- 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.
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).
* Freud, Sigmund. (1950a ). 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 Unpublished.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)
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.