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Growing up, I used a lot of image editors or clipart game producers that gave you the option to vary a color over its gradient. Now computers process things discretely enough, so the gradient would be discretely projected, albeit appearing continuous.

Color solids organize gradients, but with a relatively discrete pattern. Otoh in set theory I've read of sets of colors whose cardinalities exceed aleph-0.

Now the examples aren't strictly of Continuum-many colors, though if the cardinal chosen were believed to be the Continuum...

(Iirc Hume performs a thought-experiment about filling in a gap in color gradience via imaginative "inference"/projection, but I don't recall the outcome of the "experiment.")

Are color gradients at least non-discrete, if not continuous? Or, can they be so, though not necessarily?

Kristian Berry
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    Can humans distinguish a continuum of colors? No, they can only do so for finitely many shades. So if by color we understand human "qualia" the answer is no. In physics colors are modeled by points in color space with homogeneous RGB coordinates, and those, of course, vary continuously. It does not make sense to ask whether colors "truly" are discrete or continuous any more than whether lengths or masses are, models use them to finite precision only, and that does not discriminate between discrete and continuous. – Conifold Sep 02 '20 at 17:56
  • You should be more discerning in your checkmarks IMO. See my comment below the checked answer. – user4894 Sep 03 '20 at 05:40

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This is basically a physics questions as I understand it. Color perception in animals is based on a privileged surface of the body responding to excitation by photons whose wavelength corresponds to a narrow band of frequencies on the EM spectrum.

Note that photons can have arbitrary energies, and hence arbitrary frequencies; so in that sense we could suggest that in principle you might suppose you could produce a continuum many 'distinct' frequencies in the neighborhood of any specific frequency...

But in practice any physical oscillator is going to be "quantized", in terms of the frequencies it can generate. So as far as I understand you are not going to be able to construct a machine that can generate fully 'arbitrary' frequencies (e.g., a continuum many colors).

Joseph Weissman
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Real physical colors, such as a rainbow, grade smoothly. Each color is defined by a specific photon energy and this energy may take any value; it is even a little blurred out by quantum uncertainty, so two very similar quanta may actually overlap their color possibilities.

Perceived colors are a product of brain function. Here the number of red, green, blue and monochrome light levels that we can distinguish are all limited, so the number of perceived colors is finite. Some people can perceive more than others.

Guy Inchbald
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  • "Real physical colors, such as a rainbow, grade smoothly." There's no possible experimental verification of this fact, is there? Electromagnetism is quantized and as you yourself point out, there's quantum uncertainty. For all we know, wavelengths (not colors, which are subjective perceptions) are discrete and not continuous. It's ok though, you got a checkmark from the OP who believed you. – user4894 Sep 03 '20 at 05:39
  • ps - The crux of my objection is that if there is a perfectly smooth gradation of frequencies in nature, that would amount to instantiating the mathematical continuum -- the real numbers -- in the world. Physics has no theories to account for such a thing. If it were true, then the Continuum hypothesis would become a matter of experiment. Until I see physics postdocs writing grant applications to investigate CH, I will not believe that anyone takes smooth gradations of frequencies seriously. What do you think? Am I wrong? – user4894 Sep 03 '20 at 05:55
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    @user4894 You grossly misunderstand the nature of quantization and uncertainty. Quantum theory reeks with real, imaginary and complex numbers. So too do relativity and thermodynamics. Your continuum thesis again wholly misconceives the quantum-vs-continuum debate. There is insufficient space here to explain more, you should go seek clarification on the physics SE. – Guy Inchbald Sep 03 '20 at 08:15
  • I'm perfectly comfortable with real, imaginary, and complex numbers. If frequencies transition "smoothly," taking on every value between two numbers, they must take on, for example, noncomputable values. That would destroy all the believers that physics and/or the actual world are computable. I don't think you understand the nature of the mathematical continuum if you think frequencies can take all possible values smoothly. That's an idealized model used by physicists, but you have no way of knowing (as you claim you do) that the world works that way. – user4894 Sep 03 '20 at 08:26
  • I have had this conversation with physicists (or pretend ones on forums) and I have never gotten a satisfactory answer. Physicists don't think about the issues involved, so physics SE would not IMO be helpful. They think the real numbers are real. But thanks for the suggestion. – user4894 Sep 03 '20 at 08:28
  • See https://physics.stackexchange.com/questions/169209/is-there-an-infinite-amount-of-wavelengths-of-light-is-the-em-spectrum-continuo. Even there the checked answer is wrong and the other responses are correct. And the checked answer claims there are uncountably many frequencies but gives a different answer in the text. In a finite universe, the possible frequencies must be quantized; and in any case, we couldn't measure frequencies with sufficient exactness. Your answer is flat out wrong. You should try to think this through. – user4894 Sep 03 '20 at 09:31
  • "Real colours" seems to be an oxymoron if it implies materialism or scientific realism. Also, there is a difference between quantification being relativised to continuation by uncertainty and the uncertainty whether a photon does indeed have a given (quantified) wavelength at a given space-time. The former is a misconception of quantum uncertainty IMHO. – Philip Klöcking Sep 03 '20 at 10:23
  • @user4894 Twenty-four physicists agree with the post you complain is incorrect. You are not a physicist. "I have had this conversation with physicists (or pretend ones on forums) and I have never gotten a satisfactory answer." can hardly come as a surprise. – Guy Inchbald Sep 03 '20 at 10:27
  • @PhilipKlöcking Not at all. By say "a red colour", a scientific realist is referring to a specific range of objective wavelengths, not to some subjective quale of experience. – Guy Inchbald Sep 03 '20 at 10:33
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    I checkmarked the answer I did as it seems both concise but comprehensive enough. If light can exist as a probability amplitude deep down, then even if each "string" of light is discretely separate from others, internally it is continuous as a "string," even in a full string theory. As for perceived colors, different animals are thought to perceive larger or smaller numbers of colors (over their gradients) depending on discrete cone/etc. structure so that part of the answer seems true too. – Kristian Berry Sep 03 '20 at 15:00
  • Continuous seems intuitively correct: one can conceivably engineer a frequency of any geometric (algebraic?) number - and that includes rational numbers - which are continuous. I don't know about uncountable vs countable - but uncountable isn't necessary for continuity. – ptyx Sep 03 '20 at 15:29
  • @KristianBerry That is close enough, if a little unorthodox in language. There is one complication; although such a quantum exists as a continuum of possibilities, it can only be measured as a discrete value. Thus, while the nature of reality is continuous, observed reality is not. This is really just the eye of the observer extended to include their instruments, so I left it out. I can add it if you like. – Guy Inchbald Sep 03 '20 at 15:59
  • @Guy, First YOU are not a physicist, I checked. Secondly, the checked response over there has a headline that is the opposite of what is claimed in the text. Do you believe a frequency can be a noncomputable real number, for example? Very curious to hear a yes or no on this question. – user4894 Sep 03 '20 at 18:00
  • @phyx, There aren't enough algebraic numbers to make a continuum. You need to toss in the uncountably many transcendental numbers, including the noncomputable ones. Do you think a frequency can attain a noncomputable value? GuyInchibald seems to be claiming that. – user4894 Sep 03 '20 at 18:04