Do you think, that there are three fundamental colors due to the three dimensional space? That would mean that in order to sense four dimensions, our sight should recognize X^4 rather than X^3 colors, where X denotes the number of all possible shades of one of N fundamental colors, i.e. in computer science X=256.
I think it's incorrect, because both 2D and 3D contain the same colors, so why should 3D and 4D be different. Thus, if we generalize this, we get:
"All objects have the same spectrum of colors no matter the dimension." (|)
But, colors are the result of our brain interpretation rather than an outer factor, so that would mean the first statement has more neurology than psychics in it. That is, a cat sees a different palette, a fish sees a different palette and a human sees a different palette. So, to make the color hypothesis clearer, one should answer "Is the palette of the perceived world, constant?", i.e. Colors <live> inside objects and exist under the support of light rather than depend on ones perception.
Attempt to answer: Following the famous results of neurology (all combined neural network of trillions of neurons surrounded by synapses and communicating through *individual electrical signals* coming from senses, including sight), it yields that - since brains of "all"(<- this is a weak guess, supported statistically) known living brain-having things have the same system of neurons(another, highly likely guess), it means that "signals of all living are carried identically" => "sight signals are carried identically" => "colors living see are identical, but interpreted variously, depending on the kind.".
Okay, now what? So colors are the same, independent of the living thing's mind,
thus attached to "outer" or "empirical" objects. (this sounds little philosophically, but as much possible, with supportive arguments, think of "outer" as physics, which it is).
Now, colors and their shades... 2D = 3D why should 3D<>4D or even 4D<>5D (2nd paragraph), I simply think that color is a general property, like weight, it exists in all dimensions (all 11 of them, following string theory)
I feel like something came out, but maybe I'm completely wrong...
This doubt is explainable, since my arguments aren't as strong as
those in pure maths, so...
Any more ideas?
Maybe the above generalization (|) is too rough?