Summer Immersion: Modification of Introduction and background texts
Long before it became a medical term, the Greek word symptōma [συμπτώμα] played a central role in mathematics. The geometer Apollonius of Perga (3rd century BCE) used the plural symptomata to describe fundamental properties of conic sections. In his work Conics, a symptōma referred to a constant relation between changing magnitudes—essentially, what we would now recognize as the defining equation of a curve. For example, Apollonius described the parabola through a characteristic proportional relation: the square of the ordinate is equal to the rectangle formed on the abscissa. This relation, which he called the symptōma of the parabola, held for every point on the curve, much like how the modern equation y = mx² defines a parabola today.
What is often overlooked is that the clinical topology introduced by Jacques Lacan stands in direct continuity with this geometrical tradition. Yet post-Lacanian thought tends to situate the symptom within the familiar terrain of psychological or psychiatric discourse—as a medical or therapeutic phenomenon. This is striking, since there is no a priori reason to interpret the symptom nosologically. By its very structure, any symptom carries a topological and geometrical form—one that predates the medical conceptualization of symptoms as effects of disease or pathology. If contemporary psychoanalysis, since Lacan, is a clinic of effects, then how can it account for the symptom without once again reducing it to the psyche?
Lacan addresses this by distinguishing between a geometry of the ego and a topology of the subject. He insists that the symptom cannot be isolated without reference to topology. He goes further, claiming that the symptom was rediscovered in the work of Marx—particularly in Marx’s use of economics to introduce a mathematical construction into a political discourse. Yet just as post-Freudian analysis has reduced the symptom to the psyche (subjective experience), contemporary Marxism has reduced the symptom to the social.
It would be of considerable use—not only to students of geometry and topology, but also to those studying Lacanian analysis—to restore a clinical reading of the symptom grounded in its structural and topological foundations, rather than in the psychological or sociological reductions that dominate today.
We begin with a reading of Plato’s Meno, focusing on the problem posed by Socrates concerning the doubling of the square and the construction of a mathematical hypothesis (86c). At its most basic level, we return to the deceptively simple question: “What is a square?”—a question that recalls something infantile, perhaps even traumatic, learned too hastily and too dogmatically in early schooling. To dislodge this problem from its familiar pedagogical setting, we will turn to several texts—translated and made available on the virtual classroom: https://www.lacanlosangelespsychoanalysis.com—that approach it from both mathematical and analytic perspectives.
Throughout the course, we will trace how the construction of the symptom reopens the clinical foundation shared by geometry and psychoanalysis. No technical background is required, while the historical readings are only facultative to the presentations. Attendance is limited to 10 people, while registration is open till Friday July 4, 2025. A Zoom passcode is required for entry.
Summer Immersion 2025 Course Description
Title: From Geometry to Topology and Knots
Dates: Saturdays and Sundays: July 5, 6, 12, 13, 19, and 26, 2025
Time: 10:00 AM – 12:30 PM PST
Instructors: Scully-Robert Groome; Baba Singh
Tuition: $250
Contact: PLACE@topoi.net
The curriculum is structured as follows:
July 5: Geometry – The Problem of the Meno: Doubling the Square and the Mathematical Hypothesis
July 6:Geometry of the Group/B.Singh
July 12: The Symptom in Geometry and Topology
July 13: Geometry of the Group/B.Singh
July 19: Knot and Surface – Groups, Polynomials, and Colorings
July 26: From P.G. Tait’s On Knots to Lacan’s Sinthome
For questions or further information, please contact: PLACE@topoi.net