Okay, so this is going way back in the book (I like how way back is page 281...), but Wallace mentions a book called Flatland:

"A good quarter of the bus was yellow-highlighting copies of E.A. Abbott's inescapable-at-E.T.A. book Flatland for either Flottman or Chawaf or Thorp" (281).

I was curious, so I looked the book up online and read a bit of it. It's basically a description of a world in which everything is two-dimensional:

"Imagine a vast sheet of paper on which straight Lines, Triangles, Squares, Pentagons, Hexagons, and other figures, instead of remaining fixed in their places, move freely about, on or in the surface, but without the power of rising above or sinking below it, very much like shadows--only hard with luminous edges--and you will then have a pretty correct notion of my country and countrymen."

The companion talks about it on page 42. Burn explains that it makes sense that such a book would be required for E.T.A.'s mathematical outlook on tennis, but the book's influence seems to extend Hal's outlook on life as well. Basically, he--and his life--lack(s) depth. On page 460 he says that he sometimes cannot believe deLint is real, "and tries to get to the side of, to see whether deLint has a true z coordinate or is just a coutout or projection." And on 517: "Orin and Marlon Bain's view was always that C.T. was less like a person than like a sort of cross-section of a person." Hal has also described himself as being "basically vertical," and according to the companion, will later shift to being horizontal.

I think this ties in with the tendency of E.T.A. to treat everyone as robots with machine-like perfection with no understanding of themselves as people. Everything is so mathematical and shallow, which leaves students to struggle for self-understanding and depth.