In this lesson I want to spend some time talking about how people describe color perception and some additional phenomena that this brings to light. And there are really three ways, three descriptive terms that we use to describe color. The first is hue, the second is saturation, and the third is lightness/brightness. So let me go through these. Hue is just the way we describe the color that we actually see, red, green, blue, yellow and all the mixtures of those four primaries that we'll get to in a minute in between. Saturation is the degree to which the color that you are looking at and want to describe varies from a neutral gray. So take red for example. You can have a fire engine red or you can have any shade of pink, going down to a pink that's barely different from a neutral gray. So that degree of variation between complete saturation and complete desaturation is referred to in this way. Now the lightness and brightness that we talked about before doesn't go away with color. Of course, colors give you a sense of whether they are lighter or darker. You can have a light red, a dark red, and so on. So this is based on the same kind of intensity concerns that we talked about before. So those are the descriptors for how we discuss color. And it's easiest, I think, to think of those descriptors in a diagram like this, which is a way of representing perceptual color space, the color space that we actually are aware of seeing. And people have done this for centuries. There's a detailed book that I have on my shelf that goes back literally millennia to ways that people have used to describe color. This is one example of many ways of doing it. I think it's a simple one that you will understand. But [COUGH] the three characteristics of color, hue, saturation, and lightness or brightness that we're talking about, you can see how they're being represented in this space. So first of all, let's take lightness and brightness, which is the central axis here. So any color can be described as light or dark along this central axis. The description of hue, whether we're seeing red, green, blue, or yellow or some intermediate, is described by the periphery of these circular disks. As you go around the periphery of this disk, you go from yellow to red to blue to green and all the intermediates, of course. Saturation is represented again going to the central axis. So if you have an intense saturated color, you're out here on the periphery, but as you get closer and closer to this central neutral gray axis, the color becomes less and less saturated. So that's the general way. As I say, there are a variety of diagrams like this that people have made over the centuries, but this is the general way in which it's useful to lay out these three qualities of color. Now let's take one of these disks out of the diagram here and look at it face on as if we're looking down at it. And let's take this middle disk here. And now we're looking down, so here is the central axis of neutral gray. Here is the periphery of completely saturated hues. Lightness and brightness, of course, is just that one level for this slice of the disk that we have taken out. But there's another thing, and I want you to notice here, that I think is very important and an enormous challenge to people who want to explain color vision, and that is that we basically see four hue categories. We see a category that we call green, we see a category that we call yellow, we see a category that we call red, and another category that we call blue. Now why do I say these are categories? It's because if you take subjects, and, again, many people have done this over the last 100 years or more, if you take a bunch of tiles that you can lay out on a table that differ just a little bit in their color qualities. So imagine a bunch of tiles that take in the whole array of colors that you see represented here. If you lay that out on a table and ask people to arrange them according to the minimum difference that they see between one tile and another, first of all they lay them out in a circle like this, which validates the general idea that we see color in a circular fashion. Newton realized this, and the circle is sometimes referred to as the Newton color circle. But what's especially interesting and important in this is that there'll be one tile, and usually in the set of so-called Munsell tiles there are hundreds of tiles that are used. There'll be one tile that's seen as uniquely blue, one tile that's see as uniquely green, one tile that's seen as uniquely yellow, and one tile that's seen as uniquely red. What do I mean by unique? When people, you or I or any of us, look at these tiles or some other mode of assessing how we see color, you'll find that there is one tile for each of these four color categories that has no apparent admixture of any of the other categories. There's one tile that looks blue, and you say does it have any mixture of red or green? Does it go in either of these other directions? And the answer is no, it seems to be a pure blue unadulterated by any admixture of the other categories. And so it is for all of the four categories. There is a red that's unique, there is a yellow that's unique, there's a green that's unique. And incidentally, you shouldn't take the positions of these dots here too literally. This varies a little bit from person to person, and of course, this is just a conceptual representation, not real data-derived representation. But the point is that everybody sees a unique value for these four color categories. Red, green, blue, and yellow are the categories, and each one has a unique tile or a unique percept that doesn't have any admixture of the others. So this is the basis for calling these color categories, categories. So if you take, for example, an orange or a purple or an aquamarine or a greenish yellow. There are, of course, dozens of tiles, dozens of percepts, that represent these intermediate categories. But in each one of those tiles, in each one of the color percepts that derive from these intermediate values, you see it as a mixture of, let's take purple, you see a purple as a mixture of, it's got some blue in it, it's got some red in it. You see an orange, you say, yeah, it's got some yellow in it, it's got some red in it. And in each of these intermediate cases, it's obvious that there is no unique hue there, it's an admixture of two of the four categories. So that's really a challenge. Why do we have four color categories, and why is there a unique hue for each of these categories? And this is a question that no one has really successfully answered that stands out there as yet another challenge in color vision. But let's talk about a suggested answer that is interesting to think about. It may give some clue as why it is that we in fact see four different unique hues representing and defining these four different color categories. Why do we have four primary color percepts? Well, one way to think about this is to imagine defining, through the aegis of color, different areas on any arbitrarily complex scene that you might be looking at. So this is just a diagram of a bunch of differently shaped areas. But it might represent the areas in any scene, in any natural scene that you want to distinguish. If you want to optimally use your color vision to distinguish areas, well, you're going to want to do this in some way. And the clue that I think is interesting to think about, with respect to four color categories, is that cartographers, map makers, had realized empirically just by the nature of their trade, for centuries that they needed four colors to unambiguously distinguish all the areas on an arbitrarily complex geographical map. And of course, they could use as many colors as they want, but if they didn't use four, if they tried to use only three, they would conflate some areas. And you can see this. So here we're using only three of the four color categories, red, green, blue, and yellow. And you see if you have only three of those categories, green, blue, and yellow, it's impossible to distinguish all of these areas. Of course you can distinguish some of them, but you get conflation if you only have three colors. So if you have four colors, you can distinguish all these areas. This is called the four color map problem, and it's a very interesting problem in logic, quite apart from color vision. This was brought to attention in the 19th century by a student who took this problem to his mathematics professor and asked him, why, professor, do map makers need a minimum of four colors to distinguish all the possible areas on any arbitrarily complex map, of which this might be an example? And the math professor was a very bright guy, and he took this to the Royal Society and presented it as a problem that he threw out there to other mathematicians and logicians. And surprisingly, it took more than a century for that problem to be solved. And it’s a solution that was done computationally that if you want to read 200 pages of computer code which is what the solution entailed, well, okay, fine, but it's not really, [LAUGH] there's no simple answer to this question. But with respect to vision, you can see how this relates, how this four color map problem relates to color vision. You want to distinguish all of the areas in a scene by the ability you have to see color, you're going to need at least four color categories to do this, just as the map maker needs four color categories. So that's an interesting way of thinking about why, perhaps, we have four color categories. Why of course they are perceived by us as blue, green, and yellow, well, that's kind of a philosophical problem that opens a whole other can of worms. But these are interesting things to think about, and certainly a question that remains unanswered.
