Section 35–3 Measuring the color sensation

(Grassmann’s additive law / Additive color model / Fundamental primary colors)

 

In this section, Feynman discusses the Grassmann’s additive law of color mixing, additive color model, and fundamental primary colors. This section could be titled as Young-Helmholtz-Maxwell trichromatic theory, however, Feynman mentions Young-Helmholtz theory in the next section that also discusses color blindness. Interestingly, in his autobiography, What do you care what other people think?, Feynman (1988) writes: “When I see equations, I see letters in colors - I don't know why. As I'm talking, I see vague pictures of Bessel functions from Jahnke and Emde's book, with light-tan j's, slightly violet-bluish n's, and dark brown x's flying around. And I wonder what the hell it must look like to the students (p. 59).” This neurological phenomenon is known as synaesthesia and specifically, Feynman’s description of seeing the equations and letters in colors is sometimes called "grapheme-color" synaesthesia (Henshaw, 2012).

 

1. Grassmann’s additive law:

“Here is one of the great laws of color: if two spectral distributions are indistinguishable, and we add to each one a certain light, say Z (if we write X+Z, this means that we shine both lights on the same patch), and then we take Y and add the same amount of the same other light, Z, the new mixtures are also indistinguishable: X+Z = Y+Z (Feynman et al., 1963, p. 35–5).”

The law states that if two spectral distributions (or different lights) are indistinguishable to our eyes under a certain condition, and we add the same additional light (Z) to both of them, the resulting mixtures will still be indistinguishable. Similarly, we may state Grassmann’s (1853) additive law of color mixture as follows: if two different lights or colors are indistinguishable (metamers*), we can add another color to them and they will still be metamers.  One may clarify that many different combinations of wavelengths can result in indistinguishable color sensations, that is, human eyes are not very precise light detectors. Furthermore, there are different types of metamers, e.g., material metamers refer to two different surface reflectance curves are perceived as the same color when each is viewed using the same light source. In essence, Grassmann’s additive law is an idealization that assumes human eyes are a linear system of color perception (Oleari, 2015).

 

* Metamers: Metameric lights are lights that though of dissimilar spectral radiation are seen as the same by the observer (Shevell, 2003). 

 

“In fact, it turns out, and it is very important and interesting, that this matching of the color of lights is not dependent upon the characteristics of the eye at the moment of observation: we know that if we look for a long time at a bright red surface, or a bright red light, and then look at a white paper, it looks greenish, and other colors are also distorted by our having looked so long at the bright red (Feynman et al., 1963, p. 35–5).”

 

The phenomenon Feynman described is known as color afterimage (see below), which occurs due to the way our eyes and brain process visual information. When you stare at a red surface or light for an extended period, the cone cells in your eyes, which are responsible for color vision, become desensitized to the specific wavelengths of light associated with red. When you then shift your gaze to a white surface, your eyes continue to send signals to your brain as if they are still seeing red. Since the red-sensitive cone cells are temporarily less responsive, the signals received by your brain are weaker than they would be under normal conditions. This effect is a result of the opponent-process theory of color vision, which suggests that color perception is based on the opposition between pairs of colors: red versus green, blue versus yellow, and black versus white (Triedman, 2015). In the next section, Feynman mentions the term afterimage, but it does not seem necessary.

Source: Sight and Visual Perception - Course Hero

2. Additive color model:

“The second principle of color mixing of lights is this: any color at all can be made from three different colors, in our case, red, green, and blue lights. By suitably mixing the three together we can make anything at all, as we demonstrated with our two examples… Then any color could be made by certain amounts of these three: say an amount a of color A, an amount b of color B, and an amount c of color C makes X: X = aA+bB+cC (Feynman et al., 1963, p. 35–5).”

 

The second principle is sometimes known as the principle of additive color mixing, often used to describe how different colors of light combine to form new colors. This principle is associated with the RGB (Red, Green, Blue) additive color model (see below), where colors are created by combining different intensities of red, green, and blue light. It is an approximation model due to its reliance on a linear relationship between primary colors and their combinations, which simplifies the complexities inherent in color perception and light interaction. It forms the basis for understanding how different colored lights combine and interact in various display technologies, such as computer monitors, TVs, and stage lighting. The model is based on standard observers, but color perception varies from person to person and within the same observers during their lifetimes due to aging.

 

Source: Additive & Subtractive Color Models > DINFOS Pavilion > Article

“In elementary books they are said to be red, green, and blue, but that is merely because with these a wider range of colors is available without minus signs for some of the combinations (Feynman et al., 1963, p. 35–6).”

 

In elementary schools, students usually learn red-yellow-blue (RYB) color system when painting in an art class. On the other hand, the cyan, magenta, and yellow (CMY) color system is preferred for painting because it is more cost-effective to provide a wider range of colors. These are known as subtractive color models because colors are created by subtracting certain wavelengths of light, i.e., light is either reflected or absorbed by an object depending on its pigmentation (or composition of fabric dyes). However, it is easier to teach kids using red-yellow-blue color system because the words "cyan" and "magenta" are more difficult for them.

 

3. Fundamental primary colors:

“Now a question is, what are the correct primary colors to use? There is no such thing as “the” correct primary colors for the mixing of lights. There may be, for practical purposes, three paints that are more useful than others for getting a greater variety of mixed pigments, but we are not discussing that matter now. Any three differently colored lights whatsoever  can always be mixed in the correct proportion to produce any color whatsoever… Every set of three primaries requires negative amounts for some colors, and therefore there is no unique way to define a primary (Feynman et al., 1963, p. 35–6).”

 

There is no universally agreed upon set of fundamental primary colors partly because different color models are based on different principles of color mixing – additive or subtractive. In the RGB (Red, Green, Blue) color model commonly used in electronic displays like monitors and TVs, red, green, and blue are considered the primary colors. In the CMYK (Cyan, Magenta, Yellow, Black) color model used in color printing, cyan, magenta, and yellow are considered the primary colors. Furthermore, there are different types of RGB system, such as Standard RGB and Wide-gamut RGB, where each has its own specifications, color gamuts, and intended uses. Interestingly, imaginary primary colors are used to generate and quantify all visible colors that can be perceived by the human eyes.

Historically, Young proposed that the human eye could distinguish three primary colors, namely, red, green, and violet. Next, Helmholtz classified the cone receptors as short (violet), middle (green), and long (red); he recognized the difference between experiments done by mixing pigments and light beams. It is worth mentioning that Maxwell's contributions to the theory of color are not limited to the following: (1) Primary colors: Maxwell's (1857) experiments supported the idea that red, green, and blue are a better set of primary colors compared to the traditional set of red, yellow, and blue. (2) Distinction between Paints and Light beams: Maxwell distinguished between the primary colors used for mixing light beams and those used in painting. (3) Color attributes: Maxwell defined hue (spectral color determined by wavelength), tint (degree of color saturation), and shade (intensity of illumination).  The theory described by Feynman could be called Young-Helmholtz-Maxwell trichromatic theory, but there are other contributors, such as Newton, Grassmann, and Schrödinger*.

*Note: According to a recent research study (Bujack et al., 2022), there is a significant error in the 3D mathematical space developed by Erwin Schrödinger and others to describe how human eye distinguishes one color from another. 

Review Questions:

1. How would you explain that different combinations of wavelengths can result in indistinguishable color sensations?

2. How would you explain the second principle of color mixing of lights?

3. How would you explain that there are no correct primary colors?

 

The moral of the lesson: while the additive color model is based on the principle of additive mixing of primary colors, the complete perception of color by the human visual system involves various nonlinearities and complexities that do not conform entirely to a linear system, despite the Grassmann's additive law.

 

References:

1. Bujack, R., Teti, E., Miller, J., Caffrey, E., & Turton, T. L. (2022). The non-Riemannian nature of perceptual color space. Proceedings of the National Academy of Sciences, 119(18), e2119753119.

2. Feynman, R. P. (1988). What Do You Care What Other People Think? New York: W W Norton.

3. Feynman, R. P., Leighton, R. B., & Sands, M. (1963). The Feynman Lectures on Physics, Vol I: Mainly mechanics, radiation, and heat. Reading, MA: Addison-Wesley.

4. Grassmann, H. (1853). Zur theorie der farbenmischung. Annalen der Physik, 165(5), 69-84.

5. Henshaw, J. M. (2012). A tour of the senses: how your brain interprets the world. Baltimore: JHU Press.

6. Maxwell, J. C. (1857). XVIII.—Experiments on Colour, as perceived by the Eye, with Remarks on Colour-Blindness. Earth and Environmental Science Transactions of the Royal Society of Edinburgh, 21(2), 275-298.

7. Oleari, C. (2015). Standard colorimetry: definitions, algorithms and software. John Wiley & Sons.

8. Shevell, S. K. (Ed.). (2003). The science of color. Oxford: Elsevier.

9. Triedman, K. (2015). Colour: The Professional's Guide: Understanding and Mastering Colour in Art, Design and Culture. Hachette UK