A Fable about Virtual Form

Lying, Self-Reference, and Mortification in the Age of Computing

Donald Kunze

Penn State University

Virtual architectural spaces made possible in recent years by computer hardware and software have, for better or worse, liberated architectural representation from the fetters of rectilinear thinking, traditional construction and manufacturing practices, environmental strictures, and materiality. However, in addition to what the computer screen creates and makes possible, the screen itself is present in space and in the mind of the architect in particular ways that radically condition this new free-form speculation.

Albrecht Dürer, who stood at the edge of another revolution in visual thinking, would have understood this exactly. "An Artist and Model in the Studio" (above) is perhaps the most publicized of this 16c. artist’s œuvre because it is said to portray the dominance of the male gaze in Western visuality. However, the opposite case can be made. While it is true that Dürer seemed to know consequences of mechanizing the relationship between the viewer and the viewed, other structures are both evident and deeply informative.

Some, such as the topiary tree and water vase on the windowsill (icons found in some paintings of the Annunciation) possibly convey the notion that the work of art is a form of incarnation. Other elements seem to be very modern — the lucinda’s "pixelation" of the mediating plane, the radical pictorial division between subject and object, the right angle between the picture plane and surface of representation (cf. the split in production between input and output), the lateral position of the model ("objectivity" rather than "passivity"), the vertical obelisque immobilizing the artist’s eye and establishing a teleological relationship between the view and its representation, and the drawing paper’s duplication of the lucinda’s grid. If some elements have made the 500-year trip from Dürer’s instructional manual for draftsmen to the present world revolutionized by the microcomputer revolution, perhaps this image can say something about the creation of architecture through the use of virtual, computer-generated spaces.

The devices of the Dürer engraving have an enigmatic kind of "curvature" that makes the analogy of the Möbius band particularly apt. Properly understood, this curvature reveals symptoms of the future of architecture. I shall present these symptoms in their barest form, so that the astute reader, who "knows how the story ends," can make the ultimate connections. The Dürer image is subtle in its use of vectors and personifications, and several "experiments" are required.


Experiment One: the Blind Spot


First, reverse the presumed artist-to-model direction of the gaze. Have the model project a visual field, regulated by a device ("lucinda") that is a part of the model’s structure, and you have Jacques Lacan’s flip of the standard Derrida interpretation that has for over twenty years underwritten this condemnation of the (male) gaze. In fact, the model’s indifference, her supine tranquility, her lateral position (which leaves the artist with an end-on view) make signification into a fluid flow from authority ("the Other") to the artist-subject who is immobilized (the "barred subject," which Lacan symbolizes as $). The artist’s view is framed "from the inside" by the small blind spot — the central eye-point — which is the point at which the scene looks back at the artist. It "commands" him to be there and at no other point. Quite literally, it frames the scene from the inside out, for the scene is not the scene unless the artist occupies this one fixed spot.

We, the audience of the engraving, also have a blind spot — the lucinda. Dürer has cheated on the one-point perspective’s vanishing point by moving it to the right of where it should be. Normally, we would find it in the middle of the composition, directly behind the lucinda. If that had been the case, we would only be able to see the wooden edge of the frame. With the vanishing point between the vase and topiary tree, we can see a bit of the screen. The lucinda is like the "anamorphic" images painters inserted into images to be seen "correctly" from some extreme angle. The only "correct angle of view" for the lucinda is the artist’s, doubly confirming this element as "anamorphic."


Experiment Two: The Audience Factor (Enthymeme); Metaphor and Metonym


The thing that makes this particular illustration perennially fascinating is the angle of view taken by the audience of the engraving. This line of view is (as is normal) at a right angle to the plane of the picture. But, because the artist is also an audience, producing a "work within a work," what we see is a parody of what the artist sees. The lucinda is a pivot point, and it works somewhat like a mirror or jewel, tessellating the scene into puzzle parts but also making each angle of view depend on its internal placement.

To get from our point of view to the artist’s, we need an account, a story, a fantasia (Ø). How is it that we came to drop in on the artist in the middle of a project? And, wasn’t our scene constructed in exactly the same way, with a lucinda and a sheet of grided paper? Aren’t we seeing a sideways version of our own tunnel-like visual "cone of representation," where any one front-on view completely conceals and trumps the others that "lie behind" it?

In Latin, the verb "to lie," latere, also has the sense of "to lie concealed," as in hiding: "to lie doggo," as the British say. A standing model would have been more "visible" to the artist and to us, the second audience. This model’s repose and obliqueness to the artist is a part of the philosophical lesson of this illustration. The audience of the engraving sees stretched along its length the layers that the artist must see piled on top of each other, each using its opacity and order of appearance to conceal and, sometimes, metaphorically represent what it conceals. In the stretched out version, we see the contiguous, metonymic relationship of these layers: parts relating to parts. Normally, we take contiguity to be really "for the sake of" a metaphoric order, the machinery that enables a representation to stand in the place of something.


Experiment Three: Chiasmus, the Acousmatic Imaginary (Ø), and Flat-out Lies


If we flatten the operational vectors of this image into a diagram we get a scissors (chiasmus, fugue) whose main axis is the gaze of the artist and whose minor axis establishes our relation to the engraving both visually and philosophically. The immobilized artist is really the "victim" of the "Other," because he must sacrifice motility to use his instrument of desire. The Other overflows its frame not only by going beyond the edge of the lucinda’s grasp but by having, at its center, a stain on its otherwise immaculate surface — a point that, related to the artist’s immobility, frames the scene "from the inside." This point has a mechanical relationship to the artist and model, but for us it is the element that carries us away, through the anamorphic pivot of the center, to an image created some 200 years later, the title page illustration of Vico’s New Science (1744).



A woman with winged temples (Metafisica) is seated on a globe, leaning on a plinth whose engraving repeats in Latin the theme of concealment: Ignota Latebat ("She lay hidden"). Metafisica’s gaze constructs a triangle. A mirror takes up the role of the lucinda, and Metafisica’s eye is immobilized by the angle. In the mirror, it appears that Metafisica sees another triangle, this one modeled after a builder’s square.

To explain how there could be any resemblance between Dürer’s engraving and this 18c. image — most likely composed by practicing Rosicrucians — I will have to make an unusual claim. Giambattista Vico, author of the idea of a universal series of historical stages applicable to all aspects and objects of the human world — a radical teleological scheme — posited just the opposite idea as an antidote: an a-historical, self-engendering theory of mind. One might call this a "theory of portable origins." Vico is, I claim, the father of the field of artificial intelligence ("AI") because, in Lacanian fashion, he correctly diagrammed the "first" human moment as one where the idea of god-in-nature was "back-projected" from an "acousmatic" encounter with thunder, which the first humans took to be the word of the god. Hence, the world becomes metonymically disconnected (our relationships are written into a language structure) but visible only from a metaphorical direction, from a "victim’s point of view." According to Lacan, we can "see through" this stack of metaphors back to the origin ("name the Father"), if we but become psychotics in the process.

The first humans, who believed thunder was a word of a god, saw in nature their own psyche and form (prescience again: Lacan proposes that the subconscious is "on the outside"). Human imagination was a by-product of fearful (back-) projection of the Other (really their own nature) whose demands were put into an indecipherable code. Hence, religious texts and poetry are "by definition" radically indecipherable. Misreading is essential. It’s a system where lying (Ø) is the only escape from the all-engrossing symbolic system of meanings, escaping the injunctions of the Other and the rigidity of "true of false." The best lies are the type told by Cretans who say all Cretans are liars.


Experiment Four: Möbius, Cretan Liar, and She Who Lay Hidden (Latebat)


We need a zone for the "possibly true, possibly false," because of the twist, the rotation, the anamorphic middle of the artist’s studio, which makes of this image and our looking at it into a Möbius strip experience. What does this mean? The situation is Heisenbergian, because it has to do with matters of self-reference, recursion, and the geometry of fractals. The Cretan tells his audience, "All Cretans are liars." The audience knows that, within the "lateral" symbolic reality established by the Cretan speaker, the value of true and false must fluctuate between lie (he is a Cretan, his statement applies to him and he’s lying) and truth (if the statement really applies to him, and he’s lying, then it’s a true statement). The philosophical paradox becomes a theatrical joke when the audience is included in the syllogism (enthymeme). The "falsehood" becomes a "lie" (in the punned sense of latere) that "lies hidden" within the enthymemic structure of the relationship.



The literal form of the enthymemic syllogism, where the role of the audience is present as the "silent" middle term (it doesn’t appear in the conclusions, illustrates how the back-projection might be seen as a scissors-vector travelling through the "anamorphic" statement of the speaker to the "little other" (‘a’) that frames the speaker "from the inside" (that is, in a fractal and recursive way). Little ‘a’ is surplus to the Large ‘A’, because it lies outside of the system of signifiers that demands that the statement be judged either true or false.


Fig. 4. The audience's role is comparable to the "silent middle term" of the syllogism.


It seems that the "lateral" element of Dürer’s model is structurally related to the lateral function of "laying hidden." Little ‘a’ lies hidden within large ‘A’ as a surplus relates to the unobtainable element within the Other that immobilizes desire in a Zenonian way.


Experiment Five: Flips and the Dogs of Mortification


Let’s pause for a consideration of two other appropriations of the Dürer image. One comes from Arthur Chen, an architectural theorist working at the University of Minnesota.



The rotation of the image approximates Duchamp’s scheme of "bride above, bachelor(s) below." In The Large Glass, bachelors use machines, gimmicks, and trickster devices, but the bride’s domain remains "ineffable" in the sense of resisting representation. One is reminded of God’s cautionary response to Moses’ request to see Him, that only the hindquarters could be made visible without destroying the mortal viewer.

Another liberty might be taken with the Dürer engraving: readjusting it so that it matches the general format of Vanvitelli’s sculptural composition at the foot of the cascade at Caserta.

The statuary represents Actæon and his dogs in a group on an island on the right (we have reversed the image for reasons that will be clear later on), the goddess Diana and her attendants are on a companion island shown here on the left. The story of Actæon is informative, not just for the history of Brides and Bachelors but for the story of representation, ancient and modern. Actæon and his friends go hunting but kill more than they need. Actæon, stumbles across Diana (also related to Dianus, or Janus), the goddess of the wood, and her attendants bathing naked in a spring-fed pool. Actæon did not intend to spy upon the goddess, but he inadvertently sees her naked body and her reflection (or lack of same) in the pool. This mirroring is the key to her nakedness, as the sculptural arrangement makes clear. In retribution, Diana splashes him with water (which "contained" the would-be reflection?), transforming him into a stag, which his dogs consider to be edible. They pursue and devour him. Curiously, Ovid names and describes each of the 33 dogs in great detail, as if the process of mortification had to occur metonymically, in order of ingestion.

These two examples suggest that virtual form is a complexity not easily summarized. The fable of Diana and Actæon teaches that the discovery of form involves transformation and self-consumption. The "Duchampian" qualities in Dürer and Vanvitelli suggest that virtuality can be allegorized into a fable. We’re faced, however, with a specific turn in the history of architectural form, namely the radical upgrading of the middle element, what in the Dürer engraving is the simple lucinda/paper/obelisk machine but what now is capable of producing virtual Ladies as well as representations of real ones, reclining or otherwise.


Final Experiment: A Visual Fable


We might hear Vico, unacknowledged inventor of AI, saying . "All human intelligence is artificial." In fact, he did say, Verum ipsum factum (est), "The true is convertible with the made," meaning that, just as God has perfect knowledge of the world because he created it, humans can have perfect knowledge of the worlds they create through language and cultural institutions. Because factum is artificial; the factum can be perfect (verum). Because there really is no knowledge that can be true in this sense outside of the realm of the made, "all true knowledge is artificial" — a more radical statement than any made by, say, Marvin Minsky. Making and knowing are convertible. But, what contemporary AI theorists are often missing is the appreciation of the Möbius-band logic of this self-knowledge. In architecture as in other fields, AI is associated with computer techniques, which stop short of rendering the full story of representation and its role in thought. The computer might have a much more intriguing and comprehensive role if it were not limited, in the popular mind, to the construction of virtual spaces analogous to the ones in the current stack.

Vico constructed what might be best called a "cosmogram" — a vector-specific model of the psyche whose traces can be found in the Dürer engraving and the sculptures of Diana and Actæon. The three sources for the following collage are: (1) the frontispiece of the New Science, called the dipintura; (2) the title-page engraving of the same book, known as "Ignota Latebat" because of the inscription on the plinth, and (3) Dürer’s engraving, "The Artist and Model in the Studio," with the overtones of Duchamp and Vanvitelli cited above.



The lucinda "complex" has been unwound as a joint in the connection between the other (symbolized by the eye in the triangle) and the "immobilized" artist, the statue of Homer. The artist experiences the phallic (appearing, disappearing) divine point as an (acoustic) moment of jouissance (pleasure/pain) internally framing the array of symbols that structure the human world. The altar of sacrifice, the first human institution honoring this jouissance, has borrowed a vase and topiary from Dürer’s windowsill. The now-jointed line of view is disseminated by the jewel on the breast of Metafisica (nature), not unlike the technique of distributing light across the computer monitor’s screen. The link between all of these images is the recurring theme of winged temples. In both the Ignota Latebat image and the dipintura, Metafisica has winged temples. Lying at the foot of Homer’s statue is the helmet belonging to Hermes, god of tricky boundaries. Lacing through these eyelets allows us to string together the images into a Möbius band, where the fable about virtual space becomes the container that contains itself, accommodating any and all contradictions. The lesson of Dürer is that artists have always required such machines.