One of our most basic forms of manipulation, we encounter knots in many situations, from shoelaces to tangled wires. But beyond their useful qualities, also have historical, cultural and scientific dimensions that make them a fascinating subject of investigation.
video: a demonstration of knot throwing, or tying a knot using only a single-handed maneuver
Culturally, knots have been used as tools of representation in a variety of ways. Incas used knots in complex recording devices called quipus (‘knot’ in Quecha), capable of operations like addition, subtraction, multiplication and division. In Taoist alchemy, knots appear in magic diagrams as a regular part of its supernatural vocabulary as talismans against evil or misfortune. European traditions range from celtic manuscripts to heraldic symbolism.
from left to right: Inca Quipu, a Taoist magical diagram, a Celtic knot, and a heraldic knot (Granny knot)
Various expressions like “tie the knot” (marriage) or “to the bitter end,” (originally a nautical expression which refers to the end of a rope tied to a bitt, or a metal posting on the deck of a boat) represent knots within language. A “Gordian knot” is often a metaphor for dealing with a difficult problem in a forceful manner. Knot names themselves reveal a rich folk-history, whether or not the accounts are true. Thief knots were a way of securing one’s belongings but also as detection device; a difficult knot to tie accidentally, an untrained thief would almost certainly re-tie the knot into the similar reef knot, revealing the tampering. Another example is Matthew Walker’s knot, which could possibly refer to a particularly interesting maritime legend about a commuted death sentence (which most certainly would have involved another knot, the Hangman):
The FULL or DOUBLE MATTHEW WALKER KNOT. Lever in 1808 speaks of “MATTHEW WALKER’S KNOT” and describes the knot which Alston in 1860 calls the “DOUBLE MATTHEW WALKER KNOT.” A refinement of the original knot had in the meantime taken over the original name , which is now generally modified to “a MATTHEW WALKER.. Lever’s familiar expression, “MATTHEW WALKER’S KNOT,” suggests that he may have known the inventor, who was possibly a master rigger in one of the British naval dockyards. Many myths have grown up around Matthew Walker, “the only man ever to have a knot named for him.” Dr. Frederic Lucas, of the American Museum of Natural History, once told me the following story of the Origin of the knot, which he had heard off the Chincha Islands while loading guano in 1869. A sailor, having been sentenced to death by a judge who in earlier life had been a sailor himself, was reprieved by the judge because of their common fellowship of the sea. The judge offered the sailor a full pardon if he could show him a knot that he, the judge, could neither tie nor untie. The sailor called for ten fathoms of rope and, having retired to the privacy of his cell, unlaid the rope halfway, put in a MATTHEW WALKER KNOT, and then laid up the rope again to the end. So Matthew Walker secured his pardon, and the world gained an excellent knot. (Image from A. Hyatt Merill’s Knots, Splices and Rope Work, 1917)
from left to right: an excerpt from P. G. Tait’s treatise “On Knots (pdf)”, 1885; an electron micrograph of RecA protein-coated DNA trefoil knot, simulated rendering of a hologram manipulating light from a laser into a closed loop
Beyond practical uses for sailors, mountaineers or fishermen, knot theory was once a 19th century esoteric corner of topology, but recently has become an important field in mathematics, most notably with relevant applications in biochemistry (understanding the structural properties of proteins and potential “bad knots” and how these errors relate to disease). And in physics, scientists recently have found a way to bend and manipulate light into closed loops through specialized holograms, with a range of applications that includes a potential approach to fusion power. (The Walker recently addressed some of these issues in a lecture by The Institute for Figuring as part of the lecture series surrounding the exhibition, The Quick and the Dead.)
above: Knot Generator poster by Everything Studio
A particularly interesting recent example of knots showed up in 2008 in the form of an unusual catalogue, as part of a exhibition in Beijing. Designed by Everything Studio, the Knot Generator came out of an investigation into Celtic forms of knots, redrawn and represented as mathematical diagrams. The generator reduced the potential complexity of knot structures into 20 unique units, each representing different string relationships. They talk briefly about possible origins of knot-based works as ways of representing the divine while avoiding the taboo of idolatry. While that might be up for debate, the greater point may be that like many other basic mathematical constructs like the circle or natural logarithms, knots appear to be strongly integrated with human culture, as well as reveal much about ourselves and the observable universe.
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