What is an inversion circle? A definition would unfold like Borges’ famous Chinese encyclopedia:

• a way of predicting the future
• a prison for vampires (dæmon)
• a sanctuary for lovers (askesis)
• architectural poché (hidden spaces)
• a way to keep an audience on the edge of their seat
• protocol for founding a new city, if you are twins
• apophrades, the voice of the dead
• an astrolabe (Holbein’s anamorphosis)
• a tempietto and astronomical chronometer (Touro Park, Newport, Rhode Island)
• anamorphosis before it was anamorphosis
• delayed parallax
• the connection between psychoanalysis and ethnology, the arts, and popular culture

Obviously, a dictionary is not the best way to approach inversive geometry, but it does suggest how the uncanny of the inversion circle connects directly to ethnology in the role of a “fifth cause” (of effectiveness), that both Lacan and Slavoj Žižek have recommended we add to Aristotle’s classic four.¹ This is the cause of instrumental convergence, the antithesis of entropy that works with no apparent agency other than structure — an important point since, for Lacan, structure is the Real.

Inversive geometry is the new topology for Lacanians — if and only if they come by it intuitively, visually, ethnologically. To do this, the Dead of Night Workshop is a series of staged encounters where conversations, film study, diagram-drawing, and writing exercises consolidate the relatively simple rules of inversion to build a new body of theory in the style of Lacan’s mi-dire.²

Dead of Night as an Encyclopedia of Inversion

The 1945 British thriller classic, Dead of Night, is a masterpiece of uncanny literature. It involves the four classic themes of (1) travel in time, (2) the double, (3) the story in the story, and (4) the contamination of reality by the dream or fiction. Directed by Alberto Cavalcanti, Charles Crichton, Basil Dearden, and Robert Hamer, the film weaves together five eerie tales within a framing story. The protagonist, Walter Craig, a skeptical architect, arrives at a country house, haunted by a recurring dream that foretells the gathering of the house’s guests. As he listens to each guest recount their uncanny experiences—ranging from premonitions to hauntings and a ventriloquist’s sinister dummy—Craig’s unease deepens.

The framing narrative itself becomes a chilling commentary on fate and inevitability. As Craig’s dream aligns with reality, he succumbs to madness, culminating in an inescapable nightmarish climax that loops back to the film’s opening scene. This cyclical structure blurs the boundaries between dream and reality, suggesting that Craig is trapped in an endless recurrence. The film’s circularity not only heightens the sense of dread but also explores themes of predestination and psychological entrapment. Its innovative narrative influenced later films, making it a seminal work in horror cinema. The film’s structure remains a compelling study in how form can reinforce existential and psychological terror.

What is this form? Literary concepts are helpful (anthology, foreshadowing) and of course the four forms of the fantastic (the double, travel through time, etc.) are essential to note, but behind these is the structure of the inversion circle. Dead of Night‘s circularity not only heightens the sense of dread but also explores themes of predestination and psychological entrapment. Its innovative narrative influenced later films, making it a seminal work in horror cinema. The film’s structure remains a compelling study in how form can reinforce existential and psychological terror.

inversion circles everywhere!

The concept of the inversion circle offers a compelling lens to analyze Dead of Night, as it encapsulates the film’s thematic preoccupations with recursion, reflection, and the uncanny interplay between surface and depth. The geometry of inversion, where interior and exterior exchange roles, mirrors the structural and narrative dynamics of the film, transforming moments of perception into sites of existential disorientation.

Ground Zero: The Linking Tale: An architect, Walter Craig, is called to visit a country house on a Sunday, when a house party is in progress. As the host, Elliot Foley, brings Craig in to meet his friends and neighbors, Craig has a déjà vu experience and explains to the other guests that he has met them all before. At first incredulous, the guests recount their own experiences with the uncanny: premonitions, encounters with ghosts, spooky mirrors … The stories have a strange congruence; they all lead to a climax that will pivot this anthology to a moment of violent inversion, returning Craig to his wife waking him up early Sunday morning to take a phone call from Elliot Foley, asking him to drive down …

Story 1: The Hospital Window and Hearse: The hospital window functions as an inversion circle through which the protagonist of the second tale, a racecar driver, glimpses a premonition of death. The window acts as a threshold where the temporal order collapses; the future catastrophe is reflected back into the present. This reversal not only foreshadows the bus crash but also positions the window as a metaphorical “circle of fate” where the protagonist is unwittingly bound.

Story 2: Sally and the Hidden Room: Sally’s entry into the poché space of the mansion during the Twelfth Night party is another inversion. Here, the circularity of play transforms into an encounter with spectral time. The seemingly joyous festivities invert into a dark haunting, underscoring the spatial collapse between the living and the dead—a hallmark of inversion geometry.

Story 3: The Haunted Mirror: The third tale explicitly embodies the inversion circle as a haunted mirror that preserves the past within its reflective surface. This object operates as a trap of temporal inversion, echoing Hegel’s Aufhebung, where the 19th-century owner’s demise is preserved and raised into the consciousness of the modern-day protagonist. The mirror not only reflects but absorbs and re-projects the suppressed trauma of history into the present.

Story 4: The Golf Ghost: Two avid golfers compete for the love of a woman who cannot decide between them. They decide to settle the matter by playing a round of golf (this is a farce-episode to give the audience a chance to rest up before the final, taxing story). One golfer cheats, the other, despondent, commits suicide and returns to haunt his married antagonist. The ghost forces a deal but has forgotten how to return to heaven; the rival tries to help but inadvertently gets the signals right and vanishes himself instead.

Story 5: The Reverse Ventriloquist: Maxwell Frere and his dummy Hugo meet a fellow ventriloquist during a show at Chez Beulah in Paris. The dummy “falls for” the visitor and wants to leave his master. The dummy side of the ventriloquist’s brain has “taken over,” creating a paradoxical jealousy condition. The foreigner at the house party, Dr. Van Stratton, tells this, the most chilling tale of the five, and offers a chilling foreshadowing of his own fate at the conclusion of the film.

Each of these elements situates inversion as a dynamic process that mediates between visible and hidden, present and past, self and other. In the film’s framing structure, the circular plot reinforces this geometry, compelling Walter Craig to oscillate perpetually between dream and reality. The inversion circle, then, is not merely a plot device but a profound conceptual mechanism. It traps the characters—and viewers—within the poché space of the uncanny, where every threshold is a potential portal to recursive horror.

We should pay particular attention to Freud’s penetrating distinction of the kind of visibility involved with the uncanny: that which was hidden, that SHOULD NOT HAVE COME TO LIGHT. The addition of transgression means that every visible content that we count as uncanny comes with an implicit anamorphosis involving a prohibition: that which we should not be allowed to see. This critical element pulls us across a boundary that is inversive and implicitly ethnological in its service to the law as a warning: “do not trespass!”

stick to the theme

Inversion geometry is relatively easy to learn. Numberphile for example has clear, insightful videos on the use and meaning of the inversion circle. The project however is to connect psychoanalysis to ethnology, including the full range of cultural conditions, most of them qualifying as “uncanny,” where inversion is involves, often in the form of literal functioning inversion circles. It is easy to confuse binary ideas for inversion. Dichotomies can be made almost anywhere, but the “divided line” they force us to imagine perverts the idea of inversion and gives the false impression of a synthesis. Instead, a Hegelian dialectic should be remembered and applied. After thesis and antithesis, there is no merger, no reunion, no resolution. Rather, Aufhebung carries us to the next level. Inversion, like Aufhebung, cancels and preserves. Its negation is conservation, in the same way that Freud noted in his short essay on “Transience,” that entropy held the secret of an inner and opposite force.

The idea of inversion is simple mathematically but complex the everyday life that, subjected to the idea of the (Lacanian) clinic, appears as an array of symptoms, often disorganized. Rather than attempt to clean up the “messy room” of the subject, it is necessary to find the new form that the mess is speaking about. The thesis of inversion is that the relation of form and the formless is always inversive, always structured, always Real.

Do not avoid the mess, seek it out. If necessary, create one.³

the workshops

The Dead of Night Workshop is at first an archive of resources for a variety of study situations:

1. Personal reading and writing
2. Personal ChatGPT conversations (see CLAUDE sample)
3. Organize your own “cartel” (group of 4-7 zoomers to meet regularly)
4. Structured seminars (more than 7)
5. Special sessions at conferences (LACK, APCS, etc.)
6. Formal workshops, with host(s) and active participants, preferably live, in interesting places.

The archive includes position papers, workshop galleries, narrated instructional videos, and study guides for analyzing the film using inversive geometry. A free copy of the film is available on the Internet Archive. Separate scenes are available on YouTube.

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footnotes

¹The issue of a “fifth cause” arrises from Lacan’s observation that Aristotle had misinterpreted material cause. Passivity, for inversive geometry, is the effect of instrumental convergence that arises with the “extimation” of contents that obey the rules of entropy and “magically” take form within the void created by symmetrical difference. Instrumental convergence is permanently and radically uncanny, meaning that it is subject to the binary (ethnological) conditions cited by Ernst Jentsch, (1) the persistence of life past the moment of literal death (Lacan’s “between the two deaths” and (2) the anticipated fatalistic encounter with death, as in the ancient tale of the Appointment in Samarra. The inversive relation of the fifth cause to the normal flow of time (defined by Aristotle’s classic four causes) introduces convergence as the cause célèbre (pun intended) of inversion circles used in ethnological circumstances.

²Lacan was remarkably consistent, but he did not aspire to completeness. His strategy was to lecture and write in a way that would invite and require the audience/reader to finish his thoughts in their own manner, but with the same discipline that structured his own thinking. This means that Lacan’s legacy is not “do as I say” but “do as I do.” Lacanian theory has the obligation to take his mi-dire style as less of a style and more of a mandate. This shifts our Symbolic understanding of psychoanalysis to the Real of structure and the projects of the Imaginary. Where the gaps in the Symbolic must be patched-over by fantasy, we must see, in fantasy, the Real of structure. This is the essence of ethnology taken in the largest sense.

³The method of “creating a mess” is more disciplined than it sounds. This is the ersatz methodology employed by mathematicians who, facing a seemingly impenetrable problem, invent a bogus theorem, apply it to the data, then study the pattern of errors created. This negation method leads to the re-formulation of a new (but still ersatz) theorem, and new error data. However, patterns will emerge. In keeping with Stephen Wolfram’s demonstration of arbitrary automata (adjacent cells with random binary settings), formlessness gives way not just to form but to fractal (scale-independent, evenly distributed) schemas.