What is color?

Discussion in 'Physics & Math' started by Asexperia, Nov 24, 2019.

  1. QuarkHead Remedial Math Student Valued Senior Member

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    How can a set have a represtaion as a vector? With two uninteresting exceptions, a set has multiple elements, a vector is a single set element with additional properties, but only when considered as an element in a vector space.
    Stop posting gibberish, please
     
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  3. arfa brane call me arf Valued Senior Member

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    I'm asking myself how a binary string can represent a color, from a set of say, 16.7 million colors.

    Oh wait, I know this one. The display I'm looking at has a binary representation for each of the colors. How can a binary string be a representation of a vector in a color space? Well, that's one way.
     
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  5. iceaura Valued Senior Member

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    Which proves that the "representation" is either 1) incomplete (such as dealing with "spectral colors" and other wavelength-defined "colors" only) or 2) not a vector space.
    No, I'm not saying anything like that.
    To repeat, and shorthand for emphasis: wavelengths are not colors.
    You can manufacture an LED display that works well, usually (in the digital age) employing vectors in many clever and useful ways. Perhaps in the future someone may even come up with a design that can produce all the colors and their relationships human vision can perceive (nowhere near that yet, but it's probably not impossible).
    You cannot represent the "space" of human color vision as a vector space, or establish a distance function over it. So it's not a Hilbert space.

    Maybe it's a manifold one can represent as some kind of topological space? Dunno. But the following observed facts will be difficult to handle: 1) Yellow is both between and not between red and violet, similar considerations abound with all other colors. 2) A single wavelength of light represents several different colors, and vice versa, depending on circumstances of detection that are not part of the visual system proper.

    Why is that controversial, or important to anyone? It was a side comment.
     
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  7. arfa brane call me arf Valued Senior Member

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    That might be the case, but you can represent what color displays "do" with vector spaces. What an actual human experiences when they see a display seems to be still undefined. Somehow or other. Perhaps not so much to someone who designs color displays and refers to an industry standard, in which color distances are well-defined, useful even.

    Here's an example:

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    I'm not convinced that you can't represent human color vision as a vector space, the development of color displays relies on color models, where spectral colors are points in a Euclidean domain and where distances between colors are well-defined. At what stage in the process of color perception does this fail to hold? where does it break down?
     
    Last edited: Dec 14, 2019
  8. arfa brane call me arf Valued Senior Member

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    In the CIE chromaticity diagram above, wavelengths are the (blue) numbers along the curve. The "colors" green and red are seen to increase in the vertical and horizontal directions, respectively.
    The diagram has been embedded in an xy space, where x and y are "color amplitudes", say. The wavelength of green (y) or red (x) doesn't change anywhere in the diagram . . .

    ed. a thought experiment you can try at home: imagine you only have two types of cone cells, so you might not be able to see the color blue, say. In the diagram what might happen is you see black (i.e. no color amplitude) instead, but can still see red and green.

    I'll leave that to the physiologists, though.
     
    Last edited: Dec 14, 2019
  9. Neddy Bate Valued Senior Member

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    I would not describe the wavelengths of light as "colors". I would describe them as "hues".

    I interpret the word "hues" to refer to fully saturated colors, which do not have any white, black, or gray mixed in. Then, for any chosen hue, there is a whole x & y graph with a black & white & gray distribution, as follows:

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    The hues are the wavelengths of light, but the colors are more complex than that.
     
  10. iceaura Valued Senior Member

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    30,994
    Of course. They deal in spectral wavelengths, the physical EMR spectrum. See my first post on the matter, above.
    You can represent spectral wavelengths as a vector space. That makes my fourth? fifth? repetition of that acknowledged fact.
    Why are you still posting about wavelengths?
    They are not. Wavelength distances are.
    Color distances are not transitive, additive, unique, or even consistently ordered. This has been illustrated for you with specific examples (the various distances between, or even order of, the colors yellow, violet, and red, say).
    Colorblind human beings of the type that is missing a kind of cone do not usually (or ever?) see black in place of the missing color.
    You are confusing wavelength detection amplitude with color amplitude.

    Wavelengths are not colors.
    I've been linking to summaries of their findings, posting examples, etc. You don't need to speculate - these things have been measured, investigated, etc.
     
  11. arfa brane call me arf Valued Senior Member

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    A theme you seem keen to turn into a top ten hit.
    All you're saying, repeatedly, is that the boundary of the chromaticity diagram isn't strictly in the set of colors; with a bit of a stretch for the lower "purple line" which isn't in the same space as this boundary line. I mean the line with wavelengths on it, in nanometers.

    Wavelengths clearly are not colors, they're distances, but they do have regions around them, in the diagram, which you might confuse with a "pure" color. Like say, the color red might be confused with a wavelength on this line.
     
  12. exchemist Valued Senior Member

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    It seems to me that what most contributors have been saying that colour is a perception of the human mind, lacking one-to-one correspondence with spectral wavelength and to some degree subjective.
     
  13. TheFrogger Banned Valued Senior Member

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    Richard Of York Gave Battle In Vain. I make that SEVEN colours.

    Three primaries: red, green and blue. All other colours consist of varying degrees of each (or none) of these primary colours. Computers display these colours with an amount of red, green or blue; (255, 127, 127).

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  14. iceaura Valued Senior Member

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    No. That has nothing to do with what I said. Boundaries, any boundaries of anything, are not involved in any post of mine in this thread. Internal structure is.
    And now you know why I keep repeating the simple fact until it sinks in. You keep posting about wavelengths, when the subject was colors. Wavelengths are not colors.
    Not in my posts here.
    Try this: in your next post, do not use the word "wavelength". Do not refer to the EMR spectrum at all.
    - - - -
    Fair enough, but that doesn't deal directly with the minor tangent that took over, one hopes temporarily - the claim that colors can be represented in, or form, a Hilbert space.
     
  15. exchemist Valued Senior Member

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    You seem to know more about Hilbert spaces than I do (not difficult

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    ). However I find myself sceptical that a subjective perception of the human mind can be modelled very well by any form of mathematical construction. Is that fair?
     
  16. arfa brane call me arf Valued Senior Member

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    --https://en.wikipedia.org/wiki/Hilbert_space#Color_perception

    I have no real idea what the problem is with wavelengths. The EMR spectrum has colors in it, these have different wavelengths (in one dimension, along the spectral line). The chromaticity diagram I posted shows that wavelengths can be mixed. And we're talking about wavelengths and visible light; some kind of relation.
     
    Last edited: Dec 16, 2019
  17. arfa brane call me arf Valued Senior Member

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    Well, I don't know what all those engineers might have to say about that. In spite of the problem you cite (if it is actually a problem) doesn't seem to have delayed the development of color displays and the underlying technology thereof.

    You can define the output of an LED, call it a color. Engineers will say a monochromatic color with a single wavelength is an ideal, in practice the output has a frequency spread. What the output of an LED is called, how a human eye responds to this output, is directly connected to how the LED was constructed.
     
  18. arfa brane call me arf Valued Senior Member

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    --https://link.springer.com/article/10.3758/BF03333234

    --https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0216296
     
    Last edited: Dec 16, 2019
  19. iceaura Valued Senior Member

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    30,994
    Well that explains a lot.
    I refer you once again to the optical "illusion" above: four or five different colors from one wavelength combination, from one vector in the wavelength space. Do you see a problem with definitions of addition and distance involving that wavelength and those colors?
    No, it does not. It has wavelengths in it.

    Wavelengths are not colors.

    https://link.springer.com/article/10.3758/BF03333234
    Color in general is not invariant under that kind of rotation, and colors do not add as force vectors in mechanics (as multiple colors available from one wavelength vector in the optical illusion I linked above demonstrates, and the fact that yellow is both farther from red and closer to red than violet also demonstrates, and so forth). So one immediately assumes that by "color" they mean wavelength ( the alternative is that their model is in conflict with experiment, and therefore worthless) and sure enough - first column second page - they verify that assumption:
    Nanometers? They aren't talking about colors at all.

    To repeat: wavelengths are not colors.

    Second link:
    https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0216296
    - "Three classes of retinal cone compute linear functions of the spectral power of the retinal irradiance (I), yielding a triple of scalar responses i.e. " Uh, what are they talking about? What is "spectral power"? Apparently, this:
    English speakers, on line, identifying culturally and linguistically specified color categories. Assumptions, not measurements, of which colors are "close" and therefore where the category boundaries lie. A "categorical metric" whose number of categories is "estimated". The entire thing crammed into an RGB "cube" - a volume of arbitrary shape and size, with at least one dimension (blue) not even present in the cone response they are basing the entire analysis on. (Humans have no "blue" cone, unless they speak Japanese or some other language that uses the same word for green as for blue. Humans do have a green cone). From that you think you can define a distance function over a Hilbert space of colors?
    - - - -
    Not much, and unnecessary. All that matters here is the basic definition, which includes an addition operation and a distance function (inner product) defined over the entire space. http://mathworld.wolfram.com/HilbertSpace.html
    (one of my uncles dealt with them for a living, in robotics applications, many years ago. The main lesson he passed on was the superiority of quaternions, in his opinion, for robot guidance - which probably required a quaternionic Hilbert space, which he therefore had to understand very well. The net has many explanatory sites these days. https://mafiadoc.com/quaternions-and-hilbert-spaces_5c5e3852097c47af0d8b458d.html, but I notice that quaternions don't seem to have taken over robot programming as he expected or hoped).
    Might depend. I can imagine (and possibly sound perception provides) an essentially subjective perception that is nevertheless additive (logarithmically) and transitive and so forth within any one person, and functionally mappable between different people. So only a set of parameter values varied between people, and that variation introduced no significant discontinuities etc.
    (Warning: different language speakers or even people apparently hear the famous "falling" chord () as a rising chord - that may indicate problems similar to those afflicting color perception, obstacles to algebraic representation of human hearing in general).
     
  20. arfa brane call me arf Valued Senior Member

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    7,832
    Are you saying the industry standards are useless? It's just dumb luck that display manufacturers get it right? You need to design a color display so that what people call a color is taken into account? Displays need to be culturally aligned?
     
  21. arfa brane call me arf Valued Senior Member

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    7,832
    --https://en.wikipedia.org/wiki/Color_vision#Mathematics_of_color_perception

    It isn't a problem; it's a feature.
     
  22. iceaura Valued Senior Member

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    30,994
    The one problem is not that many wavelength combinations produce a given color, but that several different colors are produced by any one wavelength combination.
    (The other problem, closely related, is that distances between colors are neither unique or transitive).

    That's not a "feature" of any vector space, or any distance function.

    You have it - my posted observation - backwards, in other words. That seems to be an effect of your insistence on posting about wavelengths ("spectral colors", etc) when the topic is colors. I recommended that you attempt to post about colors, without reference to wavelengths or the EMR spectrum or any other irrelevancy of the kind - that recommendation stands.

    Wavelengths of EMR are not colors. Colors are not wavelengths of EMR. Four pages in, we have made at least that much progress - we can move on, eh?
     
  23. arfa brane call me arf Valued Senior Member

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    Please point to some region in the CIE diagram, or some other standard gamut, where several different colors are produced by any one combination of wavelengths.
    But if you use three reference colors with fixed wavelengths (again, this is an ideal not a physical reality), you do have fixed distances between them.
    How about posting a design of a color display, without any reference to colors?
    Of course, this design will need to refer to something; usually things like the visible EMR spectrum, duty cycles etc.

    ed. It might surprise you that there are a lot of electronics engineers who know that a wavelength isn't a color; they also know that the wavelength of a color is meaningful if the color is monochromatic (i.e. "pure").
     
    Last edited: Dec 17, 2019

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