In the Loop

Knots in Washington, a conference on knot theory, has been held every year since 1995 at George Washington University, with Jozef H. Przytycki and Yongwu Rong the topologists in charge. "Quandles -- their homology and applications" was the subject on the table the last time the conference met.

The great knot minds of the past, and surely there were many, have been pretty well forgotten. The art that they advanced is anonymous no longer. Ashley, Tait, Jones, Przytycki, Rong, Scharein -- they're all knot stars now.

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A final knot.

I like this one because it ties together chaos, order, domestic tranquility and contemporary art, which is a lot for a knot.

This knot was created in England by Bernd Krauskopf and Hinke Osinga of Bristol University's department of engineering mathematics. It is tied in colored yarn or, actually, crocheted. It's almost a yard across and looks like a target with a three-dimensional twisting, corkscrewed top.

It's name is the "Lorenz manifold." It grew out of the work of Edward Lorenz, who explained the butterfly effect and discovered hidden order in big chaotic systems: the weather, for example. Lorenz modeled his discoveries with very handsome graphs. The manifold is one of them.

Krauskopf and Osinga were sitting around together when Krauskopf asked, as guys will do, "Why don't you crochet something useful?"

"I looked at him and we thought the same thing at the same moment," Osinga told Science News. "We realized you could crochet the Lorenz manifold."

Actually, she crocheted it, in blue, with two yarns. Osinga used as her directions those that they'd devised to generate the manifold on the screen of a computer. It took her 85 hours. She crocheted 25,511 stitches. You can see their equations, and if you scroll past the blizzard of math, you can see close-ups of the manifold, at http://www.enm.bris.ac.uk/anm/preprints/2004r03.pdf (PDF).

She and Krauskopf keep the manifold at home. It hangs on the wall.