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Sunday, March 13, 2005

Women's Work

You remember the Great Summers Squall, in which my aggravation at frail and wilting biologists was matched only by my irritation at those manly men who knew all along that womens warn't no good at figurin' and such. Not like a man, nowise.

Toward the end of this post I mentioned something about writing a paper about shapes rotating in 3D. When I was studying these things in the first place, it was true that I (as befitting a girlie) found visualizing some of the geometry a little difficult.

So I taught myself how to use Mathematica to render and rotate the shapes, and figure out some angles I was having trouble with, and I was good to go.

Another woman with a similar difficulty (shared, in this instance, by many men), took a somewhat different approach. She crocheted some hyperbolic surfaces. The beauty of this approach, besides creating attractive and durable models, is that you can demonstrate such concepts as geodesics, parallel lines, and non-Euclidean triangles.

Not only that, but I think that models such as this and this would make nifty Christmas ornaments, if rendered in metallic yarn or thread.

(In this interview with married mathematicians David Henderson and Daina Taimina -- Taimina was the one who thought to crochet the surfaces -- has this disturbing note:

One of the things that's changing now is the advent of computers, which can help us to visualize mathematical objects. That is helping to bring back what's called the "intuitionist" approach, which was there in the past but got blotted out by the "formalist" tradition for much of the past century. The formalists, wouldn't accept anything unless it was expressed by equations.

I didn't realize that there was such a thing as mathematics that wasn't expressed by equations. Oh, I knew that there were calculations that were much easier when done by computational methods but I always assumed there was a big, hairy equation lurking in the back somewhere. It was too much trouble to work out, but it was there. I'm very suspicious of things labelled "intuitionist"; it's too often a synonym for "bullshit".)

Anyway, here are some instructions, if you want to try it yourself. I learned to crochet when I was little, but I find these instructions confusing. Perhaps if I had the yarn in my hand, they'd be clearer. (We -- my sister and I -- pretty much limited ourselves to Euclidean planes when we were learning.)

On the topic of mathematical yarncraft, here's a model of the Lorenz manifold, and the instructions (in the form of a PDF file) to go with it. The paper says that this is much harder than the hyperbolic surfaces. (The Lorenz manifold was found via this crocheting blog.)

And, finally, a Klein bottle woolly hat (sold out for now). Made -- not by, but to the specifications of -- the guy who also sells glass Klein bottles. The guy happens to be Cliff Stoll, who wrote The Cuckoo's Egg, and Silicon Snake Oil. The former book led to him portraying himself in a NOVA, in which he was shown showering with his girlfriend, and then scampering out naked in order to answer the phone. Niles and I agreed that, should we ever be subjects of a NOVA episode, naked scampering will be Right Out. The world will thank us.