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Monochrome vision is easy to describe--each "pixel" only has one dimension, luminosity.

Dichromatic vision--what most mammals have--has two channels per pixel. On the physical level, that's luminosity in two frequency buckets, but perceptually those are projected into the space of weighted-average frequency--hue--and total luminosity.

Trichromatic vision--what most humans have--adds a third dimension, and again the raw physical-layer inputs get processed in the brain to project them on to a different set of three coordinates; three dimensions allow us to distinguish luminosity, hue (weighted-average spectral peak), and saturation--basically, a measure of how much luminosity is in the spectral peak, vs. spread out in other parts of the spectrum.

But how does the perceptual color space work when you add a fourth dimension, like, for example, most birds have? Is it like having an extra dimension of hue, or some kind of 2D saturation, or something else entirely?

This is not a question about how things would look different with particular additional receptors, or about quantitive measures of how much extra color discrimination you would have--it is about the qualitative structure of a generic 4-dimensional color space, and how it could differ from the known structures of 3-, 2-, and 1-dimensional color spaces.

And no, "How much can I expand human color perception by adding new photoreceptors?" does not answer the question. Once again, this is not about improving color discrimination or expanding spectral range, or anythingto do with humans. It is about the qualitative differences in the structures of perceptual color spaces of different dimensionalities.

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  • $\begingroup$ Some women are tetrachromats, you could ask them. I think you could say it's just extra color bit depth, a bit like going from 16 to 256 to 4096 color palettes. $\endgroup$
    – IronEagle
    Apr 27, 2023 at 23:27
  • $\begingroup$ @IronEagle The trouble is that for them, tetrachomaticity is normal. They have no trichomaticity to compare it to. It'd be like trying to explain the extra colors to someone who is color-blind. There's just no common frame of reference. $\endgroup$
    – John O
    Apr 28, 2023 at 18:57
  • $\begingroup$ @JohnO They may not be able to communicate qualia, but there's nothing in principle preventing them from describing the vector basis of their perceptual color space and how it corresponds to physical correlates, just as we can do for trichromatic, dichromatic, and monochromatic vision. $\endgroup$ Apr 28, 2023 at 20:14
  • $\begingroup$ @IronEagle Bit-depth is a conceptually orthogonal issue. Any particular dimensionality requires 2^d bits of color information at minimum, but aside from that, you can increase or decrease color depth entirely independently from dimensionality. A dichromat with better per-channel resolution could have exactly the same color depth as a trichromat, and still have no perception of saturation. $\endgroup$ Apr 28, 2023 at 20:19
  • $\begingroup$ there are actually many question on this site about color vision, why do none of them answer your question. $\endgroup$
    – John
    Apr 28, 2023 at 23:26

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Parrots are tetrachromats. They can see in the near violet.

I think they have counted up to 16 different detectors in the eye of the mantis shrimp, from IR to UV. I don't think they actually think of sixteen dimensions of colour - more likely they have a better ability to detect motion that is not fooled by camouflage.

What might it be like to have four channel vision? Imagine having a narrow-band yellow light as a head torch. You can see reds and greens with the ambient light, but you now see colours that reflect at about 595 nm as particularly luminous because of your head torch. It is a bit like having a narrow-and yellow detector in between your red and your green vision.

So, what do you actually see? Probably not that much more because most colours that reflect yellow also reflect green and blue. Most greys are equally grey in IR and UV. Green leaves reflect IR, which is a bit unexpected but most other reflection objects look much the same. Some flowers have UV patterns that insects can see. But outdoor lighting is broadband, and most reflection spectra are fairly smooth, so there are whole new ways of colours not quite matching, but maybe not that much in terms of extra detail.

I had my eye lenses replaced due to cataracts. I ought to be able to see more in the UV. But even when I had only one eye done, I could not tell the difference.

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    $\begingroup$ Plus parrots can talk. So we can just ask them what things look like to them. Is anyone here a parrot? $\endgroup$
    – Daron
    Apr 28, 2023 at 16:01
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A Woman Artist With Tetrachromatic Vision Painted Pictures that Show a Difference

Though it’s very rare in humans, some women have tetrachromatic vision, while men are thought to be unable to have tetrachromatic vision. One woman featured in the BBC article I’ve linked is an artist, and so her paintings of real world objects provide us with a good glimpse of what tetrachromatic vision is like. Here’s a side-by-side comparison of a painting she painted and the real tree next to it:

enter image description here

As you can see in the painting vs the picture, there are a lot more colors in the painting, and everything seems more vibrant and seems to have a bit of a pink/purplish glow to it. I hope this helps you out. Here’s some more links to look into for more info:

https://www.healthline.com/health/tetrachromacy

https://www.bbc.com/future/article/20140905-the-women-with-super-human-vision

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    $\begingroup$ I'm not sure paintings are really all that useful, since the paints will also look different to someone with a different distribution of cone cell responses. And passing them through a computer screen eliminates all the spectral information that might help reveal that difference. $\endgroup$ Apr 28, 2023 at 3:31
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    $\begingroup$ If a dichromat paints what they see, with only their own perception as a guide to color matching, the result will have strange (and probably interesting) color variations to a trichromat. If a trichromat paints what they see, it will look realistic to a dichromat. So why would a realistic painting by a tetrachromat looks strange to a trichromat? If she's not trying to paint realistically, then I don't see what the painting is supposed to demonstrate. Lots of trichromats paint like that. $\endgroup$
    – benrg
    Apr 28, 2023 at 18:58
  • $\begingroup$ @benrg In the general case, that is not true. Even individuals with equal visual dimensionality will not be able to produce images that look accurate to each other unless their response curves are specially aligned. $\endgroup$ Apr 28, 2023 at 20:48
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A little more research of my own managed to turn up this absolutely lovely article: Ways of Coloring: Comparative Color Vision as a Case Study for Cognitive Science Which contains comparative color spaces for humans, bees (also trichromats, but with different frequency response), goldfish, turtles (both of which are tetrachromats), and pigeons (suspected pentachromats). And it has an excellent statement of what the problem actually is:

It is important to realize that such an increase in chromatic dimensionality does not mean that pigeons exhibit greater sensitivity to the monochromatic hues that we see. For example, we should not suppose that since the hue discrimination of the pigeon is best around 600nm, and since we see a 600nm stimulus as orange, pigeons are better at discriminating spectral hues of orange than we are. Indeed, we have reason to believe that such a mapping of our hue terms onto the pigeon would be an error: [...] “Among other things, this result strongly emphasizes how misleading it may be to use human hue designations to describe color vision in non-human species.” This point can be made even more forcefully, however, when it is a difference in the dimensionality of color vision that we are considering. An increase in the dimensionality of color vision indicates a fundamentally different kind of color space. We are familiar with trichromatic color spaces such as our own, which require three independent axes for their specification, given either as receptor activation or as color channels. A tetrachromatic color space obviously requires four dimensions for its specification. It is thus an example of what can be called a color hyperspace. The difference between a tetrachromatic and a trichromatic color space is therefore not like the difference between two trichromatic color spaces: The former two color spaces are incommensurable in a precise mathematical sense, for there is no way to map the kinds of distinctions available in four dimensions into the kinds of distinctions available in three dimensions without remainder. One might object that such incommensurability does not prevent one from “projecting” the higherdimensional space onto the lower; hence the difference in dimensionality simply means that the higher space contains more perceptual content than the lower. Such an interpretation, however, begs the fundamental question of how one is to choose to “project” the higher space onto the lower. Because the spaces are not isomorphic, there is no unique projection relation.

A common feature of all of the systems described is the production of a combined luminance channel from the raw n-dimensional cone cell inputs, as I suspected there would be, and n-1 oppositional color channels--in humans, these are the red-green and blue-yellow oppositions, which produce a two-dimensional neurological color space othogonal to the luminosity axis, corresponding to the classic color wheel, with fully saturated hues along the outer boundary and blue occurring across from yellow and red across from green. Saturation arises as the radial dimension--distance from the white-black axis--in a polar transformation of this oppositional color space.

In higher-dimensional color spaces, as determined by discrimination experiments on tetrachromatic and pentachromatic organisms, We still see the generation of oppositional color channels from retinal processing. How to generate these oppositional channels is not obvious; for example, in humans one opposition is between red and green, both of which are primary colors, but the other is between blue, a primary color, and yellow, a composite. Why that particular combination? It turns out, across different species, opponent channels are constructed to maximize decorrelation--in aother words, to remove redundant information caused by the overlapping response curves of different receptor types. Thus, the precise method of calculating color channels will be slightly different for each species, dependent on physical characteristics of the retinal cells, but they are all qualitatively the same kind of signal, and end up producing a a higher-dimensional hue-space orthogonal to the white-black luminosity axis.

Meanwhile, in any such neurological color space, there is only ever a single radial coordinate. Thus, we can say with some confidence that the extra dimensions introduced in higher-dimensional perceptual color spaces are not some extra sort of saturation or any kind of weird third thing, but are in fact additional dimensions of hue--and along with extra dimensions of hue, qualitatively different kinds of composite colors!

Our three dimensional human color space allows us to perceive two opponent channels, corresponding to 4 pure hues--red, yellow, green, and blue--and weighted binary combinations thereof--r+y (orange), y+g (chartreuse?), g+b (cyan), and b+r (purple), with one non-spectral hue. (Which, I suppose, means that the color wheel would still be a wheel even without the anomalous high-frequency response of human red cones!)

Meanwhile, a tetrachromatic system would have 3 opponent axes with 6 primary hues (r-g, y-b, and p-q), binary combinations of those hues producing secondary colors (r+y, r+b, r+p, r+q, g+y, g+b, g+p, g+q, y+p, y+q, b+p and b+q), and ternary combinations producing an entirely new kind of hue not found in the perceptual structure of trichromatic color space (r+y+p, r+y+q, r+b+p, r+b+q, etc.). Additionally, there is not merely one non-spectral intermediate color (purple) in the fully-saturated hue space, but 3--and in general, that number will correspond to however many pairs of non-spectrally-adjacent sensor types there are, which works out to the sequence of triangular numbers!

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In short: It would be like normal, but with ultraviolet vision. Imagine trying to explain trichromacy to a colorblind person. To you, it would just be normal. All the things you mentioned would be great if you were using some sort of tech to augment your 3-vision to 4-vision without fundamentally changing the way your brain processes color. However, if you are making a species with fundamental 4-vision, then they would perceive it as normal, and you as handicapped.

Or you could just ask Monet.

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    $\begingroup$ Explaining trichromacy to a dichromat: "White isn't a spectral color, and there's a whole extra quality to colors that makes any spectral color more or less like white, which we call 'saturation'". $\endgroup$ Apr 28, 2023 at 2:17
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    $\begingroup$ And Monet wasn't a tetrachromat. He just had sensitivity to a wider range of the spectrum squished into the same three buckets as the rest of us. $\endgroup$ Apr 28, 2023 at 2:18
  • $\begingroup$ That's true. But he was still more tetrachromate than most of us. 3.1-vision? $\endgroup$ Apr 30, 2023 at 14:36
  • $\begingroup$ No, he wasn't. He still had exactly three types of cone cells and 3 dimensional color space, just with a slightly expanded spectral range. The perceptual structure of his color space was identical to that of a normal human, penguin, or honeybee. $\endgroup$ Apr 30, 2023 at 14:41

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