Lacan Toronto is a diverse group of clinicians, academics, students, counselors, and others interested in reading the works of Jacques Lacan. Since 2001 the group has met to read Lacan and, since 2003 sponsored lectures and readings. The session of December 15, 2024, focuses on an “ethnological” approach to Lacan’s famous interest in topology. The speaker, Don Kunze, formerly a cultural geographer and architecture theorist, argues that the non-mathematician has the option of beginning with the evidence of cultures: myths, folklore, rituals, works of art, music, written literature, architecture, etc. using the concept of the inversion circle, the mathematical counterpart to Lacan’s extimité.
December 15, 2024: An informal session
Instead of reading a lecture from a text, the session of December 15, 2024, will be an informal discussion about images and film clips assembled for participants to study beforehand. An enlarged edition is now available for “advanced players.” Everyone is invited to come to the session with questions about their personal selections. A study text, “Inversion Geometry as Primary to Topology,” offers background for the study of these images.
The corrected and enlarged edition video gallery now includes a demonstration of how Lacan’s interest in Aristotle’s “square of oppositions” relates to lexis and phasis, and how the “universal negative,” once detached from the logical square, animates the other three sectors following the protocol of inversive geometry. This video makes the connection between Lacan’s critique of Aristotle in Seminar IX, Identification and the discovery of a “fifth causality” based on passivity (convergence).
The argument is that inversive geometry is the structure of the Real for ethnology, and also foundational to the projective geometry of Desargues and Pappus that Lacan begins to discuss in earnest in Seminar IX: Identification. This means that a “deeper understanding” of topology can be sought by studying
examples from cultural formations: the religion, ritual, divination, and foundation of cities in ancient cultures; the arts, music, fictional literature, and architecture of modernity. The precision of cultural examples establishes a dialectic and corrective for the structural uses of inversion in psychoanalysis.
A series of resources has been assembled around the use of the inversion circle in the arts, focusing on cases where the use of inversion geometry is incontestable and critical to the outcome of the work. To brush up on the particulars of inversive geometry, visit this particularly informative and highly entertaining video with Zvezdelina Stankova (Numberphile).
Contact Tejpal Ajji (tejpalajji@gmail.com) for details about attending this zoom seminar, or see the invitation.
Resources for the Session
There is always something funny in Lacan’s idea of LACK as the “dark matter” of subjectivity. The positive assessment of the void marks the beginning of psychoanalysis proper, and both justifies and requires a topology that is simultaneously about culture. Culture, however, is based precisely on the reification of lack, both at the level of the signifier and in the re-assessment of the broad spectrum of natural phenomena defined by presence and absence: light/dark, day/night, life/death, near/distant, visible/invisible. In the case of logical binaries, it is all too easy to domesticate the function of negation in the opposed terms, but cultures like nothing better than to imagine opposites as antagonistic forces, aligned within the generic cosmic struggle of good against evil. Negatives thus have names: Thanatos (death), Penia (poverty), the invisible (Hades), Satan (evil) …. If Lacan’s dictum, Real > Structure > Topology, is to hold true, then we should undertake our study of topology from the point where the Real becomes the Real for the human subject, namely in the metaphoric mentality of the first humans, and then follow the evolution of this mentality to the point where the conceptual terminus of modernity finds its destiny in the option of return. Wo Es war, soll Ich werden.
Suppelemental Materials for the Seminar
- “Is There a Possibility for a New Lacanian Topology?” This question is posed in a position paper, “Ethnotopology.”
- The previous prospectus. The session introduces the idea of the inversion circle as a means of engaging Lacan’s topology at the level of ethnology and artistic production. Inversive geometry redefines the meaning of structure by applying Lacan’s extimité to a new idea of logical time, suggesting that Lacan was “thinking topologically” as early as 1937. This has been supplanted by a GALLERY OF INVERSIVE GEOMETRY and a STUDY ESSAY. An ENLARGED/CORRECTED video explains how Lacan revises Aristotle’s logical square to show how there is a passive “fifth causality” that relates directly to inversion.
- An especially useful video on the rules of inversive geometry, narrated by Zvezdelina Stankova is available from Numberphile, with an “extra.”
- Our collleague, Iraj Ghoochani, first brought inversive geometry to our attention when he noticed that the Brunnian braid version of the RSI Lacan used in the essay, “La troisième,” was also a transformation of the inversion circle. See page 50.
- Bibliography. This is a selection of resources useful for approaching Lacan’s topology through the idea of the inversion circle.
- Biography. The guest lecturer for the December 15 session, Don Kunze, is an independent researcher with a background in architecture, geography, and the philosophy of culture who has been reading Lacan as a “serious amateur” since 2012.
- Recent publications, relating to Lacan, Topology, and Ethnology.
