Figures 2 and 3 are Lacanian diagrams for the Borromean ‘knots’ of 3 and 4: RSI and RSI plus the symptom/sinthome. Figure 4 is a trefoil knot, reinforced by additional loops, as in a compensated psychosis. Mathematically speaking, the Borromean figures are not knots; they are a way of thinking enabled partly by set theory and partly by knot theory; interpreted from the point of view of a person’s reflective subjectivity, this becomes, as Bursztein argues, a subjective topology. The symptom (the fourth loop, as in a Venn diagram of 4 sets), loops around the object-relation, potentially (or ‘virtually’, in Spinozan/Deleuzean language) traversing these three ‘jouissances’: phallic, of the Other, and jouissance of meaning.
Lacan, like Bion, argued that formalism enables the theorist to separate out the variables from the invariants, focusing on structure and function. X is the algebraic notation for a variable; Lacan’s mathemes and topologies can come into play when the analyst reflects on ‘x’ in the course of the psychoanalysis: who is this? What are their key signifiers? Where are they at, in terms of their jouissance? Bion’s innovation is the ‘grid’, a table for notation in which we might plot, session to session, the rate of change (Δx) for the indicators of alpha and beta function, that is, thinking-and-feeling in terms of presence-and-absence versus concrete thinking and feeling. Lacan’s late theory is about the structure of the psyche (RSI, the ‘third’ topology) and the object-relation (separated out into the relation to the big Other and the object little a). As in mysticism, there is a third other and fourth jouissance; the other jouissance, positioned as ex-timate, as excess, beyond conceptualisation. Earlier translations of Lacan into English (Mitchell and Rose 1985) emphasised the gendering of Lacan’s various notions of the other, translating this as ‘feminine’ jouissance.
The project I came up with was to juxtapose the rainbow flag of the LGBTQ movement to Lacan’s RSI. Although I think that Lacan’s third topology and Freud’s first and second topologies are as good as it gets in terms of a way of thinking the structure of the psyche, I am more of a field theorist. Like Ferro (2002), I argue that whatever manifests in the field of transference is a derivative of the unconscious. In addition, I suggest that we can learn from analytical work with a person living with psychosis, when transference is created moment-to-moment, again and again. Even the stable and relatively fixed psychic structure of neurotics is created moment-to-moment as sameness and in the ‘future anterior’, as ‘it will have been’.