Crocheting Esoteric Geometrica

Via Making Light is this interview with a mathemetician named daina taimina who has crocheted a model of the hyperbolic plane. The really cool thing, though, is that she and her husband just gave a talk at a place called The Institute for Figuring, which in addition to having a cool name, sponsors study at the intersection of geometry and decorative arts. The couple also have a textbook on geometry aimed at undergraduate math majors going into math education. It looks like a nice way into a lot of the more esoteric geometries.

I love geometry, and geometer is one of the many careers I would have if I had many lifetimes. At St. John's we read Euclid, and I did my undergraduate thesis on Kantian responces to the development of noneuclidean geometry, including Russell's first book. In graduate school I took a course on Friedman's book on Kant's philosophy of geometry and mathematics, which I heartily recommend.

The thing that attracts me to geometry, particularly post 19th century, is the weird feeling these hard-to-visualize and impossible-to-visualize shapes give me. I added the henderson and taimina textbook to my amazon wish list just because it emphasizes the experiential. The only time I have become hooked on a video game as an adult was when I encountered one that required you to fly around oddly shaped 3d mazes.

Although I would like to be a geometer, I know I'd be a terrible one. I have almost no spatial sense. I get disoriented if I make two left turns. I'm wretched at standardized tests that involve spatial tasks. I rotate 3d objects in my head like a girl. The only way I could do actual geometry is if I stuck to the totally algebraic and set theoretic stuff that doesn't invole visualizeation. (I guess this is still most of higher level geometry.) But then I would be avoiding the stuff I was attracted to in the first place.

The other important question, since I'm sitting here not working is this: Which would be the better way to have all of the intellectual careers I am intersted in, living several lifetimes sequentially or having multiple contemporaneous instantiations pursuing several careers all at once.