Algebra is a programming language for geometry.
If you're a computer artist or web designer, or if you know how video displays works, you're probably familiar with the RGB model of color vision, in which the three primary colors of light: red, green and blue, need to be mixed together to get with different amounts to get any other colors of light. And you probably know also that in order to get a white light, you need to mix all these three primary colors in equal amounts, as seen in the picture on the side. Right?
In 1852, a scientist named Helmholtz has made many experiments with light and colour and these experiments have bring him to very interesting, and perhaps surprising, conclusions.
He noticed, for example, that any color could be reproduced not only by mixing the usual red, green and blue, but also by mixing any three colors! The only condition is for them to be independent from each other: that is, any one of them couldn't be obtained from mixing the remaining two. For example, you can mix such colors of light as: turquoise, magenta and yellow. These three colors of light are independent from each other, so after mixing they also give you a white light. You can observe it in the above picture, too: we can assume that the central spot came out of mixing turquoise, pink and yellow light (for now, we assume that these are monochromatic colors, that is, none of them came from mixing any other light colors, contrary to what has been shown in the picture).
But it turns out that to obtine white light, you don't need to mix as many as three colors: it's enough to mix only two colours of light! :-) The only requirement is that these colors have to be complementary colors, that is, they have to complement each other. Those are the colors which are opposite to each other in the color wheel. For example: yellow and blue, or turquoise and red. Some examples are shown in the following picture:
So why were we always told, and we're being told to this day (repetitively as a hypnotic suggestion) that you need three colours, and that they have to be exactly these three: red, green and blue? Why no one tells us a word about Helmholtz's experiments?
Helmholtz discoveries could give us some new insights into color theory and the perception of colors by human beings. So, in my opinion, we should investigate them more carefully than we have done up to this day. Maybe the white light is not necessarily a mix of all frequencies, but it's somehow related to polarization (the direction of oscillations) of electromagnetic waves of light, or something in that fashion? (I'm not saying that this is the case, but I want make you think about it somewhat deeper)
It's a very interesting puzzle and I encourage you to study it further. Very soon I'll give you its solution, which I figured out during my mindstorms on this subject and the way people perceive colors, and after a series of experiments with diffracting light ;-) (I have repeated the experiments of Newton and Helmholtz, among others, so I can tell for sure that Helmholtz was right with it).
Soon I'll publish the solution of this puzzle here and you'll see that it touches a bit some other controversial topic: energy-saving lightbulbs, which are forced on us by the European Union, and their optical spectrum. So... stay tuned ;-)
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