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Comment by thaumasiotes | Hacker News Reader

> This is like saying that we need a rigorous theory of color in order to be convinced that black is darker than red.

You do, if you want to be right. The fact that you can get people to agree with you doesn't make you right, and red is frequently darker than black by some pretty normal definitions of "darker". Red and black are differentiated by the shape of their reflective spectrum, not the amplitude.

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You guys are basically arguing over Moore's here-is-one-hand problem.

https://en.wikipedia.org/wiki/Here_is_one_hand

pavelrub's point is that you sometimes have less reason to believe the axioms of your formalization than their derived consequences. We have better reason to believe the intuitive idea that 2+2=4 than we do any putative axioms of arithmetic. If we derived that 2+2=5 from some particular axioms of arithmetic, we would conclude those axioms were wrong (or rather, were not the proper system for formalizing 2-plus-2-ness) rather than conclude that 2+2=5.

Pure black is never lighter than any shade of red, by any definition of "dark" or "lightness" that I'm aware of. The point here is that again the words "dark" didn't come into language from some rigorous theory of color - the process is reversed. A theory of color can never show that red is darker than black, because this would simply be a misuse of the word "darker", in the same way that no valid axiomatization of the naturals can possibly show that 2+2 != 4.

There is no pure black in the real world.

There is theoretical pure black in any modern representation of color. If the term confuses you, you can replaces it with #000000. If the black vs red comparison still confuses you, you can replace it with #600000 vs #FF0000. You might also want to address my actual argument, instead of irrelevant technicalities.

How are you getting a "theoretical pure black" without having a rigorous theory of color? If you're just going to call some things black and some things red, you'll find that a lot of things that people call black are lighter than a lot of other things that people call red.

I’ve already told you what to do if the term “pure black” causes problems. The color represented by #600000 on my monitor is always darker than the color represented by #FF0000, regardless of the existence of any theory of color. If you claim that some formal theory of color convinced you of that, then it would mean that a different theory of color could conceivably convince you otherwise. But this is clearly impossible: We would say that any theory of color which shows that #600000 is lighter than #FF0000 is simply misusing the word “lighter”. This shows that our understand of what “lighter" and “darker" mean is independent of any theory of color, and in fact this understanding is a precondition for the development of such a theory to begin with.

But none of this is true. #600000 on your monitor might be lighter than #FF0000 on your monitor if they're compared at different times, or if part of your monitor happens to be in the shade. Or if I have a weird viewing angle to your monitor.

If you want to argue about what #600000 and #FF0000 should look like, you're back to a rigorous theory of color.

No, because I can be very specific about the condition of my monitor, without reference to any theory of color (I can just say: in the exact conditions my monitor is in at this moment, or in the conditions of a darkened room, where no external light source can make #600000 lighter than #FF0000) . I can hypothetically also show you my monitor in person, in any conditions I choose. In fact I don’t even have to talk about my monitor or those specific colors. We can talk about the color of space as seen from the ISS on the dark side of earth, versus the color of the sun when visible from the ISS. Or the color of my room at night vs the color of a candle flame. There are millions of examples we can think of without talking at all about any theory of color. I mean - it is a matter of fact that words such as “darkness” and “lightness” existed before the invention of rigorous representations of color, and that the numerical definition of those words was designed on purpose to coincide with their existing meaning, and not with some new arbitrary property of color. So I’m not even sure what you are arguing against.

But the whole argument about colors is really unnecessary, I only used it because I thought it would be simpler to understand, but I might have been wrong. If you don’t think that it supports my argument about 2+2=4, feel free to ignore it and address the argument itself.

> There is theoretical pure black in any modern representation of color. If the term confuses you, you can replaces it with #000000. If the black vs red comparison still confuses you, you can replace it with #600000 vs #FF0000. You might also want to address my actual argument, instead of irrelevant technicalities.

So you're using a numeric representation of colors (RGB) to prove to me that black is darker than red.

By doing this, you're basically proving my point.

1) different people may have different opinions on "obvious" statements

2) the simpler the statement is, the easier it is to accept or reject it

If you give me two color plates, one is black, and one is red, I might find people who disagree which one is darker.

But if you give me photo measurements, I will say that one is objectively darker with respect to a specific metric (e.g. visible photon energy flux, YCbCr luminosity, CIECAM02 luminosity).

> So you're using a numeric representation of colors (RGB) to prove to me that black is darker than red.

No, I’m not doing that at all - I’m simply creating a well-defined understanding between us about which colors we are talking about, so that there won’t be any confusion. If you were sitting next to me, I could show you some other two colors in person, with no reference to RGB or to any other numeric representation, and the exact same argument would stand.

No specific metric can ever show that #FF0000, as it is displayed on any reasonably well-balanced monitor, is darker than #600000. If somebody invented such a metric, we would say that this metric is either incorrect, or misuses the word “darker”. This would also be the case if no other metrics existed before it. Therefore it is clear that our understanding that #FF0000 is darker than #600000 is independent of any formal description of darkness, and comes prior to it.

And you are still avoiding, for some reason, my main argument, which had nothing to do with colors, and dealt specifically with 2+2=4.

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