Connections

Last week in Linear Algebra, we started in on abstraction - general vector spaces and the like. I made some brief comments on the concept of dimension - not the precise idea used in linear algebra, but a more general one - and one of the students asked about visualizing four-dimensional objects with three-dimensional images. I went off on a brief digression about tesseracts and their three- and two-dimensional shadows, drawing a picture of the latter.

Today, after class, another student came up to me and said he'd been thinking about what I'd said, in the context of Plato's Cave. It's a fairly obvious connection to draw, if you know (on the one hand) enough mathematics and (on the other) enough history of philosophy; but it's still nice to see a student drawing cross-subject connections.

I suggested that he read Abbott's _Flatland_; it's not quite in line with what he was talking about, but he might find it interesting.