Le Seminaire RSI - Book XXII by Jacques Lacan -

Jacques Lacan's RSI seminar (1973-1974), referred to the articulation of the three registers, Real, Symbolic and Imaginary, whose interlocking was the structure of the Borromean knot. While Lacan laid the knot flat to highlight its different "places", he also presented its spatial consistency. By introducing new notions such as the dextrogyratory and levorogyratory form of its configurations, Lacan enters terrain already familiar to chemists and biologists. From Pasteur and Van 'Hoff to Topochemistry, via the stereospecificity of Jacques Monod's biology of 'chance and necessity', molecules have revealed strange powers in space, to which chirality bears witness. By attempting to apply such notions to psychoanalysis, Lacan opens the way to a refoundation of psychoanalytic theory, and probably to its practice. Could "the Oedipus complex, (...) implicit in the knot" be tied in different ways? What place should be given to the different topologies of the knot? How does the object a attach to each register? An algebra of these configurations seems possible with William Rowan Hamilton's quaternion numbers.