Difference between revisions of "Borromean knot"

From No Subject - Encyclopedia of Psychoanalysis
Jump to: navigation, search
(The LinkTitles extension automatically added links to existing pages (https://github.com/bovender/LinkTitles).)
 
(19 intermediate revisions by 3 users not shown)
Line 1: Line 1:
−
Introduced by Lacan in 1973, the Borromean knot is the solution to a problem perceivable only in Lacanian theory but having extremely practical clinical applications. The problem is: How are the three registers posited as making up subjectivity—the real (R), the symbolic (S), and the imaginary (I)—held together?
+
{{Topp}}noeud borroméen{{Bottom}}         
 +
[[Image:Borromean.Knot.jpg|thumb|300px|right|The Borromean knot]] 
 +
==Jacques Lacan==
 +
[[Lacan]] used the [[concept]] or [[image]] of the [[borromean knot|knot]] quite frequently. References to [[knot]]s can be found in [[Lacan]]'s [[Works of Jacques Lacan|work]] as early as the 1950s,<ref> {{E}} p. 281</ref> but it is not until the ealy 1970s that [[Lacan]] begins to examine [[knot]]s from the point of view of their [[topology|topological properties]]. In the mid-1970s he tried to theorize the interrelation of the [[Symbolic]], the [[Imaginary]] and the [[Real]] in [[terms]] of the [[topology]] of [[borromean knot|knots]].
  
−
Indeed, the symbolic (the signifier) and the imaginary (meaning) seem to have hardly anything in common—a fact demonstrated by the abundance and heterogeneity of languages. Moreover, the real, by definition, escapes the symbolic and the imaginary, since its resistance to them is precisely what makes it real.
+
==Topology==
 +
The study of "[[knot|knot theory]]" marks an important [[development]] in [[Lacan]]'s [[topology]]; from the study of surfaces (the [[moebius strip]], the [[torus]], etc.) [[Lacan]] moves to a much more [[complex]] area of the [[topology]] of [[knot]]s. [[Topology]] is increasingly seen as a radically [[metaphor|non-metaphorical]] way of exploring the [[symbolic order]] and its interactions with the [[imaginary]] and the [[real]]; rather than simply representing [[structure]], [[topology]] is that [[structure]].
  
−
This is why Lacan identified the real with the impossible.) In psychoanalysis, the real resists, and thus is distinct from, the imaginary defenses that the ego uses specifically to misrecognize the impossible and its consequences.
+
==Knot==
 +
In this late period of his [[work]], one kind of [[knot]] comes to interest [[Lacan]] more than any [[other]]: the [[Borromean knot]]. The [[Borromean knot]] -- shown to the [[right]] -- so called because the [[List of Figures|figure]] is found on the coat of arms of the Borromeo [[family]], is a group of [[three]] rings which are linked in such a way that if any one of [[them]] is severed, all three become separated.<ref>{{S20}} p. 112</ref>
  
−
If each of the three registers R, S, and I that make up the Borromean knot is recognized to be toric in structure and the knot is constructed in three-dimensional space, it constitutes the perfect answer to the problem above, because it realizes a three-way joining of all three toruses, while none of them is actually linked to any other: If any one of them is cut, the other two are set free. Reciprocally, any knot that meets these conditions is called Borromean. Note that the subject is now defined by such a knot and not merely, as with the cross-cap, as the effect of a cut (figure 8).
+
==Chain==
 +
Strictly [[speaking]], it would be more appropriate to refer to this [[figure]] as a [[chain]] rather than a [[knot]], since it involves the interconnection of several different threads, whereas a [[knot]] is formed by a single thread. Although a minimum of three threads or rings are required to [[form]] a [[Borromean knot|Borromean chain]], there is no maximum [[number]]; the [[chain]] may be extended indefinitely by adding further rings, while still preserving its [[Borromean knot|Borromean]] quality (i.e. if any of the rings is cut, the [[whole]] chain falls apart).
  
−
Unfortunately, this ideal solution, which could be considered normal (without symptoms), seems to lead to paranoia. Lacan considered this to be the result of failure to distinguish among the three registers, as if they were continuous, which indeed occurs in clinical work. Being identical, R, S, and I are only differentiated by means of a "complication," a fourth ring that Lacan called the "sinthome." By making a ring with the three others, the sinthome (symptom) differentiates the three others by assuring their knotting (figure 9).
+
==Three Orders==
 +
[[Lacan]] first takes up the [[Borromean knot]] in the [[seminar]] of 1972-3, but his most detailed [[discussion]] of the [[knot]] comes in the [[seminar]] of 1974-5. It is in this [[seminar]] that [[Lacan]] uses the [[Borromean knot]] as, among other things, a way of illustrating the interdependence of the [[order|three order]]s of the [[real]], the [[symbolic]] and the [[imaginary]], as a way of exploring what it is that these [[order|three order]]s have in common. Each ring represents one of the [[order|three order]]s, and thus certain elements can be located at intersections of these rings. (In his view these [[orders]] are tied together in the form of a "Borromean knot".  The "Borromean knot" is a linkage of three "string rings" in such a way that no two rings intersect.  The structure of the knot is such that the cutting of any one ring will liberate all of the [[others]].  [[Lacan]] used the [[theory]] of knots to stress the relations which [[bind]] or link the [[Imaginary]], [[Symbolic]] and [[Real]], and the [[subject]] to each, in a way which avoids any [[notion]] of hierarchy, or any priority of any one of the three terms.)
  
−
In this arrangement, the sinthome has the function of determining one of the rings. If it is attached to the symbolic, it plays the role of the paternal metaphor and its corollary, a neurotic symptom.
+
==Psychosis==
−
 
+
In the [[seminar]] of 1975-6, [[Lacan]] goes on to describe [[psychosis]] as the unravelling of the [[Borromean knot]], and proposes that in some cases this is prevented by the addition of a fourth ring, the ''[[sinthome]]'', which holds the other three together.
−
Lacan also drew upon non-Borromean knots, generated by "slips," or mistakes, in tying the knots. These allowed him to represent the status of subjects who are unattached to the imaginary or the real and who compensate for this with supplements (Lacan, 2001). In such cases the sinthome is maintained.
 
−
 
 
−
By using knots, Lacan was able to reveal his ongoing research without hiding its uncertainties. The value of the knots, which resist imaginary representation, is that they advance research that is not mere speculation and that they can grasp—at the cost of abandoning a grand synthesis—a few "bits of the real" (Lacan, 1976-1977, session of March 16, 1976). Even though he knew something about topology as practiced by mathematicians, Lacan advised his students "to use it stupidly" (Lacan, 1974-1975, session of December 17, 1974) as a remedy for our imaginary simplemindedness. He also recommended manually working with the knots by cutting surfaces and tying knots. Finally, for Lacan, topology had not only heuristic value but also valuable implications for psychoanalytic practice.
 
  
 
==See Also==
 
==See Also==
−
* [[torus]]
+
{{See}}
−
* [[topology]]
+
* ''[[Extimacy]]''
−
* [[extimacy]]
+
* [[Imaginary]]
−
* [[subject]]
+
||
−
* [[cross-cap]]
+
* [[Moebius strip]]
−
* [[knot]]
+
* [[Order]]
 +
||
 +
* [[Psychosis]]
 +
* [[Real]]
 +
||
 +
* ''[[Sinthome]]''
 +
* [[Structure]]
 +
||
 +
* [[Subject]]
 +
* [[Symbolic]]
 +
||
 +
* [[Torus]]
 +
* [[Topology]]
 +
{{Also}}
  
 
==References==
 
==References==
 +
<div style="font-size:11px" class="references-small">
 
<references/>
 
<references/>
 +
</div>
  
−
[[Category:Mathematics]]
+
[[Category:Psychoanalysis]]
−
[[Category:Topology]]
+
[[Category:Jacques Lacan]]
 +
[[Category:Science]]
 +
[[Category:Figures]]
 +
[[Category:Dictionary]]
 +
[[Category:Concepts]]
 
[[Category:Terms]]
 
[[Category:Terms]]
−
[[Category:Figures]]
+
 
−
[[Category:Jacques Lacan]]
+
__NOTOC__

Latest revision as of 03:03, 24 May 2019

French: noeud borroméen
The Borromean knot

Jacques Lacan

Lacan used the concept or image of the knot quite frequently. References to knots can be found in Lacan's work as early as the 1950s,[1] but it is not until the ealy 1970s that Lacan begins to examine knots from the point of view of their topological properties. In the mid-1970s he tried to theorize the interrelation of the Symbolic, the Imaginary and the Real in terms of the topology of knots.

Topology

The study of "knot theory" marks an important development in Lacan's topology; from the study of surfaces (the moebius strip, the torus, etc.) Lacan moves to a much more complex area of the topology of knots. Topology is increasingly seen as a radically non-metaphorical way of exploring the symbolic order and its interactions with the imaginary and the real; rather than simply representing structure, topology is that structure.

Knot

In this late period of his work, one kind of knot comes to interest Lacan more than any other: the Borromean knot. The Borromean knot -- shown to the right -- so called because the figure is found on the coat of arms of the Borromeo family, is a group of three rings which are linked in such a way that if any one of them is severed, all three become separated.[2]

Chain

Strictly speaking, it would be more appropriate to refer to this figure as a chain rather than a knot, since it involves the interconnection of several different threads, whereas a knot is formed by a single thread. Although a minimum of three threads or rings are required to form a Borromean chain, there is no maximum number; the chain may be extended indefinitely by adding further rings, while still preserving its Borromean quality (i.e. if any of the rings is cut, the whole chain falls apart).

Three Orders

Lacan first takes up the Borromean knot in the seminar of 1972-3, but his most detailed discussion of the knot comes in the seminar of 1974-5. It is in this seminar that Lacan uses the Borromean knot as, among other things, a way of illustrating the interdependence of the three orders of the real, the symbolic and the imaginary, as a way of exploring what it is that these three orders have in common. Each ring represents one of the three orders, and thus certain elements can be located at intersections of these rings. (In his view these orders are tied together in the form of a "Borromean knot". The "Borromean knot" is a linkage of three "string rings" in such a way that no two rings intersect. The structure of the knot is such that the cutting of any one ring will liberate all of the others. Lacan used the theory of knots to stress the relations which bind or link the Imaginary, Symbolic and Real, and the subject to each, in a way which avoids any notion of hierarchy, or any priority of any one of the three terms.)

Psychosis

In the seminar of 1975-6, Lacan goes on to describe psychosis as the unravelling of the Borromean knot, and proposes that in some cases this is prevented by the addition of a fourth ring, the sinthome, which holds the other three together.

See Also

References

  1. ↑ Lacan, Jacques. Écrits: A Selection. Trans. Alan Sheridan. London: Tavistock Publications, 1977. p. 281
  2. ↑ Lacan, Jacques. Le Séminaire. Livre XX. Encore, 1972-73. Ed. Jacques-Alain Miller. Paris: Seuil, 1975. p. 112


Retrieved from "https://nosubject.com/index.php?title=Borromean_knot&oldid=45163"