TOPOLOGY EVERYWHERE

ScreenshotTopology is not exclusively a matter of 2d surfaces and projective geometry. In the Lacanian-Vichian view, topologies are produced “spontaneously” my myth, thought, action, and desire. Thus, without naming topology as a specific agent, the best place to look for it is in the landscape, literature, film, architecture, and on the front page of any newspaper.

The Topology Project (Inversion Circles) aims to reorganize Lacan’s interests in 2-d manifolds, knots, braids, and inversive geometry around ethnocentric resources. The nine points of the Project outline the relation of topology to Lacan’s thinking in general, the relation to theorizing required to complete Lacan’s project, and the connection of both of these to the therapeutic clinic.

The radical topology of metaphor, particularly evident in the thought of the first peoples, justifies this bottom-up approach in favor of strictly mathematical analysis. The role played by position and orientation in the construction of cultural topoi have led to cultural-artistic formations as “institutions of the Real.” Ethnographical topologies allow theory to corroborate structural relations of the Real through a dialectic between the individual subject of psychoanalysis and the collective subjectivity of cultural behaviors.

This project requires what has not yet been attempted in Lacanian or any other psychoanalysis: a connection to the 18c. Neapolitan philosopher of culture, Giambattista Vico, whose New Science [1725/rev. 1744] was grounded in a science of metaphor that was “topology before there was topology.” Vico’s “imaginative universal,” which grounded mythic thought as foundational to its evolutionary successors, heroic and conceptual thought, was a radical form of the inversion circle’s topology: ⚪︎⚪︎ → ⚪︎⃝. Inside this condensed matheme is the “toroidal” distinction Lacan makes between separation and alienation, which in ethnological terms are the stories of heroic travel and rivalry, two antipodes that create a horizon between the divergent force of repetition and the counter-force of instrumental convergence.

Lacan’s central reference is the “Injunction of Popilius,” where the Roman Consul to Egypt turns back the military expedition of Antiochus by simply drawing a circle in the sand. In his overlooked “slide-rule analogy” (Seminar XIV, The Logic of Phantasy) we find the toroidal A and a (desire and demand) related to the irrational Ø, the Golden Ratio, Lacan’s mathematical means of engaging the unary 1 in a structure of self-intersection and non-orientation. While these examples are conclusive, their reception has not been. There has been no mention of the slide-rule analogy, inversive geometry, or the relation of the unary trait’s repetition as toroidal. Perhaps this is because further mathematical clarification simply expands the significance of these Lacanian themes. Cultural examples, from folklore, ritual practices, art, literature, and architecture, however, begin to allow focus and refinement.

Ethnotopology embraces the full range of cultural production but puts special emphasis on the historic initiation of the Symbolic, the moment the speaking animal emerged from the ciphering animal, whose 1:1 bi-univocal concurrence left no room for the interpretive ψ in Freud’s neural sequence, φ-ψ-ω. Only with the topological transfer of inside to outside (and vice versa) did the ψ become Ψυχή; or, following the ancient myth retold by Apuleius,~~Ψυχή~~.