I want to re-visit your question about "why WHITE - where did that come from".

I defined f(x) like this:

f(x) = (x + 1) / 2

Then I interpreted that visually as the process of averaging the unknown color with white. 

In so doing, I had to divide by 2. What color is 2, is that DOUBLEWHITE? How come you didn't freak out about that part? 

Technically, you should also be demanding to know what color is 2 and how the heck did I know to use that color.

Well it's not a color, and 1 is not a color either. They are numbers. Or in the case of color arithmetic, actually a tuple or vector (3 numbers grouped together in a unit).

I think if we leave off any interpretation of information, everybody is comfortable with the mathematical concept of average, right? Specifically to get the average to two things, you add them together and divide by 2. No problem with that one right?

(a + b) / 2

Well that's all I was doing - just taking the average of two numbers. It just so happens these numbers are being used to interpret colors.

I made this choice because I wanted to take what was hidden and make it revealed to you.

Given that you can only see numbers between 0 and 1, I had to find a function which would produce two different results, but that both results would lie in the visual unit range 0 to 1.

In other words, given my knowledge that you don't accept the math per se, my goal was to find a straightforward manipulation of the two colors such that I'd produce new colors that were not hidden colors, and were visibly different from each other. Thus you would see that you got two different results.

To put it in magical terms, I wanted you to see two "identical" coins (as far as your eyes showed you they were identical) go into a jar, and then come out of the jar different.

So I chose to do (x + 1) / 2. This was intentional and arbitrary. There are an infinite number of other functions that would have achieved my goal. But this was a simple one and also one that had what I hoped was an obvious visual interpretation, i.e. taking the average of two colors, or "blending" paints in 50/50 proportion. What I was trying to reveal was that one of these paints was magical. Even though the two paints looked exactly the same, when I mixed these paints each with white paint, in 50/50 proportion, I ended up with different colors. Magic? Yes, if you don't know what was hidden from you. (The -1 in red.) Not magic at all to the magician, who set the whole trick up.

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Renderosity forum reply notifications are wonky. If I read a follow-up in a thread, but I don't myself reply, then notifications no longer happen AT ALL on that thread. So if I seem to be ignoring a question, that's why. (Updated September 23, 2019)