6 Dimensional visualization with a splash of color

Discussions about how to visualize 4D and higher, whether through crosseyedness, dreaming, or connecting one's nerves directly to a computer sci-fi style.

6 Dimensional visualization with a splash of color

Postby Frisk-256 » Sat Dec 30, 2023 8:35 pm

There is this thing I like to call a "Chromatic Dimension". a chromatic dimension is a dimension of color. Like how a spacial dimension is a dimension of space, and a temporal dimension is a dimension of time. humans can observe 3 chromatic dimensions, it could be the responsivity of our long, medium, and short cones in our retina, it could be RGB values on a screen, or it could be HSV in a painting program. the axis of chromatic dimensions can be defined very diferently. Like Cartesian, polar, and spherical coordinates in 3D space. if a human wanted to visualize a 6 dimensional shape, you could lay out the 6D object and your human's perception like this:

(X,Y,Z) (R,G,B)
and we can visualize our visualization like this
( x , y , z , w , v , u )
( X , Y , Z ) ( R , G , B )
I actually have a model of this, but only for 4D. The more magenta a point is, the more positive the W coordinate is, the more green, the more negative, and the point gets grayer the closer the W coordinate is to 0. The Tesseract in the example is rotating through 4D space randomly. Here is the link to the Desmos 3D graphing calculator graph
Have fun!
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Re: 6 Dimensional visualization with a splash of color

Postby Keiji » Tue Feb 20, 2024 8:09 pm

Hiya! This is something I've noticed myself actually. :)

We can express colors as RGB, HSV, and various other triples, because we see colors in three dimensions (or at least, most of us do). Colors are technically infinitely dimensional (or at least, very highly dimensional, if quantum mechanics imposes some minimum difference between two possible wavelengths). It's just that displays - and, to a lesser extent, paint and ink mixing - were developed specifically towards what we can see, and only mimic real colors. The difference from "the real thing" is imperceptible to most people.

We can also express colors as CMYK. This is a four-dimensional space, used for color printing, with K being black. We can make black by mixing C+M+Y, but doing that would be a waste of the (more expensive) color inks, and would put more ink on the paper in total to achieve the same result, meaning it's more likely to smudge or stay wet, etc. So some software algorithm will decide how much "darkness" to "move" from CMY to K. When it's actually printed, there really is a four-dimensional value physically on the paper, if you think about it: the four inks are four different chemicals, after all - they will just collapse to three-dimensional values when we look at them.

I think the situation with rods and cones is interesting: there are there types of cones, so our sight should be four-dimensional, one dimension for the rods and three for the cones. But I see that rods are generally used for peripheral vision and low light conditions, while cones are used for where we're focusing and in well-lit conditions. Perhaps, though, on the border between our focus area and our peripheral vision, and when the ambient light is somewhere between "good light" and "dim light", could both types of receptors be excited to similar extents such that four-dimensional color viewing actually becomes possible? In theory, I can't see why it wouldn't - but in order to make any use of it, you'd probably have to live your life trained to do so from an early age, which in practice would never happen :)

There is also tetrachromacy. Skimming this Wikipedia article, it's known that many humans exist whom have four types of cone cells, each detecting a distinct wavelength, but we apparently don't yet know whether anyone actually perceives four-dimensional color, or whether in these cases the responses from two cone types just get mixed together to give usual three-dimensional color perception. I think more research is needed in this area! If indeed true perceiving tetrachromats exist, then with enough effort, these individuals would surely be able to differentiate between a real object and a digital photograph of the object by color alone, at least for certain ranges of colors, because the digital reproduction of the image wouldn't match what they saw from the real thing due to being able to perceive the extra color channel. A "trichromat" (a person with "normal" color vision), compared to a perceiving tetrachromat, would be relatively color-blind!

Also, your link doesn't seem to work for me. I don't know if that's because it's been nearly two months since (sorry!) or because of something specific to my computer. It just sits on what looks like a loading animation.
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