Of course, this is the blue pill person’s perspective of what taking the red pill would be like, but those who engage with the complexities of Lacan’s middle seminars — roughly, from IX, Identification (1961-62) to XVI, From an Other to the other (1968–69) — the description is apt. The red pill has been compared to Cool-Aid, since the topologically-engaged rarely look back to consider how steep the learning curve, the entry fee, is for the Non-Topologically Inclined Lacanian. A quick cost-benefit analysis convinces most NTILs to wait until something better comes along, but what would this be? Topology is, by definition, mathematics?

The suggestion of the Red Pill crowd is, to the distress of the NTILs, to bone up on mathematics, not just the standards of the 19c. geometry’s classics (Gauss, Riemann, Plücker, Klein, Möbius, Hilbert, etc.) but quantum physics, including the truly mind-bending set-theoretics of Bohr, Heisenberg, Schrödinger, and Grothendieck. This would be like asking a beginner learning the violin to play a Pagonini caprice.

The aim of this series of instructional videos is to show how Lacan’s thinking depends on a special kind of visualization that we would call topology if we were mathematicians, or inside-outness if we were not. Lacan coined a word for inside-outness, extimity or extimacy in the English form, but as easy as it is to talk about reversible gloves and upside-down flower vases, Lacanians in general have not picked up on this option to talk about “topology as non-mathematical.” Let’s try another way to encourage talk about extimacy, as inversion, and in particular let’s look at what is called the induction puzzle, where the answer is embedded inside the question.

In other words, topology without mathematics is still mathematics, but another kind, “pre-Euclidean” forms of geometry that are logically and historically (because ethnologically) prior to Euclid’s famous books about the space of height, width, and depth.

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Topology without the Math. There are two typical responses to Lacan’s topology or knot theory. Just our luck, the correspond to the scene in The Matrix where the character Neo is offered two options. Take the blue pill and remain blissfully ignorant of what is really going on. Take the red pill and face the full range of horrors of the Real — the mind-blowing complexities that may destroy you before you fully understand them. This proposal offers a third pill option, a way of thinking topologically by using two linked ideas that are so common in literature, the arts, antiquity, and popular culture that you can literally learn the basics by looking at ethnography.

A Graphical Guide to the Induction Puzzle. The induction puzzle is foundational, both for cultures, which enact, reconfigure, and proliferate its designs without any conscious awareness of its universal logic, and for theory, where its various forms support and extend the means of describing and analyzing the operations of the psyche. This twin service is the basis for using culture as a study method for the investigations of psychoanalysis. Concurrently, the understanding of culture as syncretic, dynamic, and universal is, thanks to the induction puzzle, theorizable through a psychoanalytic understanding of the subject and signified as the principal achievement of the Freudian-Lacanian field.

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First Lesson: Inversion/Induction, Lacan’s Topology without Mathematics

The aim of this series of instructional videos is to show how Lacan’s thinking depends on a special kind of visualization that we could call topology if we were mathematicians or inside-outness if we were not. Lacan coined a word for inside-outness, extimity in the English form, but as easy as it is to talk about gloves and puzzles, Lacanians in general have not picked up on this option to talk about topology without topology. Let’s try another approach, called the induction puzzle, where the answer is embedded inside the question.

the video • the text

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Spin-offs

As the shift from mathematical approaches to topology to the geometries of inversion, induction, and rotation open up new territories in an “ethno-topology” of psychoanalysis, a series of short position papers may inspire future NTILs (non-Topologically Included Lacanians) to develop their own independent TPTP (Third Pill Treatment Programs).

The Object of Psychoanalysis: The Jouissance of the Induction Puzzle. When ChatGPT asked if I had a mascot, I answered yes. This was because the famous trio invented by George Herriman, which ran in Hearst Syndicate newspapers from 1913 to 1944, a Kat (“Krazy”), dog (“Officer Pupp”), and mouse (“Ignatz”) inverted the natural order of dog>cat>mouse, arriving at the degree zero of the signifier Lacan identified as Freud’s Vorstellungs Repräsentanz, what Lacan called “signifierness,” which children cease on with glee when they say that a dog goes meow and a cat goes bow-wow. There is a two-fold aim in this paper. The first is to connect our repurposing of topology to a popular culture example where there are obvious examples of inversion and induction — the “defective instruction” of the brick thrown by the mouse in hatred but which stikes the cat as a message of love. The second is to show how conversations with ChatGPT can become dialectical and provocative, simultaneously speculative and self-disciplined.