In the Loop

Lots of knots have lots of names. This was always confusing. Ashley's book pierced that fog. The knot once called the English knot (or the Water, Waterman's, Fisher's or Fisherman's) now is known to knotters as "Ashley #1143."

When Ashley joined the fleet, knotting wasn't optional. Sailors had to be quick with a knot to be any use at sea.

In peacetime, sailors had time to kill. And most couldn't read. Instead they turned to knotting. More than 100 pieces of their time-eating knotwork -- fancy lanyards, fancy bell pulls, sheaths, picture frames, ditty bags and blackjacks -- can be seen in the collection of the Mariners' Museum in Newport News, Va. (The museum also owns the illustrated manuscript of "The Ashley Book of Knots.")

Now that sea-going is motorized and hemp is obsolete, you might suppose all sailing knots had already been invented. Not so. Marc McAteer, the president of Atlantic Spars & Rigging in Annapolis, who works in high-tech racing, says that the newest lightweight fibers, Vectran, say, or Spectra, take new ways of splicing. Better ways of fastening one rope end to another are still being invented.

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Though a piece of string can be any length you wish, the action that's important takes place at either end. The same is true of knots. While one end pulls you toward the past through hemp rigging and lace, the other winds instead through immaterial mathematics. Beauty thrives there, too.

Here is one way to taste it. Go to http://www.knotplot.com/, scroll down to "Ashley knots," then click on "Ashley #2334." When you click again, you set it rotating in space.

Ashley found No. 2,334 at the end of a bugle cord made by Seiderman Bros. of Philadelphia. Rob Scharein of Vancouver, B.C., the computer scientist behind Knotplot, discovered it by leafing through "The Ashley Book of Knots."

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.