Thursday, 7 June 2012

Changing Images of Pictorial Space: A History of Spatial Illusion in Painting
William Seitz, a respected painter and art historian, maintains that “through one pictorial device or another the greatest percentage of the world’s painting has dealt with the representation of space” (Seitz 1983, 40). And in his recent book on painting, aptly titled Working Space, Frank Stella insists that “after all, the aim of art is to create space – space that is not compromised by decoration of illustration, space in which the subjects of painting can live. This is what painting has always been about” (Stella 1986, 5).
Space, in European painting, has been depicted by means of several methods io perspective. The most persistent of these methods was Renaissance perspective. But when most art historical writers – even such excellent writers as Erwin Panofsky and Samuel Edgerton in his book The Rediscovery of Renaissance Perspective – refer to “Renaissance Perspective”, they mean linear perspective only. It was, however, no such obvious and singular device as linear perspective that captured the imagination and guided the direction of painters from Masaccio to David Salle.
Page ix - x   
1 – Background
Note 1. The Pythagoreans believed that the definitive elements of the cosmos were limited to spatial fragments. Because the sciences of optics and mechanics were perceived as divisions of mathematics, they thought of these sciences in terms of spatial images and represented them geometrically (Burtt 1954, 122).
Though they may have been related in content, the painted objects and figures were not structurally or spatially related to each other or to the background because they were not drawn as if they were all seen from the same location. – Greco-Roman art
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Renaissance painters, on the other hand, drew each objects and figure from the same location, or viewpoint; the result was that the vanishing points of all the depicted objects coincided so as to unify and relate one object to another within the “same space”. This space, suddenly unified, possessed the two main qualities that were to characterize pictorial space until the advent of Picasso: a unified viewpoint, and a cohesive spatial relationship between all the figures and objects in a painting (Panofsky 1965, 122).
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When society changes its assumptions regarding the importance of one idea or concept over its opposite, this change is reflected and echoed throughout every system affected by such an assumption.
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 The Renaissance system of perspective was created by restructuring the elements of Greco-Roman perspective, impressionism was created by restructuring the elements of Renaissance perspective, and modern art was created by restructuring the elements of impressionism. European perspective has thus been through at least two complete cycles of separating and recombining these elements in the quest for new images. In short, the various techniques involved in mimesis – creating an illusion – have furnished fertile ground for two millennia of creative strategy in painting.
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Chapter 2 – The Middle Ages
Note 3. Here is Edgerton’s explanation: “In other words, the space one perceives is conditioned by both the wat one enjoys seeing it – perhaps as traditionally shown in pictures – and the way it is explained in contemporaneous thought, that is according to its accepted explanation by the science of the day. Pictorial representations of space in any given age are thus symbolic forms of this combined perceiving process” (Edgerton 1975, 159).
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As figure and ground came to be compressed into patterns [in medieval art], one could often not be distinguished from the other (Edgerton 1975, 158). When figure is difficult to distinguish from ground, when neither is accorded priority over the other, shapes tend to alternate in spatial dominance: first one appears salient, then the other.
(This is something I was thinking about while making the new Double Vision Mask pictures)
Because illusion held little interest for artists of the Middle Ages, they did not use spatial relationships to unify their compositions in the manner of the later Renaissance artists. Medieval artists, more subjective in the way they viewed their world and seeing each element and image separately, paid little attention to the spatial relationship between one object and another. Medieval painters felt as if they existed in, and were a part of, their pictorial world, while during the Renaissance, painters of perspective stood outside the world they represented and observed – as if through a window – from a single, unifying viewpoint.
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Cimabue: The Great Beginner
Thirteenth-century viewers of art – unlike people of the twentieth century, who have been raised on photographs, movies, and television – were not dependant on the convention of the two-dimensional illusion.
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Because Cimabue was the first painter in a thousand years to partially unify his paintings spatially and achieve some illusion of volume, historians have often considered him the link between the Middle Ages and the Renaissance. He took the first necessary steps towards reweaving the elements of illusion.
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The elements of perspective from the classical period, separated during the Middle Ages, were now beginning to be recombined in order to create a new and different image. The fourteenth century would give birth to a new illusion – an illusion so real, so unlike anything ever seen before, that it would startle viewers.
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Chapter 3 – The Proto-Renaissance
The primary focus of painters at the beginning of the Renaissance was the imitation of nature and the creation of a three-dimensional illusion on the flat surface of a painting. Italian artists made definite, though rudimentary, progress toward a systematic method of spatial representation, Bunim points out. Roof lines at the sides of buildings were drawn at a descending angle, while the lines at the base of buildings ascended, causing parallel lines to converge. Parts of individual foreshortened planes were constructed by means of a vanishing point, and objects often grew smaller as their distance from the bottom edge of the ground plane increased (Bunim 1940, 187)
The fourteenth-century attempts did not yet employ a single vanishing point located on the horizon for all the horizontal lines of receding parallel planes (Bunim 1940, 187). However, the “vanishing axis”, wherein all the planes converged to a single horizontal line but not to a single vanishing point, was “used to coordinate a number of planes, and in several instances it was applied with such zeal that it creates the impression of a unified and systematic construction”(Bunim 1940, 151). These painters learnt to diminish the size of objects and figures progressively as they receded into depth, but they still had not understood that the single viewpoint of the spectator was the connection between diminution and the system of convergence (Bunim 1940, 151).
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At this point the medieval priority of quality over quantity was once again inverted. Though it would not be apparent until the fourteenth or fifteenth century, the Aristotelian concentration on quality and essence was slowly being replaced by a more Platonic interest in qualities – measurable increments of time and space – and Europe began to concentrate once again on mathematics as the key to knowledge (Burtt 1954, 53-55). This reborn Pythagorean interest in quantity began to steer Renaissance painters away from the spiritual, toward a more materialistic depiction of reality. They began to avoid the gilded surface and concentrate on an illusion of volume and solidity. It was thus, Bruce Cole feels, that Giotto “fell heir to an art that was slowly changing from abstraction to illusionism” (Cole 1976, 39).
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The depiction of volume led to an illusion of depth and space. From this point in history, man’s thinking in philosophy, science, and art gradually began to drift toward an interest in such space – to which was finally added time – as a central concern. This concern with first space, and then time, continued to grow through the Renaissance, impressionism, then modern art until it became both the method and the content in painting.
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Giotto: Inventing a New Perspective
In Theories of Art from Plato to Wincklemann, Moshe Barasch states that this observation and recording inevitably led to mimesis: “Not a single Renaissance treatise fails to make the point that the imitation of nature is the very aim of painting and sculpture and the more closely a work of art approaches this aim the better it is. In fact the belief that art imitates nature can be regarded as a hallmark and distinctive sign of the Renaissance.” (Barasch 1985, 114).
Giotto did not continues the medieval concept of space; he anticipated what we now call “two-point perspective” by slanting his buildings in space: oblique views of objects take up more space in depth than do frontal objects (Panofsky 1965, 119). During the first years of the fourteenth century, Giotto, at the height of his maturity, began his greatest work, the frescoes in the Arena Chapel in Padua. And, in a manner unheard of during the Middle Ages, he used three new spatial devices in these frescoes in order to reinforce the unity of his work: unified shading, unified viewpoints, and the maintenance of a nearly flat visual surface in his paintings.
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The third device is Giotto’s ability to maintain a painting surface that remained visually almost flat. Painters in the Middle Ages had not maintained a visually flat surface; the medieval picture plane, though “planar” (that is, organized in flat, shallow layers of space), appeared to be constantly shifting. Each figure, or separate part of a figure, that covers the surface of a medieval painting seems to alternately advance and recede as the focus and attention of a trained modern viewer shifts and changes.    
Panofsky writes that entering the pictorial world of Giotto feels “as if we were stepping off a boat and setting foot on firm land,” and he insists that this is the birth of modern space (Panofsky 1965, 136). Giotto introduces us to a space that had, for the first time, the potential to evolve into a depiction of continuous and infinite depth (Panofsky 1965, 137).
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Giotto, like Duccio, made several rudimentary and inconsistent attempts at linear perspective.
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Vasari tells us that Giotto painted from life; he actually looked at a model when he painted, and he seemed to transform a two-dimensional surface into people and objects. Other religious paintings in the fourteenth century, however, were more medieval didactic images filled with Christian symbolism: “They were not seen simply as stimulating compositions of colour and line,” Cole emphasizes, “but as mysterious, profoundly moving icons thought to embody some of the awesome power held by the holy figures they portrayed.” Indeed, there were many reports of these man-made images performing miracles, and men had been executed for profaning a likeness of the Madonna, even the one on a Florentine coin (Cole 1980, xxi).
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The supernatural essence of a painting was so overwhelming, says Cole, that pictures were not written about as works of art. The archetypal idea that the image of a person could transmit a supernatural portion of its subject was still a vital part of fourteenth-century art: “This idea is so alien to us that we must constantly remind ourselves that earlier onlookers really saw the frescoes and panels as the sacred, visual embodiments of active supernatural forces” (Cole 1980, xx1).
With our extended experience in viewing two-dimensional photographic and painted illusions in the twentieth century, we have difficulty realizing just how shockingly real Giotto’s paintings appeared to fourteenth-century viewers. These viewers had never before encountered anything on a two-dimensional surface that seemed so convincingly real. Giotto’s synthesis of the immediate presence of illusion with the supernatural power of the icon dazzled fourteenth-century viewers beyond our ability to understand. He had invented a new form in painting, a form that disoriented viewers from the real world and involved them in the supernatural in a way that had never before been possible.
Realism is not by any means a timeless or universal standard. The degree of realism to which an object is said to be represented depends primarily on how expertly the painter captures and improves upon the image in terms of current conventions. When we say that a picture looks like nature, we mean that it matches the manner in which we have usually seen nature depicted. Giotto’s paintings may have looked startlingly real to the fourteenth-century viewer, but when new techniques and illusionistic devices were invented in the fifteenth-century, Giotto’s paintings no longer startled.
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When fifteenth- and sixteenth-century painters spoke of imitating nature, they put at least as much importance on the spatial relationships between objects as on creating a facsimile of the object itself.
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Chapter 4 – The Renaissance System of Perspective
When most writers refer to “Renaissance Perspective” they mean, primarily if not exclusively, linear perspective. Sometimes such writers do briefly acknowledge “aerial perspective”, a term that combines just the rudiments of two separate and more elaborate perspectives: atmospheric and colour. Yet the Renaissance system of perspective was actually composed of four major perspectives that, together with a unified light source, generated Renaissance pictorial space: the Renaissance illusion. These four major perspectives were linear perspective (which incorporates both converging lines and diminishing sixe), the separation of planes, atmospheric perspective, and what I shall call the classic colour theory – that colour perspective specific to the Renaissance system. The Renaissance system, then, is a complex and interrelated system for depicting what appears to be a unified, mathematically correct illusion – of volume, depth, and the accurate placement of figures and objects in space – on a two dimensional surface.
Nothing so simple and obvious as linear perspective could have managed by itself to dominate the imagination of painters for six hundred years.
Artists were so ensnared by this convention that they were not able to free themselves from it for six hundred years.
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Though Renaissance perspective may appear to mimic what can be seen with one eye from a permanently fixed viewing point (for instance, looking at a scene through a peep hole), it cannot reproduce actual vision on a flat surface. Although the Renaissance system of perspective in its time may have appeared to be an objective method of depicting the world, it has always remained subjective in execution. Painters cannot depict everything they can objectively see because each inevitable change in focus changes what is seen. They must always interpret and discriminate between what they will stress and what they will ignore. If ten Renaissance painters were assigned the same scene to paint and told to paint this scene exactly as seen, the ten paintings would each be unique.
This Chimes in with Martin Kemp when explaining certain distortion in Donatello and De Vinci
 No single painting can depict the whole “truth”. Each painting is only a supplementary view of any external “truth”.
Although central perspective may insure a rational, even a mathematical, system for depicting space, the system depends upon two important assumptions: that we see with a single motionless eye and that the plane section through the cone of sight is an adequate reproduction of our retinal image (Panofsky 1924-25, 1).
To equate the image in Renaissance perspective with sight is an extremely bold abstraction from reality, “for the structure of an infinite, unchanging, and homogenous – in short, purely mathematical – space is directly opposed to that of psychophysiological space” (Panofsky 1924-25, 1).
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Vision functions in a manner different from the painted image in Renaissance perspective. In the real world, we use two major, and several minor, visual faculties to create depth perception as well as a fluid image of space. Binocular vision – we see two separate views of the world because we have two eyes – and movement parallax – an apparent change in the position or shape of objects, or the relationships between objects, owing to a change in the direction from which they are viewed (Haber and Hershenson 1973, 316) – are the two most important faculties in our interaction with depth and space. These two faculties, however, are unavailable to those who imitate, with coloured smudges on a two-dimensional surface, the patterns of light and shade that enable us to capture frozen portraits of a three-dimensional world on a flat surface.
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The unified Renaissance system of perspective elicited strong approval from painters, the public, and the Church for three principal reasons: it appeared to be rational, scientific, and objective; it functioned as a manifestation of their belief in the existence of a rational universe; and it gave painters a new tool which they could use to create a new kind of spiritual and religious response in the viewer.
With the invention of perspective, art seemed to have become science. But any perspective, no matter how objective the method may seem, must be interpreted subjectively. Consequently, what this perspective achieved was “a translation of Psychophysiological space into mathematical space: in other words, an objectification of the subjective” (Panofsky 1924-25, 16).
In response to the Renaissance pursuit of reason, artists played their part in the search for “objective truth” and contributed to the progress of science “by finding a relatively nonsubjective way to make pictorial images which everyone, regardless of cultural background, could learn to become orientated to or respond to” (Edgertone 1975, 164).
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…Renaissance perspective was not a truth waiting to be discovered, but a convention, an invented style, instigated by society’s priorities and assumptions, and therefore matching the beliefs and ideologies of the culture so well that its limitations and boundaries were all but invisible to the Renaissance viewer.
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Linear Perspective
An architect called Brunelleschi invented Renaissance linear perspective in the fifteenth century, and Alberti explained it in his Della Pittura in 1436.
Alberti demonstrated his perspective with drawings of a cube and limited his construct of linear perspective to a one-eyed view at the eye level of the normal person; there was no departure from this low monocular viewpoint in any organized or meaningful way until the nineteenth century. It was Alberti who lay the groundwork for the whole Renaissance period with his observation that “the picture is a plane section of the visual cone” (Panofsky 1924-25, 14).
The predictable and orderly system of linear perspective likewise came to be integrated with the Christian faith as well as with Capitalism.
May help to explain why it has held sway for so long
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In the twentieth century, artists tend to think of linear perspective as simple, obvious, even heavy-handed. Yet this converging of parallel lines as they recede into depth – which creates a geometrically consistent diminishing in the size of receding objects – excited artist and viewer alike during the fifteenth century.
Linear perspective is primarily dependant on straight lines – parallels, verticals and horizontals – and it is an excellent device for depicting architecture and man-made environments because man so loves the straight and the parallel line. Atmospheric perspective, in contrast, is more useful in landscape and those situations where there are no straight or parallel lines.
Separation of Planes

 
The “picture plane” might be understood as a large pane of glass across the very front of this stage. All the objects, action, and spatial illusion took place behind this picture plane until the late sixteenth century, when the Mannerists began to allow small portions of objects to penetrate this plane visually and extend slightly in front of it.
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Atmospheric Perspective
Atmospheric perspective has been the most effective method of creating an illusion of depth for at least the last five hundred years. It has been important in various historical styles of painting – Roman, Oriental, Renaissance, impressionism, and modern – because it does not have the severe limitations that linear perspective does, and it is not so obvious. For instance, atmospheric perspective does not violate the visual surface of the flat picture plane so violently as linear perspective (White 1967, 145). Yet it has seldom been mentioned, even briefly, and no detailed explanation exists. That seems a puzzling oversight.
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While linear perspective and the separation of planes cannot be exaggerated without distorting or losing the illusion, atmospheric perspective can withstand immense exaggeration – often without attracting the viewers notice. More than two hundred miles of atmospheric perspective can be compressed into two feet of depth in a still-life, and most viewers will not notice the perspective: they will perceive the depth but not the method.
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The governing principle is dependant upon the control of the relationship of focus and value between objects and their surrounding ground. If an object or figure is sharply focused and contrasts with the value of a blurred ground, it appears to advance. If the figure is blurred and remains similar in value to the ground, it tends to recede. The idea is to dissolve distant objects into the background while sharply separating the nearest objects from the background by the use of focus and value contrast.
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In order to create a less analytical, more holistic and intuitive, mental image of atmospheric perspective, some painters visualize a foggy day and objects emerging out of the fog. Fog increases the illusion of depth because it exaggerates all the principles listed above.
The principles of atmospheric perspective, as first used in the fifteenth century and further perfected in the sixteenth century, amplify the illusion of depth and help to separate planes in space and control the visual placement of objects on the ground plane. Atmospheric perspective was one of the most important prerequisites to the achievement of the mature Renaissance illusion.
The Classic Colour Theory
The classic colour theory is the fourth of those perspectives that make up the Renaissance system of illusion. Like atmospheric perspective, colour perspective emphasizes the illusion of separation between planes and can be exaggerated so as to strengthen the illusion that one plane, or point, is behind and separated in space from the other. Exaggerating depth cues by means of atmospheric and colour perspective helps to compensate the painter for the loss of binocular vision and movement parallax. Leonardo put these principles into writing and coined the terms “aerial perspective” and “perspective of colour” (Barasch 1985, 157). 19
Note 19: one of the foremost experts on the fifteenth and sixteenth-century Italian Renaissance, Anthony Blunt, has investigated Leonardo’s notes in depth, and he insists that Leonardo’s expertise is unique and unsurpassed in the field of atmospheric and colour perspective. “Leonardo appears as a complete innovator. Earlier writers, such as Alberti, were apparently quite unaware that the edges of objects became less clearly defined and the details on them less distinct as they get farther away. They seem not to have noticed or not to have been interested in the fact that hills are blue in the distance…Leonardo was the first to carry out a really systematic study of the subject, the effects of which appear in his paintings and no less in his theoretical writings” (Blunt 1962, 29-30).
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The classic colour theory is founded on the observation that warm colours appear to advance and cool colours to recede. This observation is supported by principles that can be demonstrated in the fields of psychology, physics, and physiology. It can be easily observed that objects do shift towards blue as they recede into the distance. Physicists have demonstrated that the shorter blue rays bend far more than the longer wave lengths as they travel through the atmosphere. This tendency for the for the shorter blue light waves to bend causes most of the blue light to scatter into the atmosphere; accordingly, the sky is blue during the day when the sun is high.
Page 48
As the distance between viewer and viewed object increases, the quality of blue atmosphere that acts as a filter between them is increased proportionately: objects appear progressively bluer as distance increases. At the same time, the greying effect of moisture or dust particles in the air, combined with the blue atmosphere, tends to grey distant colours; thus, colour in the distance tends to shift towards a greyed blue.
While the atmosphere scatters and dissipates the blue light of the sun’s rays, the warmer rays penetrate straight through the atmosphere to cast their reddish light on the earth and its objects. Colours in the foreground will therefore be warmer, more saturate, and more intense.
Page 48-49
The classic colour theory is demonstrated clearly and simply in many of the paintings of Leonardo, Raphael, and other sixteenth-century painters. Warm, saturate colours are reserved for the foreground, and a cool, icy, greyed blue for the background.   
Raphael, The Beautiful Gardener, 1508. Panel (122cmx80cm). Louvre, Paris

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The fact that the eye cannot focus on long and short waves colours simultaneously may also explain why a warm figure stands out more against a cool ground than against a neutral one. Because of chromatic aberration the uncertain eye cannot focus on both colours at once, so it tends to focus on the figure (in this case the warm colour), and the ground blurs. This focusing of the figure and blurring of the background intensifies the figure-ground separation, which causes the warm figure to assert itself visually in front of the ground.

 James Green - Double Mask, I-pad drawing
Use I-pad Drawings of mask to work this out into a painting; experiment with coloured backgrounds.
Page 52
Since the beginning of the Renaissance, the most usual colour practice followed the tenets of the classic colour theory. But many artists before the sixteenth century practiced alternative colour perspectives. The most common of the alternatives employed colour relationships that were in exact opposition to the classic colour theory: blues in the foreground functioned to create salience, while reds were reserved for recession and backgrounds. A reversal of the classic colour theory was accepted in the early fifteenth century and in other periods not dominated by classicism. This method is particularly evident in medieval manuscripts (Lapicque 1959, 74-95). Gainsborough used such a reversal of the classic colour theory in Bleu Boy.
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In Greco-Roman art, space was what happened between solids, and it separated rather than unified objects.
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The Renaissance
As the new mathematics triggered the discovery of new secrets and realities in the fifteenth century, a new concept of space began to coalesce, Blatt points out – a concept of space that was itself not localized, rather than a space that defines an entity’s location.  

 
As the new mathematics triggered the discovery of new secrets and realities in the fifteenth century, a new concept of space began to coalesce, Blatt points out – a concept of space that was itself not localized, rather than a space that defines an entities’ location. Some philosophers and scientists even began to anticipate the notion that an infinite space might be the residence of heavenly bodies, in contrast to the medieval concept of the universe as a finite object (Blatt 1984, 195). This new consciousness of space – infinite, but mathematically measurable and unified – began to be evident in Renaissance thinking about art, philosophy, and science.
In addition to facilitating the imitation of nature, the new spatial and compositional unity created by perspective bolstered religious, scientific, and philosophical ideologies.
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….Edgerton reasons that linear perspective may have contributed even more to science than to the history of art (Edgerton 1975, 164).
Masaccio: The Shadow Catcher
Masaccio also observed the two most important principles of Renaissance colour perspective: he placed cool, grated colour in the background and reserved the warmer, more saturate colours for the foreground. Masaccio exploited all five of the major devices of Renaissance perspective: unified light source, separation of planes, linear perspective, atmospheric perspective, and colour perspective.
Masaccio synthesized these illusionistic innovations to function as a method of visual organization. Like Giotto, Masaccio arranged the dark and light sides of the figures and objects in all the paintings in the Brancacci Chapel so the light appears to originate from the same source. This unifying light appears to pour from the real window that admits daylight into the chapel (Cole 1980, 166). Not only does device unify the illusion from one panel to the next, but it is also responsible for the sense of actual light that permeates the surface of Masaccio’s frescoes and thereby facilitates the integration of his painted world with the world of the viewer.
Brancacci Chapel



This is something I had a go at while painting a tromp l’oile background to one of my mask paintings
Page 64
The overall unification, especially the combination of unified vanishing points with a unifies system of lighting, related each fresco in the chapel to every other fresco so the entire chapel functioned as a single cohesive body of work perceived as one unified image. When Masaccio splashed the light from the window in the real world across the architecture and the figures in his painted world, when he related the vanishing point to the viewer’s position, and when he depicted contemporary local architecture and clothing, he allowed, for the first time, the viewer psychologically to enter his painted illusion and to abide in a world of religious miracles.
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Since the fifteenth century, every style of Western painting has been dependent, to one degree or another, on the ideas that came to sharp resolution in Masaccio’s painting during the fifteenth century.

 
This new unity of perspectives, however, marked the death of other conventions and freedoms. Viewers quickly became accustomed to Masaccio’s new sacred reality. But, though the Renaissance system of perspective created an illusion of volume and space and appeared to furnish an objective description of the real world, it was, nevertheless, not the way we actually see. The execution of this apparently “objective and mathematical” style of perspective was still dependant upon subjective priorities and interpretations. Perspective itself created yet another illusion: the illusion of objectivity.
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The High Renaissance
…practice often precedes the birth of the word that describes it.
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Art began [in the early sixteenth century] to be even more strongly influenced by science as artists delved into physics, optics, anatomy, botany, and mathematics (Blatt 1984, 225).
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Leonardo’s Structure
Leonardo’s work was more “painterly”, in Wolfflin’s meaning of the word, than any before him. His painterly technique strengthened the illusion of volume (relief) by intensifying contrast in focus and blur. Because the soft, blurred edges disappear into the hazy background, the solid, rounded middle appears even more salient by contrast. “Linear”, considered in contrast to “painterly”, suggests the retention of a crisp silhouette. Linear figures are sharper edged and often contrast with the value of the ground. They often, but not always, appear flatter than painterly shapes (Wolfflin 1950, 18-54)
In addition to strengthening both composition and illusion, painterliness tends to emphasize structure over mimesis. Blatt maintains that when line and edge no longer coincided with the contour of objects, art began to break free of mimesis: “A shift occurred from the perceptual to the conceptual, from outer to inner form, from surface to underlying structure, and from concrete detail to abstract form” (Blatt 1984, 345).
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Leonardo concentrated his full attention and innovative power on form and structure in painting. More than anyone else, Leonardo was responsible for making form the major content of painting. This concept that form and structure were more important than mimesis – the imitation of nature – would gradually grow in importance, to influence Caravaggio the seventeenth century, then to dominate art theory and practice for more than four hundred years.
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…there is no single, correct, manner in which such elements should be interlocked. The elements in such structures may be recombined and restructured in many different combinations to create entirely new images.
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The Baroque Age
Descartes established a mathematical model of the universe that was fundamentally different from that of the Platonic or Aristotelian Christian view. His model allowed the hand of God only at the beginning: that is, God was viewed as the prime mover (Burtt 1954, 113). Descartes had set the stage for Boyle, Locke, and Leibniz to liken the universe to a giant clock, wound by God and kept moving by nothing more than his “general concourse” (Burtt 1954, 113).
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Medieval scientists had seen the world as friendly, finite, serving their needs, fully intelligible, and composed of those qualities that they could experience directly – colour, joy, heat, cold, and fragrance. Descarte’s world, in contrast, was a monotonous, though infinite, mathematical machine wherein not only humanity’s importance but God’s immediate influence was lost. In this world, furthermore, all those qualities that had made the medieval world beautiful were suddenly to be credited only to the human nervous system – perception (Burtt 1954, 123-24).
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While Renaissance painting had created space by linking linear perspective to size and placement of objects, baroque painting achieved an even greater illusion of depth by integrating foreshortening and diagonals with linear and atmospheric perspective.
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The projection through the picture plane seems an application of Descartes’s conclusion that space, and the objects that occupy it, define our existence. Caravaggio endowed his figures with the living illusion of Cartesian presence when he made David’s arm holding the severed head appear to extend into the viewer’s space in front of the painting. In this way, Caravaggio’s  realistic mysticism was a symbol of the seventeenth-century concept of “being” and the universe, as well as a powerful and persuasive embodiment of contemporary religious passion.
Frank Stella interprets Caravaggio’s penetration of the picture plane, his ability to develop the space in front of the painting in addition to the “stage” of the painting, as an important step in developing the potential of twentieth-century abstract painting. “Painting before Caravaggio could move backward, it could step sideways, it could climb walls, but it could not march forward; it could not create its won destiny. Without a deliberate sense of projective space, painting could not become real. The road to pictorial reality must pass through the dissolution of perimeter and surface. This is the road paved by Caravaggio to lead great art toward what we now call great painting (Stella 1986, 19).
Caravaggio, David and Goliath, 1609-1610. Oil on Canvas (49"x39") Borghese Gallery, Rome.
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The Roots of Modernism

Although the fifteenth-century made major contributions and the twentieth century has seemed a time of constant change, it was the nineteenth century that fomented more changes in the basic structures of art than any other period. During this century art and science were transformed by new concepts that had been kindled by non-Euclidean geometry, the fourth dimension, Darwin, Kant, and others.
Science, which had already begun to permeate literature and philosophy in eighteenth-century France, during the first half of the nineteenth century exerted even more influence on them. The dispassionate methods of enquiry employed by science, its combined use of observational, logical reasoning, and experiment were put to good use in other disciplines (Dampier 1966, 307). Whole new realities suddenly became available to the artist through new discoveries, such as non-Euclidean geometry.
Page 115
Manet, Degas, Monet, and Cézanne, in their first overt attempts to make space and composition the subject matter of art, struck what was to become the central theme of modern art. Conceptual, infinite space was a consequence of the spatial illusion first realized by the artist; a new “possibility then existed: to make space creation the whole criterion of art” (Read 1955, 100).
….the nature of “straight lines” would be altered and that space would somehow be curved. Thus were born several varieties of non-Euclidean geometry.
Non-Euclidean geometry led to other modifications of the concept of space. Might not its curved space add other dimensions to the three known to Renaissance spatial geometry: height, width, and depth? Whether additional dimensions also provided other levels or forms of reality, non-Euclidean geometry, which dominated the nineteenth-century painter’s new interest in space, excited artists and writers alike.
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Many prominent artists were interested in the idea of the fourth dimension. However, the artists were not experts in the practice of non-Euclidean geometry, and the fourth dimension remained only a subject for speculation. Though Kant, in the eighteenth century, had connected space and time as a priori intuitions, developed through reason and conditioning everything experienced through the senses, the fourth dimension was not defined as the relationship between space and time until Einstein did so at the beginning of the twentieth century. Yet time, which had been of interest to artists as early as the seventeenth century, became an important centre of focus in the late nineteenth century. Art, music, and science felt an increasing sense of the importance of time as a dimension of experience and reality.
Late baroque art had shifted away from images of the timeless and the eternal and toward depictions of particular events in time. This discussion was pursued further as impressionists attempted to depict the very moment of an experience (Blatt 1984, 302). Such a precise moment in time was partly implied by those paintings in which one precise area was focused sharply while details were progressively more blurred the farther they were from the center of focus. This technique was an attempt to mimic what may be seen in peripheral vision. Use of central areas of focus suggests the fraction of a second the vision may come to rest on a particular area before resuming its constant and active search for new areas of interest upon which to focus. This method is in direct contrast to what Svetlana Alpers calls a “displacement of time” as it was practiced by seventeenth-century Dutch painters when they subjected a still world to careful scrutiny and compiled detailed descriptions of a multitude of objects seemingly without end. Such obsessive attention to detail of all the objects in the painting seems to ignore or displace the element of time, for each detailed observation must take place during a separate and prolonged section of time (Alpers 1983, 109).
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 In order to hold dominion over a culture, an idea need not be “true”. We are often beguiled by the mere appearance of truth, and Renaissance perspective appeared to be so obvious, so objective, and so self-evidently true that no painter could construct a credible alternative for several centuries.  
The use of such convention does not imply that these depictions are in any way objective: every method of depicting the world is based on the subjective selection of pertinent facts (Francastel 1967, 16).
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If Algebra can function as an additional language to expand our concepts and out thinking, then we may have access to other such languages, one of which is painting. The painted image became the first writing, “a closed and mute system within which speech had as yet no right of entry” (Derrida 1976, 283). Then painting developed in two separate directions. The first direction remained painting, eventually evolving in Europe toward illusion, while the second direction began to simplify itself into “proto-writing”: first pictographs, then hieroglyphs, then the phonetic alphabet (Derrida 1976, 293).
Certainly there are other visual languages, but the one most familiar and most easily understandable to our society ids the illusion that developed during the Renaissance. We have used this illusionistic language in many forms – painting, photography, movies, and sculpture – for six centuries, and it has become so familiar that it appears to be native, natural, and self-evidently true; its boundaries and limitations have become as invisible to us as those of our native tongue.
Renaissance illusion and perspective have come to seem so self evidently true that we tend to be blind to its departures from a true representation of reality. The Renaissance system of illusion, Mitchell notes, convinced an entire civilisation “that it possessed an infallible method of representation, a system for the automatic and mechanical production of truths about both the material and the mental worlds.” This “artificial perspective” denied its own artificiality and claimed to be a “natural” representation of the way we see the world and the way things are (Mitchell 1986, 37).
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For the first time in four centuries, painters found scientific and rational grounds – in the concepts of non-Euclidean geometry – for believing there existed other powerful and equally valid ways to experience the world.
…the pre-Kantian statement by Giordano Bruno in the sixteenth century, that there are as many true rules in art as there are true artists, became even more significant. Each painter might now have a personal construct that could be used to depict only a limited and unique niche of reality.
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Experience grew and evolved as the mind reacted to its environment, Kaminsky comments: “Thus, by analysing what the mind does in giving rational form to external data, we should begin to see how the categories develop in experience. Like an art work that gradually attains form as the artist models and remoulds his clay, experience attains form as man reacts to a constantly changing environment” (Kaminsky 1962, 11).
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Late nineteenth-century painters instigated at least two major changes that would continue to guide artists during the coming twentieth century: they discovered the first logical alternatives to – or new models of – the conventional structures of Renaissance space; and each painter cultivated an individual and personal construct that ignored or excluded many of the obvious aspects of realty because these aspects fell outside the scope of their interests and investigations. Those ignored aspects of reality, though important, were nevertheless considered irrelevant to the artist’s chosen direction. In other words, important truths in the real world could be ignored in order that the artist might better pursue other specific truths in more depth.
An individuals perception of the world is limited, but reality presents an infinite variety of perceptions, and an artist may depict fresh elements or new aspects of reality not previously represented: in this case the artist will have made an “artistic discovery” (Pirenne 1970, 173)
The emphasis on individual strategies led to specialization, and the twentieth century artist was encouraged to adopt a field of interest that was narrowed or reduced to one tightly focused, microcosmic investigation.
-          A bit like a PhD?
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Doubts about representation were translated into doubts about vision, and “doubts about vision became doubts about almost everything involved in the act of painting”. This aporia, these doubts concerning the boundaries of art, vision, representation, and everything important to the act of painting became a value and an aesthetic in its own right (Clark 1985, 12).
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Monet’s Synthesis of Depth and Flatness
Instead of painting objects the way we see them, the impressionists painted the act of seeing itself, and the resulting paintings captured a multitude of sensations (Ortega y Gasset 1972, 30).
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Photography was fairly common by the late nineteenth century, and the impressionists may have been influenced by the “believability” of a photograph. A photograph seemed to be quite credible as an illusion of the outside world in spite of the flat manner in which it depicted figures.
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Photography had another important influence on the direction of painting. Painters, realizing that the camera could do particular things far better and more easily than they could, made an effort to concentrate on areas in which the camera could not compete. There “seems to be little doubt that many artists in fact have reacted to this ‘unfair competition’, preferring to use modes of depiction as different as possible from photographic perspective” (Pirenne 1970, 182).
One reason these painters [Impressionists] were seeking to avoid linear perspective was that they had discovered the expressive power inherent in maintaining the visual presence of the picture plane. Impressionists tried to avoid the deep spatial illusion of Renaissance perspective that carves illusionistic holes through the physical entity of the canvas and destroys its solidarity.
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 The impressionists wished just as fervently as the Renaissance artists to depict the world the way it appeared, but they used no straight lines, and they used patches of colour to represent a shimmering texture of light. Their technique created a dense, all-over image that treated both surface and event as items of equal importance, in place of the more traditional illusion of empty space that contained solid objects (Gablik 1977, 69).
Cézanne’s Elaborate Separation of Planes
Paul Cézanne (1839 – 1906) admired the bright colour of the impressionists, but he thought their paintings were too flat, too decorative and superficial. He insisted that they had sacrificed the structure of pictorial form – volume, spatial placement, and depth – to an irresponsible quest for colour.
In his early paintings, Cézanne composed and modelled in a method similar to the baroque manner. He used dramatic dark-light contrast to achieve volumetric illusion. But, after the influence of the impressionists began to shape his paintings, he used more colour. Although he followed the classic colour theory as it pertained to special placement, he still used a dark and light side to achieve the appearance of volume.
For Still Life with Apples and Oranges – still composed in dark and light, with cool blue used to make the background recede -  Cézanne invented a new method to create the appearance of volume in the fruit. He divided the apples into separate planes, of red (warm), yellow (transition), and green or blue (cool). The red areas establish what Cézanne calls the “culminating point” – that of the shape that appears to be nearest to the viewer – while the blurred blue and green areas induce the edges to recede behind the salient red middle of the apple.
Paul Cézanne, Still Life with Apples and Oranges, 1895-1890. Oil on Canvas (29x36") Louvre, Paris


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In a letter to Emile Bernard, Cézanne wrote that “in an orange, an apple, a bowl, a head, there is a culminating point; and this point is always – in spite of the tremendous effect of light and shade and colourful sensations – the closest to our eye; the edges of the objects recede” (from Chipp 1968, 20).
Something like this was also said by Giacometti
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One reading denies the other. When the viewer is conscious of depth, the flat surface is denied; when the viewer’s awareness is dominated by the flat image, depth is denied. But neither reading can be resolved as final; both continue to assert themselves intermittently.  
Cézanne discarded the obvious device of linear perspective – specifically converging parallel lines – in order to concentrate on the spatial use of colour and the separation of planes. He discarded the single, unified viewer-site of Renaissance linear perspective in favour of a system similar to the Greco-Roman. He ignored the Albertian viewpoint, once again to depict each object from its own particular frontal view, unrelated to the viewpoint of other objects or to the overall space of the painting. Cézanne consistently changed perspective and viewpoint within the picture in direct avoidance of Renaissance central perspective with its single, unified viewpoint.
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 This major innovation is a complex elaboration of the first major fifteenth-century spatial device: the separation of planes. All one need do is compare a Renaissance painting (in which value is most important) to a painting by Cézanne (which concedes hegemony to colour) to discover that each is capable of depicting certain aspects of reality that the other cannot. Each painting exemplifies a different structure and thus exposes the otherwise invisible boundaries and limitations of the other.
Cézanne created a consistent and continuous plastic space. The use of colour to depict one synthesized image of volume and spatial placement induced mass and space to coincide, coalesce, and become one undulating entity. Cézanne was perhaps the artistic precursor of Einstein, who hypothesized that the presence of mass affects the essential curvature of space.  Cézanne paintings might be thought of as a sensation of solid relief rather than as an illusion of different objects separated by empty space.
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Cézanne unravelled the traditional fibers that had constituted the Renaissance illusion. Then he negated, reversed, and recombined these fibers to create a new spatial fabric.
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John Dixon explains that a radically new vision – even as it destroys old traditions – must be realized within the bounds of those established., disintegrating traditions: Cézanne, like Giotto, fulfilled the old traditions while he initiated the new. His world was depicted as palpably three-dimensional and solid, but it no longer extended beyond the picture plane; it was translated into it. Illusion was not allowed to disrupt the flat surface of the painting. Giotto’s flat wall reappeared as the dominant plane in painting, and the painting was no longer a transparent plane through which viewers gazed but an object in their presence (Dixon 1984, 293).
 Cézanne’s fractured perspective, which fragments the location of the viewer into a myriad of disconnected locations – one for each separate object, plane, or view – may be seen to suggest a pluralistic, rather than a single, viewer.
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