The most important means of examining perspective is exploratory motion----simply moving your head left to right is enough to reveal to us whether or not we look at a flat picture or are looking at the real thing. A real thing in three-dimensional space can be walked around and perspective flows continuously. Or we can rotate the object in front of us. If we look at a drawing of a hypercube, no matter how we move around that image it remains static, frozen in the perspective its depicted in--with just the information to suggest depth available to us--but was is depth in the fourth dimension?
This is where animation enters the topic of perspective----an animation can simulate the exploration of true depth in three-space by presenting a continuous series of perspective drawings capturing the flow of motion experienced in changing points-of-view. . . which reveals dimensionalities concealed or only suggested from a single point-of-view: even though we live in three-dimensions and see in greater ways than Flatlanders, we see essentially a world processed via a 2ish dimensional retinal image.
This chapter made me think of holograms----a hologram can be a flat plate which still reveals true perspective and as it is rotated reveals a three-dimensional representation----it's not like the flat photograph that obviously isn't the "real" three-dimensional thing; it's an image which preserves depth and perspective even after undergoing exploratory movement----how can holography be used (possibly along with animation if such technology was available) to image four-dimensional figures? I don't know.