Introduced by {{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 1973[[Lacan]]'s [[Works of Jacques Lacan|work]] as early as the 1950s, <ref> {{E}} p. 281</ref> but it is not until the Borromean ealy 1970s that [[Lacan]] begins to examine [[knot is ]]s from the point of view of their [[topology|topological properties]]. In the solution mid-1970s he tried to a problem perceivable only in Lacanian theory but having extremely practical clinical applications. The problem is: How are theorize the interrelation of the three registers posited as making up subjectivity—the real (R)[[Symbolic]], the symbolic (S), [[Imaginary]] and the imaginary (I)—held together?[[Real]] in [[terms]] of the [[topology]] of [[borromean knot|knots]].
Indeed, ==Topology==The study of "[[knot|knot theory]]" marks an important [[development]] in [[Lacan]]'s [[topology]]; from the symbolic study of surfaces (the signifier) and [[moebius strip]], the imaginary (meaning[[torus]], etc.) seem [[Lacan]] moves to have hardly anything in common—a fact demonstrated by a much more [[complex]] area of the abundance and heterogeneity [[topology]] of languages[[knot]]s. Moreover, the real, by definition, escapes [[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]], since its resistance to them [[topology]] is precisely what makes it realthat [[structure]].
This is why ==Knot==In this late period of his [[work]], one kind of [[knot]] comes to interest [[Lacan identified ]] more than any [[other]]: the [[Borromean knot]]. The [[Borromean knot]] -- shown to the real with [[right]] -- so called because the impossible.) In psychoanalysis, [[List of Figures|figure]] is found on the coat of arms of the real resistsBorromeo [[family]], and thus is distinct froma group of [[three]] rings which are linked in such a way that if any one of [[them]] is severed, the imaginary defenses that the ego uses specifically to misrecognize the impossible and its consequencesall three become separated.<ref>{{S20}} p.112</ref>
If each of the three registers R==Chain==Strictly [[speaking]], S, and I that make up the Borromean knot is recognized it would be more appropriate to refer to be toric in structure and the this [[figure]] as a [[chain]] rather than a [[knot is constructed in three-dimensional space]], since it constitutes involves the perfect answer to the problem aboveinterconnection of several different threads, because it realizes whereas a [[knot]] is formed by a single thread. Although a three-way joining minimum of all three torusesthreads or rings are required to [[form]] a [[Borromean knot|Borromean chain]], while none of them there is actually linked to any other: If any one of them is cut, no maximum [[number]]; the other two are set free. Reciprocally[[chain]] may be extended indefinitely by adding further rings, any while still preserving its [[Borromean knot that meets these conditions is called |Borromean]] quality (i. Note that e. if any of the subject rings is now defined by such a knot and not merelycut, as with the cross-cap, as the effect of a cut (figure 8[[whole]] chain falls apart).
Unfortunately==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 ideal solution[[seminar]] that [[Lacan]] uses the [[Borromean knot]] as, which could be considered normal (without symptoms)among other things, seems to lead to paranoia. Lacan considered this to be a way of illustrating the result interdependence of failure to distinguish among the [[order|three registersorder]]s of the [[real]], the [[symbolic]] and the [[imaginary]], as if they were continuous, which indeed occurs a way of exploring what it is that these [[order|three order]]s have in clinical workcommon. Being identical, R, SEach ring represents one of the [[order|three order]]s, and I thus certain elements can be located at intersections of these rings. (In his view these [[orders]] are only differentiated by means tied together in the form of a "complication,Borromean knot". The "Borromean knot" is a fourth ring that Lacan called the linkage of three "sinthome.string rings" By making in such a way that no two rings intersect. The structure of the knot is such that the cutting of any one ring with will liberate all of the three [[others]]. [[Lacan]] used the [[theory]] of knots to stress the relations which [[bind]] or link the [[Imaginary]], [[Symbolic]] and [[Real]], and the sinthome (symptom) differentiates [[subject]] to each, in a way which avoids any [[notion]] of hierarchy, or any priority of any one of the three others by assuring their knotting (figure 9terms.).
==Psychosis==In this arrangementthe [[seminar]] of 1975-6, [[Lacan]] goes on to describe [[psychosis]] as the sinthome has the function of determining one unravelling of the rings. If it [[Borromean knot]], and proposes that in some cases this is attached to prevented by the symbolicaddition of a fourth ring, it plays the role of ''[[sinthome]]'', which holds the paternal metaphor and its corollary, a neurotic symptomother 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.==See Also=={{See}}* ''[[Extimacy]]''* [[Imaginary]]||* [[Moebius strip]]* [[Order]]||* [[Psychosis]]* [[Real]]||* ''[[Sinthome]]''* [[Structure]]||* [[Subject]]* [[Symbolic]]||* [[Torus]]* [[Topology]]{{Also}}
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 ==References==<div style="bits of the real" (Lacan, 1976font-1977, session of March 16, 1976). Even though he knew something about topology as practiced by mathematicians, Lacan advised his students size:11px"to use it stupidlyclass=" (Lacan, 1974references-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.small"><references/></div>
==See Also==[[Category:Psychoanalysis]]* [[torusCategory:Jacques Lacan]]* [[topologyCategory:Science]]* [[extimacyCategory:Figures]]* [[subjectCategory:Dictionary]]* [[cross-capCategory:Concepts]]* [[knotCategory:Terms]]
[[Category:Mathematics]][[Category:Topology]][[Category:Terms]][[Category:Figures]][[Category:Jacques Lacan]]__NOTOC__
