Concentricity of Laws of Form

Thanks to Ellie Ragland’s introduction of George Spencer-Brown’s Laws of Form in Lacan: Topologically Speaking (2004), Lacanians have been aware of the curious coincidences linking Lacan’s work to the British mathematician’s novel “pre-Boolean” calculus. Lacan’s contention that signification begins with a cut that simultaneously indicates value parallels Spencer-Brown’s principle of the “coincidence of distinction and indication” (CDI). Thus, the primary axioms of the calculus constitute a Rosetta Stone connecting the timeless subject of the clinic with the transient subject of ethnology. The critical feature of CDI’s concentricity is paralysis, a function of the self-intersecting and non-orientable surface of the Real Projective Plane. This creates the predicament suffered by Daphne, who found that she was trapped as soon as she determined to flee the advances of Apollo—that it was space itself that had trapped her, that the arrow that inflamed Apollo with love and Daphne with hate had, true to the definition of “a one-dimensional subspace in the projective plane,” moved in opposite directions simultaneously. Lacan’s retelling of this story in The Ethics of Psychoanalysis proves topology to be both logically and historically primary to Euclid. The importance of this would not be clear until, in Identification, he developed his “toroidal” thesis of demand and desire through a figure called the “fundamental polygon.” Until we understand this polygon, we will be unable to properly theorize the role of topology in psychoanalysis or architecture.