Mentally simulating objects in higher dimensions is one of the most straightforward examples of the limitations of the human brain that an AGI would not have. Mathematically, there's little difference between 3D and 4D. It's trivial to program a computer to simulate either. But to us humans built by evolution in a 3D world, such things are off-limits.

...Or are they? Humans can learn echolocation, despite that seeming like a pretty hardcoded sort of sensory ability, and not one that humans evolved to use normally. Blind mathematicians may make better topologists, working with such concepts in a way that does not privilege 3 dimensions. This implies that 3D visualization too is a learned skill rather than an innate one.

Taking some inspiration from Mikhail Samin's recent success at a similar task, I would like to learn this skill. The most promising avenue I think would be to tape my eyes shut for several years to see if I can recreate the experience of being blind. But that would be a little more disruptive to my other pursuits than I'm willing to put up with. I'm open to other ideas.

If we gain the ability to make this happen via technology, it counts towards this market only if I retain the ability once I am back in the normal world. The same for if such an experience is induced by drugs; I must retain it once I'm back to my normal self.

If my mind is altered permanently to the point where this stops being an interesting question, this resolves N/A.

To resolve YES, my ability to answer questions about characteristics and movements of conceptual 4D objects must be roughly equal to my ability to do so with 3D objects, though I'll accept a small penalty since even to a computer the overall complexity of N^4 points must be higher than N^3.

I should be able to play games like 4D golf, 4D Minecraft, and Miegakure without the massive disorientation that most players experience. (Though of course trying to learn the structure of such worlds from a 2D screen is equivalent to trying to learn the structure of a 3D world via a single row of pixels; an extremely limited bandwidth channel. So I still wouldn't expect complete fluidity.)