Unlike Bloom’s categorical thinking, Jacques Lacan’s style (lexis, λέξις) did not tend to produce orderly lists. It could be considered as the final product, however, of clinamen/tesseræ, dæmon/askesis, and kenosis/apophrades if viewed from the side (Žižek: “awry”). This involves taking Mladen Dolar’s hypothesis seriously, that all of Lacanian psychoanalysis might be viewed as various cases of anamorphosis. I agree with this provocative claim, but only if anamorphosis can be expanded from its limited role as a special case of the Imaginary. Dolar remains within a literal analysis of Hans Holbein’s The Ambassadors (1533), an unnecessary handicap the puts his thesis on hold. To break this embargo, a new ars topica is required. The terms are abbreviations, but hopefully their redundancy will suggests pairings and triplicities.

• The mirror is a cut. If the surface of Holbein’s The Ambassadors is considered to be a cut rather than a transparent window facing the viewer, the relation of the recto to the verso is that of a hinge mediated by the anamorphic skull’s requirement that the corrective view, at a small angle ∂ to the surface of the wooden planks, reveals an “idempotent” geometry determined by the number 3. The surface of the mirror reverses left and right but not up and down because the mirror does not reflect; rather it cuts space into a virtual and non-virtual dual. This can be demonstrated by laying the mirror flat so that its relation to the horizon is co-planar rather than orthogonal. The chirality of the mirror derives from the chirality (handedness) of the Imaginary, which is a “stereognosis” easily conflated to other binaries: odd and even, day and night, life and death. These recto/verso relations are, as Ernst Cassirer noted, also mutually cross-inscribed and geometrically projective. The two conditions of the uncanny defined by Ernst Jentsch — the living person fleeing death but inadvertently drawn to death and the dead person who is unaware of being dead — are parallel to the criss-cross relations of complementary colors, where staring at green creates the opposite effect of seeing red.

  

• Symmetry of the lack. Lacan describes the void marking the union-without-intersection of two Euler circles as “symmetrical difference.” Imagine two Euler spaces, with five places filled by only three numbers: 1 2 3 _ _; and _ _ 3 4 5. In union they remedy their lacks without intersecting: 1 2 3 4 5. This is a simplistic and somewhat inaccurate way of characterizing union without intersection, but it shows that the Euler void is both symmetrical and reversed, hence it is an adequate representation of the criss-cross effect of the mirror as cut. I call this the “Gift of the Magi,” since it is exemplified by O. Henry’s famous Christmas-time short story of the wife who sold her hair to buy her husband a gold chain for the watch he sold to buy her ornamental combs (see “Story Closure” below).
• Euler not Venn. Lacan uses the Euler circle to demonstrate the void of the forced choice (the Cretan Liar’s TF>FT>TF …) because Euler circles, unlike Venn circles, cannot cover the full range of Boolean conditions. They enclose only “real life situations” and thus are marked of the Real as it disrupts the otherwise smooth flow of signifiers in the Symbolic. Clinamen.
• Ex falso sequitur quodlibet. Hegel criticized the “indisputable truth of Boolean logic’s foundational statement of identity, A=A, with the humorous quip, “Is this all?” In establishing its foundation, logic had provided a boring non-conjecture, an axiomatic clarity that it had counted on being uncontroversial. Of course we have the whole of Hegel’s Phenomenology to show just why and how A=A is misleading at best, false if we pursue the case. Rather, the case of A=~A is more interesting, and more consistent with psychoanalysis’s equation of the Real with the Impossible. The principle of ex falso sequitur quodlibet is the principle in logic that claims that the true proposition requires everything that follows it must be true, while the false proposition (think of the Cretan Liar), allows for a full and dialectic consideration of all possibilities. This is equivalent to Seminar IX’s claim that Dostoevsky’s proof of God (“If God doesn’t exist, then everything is permitted) divides into hypothetical and assertive formulations, comically inverting Anselm’s proof of God as beyond explanation. The Flagg Resolution discussed by the mathematician Louis Kauffman explores the A=~A from the perspective of George Spencer-Brown’s Law of Form, which interestingly involves the issue of odds and evens. Note that the Laws of Form is “pre-Boolean” and topological. Like the Euler circle, it is able to flag situations that are Real and ethnologically uncanny.
• X = 1 + 1/X. In Seminar XVII (The Other Side of Psychoanalysis) Lacan uses the algebraic formula for the  Fibonacci Ø ratio that produces the Golden Rectangle, noting how recursion (the need to “plug in” the question to itself to find the answer) is key to understanding the unarytrait, which he consistently represents by writing “1” instead of “one.” The unary trait is a contentless floating signifier, a signifying effect (s”), a signifier that has “forgotten how to die” and is thus, like the newly deceased, a traveler along the fractal path of the Thesean Labyrinth. This is the building designed to insulate the Minotaur (another case of askesis), emblem of the space of the tomb, where insulation is traditionally bi-directional and projective. The recursive algebra reverts to what Stephen Wolfram (A New Kind of Science) has described in terms of empty specifications of adjacencies that, in successive regenerations, produce fractal patterns.
• Idempotency. Lacan does not use this term, but his engagement with projective geometry surfaces (Möbius bands, cross-caps, toruses, etc.) combine to define the mandate of the finite surface without boundaries. In electrical engineering, the elevator button is an example of idempotency: the switch remains on once pressed, and further actions are defeated. But, idempotency also preserves a unary or “first” state, as St. Jerome argued on behalf of Mary’s durable virginity.
• Metaphor as paradigm of the circuit. The mirror cut of the visual field can be described as a union of Euler circles (720º) because of the continued virtuality of spaces without literal mirrors (a perpetual “secondary virtuality” of the neurotic unconscious) — the deduction that, in seeing, we are reciprocally being seen. At the same time, the mirror creates a void at its interface with the reflected world, thanks to the union without intersection (the mirror’s “veracity,” or union, and its simultaneous flatness, it’s “either/or” or non-intersecting condition). This is a 180º subtraction, where the vesica shape frames (internally) the limit of the Imaginary in terms of a half-circulation that is durably half (180º despite its bi-directionality). At the same time, the space of the human subject (who speaks) fills an imaginary 360º planar disk view limited

  

  by the circle of the horizon. The simultaneity of 720º (the reflected and reflecting spaces on either side of the mirror’s cut), 180º (the omnipresent function of the cut as void), and 360º defined by the circular horizon constitute an idempotency that can be explained only in
  terms of projective geometry. Lacan’s formula for metaphor, M/S’ • S’/x → M(1/s”), captures this dynamic by introducing a cut, •, to describe a void held together by a “symmetrical difference” (the inversion of the signifier suppressed by M, S’, that allows Lacan to appear to “cancel out the two S-primes). The cut allows the formula to carry across the unknown ‘x’ to a position of the “signified effect,” s”, in relation to the unary 1. Attempts to read, as Lacan himself seems to encourage, the formula algebraically leads to important impasses. (1) Is the • that seems to allow the two S’ terms to cancel a multiplication sign in any other sense? (2) Is the genesis of denominators for the second S’ — ?, x — algebraically related to the signifying effect, s” — namely, is the metaphor first an interrogation into meaning that can be symbolically abbreviated as an “unknown,” an x; and, is this interrogative sense the basis of the signifying effect’s relation to the unary trait? and (3) Does the fact that the 1, sometimes an I, seem to “appear out of nowhere” a way of describing the unary trait’s equal disdain for time and space relations.

• Symptom/Repression=1. The fourth consideration in relation to Lacan’s metaphor formula justifies its own space. Is the reciprocity between repression and symptom represented by the “repression” by which M pushes S’ “beneath the bar” in M/S’ and the mirror of “expression” on the right of the • in S’/x? If so, then the • is the function by which the symptom is always the “return of the repressed,” i. e. the Real. In the sayings, (1) that the letter always reaches its destination; or (2) that the repressed returns but in reverse order. The criss-cross is a simultaneity that can also be delayed and transported. The simplified expression, symptom/repression=1, emphasizing the reciprocal and immediate effect of repression in the emergent symptom, suggests another principle, namely that this reciprocity is the essence of the “1” associated with the unary trait. Lacan does not write “one” but “1” when he uses the number one in relation to the unary trait. Algebraically, any cancellation of the form X/X=1, meaning that a self-intersection function is also in some way about the trait that Freud described as independent of content, time, and place. Reversing the order of the metaphor matheme, we might say that the answer to “what is the unary trait” is first expressed as 1/s”, whose predecessors of s” include ‘x’ and ‘?’, basically repeating the question “what is the 1?” When Dan Collins

  

  says that s” brings to an end the compulsive pursuit of meanings, he alludes to metaphor as a gateway to meaningfulness over meanings defined as signifieds.

• The Gettier Field. Dan Collins has expanded the Gettier Problem (= the failure to define truth in terms of “justified true belief,” JTB) into a field of combinations of the three terms to produce “palindromic relations” of folded pairings. From knowledge (111) to science (000) the relation, clearly, is not one of cancellation but destiny, moving from science’s imposed denial in Popper’s modus tolens principle (that nothing can be considered as a scientific fact unless it is able to be refuted) to knowledge’s imposed ideal in relation to the claims made about it (justifications, in the Symbolic mode) and our beliefs in it (the evidence of the senses, in the Imaginary mode). This emphasizes the role of the Real of truth, which becomes not a factual truth but the Lacanian “truth of truth,” which involves the Unconscious in relation to the desire of the Other, and the necessity to go beyond the limits imposed by the Kantian “transcendental aesthetic” as a space-time medium dominated by Euclidean ordering (perspectivalism). The issue around the three part of the JTB table relate to the Borromeo knot’s three Lacanian domains. The glue of the knot is the “silent middle” just as it is in the enthymeme and Euler alternative to the de Morgan Laws of the excluded middle. The unconscious’s (silent) neutralization of negation means that the void becomes a cornucopia of meaningfulness, thanks to the principle of ex falso sequitur quodlibet, the Latin principle of “explosion” articulated in Seminar XIV (Fantasy).
• The Doris Day Joke. If Oscar Lavant’s claim was true, “that he knew Doris Day before she was a virgin,” then he anticipated Lacan’s logic of asking, in Seminar VII (The Ethics of Psychoanalysis) what anamorphosis was before artists of the 1500s undertook it with tricks with curved mirrors and unique viewing points. My proposed answer to his question is “the uncanny,” in the most general sense of an ethnology of rituals, beliefs, material artifacts, and architectures that embodied the criss-cross relations of suppression and symptom that Lacan formalized with his expression for metaphor. This answer would allow Mladen Dolar to carry out his claim, that the entirety of psychoanalysis can be brought under the heading of anamorphosis. This claim makes sense as long as the term expands to fill out the idea of metaphor as an empty structure facilitating the exchange of suppression and symptom that relate to the “meaning effects” of the unary trait, in particular its portability and content emptiness. Note that this converges with Giambattista Vico’s idea of metaphor, the “imaginative universal” (universale fantastico), which he said had cost him a good twenty years to discover and was the basis of his major work, The New Science (1725; 1744). The claim that Vico was a precursor of Lacan rests on this identification, but also on understanding Lacan’s metaphor in relation to the unary trait. Is not Vico the “experiential first” and Lacan the “logically prior position”? Doesn’t it make sense to say that “Vico must have been reading Lacan”? The boring alternative, that Lacan must have been reading Vico is true chronologically if we allow that, in reading James Joyce’s Finnegans Wake, he was saving both the baby and the bathwater.
• Blah blah blah. In the L-schema, Lacan portrayed the auditory interchanges between the Analysand and Analyst as a free flow of signifiers characterized as a “blah blah blah” between the poles of the two egos, a and a’, or other. To break past this flow, the Analyst had to employ a strategy of “too late,” >, a cough or rustle to take note of the Analysand’s repetition or bungled explanation, or a “too early,” <, of suggesting a line of thought or provoking a question. Between the < and >, the ◊ of the Analysand’s fantasy might give way to the unconscious Other, assaulting or returning to the Es or S position, in tune with Freud’s saying, Wo Es war, soll Ich werden — that the ego will return to the position held open by or defended by the Id. This was James Joyce’s idea of epiphany, his records of overheard conversations seeming to be idle exchanges of no particular importance, brought into new meaning through sheer detachment and uncertainty, just as the random details of a divination procedure become the basis for prophetic truth. It is important to see how the blah blah blah constitutes the “fuel” of the Symbolic in its role as mask of the unconscious. It would not be too much to ask the reader to connect the blah blah blah to the Lucretian clinamen, where

  

  turbulence is defined as the <> or ◊ of the “any which way” of the ex falso. The blah blah blah’s excess is read from the speaker’s side as unlimited semiosis, but from the attentive ear of the Analyst as a Heraclitan river that does not allow any second to follow a first — in other words, a “unary trait” that breaks (tesseræ) from the flow.

• The Other as Automaton/Structure, the empty signifier, working as a structure whose purpose is mainly to “direct traffic flow.”
• Lateral Transfer, the movement from the suppression (of one signifier by another, in the synchronic process of metaphor) to emergence of the symptom, without any specified meaning, hence the ‘?’, ‘x’, or s” of Lacan’s formula for metaphor. Lateral transfer in ethnological terms is the problem of concealing the “defection” of one of Hestia’s attendants, a daughter who marries and must therefore pledge allegiance to another family’s hearth. The ruse for this lateral transfer is abduction, the sign that the bride resists, present even today in the practice of carrying the bride over the threshold of the new house.
• Internal Bijection. Within the chiastic cross-inscribed structured pairings (union without intersection) of such entities as Speaking/Being, which are, as Lacan says, “not bi-univocally concordant,” there are internal bijective (indexical) features.
• Idempotency as Local/Locale (vs. Global). Idempotency, geographically, is the creation of a protected space through military, architectural, or natural features. Even specific structures qualify as “locales,” interchangeable with the autonomy of the cyclopean hearth.
• Homeostasis, the basis of the circuit’s maintenance of near-zero energy flow, hence its idempotency function. Homeostasis is another name for idempotency. Since Freud’s 1895 essay “Towards a Scientific Psychology,” the question of the binary and its relation to the need to restore balance at the neural, semantic, and affective level drove Lacan to seek satisfaction in the law courts of logic, where de Morgan’s principles of the negation of a conjunction and negation of an injunction (from which we get the concept of the “excluded middle”) bear even on  Lacan’s consideration of the alternating forces of suppression and symptom.

  

• Idempotency, the maintenance of balance, order, or energy state, through the creation of buffers, insulations, internal symmetrical exchange, distance, or distance substitutions. In the broadest sense, idempotency also covers meditation, solace, ignorance, and death. It is not simply the maintenance of the same but the relation of the same to the different, the stimulus, the chance event. A literalistic idea of idempotency involves seeing a circuit whose goal is the maintenance of homeostasis as, necessarily, a conjunction of balanced potentials, 180º+180º, a closed system, 360º. and a fully overlapping mechanism that maintains balance between two states, 360º+360º, or 720º.
• Ethnographic Circuits. This is the idea that rituals, customs, fetish objects, folk beliefs, and other paraphernalia of the uncanny (which Vico would attribute to the dominance of the structure of metaphor, a structure that Lacan would spell out explicitly) are grounded in the neural-perceptual idea of the circuit, a ring whose completion aims at homeostasis but whose geometry preserves non-orientation along with self-intersection. Thus, the uncanny of ethnological traditions is a matter of projective geometry and the “surfaces of no escape” that Lacan described in Seminar VII, The Ethics of Psychoanalysis, tale of Apollo and Daphne. Had Lacan included important background to this metamorphosis recounted by Ovid, he would have found even more compelling evidence to make his case, that Daphne’s conversion to the evergreen laurel could be traced back to “the murder weapon,” a bi-directional, non-oriented arrow crafted by Eros in revenge for Apollo’s insulting remarks about the young god of love’s archery skills. The following list items are forms derived from this murder weapon.
  • Thaumatropes. This 19c. toy was also a pre-historic prayer-token, a disk spun to combine the images painting on recto and verso.
  • Story Closure. Lacan’s two forms of critique, “by the cut” and “by punctuation,” take up respectively the contrasting logics of (1) binary division (subject/object, metaphor/metonymy, synchrony/diachrony, ego ideal ideal ego, separation/alienation etc.) and (2) strategies, functions, and structures of closure: retroaction (après coup), the récit fort, return of the Real, and Lacan’s famous slogan, “the letter always arrives at its destination.” In the story, a certain symmetry of the remainder must take place. As in the famous O. Henry story, “The Gift of the Magi,” the husband sells his watch to buy combs for his wife’s beautiful long hair, while the wife sells her hair to buy a gold chain for her husband’s watch. The “twist plot” was a famous technique of the fictional uncanny in U. S. literature of the 19c.
  • Death Dreams. Is the narrator reliable or unreliable? This unanswerable question is at its purest when the case focuses on the issue f whether the narrator is dead or alive.
  • Chaismus. The X-shaped structure is not confined to Biblical or Classical literature but is the basis for artistic and musical figures as well (the fugue and counterpoint).
  • Enthymeme. This rhetorical syllogism has a silent middle term (bridging the major and minor premises) that corresponds to the latent terms in the Lacanian formula for metaphor. No one has yet compared the two forms or drawn parallels to the utility of the enthymeme in persuading an audience by advising them to do the opposite of what you wish. Looking at the metaphor formula, the major premise would correspond to M/S’, the minor to S’/x. The conclusion would, as M(1/s”), indicate the way latency results into a “meaning effect,” s”, that “brings to an end the obsessive pursuit of new meanings” — in other words, consensus.
  • Apophasis. Signification through omission. This seems to be the rhetorical term (and tradition) behind the “symmetrical difference” that occurs at the intersection of the two Euler circles that relates to the void of the forced choice. When Lacan intentionally chose a rhetorical style emphasizing lexis, style, he exercised this option by limiting the opposite function of phasis, meaning. Lexis and phasis are a zero-sum action. Like other zero-sums Lacan singles out (speaking v. being, content v. act) we realize the dynamic of libido: that it is a fixed commodity and so an “economy” of balance is attached to all transactions. The same could be said of any circuit aiming to maintain homeostasis.
  • The “Ethnological Unary Trait.” You don’t know you’re counting until you reach number 2. Only then is the 1 a 1, but it is by then a “one of 1.” The unary trait is the count that extends without accruing. It’s mathematical formula is x + x = x ( or x • x = x). To speak of an ethnological unary trait is to return to the source, since Lacan cites as evidence of the unary the paleolithic hunter’s use of notches on a bone to indicate kills in hunting. Each notch is a “1,” a unary instance. In modern times, each kill

    

    of a serial killer has the same status, as both cumulative and unary, a portable “hapax.”

  • Emergence. The sudden appearance of novel practices, such as the cluster of artistic plays with curved mirrors, concealed images, and unique vantage points in the 16c. raises the question of what was happening before that made such clustering possible. Emergence demands a theory of latency, of how phenomena that must work right “the first time” have been tested and adjusted over a long period of time, but under another name. The formal mathematico-logical treatment of this is …
  • Sorites, the phenomenon of the “one grain more” or “one hair less” that conjoin two kinds of time, a “long time” in which there is the equivalent of the psychoanalytic “blah blah blah,” and a simultaneity of miraculous effectiveness. The sorites has long been a staple in the cabinet of close-up magicians and hypnotists, who employ random arrangement, detachment, repetition, anesthesia through repetition and voice, and other means of inducing latency. We should pay attention to the similarity between latency in Lacan’s understanding of metaphor and Vico’s “silent mental language,” the basis for the enthymeme’s effectiveness in the rhetoric of civil (heroic) discourse.
  • Body Loading. This trick of pickpockets induces numbness in precise zones that are then idempotent shields covering the thief’s invading hands. The logic of sorites prevails in this place-specific strategy that differentiates zones within a physical–conceptual whole (a body, a region, a city, a building) for the specific purposes of latent operations. Like the passageways made for the circulation of servants and utilities, the spaces of latency are officially uncounted but intensively active, aiming for the moment of emergence.