In a mode borrowed from mathematics, I use “ersatz speculation” to pose unlikely hypothesis in order to generate “error data” (evidence of folly) that provokes a spontaneous generation of a second ersatz formation, where there is then a presence of “outward” speculative adventure combined with “reality consciousness.” Drawing from the tradition of fou-litérature, what Lewis Carroll referred to obliquely as “litterature,” conversation proceeds within a thin layer separating tongue-in-cheek irony and mantic discovery, never saying which. Although the writers of Romantic Irony sought refuge in the fairy tale, I retreat into the fake fortresses of academic form, the critical essay where, as Lacan would advise, “criticism of the cut” meets “criticism by punctuation.” Together, these forms mimic the principle features of projective geometry’s “self-intersection” (punctuation) and “non-orientation” (the cut). The laminar structure of the cut is about loft and parallelism, the need to create an orthographic map that, in falsifying the surface along which it must travel to represent and represent to travel, inadvertently creates a silent middle, a “no-man’s land,” just as in World War I, the overlap of the two armies’ fronts created a zone where deserters from both sides formed self-sustaining multi-national utopias able to survive fire from both sides.
No Man’s Land was orthographic in that, by the mechanisms of emergence, a “true” version of what the armies could not achieve appeared out of dialectic opposition. This variation on the theme of the Hegelian Absolute is simultaneously anamorphic (what is sought is what has been “hidden there all along”) and virtual (the space of this hiding is itself hidden). Because one aspect depends on the other, we must use the new ideas of “co-virtuality” and “co-anamorphosis.”
The notes will be one-sided (made while in conversation) but largely provoked by my conversants’ projects — papers, dissertations, projects, etc. The absence of one party of the conversation will create an unavoidable fragmentation, as when in a movie someone is speaking on the telephone but the speaking partner is unheard.
Framework
Speculation must begin with a foundation that, initially, sets up parameters for assigning “wins” and “losses.” Otherwise, there would be no pain or gain from conjecture. In this sense, ersatz speculation resembles what Lacan said about castration, that it was the threat of either success or failure that terrorized the subject. Thus anxiety over the privation or promise of jouissance fuels curiosity by constantly shifting the margins of discourse, creating a “heads I win, tails you lose” situation.
The framework chosen for ersatz conjecture follows Lacan’s lead. It could be said that nothing interested the Catholic French acolyte more in his Jewish-Austrian master more than the role of negation in constructing the relation of the subject to the signifier. Where Freud had seen three independent categories of negation (Verneinung, Verleugnung, and Ververfung — loosely, denial, disavowal, and foreclosure), Lacan saw an interrelation. Each form of negation, in effect, negated the “previous” form, in the same way Lacan was to recognize, in the Borromean knot, each ring was both in a top, bottom, and middle position, being covered by and covering its nieghbor.
As is well known, Lacan converted the three types of negation to the diagnosis of the three classic subjectivities, the neurotic, the pervert, and the psychotic. What is less recognized, however, is the way the three types of negation relate to the three “moments” of the induction puzzle Lacan used in his essay on Logical Time, Three Prisoners’ Dilemma. These were (1) the moment of the gaze, (2) the moment of comprehending, and (3) the moment of concluding.
What makes the Three Prisoners’ Dilemma an induction puzzle is the fact that the Warden’s instructions were flawed. Thanks to the fact that no black dots were used from the set of five pinned to the prisoners’ backs, the moment of the gaze was incapable of producing the necessary view of the winning prisoner: two black dots. The first negation, structured by the gaze, revealed the key flaw in the warden’s definition of “the one who would win.”
The second moment, also a paralysis, subjected the first pause to reflection. The “truth of knowledge” came about through a Peircean abduction: what would make this “astounding” event understandable? To exorcize the “demon” of the first paralysis, it was necessary to question the frame of the game. As in the classic induction-puzzle example, “There are three erors in this sentance,” the third error would be the fact that there were actually only two errors. The puzzle would be its own answer.
The Three Prisoners’ Dilemma featured in Lacan’s early essay on Logical Time came from a dinner-table conversation Lacan had in 1937 (Rodinescu). But, from this moment on, Lacan was alert to the issue of triplicity. The structure that held the Prisoners’ in a tight logical sophism was the same, Lacan realized, as the irony holding together the three types of Freudian negation. From here it was but a short jump to the Borromean structure of the Real, Symbolic, and Imaginary, first as a stack of equal-sized rings, but later as the inversion-circle transform, a cross of orthogonal lines representing the Real and the Symbolic, laced by a circle of the Imaginary (“La Troisième”). From here, it was possible to deduce a novel variation for the four discourses, as well as a temporality implicit in the creation of metaphor.
Lacan’s triplicity far exceeded the ambitions of Freud’s Ego, Super-ego, and Id, but Lacan never forgot Freud’s ambition, to uncover structure beneath symptomatic surfaces. In the L-Schema, triplicity unfolds the RSI as a zig-zag from the ES to the Unconscious and back, a circuit that, on account of the Imaginary’s duplicity, made two turns (720º) from one (360º), an interior-8 and, hence, a toroidal subjectivity.
To guide ersatz speculation, a series of analogical tables develop the idea of triplicity through comparisons to the standard joke about the broken kettle, to the 2-d non-orientable torus, to the so-far unvisited issues of sorites (“one grain more, one hair less”) as a model of emergence that Žižek has discussed. Even Lacan’s formula for metaphor has a triplicity in its sublation of one signifier by another, the production of a “parapractic” signifying chain, and the conclusion of the s” that terminates what Dan Collins has called the “endless search for new signifieds” by revealing that the ‘1’ is not a number but, rather, an endless iteration.
For more, see “Triplicity in Spencer-Brown, Lacan, and Poe,” a chapter in
Conversations with ChatGPT
Another proper name for ersatz conjecture is the induction puzzle, where at a “presentational” level, defective instructions are given that are resolved at a “demonstration” level, in such a way that the two levels reveal a co-dependency that could be compared to symmetrical difference. This is the essence of the Lacanian “lack”: it is inherently double, inherently reciprocal, inherently dynamic. Thus, it is more productive to talk about a double circuit structured by the interior-8. This is particularly evident in the question of Logical Time, where Lacan and his commentators needlessly and tediously carry out the “sophistic” of the puzzle of the Three Prisoners, deducing that the matter concludes with the enigmatic issue of the Big Other, but fail to say who this Big Other is for, or how the riddle is structured thereby.
This and other conversations with ChatGPT have proved to be productive and well-informed, thanks to the extensive search-engine capabilities of OpenAI.
- The Warden’s Big Other Problem. Here, Chat suggests a program to generalize the structural paradigm of the Induction Puzzle, to include a range of cases involving defective instructions (enthymeme).
- On Incompleteness. Thinking of how many rhetorical figures attempt to manage the utility of the premature ending, I asked ChatGPT to reflect on the meaning effects and techniques of this age-old device.
- Freud’s Theory of Libido and the Quest for an Energetics (Circuit) Model of Psyche. In short, Freud’s genius lay in the way his libido/energetics model for the brain’s circuitry was a conservation mechanism requiring complex units on the order of a+bi, a rational or “countable” element and an irrational element that could, like the irrational i, could be subtracted/suspended and added back later (±i). This invigorating conversation holds out hope for extending Freud’s cathexis idea to popular culture.
- EFQ and Beyond. Lacan mentions the EFQ principle (ex falso quodlibet sequitur) in several places; it remains to his readers to extend this to the idea of the induction puzzle, where defective instructions create a symmetrical difference between presentational and demonstrational levels.
Conversation with Francesco Proto
This working paper looks at Lacan’s RSI domain system to focus on the “thaumatropic” function of the Imaginary, as converting the function of the “perpetually absent ring” (in the Borromeo knot representation of RSI) to the functions of “co-anamorphosis” and “co-virtuality.” Thanks to work by Dan Collins in explicating the (inadequate) idea of knowledge as justified true belief (“A Short Digression on the Meaning of Knowledge,” Lacuna 18, June 2019), the theme of paralysis in Plato’s parable of the Cave can be read as an account of the role of idempotency in dreams as well as ethnographic examples, as the logic of the boundary — both an insulation and conversion device.
In the latest addition/edition to this rambling scramble over the RSI’s mappability, the idea of apophasis, the Medieval rhetorical practice of describing something by saying what it is not, was added, thanks to Elaine Kunze’s random comment about something she was reading in The London Review of Books. This is pure zairja! Apophasis is the orator’s version of “symmetrical difference,” which opens up new territory that includes the funny après coup of Genesis, that the first day is not described and the last day is God’s time off, the sabbatical. In this “twist of the two remainders,” we have the idempotency function of x+x=x, which happened to be exemplified in the February 18 seminar on Rear Window, the discussion about the status of the wedding ring, which can be called a circuit measured by 360º, 180º (one of a pair), or 720º (also implication of a double). These circuits return (hah hah) us to the issue of seeing (180º) implying being seen (+180º, or 360º … or is it 720º?). Armed with such speculations, we can return to Lacan’s classic diagram of the gaze, two intersecting triangles, and feel more confident that we might be able to say something about the screen that divides/joins them.
If you would like to weigh in on this conversation, send in notes or, better, a list of issues that push the claim that there is a “mappable RSI,” or that there is a “Gettier RSI,” or whatever else might come to mind. The current discussion looks at the surfaces between representation and the surfaces of human action, orthography, and the weird idea of idempotency as a buffer and reversal machine. Even more challenging is the issue of the lipogram in relation to the map’s “failure” to map the unmappable — psychosis and perversion.