The Borromean Knot: Cut One Ring

Three rings hold together, yet none passes through another. Cut one: the other two fall apart. In the 1970s Lacan thought the Real, the Symbolic and the Imaginary were tied together in this way.

What does it show?

The Borromean rings take their name from the coat of arms of the Borromeo family of Italy. The three rings in the model are three ellipses lying in three mutually perpendicular planes. Taken two by two, no pair of rings is linked; you can test this by cutting one ring and watching the remaining two separate without catching on anything. What holds the knot is the structure the three form together. In mathematics chains with this property are called Brunnian links, after Hermann Brunn, who studied them in 1892.

Lacan introduced the knot on 9 February 1972, in the seminar ...ou pire, and in the following years thought of the Real (R), the Symbolic (S) and the Imaginary (I) as three rings tied together in this way. In this structure no register comes before the others; when one comes undone, the subject’s world falls apart as a whole.

The “lapsus and sinthome” mode concerns Lacan’s seminar Le sinthome (1975–1976). Lacan suggested that in Joyce the knot was tied wrongly at one crossing, that the Real and the Symbolic were chained directly together and the Imaginary, the body image, slipped away. Joyce’s writing, an effort to make a name for himself, works as the fourth ring that repairs this error, the sinthome. This mode of the model is schematic: it shows the logic of Lacan’s drawings, not their topological detail.