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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-
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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.
Second argument: the object to be projected must itself lie in direct sunlight. This was precisely true of the Baptistry during the morning. Third argument: the projection surface must be a certain size. If it was too large the image would become dark and blurred, but if it was too small Brunelleschi's hands would not fit between the perforated disk and the projection surface. With the meticulous use of actual architectonic relationships in Florence and trigonometric functions, Tsuji elegandy shows that Brunelleschi's chosen image size was ideal
for his purposes.
Fourth argument: in Brunelleschi's time there were still no geomet-
ric devices that could manage to reverse pages automatically.
In other words, a reversed image could hardly have been produced by hand in 1425. If Brunelleschi had painted by hand, he could have simply not used the mirror and instead turned the front of his painting towards the observer (rather than the back).
To me, at least, Tsuji's arguments are completely clear. An inven- tor of a process may thus have been identified only by means of cir- cumstantial evidence, a rare occurrence in the history of media. But
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TsuJi nghtly emphasizes that even if Brunelleschl actually Invented the camera obscura as a practical painting device, he did not solve all of the problems of linear perspective painting. The camera obscura only works in the real world. This was conclusively proven by its development into the photographic camera, which cannot record anything that does not exist. But the painters of the Quattrocento and the following centuries were very frequently ordered to paint what did not exist: God, saints, and the beauty of earthly rulers. The sImple questlOn for Brunelleschi's successors, therefore, was how to take the geometrical automatlsm of the camera obscura and transfer It to other media.
2. 1. 2. 2 Alberti
The only other medium that was possible at that time was paper, which reached Europe from China via Arabia to then revolutionize mathematics, science, and accounting. The problem was how to con- struct perspectival drawings on paper geometrically, especially when these drawings were pure fantasy or- in the case of new building plans - pure dreams of the future. This problem was first solved by a younger friend and pupil of Brunelleschi's, who attained fame as an engineer-artist and all-purpose inventor: Leon Battista Alberti.
Like Brunelleschi, Alberti certainly also used the magic of the dark- room to astonish the Florentine people. An anonymous biographer recounts beautifully:
Through painting itself he also produced things that were entirely
incredible and unbelievable to spectators, which could be seen through a small opening in a small box. There one caught sight of high moun- tains and broad landscapes surrounding an immeasurable lake as well as regions so distant that they could not be discerned with the eye. He called these things demonstrations, and they were meant to be seen as natural phenomena rather than paintings. There were two kinds, which he called day demonstrations and night demonstrations. In the latter, one could see Arcturus, the Pleiades, Orion, and other shimmer- ing stars, and the moon rose behind steep cliffs and mountain peaks by the light of the evening starSj in the day demonstrations the shining god was unveiled, who according to Homer was announced far and wide around the world by Eos, the bringer of morning. (quoted in Vasari, 1983, p. 347)
The camera obscura can hardly be defined more clearly: it is the sun cult, as for the Greeks - the return of the gods, the enemy of all
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Christianity. This was the reason why it was so important to spread the renewed unveiling of being in its entirety, which Helios and/or Alberti achieved, to the world outside Florence. Alberti takes up his pen - Gutenberg had not yet invented his art - and as a grateful pupil dedicates his Three Books about Painting to Brunelleschi - first in Italian in 1435 and in scholarly Latin the following year.
The first book of this treatise presents "unheard-of and never- before-seen arts and sciences," which are explicitly without ancient "teachers" (Alberti, 1966, p. 40). To describe linear perspective as a free geometric construction, Alberti developed the concept of an ideal or simply imagined window. This fenestra aperta could be con- sidered to be the ancestor of all those graphic user interfaces that have endowed computer screens with so-called windows for the past 20 years. Alberti's window - like Microsoft Windows - was natu- rally rectangular and could thus be easily broken down into smaller windows. As a model or metaphor for this scanning technique, which was his greatest invention, Alberti employed a semi-transparent veil divided into small rectangles using vertical and horizontal threads of canvas. It could thus be said that in Alberti's work Brunelleschi's single hole became a thousand-eyed Argos. Indeed: Alberti, and later also Diirer, assigned the eye the task of looking through everyone of these countless holes into the world of either real models or ideal art objects.
Alberti's real trick, however, was to make even this activity of the eye as virtual as the concept of the window. To do this he used not canvas - the material hasis of all painting - but rather paper. The scanned rectangle was transferred out of the world and onto the paper, where it appeared as a checkered pattern, so to speak. This pattern then allowed geometrical constructions to be performed - in other words, operations with Diirer's ruler and compass - to such a high degree of accuracy that the resulting drawing obeyed all the laws of linear perspective. Alberti explicitly emphasized that he had written his treatise for artists and not for mathematicians, which is already clear from the title. For this reason, as I have implied, the applied mathematics still adhered to the good old Euclidean propor- tions between lines and angles. In other words, it did not look for help from the new trigonometric tables. Even more gratifying and enigmatic is the historical fact that Regiomontanus, the creator of the best trigonometric tables, undertook a trip to Italy, and during this trip - in Ferrara - he reportedly met Alberti. I would be a happier man if I knew what they had talked about.
Not knowing this is one of the reasons why a simple histori- cal question cannot be completely clarified: what was the practical
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cause of this radical shjft in the fifteenth century - from the two- dimensional miniature to the perspective panel, from the pictorial nature of all God's creatures to the mechanics of the camera obscura?
It hardly needs explaining why it was necessary to learn to see in perspective when shooting, whose invention I previously alluded to. The reason why it was necessary for painters to learn to see in perspective following Brunelleschi's experiment, however, was previ- ously attributed by art historians to a Stilwillen - or "will to style" - that simply led to the new Renaissance art. A better explanation is already Implied by the fact that in the very beginning, experiments with the camera obscura could only be conducted in darkened yet otherwise normal-sized chambers or rooms, but they soon changed to become small, transportable boxes. (Consider the difference between literally fixed temples and transportable Bibles. ) Painters who had a camera obscura could thus "paint according to nature," as the lovely phrase goes, simply because the small, portable box allowed the light and everything it illuminated to be conveyed onto a surface, which the hand of the painter then only had to paint over. People have always painted according to nature in some way, just as when the puppeteers in Plato's allegory of the cave produced silhouettes of jugs and similar tools, but they have not always made the hands of the painter into dependent functions in an experimental procedure. As if anticipating Arnheim's theory of photography, on the other hand, the camera obscura combines for the first time the optical transmis- sion of information with the optical storage of information; the former function is already fully automatic, whereas the latter is still manual.
We will not dwell on this manual limitation, but rather we will stress that the number of drawings and images generated with the aid of a camera obscura is probably beyond the wildest dreams of a hermeneutic history of art. The benefits are obvious: the draw- ings that result from this union of optical receiver and human data sink, camera obscura and painter, naturally have a greater level of precision. This precision also became, as in Durer's work, a theme of triumphant and self-referential drawings, which then once again recorded (for educational purposes) how the painter captures the image of a woman on paper either through a lattice placed in the room or by way of a camera obscura. I will only point out here that it goes without saying that women were once more the subjects of such experiments, but since this is a media history and not a love story, I prefer to steer clear of my suspicions concerning the purpose
of the whole episode.
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As I said, we do not know whether Alberti spoke with Regio- montanus about trigonometry and linear perspective at the court of Ferrara, but we do know the content of another conversation that Alberti had in his old age. This conversation has come down to us from Alberti himself, and it gives unexpected information about the causes that drove the modernization of technical media in the middle of the fifteenth century. In 1462 or 1463 - we do not know exactly - Leon Battista Alberti took a stroll in, of all places, the Vatican gardens with, of all people, a certain Dato, who was by profession secret scribe to the Pope. I should explain that the field of encoding and decoding texts, which began in the ancient world, was to some degree neglected in the Middle Ages. Cryptographic specialists were only employed in the Vatican and by the Signoria in Venice, where modern diplomacy in general originated. Dato, with his absolutely appropriate name, whose plural is "data," was one of them.
Alberti opened the conversation quite differently. He said that while an hour of chatting was spent in the Vatican garden, the "man in Mainz" had probably made another dozen or hundred copies of a rare and irreplaceable manuscript of ancient knowledge by laying it under his printing press. In other words, Alberti explicitly saw himself as a contemporary of Gutenberg. Dato must have answered - no one knows for sure - that in spite of all the Gutenbergs of this world, cryptanalytic encoding, his own profession, unfortunately is and remains a lengthy process.
It seems to me that this complaint preyed on Alberti's mind. He immediately sat down, with a quill in hand naturally, and thought about how the process of encoding and decoding secret messages could be accelerated, just as Gutenberg's movable type had acceler- ated handwriting or made it entirely superfluous. What emerged was a treatise on ciphers, which continues to be the basis of all cryptogra- phy, even in the computer age, as David Kahn, the leading historian of cryptography, emphasizes.
Albert introduced two innovations. One, strictly according to Shannon, on the side of the sender, the othel; again strictly according to Shannon, on the side of the receiver. When Roman emperors like Caesar or Augustus encrypted their messages, they simply moved all the letters one or two places further along in the alphabet, although Augustus never mastered modulus mathematics and therefore did not code the last letter X as the letter A (Suetonious, 1979, pp. 39 and 102). It was quick but also easy to crack. Alberti transferred the principle of movable type from Gutenberg's printing press to cryptography. Whenever a letter was shifted alphabetically and then
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written down according to the code, the code itself also changed. The next letter to appear on the paper was shifted one additional place in comparison with the original text. This remains the basic principle of polyalphabetic ciphers today.
Alberti's innovation in the field of decryption was decidedly Guten- bergian. The printing press had already made it plain that in order to print normal texts many more E's were needed than, say, X's or Y's. A glance in any typesetter's case will confirm this. Alberti, like Edgar Allan Poe's X-ing a Paragrab, threw preCIsely thIS glance at texts encrypted in the old-fashioned, manual way and not through his polyalphabetic method. When there are far more Y's than E's in such a text, this means plamly and simply that the letter E has presumably been encrypted as Y. In other words, Alberti transferred the coldness of numbers to the sacred realm of everyday grammatical sense or semantics.
2. 1. 3 Impact
2. 1. 3. 1 Perspective and Letterpress
This long digression into the history of textual media should make one thing clear: Alberti mathematized old manual techniques like painting and writing, and at the very least he had explicitly made ref- erence to this modernization before Gutenberg. The question remains whether this reference before and to Gutenberg is not also true of Alberti's mathematization of painting. Busch cites a remarkable passage, though I have not been able to verify it. No less a person than Giorgio Vasari, the contemporary and biographer of all of these painters, wrote in his 1550 book Lives of the Most Eminent Painters, Sculptors and Architects that "in the year 1457, when the very useful method of printing books was invented by Johann Guttenberg, a German, Leon Battista discovered something similar," albeit merely in the field of painting (Vasari, 1983, pp. 346-7). In an age of growing national pride, this was probably supposed to imply that Italy's technical achievements had caught up with Germany's.
Contemporaries thus already saw a connection between the art of artistic writing and the art of artistic perspective, ars artificialiter scribendi and perspectiva artificiosa. This supposition can be theoreti- cally substantiated.
The content of a medium, McLuhan decreed, is always another medium. All of the Renaissance drawings, which described how to build a camera obscura and how best to install it between the painter
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and the living object, were stored and passed down in books, particu- larly in textbooks. For the first, yet certainly not the last time, we are encountering something like a union of media: the printed book, on the one hand, and the drawing brought to a higher level of precision throngh the camera obscura or linear-perspectival geometry on the other. As soon as one recognizes that, the lowest common multiple of the two media becomes obvious. Through Gutenberg's invention it was possible for the first time that all of the copies of a book, or at least of an edition, presented the same text, the same printing errors, and the same page numbers. As Hans Magnus Enzensberger wrote in a poem about Gutenberg, "How greatly this page here resembles a thousand other pages" (Enzensberger, 1976, p. 4). (Not to mention the uniformity of computer software, with which my lecture notes and the notes of countless others have been drawn up. )
Elizabeth Eisenstein very convincingly argues that the new, mechanically perfect reproducibility of the medium of handwriting also put competitive pressure on other manual arts. The reproducible book as such required illustrations that were equally as reproducible and exact - not to make readers or art lovers happy, but rather to store and transmit technical knowledge, the most shining example of which was the invention of the letterpress itself. Eisenstein directly connects the great upturn in technology, science, and engineering in Europe in the modern era with the availability of technical drawings, construction plans, and sketches, which looked the same in every printed copy simply because they were indestructible reproductions of a single original. As we know, the techniques of wood engrav- ing and copperplate etching, which were developed or perfected at that time, provided this reproducibility, whose lack in other cultures resulted in drawings showing more mistakes - or more noise - as they were copied from copies of copies, etc. But who or what ensured that the original was a correct reproduction of its original, which may have been a woman or the camera obscura itself? My supposition: scientifically based perspective and its technical implementation - in other words, none other than the camera obscura once again. Even though the camera obscura was not a camera in the sense of photog- raphy or film, and consequently it could not replace the manual work of drawing and painting, these handicrafts nevertheless fell under its scientific-technical control. When one realizes that in the centuries before Gutenberg's invention the operational secrets of all manual workers were always only communicated from master to jonrney- man, from generation to generation, and when one realizes that secrecy was so important and promising, that entire cults and rituals
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were erected around it (hke wrought-Iron work), one can appreci- ate what it means to be able to entrust building plans along with explanatory texts henceforth to the printed book. Real guild secrets were replaced by the knowledge of engineers, which was in principle also possibly autodidactic, and ritual guild secrets were replaced by the specially invented and complementary secrets of associations like the Freemasons, which made imaginary theories out of the former practices of masons.
Print technology made the autodidact possible - rhat IS the point upon whiCh everythmg depends. The book became a medium in which technical innovations as such could take place. They could be stored, shared, and even advanced with rhe help of technical drawings in the text. Models of a mill or a camera obscura are easier to understand than their so-called reality. This is rhe reason why the excursion into letterpress was not a digression, but rather it furnished the historical foundations for the astonishing and otherwise inexplicable fact that Europe, in contrast to other cultures, has produced one technical medium after another since the Renaissance. It can concisely be said that Gutenberg's letterpress made the techniques that superseded it - from photography to the computer - possible in the first place. It was the unique medium that set other media free. This is true for Diirer's age as well as today. Without specifications, manuals, and technical drawings new generations of computers would be an impossibility.
2. 1. 3. 2 The Self-Printing of Nature
There is evidence to support this hypothesis about the practical uses of linear perspective and the camera obscura. The first piece of evi- dence also brings up an important detail from rhe prehistory of pho- tography. Namely, the seventeenrh century had already attempted to eliminate the great handicap of the camera obscura, rhat is, the necessity of manually painting over the images that emerged. Anato- mists like Vesalius in Bologna or botanists like Gessner in Basel took on the epoch-making task of pouring everything knowable about the human body or the plant world into printer's ink and printing, which greatly increased the need for precise illustrations. From 1657 onwards, therefore, nature researchers have also experimented with the possibility of transferring the objects of their research onto paper without the mediation of a wood or copperplate engraver. A Dane named Walgenstein, who will soon be mentioned again in connec- tion with the lanterna magica, reportedly succeeded in preparing the leaves of plants so that an imprint of them could be made. At the
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start, the leaves were simply held in smoke until they were black euough to leave behind an impression, but later on the very same material employed in the printing of Gutenberg's letters was also employed to print objects, as the leaves were prepared with printer's ink. In any case, the images emerged in their natural size and witb all the detail, but unfortunately only relatively few Gutenberg leaves could be produced from one botanical leaf. After tbat, it was worn out and had to be replaced by another leaf. Such attempts at least show, as Eder has already emphasized in his lengthy and old History of Photography, the clear tendency to set technically reproducible scientific illustrations alongside technically reproducible type (Eder, 1978, p. 33) - not only, as Eder assumes, to save the high costs of copperplate and wood engravers, but also to be able to compete with the precision, and that means from that time on the scientific nature of reproductions. This clarifies the connection between perspective representation, the camera obscura, and Gutenberg technology. In short, we can say that leaves (of plants) became leaves (of books) - while plants of the field, forest, and meadow became the content of optical media.
2. 1. 3. 3 Europe's Colonial Power
The second piece of historical evidence is even more amusing or elo- quent, at least for people who do not suffer from political correctness. In his wonderful book, The Heritage of Giotto's Geometry, Samuel Edgerton also recounts the history of the Jesuits who invaded China in droves during the Ming Dynasty, starting around 1600, in order to preach their faith - and not without success. The reason why the missionaries belonged to the Jesuit Order of all people is still being considered today.
In Peking, Father Matteo Ricci and his successors started an enor- mous enlightenment campaign. They equipped their own library with scientific books, and would you believe it, 19 of these titles were about perspective (Edgerton, 1991, p. 261). Rather than educating the heathens, though, the Jesuits planned to convert them by produc- ing and distributing Christian images, which had already helped an otherwise very insensible theology to triumph in Central and South America. However, the Jesuit in the Vatican who was responsible made a bad mistake. He determined that the native draughtsmen and copperplate engravers who were supposed to translate the images of Christianity into the image universe of Chinese culture should not be trained in Peking itself, but rather in distant Japan (Edgerton,
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1991, p. 266). In other words, the 19 treatIses on perspective, from which the so-called natives could have learned to draw, were not available.
Thus it happened as it had to happen. In 1627, Father Johannes Adam Schall von Bell decided to send four ambitious volumes with "diagrams and explanations of curious machines from the Far West" to the printing presses in Peking (Edgerton, 1991, p. 271). The so-called Theatra Machinarum, a book genre that not coinciden- tally had flourished since the Renaissance, normally contained exact perspective copperplate or wood engravings of existing or merely fictional machines - sketches, therefore, which supposedly enabled the observer to successfully recreate three-dimensional machines from two-dimensional images. Schall's native, presumably Japanese, wood engravers accordingly went to work. They had the European books along with a Chinese translation of the texts directly in front of them, but they were nonetheless completely incapable of correctly copying the proportions in perspective.
Up until the first decades of the nineteenth century, imperial China continued to print these kinds of incorrect graphics in encyclopae- dias and scientific-technical manuals. You can imagine the results. China was the most technologically advanced country in the world during the Middle Ages, but it remained trapped in a state that made it very easy for the English and other European powers to defeat China in one war after another from 1840 onwards. Perhaps the lesson to be learned from this is that linear perspective was not simply an aesthetic or artistic shift in taste, but rather a thoroughly technical re-evaluation of all optical values, which was inconceiv- able without the corresponding mathematical qualifications, such as during the Ming and Manchu dynasties in China. In a story by E. T. A. Hoffmann, which I will return to later, a "Chinaman" of all people poses the "stupid question": "How is it that objects grow smaller as they recede? " (Hoffmann, 1952, p. 77). Linear perspective remained one of the arcana of modern European power
until approximately 1850, when it once again reached Japan and elsewhere.
So much for linear perspective from the perspective of what Shannon calls the receiver side. The camera obscura captured light and cast it further, but it did not send it. For thousands of years, that was left entirely up to simple signal systems consisting of mirrors and torches, which would determine the outcome of battles. Long before Einstein's proof that the speed of light could not be surpassed, sol- diers already knew the advantage of rapid communication.
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