The Case of the Missing Magenta | Hacker News Reader

The Case of the Missing Magenta

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67 pointscaptn3m045 comments

A slight elaboration about the way your eye works: The cones are not on-off affairs, and they are not limited to specific wavelengths. Each type of cone has a response curve, and these curves overlap (see e.g. the Wikipedia article about Cone cells: http://en.wikipedia.org/wiki/Cone_cell ). So different colors are not really "made up" by filling in the gaps between the wavelengths. Each color we see corresponds to a specific cone response pattern. So for example, 500 nm would lead to responses of (roughly) 0.3, 0.4, 0.1.

This means the explanation here is slightly misleading, as it compares yellow (which is a color that does exist as a single wavelength) with magenta, which is by definition a mix of at least two wavelengths.

You could say that magenta is a compound color, the interpretation by our brain of the simultaneous stimulation by at least two wavelengths (i.e. two or more cone response patterns). This means, of course, that magenta is far from the only color for which this is true. Any combination of at least two wavelengths is a compound color, and the interpretation of each of these combinations will not be found on the visible spectrum.

So, interesting article, but a bit oversimplified, in my view.

Thank you, this makes more sense.

> Any combination of at least two wavelengths is a compound color, and the interpretation of each of these combinations will not be found on the visible spectrum.

Is it really impossible for the cone response to a compound color to match that of any single wavelength? There are yellow wavelengths, but we display yellow as a compound of red and green instead. That doesn't mean yellow can't be found on the visible spectrum.

> Is it really impossible for the cone response to a compound color to match that of any single wavelength?

Yes.

Look for a "chromaticity diagram" to see the colors we can perceive. It is a convex shape, like a truncated parabola, and the pure colors are on the edge of the parabola curve. Any time you mix two pure colors, you end up inside the parabola instead of on the edge. Conversely, any color on the inside of the parabola cannot be a pure wavelength and must be a compound color.

There are a lot of colors we call "yellow". Some are pure colors and some are compound colors. The ones that your monitor display are compound colors that cannot be found on the spectrum.

A decent monitor will represent brilliant yellow colors fairly well. This is due to the low curvature of the edge of the chromaticity diagram in the green-red range, which in turn can be ascribed to the similarity of the response curve for the L and M cones in the eye, compared to the S cones. However, brilliant turquoise and aqua colors won't show up on your monitor.

Also, because of the overlap between the response curves of the different cone cells, there are colours that cannot be produced by any combination of frequencies of visible light but that the brain can still perceive: http://en.wikipedia.org/wiki/Impossible_colors

(Another side-effect of this: any display based around additive mixing of three colours, such as the computer display you're reading this on, cannot reproduce the full spectrum of colours available in the real world. Standard computer and TV displays are particularly limited in the range of greens and blues they can reproduce.)

re: the latter, there's a nice illusion for getting a feel for that: http://i.imgur.com/G3EoK.png – an optical effect that allows you to see true cyan vs. computer display cyan

I make a study of funny colors. For example you can get weird vibrations via certain patterns of strobed color combinations and frequencies.

This is an interesting study of such (warning! strobes!) :

https://www.youtube.com/watch?v=dL0lNGXoP8E

Wow, anyone who can watch that without becoming epileptic is immune :).

Interesting effects though.

this is beautiful

The really interesting thing, which I only learned a few years ago, is that there is actually a reason that we perceive colors in the "purple" range (including violet and magenta) as falling between red and blue on a "color wheel". Specifically, the "red" cones in our eyes have a minor secondary region of sensitivity that's way out in the blue-violet range. So violet light also partially stimulates our red receptors, making our brains interpret it as a mixture of red and blue.

Here's one source: http://midimagic.sgc-hosting.com/huvision.htm (I know I've seen other sources as well, but this phenomenon isn't discussed terribly often so I'm a little bit skeptical about it.)

Another interesting color fact: many birds have four independent color channels instead of our three [1]. Which means they can see a whole additional dimension of colors we cannot even imagine. I like to think how it would be to wake up one day and suddenly being able to see all those additional colors...

[1] http://en.wikipedia.org/wiki/Tetrachromacy

Similarly, some people who have undergone eye surgery and lose part of the eye that filters it, are able to see ultra-violet light. It's theorized that this happened to Monet, and accounts for his painting of some flowers differently post cataract surgery.

I think it'd be wonderful to experience this, temporarily at least!

http://en.wikipedia.org/wiki/Aphakia

I have had my lens removed and I do experience this. To me its more annoying than exciting though. Those black light lamps used in things like club lighting are somewhat blinding to me. My glasses do filter it though.

I as well see it, like a faint hazy halo around the black light, and it really messes with my vision. I cannot go into a club anymore, nor go to haunted houses, as the black lights are really disorienting.

I have had both my lenses removed and have implants now. Since I was young when they were removed, I thought everyone saw this until a couple years ago.

This brings me to a question I've always had: What if the colors we see are specific to us? I.e., what if what I perceive as blue and you perceive as blue don't look the same to us, but because we've always been taught that that color we see is blue, our differing perceptions lead us to that conclusion?

I know I'm not explaining this correctly, I've been trying to wrap my head around it for a while.

Perhaps you're referring to "qualia"? Supposedly, it's an open question in philosophy. I'm no expert myself, but I figured I'd mention it in case you found the subject worth pursuing.

http://plato.stanford.edu/entries/qualia/

http://en.wikipedia.org/wiki/Qualia

Obligatory xkcd:

http://xkcd.com/32/

That's not an uncommon question at all. This is a single instance of a set of philosophical questions related to qualia[1], i.e., the question of subjectivity and conscious experience. Richard Dawkins stretches the question a little more by taking into consideration the experiences of other species, such as bats [2] —spatial sense through audition—, and it's not hard to find more[3][4][5]

Fun questions to ask (and hard to put into words indeed, I had my share of trouble trying this exact same thing), but I don't think we're anywhere close to answer them. At least not until we really understand what consciousness is.

[1] http://en.wikipedia.org/wiki/Qualia

[1] http://plato.stanford.edu/entries/qualia

[2] http://old.richarddawkins.net/articles/479563-sky-blue-pink-...

[3] http://www.huffingtonpost.com/mark-changizi-phd/perceiving-c...

[4] http://www.sciencedaily.com/releases/2005/10/051026082313.ht...

[5] http://www.dailymail.co.uk/news/article-2166917/We-DONT-colo...

Ah to be a tetrachromat. Interesting reference to the June 2012 study.

And then there is the mantis shrimp:

http://theoatmeal.com/comics/mantis_shrimp

I never understood why we have three trichromatic vision and not tetrachomatic vision.

We have rods and three types of cones, which look like four channels to me. In very low light the cones don't fire and we see in black and white. In reasonably bright settings I can imagine that the rods saturate and we only have three useful channels. But there must be a level of light where both cones and rods are within their dynamic range. What am I missing?

The wavelength curve the rods are sensitive to spikes in the middle of all the wavelengths curves for all the cones. So I think the mental sensation of gray is pretty accurate, actually, since it is close to being just a rough measurement of all the others.

You are saying that the rods' spectral curve response is collinear with the cones. That would do the trick, but I'm a bit surprised as I don't see any reason for evolution to push you in that direction.

Do you have a reference for this? Quick googling seems to show that the rods' response curve is not, it seems to be a most sensitive at a wavelengths between the peak of the blue and green cones.

I'm not sure if this will satisfy you, but you can give this a shot:

http://en.wikipedia.org/wiki/Mesopic_vision

http://en.wikipedia.org/wiki/Purkinje_effect

>> But there must be a level of light where both cones and rods are within their dynamic range. What am I missing?

I am not sure if human vision is using one or the other. When both rods and cones are within the dynamic range, possibly response from both get utilized by the brain. I am not sure.

Spitballing here: it's not just the sensors, but what you do with them. Is the visual processing for rods handled differently than the visual processing for cones?

Actually, I feel very good about this line here:

"More than one thousand times as sensitive as the cones, they can reportedly be triggered by individual photons under optimal conditions." http://hyperphysics.phy-astr.gsu.edu/hbase/vision/rodcone.ht...

So while rods have a response curve which is similar to codes, that response curve is shifted to be a thousand times more sensitive than cones. So at any lighting level which activates the cones, your rods are just maxed out, screaming "YES, IT IS VERY BRIGHT", and you don't get any useful information out of them.

Hence, no integrated, tetra-chromatic vision.

Some women have tetrachromacy, as well. (In your quoted article, actually.)

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> All the colors the monitors show as are actually just a mix of red, blue, and green light. If you could magnify your screen, you’d see something like this, and you’ll notice that there are only three colors there.

The easiest way to do this is to get some water on the screen. Red, green, and blue pixels will be apparent under the water droplet.

Violet is in the rainbow. Like magenta, it is a combination of red and blue (#8F00FF). This is because there's a second hump in the frequency sensitivity of the red receptor. See: http://en.wikipedia.org/wiki/CIE_1931_color_space#Color_matc...

So there is a "between red and blue" in the spectrum. Just no place where there's more red than blue.

It's not in the rainbow as in the diagram you link to ("CIE 1931 color space chromaticity diagram"). The diagram has the

         R

     G       B

"in 2 dimensions" and the values between and the rainbow has it as

    R     G      B

"in one dimension" and the values between.

Edit: under "it" I wrote about magenta, as the main article writes too. The "drawings" are about the appearance of magenta. I see you talk about violet. Yes it is an interesting observation about how we see the colors.

What happens if your eye sees pure 400nm light? There is some stimulation of the "red" receptor and more stimulation of the "blue" receptor. I think the fact that we DO see violet in the spectrum is more interesting than the fact that we DON'T see magenta.

See this: http://en.wikipedia.org/wiki/Violet_(color)

Wavelength: 380–450 nm

Hex triplet: #8F00FF

I think it would have been a better explanation if it included a color space graph, with the different directions corresponding to stimulating the different cones. You'd need a lot less text and people would grasp a lot more intuitively that a a line cannot stimulate 3 different cones in all the combinations.

So what would be the shortest explanation using concepts from linear algebra?

The stimulus is a spectrum. Discretizing wavelengths for simplicity of explanation, the stimulus is a vector where each element specifies the amplitude at each wavelength.

The color bar of rainbow colors is a sub-sampling of this spectrum where only one element is taken at a time. In other words, those are monochromatic colors. Alternatively, each point in the rainbow is obtained by multiplying a delta function with the stimulus and integrating over the wavelengths. This sub-sampling cannot possibly cover the entire color space. In fact, the majority are missing, including magenta which is not a monochromatic color.

The human eyes also sub-samples this space. However, it does not use delta functions. Each cone has its own vector (or more precisely a function of wavelength) and the sensed amplitude is integral of this vector multiplied by the stimulus. This is very much a dimensionality reduction problem where given the spectrums of natural objects around us, nature chose a smaller space that allows distinguishing the objects as much as possible.

Quite obviously, the sub-sampling done by the human eye also leads to loss of information. There would be spectrums which are different but would map to the same perceived color. See metamerism: http://en.wikipedia.org/wiki/Metamerism_%28color%29

Electronic-displays use RGB because those three colors then cover a good percentage of the colors human eyes can perceive. When more than three primary colors are used in the display technology to enhance color gamut, etc., avoiding metamerism issues becomes an interesting concern as we need to make sure colors which should appear the same do not appear different given that the cone response curves varies somewhat between humans, varies with age, and also surrounding illumination can impact the two rendered colors in different ways.

See also my older related comment on the topic: https://news.ycombinator.com/item?id=5931005

That's not as helpful as the original article. It's all in science terms (delta functions, vectors, stimulus, discretizing wavelengths), without really explaining them.

it was a reply to somebody kindly asking an explanation using linear algebra concepts.

Wouldn't magenta just be red mixed with white? That's how you do it with paint.

Paints and light mix differently. One is subtractive, the other additive.

With paint, you start with white (full reflectivity) and add pigment to block out reflected light.

With light, you start with black (darkness) and add photons of different wavelengths. When you have an even mix of all wavelengths, you have white light.

No. You'd have to mix in some blue, and then you'd just end up with a muddy purple.

You can prove it to yourself by looking at any painting from before about 1860. See any magenta? No. Magenta pigment was not available until 1859, and it could not be mixed from other colors without getting a muddy result.

Edit: Here's an example: http://en.wikipedia.org/wiki/File:Bouguereau-Psyche.jpg

The painting (Psyche by Bouguereau) was done in 1890 and could not have been made thirty years earlier.

Thanks for the interesting reply.

No violet either, can't get violet out of a mix of red, green and blue. (True violet, the stuff that is after blue on the spectrum).

"Magenta (often called pink)"

- Aaaaargh. What next, "purple"? Please.

tl;dr: magenta = blue + red

Long version: brains interprets green+orange as yellow because they are close enough and it save one kind of photoreceptor ; blue + red is not interpred as another color are they are far enough, hence magenta (not a simple color ray)

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