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KNOT

Jacques Lacan used a topological structure of the knot to define the relationship of the symbolic, the real, and the imaginary.

In particular, he referred to the structure of rings on the coat of arms of the Borromei family. After introducing this notion on February 9, 1972, in his seminar ". . . ou pire " (. . . or worse), he made the knot a central focus of his theory.

In mathematical terms, a knot is a simple closed curve (Jordan's curve). Lacan mainly considered two nodal structures (Figure 1):

• The Borromean Knot: three component loops joined together in such a way that when one loop is cut the other two are no longer connected;
• The clover-leaf knot: the three components have been connected together into a single continuous loop.

For Lacan, the knot symbolizes the Imaginary. As an imaginary construct, it gives consistency to the symbolic. Taken symbolically, the knot represents the undecidability of the real or imaginary.

The knot is an object located in space. A two-dimensional representation of it is made by means of crossings over or under. The knot's structure is determined by what crosses over or under what. However, the knot's structure is not dependent on its representation. Indeed, it was to translate representation into structure that an algebraic writing system for knots was developed. This writing system was refined over the course of the twentieth century and gradually made it possible to distinguish among different types of knots. In this system, the knot's topological loops become letters (in the form of polynomials). This marks the fact that the knot originates in the lost letter.

In Lacan's spoken lectures, the knot functioned first and foremost as a piece of writing. This called into question of the relationship between speech and writing, and showed that "writeability" is essential to the formation of the unconscious (Sigmund Freud's "Letter 52" to Wilhelm Fliess). "The unconscious can only be expressed in knots of language" (Lacan).

Henri Cesbron Lavau

Bibliography

Darmon, Marc. Essais sur la topologie lacanienne. Paris:Éditions de l'A.F.I., 1990.

Freud, Sigmund. (1950a [1896]). Letter 52. Stratification of memory traces. SE, 1 : 234-240.

Lacan, Jacques. (1971-1972). Le séminaire Livre XIX: . . . Ou pire. Unpublished.

. (2002). The instance of the letter in the unconscious, or Reason since Freud. InÉcrits: A selection (pp. 138-168). (Bruce Fink, Trans.). New York: W. W. Norton. (Original work published 1966)

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knot

knot1 / nät/ • n. 1. a fastening made by tying a piece of string, rope, or something similar. ∎  a particular method of tying a knot: you need to master two knots, the clove hitch and the sheet bend. ∎  a tangled mass in something such as hair. ∎  a complex and intractable problem: a complicated knot of racial politics and pride. ∎  a tied or folded ribbon, worn as an ornament. 2. a knob, protuberance, or node in a stem, branch, or root. ∎  a hard mass formed in a tree trunk at the intersection with a branch, resulting in a round cross-grained piece in timber when cut through. ∎  a hard lump of tissue in an animal or human body. ∎  a tense constricted feeling in the body: the knot of tension at the back of her neck. ∎  a small tightly packed group of people: the little knot of people clustered around the doorway. 3. a unit of speed equivalent to one nautical mile per hour, used esp. of ships, aircraft, and winds. • v. (knot·ted , knot·ting ) [tr.] 1. fasten with a knot: the scarves were knotted loosely around their throats. ∎  make (a carpet or other decorative item) with knots. ∎  make (something, esp. hair) tangled. 2. cause (a muscle) to become tense and hard. ∎  [intr.] (of the stomach) tighten as a result of nervousness or tension. PHRASES: tie the knot inf. get married.DERIVATIVES: knot·less adj.knot·ter n. knot2 • n. (pl. same or knots ) a small, relatively short-billed sandpiper (genus Calidris) with a reddish-brown or blackish breast in the breeding season. Two species include the red knot (C. canutus), which breeds in the Arctic and winters in the southern hemisphere.

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"knot." The Oxford Pocket Dictionary of Current English. . Encyclopedia.com. 28 Jun. 2017 <http://www.encyclopedia.com>.

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knot

knot in nautical usage, knot denoted any of a number of divisions marked by knots at fixed intervals on a log line and used as a measure of speed (originally from the rate the knots run out while a sand-glass is running). From this comes the sense of a unit of speed equivalent to one nautical mile per hour, used especially of ships, aircraft, or winds.
knot garden a formal garden laid out in an intricate design; knot was used from the late 15th century to denote a flower-bed laid out in a fanciful or ornate shape.

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Knot

a small cluster or group of persons or things.

Examples: knot of astrologers; booksellers; clubs [social], 1853; of idioms, 1875; of islands, 1698; of men, 1601; of mountains [where mountain chains meet]; of palm trees, 1825; of people; of politicians, 1874; roots [personal links]; of separatists, 1849; of small stairs, 1607; of talk; of thread or yarn; of toads; of Windsors [chairs]; of witches; of young snakes.

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knot

knot1 intertwining of parts of rope, etc. (fig. something intricate) OE.; hard lump XIII; thickened tissue of a plant; cluster or small group XIV. OE. cnotta = Du. knot, MLG. knotte, MHG. knotze knob, knot :- WGmc. *knuttan-; cf. OHG. knodo, knoto (G. knoten), ON. knútr knot, knǫttr ball.
Hence knot vb. XVI. knotted XII.

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"knot." The Concise Oxford Dictionary of English Etymology. . Encyclopedia.com. 28 Jun. 2017 <http://www.encyclopedia.com>.

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knot

knot
1. An intersection of arcs in a graph that is not a planar graph. Where the arcs represent linear code sequences in a program, and the nodes represent branch points in the program, then the presence and frequency of knots is a measure of the complexity of the program (see control-flow graph).

2. See spline.

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"knot." A Dictionary of Computing. . Encyclopedia.com. 28 Jun. 2017 <http://www.encyclopedia.com>.

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knot

knot A unit of speed equal to one nautical mile per hour (0.515 m/s). It is still used in many countries as a measure of wind speed and current velocity (as well as for the speed of ships and aircraft).

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"knot." A Dictionary of Ecology. . Encyclopedia.com. 28 Jun. 2017 <http://www.encyclopedia.com>.

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"knot." A Dictionary of Ecology. . Retrieved June 28, 2017 from Encyclopedia.com: http://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/knot-0

knot

knot Unit of speed equal to one nautical mile per hour (0.515 m/s). It is still used in many countries as a measure of wind speed and current velocity (as well as for the speed of ships and aircraft).

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"knot." A Dictionary of Earth Sciences. . Encyclopedia.com. 28 Jun. 2017 <http://www.encyclopedia.com>.

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knot

knot Unit of measurement equal to one nautical mile per hour – 1 knot equals 1.852km/h (1.15mph). The speeds of ships, aircraft, winds and currents are generally expressed in knots.

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knot

knot.
1. Boss or finial.

2. Ornament resembling a bunch of leaves or flowers.

3. Architectural treatment resembling tied ropes, as in a knotted shaft.

4. Strapwork.

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"knot." A Dictionary of Architecture and Landscape Architecture. . Encyclopedia.com. 28 Jun. 2017 <http://www.encyclopedia.com>.

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knot

knot2 red-breasted sandpiper. XVI. of unkn. orig.; later vars. were knat, gnat.

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knot

knotallot, begot, Bernadotte, blot, bot, capot, clot, cocotte, cot, culotte, dot, forgot, garrotte (US garrote), gavotte, got, grot, hot, jot, knot, lot, Mayotte, motte, not, Ott, outshot, plot, pot, rot, sans-culotte, Scot, Scott, shallot, shot, slot, snot, sot, spot, squat, stot, swat, swot, tot, trot, twat, undershot, Wat, Watt, what, wot, yacht •robot • hotshot • peridot • microdot •Wyandot • polka dot • fylfot • mascot •Caldecott • carrycot • apricot •boycott • dovecote • sandlot • melilot •polyglot • Camelot • ocelot •monoglot • sub-plot • Lancelot •cachalot • counterplot • Wilmot •guillemot • motmot • bergamot