Moebius bands are neat; they seem to me to be almost literal "wrinkles in time," or rather in space, and it seems that they can provide a transition into higher dimensions. A Moebius band itself seems to be intermediate ground between the second and third dimensions.
I like the handedness discussion as well (enantiomorphic pairs). I like the fact that objects can be completely analogous but still not quite the same, in fact, in a certain sense, almost opposite to one another. It's interesting that a Moebius strip gives this kind of pair the necessary freedom to become identical. I think it all comes from the twist in the band, if we could duplicate that twist from three- into four-space, we would have the gateway into the fourth dimension. So, it's maybe more a question of a twist (or a wrinkle) than a jump into a higher dimension. I like that.
Would a Moebius band do weird things to perspective if we were small enough (or it was large enough) that we could wander around on it? What about if the Moebius band wasn't made from the semi-transparent material described in the book, but rather from a shiny, reflective surface? What about a Klein bottle?
Prof. Banchoff's responseAnya Weber