A Fable about Virtual Form
Lying, Self-Reference, and Mortification in the Age of Computing
Donald Kunze 杜拿德、昆泽
Penn State University 宾州大学
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 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.

有些结构,譬如,修剪装饰的树及窗框上的装水花盆,(在圣母画派Annunciation 的一些图画里被发现的图像),可能传递这个观念:艺术作品是圣灵化身的形式。其它因素是非常现代—中介层次的栏栅的点位化,在主体与客体之间的强烈的画面的区分,在画面层次与符号再现的表面之间的适当角度。(譬如,在输入与输出之间的产品的分裂),模特儿的倾斜位置 (客观化,而不是被动化),让艺术家的眼睛不能动弹及建立目的论的关系的垂直中介物,处于景象跟它的再现之间,以及栏栅的框格的画纸的复制到目的论关系。假如一些因素已经让这500年的旅行,从杜瑞尔的画匠的教导手册,到微电脑的革命所革新的目前的世界,或许这个意象能够说出某件东西,关于建筑的创造,凭借虚拟的由电脑制作的空间的使用。

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.

首先,倒转假设的艺术家跟模特儿的凝视的方向。将模特儿投影到一个视觉的领域,由一个类似栏栅的设计,那是这个模特儿的结构的一部分。你就理获得雅克、拉康的翻阅标准的德希达的解释,这种解释过去二十年来,饱受男性凝视的文字的谴责,事实上,模特儿的漠不关心,她的脸孔上扬的宁静,她的倾斜的位置,(让艺术家处于一种观看的目的)。这造成意义的流动,从权威(大他者),到不能动弹的艺术家的主体(被划杠的主体, 拉康给予符号象征$)。这个艺术家的观点「从里面」被给予框架,由于这个小小的盲点—中央的眼睛点—在这个点,这个场景「回顾」艺术家。它「命令」他在那里,而不是在其他的点。从实质上来说,它从里面向外框架这个场景。因为这个场景并不是这个场景,除非艺术家佔有这个固定的地点。
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.

让这个特别的说明长久令人著迷的东西,是雕塑的观众所採取的观看角度。这个观点的脉络 (属于正常状态),针对图画的层次的适当角度。但是,因为艺术家也是观众,产生一种「作品中的作品」,我们所看见的是一种模拟,对艺术家所看见的东西的模拟。这个栏栅是一个枢纽点,它的运作就像是一面镜子或珠宝,将这个场景配套成为组合的部分,但是也让观点的每个角度依靠它内部的位置。
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.

在拉丁文,「to lie」latere的动词,拥有「隐藏位于」的意涵,像是在玩躲藏遊戏:「召魂」,如同英国人所说。一个站立的模特儿本来会更加地「可观看得到」,对于艺术家及我们,这第二个观众。对于艺术家,这个模特儿的安逸与倾斜是这个说明的哲学的教学的一部分。雕塑的观众看到这几层被延伸,沿着它的长度,艺术家必须看见它们互相被堆积在彼此上面,每一层都使用它的模糊及表象的秩序来隐藏。有时,它们隐喻地代表它所隐藏的东西。在这个被延伸到版本,我们看到这几层的这个靠近的,换喻的关系:部分跟部分的关系。正常来说,我们将这个靠近,确实是「为了」隐喻的秩序,这种机械结构让符号再现能够代替某件东西。、
Experiment Three: Chiasmus, the Acousmatic Imaginary (Ø), and Flat-out Lies
试验三:灵肉交错,声音的想象(大他者被划杠) 及扁平的谎言
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 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.

三段论法的实质形式,在那里,听众出现作为这个「沉默的」中间术语 (它没有出现在结论里,说明这个反射投影可能被视为一个剪刀的向量,旅行越过言说者对于这个小他者(a)的「变形」陈述,架构言说者,「从里面」(也就是,以一个微分而重复的方式)。这个小它者(a)是大他者(A) 的剩余,因为它位于能指的系统的外贸,要求这个陈述应该被判断为真实或虚假。

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.

阿塔安偶遇戴安娜,这位森林之神,跟她的侍女,正赤裸地在温泉水池沐浴。阿塔安并没有意图要窥视女神,但是他偶然地看到她赤裸的身体及她在水池里的倒影 。这段镜子映像是她的赤裸的关键,如同雕刻的安排显示的。作为报复,戴安娜对他泼水,将他转变成为一隻雄鹿,让他的狗群认为是佳肴。它们追逐并吞吃他。耐人寻味地,奥维德非常详细地命名及描述这33隻狗的每一隻,好像羞辱的过程,必须换喻地发生,按照消化道顺序。
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.

维科建构最恰当所谓的「几何宇宙图」心灵的向量的模式,心灵的这些痕迹能够被找到,在杜瑞尔的雕塑及戴安娜跟亚塔安定雕刻里。以下的併贴的三个来源是:一、「新科学」的前景,被称为dipintura 。二、相同的那本书的标题页的雕塑,众所周知的Ignota latebat, 因为在支撑基座的铭记。 三、杜瑞尔的雕塑,「艺术家及工作室的模特儿」,具有以上被引述的杜张普与范维特里的风格。

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.

在所有这些图像之间的这个关联,是太阳穴长出翅膀的重复的主题。在Ignota Latebat 与dipintura的图像,梅塔非思卡的太阳穴长出两个翅膀,躺在荷马的雕像脚下,是属于战神赫密士的头盔,这位戏弄边界的神祗。通过这些眼洞的镶边,让我们能够贯穿这些图像,成为莫比斯环带。在那里,有关虚拟空间的寓言变成包容它自己的容器,收容任何以及所有的矛盾。杜瑞尔的教训是:艺术家总是要求诸如其类的机器。


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