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Oblique drawing & Bazin’s error

By Richard Marshall.

Massimo Scolari, Oblique Drawing: A History of Anti-Perspective, MIT Press 2012

Is there a subtle mistake that Bazin makes about the ontology of the photographic image that Godard imports wholesale and explicitly into his masterpiece Le Mempris? The mistake may be of no matter given the resulting fertility and creativity. But if it’s there then it does open a rift between what a creative artist thinks and what is really happening. And if, as Colin McCabe contends, Bazin’s 1954 ontological essay ‘places cinema in a cultural perspective that takes in the 4000 years from Egyptian funerary art…is absolutely crucial to understanding Godard’s oeuvre..[and]…is… the “axiom” from which all of Godard’s theorems derive’, then the error seems one that we should at least note, even if we approach it dialectically and without hostility. According to a fascinating essay by Jonathan Law in the pregnant new book Godard’s Contempt edited by McCabe and Laura Mulvey, works by Chris Marker, Alain Resnais, Roberto Rossellini as well as Godard are co-opted into what playfully might be called Bazin’s error.

Bazin says that still photography preserves the objects that they reproduce. This imports without questioning the notion that a single perspective ‘preserves the objects that they reproduce.’ But the photographic single perspective reproduces a phenomenology of seeing, of how things seem from such a perspective, rather than the thing itself. In other words, they reproduce how things appear from a single perspective. And of course the relationship between this and reality is not straightforward. Bazin’s further idea that photography can be objective because photographs can be taken without human presence is unconvincing. All that shows is that we have an instrument capable of autonomously reproducing single perspectival images and doesn’t speak at all to the idea of objective truth.

Secondly, Bazin refers us to the funerary practices of the Ancient Egyptians who ‘saw survival as depending on the continued existence of the corporeal body’ and statues as ‘the preservation of life by a representation of life.’ So does Bazin think the statues were representing how the dead appeared to us? This would then have them functioning as the photographic images. But if so, we would expect them to create statues like those made by Giacometti, whose figures are about showing in 3D form how figures appear, rather than how they are. Well, the Egyptian figures are not like Giacometti’s. But here’s the thing – the Egyptian statues aren’t like the classical statues that Marker in La Jetee, Godard in Le Mempris, Resnais in L’annee derniere a Marienbad and Hiroshima mon Amour, Rossellini in Viaggio in Italia reference either. The Egyptian statues aren’t 3D idealised models of reality but like with their drawings and paintings, are to be understood diagrammatically. The deep shadowing used in all the images of the statues in the films would make different sense to the Ancient Egyptians. Massimo Scolari’s sensational book doesn’t discuss these issues directly but after reading it there’s no doubt his subject is potentially corrosive of Bazin’s error.

Panofsky’s seminal book Perspective as Symbolic Form of 1927 dominates discussion of visual representation and secured the hegemony of central perspective in contemporary discussion of painted and drawn representation of 3D space. But this hegemony distorts history by obliterating alternatives. Parallel projection or axonometry was dominant at least twice in the last 2000 years. Greek vases, the art of Pompeii, Byzantine mosaics, the Italian Renaissance, and the historical avant-garde prefer it to central perspective. Leonardo da Vinci used axonometry even when perspective dominated. Axonometry first entered the west in the 4th century and still dominates in China. Scolari thinks Da Vinci chose axonometry because it better represented the space of an object. Perspective better represented the object in space. Drawing for mechanical and functional ends developed axonometrical approaches because they were able to prove the three-dimensional buildability of a plan better than central perspective.

Perspective was a formulated code by the end of the sixteenth century thanks to Alberti and Pieri della Francesca. Axonometry wasn’t. But Descartes thought perspective was dissembling, and in this Descartes reveals his military, pragmatic preference for clarity. Stone-cutters also preferred axomometry because it was more accurate than single perspective. Military architects demanded rapid measurements from plans and single perspective couldn’t supply that. Axonometry could. The Turkish threat after 1550 focused minds. Precision of drawing was a matter of life and death, disaster and glory. As Diego Gonzales de Medina Barba said, ‘an imperfection of a line could mean the loss of an army.’ Soldier engineers were uninterested in the seductions of perspective. For the next three hundred years military drawings of fortresses used axonometry but continued to call the drawings perpectival. To make the distinction between these approaches and Euclidan perspective adjectives such as ‘simplicity’ and ‘practicality’ and ‘common’ were added. A soldier-theoretician Giovanno Battista Belici (Belluzzi) said that in war: ‘one single view does not serve, since the whole has to be shown.’ Euclid’s theory of vision proposed ‘a visual pyramid’ where visual rays were sent out from the eye. Cleaned of metaphysics and biology by the fourteenth century it became a key to Renaissance perspective. It was unknown in China where representations of shadow are seen as obscuring stains. But the application of geometry in optics originally ignored Euclid and preferred Arabic formulations of Alhazen and Al-Kindi. Roger Bacon and Witelo thought these were more scientific. Light became ‘the original essence of the created being, the truths of reason of the unity, which produces space and time.’

This reverses the Euclidean view. Visual rays don’t emanate from the single eye to the objects, but from objects beaming back to the eyes. Bacon writes: ‘the universe from each of its points radiates influences in all directions, rays and species, so that each point is per se an active centre, a sort of eye sending species over the entire universe and receiving them from the entire universe.’ These light lines, the species, were physical, not Euclidean dimensionless abstracts. This gnomic tradition had nothing to do with perspective but rather preferred developing the idea of a Sun’s eye view, via a theory of shadows that conceived that such a Sun’s eye view could never see the unilluminated side of an object and whose represented didn’t require lines of sight to converge as in perspective. Parallel lines were always represented as parallel by convention, although there was controversy in the middle ages as to whether they converged in the vast distance or not. The middle ages lacked a concept of limit. That wasn’t developed until the seventeenth century by Desargues. Plotinus thought an image was to represent the appearance of an object and also its nous, the intellect and the universal soul. To do this we need to have the physical acquaintance of the physical nature of vision. On this view of Plotinus only close-ups could be true to the object seen, so depth was to be avoided in pictures, along with shadows which were obscure and empty of matter. The eye had to become ‘equal and similar to the object observed in order to contemplate it… one can never see the sun without becoming similar to it, and a soul can never contemplate beauty without being beautiful itself.’ He said ‘there is no point at which one can fix one’s own limits and say: this is as far as I am up to here.’ Perception ‘clearly takes place where the object is … to see, it is necessary to lose consciousness of one’s own being, it is necessary in some way to stop seeing.’ These ideas that condemned appearance influenced representational art throughout the Middle Ages.

Leaping forward into the last century Paul Klee in the Bauhaus in 1921 said, ‘the point of the entire process is simply to be able to exercise control’, that ‘accurate perspective drawing has no merit whatsoever, if for no other reason that anyone can do it.’ He thought ‘there is absolutely no necessity for a single viewpoint. For some time now, though not that long, we have been able to do without it.’ Klee talked about ‘stray centres’ and ‘stray viewpoints.’ Panofsky in a famous lecture at the Warburg talked about ‘fishbone‘ perspective. Scolari thinks Klee’s painting ‘Uncomposed Objects In Space’ of 1929 is not even a fishbone perspective because ‘perspective is so off centre’ Klee avoids fixing the ‘muddiness of reality’ to a human perspective. Scolari likens Klee’s approach to a musical pentagram, ‘a device for ordering notes that in no way dictates how they are to be composed.’

The vanishing point of perspective doesn’t appear in the picture, but creates the illusion of 3D space particularly effective in built environments. Perspective makes the painters body important by representing what appears in a person’s vision rather than what is actually there. But alternatives to creating illusions of depth and 3D were known to have been used hundreds of years before. The stray centres of Paul Klee were not new; they were around centuries earlier.

Ancient Egyptian pictures were also made with an understanding that what was being portrayed was not a physical object or organism but an ideogram, ‘with all the dislocations and rotations that the principle of maximum evidence imposes on a lucid exposition.’ Symbols survive such distortions, like letters survive bad handwriting. The advent of Christianity occluded the ancient artistic heritage. Christianity didn’t practice divination, preferring ecstasy and annunciations, allegories and strange signs. Christians were stubborn in their resistance to being part of the world.

Scolari writes of the Christian: ‘He is afraid of the dark Underworld from which the black dog, the rat, and the gigantic Ethiopian emerge. He is afraid of the “messages of temptations from Satan’s tribe of daemons.” The fear substitutes faith for knowledge. The Christian takes the fruits of science but doesn’t participate. Claudius Mamertus writes: “thanks to faith, the quiet believer inherits the fruits of science and harvests the fruits of labours in which he took no part.’ Augustine separates words from facts, virtue from gentes, form from content and so enabled Christians who felt isolated from knowledge to connect with learning. Classical culture became the profane history of Christianity, even though it was only fragmentary. Greek storytelling culture had been overwhelmed by the Roman engineering culture, now Christian detachment and isolation from the world returned it through that prism which ordered ‘love not the world, nor the things of the world.’

But this obstinate otherworldliness ended antiquity wherein Pharoes had guaranteed justice, Emperors clemency and philosophers truth. Greek classicism faded. Honour and dignity lost their meaning. What saved classical culture from being lost altogether? Islamic warriors were more curious and intellectually refined. By contrast Augustine and Tertullian closed down classicism. Augustine thought knowledge ‘morbid’ and experimentation to ‘scrutinize the secrets of nature… absolutely useless.’ Justine said that ‘everything that has been said righteously among men is the property of us Christians.’ Tertulian said that, ‘For us curiosity is no longer necessary after Jesus Christ, nor research after the Gospels.’

Plotinus was Egyptian and he had wanted to return to the idea that there were things behind appearance and so brooded on classical form and proportion, asking ‘why do perceptible beauties, images and shadows…descend into matter, order it, and then move us by its appearance?’ A quality without a number illuminates the thing and can be taken as beautiful only by someone possessing the same beauty, thought Plotinus, returning us to the ‘Thaeatetus’ of Plato. Augustine unbaptised had been even more Greek in his ideas of beauty. After Ambrose baptised him in 387 in Milan Augustine abandoned his Pythagorrean ideas. After April 24th that year Christian art began to forget the Greek virtues. Scolari says ‘Western painters were seized by figurative hypochondria.’ Church dogma contracted space and the frontal viewpoint of believers.

Habits of representation are obstinate and without political power difficult to change. Attitudes to difference are also stubbornly conditioned. Anti-illusionist Christian art strikes moderns as deficient. Yet medieval artists were required to represent the holy sepulcher simultaneously, resulting in figures of four or more sides being represented as circular or comparable with a circle. Copying wasn’t a matter of mirroring but of reproducing types. Greek originals proliferated, because each statue was an original copy of a type.

Christian art is not deficient but is different. Naturalistic elements and classical precision – a sign of Imperial arrogance – are replaced or played down. The silence of the Christian West, its closing down classical antiquity, meant that it was the Islamic east that maintained the tradition of Greek classicism. Justinian and Theodoria in the east restored Byzantium orthodoxy. After Justinian, Greek culture was reinforced. Greek replaced Latin. Painting was abandoning the world, says Scolari. Iconoclasm was severely restricted. 3D was replaced by a concrete space of man. Unexpectedly this led to the representation of depth using axonemetric techniques.

Shadows were banned because they detracted from clarity and were the equivalent of confused speech and bad grammar. Christian pictures placed objects that were important to liturgies and stripped away irrelevancies. Christian culture forbade worshiping pictures but tolerated their existence. Scolari writes that ‘on the eve of iconoclastic frenzy, the church could deny the adortation of images while at the same time leaving the art of icon painting to the byzantine monasteries, where it reinforced quietism and offered a theatre of memory for the Christian masses: it goes without saying that the images, conceived as a sublimation of writing, were absolutely necessary for the creation of the Christian mythos.’

Charlemagne pushed back against the loss of painterly memory in the West. Painting was to become not a badge of orthodoxy as in the East, but educative. Yet it didn’t become a mode of intelligibility, as it had been for Plotinus and the ancient Greeks. Greek art was conceived of as being just concrete history that the Frank admired and wanted to
use for his own Christian ends. His attitude freed art from orthodoxy and dogma and techniques of scientific illustration, geometry and cosmology were reintroduced.

Christians used the idea of the prototype to reveal the likeness of the object represented. It returned to the shadow as the prototype. In ancient Greek the shadow is the origin of the painting itself. ‘The shadow fixed the figure in an attitude that showed it off to its best advantage, in profile, like the everescent, dark impression of a seal magically representing its being’ says Scolari. Plato saw shadows as hypocritical and inexact, depending on sensory weakness. But though in ancient Egypt the dead king’s horror is darkness the shadow figure is a creative force and men’s shadows a manifestation of his being. Kings are the protective shadows of his soldiers. Peter cured the sick by touching them with his shadow. Muslims believed the dead and demons have no shadows. (But al-Biruni warned that at midday ‘men walk on the backs of their own necks.’) In equatorial space people stay indoors to avoid walking without shadows.

In the 1960 Visconti film Rocco e I suoi fratelli the protagonist remembers that to build a house a foreman must first throw a stone on the shadow of a sacrificial passerby to ensure the house has sure foundations. Sacrifices in ancient Egypt and Mesopotamia were to create dark deposits that functioned as shadows. Laying the first stone is the neutered contemporary memory of this. Acts 5: 15-16 reiterates the magical power of the shadow. This adds to the power of Marker, Resnais, Godard and Rossellini as we read this back into their palleomodern mis en scenes, but it escapes any foregrounded Bazinean theory.

A distinction is made between projected shadows and shadows revealed as merely no light. As the latter they are merely gloomy. In classical art shadows are shown tonally. In 4th century Christianity shadows were concealing and obscure, containing the hiding devil who an onlooker might meet in his unknowing gaze and be sucked to hell. Illustrated classical texts were a storehouse for Christian iconoclasm. But scientific drawings survived impositions of iconoclastic rules. Islamic culture had tended these. These were independent of time and finite space, hence they denied the drawn line of the flat earth. ‘The cube has no memory’ is Scolari’s take on this. Plato saw it as a symbol of the earth. Expressed on a flat surface it was the cross.

Architectural elements were introduced but there are no seaports, rivers, woods, fields, mountains etc. Figures in the foreground are impassive, isolated from the world and sanctified in a strange aloneness and stillness. This again reminds me of Resnais and Marker and Godard and Rossellini. Cities portrayed as boxes ‘act as background, frame, separations’ and ‘this means the depiction withdraws from the judgment of a unitary vision.’ They work like significant pauses in poetry, lending also a rhythmic quality to the succession of scenes.

This is the use of stray centres as in Klee. By the twelfth century of modernity Latin substituted Arabic versions of Greek originals. Exegesis of Averroes brought Aristotle back into the arts. Averroes reintroduced the idea of double truth via questioning and introduced rational thinking to the Christian. Why is Aristotelianism significant? It eroded the idea of symbolism, where a figure is a figure and also a represented truth. It eroded pictorial representation that scattered knowledge. Geometry began to be used to hold pictures together as a single body of truth. Trees of virtue, cubes of elements, wheels of radiance and squares of opposition began to be formed. In these various attempts to impose order the painter could not fix a single viewer perspective.

The spectator commands nothing in Byzantine art. She is rather read from the infinite distance ‘by parallel visual rays that are without beginning or end, without interest or pity… an infinite distance seperates the sacred from the world that admires it.’ Christ never smiles because his face is fixed by the same distance. Pericles is fused with hierarchical Byzantine impassivity in Piero della Francesca. Everything else is the muddy flux of life, contingent and rattling about the surfaces in contrast to the calm solemnity of mystery plays. Man is a shadow dream whose stories are messed by the light of divine transfiguration, as Pindar explains. In the 13th century lives of saints replaced Christological themes. These in turn are then combined with lives of merchants. In this move artists were ‘asked to offer to the church the talent conceded to them by God so that the sacred might be brought closer to the common people.’ Dante is a key figure, opening the culture of monasteries to the laity.

Mercantile maths, abacus culture, Arabic numerals, positional notation, cities, spatial saint-lives in the boxes of Giotto and Duccio freed artists in the west from centuries of amnesia. Giotto introduced shadows to bring depth into these representations, replacing golden backgrounds with corporeality. ‘Painted figures stepped down from the architectonic structures that framed them and into real life.’ Time was reintroduced, replacing the circular timelessness of monastic time. Machines were built with levers and gears that calculated wealth of merchants. Bodies and earthly things were restored: Dante’s wood, Petrarch’s streams and Siennese good government appeared. Giovanni Dondi was a horological expert of the first half of the fourteenth century whose Astraium was more Leonardo than medieval. Occam freed physics from metaphysical obstruction. Philosophy was separating from theology, whereby anything not revealed was up for investigation.

So Scolari’s ‘descent from of the point of view’ from the thirteenth century onwards in Europe moved from people receiving the Christological rays of God shining an infinite number of eternal points of the universe into them, whereby ‘a brilliant splendor enfolds him and his existence becomes as sweet as honey,’ as Pindar said, to the single perspective where ‘[f]rom the infinite distance of parallel perspective, pictorial representations converged, perforating the veil that concealed reality behind the symbol: somebody looked inside the scene and traced the line to the horizon.’

Dante’s secular verse and the names of ex-voto donors to the window’s of Chartres cathedral signify this. The divine is diluted to the lives of saints and replaces Christological themes. In the early fifteenth century Brunelleschi and Donatello were measuring building elevations from a distance. Fibonacci and Pelacani de Parma’s old techniques were rediscovered. Distances were measured from the single point of a spectator to the highest point of a building. Similar triangles establish a proportional relationship between heights of an object and representation on a plane. Ptolemy’s Geometry and Optics have obscure roles in this, moving without theological impediment through these Roman developments. Scolari identifies 7th July 1436 as the beginning of the Renaissance when Leon Battista Alberti wrote to his friend Brunelleschi: ‘I desire that you before all others should correct my faults, so that I will not be savaged by my detractors.’ By the division of the visual pyramid by a single plane ‘that which was seen became that which was represented, and the extraordinary koine of the Renaissance began.’ In this move space was theatricalised, it became the point of view of the eye.

Scolari hints at the connection between the rediscovery of the single perspective and the vanishing point with the ability and desire to seek out new lands. The multiple perspective of the Egyptians is contrasted with this where the movement of frontiers outwards from the centre was merely a strategy for holding together its own territories and to keep the threat of the nine bows at bay – Asian, Libyan and Nubian threats. Scolari notes the date of Columbus’s discovery of America for Europeans as a rather retrousse coda.

Leopardi feared that the perfection of single perspective blocked the force of poetry. The mythical dimension retreats before the domesticated eye of the scientific eye according to this complaint. Homer remains the poet admired as an architect as well as poet, putting the form of the city in harmony with surrounding nature. Islam was hostile to painters who were seen as trying to compete with the creator and as such were equivalent to usurers and possessors of dogs.

The architectural model is a tool for architectural design. The model can initiate the architect into the unbuilt presence of a building. Its miniature form imitates stability where perhaps there is none, and can conceal compositional and distributional uncertainty. Vitruvian theories of architecture relegate the model to the material dimension of techne. It is the product, according to Vitruvian theory, of sheer manual skill. They were part of the job-lot cost, without special mention or attributional role. They are found long before Vitruvius ordained their low status in burial objects of Ancient Egypt, Etruscan Tombs, Mesopotamian reliefs and Roman Pompa Triumphalis. But it was not until the thirteenth century that they are discussed in architectural literature.

The fifteenth century saw a gradual erosion of preexisting Gothic architecture for the new Renassiance approaches and models became a way of showing what the new procedures and measurements would look like. They were a kind of guarantee that the plans would work, a kind of ‘writing for illiterates.’ The sixteenth century saw an increasing distinction between the conceptual stage of building and its practical stage. Models were used increasingly as a specialised form. Risk aversion, born out of disasters of Gothic architectural experiments, gave models increasing importance in reassuring Florentine masters of projected projects. Models however give the game away to rivals and competitors: Bruneschelli often hid models or else ensured his models never remained faithful to what was actually going to be built so that his secrets remained hidden. Later, models began to be built by other people and in the open to acute degrees of accuracy and diligence. The makers of models were master craftsman, despite Vitruvius snobbishly bad mouthing them. A Vitruvian legacy is still hegemonic in many western cultures wherever concept-work has higher status than craft-work.

Alberti broke with this bias, arguing that architectural projects were mental activities and models and sketches were essential. Filarete went further and opened them out as exercises of the imagination. They were necessary to allow ideas to gestate and change according to differently conceived notions. The model is a generator not what is generated. Francesco di Giogio Martini’s fortress drawings seem to do the same, as were the x-ray drawings of the dome cladding of Milan cathedral by Leonardo. These are drafts and flights of possibility and invention for the imagination to connect with rather than merely the record of a solution. Anti-Vitruvian architectural thought gathered force. Alvise Cornaro says models are necessary. Italian architects and military engineers experimented using models and drawings. This spread to France when Leonardo, Giocondo, Serlio and Castriotto worked there. The French Renaissance was indebted to this. Philibert de l’Orme only trusted projects that involved skilled modeling that show the idea rather than manufacturing skill, that show front and elevations in wood, card or stiff paper. The artist-scientist was a key anti-Vitruvian figure without which architectural masterpieces couldn’t have been built.

Models were used where geometrical theories of perspective were unknown. A 3D model substituted for any ignorance of math. Many of the fortification architects of the early sixteenth century were made using these. Models were an alternative to geometrical thinking. So in Venetian architecture of this time there are few drawings but many models. There is an impatience with the drawing of a single perspective by artisans and military leaders because ‘the only proportion that matters is the range of fire, for at the moment in which the projectile passes beyond the frame of appearances to shatter its target, all perspective is dissolved.’ What is at stake is not beauty but kingdoms and principalities. To hell with Vitruvius was the attitude of Gabriello Busca and Giovani Battista de’ Zanchi. Drawings are misleading. Models are the site of modification and transformation through the eye of the general. Pleasing drawings weren’t needed. By the end of the sixteenth century the model was a routine procedure for military architecture. By the eighteenth century the model functioned as a parallel projection drawing.

Drawings using the axonometrical perspectives improved on small models. Small models were often too small for details to be properly seen. Axonometrical drawings could be scaled up so that the generals could attend to everything in the minutest detail. Axonometrical drawings from a raised perspective allowed the scene to be surveyed but diffidence towards design reemerged and models again became predominant. Girolamo Fransesco Cristiani in his ‘Civil Engineer of the Serenissima’ writes: ‘already for some time the mathematicians have been induced to prefer the use of models over the use of drawings.’ He thinks models have the advantage of being ‘an idea that is material, made of wood, card, of clay or other’ and must replicate the thing it portrays so that it ‘corresponds in everything and in every way to the things represented.’ Models were the apotheosis of clear ideas, giving the imagination more ideas through direct images than any drawing could.

Scolari takes Brunelleschi’s model for the dome of Santa Maria Del Fiore in Florence and the Gheradi drawing as a focus of study. The collapse of previous domes led to this project. Giovanni di Gherardo Gherardi’s is the only extant drawing relating to the dome construction. In 1425 a third of the dome had been built but there were doubts as to whether the calculations were correct. Experts in practical arithmetic were brought in to calculate whether the project would work. Asserting his theoretical approach, Gheradi attacked the model building Brunelleschi as ‘someone who invents irrational things.’

Gherardi’s drawing was a supplement to his attack on Brunelleschi, adding to the rhetorical sleights of hand that linked the Florentine project with a completely separate project, the failed attempt to extend Sienna Cathedral. But Brunelleschi and Donatello during this time had surveyed Roman building heights using ‘strips of parchment…bearing the numerals used in the abacus.’ This referred to his awareness of how measurements varied in inverse proportion to the distance, and he had taken this method from his study and collection of ancient codices from the Greeks, just as Petrarch and Boccaccio had done with ancient literature and philosophy. Brunelleschi therefore reinvented perspective. One point perspective was born of architectural surveying. Sironi argues that his insights into the ‘ancient way of building’ was what Gherardi didn’t understand.

At this point we find drawings that can mix representation for appearance with representation for demonstration and reasoning. This contrast between single perspectival representation and diagrammatical representation means that some drawings address the eye of the intellect, others the eye of the body. Mistakes are made if inferences to one or the other based on prejudged assumptions of representation are made. What may seem obviously an attempted single perspectivalism may on further investigation be an attempted diagrammaticalism. Mathematical reasoning detaches us from the world of appearances, says Proclus commenting on Euclid. Plato’s Theatetus contrasts the bewilderment and confusion caused by attempts at representing appearances with line drawings without solidity and parts, the point and the line, which produce reasoning and clear thought.

Knowledge understood in terms of reasoning must represent figures and yet renounce them. Geometrical points are ‘without extension’ and lines ‘without thickness.’ Points and lines that appear, as they do in geometry, are therefore ontologically defective from this perspective. The diagram is the solution to this puzzle, is how such renunciation is enacted.

Aristotle said that only diagrams and sketches were appropriate for scientific illustrations. Diagrams are vital in Greek thought as demonstration figures. Geometrical figures are bodiless transparent entities, where construction not visual appearance was important. As the new single perspective was developed by Leonardo and others at the turn of the fifteenth century there are traces of this ancient knowledge being used alongside the new. Sironi brilliantly establishes this through investigating a strange almond shaped ellipse produced by Leorado’s fellow worker Pacioli. In a tour de force of detective work through a vast range of works that attempts to find out if the strange ellipse shape used in this early sixteenth century drawing had precedent in earlier representations that Pacioli would have had access to the classical origin of the axiometrical approach is established. Sironi finds evidence for the ranking of thought over sight in classical texts produced at the time of Aristotle and Ptolemy. The strangeness of Pacioli’s drawing is not a failure of understanding perspectival drawing – and therefore a lack of drawing skill – but rather an example of his drawing on this ancient axiometrical approach. He draws together evidence that many drawings were constructed transcribing what is measured rather than what is seen.

Vitruvious wrote that all machinery ‘is true and faithful imitation of nature’. The engineer and technician was thought a necessary magician by Plato and his culture. The bridge between the classical eras’ engineers and the sixteenth century Europeans was Arab scholarship. Roger II of Sicily recruited Islamic mechanics to his court. The Hohenstaufen Kings following him collected manuscripts of the preserved drawings. Al-Jazari’s Book Of Knowledge Of Ingenious Devices served as a model for other works known to Latin culture. This and other documents ‘kept strictly to showing such information as was absolutely necessary, without any concessions to aesthetics.’

In the thirteenth century machines were like monsters created by Hephaestus, forger of Achilles shield, used in war to throw large boulders and cross torrents, were scorpions, battering rams, bladed chariots, towers with bridges, later to become by the end of the next century trebuchets, crossbows, ballistae, armored towers with rams’ heads all created to terrorise the enemy and materialise brute fear. They were represented as diagrams not as representations of appearance. These drawings abandon the ‘comfortable, convergent vision of Greek space.’ No allowance is made for the presence of an observer in space. There are no indications of top or bottom or back and front. ‘Geometrically, the object is considered solely in terms of its measurements, and not according to the geometry of various viewpoints that examine the object from the exterior and from the distance.’ Sironi alerts us to this: ‘This is what distinguishes a painting from an architectural drawing and from the drawing of a machine.’

By the fifteenth century perspective began to influence machine drawings. As machines had made old walls round cities redundant, battlements of cities were redesigned. The art of war was revolutionised by French artillery at the end of the fifteenth century. Fortresses were built with greater rationality and precision. More complexity was built. Ditches were widened. Trajectories of missiles were calculated. War was no longer a glorious impulse of heroes and the knightly conduct of Orlando. Machines brought death from afar and ‘with hissing speed.’ A deafening empiricism was required to investigate how to proceed against such machines. Military engineers were asked to produce representations that corresponded with the geometrical power of the killing machines.

Through the development of the fortress builder a new empiricism swept aside scholarly abstractions. ‘Anatomy, mechanics, architecture, astronomy, pyrotechnics, hydraulics and pneumatics began to search in the real world for proof of the figures that had been passed down through ancient manuscripts to the era of Christopher Columbus.’ What developed in all this was a divergence from the perspective needed for the landscape artist by the artilleryman. Function doesn’t have a style but representations of function do.

When Jesuits imported single perspective to China as a vehicle of Christian iconography in the sixteenth century they entered a culture of axonometric representation. The Chinese found oil paintings disturbing. They found deep shadows troubling. The paintings were considered technical marvels but representationally inept. Euclidean geometry was not known to the Chinese then. Even when they had learned the rules of perspective they didn’t consider it a superior tool for realistic representation. Sir John Barrow quotes the Emperor: ‘On enquiry, I found that Castiglionne was a missionary of great repute at court, where he executed a number of paintings, but was expressly directed by the Emperor to paint all his subjects after the Chinese manner, and not like that of Europe, with broad masses of shade and the distant objects scarcely visible, observing, as one of the missionaries told me, that the imperfections of the eye afforded no reason why the objects of nature should also be copied as imperfect. This idea of the Emperor accords with a remark made by one of his ministers, who came to see the portrait of His Britannic Majesty, and said ‘that it was a great pity it should have been spoiled by the dirt upon the face,’ pointing, at the same time, to the broad shade of the nose.”

The philosopher Sorensen argues that the vanishing point is best understood as the inner limit of the picture, just as the frame is the outer limit. Neither are therefore represented in the picture. He thinks the self is the vanishing point of our self-identity. Wittgenstein defleshed the eye but retained an abstract single perspective for his philosophy. Do the Chinese refuse this metaphysical point? And returning to the discussion of the films at the start of this piece, has the single perspective infiltrated the creation and reception of these works to a degree that obscures their actual cinematic ontologies?

Scolari’s is yet another muscular book far cleverer than me, with footnotes and details that astonish, baffle and make reading a process that alternates abnormal contraction with relaxation in a ruthless back and forth autophagy. The mysterious last chapter on the Tower Of Babel seems to deflate and then eerily reverberates.

Richard Marshall is still biding his time.

First published in 3:AM Magazine: Thursday, March 7th, 2013.