What if you bend spacetime around the shortest path so that it becomes a straight line?
Does it work if you keep going up in the dimensions? That is, is there a 4 -> 3 equivalent of the 3 -> 2 -> 1 move you just did?
Euclid was amazing for having stood the test of time for 2000 years and is still useful in everyday situations,.
But Gauss really took us beyond to whole different realm, simply by asking the unthinkable.
I think it’s at this point that I swap over to fractional dimensions, the degenerate circles and such. Our cognitive abilities are limited for visualization, and while we could experience the flow of such a projection we would not be able to map it to our grid cells or place cells if smooth.
If it’s not continuous it might be possible to process it cognitively but if it’s a continuous rotation at the levels you’re talking, we’d be lost entirely.