Borromean knot

From No Subject
(Redirected from Noeud borroméen)
Jump to navigation Jump to search
French: noeud borroméen
The Borromean knot

In the later phase of his teaching, Jacques Lacan introduces the Borromean knot as a topological model to articulate the structural interdependence of the three fundamental registers of psychoanalytic experience: the Imaginary, the Symbolic, and the Real.[1] Far from being a metaphor, Lacan uses the Borromean knot as a precise formal apparatus to rethink the structure of subjectivity, the function of language, and the genesis of psychotic phenomena.

Topology in Lacanian Psychoanalysis

Lacan's interest in topology evolves throughout his work. Early on, he engages with surfaces such as the moebius strip, the torus, and the cross-cap to illustrate the paradoxes of psychic space, the unconscious, and the function of the Other.[2] From the early 1970s onward, his work becomes increasingly involved with knot theory, a branch of topology concerned with the interlinking of closed curves in three-dimensional space.

Lacan treats topology not as a metaphor but as a literal mode of formalization: topology is not what represents structure—it is structure itself.[3]

The Borromean Knot

The Borromean knot (or *Borromean link*) consists of three interlinked rings such that if any one ring is severed, the entire configuration falls apart. No two rings are directly connected; the knot is held together only by the mutual presence of all three.[4]

For Lacan, this structure becomes a compelling way to conceptualize how the three registers of the psyche are linked without being reducible to one another.

Chain vs. Knot

Although typically called a "knot," the Borromean structure is more accurately described in mathematical terms as a link or chain.[5] Lacan acknowledges this distinction, but uses the term “knot” more loosely to emphasize the dynamic tying together of psychic dimensions. The terminology thus emphasizes the structural entanglement of the subject in language and desire.

The Three Orders: Real, Symbolic, and Imaginary

Lacan’s topological model maps each ring of the Borromean knot to one of the three fundamental registers of psychoanalysis:

  • The Imaginary involves identification, ego-formation, and image-based misrecognition.
  • The Symbolic encompasses the signifier, language, the law, and the big Other.
  • The Real refers to what is outside symbolization—what cannot be integrated into the Imaginary or Symbolic.[6]

Each order is necessary for the coherence of subjectivity. The Borromean knot demonstrates that this coherence is not rooted in essence but in structural articulation.

Knotting and Subjectivity

In Lacan’s formulation, the subject is not the Cartesian cogito but a structurally knotted formation in which the registers are intertwined. The symptom is one such knotting point—a formation that binds the Real, Symbolic, and Imaginary.[7]

The Borromean model allows Lacan to formalize the unconscious in terms of knot logic: where the links are made, how they are held together, and where they may unravel.

Psychosis and the Sinthome

Lacan’s theory of psychosis finds new elaboration through knot theory. In psychosis, one of the three registers—often the Symbolic—is foreclosed, leading to a failure in the knot.[8] The result is a psychic disjunction: hallucination, delusion, or invasion by the Real.

In his seminar Le sinthome, Lacan introduces the idea of a fourth ring, the sinthome, which can re-knot the Real, Symbolic, and Imaginary even in the absence of a normative linkage. The sinthome functions as a singular solution that stabilizes the subject and supports jouissance (enjoyment).[9]

Clinical Implications

The Borromean knot is not only a theoretical tool, but also has clinical significance. It offers a structural approach to diagnosis:

  • In neurosis, the knot is intact but under tension.
  • In psychosis, the knot unravels due to foreclosure.
  • In perversion, the knot is sustained through a compensatory identification with the object.

The model allows analysts to conceptualize psychic consistency in formal rather than empirical terms, enabling new forms of diagnostic and interpretive precision.[10]

See Also

References

  1. ↑ Lacan, J. (1974–1975). Le Séminaire, Livre XXII: RSI. Unpublished seminar, 1974–75.
  2. ↑ Lacan, J. (1966). “Science and Truth,” in Écrits, trans. Bruce Fink. New York: Norton, 2006.
  3. ↑ Lacan, J. (1973). Le Séminaire, Livre XX: Encore. Trans. Bruce Fink. New York: Norton, 1998.
  4. ↑ Lacan, J. (1975). Le Séminaire, Livre XXII: RSI, session of 18 March 1975.
  5. ↑ Borromean rings. In: Adams, C. (2004). The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots. American Mathematical Society.
  6. ↑ Lacan, J. (1953–1954). Le Séminaire, Livre I: Les écrits techniques de Freud. Paris: Seuil, 1975.
  7. ↑ Lacan, J. (1975–1976). Le Séminaire, Livre XXIII: Le sinthome. Ed. J.-A. Miller. Paris: Seuil, 2005.
  8. ↑ Lacan, J. (1955–1956). Le Séminaire, Livre III: Les psychoses. Trans. Russell Grigg. New York: Norton, 1993.
  9. ↑ Lacan, J. (1975–1976). Le Séminaire, Livre XXIII: Le sinthome, session of 11 November 1975.
  10. ↑ Miller, J.-A. (2004). “The Unconscious and the Body Event.” In: The Symptom, Issue 5.


Retrieved from "https://nosubject.com/index.php?title=Borromean_knot&oldid=58606"