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References to knots can be found in [[LacanTopology]]'s is increasingly seen as a radically [[Works of Jacques Lacanmetaphor|worknon-metaphorical]] as early as way of exploring the 1950s,<ref> {{E}} p.281</ref> but it is not until [[symbolic order]] and its interactions with the ealy 1970s that [[Lacanimaginary]] begins to examine knots from and the point of view of their [[real]]; rather than simply representing [[structure]], [[topology|topological properties]] is that [[structure]].

==Knot==[[Image:BKNOT.jpg|right|The study of "Borromean knot theory" marks an important development in [[Lacan]]'s [[topology]]; from the study In this late period of surfaces (the [[moebius strip]]his work, the one kind of [[torusknot]], etc.) comes to interest [[Lacan]] moves to a much more complex area of than any other: the [[topologyBorromean knot]] of knots.

The [[TopologyBorromean knot]] is increasingly seen as a radically non-- shown to the right -- so called because the [[metaphor]]ical way List of exploring the [[symbolic orderFigures|figure]] and its interactions with is found on the [[imaginary]] and coat of arms of the [[real]]; rather than simply representing [[structure]]Borromeo family, [[topology]] is a group of three rings which are linked in such a way that [[structure]]if any one of them is severed, all three become separated.<ref>{{S20}} p.112</ref>

In this late period of his work==Chain==Strictly speaking, one kind of knot comes it would be more appropriate to refer to interest this figure as a [[Lacanchain]] more rather than any other: a [[knot]], since it involves the interconnection of several different threads, whereas a [[Borromean knot]]is formed by a single thread.

The ===Three Orders===[[Lacan]] first takes up the [[Borromean knot]] -- shown below -- so called because in the figure is found on the coat [[seminar]] of arms 1972-3, but his most detailed discussion of the Borromeo family, is a group of three rings which are linked [[knot]] comes in such a way that if any one the [[seminar]] of them is severed, all three become separated.<ref>{{S20}} p1974-5.112</ref>

Strictly speaking, it would be more appropriate to refer to It is in this figure [[seminar]] that [[Lacan]] uses the [[Borromean knot]] as , among other things, a chain rather than a knotway of illustrating the interdependence of the [[order|three order]]s of the [[real]], since it involves the interconnection of several different threads[[symbolic]] and the [[imaginary]], whereas as a knot way of exploring what it is formed by a single threadthat these [[order|three order]]s have in common.

Although a minimum Each ring represents one of the [[order|three threads or rings are required to form a Borromean chainorder]]s, there is no maximum number; the chain may and thus certain elements can be extended indefinitely by adding further rings, while still preserving its Borromean quality (i.e. if any located at intersections of the these rings is cut, the whole chain falls apart).

--- [[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 [[order]]s of the [[real]], the [[symbolic]] and the [[imaginary]], as a way of exploring what it is that these three [[order]]s have in common.  Each ring represents one of the three [[order]]s, and thus certain elements can be located at intersections of these rings. ---==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.