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If you add red light (~440 THz) and green light (~560 THz), you get what we perceive as yellow light (~520 THz). But I assume what you really get is a mixed waveform that we perceive as yellow? Suppose the red is a perfect sine wave, and so is the green, the mix of both will not be a perfect sine wave but a wobbly composite thing - right? Which is different than a perfect sine wave of ~520 THz. But we call both things "pure" yellow. Is that correct?

If so, are there animals that can discern composite pure yellow from singular pure yellow, like we can discern the mixture of multiple audio sine waves as a chord? Or is there machinery that can do that?

See also: Why both yellow and purple light could be made by a mix of red, green and blue?

Emilio Pisanty
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commonpike
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  • I interpreted the question's "mix" and "add" to mean create a light which is of an average frequency. I.e., yellow light can either be a mix of wavelengths that "sum" to yellow when interpreted by the photoreceptors, or it can be monochromatic yellow light (which trivially sums to be interpreted as yellow). – piojo Aug 10 '17 at 07:19
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    @piojo By that logic, if we mix equal amounts of red light (~450 THz) and blue light (~640 THz), we would get ~545 THz, which would be green light. But as we all know, mixing red and blue light gives magenta which is not a spectral color. Hence this theory is obviously fundamentally flawed. – jkej Aug 10 '17 at 09:38
  • @jkej I'm not sure that invalidates the point at all. Red and blue are opposite ends of the spectrum, and everything is between them. We see three dimensions of color, so of course you can't cram everything into a linear spectrum. But if you take my point to apply to the linear regions of color perception (the regions between the perceptual spikes of the photoreceptors), is it wrong? I don't see how it could be, given how photoreceptors pick up the frequencies they do. – piojo Aug 10 '17 at 10:45
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    @piojo Yes, this roughly works for the red-to-green spectrum and the green-to-violet spectrum separately, but as you hint at, this is a peculiarity of our color perception, not because light frequencies somehow physically "average out". Even if it sort of "works" in some cases I think it is still pedagogically misleading to explain mixed colors in terms of averaged frequencies, and I chose to illustrate this with a case for which is doesn't work. – jkej Aug 10 '17 at 11:19
  • @jkej Far point. Though I suspect the relationship holds for any species that perceives chroma as a continuous space. That said, you're right to point out that frequency is a one-dimensional continuum and our perception is not, so taking this model too far will lead to confusion. – piojo Aug 10 '17 at 12:28
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    Obligatory reminder: Comments are for improving and clarifying the question, not for providing answers to it. I have removed a bunch of comments which did the latter. – ACuriousMind Aug 11 '17 at 22:39

6 Answers6

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Our ability to separate different colors from each others depends crucially on how many different receptors we have for colored light.

Humans have three different receptors for light, which means that we can characterize colors by three numbers, just like the RGB-codes of colors on your screen.

At the end of the day, what determines with colors we perceive is how the wave-form is projected onto these three numbers. Since there is an infinite set of wave forms, there is an infinite mixture of colors that we will perceive as identical (for every perceived color).

Some animals have more than three types of color receptors, and can therefore distinguish more wave-forms of light. You can say that their color perception is higher dimensional (4D,5D,... etc) than our 3 dimensional color perception.

Mikael Fremling
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    Some humans actually have a 4th color receptor (if I'm reading this correctly): https://en.wikipedia.org/wiki/Tetrachromacy#Humans – tonysdg Aug 09 '17 at 16:57
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    Mantis Shrimp have 16 different types of light sensing cones. Compared to them, we are color blind. – Shufflepants Aug 09 '17 at 21:29
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    It might help, as an intermediate step, to note that the color receptors in human eyes are not monochromatic, and pick up a spectrum of frequencies in an approximate bell-shape. See the image at: https://en.wikipedia.org/wiki/Cone_cell. This builds on WillO's answer. Also uniform colors formed from different combinations of monochromatic light are called "metamers" to denote that they are fundamentally different, but are perceived the same way by trichromat humans. See: https://en.wikipedia.org/wiki/Metamerism_(color) – do-the-thing-please Aug 09 '17 at 23:18
  • After more than 25 years of searching, neuroscientists in the UK recently announced that they’ve discovered a woman who has an extra type of cone cell — the receptor cells that detect color — in her eyes. – John Alexiou Aug 10 '17 at 12:50
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    Describing perception of colors as “dimensional” is not really very useful, and rather misleading. I.e. what is a ‘dimension’ to you? There is a difference between three points on a one–dimensional line and three points in a two–dimensional plane … – can-ned_food Aug 10 '17 at 13:57
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    @can-ned_food ON the contrary, I think that talking in terms of dimensionality (especially for humans, dogs and birds) makes sense. To answer the question: dimensionality is the number of pices of information you need to describe a perceived color. For humans you need three numbers, whereas for dogs you only need two. See https://en.wikipedia.org/wiki/Color_vision#/media/File:Cie_Chart_with_sRGB_gamut_by_spigget.png for instance. The colors of the rainbow is actually a particular path through this 3D color landscape. – Mikael Fremling Aug 10 '17 at 14:09
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    Hmm. I prefer to use a more strict definition of the concept ‘dimension’ — but you are correct. There are looser vernaculars, even in mathematics, which do not add the geometrical and fundamental Euclidean stipulations to the word. – can-ned_food Aug 10 '17 at 14:12
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    @canned_food I couldn't disagree more with you. Realizing that a light spectrum is an infinte-dimensional vector and that our color perception projects that vector onto a 3-dimensional space was a true eureka moment for me (happened many years ago). Before that there were always a number of questions about light and color (such as the OP question) that I couldn't quite wrap my head around. I'm amazed that this was never pointed out to me during my undergraduate physics studies. – jkej Aug 10 '17 at 15:14
  • @jkej: I think partly it is not explained in physics because colour perception is not really in the scope of physics, it is something that only happens in the eye and brain. When observing real-world objects (as opposed to pure patches of colour as this question and answer cover), things get even more complicated. – Neil Slater Aug 11 '17 at 07:35
  • Cephalopods may use chromatic distortion to see colour frequency as more of a continuum (similar to how we perceive sound) rather than as a 3, 4 or 16 dimensional point - https://phys.org/news/2016-07-explanation-cephalopods-black-white-vision.html – Pete Kirkham Aug 11 '17 at 15:02
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    @can-ned_food, "dimension" is a concept in linear algebra. It is a characteristic propery of a vector space. Specifically, it is the maximum size of any set of linearly independent vectors from that space. The concept applies both the human color perception, where the colors that we perceive can be meaningfully represented as 3D vectors, and also to physical colors, where each possible power spectrum can be meaningfully represented as a member of a function space (a kind of infinite-dimensional vector space). – Solomon Slow Aug 11 '17 at 15:19
  • Is there a planck limit on waveform frequency? – corsiKa Aug 11 '17 at 19:05
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Mikael Fremling's answer is excellent, but here is just a little more detail:

The light that hits your eye is a mixture of many different pure wave lengths, all at different intensities.

The red sensor in your eye computes the weighted average of those intensities, with weights that are concentrated around 440thz. The green sensor computes a different weighted average, with weights concentrated around 560thz, etc. (This is a stylized example; they're surely concentrated near some other wave lengths, not exactly 440 and 560.)

Each type of sensor computes one number. Your brain interprets those three numbers as a color.

There are many different combinations of intensities that all produce the same three weighted averages and therefore all look identical to your brain.

WillO
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    There is no yellow sensor in your eye. The sensors in a human eyeball are called cone cells, and there are three kinds; "Red", "green", and "blue." That is why our color computer and TV screens only need red, green, and blue emitters. – Solomon Slow Aug 09 '17 at 17:20
  • @jameslarge: As I said, this is a stylized example. It's meant to explain the mechanism, not to nail down the details. But I'll change yellow to green. – WillO Aug 09 '17 at 17:37
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    @jameslarge going off peak response, it's more like yellowish-green, green, and blue-violet. Proper names are S- (short), M-, and L-cones – Nick T Aug 09 '17 at 19:00
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    @jameslarge We don't call them red, green and blue any more - mainly because what used to be called "red" cones actually respond most strongly to yellowish green. Call them long, medium and short wavelength cones, or $\rho$, $\gamma$ and $\beta$. And your assertion about computer and TV screens is an oversimplification - the gamut of colours that a TV screen can display is much smaller than the gamut of colours you can get by filtering out different parts of the visible spectrum. – Dawood ibn Kareem Aug 10 '17 at 08:46
  • @jameslarge : Rods of course, don't exist. Peaking in sensitivity around 500 nm (about 600 THz) and trailing off at about 640 nm (470 THz) , have no relevance to the Question. – Eric Towers Aug 13 '17 at 05:01
  • @EricTowers, Yes, I agree, and the article to which you linked also agrees; rod cells have no relevance to the question. The question was specifically about how we perceive colors. – Solomon Slow Aug 14 '17 at 13:16
  • @jameslarge : My experience with pink lasers (high intensity NIR lasers that excite the long wavelength fat tails of rods and barely excite the L cones) tells me otherwise. – Eric Towers Aug 20 '17 at 05:35
  • @jameslarge : Your claim was "The sensors in a human eyeball are called cone cells", not "The sensors relevant to your question are called ...". They come in a surfeit of kinds. 85 variants of the L cone in human males are reported here having peak absorbance shifts up to about 15 nm. Some women are tetrachromats, expressing two different L cones in both eyes. Another set of light sensitive cells synchronize circadian rhythm. – Eric Towers Aug 20 '17 at 05:40
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The answers here are correct, but have not answered your question about whether other animals can detect such a "pure" color.

The first tricky part of this is that there is no way to observe a "pure sine wave" as a single frequency. If you want to know the math, you can investigate Fourier transforms, but basically the mere fact that you cannot observe the signal for an indefinite period of time actually forces the tiniest smearing of the frequencies. This effect is far smaller than other factors like noise, but I point it out because it shows that it is mathematically impossible to observe a single frequency of light. You must always observe a band. And, in fact, that band must have some sensitivity at all frequencies. That's just the math. We can talk about a reasonably pure sine wave, but there are mathematical limits that prevent us from every observing something perfectly.

With that in mind, we can talk about whether there is a creature which can observe the band of "yellows." 510-540THz is a typical range of frequencies that we may assign a "yellow" color (actual ranges depend on personal perceptions, which are way beyond the scope of this question). So you might ask if there is an animal that can recognize 510-540THz sine waves, and distinguish them from a mixture of red and green that you and I might interpret as yellow because we are trichromats.

As it turns out, there is such a creature! It is the Mantis Shrimp. The mantis shrimp has sensors which are sensitive to 16 different bands, rather than our measly 3. However, the linked Oatmeal comic misses out on an interesting limitation of the Mantis Shrimp. Studies have shown that the Mantis Shrimp doesn't actually have all that good of color perception. Unlike us, it doesn't process the colors together. It doesn't take the reds and greens and figure out how yellowish the object is. Instead, each color band is processed independently.

While this means the Mantis Shrimp can't see color as well as we can, it does mean its style of vision is an exact match for what you want: sensitivity to a band of frequencies.

Cort Ammon
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  • "Can't see color as well as we can" is a subjective statement. Mantis Shrimps can "see color" well enough to do whatever shrimps do with color information - otherwise they would have either evolved or become extinct. Humans are exactly the same, in that sense. But most humans don't "use" color vision for the same purposes that shrimps do! – alephzero Aug 10 '17 at 04:51
  • @alephzero True, if you took extra care to craft a definition of seeing color well which emphasized the speed of detection over the number of discernible colors, you could argue that the mantis shrimp is better. However, the fact does stand that we can detect different shades of color which are closer together than the mantis shrimp can. – Cort Ammon Aug 10 '17 at 05:01
  • The answer could use a pic like this http://www.physicsclassroom.com/Class/light/u12l2b2.gif. Interestingly, human eyes should be able to distinguish "pure" yellow from a red-green mix because the response of the blue cones would differ. No clue if the optic nerve or brain can distinguish them though. – user126527 Aug 10 '17 at 10:42
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    @JollyJoker Yes, the $\beta$ cones do respond less for pure yellow than they do for red + green; but consider the difference between yellow + a tiny amount of white, and red + green. Both will stimulate the $\beta$ cones, and depending on the exact colours and strengths used, the responses by all three sets of cones to "red + green" can be identical to the responses to "yellow + a little white". The brain tends to ignore odd stray bits of white light when evaluating what colour it's seeing. – Dawood ibn Kareem Aug 11 '17 at 02:27
  • @DawoodibnKareem More accurately, it's the human visual system. The initial work combining cone signals is done in the retina, before the signals even reach the optic nerve. – H Walters Aug 13 '17 at 19:38
  • @HWalters I know I'm always torn when human-perception questions come up on Physics.SE as to where the line should be drawn in our signal processing chain. Too close to the retina, and you get misleading answers. Too deep into the brain, and you get really weird answers. – Cort Ammon Aug 13 '17 at 19:42
  • @CortAmmon That's precisely why I like the phrase "the human visual system"... it erases the line (especially when both sides play major roles). – H Walters Aug 13 '17 at 20:07
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As an add-on to the existing (excellent) answers, to address the last point in your question,

Or is there machinery that can do that?

the answer is yes: they're known as spectrometers, and they let you split the light into its component colours up to very high resolutions, giving you output that looks something like this:

Image source

Spectrometers can be very complicated machines, but for simple examples you can just use a triangular glass prism or even a blank CD as a diffraction grating $-$ and, indeed, the source for the image above has a nice tutorial for how to build a DIY spectrometer at home, which will show very clear differences between e.g. clandlelight vs LED-based flashlights vs incandescent light sources.

Emilio Pisanty
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    a prism ! :-) really ? That is, if I mix red and green light, and throw that through a prism, would it really return red and green, and no yellow ? – commonpike Aug 09 '17 at 20:08
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    Indeed. Try it out with white sunlight vs. “white” fluorescent light. – leftaroundabout Aug 09 '17 at 20:50
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    @commonpike Yes, it will. The image source also has a good tutorial for building a good-enough spectrometer with a CD and a cardboard box. Other interesting light sources are a smartphone flashlight (or other white LED lights, both cool and warm), smartphone / laptop screens, and candlelight or other thermal sources. – Emilio Pisanty Aug 09 '17 at 22:52
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    @commonpike - Yes, absolutely it would. It's the human brain that decides that "red and green mixed together" and "yellow" are the same thing - it's not a property of the light itself. And a prism isn't smart enough to make the same decision. – Dawood ibn Kareem Aug 10 '17 at 08:50
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Light is infinite dimensional (up to quantum fuzziness).

The number of photons of each frequency of light is independent of the photons of other frequencies of light, even ones the smallest distance away.

Our ability to sense light is based on (usually) a three pigment system in our eyes (some humans have 4, some have 2 and some have 1 or 0). These three pigments, plus our brain, map this infinite dimensional space into a 3 dimensional one.

When we see "pure red" plus "pure green" looks like "yellow", this means that when we excite the pigments in our eye with "red" and "green" photons in equal amounts, the result is the same as if we excited the pigments with "yellow" photons.

The "red" and "green" photons never become yellow photons. Your inability to distinguish red+green from yellow is in effect an optical illusion caused by limitations in how you see.

A creature with certain kinds of different, or more, pigments would not confuse "red+green" and "yellow"; the two might look completely different.

Because of how we sense light, there are colors we can see that do not correspond to any single frequency of light. There are no "brown" photons, nor are there "white" photons. These correspond to certain mixtures of photons in the 3 dimensional projection of the infinite dimensional color space that is real light.

There are tools that let us distinguish between "red+green" and "yellow" light. The easiest is a prism -- each photon of light will be bent differently from it, so a narrow point-source of "yellow photons" will bend together, while "red+green" will be split apart by the prism.

Note that this doesn't match your art class colour mixture. Paint mixes via subtraction (each pigment absorbs certain colours and reflects the rest, and when you mix two both of their absorbtion occurs to some extent).

Photons or light mix by addition.

A big difference is that if you mix all your pigments together, you get a muddy brown or black (mixing many pigments can violate the region where the "absorbtion combines" approximation works, preventing it from being black). If you mix all your lights together, you get white (assuming they are in the right balance).

Yakk
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    This is an excellent answer, that explains the phenomenon of colour vision extremely well. – Dawood ibn Kareem Aug 11 '17 at 08:18
  • Except, yellow and blue light added is perceived as white (or grey), not green. The addition of green and red light is perceived as yellow. – commonpike Aug 11 '17 at 14:43
  • @commonpike True. My grade-school art class color mixture has left me with the wrong colour mixtures in my head. Photon mixture changed to additive, an anendum on how I screwed up added. – Yakk Aug 11 '17 at 14:49
  • If you start with a greenish enough yellow, and a greenish enough blue, you can indeed get green light by mixing the two. But for most yellows and most blues, you'll get a fairly indeterminate kind of colour close to grey or white. – Dawood ibn Kareem Aug 12 '17 at 05:11
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To the question "are there animals that can discern composite pure yellow from singular pure yellow":

Yes. Humans (who wear glasses). I first realized I could look through the edge of my glasses (and thus through an ad hoc prism) at spectra containing "purple" and distinguish between violet (405 nm (about 740 THz) from a laser diode) and red+blue = purple spectra. The laser diode has a spectral width of about 1 nm (corresponding to about 2 THz), so is a relatively pure real source of light. The red + blue were various organic fluorophores, so were not nearly as spectrally pure.

There's nothing special about "purple" in this story. This would work just fine for yellow versus red + green = yellow.

Eric Towers
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