Mar 20, 2007

knowing knots

Jason Kuznicki points to a lovely if sad article on the state of knot knowledge. An excerpt:
Knots, of course, have order. But the T square and the triangle aren't much use in discerning it. Classical geometers, regarding knots as squishy, pretty much ignored them. To investigate the complicated patterns wound into the knot takes freer modes of thought.

Knot theory got started in the 19th century when the Victorian scientist Lord Kelvin (William Thomson) had the beautiful idea, beautiful but wrong, that atoms were tiny knots tied in the omnipresent ether that pervades all space. There isn't any ether, but before its absence was determined Victorian mathematicians had begun to study knots.

By 1877, P.G. Tait had classified all knots with seven or fewer crossings. Knot theory since then has blossomed like a garden.

The Fields Medal, mathematics' highest honor, was won in 1990 by Vaughan Jones, a Californian windsurfer, for his "Jones Polynomial," an unexpectedly powerful and entirely abstract mathematical tool for distinguishing between knots.

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.
Remarkably, an article that mentions "knot theory" has nothing to say about its contemporary equivalent, string theory.

Kuznicki muses,
It’s remarkable testimony to the unexpected uses of knowledge in an advanced civilization, complete with the tradeoffs, the costs and benefits, that each of us face.
It's just like Asimov's lament for the loss of "clockwise," or Emerson's complaint that we can no longer steer by the stars. How much--and how little--we know.


Mark said...

Did you notice Terrence Tao has a blog, "What's New"?

Jim Anderson said...

I did not. I didn't even know who he was until today. I'm even more of a pseudo-polymath than you are.