Image credit: Anthony at pexels.com (source)

The Contradictions in How We Explain Colors

Humans are fascinated with colors. We surround ourselves with colorful objects. Our decisions on what to buy, eat, collect, or look at are strongly influenced by colors. Our conversations are peppered with references to colors, and we have developed a wide range of cultural associations with various colors. Even when we talk to tiny children, a major topic is colors. Being human, we create mental models to explain the nature of colors — and then we teach these models to others. A popular model that we teach to young children is that there are three primary colors — red, blue, and yellow — and that all other colors can be created by “mixing” these three. But then, as we grow older, we become exposed to other models to explain colors — and soon the contradictions appear.

The first contradiction is that our communication technologies employ different primary colors. In our electronic screens (TVs, computers, smart phones, tablets) the three primary colors we use are red, blue, and green. In our printed materials, the three primary colors we use are cyan, magenta, and yellow. If we inquire about this, we might be told that one is “additive” and the other is “subtractive” — but this doesn’t really explain why the additive and subtractive approaches require different primary colors, and it certainly doesn’t explain why both of these models are different than the red-blue-yellow model that we teach our children.

The contradictions increase when we learn about the visible spectrum of light. We are taught that white light is actually a mixture of all the colors of a rainbow — red, orange, yellow, green, blue, indigo, and violet. (What a strange decision to include “indigo” in this list!) Newton used a prism to break a beam of sunlight into all of these colors, and then he used another prism to put them back together into a beam of white light. But the kicker is that all of these colors have different wavelengths. In the spectrum, orange is not a “mixture” of red and yellow — orange is actually a different wavelength, intermediate between red and yellow. Green also has its own wavelength, between that of blue and yellow. It gets stranger still. Purple is off at one end of the spectrum — not located between red and blue. Furthermore, there are countless intermediate colors, each with its own wavelength. For example, orange-red is located between red and orange, with a wavelength that is different than either red or orange.

The upshot is that while we teach children that a rainbow — our most familiar embodiment of the visible spectrum — consists of seven colors, in fact it consists of an infinite number of colors, and none of them are in any way “primary”. We may prefer the colors for which we have simple names, such as red and blue, but there is nothing in the nature of the spectrum that make red more important than orange or red-orange or any other color.

And yet, even though the visible spectrum contains an infinite number of colors, there are other colors that are missing — such as brown, gray, and pink. We have simple, common names for these colors — indicating that they are culturally important to us — and therefore we need a model to explain them. One such model is the Munsell Color System, in which all colors are defined by three values — hue, chroma, and value. If you think of it in terms of paints, this model is equivalent to starting with a bright, fully saturated color from the rainbow, and then mixing it with varying amounts of black and white paint. The results include colors such as pink, gray, and brown.

So are all of these models “true”? If so, then how do we reconcile the apparent contradictions?

The first point to consider is that most of these models are based on human perception, which in turn depends (in part) upon human physiology — specifically, the manner in which our eyes work. Of course, perception actually occurs in the brain — and therefore most of these models also depend upon how the brain works. Colors, as described in most of these models, are something that happens in our head, rather than intrinsic attributes of the objects around us. On the other hand, the spectrum model is based on the wavelengths of light — which is completely independent of human perception.

When we look at a rainbow, we see the spectrum of visible light — in other words, the wavelengths of light that our eyes can detect. The true spectrum of light goes well beyond what we see in a rainbow. If our eyes worked a bit differently, allowing us to see a slightly broader range of colors, then a rainbow might appear thicker, with another color above the red band at the top, and still another color below the purple band at the bottom. But the full spectrum of light goes much farther than that, ranging from gamma rays (with a very short wavelength) to radio waves (with a very long wavelength).

To evaluate the “truth” or reality of the models we use to explain colors, we need to relate these models to the spectrum of light. But we also need to understand why most of these models involve the concept of “primary colors”, a feature that is not present in the spectrum model.

How the Trichromatic Models Work

The trichromatic models (red-blue-yellow for paint pigments, cyan-magenta-yellow for printing inks, and red-green-blue for television screens) all depend upon the way that the human eye and brain construct color vision. Light that enters the eye is focused onto the retina in the back of the eye. Photoreceptor cells in the retina collect information about the light that strikes each cell. This information is then sent to the brain via the optic nerve. The brain integrates and interprets the information in a complex process that results in “vision” or “seeing”.

However, not all of the cells that line the retina have the same sensitivity to light. There are two kinds of photoreceptor cells, called “rods” and “cones”. Rods do not contribute significantly to color vision, but they are effective in dim light, while cones are not. Therefore, in very dim light, we rely primarily on the rods for our vision, but we lose our ability to distinguish colors. Cones provide us with our color vision — and they can do this because there are 3 kinds of cones, each of which responds to a different range of wavelengths of light, as shown in the diagram below.

Image credit: Wikimedia Commons (source)

Each “color” of light that enters the eye will stimulate these 3 types of cones in a unique combination of proportions. In other words, every color that the brain can perceive is actually constructed from a mix of 3 inputs. This makes it possible to generate the perception of any visible color by mixing just 3 different colors of light — provided that the 3 colors are chosen carefully.

The three kinds of cones are traditionally called “S” (for short wavelength), “M” (for medium wavelength), and “L” (for long wavelength). The S cones respond most strongly to blue and violet light, with a peak response to wavelengths that are around 420 nanometers (nm) long. The M cones respond most strongly to green and yellow, with a peak response around 530 nm. The L cones respond most strongly to yellow and orange, with a peak response around 560 nm. As you can see, the peak response for the three types of cones is not evenly spaced. The M and L cones have nearly identical response, with a great deal of overlap in the two curves. The S cones respond to much shorter wavelengths than the M and L cones, with relatively little overlap. The reason that yellow appears to be the brightest rainbow color is not due to an intrinsic feature of yellow light, but simply because it strongly stimulates both the M and L cones.

The brain, in order to create color vision, relies on the difference in response between the 3 types of cones. For example, if the L cones in a particular part of the retina are strongly stimulated, but the M cones are only weakly stimulated (and the S cones not at all), then the brain interprets this point in our field of vision as “red”. But if the L cones and M cones are both strongly stimulated to a similar degree (and the S cones not at all), then the brain interprets this as “yellow”.

How the RGB Model Works

The RGB model that we use for our electronic screens is based on the fact that the wavelengths corresponding to red, green, and blue light result in very different responses from the 3 types of cones. Each “pixel” on the screen has three phosphors — R, G, and B — that can be illuminated to various degrees of intensity. Each of the 3 primary colors in the RGB model corresponds to a specific type of cone in our retinas:

1) R (red) is included because red light stimulates the L cones much more strongly than it stimulates the M or S cones. Note that the peak response for the L cones actually occurs in the yellow-orange part of the spectrum (not red) — but this wavelength of light also strongly stimulates the M cones. In order to stimulate the L cones while minimizing the stimulus to the M cones, we use red light.

2) G (green) is included because certain shades of green will stimulate the M cones much more strongly than the L or S cones. However, because of the overlap in the M and L response curves, the most effective green does not correspond to the peak response of the M cones, which would be a yellow-green. Instead, the ideal color is a much deeper green with a shorter wavelength, to minimize the stimulus to the L cones.

3) B (blue) is included because blue light stimulates the S cones much more strongly than it stimulates the L or M cones.

If the red, green, and blue phosphors in an electronic display are carefully chosen and expertly manipulated, then we can cause the human brain to perceive most (but not all) of the millions of colors that we are capable of discerning in the “real” world. The upshot is that each color in this model can be expressed by using just three numbers, corresponding to the intensity of red light, green light, and blue light emitted by the phosphors. But in reality what actually matters is the degree to which the L cones, M cones, and S cones are each stimulated — because this is what determines what our brain sees.

Note that this model does not explicitly include black or white, which are required to produce colors such as pink, gray, and brown. However, the phosphors are displayed on a black screen, and each of the phosphors can glow with a range of intensities. If all three phosphors at a particular point are dark, then we perceive that point as black. If all three phosphors (R, G, and B) are illuminated to their maximum intensity, then we perceive that point as white. The upshot is that the RBG model can indeed produce both black and white, which means that colors such as pink, gray, and brown can also be produced.

Also note that there is a range of wavelengths, from violet through blue, that stimulate the S cones more strongly than the M and L cones. In fact, for each of the three types of cones, you can identify a range of wavelengths (rather than a single wavelength) that stimulates that type of cone much more strongly than the other two types. The upshot is that we don’t have a precise definition for the “red” in RGB, nor a precise definition for the “green” or the “blue”. The colors of the RGB phosphors can vary somewhat from one display device to another, and yet do a reasonably good job of generating most of the humanly visible colors. In fact we build color displays using a variety of different technologies — which necessarily result in slightly different colors. Below is the emission spectrum for one typical RGB device:

Image credit: Deglr6328 at the English language Wikipedia (source)

As you can see, none of the three colors emitted by this device corresponds to a single wavelength. Instead, each dot of color includes a range of wavelengths. If you compare this spectrograph with one from a different RGB device, especially one that uses a different technology to generate the dots of light, then the spectrograph will look distinctly different — although again you’ll have one phosphor that peaks somewhere in the reds, another that peaks somewhere in the greens, and a third that peaks somewhere in the blues.

The Concept of Pigments

The RGB model is the most straightforward of the trichromatic models, because it is based on dots of light rather than pigmented materials. The result is an additive model — in other words, as we combine the primary colors, we add more wavelengths to the mix in the resulting light. But the models that rely on pigmented materials are subtractive, because each pigment selectively absorbs certain wavelengths of light, removing them from the mix. Therefore both the CMY (cyan-magenta-yellow) model for printing ink and the RYB (red-yellow-blue) model for children’s paint are subtractive in nature.

The term “pigment” is a surprisingly human-centric term. Any chemical compound that absorbs light in the visible spectrum (that is, visible to humans), is considered to be a pigment. All chemical compounds, and therefore all materials, do indeed absorb certain frequencies of light. But most compounds don’t absorb light in the visible spectrum. For example, pure table sugar (sucrose) and pure table salt (sodium chloride) are both colorless crystals that appear to be white. In fact, the vast majority of pure chemical compounds are colorless. Although it seems that most things in the world are colored, this color arises from a small minority of chemical compounds. Because of this special attribute (from a human-centric standpoint), we call these compounds pigments.

(Note: Some colors that we see in the world are caused by other phenomena, not pigments. For example, the green we see in the head of a male mallard is caused by diffraction, not pigments.)

Even the photoreceptor cells in our eyes contain pigments. These cells must absorb visible light in order to do their job. Thus the L cones contain a pigment that absorbs most strongly in the yellow-orange portion of the visible spectrum. The M cones contain a pigment that absorbs primarily in the yellow-green range, and the S cones contain a pigment that absorbs primarily in the blue range.

The CMY and CMYK Models

Now that we have defined the term “pigment”, let’s look at the CMY (cyan-magenta-yellow) model, which is often used for the inks in color printing. (As we’ll see, the CMYK model is simply an extension to the CMY model.) In the following diagram, you can see an intriguing parallel between the RGB model and the CMY model:

A key concept to grasp here is how the colors in the CMY model interact with the cones in our eyes. While the RGB colors each primarily stimulate a single type of cone, the CMY colors each stimulate two kinds of cones. Yellow stimulates the L and M cones, cyan stimulates the M and S cones, and magenta stimulates the L and S cones. Note also that while magenta is present in our color wheel models (linking red with violet), this color does not appear in a rainbow — because no single wavelength of light is capable of stimulating both the L and S cones. (It requires a mix of wavelengths to do so.)

It might seem odd that the leading pigment-based model should use colors that each stimulate two kinds of cones. But because this is a subtractive model, each color of pigment has been carefully chosen to remove a single cluster of wavelengths from the mix of light. Cyan removes the red wavelengths that would otherwise stimulate the L cones. Magenta removes the green wavelengths that would stimulate the M cones. And yellow removes the blue wavelengths that would stimulate the S cones. Because each of the CMY pigments removes the wavelengths that primarily affect a single type of cone, this model — like the RGB model — provides a lot of flexibility for simulating a wide range of colors.

The principal drawback to this model is that by selectively removing these three clusters of wavelengths, some of the in-between wavelengths are ignored, making it difficult to produce a true black. In particular, wavelengths in the yellow band present a problem, because they stimulate both the L cones and the M cones. Therefore, none of the three CMY pigments should remove yellow from the mix. Yellow should only be removed when we need to reduce the stimulation to both the L cones and the M cones. The typical solution is to introduce a fourth color of ink — black — to address this situation. The K in the CMYK model represents black, often called “key black”.

Although the name of the CMYK model does not explicitly mention white, it is definitely part of the model, because of the white paper on which the inks are printed. The ink is applied as tiny dots to the paper, often leaving white space between the dots. The intensity of the four colors of ink is manipulated by adjusting the size of the ink dots, which in turn affects how much white space is left between the dots. The white paper reflects all wavelengths in the visible spectrum. The three principal inks (CMY) each selectively remove wavelengths that stimulate a single type of cone, while the black ink absorbs nearly all of the visible light, allowing for much greater contrast.

The Red-Yellow-Blue Model

There is still one more major trichromatic model to consider — the model that we are taught as young children, where the primary colors are red, yellow, and blue, and the secondary colors are orange, green, and purple. Like the CMY model, the RYB model is based on pigments, and is therefore subtractive. The theoretical principal behind the RYB model is the same as the principal behind the CYM model. So are the two models interchangeable? Are they equally good models?

As kids we are taught the RYB model in connection with poster paints, modeling clay, food coloring, and so on. Kids are natural experimenters, and their experimental results in mixing colors are often broadly consistent with the RYB model — but only to a degree. If we mix red and yellow poster paint — or clay or food coloring — then the model says that our result should be orange. Red mixed with blue should yield purple, while blue and yellow should yield green. But in actual practice, the results are often rather muddy, rather than the brightly colored output we had anticipated.

In fact, the RYB model is distinctly inferior to the CYM model. The range of colors that you can produce by mixing red, yellow, and blue pigments is far more limited than the range of colors that you can produce by mixing cyan, magenta, and yellow pigments. The problem is that red and blue pigments are not optimal for the subtractive process, because they each subtract wavelengths that affect two different types of cones. We cling to the RYB model for teaching kids not because it actually works well, but primarily for cultural reasons. In particular, we want our “primary” colors to be chosen from among the most culturally important colors — a criterion that excludes both cyan and magenta. Therefore we continue to teach our children a traditional model of colors that isn’t actually true, and that deviates considerably from the color models that we actually use in our communication technologies.

The Color-Temperature Model

One other model that is fairly common is the color-temperature model. In this model, a color is expressed as a temperature in Kelvin, such as 4500 K. This model is usually limited to lighting and photography. For example, you may have seen a color-temperature value printed on the packaging for a light bulb. This model is based on the concept of “black body radiation”, and is therefore independent of human vision. (See Unraveling the Mysteries of Radiation and Light.) However, the model is only capable of expressing a very limited range of colors, in a gradient from red to pure white to blue. There is no way to express “green” or “magenta” in this model, nor most of the other colors that humans can discern. However, it is a handy way to distinguish between “warm” lighting (tending a bit towards red) and “cool” lighting (tending a bit towards blue) — and more importantly, to specify just how warm or cool the lighting is. The hilarious irony in this system is that cool colors correspond to higher temperatures, while warm colors correspond to lower temperatures.

Color Screens for Bees, Birds, and Dogs

Our RGB display devices are all optimized for human vision, based on the three types of cones in our eyes. But if a mad scientist wanted to create the ideal television screen for bees or birds or dogs, then would the device work in exactly the same way as our RGB screens, or differently?

The good news is that a television screen optimized for gorillas, chimpanzees, and some kinds of monkeys would be identical to a human television, because we all share the same trichromatic vision system — that is, the same three types of cones in our eyes. So feel free to invite your gorilla friends over for an evening of TV. The bad news is that a television optimized for almost any other kind of animal would be different. The worse news is that if you wanted to accommodate all of your animal friends, you’d need several different TVs.

Bees, like humans, have trichromatic vision, but it is shifted towards shorter wavelengths. Instead of having L, M, and S cones, they have the equivalent of M, S, and UV cones. As a result, bees cannot see red, but they can see ultraviolet. A flower that looks pure white to us can look highly patterned to a bee — if that flower has a patterned distribution of a pigment that absorbs in the ultraviolet range. In fact, it is fairly common for bees to see patterns in flowers that look white or solid-colored to us. Therefore your bee-TV would not need the red phosphors, but it would definitely need some UV phosphors. Instead of an RGB display device, you might have a GBU device (green-blue-ultraviolet). Or more likely, you would have a YBU device. Because a bee has no L cones, the optimal color to stimulate the M cones without stimulating the S cones is actually yellow, not green. So if you asked a bee to define the primary colors, she would probably say yellow, blue, and ultraviolet.

Most kinds of reptiles, amphibians, birds, and insects have tetrachromatic vision, which means that they have four kinds of cones (or equivalent) in their eyes. With four distinct kinds of color photoreceptors, these animals should be able to discern more colors than humans can. The ideal TVs for these species would have four kinds of phosphors, although not necessarily the same four phosphors for all species. So if you asked your robin friend to explain the primary colors to you, she would name four of them.

On the other hand, your pet dog, like most other non-primate mammals, has dichromatic vision. As far as Fido is concerned, there are just two primary colors in the world. Therefore two kinds of phosphors would be adequate in your dog-TV. However, such a TV might not provide any advantage to Fido over your existing human-TV.

Summary

So what is the “truth” with regards to primary colors? Is there an objective truth at all? It really depends upon how you define the term primary colors.

We can objectively state that red, green, and blue (RGB) are the three best colors of phosphors for constructing an electronic display intended for humans — although the precise definition of these three colors is a bit fuzzy. Likewise, we can say that cyan, magenta, and yellow (CMY) are the three best colors of ink for printing full-color illustrations intended for humans, if we must limit ourselves to three colors. (Some fancy printing devices go beyond CYMK and include other inks.)

But what should we teach our kids? Perhaps it is time to completely abandon the RYB model, replacing it with a six-color wheel (ROYGBV) in which all six colors are considered equal. But at a relatively early age, let’s also teach our children the RGB additive model and the CYMK subtractive model. After all, these are the two “primary color” models that actually correspond to human vision. Even more important, these are the two models that explain the communication technologies — electronic screens and printed materials — that are going to play such an important role throughout our children’s lives.

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