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On the high-wavelength side of things, we see almost-infrared as reddish, with a slight tinge of magenta. On the low side, we see violet fading into the same magenta color. Why is that?

You can see it clearly on any hue chart. There's an unbroken flow from one to the other, even though the wavelengths are literally as far apart as they can be while still remaining visible.

I understand that color vision is limited due to several biological factors(cone receptivity, absorption, etc), but why do the colors on both side fade into each other? Is it just our brain making things "neat" and continuous?

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Basically. You are most likely looking at the electromagnetic spectrum, which is linear and conveniently makes sense... except for magenta.

Colors as we perceive them are additive and made up of Red, Green, and Blue; this is opposed to subtractive color we learned about while finger-painting in kindergarten (Red, Yellow, Blue). The three types of cones in our eyes each are sensitive to one of these colors, and it is from the combinations of Red, Green, and Blue that we see all the colors we see. Yellow, for example, is when the red and green cones are both stimulated. Purple/violet is from red and blue stimulated together. This is the single special case, as you point out, because red and blue are at opposite sides of the spectrum from each other. Our brain has two options:

  1. Use the color smack-dab in the middle aka Green
  2. Make a new one as if they wrapped around

Green is far away and already taken, so our brain intelligently invents Magenta. This produces, instead of a linear EM spectra, a circular color wheel that looks very intuitive.

Hue circle

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I understand RGB(software developer), and I see what you mean about a red/blue mix needing an invented color, but what about (almost) pure infrared? With a (strong) very-near IR laser, you'd expect it to appear as red, but it still gets closer to magenta as wavelength increases, even though there shouldn't be any blue/violet light to mix. For example, in a very dark room, I can see my TV remote IR led, and it is definitely not just "red". –  Geobits Aug 29 '13 at 16:39
    
TV remotes are often not pure IR. At that level, the long tail of the faint visible colors can be enough to stimulate a color; you are not seeing the IR being rapidly sent. Some cameras (my laptop does it) will show IR, often as a neat little purple. That's a good test to see what you're not seeing. –  Amory Aug 29 '13 at 17:16
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Yes, playing with my camera is what led me to the question, since even there they pick it up as some shade of purple, depending on hardware. I think the bit about the faint visible colors is the primary answer. –  Geobits Aug 29 '13 at 17:32
    
@Geobits yes, I have noticed this in my UV-camera image sensor observations –  user3795 Aug 29 '13 at 20:19
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The question has an invalid premise. Namely, that the UV light looks like magenta/purple. It is not the case. While it it true that approaching UV end the perceived color becomes more purple (because the red protoreceptors have a second maximum there), moving further to the UV area (which is possible if the eye has the lens removed), makes the perceived color more whitish/light blue because the green receptor also has a second maximum there (somewhat further than the red one).

I do not know why the IR has magenta color though. It could be because of not pure source. Try using a warm piece of metal to see if it becomes more purple as it cools, I think it does not.

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