Ripheus23

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Research using virtual reality finds that humans, in spite of living in a three-dimensional world, can, without special practice, make spatial judgments about line segments, embedded in four-dimensional space, based on their length (one dimensional) and the angle (two dimensional) between them.^[12] The researchers noted that "the participants in our study had minimal practice in these tasks, and it remains an open question whether it is possible to obtain more sustainable, definitive, and richer 4D representations with increased perceptual experience in 4D virtual environments".^[12] In another study,^[13] the ability of humans to orient themselves in 2D, 3D and 4D mazes has been tested. Each maze consisted of four path segments of random length and connected with orthogonal random bends, but without branches or loops (i.e. actually labyrinths). The graphical interface was based on John McIntosh's free 4D Maze game.^[14] The participating persons had to navigate through the path and finally estimate the linear direction back to the starting point. The researchers found that some of the participants were able to mentally integrate their path after some practice in 4D (the lower-dimensional cases were for comparison and for the participants to learn the method).

That's from the Wikipedia article about four-dimensional spaces in general. It makes me wonder if my notion of a sort of "purpose" in the universe, consisting in the transformation of our physical perception into a geometrically (not---quite---mystically) higher-dimensional form, is possible, at least in the sense that concrete understanding of 4D-space would help with deontic logic, say.

Now, actually, I haven't mentioned it fully yet, but there's a cognitive argument for a 5-dimensional limit on our physics theories, sort of. Namely, we can use dimensional analogies to "intuitively" compute 4-dimensional structures, e.g. as by saying that the net of the tesseract is a layout of cubes just as the net of the cube is a layout of squares. We also have faithful rotational analogies (the gem-like imagery on Wikipedia, for example), stereographic projections, etc. We have some of these for 5D-space, but they are intuitively weaker, depending more on abstract than tangible geometrical analogies. So, 5D-space is the "cognitive limit" of analogical intuition, so (on Kant's scheme, say), it is the limit of what we can acquire empirical evidence of (for the time being!).