Check out Margaret Wertheim's interview with geometers David Henderson and Daina Taimina for Cabinet Magazine. When I saw the images of Taimina's crocheted hyperbolic figures, I was immediately struck by how instructive it could be as an applied tool to teach non-Euclidean geometry, because—well, I don't know anything about crochet, but I get the sense that this is true—one could viscerally experience ultraparallel lines or even space curvature. It turns out that Taimina, in fact, invented the first workable model of Lobachevskian, i.e., hyperbolic geometry by abandoning paper and turning to crochet. Certainly makes a great deal of sense after the fact, doesn't it?
Daina Taimina, Crocheted model of hyperbolic plane, 1970s.
See Taimina's pseudosphere, too. And the interview isn't a bad introduction to non-Euclidean geometry, either.
I'd definitely love for them to have expanded on the conversation about hyperbolic forms in nature, particularly the nudibranch. I was happy to see that Taimina was appropriately dismissive of hyperbolic lettuce, which one can find in the grocery store but not nature. The purist knows that exotic forms of geometry are to be found under the sea, damnit. (In another life, I study the Ordovician Period ancestors of my favorite cephalopod and sea creature, the chambered nautilus—how time has humbled that once fearsome predator!)
Nature, Nudibranch, Cambrian period.
And on an unrelated note: If you're interested to see the form of awesome executed in nature, see the eurypterid, the ancient chambered nautilus's greatest enemy (except the former was freshwater and the latter seawater, so they never fought per se though I don't see how that's relevant).
Posted by Kriston at March 22, 2005 10:12 AMtrue story: i once set out to crochet a set of my favorite marine invertebrates, but got only as far as Vampyroteuthis infernalis . now i realize this is probably because my geometry skillz are weak.
the crochet should be taught alongside the mathematics in schools, fer sure. can instructional patterns be found for these yarny hyperbolae?
I think so. The interviewer said:
I have crocheted a number of these models and what I find so interesting is that when you make them you get a very concrete sense of the space expanding exponentially. The first rows take no time but the later rows can take literally hours, they have so many stitches. You get a visceral sense of what "hyperbolic" really means.Which is a cool comment, and also leads me to believe that there must be patterns out there or that they could be obtained. I bet you could e-mail her.
awesome. i will seek to do so, surely.
Posted by: valerie at March 22, 2005 10:50 AMAwesome post. Thanks for bringing this article to light.
Posted by: James at March 22, 2005 5:11 PM"Nature, Nudibranch, Cambrian period."
Outstanding.
Posted by: matty at March 22, 2005 6:14 PMPhotos beautiful! Nudibranch of the week!
http://slugsite.tierranet.com/
Posted by: Joseph Barbaccia at March 22, 2005 6:46 PMHigher dimensional consideration could have been applied to Gaussian curvatures, and was necessary to understand that this was implemented in Einsteins GR?
Pics from the talk they gave on Flickr
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