Summer Immersion 2014: Algebra, Logic, & Topology
Tuition: $300.
First Meeting: 11:00-1:30 Saturday July 12, 2014; then three more Saturdays till Aug. 2.
Requirements: Open to the Public. The immersion is for all levels and requires no previous background in logic or mathematics.Class limited to first six applications (reception of tuition required to confirm registration).
Descriptive: The immersion will concentrate on developing a translation between Algebra, Logic, and Topology. It proceeds in the manner of an atelier in the sense that the participant will need paper, color pencils-pen, scissors to construct topological objects and images that conform to the writing of Logic and Algebra.The immersion is not a lecture, but is a collaborative effort in presenting constructions that responds to a problem posed during the course.The immersion is developed in the context of the recent 'Constructing Oedipus' course, especially the problem of symmetries and dualities in space. This much said, the immersion will not develop the translation into the psychoanalytic vocabulary, but will concentrate solely on the Algebra, Logic, and Topology.
Text: The immersion will use as its reference Groups and Their Graphs by Israel Grossman and WIlhem Magnus; American Mathematical Association, 1964.
Pre-immersion assignment: it is advised to read Groups and Their Graphs chpts. 1–4 with a focus on writing a presentation of a triangle in space (2 and 3 dimensions).
Plan of Immersion
I - July 12: Call for presentations and constructions of the Group of a triangle in space. Call for the presentation of the multiplication table of the Group for the triangle. Call for the presentation of the axioms of a Group.Discussion of problems/results: symmetries, rotations, identities, etc.
Assignment for July 19: Read Chpts. 5, 7,10. Focus: writing the presentation of a tetrahedron in space
II - July 19: Call for presentations of the graph of the group of a triangle. Call for presentations and constructions of the Group of a tetrahedron in space (3 dimensions and 4). Call for the graph of the group of a tetrahedron.
Assignment for July 26: Read 11,12, 13.
III - July 26: Call for presentations and constructions of the Normal Sub-group, Galois Groups, and Quarternions.
Assignment for August 2: Read Chpt. 14 on the Group of Links and handout of immersion on Groups of Knots and Logic. Focus on the Group of the Knot, Link, and Lock – with the translation in to Logic.
IV - Aug. 2: Call for constructions and/or presentations of the Group of the Knot, Link, or Lock.Call for a translation of the Algebraic (Group) notation into a Logic of the Knot.Concluding summaries from the participants (if they have one) and proposals for future work.
The 2009 Summer Intensive aims to introduce a theory of knots without vulgarizing. This much said, no previous mathematical or technical competence is required to participate, just a certain amount of perseverance, colored pens, and paper.
INSTRUCTOR
Robert Groome and invited guests.
PLACE & TIME
It will take place on every Saturday from 12:00-2:30 from June 6th to July 18th in Santa Monica, CA.
COST
Participation costs: $750.
COURSE ADMISSION
Open. Limited to 5 participants. Pre-registration suggested. To enroll contact – Place@topoi.net – for code and access to class via the website.
COURSE SUMMARY
1. Introduction to the theory of Links, Locks, and Knots: Problems, Theorems, and Conjectures.
2. The Object of Knot Theory: Duality, Symmetry, and Projection
3. Methods of Knot Theory: Codes, Graphs, Groups, and Polynomials
4. Reformulation of the Classical Theory of Knots: Lock Theory
5. Generalized Lock Theory
6. Modern Analytic Constructions: Lacan, Soury, Vappereau, and Bertheux.
7. Open questions and final presentations
TEXTS
Adams, The Knot Book, 1994.
P.G. Tait, On Knots, 1876-85.
R. Groome, Return to On Knots: New Elements For An Analytic Construction, 2009.
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