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STEVE ZOLIN |
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For anyone that's been following my long-time interest in curved perspective, below is a draft of a paper I've been working on: A Brief History of Curved Perspective. As far as I can tell there is no book at all that traces its history. I start from its first known roots at Pompeii (if you can believe it) to the present day. I am still working on a section about Vermeer and some amazing spherical images I saw at the NY Armory Show recently.
A Brief History of Curved Perspective, and the Search for Truth The problem of how to interpret the three-dimensional world on a two-dimensional surface has existed for many thousands of years. The very fact of the flatness of visual artists’ supports inherently limits the level of “reality” an artist can achieve. Many methods for creating the illusion of three-dimensionality on a flat surface have been developed over the centuries, some literal, some symbolic, and some mathematical. The overlapping of painted objects creates a literal idea as patches of paint literally overlap, creating a sense of space where one object is in front of another. A symbolic sense of space involves showing objects from an “objective” view. If we draw a tabletop as a rectangle, the image becomes a symbol for a table. We “know” the table is rectangular, so why not draw it that way, instead of showing it obliquely, as from our actual point of view, forming it into a trapezoid or parallelogram? The answer to this lies in the third category of spatial conventions: the mathematical. Ever since the Ancient Greeks poured their wisdom on what became the West, the ideas of categorizing and measuring everything have become staple ways to understand and interpret the world around us. Philosophy, for example, parses ideas into smaller more nuanced ideas, and splits those even more in an attempt to discern the true nature of things. It seems a distinctly Western idea that if one weighed and measured everything closely enough, the rules and nature of the Universe (Truth) could be revealed. The development of Math has contributed greatly to our understanding of the world, but math is not Truth, despite what mathematicians or physicists may contend. All equations they use to explain the Universe end in infinite remainders or results that always are approaching, but never reaching zero. Math may approximate, approach, or stand for Truth, but is not Truth itself. Math is true enough in the mundane sense: Bridges stand, the Bomb works, but these are local phenomena, limited by their gross parts, and functioning within a certain acceptable margin of error, no matter how minutely small. A table seems flat, but is it really? Einstein showed that space is curved. If the table went on forever would it still seem flat and strait? As an idea, yes. As a reality, no. Even though a pool table is flat enough for playing on, there is only the idea of an actual flat plane: there is no such thing in reality. But if things work well enough with Math, does it matter if Math’s results are not entirely 100% accurate? The answer to that question may be discerned using the conventions of linear and curved perspective in two-dimensional art as topics of discussion. All traditional perspective schemes use mathematical principals such as points, lines, planes, rays, parallel lines, and so forth. When perspective was invented, the spatially convincing images it produced were so stunningly lifelike, that artists did not bother to think about its shortcomings. Any bugs in the system seemed meaningless and therefore ignored. Artists in every generation since the Renaissance have fully embraced artificial perspective, creating a continuous tradition of its use to this day. Also known as linear perspective, artificial perspective has variations of one, two, and three-point perspective, providing an empirical, mathematical framework, within which artists can easily create scenes and objects in proportion to each other. The points, also known as vanishing points, represent that place where receding lines understood to be parallel to each other, and also called orthogonals, meet at the horizon in a picture, much like looking down a flat two-lane highway in West Texas until it disappears on the horizon. There is another tradition, not a continuous one, but a occasional, yet insistent, reoccurrence of another spatial idea in Western art: curved perspective. Like a redheaded stepchild in the story of artistic perspective, curved perspective pops up every so often, always idiosyncratically, never as a tenet of the canon of art. There is no continuous history of curved perspective as there is for linear perspective, no great book on the subject, no series of great masters on the subject like Brunelleschi, Alberti, and Ghiberti. Its appearances are always alone, unsupported, and usually fail to produce intergenerational fruit. Curved perspective is not taught in art school. Ever. Under any circumstances. Any yet, if only by its historical refusal to go away entirely, we can infer its necessity. Because of the distortions inherent in any spatial scheme, no approach can be said to be perfect. The fact is, that like the peeling of the globe onto a flat map, translating the 3-D world into 2-D cannot be done without some amount of distortion. There are many ways to hide the distortion, to trick the eye into not seeing it, or to compensate for it, but many artists are not even aware that such phenomena occur. They are content to believe that artificial perspective as discovered by Brunelleschi and written about by Alberti, is the beginning and end of illusionistic space, and that perspective has nothing left to show us about the nature of space. But there is a long history of attempting to make space seem illusionistic. Before Brunelleshi discovered the empirical framework within which perspective could take place, artists used their eye to measure angles and determine the proportions recession. A good artist could emulate what he saw fairly well, but like the artist whose figure drawings come out somewhat lumpy from a lack of skeletal and muscular knowledge, something was off in most of these perspective works because there was no underlying knowledge of a spatial framework, only pieces of one. These days of perspective in pre-Renaissance art are not wholly mathematical, but largely intuitive, where the artist’s observations are his main guide. But what drove artists to attempt this illusion of space? What is Illusion? An illusion is something that appears to be there, but is not. Most art creates illusion. Just the mere idea that art is a psychological place set aside from life, for the contemplation of it, is an illusion, like a play where we the viewer witnesses events on stage. A murder on stage is not a real murder, and we know this because we agree that the stage is a special place where events and ideas can be expressed as commentary on life, not life itself. We allow ourselves to suspend our disbelief and enter the world of the art, to dive into it and plumb its depths and meanings, knowing that we will emerge on the other side back into the "mundane" world. While art always creates a psychological space, historically there has always been a great vacillation between art that symbolizes an object and art that attempts to create the illusion of an actual object. That is, at some points in history objects are depicted formulaically, based on tradition and not on observation. These periods give way to eras where artists want more and start to observe the natural world and inject their findings into their art. The Classical Greek period contains a clear example of this change, from the strait, symbolic Kouros figure which stands frozen like a popsicle, to the naturalistic contra-posto figure which allows the illusion of an actual person to materialize. It is this illusion that concerns us here, this development of depicting "real" objects is "real" space. The Ancient Romans went to far as to develop a style of figurative sculpture so real, it included a person's warts and all. This change represents a dropping of the symbolic form of representation in favor of a striving towards an empirical, naturalistic form which. Milton Brener writes, “Expressiveness in portraiture and three dimensional perspective have traveled in tandem throughout history. They have come and gone like inseparable twins, sometimes hand in hand, and when one appears, the other cannot be far behind,” (M.E. Brener, Vanishing Points p.112). Although Brener believes the struggle for increased figurative illusion comes from a desire to more deeply convey the mind of Man, he does not explicitly explain why these developments go hand-in-hand. It is precisely because they both expand the scope and quality of the artistic illusion that they do so: real objects in real space create a more convincing illusion. Once artists were no longer symbolizing objects, but trying to as accurately as possible to recreate them, a way was needed to regulate the space in which these objects resided to evoke a visual experience that would reflect the way we experience the world around us. Vitruvius writes that ancient Greek playwrights had set designers create the illusion of depth on their theatrical backdrops. He describes set design thus: “…sceneography is the sketching of the front and of the retreating sides and the correspondence of all the lines to the point of the compasses,” (White, Birth and Relation of Pictorial Space, p.251). Sounds like perspective, doesn't it? But no examples survive and there has been a lot of contention as to whether the Greeks discovered a mathematical perspective scheme. I am pretty sure they did not, not for a lack of physical Greek evidence (for which there us none), but for a lack of Roman evidence. It is well known that the ancient Romans copied generously from the Greeks in all aspects of life, from their arts, to even their gods. Many Greek sculptures today are known solely through Roman copies. Surely if the Greeks had invented perspective it would have shown up in Roman painting and covered the artistic landscape like it did after Alberti's book came out in the 1400's. Pompeii, originally a Greek settlement, shows much of what ancient Roman painters were capable. And while there were many extraordinary achievements there, as we shall see, no empirical perspective scheme has been found there. A Perspective Laboratory Frozen in Time The wall frescos at Pompeii are like living breathing laboratories of illusionistic space. While the Ancient Romans had very advanced figure painting, they were still experimenting with perspective. Therefore, to keep an image from suffering by comparison, the highly naturalistic figures tended to exist in shallow spaces with little background. This indicates that the artists knew there was something amiss with their illusionistic spaces. The many remedies they attempted resulted in a plethora of variations on types of perspective for us to see.. Pompeiian artists were very good at foreshortening of objects (fig. 1) especially architectural elements viewed from strait on, which is a remarkable achievement. Many of them were also starting to get the hang of parallel perspective, where all the orthogonals remain parallel and never meet (figs. 2,3). And there are frescos, like those of the Villa of the Mysteries, which exhibit many vanishing points in the same painting, which can be done if within an overarching structure, but here comes off like beautiful frosting on an unstable cake. But they did not know how to make this cake. It was through trial and error. Some frescos comes very close to linear perspective with a vanishing point, (fig. 4) but upon closer inspection, one can see that it was through sheer force of will and exacting observation that the artist was able to create a simulacrum of perspective, not the empirical system of perspective itself. Amazingly, there is also an example of curved perspective at Pompeii in the atrium of at the House of Ara Massima (fig. 5). This expanded view of an interior with a back wall and two side walls has been painted to show the most space possible. When one walks down a hall, the end wall can be seen clearly, but the side walls appear extremely oblique and distorted to the eye. In this freso, the artist widened out the perspective to display the side walls. What happens when this is done is that linear perspective does not accurately describe the proportions of the space any more. As the "V" of the orthogonals widen, more than one view comes to be included in the picture. Vision as we know it occurs to us as a cone of about 60 degrees. In order to see all that the artist has included would entail looking left, then strait, then right. To meld all these views into one coherent image in the realm of believability the artist intuitively curves the space of the painting. Note the bottom right border of the fresco and how it curves upwards to the right. Note also how the bottom of the painting within the painting also curves, however minutely. Imagine a large book with all its pages shuffled open. This represents the curved perspective scheme of this picture. Imagine the vertical spine of this book behind the flat wall with the painting within the painting, and that each cover of the book represents a side wall. If the spine were all the way open the walls would look flat. But with the book covers slightly closed the walls appear bent. Now imagine the arc that the shuffled pages of the open book would make starting with one wall, moving into a sharp foreshortened elipse and then back to the other wall. This shows a truth with which linear perspective never deals: that the ends of objects of the same length that approach the viewer do not and cannot terminate at the same horozontal point. In the book metaphor all the pages in a book are the same size, here, the size of a side wall. Imagine the first page of this book swinging from left to right like a door. The vertical edge of this page does not stay the same size on its journey left to right, but grows both above and below as it swings into a tight elipse closer the viewer, and then shrinking as it approaches the other side. This is precisely why linear perspective pictures always look funny in the lower corners, because the proportions of objects are distorted to reach them. As the pages of our "book" swing, they would have to get longer, then shorter in the middle, than longer again in order to maintain a horzontal line, not unlike the visual result of a flat-top haircut. This fresco has another amazing fearture. Though I suspect the artist did not fully understand what he was doing, he nevertheless has taken curved perspective to yet another level. Note how the left and right walls in the picture contain no long strait orthogonals, but contain many small lines, all understood to be parallel and yet with widely varying trajectories. The lintels above the doors, the cornices above the figures' heads, and the baseboards below them: Can you see how the sum totals of these varying small lines add up to not a simple strait line trajectory, but a curved one? Though there is some confusion and no common vanishing point for these lines, it is evident from the severely foreshortened angles of the left and right cornices that the artist intended the central space to feel like it is in front of the viewer (like the imaginary hallway I talked about earlier) with the left and right sides curving away from that main point of view where the vertical spine of the book lies. Picture two more imaginary "books" with their vertical spines at the very left and right edges of the fresco. Half of the shuffled pages of these books can be seen, the other half swing out of the picture. But the ones that swing in would match the overall curve of the architectural cues the artist has given us. This is the beginning in understanding curved space in art, and how it can be made infinte, with, to continue our metaphor, an infinite number of overlapping "books".The artist probably can not understand why he has to curved the space. He tries hard to fit what he knows are strait lines of strait objects into his painting. Why won't it work right? He does his best to solve the problems, and while the are still some perspectival incongruities, in the lintels and steps for example, the artist discovers some extremely advanced spatial solutions in cobbling this scene together. But consider what was happening across town in the house of Gladiator Actius Anecetus. The painting is of the brawl at the local ampitheater (fig. 6) It is obvious the artist wanted to create an illusionistic space, as the ground plane, seen from above, recedes into space. The ampitheater sits on this ground, but the back is tilted upwards to show what is happening inside. And the front steps are done symbolically, not in perspective. The building and field to the right are drawing diagonally to give the feel of spatial recession and perspective, but nothing gets smaller, even the people. This picture, on the wall of a gladiator's house, is based on an actual even which occurred in 59 AD. Pompeii was destroyed in 79 AD, which means that either there was an extraordinary surge in creative spatial developments in this 20 year period, or as I suspect, there were many concurrent levels of spatial mastery with no one dominant or dogmatic. They were still feeling around for spatial rules individually. Twenty more years and I believe they would have discovered linear perspective. But Alas! As the Middle Ages settle in, dogma crushes creativity. The need for an empirical spatial scheme disappears as the depiction of objects move back into the realm of symbolism. This devolution is well marked, though there has been endless debate as to why exactly it happened. It takes a thousand years before Giotto decides that there is a necessity for an overall spatial scheme in art. He developed his own system for dealing with architecture in space, what seems to be a variety of parallel perspective mixed with a light version of one-point-perspective. Here, in this detail from the arena chapel, (fig. 7) the architectural elements are either gently above or below the eye level. Our perception of reality shows us this phenomenon. Architectural corners bend in opposite directions depending on their relation to our eye level. Artists had tried to employ this visual cue before, often with disproportionate results, because, unlike Giotto they could not visualize the regular intervals that the orthogonals needed to take to approach the complementary angle. They just flopped the angles from one side to the other with no gradation, as in these two figures, one from Pompeii and one from medieval illumination (fig. 8). When the orthogonals are proportionally gradated, they imply the existence of a vanishing point to which they all recede. In this piece by Giotto, The horozontal gold bands that angle away from the front face of the castle are, because of Giotto’s excellent eye, proportionally gradated. Parallel perspective is easier for the artist to understand. Orthogonal lines recede away from the picture plane and are understood to be parallel even though they are not drawn that way. In the case of parallel perspective, they actually are: There is no vanishing point. When you see an object at close hand like a box or a chair, it is hard to imagine vanishing points because you can see the entire object and how the opposing sides look parallel. It seems that distance is an attribute which causes the phenomenon of vanishing points to appear: The viewpoint expands and all lines are not right in front of the viewer, differences in angles can be perceived from one side to the other. But artists have expanded parallel perspective to large objects and architectural scenes because it is easier to visualize and results are fairly realistic. The artists at Pompeii even had a handle on it. The front facing gold bands in Goitto's picture seem to be parallel, but if you look very closely at the two towers you will see the implication of a second vanishing point concerning the orthogonals of that axis. The towers at first glance seem exactly the same, but the right one shows considerably more underside to the roof and its eves due to a more severe angle where the plane changes, indicating a different point of view, closer to that tower. The right tower is also slightly higher both in literal size and in its relation to the top edge of the painting. The case for a second vanishing point would be quite wrapped up if we could see where and how the lower left corner of the castle meets the ground. If it complements the angle of the upper gold band, then a reduction in scale as distance increases would be easy to see. But Giotto purposefully obfuscates this area, the castle's contour melding seemlessly into the robes on the man on the left, creating a visual line down to the bottom of the picture and reinforcing frontality and lack of recession in the castle. It is as though while Giotto found ways to indicate regular spatial masses, he did not want to stray too far from the flatness expected by tradition. Additional evidence for this lies in the bricks of the castle. They run right across the surface in horizontal lines with no gradation up or down whatsoever. I believe this is purposeful, as it would have been fairly easy for someone with Giotto's eye to incorporate them into the overall spatial framework he had already created. Leonardo da Vinci It is a little known fact that Leonardo wrote an entire book on perspective. The final draft of it was stolen and all that remains are some of his notes and accounts by other artists (207-214 birth and relation). What also remains is definite evidence that he developed a curved perspective system. The diagram pictured in figure nine appears several times in his notes. The point of this drawing is similar to the book metaphor I used eariler. John White explains this way: Leonardo "demonstrates that only if the visual pyramids of three equal circles placed in a strait line are cut by an acr (g,f) centered on the focal point, will they bear their natural relation to each other and appear to diminish as the line is extended in eaither direction. If the intersection is by a strait line (e,d) as it is in artificial perspective, it will cut through the pyramids more and more obliquely, and the circles will in representation grow larger instead of smaller as they receed from the eye." (white p210). This is why things start to look weird in the corners when using standard perspective. On Point of View Note the angle of the arc in Leonardo's drawing. See how at the center of each arc segment is a point where a line can be drawn perpendicular to the line of sight for each cone. Imagine a flat screen in front of your eyes through which you see the world. This screen moves every time you move your head, always remaining perpendicular to your line of sight. This screen represents a point of view. In standard perspective all three circles are taken in one view, one look through the screen, represented by the flat line (e,d). Along the arc (g,f) we are given three distinct points of view as we imagine looking directly at cone b, then turning our head both left and right to look directly at cones c and a. The arc forms a continuum of points of view, allowing the artist to stretch how much space can be realistically seen in a picture. I put the amount at slightly less than a full hemisphere of 180 degrees. What does this mean? If one were to fully describe a single point in space, the result would be a painting inside a giant sphere one could walk in to, because any point in space, or any point of view can only be described by what is around it. If an artist paints a plein air landscape is he really describing the landscape? In part, but he is also describing a portion of his point of view, that spot somewhere behind the eyes where his sense of self is. Remember, someone looking at the same spot of land from a ridge opposite our artist will see something else entirely. If our artist wants to show a lot of the landscape, he can open up the 60 degree cone of vision to almost 180 degrees. At 180 degrees points of view directly opposite each other start to appear which is contradictory to how we experience the world, one point of focus at a time. The flat two-dimensional surface of an illusionistic painting represents the idea of one point of view, the idea of not having to turn your head to see it all (from the right distance of course). The result is that an illusionistic painting can be stretched spatially a lot, but only so far as the artist is able to convince the viewer that all that is shown can be seen from one point of view, even if it can't. A famous example is the drawing of the Pantheon. One would have to look through a hole in the wall from the outside of the building to acquire the point of view pictured. The viewer believes the illusionism because theoretically it is possible, even though the artist would have to remove the side of the building to get it. As long as there is one mathematical point from which a particular view is possible, a skilled artist can make the illusion work. Jean Fouquet the French illuminist traveled to Rome between 1445 and 1448 and certainly benefited from seeing the work of the early Renaissance. Leonardo was born in 1452, so Fouquet did not encounter his ideas on curved perspective that came into the public realm mostly through the work of his ardent supporters and followers, most notably Uccello. However, Alberti's book On Painting had been finished in 1436 and Fouquet almost certainly was exposed to these new ideas about perspective. Ironically, little evidence exists in his own work to suggest that he took them to heart (birth and relation p225). The convention of artificial perspective, so embraced by Renaissance artists (including an increasing number of Fouquet's French contemporaries and almost every generation of Wesern artists since), held little sway over Fouquet. The presence of curved perspective in at least 10 of his works reflects his knowledge that three-dimensional representations on two-dimensional surfaces distort at the edges, a phenomenon artificial perspective only canonizes. It seems clear that Fouquet saw that artificial perspective did not solve this spatial problem, rejecting it for his own methods. While there still is some awkwardness in his spatial constructions because of the lack of a clear system, Fouquet used his intuition in the matter very well. When we look at The Annunciation of the Death of the Virgin (fig.10) you can see how he curves the main support beam in the ceiling, compared to the one receding in the middle-ground. The supporting beams which act as orthogonals also curve away to the right, staying in proportion to each other as they approach the down-curving main beam. These supporting orthogonal beams act like the pages in our "book" from Pompeii. Also, the rug on the floor curves up on the right echoing the slight spatial compensation above. How curvature supports the presence of different points of view, as we discussed in Leonardo's model can clearly be seen in Fouquet's The Arrival of the Emperor at St. Denis (fig.11). The horizontal composition of the two horses and the strait left-to-right visual band of people and objects across the middle of the image cannot be mistaken. He staunchly uses these devices to counter the spatial construction, which is curved. As he has no set system, Fouquet tries to artfully meld these two approaches. The tile street and the houses on the left curve until the point of view is looking down the street instead of across it. The point is to show more of a journey, to show where the procession came from, not just from off the picture plane, stage right. Velasquez’s “Christ’s Driving the Traders from the Temple” This theatrical notion of space carries through all Old Master paintings. Every single painting, where the ground plane is shown, uses the bottom edge of the painting as the “floor”, like the edge of some stage. Objects never continue past that point into the nearer foreground. The one exception I have ever found is by Velasquez, who while a master figure painter, still had an awkward moment when he stuck himself and some friends and artist heroes into the lower right corner of this painting (fig.12). The lower right figures and the painting must be cropped as they are, because the figures would look like they were half stuck in the floor if the painting kept going, unless he added more descending stairs to another level. Also, the four leftmost columns in the painting constitute a strange spatial device. In order to expand the space available in the middle-ground for the figurative action, Velasquez nearly invisibly switches the plane of the four columns from that of depth, like the right three columns to that of width, remaining equal in size across the painting. The visual trick that these columns perform, is the appearance that they continue to move forward and curve away to the left like the columns on a rounded building. This is accomplished by increasing the intervals of space between the columns as they move from right to left. This illusion of curvature is supported by the wedge shape that the figures make, the apex of which seems to come down the hall, expanding as if curves to the left, then spilling off the left edge. All these intimations of curvature show a full understanding of the limits of linear perspective and how the idea of icurved space can help a composition. The tops of the four left-hand columns can just barely be made out, indicating that they actually are the same size on the same horizontal plane and not curving towards the viewer as the gestural illusion implies. The bottoms of all the columns are obscured to help this illusion. As with the figures in the lower-right, Velasquez knows just how much he can show to keep the illusion working. Photography One of the less recognized but most important contributions photography made to two-dimensional art was compositional. The stage-like quality of preconceived compositions gave way to an incredible range of cropping, balance, and scale as all kinds of random photos were taken, and new kinds of compositions were discovered. Now artists could draw objects in space much closer to the viewer than the imaginary stage of space that starts at a painting’s bottom’s edge, but the space that starts an inch from the viewer’s nose. Toulouse- Lautrec's "At the Moulin Rouge" addresses these issues as objects pop into the frame in the extreme foreground (fig.13). They are not only larger in scale and imply a continuation of space below the painting, but put the viewer right into the painting, not as a theatrical viewer from far away, but as an active participant as the objects closest to him are shown in human scale. And where and how do these objects hit the imagined ground plane? As one has to look down to see one's feet, and to look out to see a man across the room, there is an implication of a continuum of viewpoints as one moves one's gaze from feet to man and an implicit curvature if these views are combined. Lautrec, however, did not curve space; he found another way: He just tilted it. He drew his figures if they were people standing erect on a pitched roof. "Monsieu Samary at the Comedie Francaise" shows this very well (fig.14). In the foreground you are looking down at the floor, but in the middle-ground you look out at the man. The curvature that needs to happen to combine these points of view always occurs in the ankles of Toulouse-Lautrec's figures. Their bodies stand strait while their feet tilt to accommodate the pitch of the ground. The resultant illusionistic space is somewhat rickety, but Lautrec got this device to work in many compositions, and Degas used it a lot as well. Once very close objects had been introduced into compositions, the question of what the bottoms of those objects were doing and how do they hit the floor had to be asked. The question of what the floor would look like down there at your feet compared to the floor under the man across the room had to be asked as well. They did not have to draw it, but it had to be considered if an artist was going to paint part of a large object in the foreground. Enough visual information needed to be given that the whole object could be visualized. If the artist did not have that visualization the viewer would not either. Photomantages by David Hockney would later show how these points of view relate as he presented multiple views from his feet out to the horizon and to the sky above. The Mystery of the Ten Dollar Bill This subtle braiding of curved perspective into seemingly strict linear perspective schemes continues into Modern times. One day I was looking at the back of an old ten dollar bill, the kind before the “big head” presidents (designs #201, #202, #203). It had an oblique view of the Treasury Building on it. It looked like strict standard linear perspective with a strict Classical style building. But the more I looked, the more I realized that way down the street in the back of the scene, the engraver starts to bend the space towards the horizon, not too noticeably, but if drew a line to map the general trajectory of the street, you would see that the buildings and trees start to pitch to the right (fig.15). The same is true of the foreground. At first glance, it looks like linear perspective, but the curb bulges and curves ever so slightly. And you can see that the trajectory of the car in the street is also arcing off of strait. A lot of artists use curved perspective without even realizing it or knowing why. Richard Estes: Hard Core Estes, the famous photorealist painter, works very hard to counteract the curvature of space in his pictures. What seems like the strict artificial perspective of one viewpoint, upon closer inspection is an amalgum of multiple viewpoints that, overall, create a curved perspective. Through a tour de force of visual trickery and uncanny technical ability, Estes lends verisimilitude to his objects and so one is not likely to question the believability of his spaces. A cursory glance of his work shows no bending of space; all orthogonals seem to recede quite strait to their vanishing points without exception. His work obeys the rule I set forth eariler, that because of our limited cone of perception, the degree of space the artist shows cannot reach 180 without it looking false to our perception of the world. Estes combines multiple viewpoints into the maximum allowable vista for one viewpoint, often using streets and architectural elements that can be construed as being not be perpendicular to each other to cover the extended spatial distortions, as in "View of Paris" (fig.16). The bridge at the right hand side of the painting must cross the river diagonally for this view to be possible. If it were set strait across the river we would not see any of its face as it would swing to the left and meet the large stone railing. The ground underneath the cars parked on the river frontage in the foreground represents still another view. Estes knows that multiple viewpoints must curve in order to seem proportional to each other. But he will not show this curvature beyond what a very close inspection might perceive. The street in itself seems strait and flat. But if you drew a line that was understood to be perpendicular from the river edge across the street, it would follow the scuffs on street and go down off the bottom of the painting. However, as the point of view moved the imaginary trajectory of this line would curve, level off, and rise as it travels left across the painting, like the elipse in the "book" metaphor we have discussed. But Estes never shows you perspectival segments longer than he make seem absolutely strait. It is basically curved perspective without the curves. The space curves, but the objects do not. It acknowledges the necessity of counteracting spatial distortions, but refuses to move beyond the literal idea of what we believe about strait objects: that they are indeed strait and must always be depicted at strait. This notion may not be bad as it helps the viewer place the image in the “real” world. Once again, it is the foregrounds where the spatial problems must be more heavily tackled. And, while Estes gets his combined viewpoints to work as a single spatial scheme, the price is a certain awkwardness in the extreme scale reductions and foreshortening from foreground to the background. The backgrounds of multiple viewpoints can be more easily combined into one view because the small scale changes more slowly, even as foreground views change quickly, like how mountains seem to move slowly on the horizon when you are driving, while closer objects like trees and houses zip by. There is a great Truth that underlies curved perspective. It was long thought that stillness was matter’s natural state. Now we know that everything moves at all times. Everything vibrates, creating a literal “music of the spheres”. Time has been described using adjectives like, “eddies”, “ripples”, and “wrinkles”. Shakespeare described this life as a “mortal coil.” Einstein proved that Space and Time are one thing, and that Spacetime is curved. The Universe has been called an inifinite sphere, whose center is everywhere and whose circumference is nowhere. I came to the conclusion that Space is curved, just by playing with perspective. And if one subscribes to the Big Bang Theory, it is not hard to apply it to perspective. In a picture, a vanishing point is the singularity from which all emanate. We tend to think of things receding towards the vanishing point when in fact they are actually coming towards us from it. Art learning has commonly gotten only so far as three-point perspective where all three axis recede to vanishing points. But I have invented something called infinte perspective, which contains an infinite number of vanishing points. Like parallel perspective, this spatial scheme can continue forever in any direction, which makes it ideal for creating very long or tall compositions. Unlike parallel perspective, infinite perspective contains multiple points of view, looking down, out, and up. It uses the idea that equations about the Universe always approach, but never reach inifinity or zero. Orthogonal lines curve towards the horizon, always approaching, but never reaching, horozontality. This corresponds the infinite sphere concept, the arc of which is always approaching, but never reaching zero. If it reached zero, it would not be an arc, and hence no sphere, and its arc must always approach zero out of the range of measure. It must be so incalculably small that it cannot be measured, for if it could, than the sphere would not be infinite because its size could be projected through the angle of the arc. So, because an infinite sphere cannot be measured, and a singularity takes up no space (even an infinite number of singularities take up no space) essentially we are left with the notion that space has no space, only the idea of space. I believe perspective uses this notion whenever you see ground plane and a sky plane meet at the horizon. I tend to think of this as the gradual pulling apart of a cosmic 2-ply paper towel to show this almost place in which we almost exist. So in infinite perspective I use many arcing lines that when they reach the impossible places near zero arc, I overlap them with other, closer arc lines, which produce an overall effect of space, where mathematically none should exist. From an artistic point of view, it is difficult to draw these concepts naked because we are used to experiencing the world from one narrow point of view at a time. I believe a combination of overall structure with flexibility works best. Visual flexibility was lost when the structure of artificial perspective was formed. Its rigidity was at once a great asset that allowed amazing spaces to be drawn, as well as a liability with a lack of understanding of what to do when the narrow point of view for which artificial perspective works well gives way to distortion at its outer edges. Like a computer that cannot understand why it cannot compute pi, artificial perspective crashes without creative intervention by the artist. This is in part why curved perspective pops up as an occasional thread in the braid of spatial history, as a way of creating flexibility in visual space. Most people think of curved perspective as something with a “fish eye” lens effect. Truly it would be if it were applied with the mathematical rigidity of linear perspective. But with a more subtle, flexible application, many things are possible. I believe I have shown that a blending of these approaches conveys a more lifelike image than either alone, and that awareness of overarching structures, both within one’s art and within the Universe itself, definitely lends to the Truthfulness of the art. For Art itself is capable of being a metaphor for Truth. If Math comes to Truth empirically, then Art comes to it intuitively. Ultimate Truth cannot be stated, but it can be implied. If an artist shows you a slice of a pie, you can imagine the rest of the pie. Some work by Ellsworth Kelly uses this idea, where one of his color field paintings is a long slow arc, a giant piece of some even larger unbelievably gigantic imaginary circle, the idea of which then pops into existence in the viewer’s imagination. It is because we have the ability to extrapolate that these things are possible. Here it is that Art has the advantage over Science, bolding going where numbers cannot tread. Partial Bibliography Allison, Ellyn Childs, Editor, Perspective, Harry N. Abrams, NY, 1977 Brener, Milton E., Vanishing Points: Three Dimensional Perspective in Art and Art History, McFarland & Company, Inc., NC, 2004. Coombes, William, Background to Perspective, Adam & Charles Black, London,1958. Ivins Jr, William M. On the Rationalization of Sight, Da Capo Press, Inc., NY 1973 Massey, Lyle, Editor, The Treatise on Perspective: Published and Unpublished, Yale University Press, New Haven., 2003. Norton, Dora M. Freehand Perspective and Sketching Bridgman Publishers, NY, 1929. Vero, Radu, Understanding Perspective, Van Nostrand Reinhold Company, NY, 1980 White, John, The Birth and Rebirth of Pictorial Space, Faber and Faber, London, 1967. |
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