I just reread Flatland...remember the part where the sphere takes A. Square out of Flatland and shows him the 3D world? Well, I don't think he could possibly understand it the way he does in the book. As we already know A. Square's vision is a line, meaning the sphere could not show him a cube the way the sphere sees it. All A. Square would see is one line of it. Even if he were moved past a cube or a sphere all he would see is lines. So really the only way he could understand it is if he was smart enough to visualize it and see it for what it really is.

So my question is this: is it possible for any being of n dimensions to truly visualize a figure of n+1 dimensions? Obviously A. Square does so for the purpose of the plot, but could he actually do it in reality? I'm not so sure.