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

Section 35–2 Color depends on intensity

 (Dark-adapted vision / Purkinje effect / Peripheral vision)

 

In this section, Feynman discusses the dark-adapted vision, Purkinje effect (related to mesopic vision), and peripheral vision that depend on the intensity of light.

 

1. Dark-adapted vision:

“If the intensity of the light is very low, the things that we see have no color. It is known that this dark-adapted vision is almost entirely due to the rods, while the vision in bright light is due to the cones. As a result, there are a number of phenomena that we can easily appreciate because of this transfer of function from the cones and rods together, to just the rods (Feynman et al., 1963, p. 35–2).”

 

It is potentially misleading to say “if the intensity of the light is very low, the things that we see have no color.” In very low-light conditions, we rely on our rod cells, which are highly sensitive to low levels of light, to see in shades of gray (or grey). While rod cells do not provide detailed color information, they allow us to distinguish different levels of brightness and perceive objects in a grayscale view. On the other hand, gray is a color because it can be achieved by adding and adjusting the intensity of red, green, and blue light (see below). However, rod cells may take about 20-30 minutes for the human eye to become fully dark-adapted, that is, allowing the rod cells to reach their maximum sensitivity in the dark night.

 

Source: Butler, 2005

Dark-adapted vision primarily refers to scotopic vision, which is the vision that occurs in very low-light conditions. In his autobiography, Feynman (1997) mentions that he could see colors during an atomic explosion in the dark: “… a big ball of orange, the center that was so bright, becomes a ball of orange that starts to rise and billow a little bit and get a little black around the edges, and then you see it's a big ball of smoke with flashes on the inside, with the heat of the fire going outwards. All this took about one minute. It was a series from bright to dark, and I had seen it. I am about the only guy who actually looked at the damn thing--the first Trinity test (p. 134).” In a sense, this is another reason why it is incorrect to say that the things that we see have no color in the dark. (Interestingly, some claim to achieve beatific vision during the dark night.)

 

2. Purkinje effect:

“It turns out that the rods see better toward the blue than the cones do, and the cones can see, for example, deep red light, while the rods find that absolutely impossible to see. So red light is black so far as the rods are concerned. Thus two pieces of colored paper, say blue and red, in which the red might be even brighter than the blue in good light, will, in the dark, appear completely reversed. It is a very striking effect. If we are in the dark and can find a magazine or something that has colors and, before we know for sure what the colors are, we judge the lighter and darker areas, and if we then carry the magazine into the light, we may see this very remarkable shift between which was the brightest color and which was not. The phenomenon is called the Purkinje effect (Feynman et al., 1963, p. 35–2).”

 

Historically, Jan Evangelista Purkinje observed that his favorite flower appeared bright red in the afternoon, but it became bluish-red in the evening. We can explain Purkinje effect as follows: (1) Lighting conditions: It pertains to the shift in perceived colors under different lighting conditions, specifically during transitions from bright light (photopic vision) to low-light conditions (mesopic vision). (2) Color perception: In bright light, shorter wavelengths dominate our perception, making blue and green hues more vibrant, whereas in low-light conditions, longer wavelengths become more prominent. (3) cone cells: The effect occurs due to the different sensitivity of S-cones*, M-cones, and L-cones under different lighting conditions. In short, Purkinje effect may refer to red objects that appear darker under dim lighting conditions compared to green objects due to the reduced sensitivity of the cone cells to red wavelengths (See below).

*Humans have three types of cone cells in the retina, each sensitive to different wavelengths of light: short-wavelength cones (S-cones) are sensitive to blue light, medium-wavelength cones (M-cones) are sensitive to green light, and long-wavelength cones (L-cones) are sensitive to red light.

 

In Fig. 35–3, the dashed curve represents the sensitivity of the eye in the dark, i.e., using the rods, while the solid curve represents it in the light. We see that the peak sensitivity of the rods is in the green region and that of the cones is more in the yellow region. If there is a red-colored page (red is about 650 μm) we can see it if it is brightly lighted, but in the dark it is almost invisible (Feynman et al., 1963, p. 35–2).”

Feynman initially explains the phenomenon using two pieces of colored paper, blue and red, but elaborates the spectral sensitivity of the eye involving the cones that is more in the yellow region. However, it could be explained in terms of photopic vision and scotopic vision: (1) Photopic vision: When our eyes are exposed to bright light conditions, such as well-lit indoor environments, they are in a state of photopic vision. In photopic vision, our eyes (cones) are most sensitive to the yellow-green part of the spectrum, about 555 nanometers (nm) wavelength. (2) Scotopic vision: When our eyes are exposed to very low-light conditions, they gradually adapt to scotopic vision, which is highly sensitive to dim light. In scotopic vision, our eyes (rods) are most sensitive to about 505 nm wavelength, which corresponds to the color green on the visible spectrum.

 

3. Peripheral vision:

“Another interesting phenomenon is that the periphery of the retina is very sensitive to motion. Although we cannot see very well from the corner of our eye, if a little bug moves and we do not expect anything to be moving over there, we are immediately sensitive to it. We are all “wired up” to look for something jiggling to the side of the field (Feynman et al., 1963, p. 35–3).”

 

The phenomenon described by Feynman is related to the distribution of rod cells in the human retina and how it affects our peripheral vision. We may define peripheral vision (or side vision) as follows: 1. Field of vision: It covers a wider field of view compared to central vision. 2. Sensitivity to motion: It is highly sensitive to motion and is crucial for detecting movement in the surrounding environment due to a higher density of rod cells. 3. Lower acuity and color perception: It has lower visual acuity and reduced color perception compared to central vision due to a lower density of cone cells. Thus, the periphery of the retina is better suited for detecting motion and objects in dim lighting conditions.

 

“Another interesting effect of the fact that the number of cones decreases as we go farther to the side of the field of view is that even in a bright light color disappears as the object goes far to one side. The way to test that is to look in some particular fixed direction, let a friend walk in from one side with colored cards, and try to decide what color they are before they are right in front of you. One finds that he can see that the cards are there long before he can determine the color. When doing this, it is advisable to come in from the side opposite the blind spot, because it is otherwise rather confusing to almost see the color, then not see anything, then to see the color again (Feynman et al., 1963, p. 35–3).”

 

It is unclear if one can almost see the color of moving cards, then not see anything, and see the color again while we are looking in a fixed direction. Firstly, the phenomenon related to the blind spot typically occurs when observing a stationary object, not a moving one. When the eyes are fixated on a specific point, the brain fills in the missing information from the blind spot, creating the illusion that the object is still visible, even though it is not being detected by the photoreceptor cells in the blind spot area. This occurs seamlessly and almost instantaneously, so one does not notice the gap in the visual field due to the blind spot. On the other hand, the decrease in the number of cones and the dominance of rod cells in the peripheral vision result in reduced color perception and decreased visual acuity in the outer edges of the visual field. This effect can make colors less noticeable as the object moves toward the side of our visual field.

 

Feynman initially mentions that another interesting effect is: even in a bright light, color disappears (instead of almost disappear) as the object goes far to one side. This is related to the near absence of cones and abundance of rods in the outer part of retina that is the reason for our not getting color or detailed information from our peripheral vision. However, a more interesting phenomenon is Troxler’s fading, which occurs when the eyes fixate on a particular point. As a result, details of objects located in the periphery of the fixated point can fade away or become less visible. One common example of Troxler's fading is staring at a small, high-contrast object (like a dot) in the center of a large, uniform background as shown below.

Source: Pegoraro, 2016

 

Review Questions:

1. How would you explain dark-adapted vision and whether one may see colors under very low light conditions?

2. How would you explain the Purkinje effect?

3. How would you define peripheral vision under normal light conditions?

 

The moral of the lesson: human vision depends on the intensity of light because it is based on rods (sensitive to dim light) and three types of cone cells: S-cones (sensitive to blue light), M-cones (sensitive to green light), and L-cones (sensitive to red light).

 

References:

1. Butler, Y. (Ed.). (2005). The Advanced Digital Photographer's Workbook: Professionals Creating and Outputting World-class Images. Taylor & Francis.

2. Feynman, R. P. (1997). Surely You’re Joking, Mr. Feynman! : Adventures of a Curious Character. New York: 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. Pegoraro, V. (2016). Handbook of Digital Image Synthesis: Scientific Foundations of Rendering. CRC Press.

Section 35–1 The human eye

 (Functions of eye / Structure of retina / Eye-brain system)

 

In this section, Feynman discusses functions of human eyes, the structure of human retina, and the eye-brain system.

 

1. Functions of eye:

“Light enters the eye through the cornea; we have already discussed how it is bent and is imaged on a layer called the retina in the back of the eye, so that different parts of the retina receive light from different parts of the visual field outside (Feynman et al., 1963, p. 35–1).”

 

Perhaps Feynman could have explained the human eye, a biological organ, using more physics-oriented explanations, physical principles, or physical analogies. For example, the human eye functions in a manner similar to a camera, both collecting, detecting, and processing light from the surrounding environment. In addition, light enters the eye through the cornea, the transparent front part of the eye. Similarly, light also enters the camera through the camera lens, which is analogous to the cornea in the human eye. On the other hand, the retina contains two types of photosensitive cells or photoreceptors: rods (responsible for night vision) and cones (responsible for color vision). It is analogous to the camera’s sensor that acts like tiny photosensitive receptors, detecting the intensity of light that falls on it.

 

In his autobiography, Feynman shared how he viewed the explosion of atomic bomb using the truck windshield. In his words, “They gave out dark glasses that you could watch it with. Dark glasses! Twenty miles away, you couldn't see a damn thing through dark glasses. So I figured the only thing that could really hurt your eyes (bright light can never hurt your eyes) is ultraviolet light. I got behind a truck windshield, because the ultraviolet can't go through glass, so that would be safe, and so I could see the damn thing (Feynman, 1997, p. 134).” It is worthwhile to have some knowledge of human eye functions and how to prevent damage in the retina. For example, the lens of the eye can absorb some ultraviolet (UV) radiation and provide a certain degree of protection to the retina, but this natural UV filtering capacity is limited.

 

2. Structure of retina:

“The retina is not absolutely uniform: there is a place, a spot, in the center of our field of view which we use when we are trying to see things very carefully, and at which we have the greatest acuity of vision; it is called the fovea or macula (Feynman et al., 1963, p. 35–1).”

 

In the Audio Recordings* [5 min: 25 sec] of this lecture, Feynman says: “it is called the fovea and that’s here” instead of “it is called the fovea or macula.” The macula is the central portion of the retina with a high concentration of cones, contributing to central vision and color perception. The fovea is a specialized pit structure within the macula that contains only cones and provides the greatest acuity of vision, making it responsible for the highest detailed and sharp visual perception. We may rephrase the above-statement (highlighted in yellow) as: “The retina is not uniform, and there is a specialized region in the center of our field of view known as the fovea, which is part of the larger macula. The fovea is the area where we have the greatest acuity of vision and use for tasks that require precise and detailed visual perception.”

*The Feynman Lectures Audio Collection: https://www.feynmanlectures.caltech.edu/flptapes.html

 

The retina can be distinguished into at least 3 regions: fovea, macula, and periphery (see figure below). In the fovea (0.35 mm in diameter), the density of cones is highest, while the rods are completely absent. Moving away from the fovea, the density of cones is lower in the macula, but it is relatively high compared to the peripheral retina. This allows for good visual detail and color perception in the central part of our vision. As we move towards the periphery, the density of cones decreases, but the density of rods increases. The periphery of the retina is more sensitive to low intensity light and is better suited for detecting motion and objects in the dark. Specifically, rods are more numerous in the peripheral retina, enhancing our ability to perceive movement and objects in our side vision.

Source: Why don't we get color or detail information from our peripheral vision? | Socratic

3. Eye-brain system:

“Now the interesting thing is that in the retina each of the cells which is sensitive to light is not connected by a fiber directly to the optic nerve, but is connected to many other cells, which are themselves connected to each other. There are several kinds of cells: there are cells that carry the information toward the optic nerve, but there are others that are mainly interconnected “horizontally.” There are essentially four kinds of cells... (Feynman et al., 1963, p. 35–2).”

 

Feynman mentions that there are essentially four kinds of cells and there are cells that are interconnected “horizontally.” Perhaps he could have explained that the horizontal cells are interconnected laterally instead of horizontally. The term “horizontal cells” is derived from their horizontal (side-to-side) connections with the neighboring retinal cells, emphasizing their function in integrating and regulating signals across the retina. Instead of saying four kinds of cells, some may emphasize that there are six kinds of retinal cells, namely, horizontal, bipolar, amacrine, interplexiform, ganglion, and photoreceptor cell (Dowling, 2012). For example, amacrine cells are involved in fine-tuning the signals transmitted between bipolar cells and ganglion cells, i.e., they play a role in modulating contrast and sensitivity to different light intensities.

 

Source: Human eye - Retina, Optic Nerve, Vision | Britannica

“…the information from the various cells does not immediately go to the brain, spot for spot, but in the retina a certain amount of the information has already been digested, by a combining of the information from several visual receptors. It is important to understand that some brain-function phenomena occur in the eye itself (Feynman et al., 1963, p. 35–2).”

 

Although the human retina is physically located within the eye, its role extends beyond simple light detection. The retina’s functions and connections are closely tied to the brain, which processes the visual information collected by the retina. In essence, the retina is an integral part of the eye-brain system, where the eye captures light and initial visual information, whereas the brain processes and translates this information into the visual experiences that humans perceive. The processing and interpretation of visual information occurs in the brain, making the retina and the brain tightly interconnected. In a sense, photoreceptor cells can be compared to the pixels on a camera sensor. Just as pixels on a camera sensor detect light and convert it into electrical signals, photoreceptor cells in the retina (rods and cones) detect light and convert it into electrical signals, initiating the process of visual information.

 

Note: In Chapter 36, Feynman explains: “As a matter of fact, people who study anatomy and the development of the eye have shown that the retina is, in fact, the brain: in the development of the embryo, a piece of the brain comes out in front, and long fibers grow back, connecting the eyes to the brain. The retina is organized in just the way the brain is organized and, as someone has beautifully put it, ‘The brain has developed a way to look out upon the world.” The eye is a piece of brain that is touching light, so to speak, on the outside. So it is not at all unlikely that some analysis of the color has already been made in the retina’ (Feynman et al., 1963, p. 36–2).”

 

Review Questions:

1. How would you explain the functions of human eyes?

2. How would you explain the structure of the retina (fovea, macula, and periphery)?

3. How would you explain whether the eye is a part of the brain?

 

The moral of the lesson: the eye-brain system contains two types of photoreceptors: rods (for night vision) and cones (for color vision) that are related to six kinds of retinal cells (horizontal, bipolar, amacrine, interplexiform, ganglion, and photoreceptor).

 

References:

1. Dowling, J. E. (2012). The retina: An approachable part of the brain. Cambridge, MA: Harvard University Press.

2. Feynman, R. P. (1997). Surely You’re Joking, Mr. Feynman! : Adventures of a Curious Character. New York: 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.