extended to other perceptual and conceptual domains, although both the underlying experiential components and their relational structure will necessarily differ.
Behavioral scientists aren't alone in working within the constraint of isomorphism, for it also exists in mathematics. A mathematical domain is formalized by specifying a set of primitive elements (such as the points, lines, and planes of Euclidean geometry) plus a set of axioms that specify the relations among them (such as the fact that two points uniquely determine a line, and three noncollinear points determine a plane). But the elements to which the axioms and theorems refer cannot be fixed in any way except by the nature of the relations among them; they refer equally to any entities that satisfy the set of axioms. That is why mathematicians sometimes discover an alternative interpretation of the primitive elements-called a dual system-in which all the same axioms and theorems hold. The brilliant French mathematician Poincaré (1952) put the situation very clearly. "Mathematicians do not study objects," he said, "but the relations between objects. To them it is a matter of indifference if these objects are replaced by others, provided that the relations do not change." The same can be said about behavioral scientists with respect to consciousness: we do not study experiences, but the relations among experiences.
As I have formulated it, the isomorphism constraint defines the limits of what can be known via behavior. Figure 5.3 shows how far this can take us in the domain of color. Behavioral measures define the standard equivalence classes of color perception: so-called normal trichromats, three varieties of dichromats, and four types of monochromats. There are some further classes of so-called color weakness among trichromats, but this classification will do for now.
[Insert figure 5.3 about here; figures not yet available]
With respect to behavior these are indeed "equivalence classes," but with respect to statements about color experience, it would be more accurate to call them "difference classes." Pairs of individuals in different difference classes certainly have different color experiences, and within each difference class the isomorphism constraint certainly holds. But beyond that, we cannot say. There may be many varieties of color experience within the set of normal trichromats, many others within the set of protanopes, and so forth. We just cannot tell on the basis of behavior alone.
This raises the important question of whether we can go beyond the level of isomorphism by applying biological methods, either alone or in concert with behavioral ones. It is tempting to believe that if consciousness is fundamentally a biological phenomenon, the answer must be, "Of course we can!" I am less optimistic, but do not see the situation as completely hopeless, at least in principle, for reasons I will now explain.
It seems at first blush that one should be able to study subisomorphic differences in color experiences between two individuals by identifying relevant neurobiological differences between them and correlating them with differences in color experience. But this will not work. The problem is not in finding biological differences. We will presumably be able to work out the hardware differences at whatever level current technology allows. The problem is that, try as we might, we cannot identify any subisomorphic differences between our experiences to correlate with the biological differences. The reason is simply that the subjectivity barrier is still very much in place. Whenever we try to asses how two people's experiences might differ, we can get no further than the isomorphism constraint.
Even so, quite a different line of thought suggests that, at some level, biology must provide important constraints on the answer to the Color Question. It seems highly plausible, for example, that two clones, who have identical nervous systems, should have the same color experiences in response to the same stimulation. This is, in effect, a corollary of Kim's (1978) principle of supervenience: If the underlying biology is the same, the experiences will be the same. Most cognitive scientists and neuroscientists tend to believe something like this, although it is logically possible that the nature of experience depends on subbiological facts about quarks, quantum gravitational fields, or some other physical feature by which clones can be differentiated. Nevertheless, I will proceed on the assumption that clones have the same color experiences.
Assuming this clone-assumption to be well-founded, is there any way this presumed subisomorphic level of conscious experience can be tapped? The only effective route I can see is to avoid the subjectivity barrier by using within-subject designs. The idea is to use a biological intervention on an individual and ask for his or her report about any changes in color experience from before to after the intervention. Suppose, for instance, there were a drug called invertacillin that exchanged the light-sensitive pigments in the M- and L-cones. Assuming that the drug acted reasonably quickly and that it didn't also mysteriously alter people's long-term memories for object colors or the associations between internal experiences and verbal labels, subjects would indeed notice, and could reliably report, changes in their color experiences due to taking the drug. They might report that blood now looks green and that grass now looks red. These are extreme examples, and subtler changes in experience would, one hopes, also be detectable. But the crucial point is that the same subisomorphic color transformations that are quite impossible to detect between individuals seem, in principle, quite easy to detect within individuals. Notice that we, as experimenters, have still not penetrated anyone's subjectivity barrier, for we don't actually know how blood or grass appeared to the subject either before or after the change. We only know that it changed by reversing the red-green dimension of color experience, whatever that dimension might be like for that observer.
For the sake of argument, let us further suppose that we can figure out what the biological effects of the drug are and that it affects everyone's color experiences in the same way: namely, by reversing the red-green dimension of color space. Armed with this information, we can then divide the set of behaviorally defined trichromats into those who naturally have the biological structure associated with the result of the invertacillin intervention (the dashed circle labelled "Red-Green Invertomats" in figure 5.3) versus those who do not. Notice that this biologically defined class does not imply equivalent color experiences for individuals within it. With respect to color experiences, they still constitute a difference class, just like the behaviorally defined difference classes we mentioned earlier. People in different difference classes have different color experiences, but people in the same class may or may not have the same color experiences. We could not know that until we had exhausted the set of all the relevant biological factors and all their possible interactions, which is a pretty large set.
But suppose, for the sake of argument, that we could determine the complete catalog of the biological factors that are relevant to color experience in this way. Then we could, in principle, define true equivalence classes of people who have the same color experiences as people whose color systems all have the same values on the set of relevant biological features (e.g., association between photosensitive pigments and cone types). Notice that such statements would always be inferences about whether two people have the same experiences based on indirect evidence, much like our earlier inference that two clones would have the same experiences based on knowledge that their biology is the same. We have plausible scientific reasons to believe that they would, but no way of testing it directly because of the subjectivity barrier. The clones themselves can neither confirm nor deny the conjecture, of course, because the subjectivity barrier exists for them as much as for everyone else.
If we were able to carry out this research program-and that is a very big assumption-it seems that we would, in principle, be able to infer what colors look like to other people. People who are in the same biological equivalence class as yourself would experience colors in the world as you do, within some reasonable margin of error. And people who are in a different equivalence class would have color experiences that differ from yours. In some cases the nature of those differences can be specified; in others, not. If I am a red-green invertomat, for example, and you are a "normal trichromat" and if the corresponding physiological difference were the only one in our chromatic neurobiology, then our experiences would differ specifically by the red-green inversion transformation reported by subjects who took the invertacillin drug.
You could then know what my color experiences of the world by taking invertacillin yourself or undergoing whatever biological intervention it was that supported the establishment of the differences between our subisomorphic biological classes in the first place. But the possibility that these color-transformed experiences enable you to know what the world looks like to me is necessarily based on inferences. You cannot have my experiences in any direct fashion because of the subjectivity barrier. The inference is based on at least two important assumptions. One is what we called the clone assumption: that any differences in experience must necessarily rest on standard biological differences. The other is that all the relevant biological differences have been exhaustively cataloged. If either is false, then the conclusion that you know what it is like to have my color experience by taking invertacillin may also be false. Given the dubious nature of at least one of these assumptions, the chances of being able to bring this project off in reality are vanishingly small. Even so, the very possibility is intriguing.
This chapter was facilitated by grant 1-R01-MH46141 from the National Institute of Mental Health to the author. It is based in part on an article currently in press in The Behavioral and Brain Sciences.
Berlin, B., and Kay, P. 1969. Basic color terms: Their universality and evolution. Berkeley: University of California Press.
Kim, J. 1978. Supervenience and nomological incommensurables. In American Philosophical Quarterly, 15:149-156.
Locke, J. 1690/1987. An essay concerning human understanding. Oxford: Clarendon Press.
Poincare, H. 1952. Science and hypothesis. New York: Dover.