Inhabiting the world of textiles is like living in a castle where I’m constantly finding hidden doors that lead to whole wings full of treasures that I hadn’t imagined existed. I’ve come across two instances of that this week. Both have Latvian roots. I’ll comment about one today and the other tomorrow.
Donna Druchunas, author of Arctic Lace, brought a small, amazing book along on the trip we both took recently to Alaska. She loaned it to me to read on the flight home, although I ended up trying (unsuccessfully) to sleep instead.
Last night, I opened the book and read the whole thing. It’s A Field Guide to Hyperbolic Space: An Exploration of the Intersection of Higher Geometry and Feminine Handcraft, by Margaret Wertheim. Although the topic is non-Euclidean geometry and my last math class was algebra 2 in high school, I loved this well-written, beautifully designed little book. It talks about theoretical math in terms I can understand: crochet.
Here’s a note from the web site of the publisher, The Institute For Figuring, that explains the basic concept better than I can: "For two thousand years mathematicians knew about only two kinds of geometry—the plane and the sphere. But in the early nineteenth century they became aware of another space in which lines cavorted in aberrant formations. Offending reason and common sense, this new space came to be known as the hyperbolic plane, in homage to its abundant excess of parallel lines. Though the formalities of this space were known for 200 years, it was only in 1997 that mathematician Daina Taimina finally worked out how to make a physical model of the hyperbolic plane. The method she used was crochet. Here, IFF director Margaret Wertheim presents a brief history of hyperbolic space and a field guide to its crocheted manifestations."
Latvian mathematician Daina Taimina (she’s now at Cornell University) first tried making a model with knitting, but the number of stitches that accumulated on the needles made the results cumbersome and impractical. So she shifted to crochet.
I read an article about Taimina’s work by Michele Lock in the 2005 issue of Interweave
Crochet, but I didn’t connect with it at the time: hmmm, interesting; not WOW! I’ve needed to go back and rediscover the article. Sometimes the time is right for the lightbulb to go off.
That article includes instructions for crocheting one type of hyperbolic plane. A Field Guide to Hyperbolic Space suggests several other ways of playfully approaching this exercise. While we’re talking serious mathematical theory here, we’re also talking fun that is showing up in the ways that contemporary crochet designers are manipulating hook-and-yarn.
The Institute for Figuring has asked people to send in images of their hyperbolic planes (at their web site, see "Gallery" and then "The People’s Hyperbolic Gallery"). There’s a related interview on the site as well . . . one that my daughter, who minored in math, may need to read, too. . . . If you look at it and start glazing over because you’re not a mathematician, I’d recommend that you check out the book anyway!
If Taimina had not been born into a culture that valued handcrafts and had not also trained as a mathematician, the ideas of hyperbolic space might have been developed but there would probably be no effective model. There certainly wasn’t one before she had her AHA! moments. And the models that she has devised explain the concepts (and thus prepare the way for further extensions of the ideas) in ways that no other medium could manage.
You can get as deeply and as seriously into this as you like, or you can just dip in a toe and play. Math that seems like magic, and that connects with my fingers, yarn, and a crochet hook, cavorting in aberrant formations, offending reason and common sense. . . . Does life get any better?