In the Loop
What Goes Around Comes Around, All Tied Up in Knots

By Paul Richard
Special to The Washington Post
Monday, March 19, 2007

Knots made humans human.

They gave us lashings for the lean-to, bindings for the stone ax, packages with handles, and ways of hanging stuff from belts. From knots we got the bracelet, ways to tie the hair up, snares to snatch the rabbit, the basket and the bow.

But that was long ago. The technologies of tying are fading all around us. The knot's gone obsolete.

Kids can barely tie their shoes now. Their sneakers close with Velcro. The clerk, when you went shopping, used to tie your parcels up with string. Now they come in plastic. Surgeons laser-fuse and staple where they used to stitch.

Each distinctive trade (the stevedore, the dressmaker, the carter, the hangman) once had its own distinctive knottings. Now, except for hobbyists (knitters, sailors, rock climbers), who ties knots at all?

* * *

Think of what we owe the technologies of tying.

Without knots we'd be naked. Pelts slide off the shoulder unless laced together. Knots led us to the needle, and after that to weaving and every kind of cloth.

Without mooring lines and nets, the bowline and the clove hitch, we'd have never gone to sea.

Or high into the mountains. The ice man with the copper ax found frozen in the Alps knew nothing of weaving but much of knots. He'd tied eight different kinds of them. He carried spare rope and spare yarn. His shoelaces were long. His stone arrowheads were bundled with a string.

To knot, you have to comprehend, remember and repeat -- as you do in ritual, as you do in art. Knots are tied to memory. The first rosaries were knotted. To retrieve their long songs, the bards of ancient Ireland fingered knotted strings. Jews tie knots in the fringes of their prayer shawls.

Knots in painting are a presence. The most beautiful of all may be those on the pages of the Book of Kells, which are more than decorations. Twelve-hundred years ago, when that great book was produced on an island off of Scotland, and few people could read, its interweaving lines evoked the teachings of the Bible. Those spiral interlacings with their leavings and returns were reminders of the teachings, now hidden, now apparent, woven in the Word, and the parables of Christ.

Leonardo drew knots. So did Albrecht Durer. Their ingenious intertwinings demand your full attention. Today few viewers bother. They're in too much of a rush.

* * *

Old knots of many kinds are found all through the museums. The antique Persian rugs in the Textile Museum are intricately tied. So, too, are the snowshoes of wood and knotted thong in the National Museum of the American Indian. The Cone sisters of Baltimore, though better known for buying Picassos and Matisses, also brought together the 400-piece collection of Belgian, Parisian and old Venetian lace at the Baltimore Museum of Art.

There are complex interlacings in the medieval manuscripts at the Walters Art Museum. The example reproduced at left is from a Carolingian Bible from France, from the 10th century.

At the Arthur M. Sackler Gallery and Freer Gallery of Art, ornately knotted necklaces are draped around the necks of Chinese bodhisattvas. The Japanese tied knots shaped like turtles and like cranes. By how he tied his knots the tea master kept track of whether his containers were full of tea or empty. You can't rightly show a hanging scroll unless you have been taught how to tie the proper knots.

There's a great knot from the Renaissance in the National Gallery of Art. "The Sixth Knot" is a woodcut printed from a block that Durer cut in Venice or in Nuremberg 500 years ago.

Knots survive on bookshelves, too. The Library of Congress owns all 25 volumes of the series "Knots & Everything." The Inca of Peru used tied-together groups of colored knotted cords for recalling sacred numbers and calculating sums. Those seeking to decipher their knotted mathematics can consult the "Code of the Quipu" by Marcia and Robert Ascher (1981). Another kind of knot book, "The 85 Ways to Tie a Tie" by Thomas Fink and Yong Mao (1999), is available for those aiming to dress up.

Also on the shelves is the greatest knot book of them all, the one knotters call their bible, "The Ashley Book of Knots."

Published in 1944 and still in print, the "Ashley" is a marvel. Its thousands of line drawings are so clear in execution, so mentally demanding, so full of lore and learning and intricate ideas, you would have to say that they qualify as a major piece of early American conceptual art.

Clifford W. Ashley was born in 1881 in New Bedford, Mass., as in "Moby-Dick." Young Ashley served what he would call his "apprenticeship in knots" aboard the whaling bark Sunbeam, "probably the last merchant square-rigger to put to sea with hemp standing rigging." Then he turned to art. He went to school with N.C. Wyeth, studied with Howard Pyle and earned his living painting swashbuckling illustrations (he always got the rigging right) of hard men out at sea.

But then he got consumed by knots.

In the 619 pages of "The Ashley Book of Knots," each knot gets a paragraph, a number and a how-to drawing. Some specialists contend his book has duplications, but I have yet to find them. His black-and-white line drawings number 3,854.

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.

* * *

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, 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.

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.

* * *

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 (PDF).

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

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