Following a clairvoyant suggestion made by collaborator Iraj Ghoochani, the phenomenon of the “Fisherian Runaway” quickly became a provocative component of a proposed project on melancholia. Although melancholy’s secrets seem (still) to be bound up in Albrecht Dürer’s mysterious reference to the limen coeli (anagram of “melencholia,” deliberately misspelled by the artist in his famous engraving), as played out by the mathematician David Finkelstein in his short work, The Melancholia Manifesto (2016, Morgan and Claypool), the Fisherian Runaway proposes the dominance of sexual selection over natural selection, dependent on displays of the male to the female that are otherwise negative factors of selection. The large elaborate tail of the peacock put the male at risk, yet the genes producing large elaborate tail feathers are preserved and reinforced, as if the beauty of the feathers’ colors had become “esthetically adaptive,” despite obvious practical advantages.

position papers

paper 1: D. Kunze, “Do It Anyway,” (PDF, MS-Word) What is melancholy? Is it a “trope” of creativity and those who excel in the arts? Is it the name of a set of symptoms attributed to those who are simultaneously productive and self-destructive? We review the legacies of melancholy the date from before Assyrian astrology to conclude that melancholy holds the key to the idea of renewal, self-destruction, and apotheosis, where entropy (decline, dysfunction, termination) is structurally built into mechanisms of survival and development. At the same time, this entropy, understood as a structure, is essential to whatever it destroys. The idea of instrumental convergence (to an apocalyptic end) can be topologized using the idea of “extimity” — the inside-out conversion that may be more productively theorized as an “indifference” to distinctions of containers and contents. This indifference is nothing less than the intellectual achievement of melancholy and the reason (preserved in historical traditions of melancholy) for the melancholic’s central ambiguity, a “contronymic” combination of death and immortality.

paper 2: D. Kunze, “The Problem of the Double Circuit,” (PDF). The Melancholy Conference (Marywood University, 2025) offers a means of presenting a theoretical position joining central interests of architecture (position and orientation) in Lacanian terms. The components of this theoretical foundation rely on topology and the “energetics” Freud sought to clarify in his 1895 essay “Project for a Scientific Psychology.” The failure of this project may lie in the concept of the circuit, which is doomed if electrical energy is conceived as a flow of electrons.

[Send position papers and commentaries/critiques of existing position papers to kunze767@gmail.com]

topical chains

One way of developing a project is to suggest series of topics linked by logic, association, cultural proximity, or just accident. These take the form of X>Y>Z, where the principle of ex falso quodlibet sequitur (“anything can be deduced from a ‘false’ assumption”). The “false assumption” is, in research terms, the falsifiable assumption or proposition, the sine qua non of an scientific conjecture. The standard procedure is the method of the negative hypothesis. The aim is to disprove an assertion that should be, to make the process both exciting and useful, as improbable as possible. To find out that something that sounds on the face of it highly improbable or even impossible is actually true is astonishing and ground-breaking — a discovery of consequence. Therefore, conjectures should make claims that are, at first glance, highly unlikely, then move quickly to disprove them.

The esthetic aspects of sexual selectivity as a force equal or superior to the natural selection of predation is just such an unlikely proposition, especially if, as in the case of the peacock, the survival advantages via sexual selection seem hardly equal to the disadvantages of natural selection. The analogy of the melancholic makes sense in terms of a comparison of ratios. Of all four of the original “humoristic” types, melancholy seems to have only the advantage of creativity. Sanguine natures would seem to be the most beneficial to society, since they give rise to love, marriage, and sexual reproduction. The choleric nature of the hero, willing to take risks on behalf of the group,  is equally essential. Phlegmatic pragmatism and caution are counterweights, making choler and phlegm function as a pair.

Melancholy, in contrast to these three culturally essential humors, seems to be useless. It is a sickness more than a disposition. While melancholics are productive in a manic sense, they are equally disruptive in depressive phases. Ever since Aristotle’s “Problemma XXX.1,” melancholics have been judges to be prone to self-doubt, to the point of suicide. When manic, they are disruptive, unruly non-conformists. The fact that the melancholy type has survived for centuries and across diverse cultures with its symptoms intact indicates that there is probably some underlying structure of melancholy that, attuned to other survival benefits, has preserved this malady from antiquity to the present.

The following topical chains aim directly at the question of structure. Using Lacan’s schema of the four discourses (a fifth discourse, of “capitalism”) and Lacan and Vico’s equally durable formulas of (root) metaphor, each string will be tested and compared.

string 1

Fisherian runaway > sexual selection v. natural selection > katagraphic cut (instrumental converence as entropy built into each “growth project”)

Sub-string: katagraphic cut > inverter circle logic …

Commentary. This pathway moves from the biological argument to the function of the cut. This is, in biological terms, the division between survival through sexual reproduction and the transmission of traits genetically and survival as the avoidance of dangers and domination over others in any ecotone. In the former, appearance is critical and open to a set of independent (“aesthetic”?) variable. Despite species specificity, there is reason to ask why what a female peacock considers to be advantageous is also something that humans find beautiful. What “aesthetic principles” could be so strong, so universal, as to jump across the vast differences between human and ornithological perception? The katagraphic cut is topologically distinctive. It is a cut that generates difference as it cuts, an action that presupposes the priority of cutting over the material being cut. This opens the possibility that the cut is the primary force/action of what is known as instrumental convergence, where convergence, like the cut, seems to happen without there being anything prior convergence. What converges is not knowable prior to the act of convergence, and comes into being only retroactively. Read Jean Gayon, “Sexual Selection: Another Darwinian Process” for a discussion of the two survival systems and the theorists who have debated their differences. Comptes Rendus, Biologies 333, no. 2 (2010): 134–44.

string 2

katagraphic cut > inverter circle > perceptual space creation > species-specific perception > rhetorically conditioned perception (Lacan’s Hysteric/Master/University/Analysis system; amended by a discourse of the consumer).

Commentary. The inverter (or “inversion”) circle is the horizon of Lacan’s idea of extimity, a cut whose generated division creates parts that are inside-out versions of each other. The topology of the inverter circle is rather simple and stable. Any form that touches the center is relocated to infinity, and any element at infinity is, in the other direction, converted to the central point. Circles retain their shape but may vary in size. Points tangent to the circle require any subsequent estimated form to remain attached to the inversion circle.

string 3

Melancholy > “melencholia §1” (Dürer) > limen coeli (“gate of heaven”) > cœlum = burrin, wedge, heaven > the Hegelian contronymic of Aufhebung (cancel/preserve) as well as dialectic in general as a “face to face” > contention > difference > aggression v. humiliation (Edmund Bergler).

Commentary. David Ritz Finkelstein’s study focuses on the cut created by the contronym, cœlum, by means of his discovery of the anagram concealed in Dürer’s intentional misspelling of melancholy (“Melencolia”). The limen coeli in his famous engraving is framed in the background by a “moonbow” — like a rainbow but created by moonlight instead of sunlight. Finkelstein’s  analysis ambitiously inventories every item of the engraving, but it is his primary investment in the (katagraphic?) cut that promises to unify the emblem on behalf of melancholy, under the thesis that this humor, like the hole in the firmament that is a gate of heaven, is topological rather than Euclidean: a hole that, in two dimensions, is essentially a fold with a twist. When Bergler pairs humiliation and aggression, he is essentially claiming that there is a circuit (with a hole or twist) that explains why aggression is actually intended to end in humiliation. The return to a “degree zero” is always a nothing that is something, and vice versa.

string 4

contronym as the “melancholy signifier” > sexual/natural > sexual difference as a not-all lalangue > gate theme (Vico: cœlum as “heaven” and “wedge”) > humors as discourse.

Commentary. A melancholy signifier would be one that fails grammatically to fulfill the standard communication needs that domesticate each utterance as meaningful. Lalangue is distinctly “useless,” but it is at the same time intensely evocative and feminine. Chomsky’s attempt at meaninglessness, “Colorless green ideas sleep furiously,” is both grammatical and poetically provocative, contra Chomsky, since it brings up the idea that colors are not colors without light, but that they could possibly remember, in a distinctly melancholy way, during their sleep in darkness. In Lacan’s theory of retroactive meaning (the beginning of the sentence is not known until the end is reached) is condensed into the idea of a single melancholy signifier that, like Vico’s “imaginative universal” (universale fantastico) would return to the inception point as to a void.

string 5

Kant’s Critique of Judgement > beautiful v. the sublime > utility theory > gadgets > Shaker/Amish theories of mechanism > the Devil’s promotion of idleness > Lacan’s alethosphere, with holes > holes in the 3rd Critique > vista lookouts > Poe’s “Arnheim” > Poe as melancholic (the useless writer, the uselessness of writing) > the 3rd Critique as useless.

Commentary. The contrast between the beautiful and sublime, made into a popular topic by Edmund Burke, begins with a discussion of uselessness (“disinterest”) that affords a definition of the beautiful and sublime in terms of a contrast of harmony and disharmony. The latter is coupled with the risk of annihilation and revisits the theme of the Fisher Runaway. Danger, in the Runaway, is introduced genetically, in that beauty is produced at a cost of increased liability. Lacan’s example of the coupling protocol of the praying mantis bears directly on the idea of the cost of sex and the ambiguity of sexual attraction. If uselessness is essential to disinterest, the question of the gadget is shifted to the kind of uselessness involved. Shaker/Amish discussions of technology require tools to relate to the creation of free time, which can then be devoted to prayer. In other words, utility > leisure. In secular terms, gadgets convert religious devotion to idleness-enhancement. The arts could be considered as a massive idleness enhancement protocol, and a new contronym is created out of an imagined transfer of happiness from the (now) melancholic creator to the (idle) audience, materializing happiness algorithm as a “fixed-sum” that, to benefit one, must abandon the other. This is reflected in popular culture characterizations of the artist as “empty,” “alone,” and melancholic.

The question, “useless for what” and “useless to whom” are key to the Kantian concept of disinterest (indifference). In mathematics, disinterest is the same as equality (=). The equal sign of equivalency is also translatable as “can be confused with.” The dynamic of exchange leads to the logic of silent trade, analyzed effectively by Norman O. Brown’s Hermes the Thief.

string 6

The fourth wall in cinema > soliloquy > katagraphic cut > inside frame (Žižek et alia) > infra-thin (Duchamp) > suspension of disbelief (Coleridge) > induced coma (El sueño de la razón produce monstruos) > suppressed cubic > the method of removed/returned 9’s (Cecil Balmond) > Whatever Works (Woody Allen, 2009).

Commentary. Slavoj Žižek claimed that the question of the inside frame was discovered by him, accidentally, during a lull of conversation at a boring conference. In fact, the idea is as ancient as the story of Zeuxis and Parrhasius, the contest between two superstar artists, where the former painted a mural depicting a bowl of fruit so realistic that a bird flew into the wall and broke its neck. The judges thought that Parrhasius could not possibly win after this decisive spontaneous demonstration of natural authenticity, so they became impatient for the second artist to draw back the curtain concealing his contest entry … but the entry was the curtain, which fooled not just a bird, with natural intelligence, but the keenly critical judges, who in their anxiety to declare the truth of natural depiction were blind to the artificial cover. This anecdote has not yet been theorized in terms of the induced coma, the “sleep of reason.” The curtain always conceals monsters: “a” monster or “the” monster (cf. The Testament of Dr. Mabuse, 1933).

string 7

Are melancholics hysterics? > Freud’s “Project for a Scientific Psychology” (1895) > compulsion & repetition > hysterics’ repetitions are not explicable > repetition as fact generates (retroactively) the “what” that is being repeated > compulsion invents its own basis > the melancholia of the hysteric’s “non-reality” > hysteric’s discourse (Lacan) as a cancellation of the (hygienic) mandates of the Big Other > “dirty words” > trespass (Remus) > the attractiveness of transgression > wickedness invented to account for the curious attractiveness of others  (Oscar Wilde) …

string 8

Agutezza (theory of genius, 17/18th century) > Don Quixote > witty but non-genius of Sancho Panza (and why) > relation of the journey to agutezza > Henry Johnstone’s theory of travel as wit > the melancholy exile > travel and delay > induced coma > suppression of the cubic > inverter circle infinities > point line and plane, revised > the picture plane > fourth wall.

Commentary. The theory of wit has been isolated from mathematics, so the keys to the inverter circle are held by ethnology, folklore, and literature, particularly in the theme of the katabasis, the suspension of time correlated to the extroversion of travel space in classic examples of heroic travel. The ancient hero was notoriously melancholic, to the point of madness. This was coupled with destructive mania, the other dry humor, so the choleric and melancholic establish a vertical (dry) axis in contrast to the horizontal humors, blood and phlegm. Is the verticality humor-axis related to the “vertical” (synchronic) axis of metaphor, and the accompanying universality of the expressive function (Cassirer: Ausdruksfonktion)? This would contrast and emphasize the horizontality (extension) of the travel landscape in relation to the inverter circle (where the edge is identical to the center).

string 9

Piranesi’s series of fantasy prison scenes, i carceri > … [this string will be the most commonly taken, so we leave it to others to develop; however what will be missed involves the relation of the infinite prison to the Library of Babel (Borges) and the geometry of Pappus and Desargues. Tant pis!

Commentary. Architecture theorists have not yet added projective geometry to their ars topica and thus will deny the relevance of topology to Piranesi’s most famous work. “Primal allergies” afflict this discourse thanks to a misunderstanding of the imagination, which can be traced back to the work of Richard Kearney (Wake of Imagination, 1988), whose jump from esthetics to theology is correlated to a Catholic/New-Age interpretation of the sacred, not as a contronym, as Freud advised, but as a (hyper-)parabolic limit that is un-theorizable. Kearney’s influence is correlated with a general rejection of the Frankfort School and domestication of Walter Benjamin’s work, possibly to avoid ideological identification and, consequently, social controversy, in order to focus on an Ellulian/Mumfordian binary in opposition to Modernism’s Enlightenment legacy. Kearney’s influence can be felt as far as the general preference for a “criticism of captions” versus a “criticism of structure,” or “examples over causes.”

string 10

Inversion circle > repetition types (linear, cyclical) > “kissing” (tangency) > agutezza (theory of genius) > instrumental convergence > black bile as toxic in any amount (tangency) > paralysis

Commentary: This string allows melancholy to offer a rationale for connecting topology to ethnology. The inversion circle is a mathematical device of inversion. The structure of the inside of the circle is inverted (Lacan: extimité) with a precise translation protocol. Any circle inside the inversion circle that touches both the perimeter and the center becomes a line extending to infinity, or rather “two infinities which are actually one infinity, equivalent to the center of the inversion circle.” No shape inside the inverter circle is preserved except circles. Circles that don’t touch the center are extroverted as circles, but those that touch the circumference must remain in contact. The center of the inversion circle is equivalent to a “horizon” lying at infinity outside the inversion circle. The cut is what makes the melancholic melancholic, a condition comparable to paralysis, which in the first Cyclopian societies created the “Promethean protocol” of worship of the flame and religion of Hestia. Paralysis is the theme of Odysseus’s encounter with the Cyclopes, indication that by the 800 BCE a modern mentality had subtended a “metaphoric” primary mentality. While Milman Parry is credited with discovering the “collectivity of Homer” the credit should go to Giambattista Vico, whose New Science (1725) contained the explicitly worded claim “Discovery of the True Homer.” Vico must have been aware of the logic of the inversion circle in that he himself employs it in the structure of The New Science and at the same time understands its function in culture, i. e. in the narrative structure of The Iliad and The Odyssey. James Joyce did the same.

string 11

Hysteria > silent trade > the role of the pivotal third element > sorites > enthymeme > instrumental cause > expressive function (Cassirer) > silence in general.

Commentary: The katagraphic cut (between causal order and cyclicality) can be resolved through a legal fiction that is first evident in the practice of silent trade, where two or more parties exchange surplus goods at a remote crossroads (metaphor for pathway intersection) and, to account for how goods left and later exchanged by a passerby for goods of equivalent value, a “vertical signifier” is created: metaphor, namely the metaphor of Hermes. The relation of metaphor to parapraxis, specifically Freud’s parapraxis of travel, is key to Hermes’ function as a messenger with diplomatic immunity, but also to Hermes other “inexplicable” functions. Equivalency (indiffenence) is the conceptual product of silent trade, and thus mathematics is born out of the emergent equivalencies arising from the delay of exchange. This is later “discovered” by Francis Galton in his famous experiment with wrong guesses of a prize bull’s weight at a county fair. This “wisdom of the crowd” can be summarized as a “truth of error,” as when a sufficient number of people (>40?) are asked to guess the number of jelly beans in a jar. None have the correct answer but the average comes remarkably close. This is the principle that Lacan cites in Seminar XIV, The Logic of Phantasy (Gallagher translation, 42, 45): ex falso quodlibet sequitur, the “principle of explosion,” in that “from a false premise, anything (and everything) may be deduced. The ex falso explains why Freud was required to continue his journey to create a “loft” between the chiralistic projects: seeing the Adriatic lands and exchanging stories with fellow travelers and, a the same time, trying to remember the name “Signorelli.”

string 12

Melancholic hysteria > topical viscosity (“stickiness”) > “stuck on a point” > lamination of levels produced by a katagraphic cut > agutezza > “osculating power” (Lacan) > tangency > chirality > inverter circle (extimité) > center = hole > contradiction as ex falso quodlibet sequitur (“from the false, everything follows”).

From Seminar XIII, The Object of Psychoanalysis: This is what we will be able to illustrate … by showing what it is, that is to say pure and simple cut, that is to say support necessary for us to have an exact structuring of the function of the subject, of the subject as this osculating power, this taking of the signifier on itself which makes the subject necessarily divided and which requires that any overlapping within itself does nothing else, even when pushed to its more extreme, than reproducing — more and more hidden —its own structure. The translator Cormac Gallagher has “ausculatory,” a term indicating the silence of the heartbeat in the manual measure of blood pressure. There is no relation, however, between Lacan’s French word, osculating (“osculatrice”) and “ausculatory.”

String 7 comes into play if we consider that the katagraphic cut divides layers that are as radically separated as they are radically held together. One layer implies the other, in a relation that is both chiralistic (left-right oriented) and laminated. The relation to viscosity (stickiness) brings the question of melancholy to bear on the matter of time suspension, demonstrated in the Navier-Stokes equations for viscosity. The melancholic’s historically heightened sensitivity to memory and prophecy suggest an ethnological method of confirmation, where connections between melancholy, viscosity, and time-relations will be (re-)discovered.

Further: Because the melancholic occupies the lower quarter of the “Fortuna Wheel” arrangement of humors (blood, choler, phlegm, then melancholy as a ricorso leading to rebirth/reincarnation at the sanguine position), this “timeless” segment should be considered in relation to circle inversion. Extending this to the relation of the katagraphic cut producing the Möbius-shaped opposed faces (an inverted Janus?) to the ethnographical famous journey to the underworld (katabasis) will show other connections to circle inversion and the tangency that Lacan describes as “osculation,” the kiss.

string 13

Commemoration > entropy (cf. Gregory Bateson’s “accidental” pairing) >space of rotation (2π/4π circuit) > instrumental convergence > instrument emergence (Cassirer’s expressive function, Ausdrucksfonktion) > torus > paralysis of the melancholic > 2π/4π as dynamic stasis.

Commentary: This string will make no sense without sufficient background. Bateson connects commemoration and entropy in an off-hand way, as an example of the range of topics he covered in his lectures at U.C. Santa Cruz. Presuming the topics to be random and unrelated, they turn out to be critically linked in relation to one topic: repetition. They are the two perspectives from which repetition is conceived within contexts that are either linear or circular. These “options” are related by the logic of the inversion circle and are, thus, “two sides of the same coin” (a thaumatrope) or, as has been said, “a coin with one side.” The same problem is confronted by Paul Dirac, who, wishing to demonstrate the logic behind the electron’s 2π/4π spin (the particle takes 720º to return to its original “state”), Dirac devised the “belt demonstration,” where a belt twisted once cannot be untwisted but twisted twice can return to its original flat state.

Paradox is a state of conceptual paralysis. The melancholic, who is nowhere better represented than by Rodin’s famous sculpture of The Thinker or Picasso’s fifth figure in Les Demoiselles d’Avignon — both are drawn from the emblem books of the 16th and 17th centuries — ultimately derives his/her tradition of paralysis from the system of humors. Positioned between phlegmatic and sanguine humors, melancholy is, unlike its adjacent conditions, not a matter of finding a proper balance between too much and too little. You cannot have too little melancholy! You will be afflicted with the tiniest amount of black bile! This is the idea of infection as well as that of a lethal poison. Where there is no balance, there is the paralysis of paradox, and the paradox of paralysis. This chiasmus points to the 2π/4π conundrum of the space of rotation, and the ultimate functioning of the inversion circle. This is as close as we might come to a “topology of melancholy.”

Key Texts & Artworks

Aristotle, “Problemma XXX.i.” (Texts available online.)

Irwin Panofsky, Fritz Saxl, and Raymond Klibansky, Saturn and Melancholy (text available on-line through member-university libraries)

David Ritz Finkelstein, The Melencholy Manifesto

Sigmund Freud, “Project for a Scientific Psychology” (1895). Text available through PEP-Web.

art to consider

August Rodin, The Thinker

Pablo Picasso, Les Demoiselles d’Avignon

René Magritte, The Memoirs of a Saint, 1960 (The Menil Collection)