# Borromean Knot

Borromean knot (noeud borromÈen) References to knots can be

found in Lacan's work as early as the 1950s (e.g. E, 281), but it is not until the

early 1970s that Lacan begins to examine knots from the point of view of their

topological properties. The study of knot theory marks an important develop-

ment in Lacan'S TOPOLOGY; from the study of surfaces (the moebius strip, the

torus, etc.) Lacan moves to the 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 real and the

imaginary; rather than simply representing structure, topology is that struc-

ture. 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 in Figure 1), 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 (S20, 112). 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).

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 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.