No More Learning

Zeuxis wanted to pull the veil away in order to take a better look, but when he attempted to extend his hand towards the veil he realized it was also painted. Tbe first-order simulation was thus able to fool the eyes of animals, while the second-order simulation was also able to fool the eyes of humans.
This anecdote actually shows quite beautifully that art and media are fundamentally about the deception of sensory organs (Lacan, 1981, p. 103), but this seems to be just as beautiful as it is problem- atic. It implies that people can deceive others ahoUl the status of their own creations through the use of manual tools and abilities, such as painting, writing, or composition. "Whoever believes it is possible to lie with words might also believe that it happened here," wrote Gottfried Benn about his early novels. He himself believed it as little as I do. When one sees the remaining Greek panel paintings today, which have admittedly been poorly preserved, the anecdote about the two painters seems very doubtful, as these paintings were obviously done using a palette that included certain colors and simply lacked others. In place of the so-called truth of nature, therefore, these paint- ings reflect a convention that one must first ignore or overlook in order to fall under the spell of the illusion. In this respect, despite its realistic veneer, painting is not so very different from other arts like music or literature, whose encoding, and this means conventionality, is more readily apparent. The thesis would thus be that traditional arts, which were crafts according to the Greek concept, only pro- duced illusions or fictions, but not simulations like technical media. Everything that was style or code in the arts registered a distinction that is quite the opposite of technical standards.
Artistic styles were certainly ways of acting on the senses of the public, but they were not based on measurements of the abilities and inabilities of visual perception like the standard use of alternating images in film; they were based on approximations, conventions, and the pure chance involved in the historical availability of raw materi- als. Certain artistic effects would not have been possible without oil- based paints, and therefore without petrochemicals and their world wars. If Foucault had been able to write his book about painting as the history of available pigments - as promised in The Discourse on Language - we would know more. But it is clear that pigments are just as visible as what they are supposed to show on the canvas. For
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this reason, European culture up to early modern times was under the control of what Hans Blumenberg called the "postulate of vis- ibility": that which exists also allows itself in principle to be seen (Blumenberg, 1983, pp. 361-75). Plato's concept of theory, which has already been touched upon, even implies that what exists in the highest state of being, namely in the realm of ideas, can itself be seen, although or because it remains absolutely invisible to the naked eye. Technical media and only technical media - according to the thesis of these lectures - destroyed this postulate of visibility. Being, in an eminent sense, allows itself in principle not to be seen today, although or because it allows the visible first to be seen. In this way, the history of optical media is a history of disappearance, which also allows me the freedom to disappear for today.
It is astonishing that the anecdote about the optically deceived birds has returned today in the form of a scientific theory: first, behaviorism has actually established that with female pigeons the ovulation necessary for fertilization occurs not only when they see a cock pigeon, but also when the laboratory deceives them with a two-dimensional dummy. In a second step, French psychoanalyst and structuralist Jacques Lacan then based an entire terminology on the experiment, which has since also made careers among film scholars, particularly in Anglo-Saxon countries. For Lacan, all of the phenomena associated with figure recognition go by the method- ological title of the imaginary, and the point is actually that they are just as automatic as they are deceitful. Lacan cites both the pigeon experiment and the ancient painter to support his theory (Lacan, 2002, p. 5), but the example he offers is different: unlike animals, human infants learn from an early age, approximately in the sixth month, to recognize themselves in mirrors. The point of this early childhood figure recognition, however, is that it is also simultane- ously a misrecognition - simply because the apparently superior sensory capabilities of human infants as compared to those of baby animals, who see adversaries in the mirror rather than themselves, are inversely proportional to or compensate for their delayed motor skills. It is precisely because they are not yet able to walk and their immature central nervous systems have not yet registered the unity of their own bodies that they project a closed, visually perfect identity onto the mirror image. The tremendous joy they express upon recog- nizing themselves in the mirror conceals the reality that their bodies are still physically uncoordinated. According to Lacan, this is how the ego itself emerges from the imaginary. And the fact that Lacan found proof for his theories in a scientific experimental film that
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demonstrated this process of self-(mls)recogmtion in the mirror also clearly shows how the mirror stage and the imaginary are related to film. I will return to this complex in my discussion of early German silent films, which were full of mirrors and doppelgangers.
For the moment, it is more important to emphasize the idea that the imaginary represents only one of the three methodological catego- ries of the structuralist theory. According to Lacan, the dimension of code, which I have just illustrated through artistic styles and aesthetic rules, appears under the title of the symbolic, which turns out to be essentially at home in the code of everyday language.
The third and final category is called the"real," but please do not confuse this category with common so-called reality. Le reel refers only to that which has neither a figure, like the imaginary, nor a syntax, like the symbolic. In other words, combinational systems and processes of visual perception cannot access the real, but - and this is one of the leitmotifs of tbese lectures - this is precisely why it can only be stored and processed by technical media. The present can be distinguished from every earlier period by the fact that we live at a time when, with the help of Mandelbrot's fractals, clouds can be calculated in their full randomness and then be made to appear on computer screens as calculated, unfilmed images. Practically speak- ing, however, this means that we must employ a considerable part of film theory - which usually goes by the name of film semiotics - in
order to clarify the radically new ways in which optical media handle the symbolic. This concerns, more concretely, techniques of montage and editing, and thus everything that has been regarded as specific media aesthetics since the time of Walter Benjamin. Above all, it must be made clear how media, in contrast to all of the arts, can neverthe- less include the impossible real in their manipulations, techniques, or processes, and thus treat the pure chance of a filmed object or a television camera setting as if it had the same structure as the manipu- lable codes in the arts. To shed some light on this possibly vague suggestion, I will conclude these comments on media technologies and the body with a quotation from Rudolf Arnheim's film theory. In an essay on the systematics of early cinematographic inventions, Arnheim claims that "since we have known photography" there has been a new and "more ambitions demand placed on the image": "It is not only supposed to resemble the object [as in all representative arts], but it is also supposed to guarantee this resemblance by being
the product of this object itself, i. e. by being mechanically produced by it - in the same way as the illuminated objects in reality mechani- cally imprint their image onto the photographic layer" (Arnheim,
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1977, p. 27). Th,s passage hopefully shows what a mampulatlOn of the real can be in contrast to all figures and cultural codes. And if the body belongs to the real, as Lacan argues, then this introduction to optical media and the body is where it should be.
In terms of methodology, it only remains to be noted that I am employing Lacan's terms as a useful set of conceptual tools, not as immutable truth - for the simple reason that over the course of the semester we must ask whether the basic concepts of current theories are absolutely independent and thus true frames of reference or rather a dIrect result of the media explosion of our own epoch. Lacan's notion of the symbolic as a syntax purified of all semantics, meaning, degrees of figuration, and thus also every conceivability could 1ll the end coincide with the concept of information in telecommunications.
The question still remains as to where the untraditional concept of information itself - the basis and goal of all technical media - origi? nally comes from. To get to this, as well as the relationship between media and war, I will stay with the example of photography and quote an extremely early passage from 1859, in which (as far as I can see) something like media-technical information appears for the first time. Oliver Weridell Holmes, Sr. , the first real theorist of photography, wrote at that time:
Form is henceforth divorced from matter. In fact, matter as a visible object is of no great use any longer, except as the mould on which form is shaped. Give us a few negatives of a thing worth seeing, taken from different points of view, and that is all we want of it. Pull it down or burn it up, if you please. (Holmes, 1859, p. 747)
According to Holmes, therefore, modern information conceals itself under the ancient philosophical concept of form: the possibility of storing, transmitting, and finally processing data without matter and also without the loss of accuracy that was unavoidable in artis- tic reproductions. The point of his example, howevel; is only that chemically pure information becomes a correlate of chemically pure destruction. What Holmes is describing already sketches out the path to the bomb over Hiroshima, which, according to the similar insights of Thomas Pynchon and Paul Virilio, represents both a photographic flash and an annihilation, or that Black Forest mine station where the plans and photographs of all of our monuments have been stored in bomb-proof shelters by the federal government of Germany.
In other words, the concept of information itself has a military, stra- tegiccomponent. It is no accident that the age of media technologies
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is at the same time also the age of technical warfare. French archi- tecture and military theorist Paul Virilio has made this point quite clearly, especially in the case of optical media. In Germany, however, he is overlooked by most media theorists - with the exception of Heide Schliipmann and her lucid discussion of silent film and World War 1. These lectures must and will therefore satisfy a pent-up demand to catch up with his work.
Virilio's argument, above all in his book about war and cinema, follows two separate tracks: the first concerns everything tbat optical media produce that can be considered imaginary, in the sense that I have just defined, such as all the means of fascination, blinding, dis- guise, or - to use a term from tbis media-technical century - optical illusions in general. And because Virilio defines war first of all as basically a game of hide-and-seek between two enemies, he is able to show how media effects are linked to military stratagems through optical illusions. This appears to be a rather simple model to explain the present global image trade and image war. For this reason, I prefer to follow Virilio's second line of argumentation, which espe- cially concerns optical media. In contrast to sound waves, which are known to cover a distance of approximately 330 meters per second at normal temperatures (and completely ignoring the speed of letters or orders sent by mail or pony express), the speed of light waves or light particles is Einstein's constant c, which cannot be surpassed by any other speed. Accordingly, Virilio's second argument is that the strategic interest in faster information - the supervising and direct- ing of one's own troops, the monitoring and surveillance of enemy troops, and above all the supervising and directing of one's own response to enemy actions, which should be as immediate as pos- sible - crucially accelerated the explosive rise of optical media over the last hundred years.
It seems necessary to absorb this point and trace it through film and television to the digital future of image technology. I will thus attempt to pass on the factual evidence Virilio has laid out, which in other contexts has been simply ignored, and on the basis of this evidence I will attempt to demonstrate the plausibility of his often radical theories, such as his claim that between the wars popular cinema was (to use Eisenhower's famous phrase) a military-industrial complex.
This naturally implies, as has already been emphasized, that the list of technologies to be addressed does not end with popular films and television programs, but rather the category of optical technol- ogy also encompasses such cryptic things as radar or night vision
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devices. In these times, when a wall separating Germany has fallen, perhaps it is also possible to conceive how relative every distinction between civil and strategic image technologies has gradually become: apart from the eastem European delay in informatics and computer- controlled production, which Gorbachev himself admitted and which he described as a motive for opening his country to the West, this wall fell as a result of a constant 25-year bombardment of television broadcasts.
And such events, which are triggered by technical media, possi- bly represent the conclusion of more than just a chapter in postwar European history. Perhaps telecommunications brings history itself, which was always a metaphor for the possibility of written inscrip- tion, to a point beyond which it is no longer history in the traditional sense. In any case, it is worth reconstructing the history of film and television within this context. After all, events that exist as nothing but documentary films or television recordings (Kennedy's murder in Dallas, the attack on R~agan in New York) continue to multiply. Such events can no longer be traced back to other, historically correct (that is, written) sources, just as it is also impossible to magnify the corresponding film documents any further without ending up in the pure grain of the celluloid and therefore in a white noise where there is nothing more to recognize (as Antonioni proves in Blow Up). It could thus be said that whereas history has handed down to us the opposition between writing - a manual art - and the ocean of undocumented events that remain inaccessible, this is precisely where the new opposition of the media age between technical information and white noise, the symbolic and the real, emerges.
Now that the concepts of information and noise have at least been introduced, I can finally conclude this methodological introduction, as promised or threatened, with a brief sketch of Shannon's technical model of communication and information.
Claude Elwood Shannon, a leading mathematician and engineer in the research laboratory of AT&T, which remains at present the largest telephone company in the world, outlined this model in 1948 in a work with the modest yet equally ambitious title The Mathemati- cal Theory of Communication. After the Second World War brought about a surge of innovations in all fields of telecommunications, par- ticularly in television and radar, it became historically necessary no longer to produce theories about individual media, as everyone had done for film from Hugo Miinsterberg to Walter Benjamin, but rather to pose the simple and common question of what media technolo- gies in general do; what are their functions and constituent elements
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that enable information even to occur? Shannon was able to answer this qnestion thanks to mathematics and its elegance. Althongh this mathematical aspect must be toned down for it to come in useful here, for our purposes it offers the advantage of introducing clearly delineated concepts that make it possible for the first time to compare the performance and limits of individual media, like film and televi- sion, with each other. Once the general functions and elements are known, they can be found at the most varied degrees of technical complexity, from the simple, old-fashioned book to the newest com- puter screen.
There are five interconnected elements in Shannon's general model of a communication system: first, a data source that generates a message; second, one or more senders that translate this message into signals according to the rules of a prearranged code so that the system is able to transmit them; third, a channel that actually conveys the transmission (with a considerable or slight loss of information); fourth, one or more receivers that treat the signal in the opposite or inverse way to the senders, if possible, and reconstruct or decode the message from the received flow of signals; fifth and last, one or more data sinks to whom, Shannon writes, the message is addressed. According to the mathematical theory of communication, it is com- pletely unimportant what kinds of entities serve as data sources that transmit a message and data sinks that receive a message, such as humans or gods or technical devices. In contrast to traditional phi- losophy and literary studies, Shannon's model does not ask about the being for whom the message connotes or denotes meaning, but rather it ignores connotation and denotation altogether in order to clarify the internal mechanism of communication instead. At first glance this appears to be a loss, but it was precisely its independence with regard to any sense or context that allowed technical communica- tion to be emancipated from everyday languages, which are neces- sarily contextual, and that led to its global victory. When Shannon explicitly says that we have no need for a communications system for eternal truths, whether of a mathematical or even, I would add, religious nature because such truths must be continuously reproduc- ible at different times and places without technical transmission, it
becomes abundantly clear how the essence of media diverges from our everyday concept of faith. Let us therefore forget humans, lan- guage, and sense in order to move on to the particulars of Shannon's five elements and functions instead.
Because it is conceived without reference to any semantics, the message can be of an arbitrary type: a sequence of letters as in books
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or telegraph systems, a smgle quantity that changes over tIme hke the vibrations of voices or music on the radio or on records (if we dIsre- gard the two variables of stereophony), or, in an extremely complex case like color television, it can also be an entire conglomeration in multiple dimensions of both space and time. For a single color image to be seen, the two spatial dimensions of a red value, a blue value, a green value, and a brightness value must be transmitted at the same tIme as the temporal dimension of sound.
Tbe sender, the second link in the cham, predICtably bas the func- tIOn of serving as tbe interface between the aforementioned message and the technical system; it must therefore find a happy medium or compromise between the complexity of the message and the capacity of the channel. In principle, there are two possible solutions: in the first case, the signal generated by the sender corresponds proportion- ally to the message, which means that it follows all of its changes in space andlor time. This is called analog communication, as in the case of gramophone, microphone, radio or even photography, and while it is more familiar it is also unfortunately more difficult mathematically. In the second case, the message is broken down into its pure constitu- ent elements prior to transmission in order for it to fit the capacity of the channel, which is in principle always physically limited. These elements are entirely of the same type, such as letters in the case of a spoken message or numbers in the case of computer technology or the individual pixels of a monitor. Because these elements can only assume certain values - there are, for example, far fewer Latin letters than the number of possible sounds produced by the larynx and mouth - they cannot match all of the variations, intricacies, and details of the message. Communication systems that employ such mathematically and technically verifiable signals are called discrete or following the model of the finger of a hand - digital.
And the entire difference between film and television studies will amonnt to the clarification of how the transition of a largely analog medium like film to the digital television screen changes or revoln- tionizes visnal perception.
Third, the channel is equipped for the technical bridging of space in the case of transmission media or of time in the case of storage media, and it can consist of material, like telephone wires or fiber-optic cables, or it can simply be a vacuum through which electromagnetic waves propagate, like radio or television. As a physical medium, in any case, every channel also generates interference or nois_e,_ which is the conceptual opposite of information. When a television is set on a frequency between the regular channels, this noise appears to our
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sensory organs (which are otherwise blind to noise) like snow made of points of pure light that correspond to some accidental event like spark plugs or distant galaxies. It is impossible to determine whether the noise represents a single ongoing accidental process or the sum of an endless number of such processes. In any case, for all media the technical specifications must aim to reduce the level of noise in the channel - eliminating noise altogether is impossible - and increase the level of signal. And Shannon's theoretically crucial computational result was that this is primarily possible by cleverly coding messages and repeating them until they are received with the desired level of accuracy.
Fourth and last, the task of the receiver in a communication system is to decode the technically encoded signal and thus reconstruct as far as possible and feasible the message submitted from the sender. In the case of a book, this amounts to the simple act of reading. In the case of technically complex media like television, on the other hand, an electronic signal that is not perceived by any sensory organ must first be transformed back into a form that to some degree accommodates the physiology of our eyes. In the case of digital media, like electronic image-processing, this transformation requires a digital-to-analog converter to allow for human sensory organs. What one sees in the end is therefore only the outer onion skin of an entire series of conjuring tricks that must first be invented, calculated, and optimized, and Shannon drew up formulas for precisely these calculations, which can be applied to absolutely all technical media in general. If you have noticed, like movie fans for instance, that in my lecture about the five functions of communication the seemingly fundamental and necessary function of storage does not appear in Shannon's work at all, I can only respond in two ways: first, the function of storage is concealed but also thoroughly explained by the mathematics of code optimization, which I mentioned only fleetingly, and second, it is probably an indication of our own situation if all media, as in Shannon's work, are defined as transmission rather than simply storage media. While the purpose of a Christian festival like Easter is to be ritually repeatedly every year simply because it is sup- posed to store and transmit a fixed and well-known message, namely the gospel (good news), no one is particularly pleased about repeated broadcasts on the television. Shannon's technique of measuring infor- mation mathematically was specifically developed to distinguish and determine the newness or improbability of a message compared to the mass of repetitions that are necessarily implied in every code.
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2. 1 Camera Obscura and Linear Perspective 2. 1. 1 Prehistory
By panning from Christmas to prime time television, from the Chris- tian message to technical signals, I have already arrived deep in the prehistory of optical media. To express it in one sentence: today images are transmissible; however, over the course of history images, at least in principle, could only be stored. An image had its place: first in the temple, then in the church, and finally (to Heidegger's dismay) in the museum. And because this place - according to Benjamin's theory of the aura - was far away, perhaps even "the unique phe- nomenon of a distance" (Benjamin, 1969, p. 222), there was at best the possibility of a museum visit or an image trade and at worst the possibility of an image theft. Writing, on the other hand, served not only as a storage medium for everyday spoken language, but also (I admit) as a very slow broadcast medium after the practice of inscrib- ing on walls or monuments was superseded by the use of papyrus and parchment. Books can be sold, sent, and given away. Writing was therefore not merely literature but always mail as well. And the evidence supports the assumption of Harold A. Innis, McLuhan's predecessor in media studies, that it was the portability and trans- missibility of scrolls that brought the two nomadic tribes, first the Jews and later the Arabs, to replace the worship of extremely heavy images of god with a god-given or even god-written book (Innis, 1950). The Bible and the Koran were only able to begin their victory march against all the temple statues and idols of the Near East and Europe because they were mobile relics. Because writing combines storage and transmission in a unique way, its monopoly held sway
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'I
I I? I
!
until media made letters and numbers, images and sounds technically
mobile. Instead of reeling off the prehistory of film and television as
a report about the large and small steps made by various inventors, I therefore, I will frequently represent it with regard to literature,
whose monopoly the new media first had to defeat.
Most accounts of this prehistory begin with a discussion of cave pictures from the Stone Age or Egyptian funerarv inscriptions, which supposedly were an attempt to capture sequences of movements from so-called nature in an image or a series of images by artisanal means. This is the approach taken by Friedrich von Zglinicki, for example, in order to reel off the content of his highly commendable book Der Weg des Films (The Way of Film) like a film.
Or more precisely: like a Hollywood movie. For Zglinicki begins with the thesis that humanity as such - this monstrous collective singular - always harbored the old dream of making images move and thereby making them even more like reality (Zglinicki, 1979, p. 12), and the invention of the first technically functional film in 1895 thus represented the happy ending of this dream. In contrast to such a history of motion pictures, which must bend all possible facts, one could derive the exact opposite lesson from film technology itself: rather than tracking the same continually moving image over the course of millennia, like Zglinicki, one could conceive of these millennia themselves as film cuts. I therefore try to emphasize instead the caesuras or breaks in perception and artistic practices that were necessary in order to reach the threshold of moving images.
The problem of moving images is once again the problem of image transmission, simply because movement as such cannot be stored without media and transmission itself is a type of movement. What remained in the absence of technology was the use of the very short and unreliable channels, which the physical laws of nature are able to provide. All the myths based on the shadow and the mirror revolve around the problem of image transmission. The ancient gods found the answer to this problem easy, because they themselves were already statues in the temples: their reflections, doubles, and image transformations, which mostly followed erotic goals mnch like popular movies, fill an entire mythology, instead of which I am only able to recommend Pierre Klossowski's Diana at Her Bath.
It is more difficult for mortals to manipulate moving images, or even to see them clearly as images at all. I remind you of the story of the young Narcissus from Ovid's Metamorphosis and the allegory of the cave that Plato devised in his Republic and that film theorists since 1920 - from Panl Valery to Luce Irigaray - want to read as the
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model at all films, But NarcIssus fell m love wIth hIS own reflection
in the surface of a pond precisely because this "simulacrum" made
the same fleeting gestures as he did himself. And the simulacrum in the allegory of the cave reproduced everyday objects, whose clay or wood imitations were carried past a single light source by a pair of puppeteers behind the backs of the bound cave occupants. On the wall before their eyes, only fleeting shadows come and go, which do not come to rest anywhere. To count the allegory of the cave as a precursor of film is thus, absurd. Because moving Images could not be stored in his own tIme, Plato equated the immortal and therefore self-storing soul with a wax writing slate, the medium of his own philosophy.
This writing monopoly saves us the trouble of treating simple tech- nical realizations as optical media, such as Javanese shadow puppet theater or the mirror effects of the ancient deus ex machil1a, which was supposedly made to appear at cultic festivals through a mecha- nism invented by Heron of Alexandria. Instead, we can move directly to the first solutions to the problem of how a transmitted image could also be made to store itself. As the great physicist Du Bois-Reymond discovered in 1850, from the middle of the fifteenth century onwards scientists and artists have been investigating the question of how "to make nature depict itself, so to speak" (Busch, 1995, p. 90).
What is meant by the self-depiction of nature is so-called "linear perspective," a technique employed in painting since approximately 1420, which ensured that all of the lines, corners, and proportions in an image appear exactly the same as the image they reproduce on the retina. Painting thus became the engineering of illusions, because a more or less explicit geometry stands behind every painted image. Between the Renaissance and Impressionism, this geometry absolutely dominated painting as an artistic style in the aforemen- tioned sense of the word, and since the arrival of photography it has also been incorporated into media technologies as a technical standard.
The qnestion remains as to why this geometry was not always dominant, but rather first emerged at a well-defined time. In Egyptian painting, there existed only a radical joining of frontal and side views, as we know, but Greek pottery painting was also unable to create spaces whose lines all ended at a vanishing point on the horizon. A few perspective effects appeared only in wall-paintings excavated in Pompeii, typically in the arts and crafts ambience of the bedrooms and mysterious cults of late antiquity, yet they obviously still belong to a thoroughly constructed geometry.
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2. 1. 1. 1 Greeks and Arabs
There are good reasons for this. In addition to countless other sci- ences, classical Greece also founded a science of optics, which at least managed to establish the law of reflection, if not also the law of refraction. At the latest since the time of Euclid, who in addition to his famous Elements of Mathematics also wrote about optics and the path of light (Edgerton, 1975, p. 68), it was clear to the Greeks that rays of light travel in straight lines. But witli the notable excep- tion of the materialistic and therefore atomistic school of philosophy, the ruling doctrine amounted to the foundation of all optical laws on visual rays, which did not lead from the light source to the eye (as in today's understanding), but rather in the exact opposite direction from the eye to the light source. The eye itself thus functioned like a spotlight, whose beams encountered or edited the visible world and then registered this information in the mind. Goethe had good reason, in his great enmity towards Newton's modern optics, for writing this Greek, all-tao-Greek verse: "Were our eyes not like the sun, they could never see it.
" For a discussion of the insurmountable barriers to research that this theory put in place, please consult the work of Gerard Simon (Simon, 1988).
What matters here is only that this ancient theory of active visual rays effectively excluded or prevented any conjecture about the self- depiction of nature. In a closed and finite world, which the Greeks honored with the name cosmos, meaning a well-ordered sphere, these rays could easily reach everything, even the stars that popu- lated the inner surface of the sphere itself, and at the same time the speed of light was also considered infinitely great. Linear perspec- tive, on the other hand, was based on the implicit (and later entirely explicit) assumption of an infinite universe, which corresponded to an infinitely distant vanishing point in every single perspective paint- ing; these paintings thus functioned as miniature models of the infi- nite universe itself. In a lovely book entitled Signifying Nothing, Brian Rotman attempted to grasp this infinity as the intrinsic value of modern Europe from the introduction of zero: first, the vanish- ing point of linear perspective; second, the zero from the numbers imported from India and Arabia; third and last, the money of modern financial systems - they all supposedly stand for that extremely tricky mathematical function that divides one by infinity (Rotman, 1987). But as you already know: what is forbidden in theory can have explo- sive consequences in practice. Europe, with all its states, colonies, and sciences, is possibly only the effect of a miscalculation.
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Rotman's claim that the cause of these explosive results can be traced back to an Arabic import is no less valid for linear perspec- tive than it is for the decimal place system of modern mathematics. It appears, namely, that a passing comment by Aristotle led Arabic mathematicians like al-Kindi or Alhazen to construct the first work- able models of a camera obscura, which were thus also the first models of linear perspective. In his so-called Problemata (so-called because it was apocryphal), which was hardly more than a collection ot notes concermng unsolved questions, Aristotle, who wrote about everythmg that was knowable circa 350 Be, noted not only his still momentous thesis about genius and insanity, but also a small experi- ment involving a solar eclipse, when it appears, from our earthly perspective at least; that a full moon moves directly before the sun. In antiquity, however, the sun was not defined merely by the fact that it makes everything visible except itself, as looking at the sun leads to blindness. This is precisely what Leonardo means when he says, in the passage I cited at the very beginning of these lectures, that the sun never sees a shadow. Despite or because of this, Greek mathematics had precisely begun, to the astonishment of oriental despots, to be able to predict future solar and lunar eclipses. They were thus able to see exactly what was forbidden to the mortal eye. Aristotle described the simple trick of avoiding the danger of blind- ness using optical filters. Instead of observing the partially covered sun directly, he recommended observing the entire scene on the rear wall of a room whose front wall contains a small bole.
Aristotle had thus already explained the principle underlying every camera obscura, but he only applied it to the special case of the sun, a light source superior to all others. His Arabic translators or suc- cessors were the first to investigate the aforementioned hole under empirical, and therefore terrestrial, conditions. In place of the divine sun they employed a simple wax candle, which sent its own light through the medium of that small hole and reproduced an image of itself within the chamber. A camera obscura for any light source did not actually exist in the world, but only on paper, yet this paper supposedly reached Europe through an Arabic mediator. In stark contrast to Greek mathematics, Arabic mathematics generally inves- tigated all the possible ways in which obliquely placed light sources encounter the resistance posed by opaque objects and then project the shadow of those objects on vertical walls. (The Greeks limited their curiosity to that quasi-horizontal surface known as the ground in order to be able to determine the time of day from the length of a sundial's gnomon and its shadow. ) In the realm of fairy tales,
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such research produced Hamn al-Rashid's trigonometry, which was nothing more and nothing less than a new type of mathematics. Sine and cosine, tangents and arc tangents are all - the things as well as the words - Arabic innovations. Before approximately 1450, when Europe applied all of these trigonometrical functions to very practical purposes, namely the military or colonial navigation of ships, they were first designed with the theoretical purpose of investigating the effects of light rays on flat surfaces. In the camera obscura model, for example, the tangent corresponded exactly to the projected length of the reflection of an object standing at angle x in relation to the plane of the camera (provided that all circles are idealized as a unit circle following Leonhard Euler).
In any case, neither Arabic mathematicians nor their European students - the most significant being the Nuremberg patrician Regio- montanus - had anything other than simple empirical methods of conveying such trigonometrical functions. In modern language, such functions are transcendent: they disdain all simple calculations. Sine and cosine, tangent and cotangent were thus available in endless tables, which consisted moreover of huge integers prior to Simon Stevin's invention of decimal numbers. Because he was unable to write up numbers like 0. 7071 (the sine of 45 degrees), for example, Regiomontanus multiplied all sine values by a factor of ten million (see Braunmiihl, 1900, p. 120). But such monstrous tables of mon- strous numbers were virtually unusable by artists, and consequently the history of linear perspective, at least in its first centuries, is cer- tainly not the history of mathematics. I will later come back to the question of when and through whom this changed.
2. 1. 2 Implementation
But even this mathematical weakness of early trigonometry was able to help the camera obscura achieve tremendons snccess during the Renaissance. As a device that calculated trigonometrical functions completely automatically, simply becanse it focused light into a single bundle of straight lines and then allowed them to follow their course, the camera obscura made the revolutionary concept of a perfect perspective painting possible. Devices, then as now, relieve humans of the need to calcnlate. However, perspective painting, which was unknown to the Egyptians and the Greeks, was only made possible by going one final step beyond Aristotle and Arabic optics: the camera obscura did not simply reproduce light, whether it was the great heavenly sun of Aristotle or the small earthly candle flame used by
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the Arabs, but rather it also vIsibly projected objects illuminated by the light. A problem thus emerged that was not completely solved until the invention of optical lenses at the beginning of the seven- teenth century.
The camera obscura, to use Shannon's rigorous terms, works as a noise filter: the small hole through which the rays emanating from all light sources are forced - directly illuminating lights as well as indirectly illuminated obiects - also blocks the scattered ligbts that are otherwise omnipresent and tbus makes the reflection sharp. Oth- erwise, the image in tbe camera obscura would appear as impres- sionistic as when the summer sun illuminates the woods. The gaps between the leaves of every deciduous tree function like countless out-of-focus camera obscuras, and the end result is that a patchwork carpet of completely contradictory projections emerges on the forest soil - an effect, as I have said, that interested Manet more than the artist-engineers of the European Renaissance. In the interests of their royal and religious patrons, these artists did not want and were not supposed to paint bourgeois picnic breakfasts, but rather a geometri- cally exact view of the world in general and their own architecture in particular. They thus ran into a problem that absolutely concurred with Shannon's claim that the filtering of a signal always simultane- ously also implies the weakening of a signal. The smaller the hole in the camera obscura, the sharper but also darker the image becomes; the bigger the hole, on the other hand, the brighter but also the more blurred the image becomes. It is therefore no wonder that the first descriptions of a functional camera obscura came from Italy, the western European country with the brightest sunlight: Leonardo supplied the first model around 1500, and Giambattista della Porta, the universal scientist and magician, supplied a more detailed model around 1560. Porta simply suggested darkening the window of a room that opens out onto the sunny side of the street, yet leaving a hole that casts ghostly images onto the opposite facing wall of pass- ers-by and domestic animals floating on their heads. Plato's allegory of the cave was thus implemented.
A gap of 200 years separates Leonardo and Porta from the late medieval references to the camera obscura by Roger Bacon (who will also come up in connection with the invention of gunpowder), yet it is precisely in this gap that the invention of linear perspective occurs. Contrary to all of my stories, therefore, the invention of linear perspective would hardly seem to be based on the technology of func- tioning camera obscuras. This gap or hole in the historical record, which fundamentally involves tbe invention of a hole, can only be
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filled with historical speculation, which at least has the advantage that it concerns a unique and actually existing hole.
2. 1. 2. 1 Brunelleschi
The history I will now tell concerns one of those great artist- engineers produced by the Italian Renaissance: Filippo Brunelleschi. In contrast to later artists, who remained only artists, artist-engineers were people like Brunelleschl, his younger friend Alberti, or even Leonardo, who were not satisfied with merely producing image after image, but rather for the first time ever they established the artistic and technical standard according to which countless images of an epochal style became possible and feasible. The word "image" here should not be misunderstood to refer solely to the strange two- dimensional pictures on the walls of churches, palaces, and later museums, hut rather also to such abstract yet brutally effective things as fortresses or church domes.
Filippo Brunelleschi was born in Florence in 1377. At that time, it was mandatory for novice craftsmen to serve an apprenticeship, just as it is today, and Brunelleschi served his under a goldsmith. In 1401, while presumably still an apprentice or journeyman, Brunelleschi participated in a competition sponsored by the Signoria. The Bapistry, the haptism chapel dedicated to John the Baptist that faces the Cathedral in Florence, was to be ornamented with new bronze doors. Although his design featuring the sacrifice of Isaac (which still exists today) was unsuccessful, Brunelleschi's loss was Enrope's gain. For instead of maintaining a sale focus on reliefs or art more generally, as his medieval predecessors did, Brunelleschi went on to study mathematics and architecture. Like all of the fortresses that Brunelleschi huilt as head engineer, the technically incredible dome that adorns the Santa Maria del Fiore, otherwise known as Florence Cathedral, was based on precise mathematics. He died in 1446, barely a year before the impoverished Mainz patrician Johann Gensfleisch zum Gutenberg printed his (presumably) first calendar with movable type. I will soon come back to this coincidence.
But first I want to discuss a small and, more importantly, missing work by Brunelleschi, which at first glance appears trivial in compari- son to his domes and fortresses. The fact that we even know about this missing image, which was presumably made in 1425 (Edgerton, 1991, p. 88), is solely thanks to the significant fact that simple crafts- men like Brunelleschi - in total contrast to the anonymity of the European Middle Ages - received the honor of having a biographer
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III 1450. A description of the work can thus be found in Antonino di Tuccio Manetti's account of Brunelleschi's life:
About this matter of perspective, the first thing in which he displayed it was a small panel about half a hraccio square on which he made a picture showing the exterior of the church of S. Giovanni in Florence. And he depicted in it all that could be seen in a single view; to paint it he took up a position about three braccia inside the middle door of S. Maria del Fiore. The work was done with such care and accuracy and the colors of the black and white marble were so faithfully repro- duced that no miniaturist ever excelled him. In the picture he included everythmg that the eye could take in, from the Mlsencordia as far as the corner and the Canto de' Pecori on one side to the column com- memorating the miracles of St. Zenobius as far as the Canto alla Paglia and all that could be seen beyond it on the other. And for what he had to show of the sky, that is, where the walls in the painting stand out against the open air, he used burnished silver so that the actual air and sky would be reflected in it and the clouds also, which were thus seen moving on the silver when the wind blew. Now, the painter had to select a single point from which his picture was to be viewed, a point precisely determined as regards height and depth, sideways extension and distance, in order to obviate any distortion in looking at it (because a change in the observer's position would change what his eye saw). Brunelleschi therefore made a hole in the panel on which the picture was painted; and this hole was in fact exactly at the spot on the painting where [in reality] the eye would strike on the church of S. Giovanni if one stood inside the middle door of S. Maria del Fiore, in the place where Brunelleschi had stood in order to paint the picture. On the picture side of the panel the hole was as small as a bean, but on the back it was enlarged [through the thickness of the panel] in a conical shape, like a woman's straw hat, to the diameter of a ducat or slightly more [i. e. 2. 3 em]. Now, Brunelleschi's intention was that the viewer, holding the panel close to his eye in one hand, should [turn the picture away from himself and] look [through the hole] from the
back, where the hole was wider. In the other hand he should hold a flat mirror directly opposite the painting in such a manner as to see the painting reflected in it. The distance between the mirror and the other hand [holding the panel] was such that, counting small braceia for real braccia [i. e. measured in the same scale as that which obtained between the painting and the real thing], it was exactly equivalent to the distance between the church of S. Giovanni and the place where Brunelleschi was assumed to be standing when he painted it. Looking at it with all the circumstances exactly as described above - the bur- nished silver, the representation of the piazza, the precise point of observation - it seemed as though one were seeing [not a painting
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but] the real building. And I have had It lil my hand and looked at It many times. in my days and can testify to it. (quoted in Battisti, 1981, pp. 102-3)
This story emphasizes, like no other, what was revolntionary about the new world view called linear perspective. Brunelleschi shattered or literally bored through the entirety or the imaginary natnre of a panel painting in order to reveal something even more imaginary. His image of the Florence Baptistry, whose bronze doors he himself wanted to design, proves to all hIs disbelieving colleagnes and con- temporaries that perspective vision really and truly always already takes place in the eyes. Otherwise, the eyes would not be so fooled by their own simnlation, as Manetti showed Brunelleschi's contem- poraries. The fact that such a literal demonstratio ad oculos must have been necessary at that time, yet nnnecessary today, in the age of fish-eye cameras or satellite images, already says something abont Brunelleschi's experiment.
Bnt there is still plenty left to discuss: first, in terms of media history, which images were abolished by Brunelleschi's hole; and second, how could snch a perfectly deceptive image have been achieved in 1425?
To begin with the first qnestion, I must go back a little fnrther. As we know, 90 percent of all the images and stone buildings commis- sioned in Europe in the centuries prior to 1425 were designed to serve the only true Christian faith. This faith happily adopted the Greek Catholic concept of visual rays, which make the world visible to begin with. But this eye, which can still be seen today on any dollar bill, does not belong to any human, but rather to God himself. According to Abbot Suger of St. Denis, the glass windows of the Christian church put precisely this divine visual ray in the picture. God thus presented himself in art - and from his own perspective rather than the distorted perspective from which earthly beings could look at him. For this reason, the icons of the Byzantine Empire - the prime example of the
nexus between art and worship according to Hans Belting (Belting, 1994) - principally showed God in front of a gold background that truly implemented his radiance. And, as Samuel Edgerton wonder- fully demonstrated, it is precisely this golden background that turned into the first proto-perspective medium in Western Europe. Christian philosophers like Roger Bacon, who has already been mentioned in the context of the camera obscura, represented the sacred being as an emanation or radiation of small golden bodies, or corpuscula, that travel from heaven into the eyes of humans and thus also into the eyes of those who look at the image. Bacon even employs the Latin
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word perspecttva In order to use a visual metaphor to explaIn how God's grace spreads throughout the world (Edgerton, 1991, p. 44). In paintings created by devout Italian monks, this journey can also be seen in the form of small golden rings that become detached from the body of the sacred being.
So much for the background information needed to better under- stand Brunelleschi's revolution. In his book Belichtete Welt: Eine Wahrnehmungsgeschtchte der Fotografie (Exposed World: A Percep- tual History of PhotographYi, Bernd Busch wntes: "Brunelleschi's experimental design was revolutIOnary because it established the graphic illusion of artistic iIlusttatIOn as the result of a deliberate technical-mathematical operation" (Busch, 1995, p. 65). The new combination of eye, hole, painting, mirror, and outer world starts from the eye of the observer and no longer from the eye of God.
But this eye was as nnGreek as It was unchristian. For Brnnelles- chi's image to be developed, it must first have been clear that the inner eye is a darkness into which the light sends its rays, and the pupil at the entrance to this darkness thus functions exactly like the hole in the camera obscura. Leonardo da Vinci, whose left-handed mann- scripts describe the camera obscura in great detail, also articulated this analogy between the camera obscura and the pupil (Eder, 1978, p. 39). But through this analogy the eye itself became operationaliz- able, which means, as always, replaceable. Many observers could hold their eyes up to Brnnelleschi's small hole, which also had the form of a conical visual ray. The mirror, the hole, and the painting performed an automatic image analysis for all of them.
The historical break, it seems to me, is that such an automatic image analysis was permissible at all. Under the unshakable theologi- cal condition that all creatures were, to varying degrees of exactitude, images of their creator, and that humans in particular were, as the first book of Moses says, ad imaginem et similitudinem nostram - created by God in our image (which the biblical plural "our" always implies) - image analysis itself remained forbidden. The ritualistic imperative of image worship prevailed instead, which ruled out the possibility of sending a likeness of God throngh the hole of the camera obscura (never mind the original image itself). The camera obscura put an end to this imaginary function, which drove people to recognize or misrecognize themselves only in the likeness of a saint and the saint itself as a likeness of God. )n this respect, it was not simply a new scientific device or toy, but rather a weapon in the war of religion. As we know, the media-technical basis of the Ref-
ormation was the dismantling of the Bible into pnntable letters that 57
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private individuals were allowed to decipher and interpret without the church making up their minds for them; fathers were even permit- ted to read the book aloud to their wives, children, and servants. The dismantling of images into portrayable, constructible elements like points, lines, and surfaces similarly brought an end to the painting of icons, and on this so-to-speak clean slate new forms of mathematical analysis emerged, such as Leibniz and Newton's new arithmetic and the geometry of Descartes, the inventor of our coordinate system for planes and spaces.
I would like to point out a third possibility of analysis that the modern age granted to us: namely, the dismantling of flesh and body parts using gunpowder, which became possible only slightly earlier. After all, Roger Bacon, who mentioned the camera obscura for the first time, also provided the first correct recipe for gunpowder. And Nicolas Oresme, who replaced the Aristotelian doctrine that all bodies move because they want to return to their natural place with a mathematical analysis of the individual phases of movement of flying bodies - these kinetics should already remind you of film - was a contemporary of Bertold Schwarz, the half-mythical Freiburg monk and inventor of modern guns. Third and finally, as Virilio has repeat- edly pointed out, the painters who made essential contributions to the theory and practice of the camera obscura, like Diirer or Leonardo da Vinci, at the same time also made essential contributions to the construction of fortresses and the defense of cities against these new gnns (Virilio, 1989, pp. 49-50). Diirer's 1527 Befestigungslebre (The Theory of Fortification), for example, is a description of perspective from the perspective of ballistics. In other words, the profound aim of the camera obscura, which elevated it above many other simply entertaining inventions of that time, converged with the profound aim of shooting, in order to bring down the enemy when he is finally and accurately within one's sights. Together with the new firearms of the modern age, therefore, the camera obscura started a revolution of seeing, which was nothing other than the introduction of perspective in general. Humans have painted since the Stone Age, as we know, but it is only since Brunelleschi that these paintings have been based on a constructed central vanishing point to which all the elements of the image refer.
I now come to the second question I posed myself. What made Brunelleschi employ perspective as a mathematically based painting technique rather than as the worldwide spread of divine grace? I have already mentioned how he went from being a craftsman to a math- ematician and architect after losing the competition for the design
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of the bronze doors of the Florence Baptistry. Tills mathematical, architectonic know-how offers at least a hypothetical reference to the reasons for Brunelleschi's innovation.
In his seminar The Four Fundamental Concepts of Psychoanaly- sis, Jacques Lacan dealt extensively with a topic that Freud mostly neglected: the gaze. I urge you to read the relevant chapter. It is less well known that in his seminar on psychoanalytic Transference3 he also briefly yet dramatically outlines the genesis of linear perspective. Like Hegel, Lacan begins with the hypothesis that the oldest form of art and/or worship was architecture. In contrast to Hegel, however, Lacan makes it clear that there is no god at the center of this archi- tecture, but rather, like the mterior of pyramids or temples, there is only a corpse. This corpse needs a space, that is to say, a vacated place, that is to say, exactly like Brunelleschi's image: a hole. Lacan even defines the sacred itself as this architectonic hole: as the pres- ence of an absence.
But every Egyptian pyramid shows - and this is the crucial point in Lacan's argument - how costly the preparation or maintenance of such holes can turn out to be. Millions of stones serve merely to encase a non-place. Lacan conceives of the invention of linear per- spective as a simple act of "economy. " Instead of building the sacred void, it is much cheaper to paint it as a vanishing point. This artistic innovation has an immediate influence on architecture, according to Lacan, because he conceives of early perspective painting as mural or wall painting rather than panel painting. In Assisi, for example, where the first pre-perspective paintings surfaced and were destroyed in last year's earthquake, murals cover the walls of buildings and thus give them vanishing points or holes that are not actually part of the structure, but are rather cheaper or more imaginary. I will later return to this combination of painting and architecture, like the baroque trompe l'oeil.
Unfortunately, Lacan did not know the history of Brunelleschi's hole pattern, which would have confirmed that all perspective paint- ing centers around a hole, and that there is a connection between architecture and painting. Not only is the object seen in Brunelleschi's image a work of architecture - namely, the Florence Baptistry - but it is also the prescribed place from which the illusion of perspec- tive solely becomes apparent - the Cathedral of Florence, as it was finally completed by Brunelleschi's brilliant achievement in dQme construction.
3The German word for transference, Ubertragung, also means "transmission," 59
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This leads me to the last point of this seemingly never ending com- mentary on a single image. It concerns the simple question of how Brunelleschi was able to paint his image at all. All of the answers to this question can only remain hypotheses, as Manetti himself did not write a single word about how the painting was done. Even Busch is succinct and resigned: "It is unknown precisely how the production of Brunelleschi's image panel was accomplished" (Busch, 1995, p. 402). However, Shigeru Tsuji, art historian at the Gedei (the Japanese abbreviation for the Imperial Art School of Tokyo), has presented a hypothesis that is so wonderfully plausible I can only endorse it.
Like all good detectives in crime novels, Tsuji begins with the facts in order to question why Brunelleschi chose precisely this image and no other. Why was his image so unusually small (approximately 27 centimeters square)? Why did he paint his image from the main portal of the cathedral? Why was the image obviously painted in reverse, such that only the use of a mirror would make it visually coincide with the reality of the Baptistry? The answer, which resolves all three of these questions at the same time, is that Brunelleschi employed a camera obscura. He was therefore the missing link between Roger Bacon in the fourteenth century and Leonardo da Vinci in the sixteenth.
First argument: in Brunelleschi's time there were no lenses. The perforated disk in front of the projected image thus had to be posi- tioned in a place that remained shaded even during the day. This is precisely true of the main portal of Santa Maria del Fiore.