Is it conceivable that the human brain could be genetically engineered so that people could mentally visualize higher dimensions?
I would imagine that Riemann's Conjecture might fall fairly quickly, if mathematicians could clearly picture the complex functions on a single 4-D graph—just for instance.
But mainly, I like to imagine having such an ability, because being able to create and see brightly colored N-Spheres and 4 and 5 dimensional Archimedean solids—and so on—would be incredibly beautiful.
I imagine that the more dimensions, the harder it would be to visualize. I have no great hope of enabling the brain to visualize 144 Dimensions.
Having said that, is there a logical reason to think—that if we could do it at all—that a certain number of dimensions would be a reasonable upper limit to what is achievable? 5-D? 7-D? 17-D?
There should be some way to mathematically figure out how much the demands on the computational power of the brain would increase with each dimension.