Professor Banchoff, I've only read seven and a half sections (reading from the computer screen is not fun), but I do have some problems already.
It isn't that easy reading from a screen. Maybe someone should invent a laptop that feels like a paper book.
For instance, what does it mean that studying and upholding one's intellect can increase a Flatlander's angle as much as genetics? And how are there any lower-class citizens at all, if, with each successive generation, the number of sides increases? If evolution does not follow the same rules in 2D and 3D, what natural processes are different in 4D and 3D? Also, does the pull toward Flatland's southern direction correspond to our force of gravity?
The idea that acquired characteristics can be passed on to offspring was a controversial idea at several stages in the history of science. Perhaps it would be good to investigate the status of this "Lamarkian" idea in Victorian England. The equilateral class is replenished by isosceles triangles who make the grade only after many generations of approaching 60 degree angularity. That is discussed somewhere in the book, perhaps later on. The precise demography is not all that well developed. The gravity notion is not so clear. It may be due to some curvature of space, or perhaps a slant of the otherwise horizontal plane? It may also be useful to think of Flatlanders as rather flat fish in a narrow vertical aquarium.
I found the allegory of the cave very helpful in understanding that we take for granted our perception of reality and that things that seem shadows or reflections in our world could actually have more substance.
It's one of the best allegories for this study.
Drawing a hypercube, however, is still not easy. I'm looking forward to making more clear my very muddy understanding of all this.
Hypercube drawing comes much more easily with practice. We'll do a lot.
--Alison_Tarbox