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Kim H. Veltman Perception, Perspective and Representation in North America Published in Italian as: “Percezione, prospettiva e rappresentazione nell’America Settentrionale”: Specchi americani. La filosofia europea nel nuovo mondo, ed. Caterina Marrone, G. Coccoli, G. Santese , F. Ratto, Rome: Castelvecchi, 1994, pp. 287-345. (Contatti 6, III convegno di studi filosofici di San Sepolcro).

1. Introduction 2. Spherical Perspective 3. Multi-View Perspective 4. Space and Time 5. I.A. vs. A.I. 6. Fractals 7. Space and Ahistorical Timelessness 8. Conclusions.

1. Introduction

In 1956, Sir Ernst Gombrich gave the A. W. Mellon Lectures at the National Gallery in Washington. These became his famous Art and Illusion (1960). The subtitle of that work, A study in the Psychology of Pictorial Representation, could well serve as a summary of developments in North America in the fields of representation, perspective, perception, and vision. This paper begins with a survey of some major trends in these fields, noting the European roots of American views. Particular attention is given to the development of alternative methods of perspective which are related to recent developments in virtual reality. Two different interpretations of these trends are offered. The paper ends with questions concerning the philosophical implications of these developments. In the European tradition there has been a debate almost as old as philosophy itself whether perception is innate (Plato, Descartes) or learned (Aristotle, Locke), with notable figures such as Kant who tried to find a middle ground between these extremes. In the United States these traditions, characterized as nativism versus empiricism by authors such as Hochberg1 (1963), have tended to be treated as polarities, oppositions in which nativism has triumphed over empiricism. As a result Descartes receives particular attention; a mitigating figure such as Kant is frequently cubbyholed as a nativist and particular emphasis is given to psychological dimensions and conventionalism, even though realism continues to have its defenders. In Europe perspective had traditionally been seen as one of the pillars of objectivity, but in the course of the past century, there have been some proponents of its conventional nature (e.g. Mach, Panofsky, White). At Oxford, the physiologist, Pirenne2 (1952), presented careful evidence that it was an objective method. Gombrich3 (1960) defended the claim that perspective was objective while exploring how it might be considered a convention. In the United States, the view that perspective was a convention triumphed, partly through the philosopher, Nelson Goodman who, in his Languages of Art (1969), developed the metaphor of learning to read pictures4 which had emerged in the Russian structuralist school of Florenskij5, Shegin6 and Uspensky7. These structuralists in turn cited the German physicist Mach8 to support the idea that linear perspective was but one

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of many possible methods. Goodman's work provoked Gombrich9 (1972) to clarify his position and argue more strongly for the objectivity of perspective. Other aspects of these questions were taken up by the psychologist, J. J. Gibson at Cornell and led him into important debates10 with Gombrich on the nature of perspective pictures. Gibson focussed attention on the the senses in context. He argued that there were fundamental distinctions to be made from the way we see the environment which is a practical necessity, and the way we see pictures, which is a luxury activity. By contrast, Gombrich11 claimed that the rules of vision which applied to the world of nature applied equally to the represented world in paintings. Gibson's emphasis on the visual environment focussed on problems of motion. It is well known that his practical experiences as a pilot during the second world war were an important impetus for these studies which led him into further lively debates with Gombrich and Goodman as well as Arnheim. It is less often recalled that Mach's Analysis of Sensations was another of his points of departure.12 In that classic study Mach13 had attempted to draw the field of vision and its environment as seen by the left eye. Gibson, who referred to Mach's drawing as an illustration of "the visual ego", made "an updating"14 of this drawing in his Perception of the Visual World (1950) and developed this in his Ecological Approach to Visual Perception (1979) where he illustrated how fields of view overlapped when turning one's head from left to right. In the case of the Gestalt school the European roots are obvious. Two of its founding members, W. Koehler and K. Koffka, came from Europe to Smith College and their work was a point of departure for the studies of the most famous representative of the Gestalt school in our generation, Rudolf Arnheim who made the provocative claim (1969): “that all thinking (not just thinking related to art or other visual experiences) is perceptual in nature and that the ancient dichotomy between seeing and thinking, is false and misleading.”15 In England Gablik (1976) attacked this radical position and suggested an equally dramatic alternative, that one needed: “an epistemological model of art history, which is based on cognitive theory, rather than on a neurophysiological model of perception such as that found in Gestalt theory.”16 To defend this position Gablik cited experiments in the development of children by the Swiss psychologist, Jean Piaget.17 In the United States, the psychiatrists Blatt and Blatt (1984) took these debates considerably further arguing that although vision and representation had traditionally been viewed as a problem of perception, they now fell within the domain of cognitive psychology. As evidence they cited both Piaget and Gablik along with a series of other structuralists including Chomsky, Jakobson, Lacan, and Levi-Strauss.18 In the Blatts' interpretation Kant, Cassirer, Koffka and to an extent even Gombrich could all be seen as part of this general trend towards a cognitive model of both vision and representation.19 Accordingly visual perception was not crucial in the artistic process. Artistic creation was an intellectual activity that occured in the brain: it was cognitive. From the above it is clear that European ideas have been an important source for American discussions on key issues of perspective, namely, whether it is an objective method or a convention; and fundamental questions on the nature of representation: whether it is perceptual or conceptual. Since a comprehensive survey of all aspects of these developments is beyond the scope of a paper, I shall focus on the emergence of alternative methods of perspective and particularly spherical and multi-view perspective. These methods also have their roots in European examples and are important for at least four reasons. First, they explore the

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artistic possibilities more systematically than their European counterparts. Second, they relate perceptual problems of space to those of time, which are connected with new approaches to photography. Third, these explorations of alternative methods of representation are a manifestation of a larger quest towards integrated sensual experiences epitomized by the emerging emphasis on virtual reality. Fourth, as will be seen, they invite some very interesting philosophical questions. Each of these aspects will be considered in turn.

2. Spherical perspective.

While the precise origins of spherical perspective are not known, some details of its long history are well documented. We know, for instance, that in the late fifteenth century Leonardo explored cylindrical and spherical perspective when faced with the problem of producing images equidistant from the convex surface of the eye.20 From a French manuscript of Boccaccio we know that as early as 1405 there was a more practical context for these concerns. Convex (spherical) mirrors offered artists a handy tool when faced with the challenge of making self-portraits. This idea was soon adapted for other purposes. Van Eyck used it to represent the surrounding room in his Arnolfini Wedding (London, National Gallery, 1434). Petrus Christus used it in his Saint Eligius (New York, Metropolitan). In Italy there had been a preference for flat mirrors as an artistic aid during the fifteenth century but by the sixteenth century the northern technique of convex mirrors was also in use there as witnessed by the figure of Prudence in Raphael's Stanze (Vatican, 1511) and by the famous Self-Portrait of Parmigianino (Vienna, Kunsthistorisches Museum, 1524). The nineteenth century introduced two new reasons for interest in spherical and curved projection methods. One was the rise of non-Euclidean geometry through Bolyai, Lobachevsky and Gauss.21 Another emerged from the experiments of Hering and Helmholtz which suggested that in the case of objects near they eye, curved lines appear straight and conversely.22 The curvature of the retina was posited as a possible explanation for this phenomenon and led Helmholtz to raise the possibility that visual space might in fact be non-Euclidean. A generation later, Hauck23 (1879) went much further to argue that curvatures in the eye had been an inspiration for the subjective curvatures on the Parthenon and elsewhere in Greek art. Late nineteenth century artists such as Cezanne and Van Gogh were also rendering straight lines as curved in their paintings. An American philosopher of science, Heelan, has explored the significance of these artistic works in his Space Perception and the Philosophy of Science (1983). Late nineteenth century century developments in neo-Kantianism (e.g. Cohen) which suggested necessary links, between a given world view, theory of vision and method of representation gave new impetus to these discussions.24 Further experiments ensued in Europe with Blumenfeld25 (1913).In the United States experiments concerning subjective curvatures in vision and representation were taken up by the artist A. E. Ames,26 who was painting with his sister (c. 1910) and believed that: "if they could make an exact reproduction in form and color of a scene they would have a technically satisfactory work of art".27 To this end they made a set of thirty five hundred colored cards. But the results were "tight", hard" and lacking in atmosphere.28 This led him into a detailed study of optics including experiments on optical aberration and resulted in a scientific paper with the physicist C. A. Proctor. The authors (1921) made a careful survey of earlier work, notably Helmholtz, Donders, Drualt and Matthiessen, and found distortion in the eye greater than that

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due solely to the effect of the spherical shape of the retina....It can be concluded therefore that the distortion caused by the optical system is also barrel in its nature and increases that caused by the spherical shape of the eye.29

Ames' visual experiments were carried out at Dartmouth College. Luneburg also carried out his studies on the metric of binocular visual space at Dartmouth College. Luneburg cited the earlier European work of Helmholtz, Hillebrand and Blumenfeld as a background for his own experiments. He claimed that the so-called visual space:

has a uniquely determined non-Euclidean metric or psychometric distance function, the numerical parameters of which depend on the individual observer....But its general form is invariant; it is the metric of the three-dimensional hyperbolic geometry.30

These claims were taken up by his follower, Blank31 (1959); questioned by American psychologists such as Graham32 (1951) and Ogle33 (1962); challenged by Pirenne34 (1975); and subsequently proven wrong as noted by Heelan35 (1983). No simple mathematical formula for subjective dimensions of vision has been found by scientists. Meanwhile twentieth century artists have increasingly insisted that such subjective curvatures be included in their works of art. Perhaps the first to write a book on the problem was the Canadian artist, Ivan Jobin36 (1932). His starting point was one of the standard books on perspective by Cassagne37 (1897). However, claimed Jobin, two recent developments necessitated a modification of these traditional rules of perspective: the advent of skyscrapers and the aeroplane.38 These introduced such radically new heights that it was necessary to introduce perspectival effects in the vertical plane which he claimed should involve curved lines. From the mid-nineteenth century onwards artists had been recommending curvilinear alternatives to linear perspective.39 But these efforts were almost inevitably sporadic with minimal cumulative effect. In the 1960's and 70's this changed. Artists continued to invent their own systems but also became aware that they were part of a larger movement. Seminal in this context was a French book by Barre and Flocon entitled La perspective curviligne (Curvilinear Perspective, 1968) which was subsequently translated into German (1983), Spanish (1985) and English (1987). The translator of the English edition was the artist-philosopher Robert Hansen, who had come to similar conclusions completely independently in the 1950's. He had published his own alternative method, hyperbolic linear perspective40 (1973), and drew attention to an international community of artists concerned with these problems including Jaqueline Lima, Fernando Casas, David Hockney, Lucien Day and Dick Termes in the United States. Hansen and Flocon did not learn of each others' writings until the late 1970's and did not meet until Hansen was completing his translation of Barre and Flocon. Barre and Flocon were convinced that their efforts were objectifying what might traditionally have been thought of as subjective aspects of vision and representation. They studied cartographical methods using spherical projections. They worked with the mathematician Bouligand to assure the accuracy of their work. This insistence on a quantitative, mathematical systematic approach to the problem was challenged by Hansen (1973, 157): "I am not prepared to prove that we see mathematically defined hyperbolas, but I am convinced that every straight line appears to us like a hyperbola, a curving ligament connecting two straight orthogonal asymptotes". Hansen saw his efforts specifically as an attempt to represent what Gibson had termed the visual field and went to the trouble of constructing a physical transparent hemisphere with which he experimented. Flocon tried it on when he visited. Hansen's method provoked Arnheim41

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(1974) to an article and both were cited by Turner42 (1976), who offered his own alternative method which he compared with yet another version by Reggini43 (1975) from Argentina. Michael Moose created a variant method known as fisheye perspective44 (1986). Marcia Clark45 (1987) recently brought together the work of several of these artists in a New York exhibition. Nor is the movement limited to the United States. In addition to Horacio Reggini in Argentina, Tomas Garcia Salgado46 (1988) in Mexico has been developing similar methods. All these artists are striking for the interdependence of art, mathematics and philosophy in their works and for the manner in which they explore new combinations of panoramic views, bringing deliberate distortions which are frequently very effective. Some of the most beautiful and thought provoking paintings to emerge thus far from this group are the termespheres produced by Dick Termes from Spearfish, South Dakota. Here again European connections can be traced clearly. For instance, the late Maurits Escher used to have a spherical mirror and once had himself photographed peering into one.47 Mr. Termes also has such an instrument, the American term for which is a mirror ball, and has also been photographed with his reflection therein. Escher (fig. 1, 1935) once did an engraving on a flat piece of paper showing his hand holding up such a spherical mirror which reflected his portrait. Termes (figs. 2-3, 1983) painted this reflected portrait of Escher onto a spherical surface in such a way that from one view it looked nearly identical with Escher's flat original, but when the sphere was turned it revealed a semi-abstract arm becoming a very realistic hand. Escher's one engraving had in fact become a combination of paintings in Termes' sphere. Similarly Escher (1951) had done a Study for the Litho Stairwell, which had an interlacing network of girders which curved to varying degrees such that beams which were vertical in one part of the drawing became horizontal in another part. Termes, in Finishing an Escher (1977), transposed rows of painted girders onto the surface of a sixteen inch sphere which introduced a series of visual transformations as one walked around it. The theory underlying Termes' paintings is his own. Traditional laws of linear perspective are governed by one, two and three point perspective. Unhappy with the limitations these imposed, he posited that one should also be able to have four, five and six point perspective. In practice this involves coordinating the vanishing points of different scenes on a single sphere. The paradoxical results are conveyed both by the paintings and their titles, such as North is South (1979), painted on a twenty-four inch sphere. In this particular case we find ourselves from one point of view looking directly into a room. On the ceiling of this room are five wooden beams orthogonally positioned such that they converge towards a central vanishing point. We see another room opening beyond this. From another point of view we are looking at this first room from the side and we see the wooden beams on the ceiling as running parallel at ninety degrees to the visual pyramid. Now the wall opposite us has windows beyond which we see a landscape. From another point of view we are very near one of these windows and can see the landscape directly beyond us. From yet another point of view we are in the second room which we had seen from a distance from the first viewpoint. The source of these paradoxical effects can be identified. Termes paints enclosed rooms with windows and openings giving us a sense of looking into one space and beyond this to other spaces, except that they are not transparent in the way that they appear, so that when we move to another position we can be confronted with a completely different image. This creates surprising contradictions in orientation: North is South. Escher had explored related effects on a flat plane with up and down staircases in his Stairwell I (1951), Stairwell II (1951), and Relativity (1953). Termes extended this concept of paradoxical and seemingly contradictory orientations in his Up is Down (1982), and in Floor is Ceiling where the viewpoint shifts continually as we move around a sixteen inch painted sphere.

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In the seventeenth century, Pieter Saenredam had made the interior of the Sankt Bavo Church in Haarlem the subject of a series of drawings and paintings.48 Escher in one of his earliest drawings in black ink (figs. 4-5, 1920) depicted the interior of this church seen from a special viewpoint where the spherical base of the central candelabra reflected both the church and painter in spherical perspective (but on a flat surface). Termes' version of this theme in his God's Eye View (figs. 6-7, 1988), depicted the interior of Santo Spirito in Florence.49 Whereas Escher had drawn a reflection of the church interior onto a representation of a sphere on a flat surface, Termes painted a reflection of the church interior onto an actual spherical surface. As a result a viewer is able to look straight down the aisle of the nave towards the main altar and then move around such that they can look directly at a side view of the same interior. At all times the observer's viewpoint is from an imaginary point in space just above the height of the columns, a fictive position that can be mathematically located in real space, hence God's Eye View. Some of the termespheres are relatively small: sixteen or twenty four inches (cf. fig. 14). Others are much larger. For instance, Order and Disorder (1985), commissioned by the Wyoming Law Enforcement Academy at Douglas, Wyoming is seven and a half feet in diameter. This began as a large transparent sphere inside which Termes then stood in order to paint it. From this position it thus became an equivalent of the entire visual sphere. This helps to explain the extraordinary panoramic effects of these paintings and how they can offer such very different vistas when seen from different sides. In Pieces of the Whole (1984), for example, we see a young man painting a picture. To his left is a boy looking into a sphere. As we move around we find that the seated boy now appears to the right of scene (fig. 8). In the centre there is a different easle with no one in front of it (fig. 10), while to the left there is an easle with another young person in front of it. If we move around further we find a third easle, with a seated boy in front of it (fig. 9). If we take a closer look at these easles (figs. 10-11), which are depicted as being rectilinear, we notice that each of them records aspects of their spherical context. So the boys are painting pictures which are rectilinear pieces of the spherical picture in which they stand: Pieces of the Whole. No less complex is Pull to the North (1984) where we see a snow-bound arctic landscape from one viewpoint which, as we move round, gives way to totem poles connected with wooden beams, so arranged that they evoke images of pipelines, then become pipelines as we move further around, only to become transformed in turn into the girders of an urban view as we move round further still. This act of standing inside a sphere while painting a scene intended to be seen by viewers standing outside the same sphere also helps to account for yet another feature of these paintings: a strong ambiguity between interior and exterior, explicitly reflected in one of the works entitled Within the Outside (1977). Here the observer looks in at the back of a painted figure who, though looking inwards relative to the observer's point of view, is looking outwards through a window from their point of view. From another side of this sphere the observer finds themself looking inwards at two painted figures looking outward and facing the observer. Such ambiguities are more than visual contradictions. Termes refers to them as visual puns. Sometimes these puns are verbal as well as visual and involve the title of the painting as in Cubing the Sphere (n.d.). On occasion they are blatant puns as in Hole Sphere (1973). At other times the title offers a seeming opposition which is not as in Man/Nature (1977) or the title may even be a seeming contradiction as in the form filled painting, Emptyness (1986), reminding us of Shakespeare's phrase: And nothing is but what is not.

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3. Multi-View Perspective. A single sphere ultimately allows a limited number of such viewpoints. A next logical step would be combinations of such spheres. In Mitosis (1982), Termes combined a ten inch and a sixteen inch sphere to create a more complex nexus of viewpoints. In Reflecting Back (1989), he painted the four walls, ceiling and floor of a room respectively on six seventeen inch spheres which he joined together, thus permitting one to see six viewpoints from one viewpoint, which then change as one moves around the spheres. The views for these spheres were based on photographs of an actual room. A next step was to project images onto various sides of regular and semi-regular solids. In his Flat Sphere (1988) Termes began with twelve flat diamondlike shapes each sixteen inches high (fig. 12). These were then folded together to create an irregular dodecahedral form. In other cases he used regular polyhedral shapes. A tetrahedron was used to make a tetrahome. A dodecahedron was employed to construct a dodecaperspective. Similarly an icosahedron was used to create new combinations of views. Termes experimented how these multiple viewpoints could be systematically related to a series of photographs. He built physical models of regular polyhedra, such as the dodecahedron. He then took photographs from a viewpoint corresponding to the centre of this shape and took twelve photographs corresponding to each of the twelve sides. This idea he patented in 1980.50 He named these combinations of photographs "total photos" (figs. 13, 15). Europe has its own equivalents of such spherical and multiview perspective paintings such as Adams' tetraconic perspective51 in London or Nöel Blotti's work now on display at La Villette in Paris.52 One difference is that North America has explored these possibilities much more thoroughly. 4.Space and Time. There is more to these experiments than a simple collection of different spatial views. Each view also took place at a different time. So these are also experiments in relations of time and space. Hockney was conscious of these problems when he began his collages of photographs from different viewpoints:

I began to make experiments. The first picture is of somebody swimming in a pool and I did piece them together and naturally the picture has some interest in a sense that it is a different time in the top-left hand corner and a different time in the bottom right. It's a different time in each square and as I went on I found, suddenly at times, incredible spatial effects happening which made me realize that time was deeply related to space - maybe they were the same thing - and immediately I noticed its connection with cubism which always had interested me and then perplexed me.53

Termes also became aware of this interdependence of space and time and used one of his dodecahedral perspectives to combine twelve different views of a wedding: one scene showing the newly-weds together, the other scenes showing either one of the partners looking in on preparations for and different stages of the event, such that a single "total picture" records several hours of experience. These developments can be seen in the context of a larger trend towards visualization which is by no means limited to the domain of art, and includes the remarkable and sometimes frightening images in video-halls which now include hologram figures as well as recent developments in computer graphics ranging from simple products available for a PC environment that enable transformations of surfaces. For instance, products by

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Image Ware (parts of which are available through the Aldus Software Company), enable one to take a photograph and add craquelure effects, wave patterns or any of sixty four other changes in a matter of seconds. Autodesk products such as AutoCAD and 3-D Renderer permit one to recreate spaces perspectivally. The frontiers of Geographical Information Systems (GIS) allow one to take an aerial photograph, coordinate this with information of a map of the same place and arrive almost instantly at a three dimensional scene showing the contours of mountains and valleys, permitting one to choose different imaginary standpoints miles apart within seconds. At the high end of this spectrum of new tools are products from Alias Research Inc. which made the software for the incredible figure that melts and recomposes seamlessly in the film Terminator II. The perceptual and aesthetic consequences of these new techniques have not yet been studied. But one thing is clear. When Lessing wrote his Laokoon he made a basic distinction between poetry which he claimed was suited to time and painting which he felt was linked to space. The recent photographic art by Hockney, the polyhedral paintings and photographs by Termes, as well as the software products of Image Ware, Autodesk and Alias, show that Lessing's claims are outmoded. And while these works also show that perception still plays a very important role in contemporary art, they also evidence a significant shift in the nature of perception. The Renaissance view of an eye which records reality through a single window at a given moment has been replaced by new coordinations of a series of windows and moments, space-time continuums in a new sense. The significance of these trends is open to very different interpretations. In the role of devil's advocate one can ask about the possible limitations of these alternative expressions. They present in mathematical terms, as if they were standards of objectivity, methods which would traditionally have been termed subjective in Europe; a term, incidentally, which nineteenth century thinkers such as Hauck referred to in very positive terms. In America, by contrast, one of the leading artists of spherical methods was very offended when I referred to his work as subjective, because that implied something unscientific, unmathematical and very negative. The reason for the misunderstanding stems from different definitions. In Europe it has traditionally been assumed that mathematical relations involving objects are objective. Relations involving subjects in the sense of persons are subjective. By contrast,in America it is assumed that mathematical relations can be established with both objects and subjects. Hence psychology is treated as a science and only non-mathematical relations with subjects are subjective. The manifestations of this trend are often unexpected. Hence we find Buckminster Fuller describing teleologic designing processes as a shift from "subjective to objective, i.e. from subconscious to conscious adoption",54 as if extrovertedness was something that can simply be increased as one pleases. The problems at hand go deeper than different definitions of a term. There is also something about the paintings themselves. In the past looking at a Botticelli or a Rembrandt gave us, or at least so we have believed, important insights into the personal worlds of these artists, even when they were doing official commissions for public places. Are these modern alternatives more personal or less personal? What is happening with the great proliferation of viewpoints in these paintings? Are they a flight from courage to defend a fixed viewpoint? Are they symbols of a new universalism which accepts the validity of all viewpoints? Here there are interesting parallels with literary criticism where the quest for understanding the meaning of subtexts has led in many cases to a fear of asserting anything, where critics are so aware of possibilities that a paralysis of interpretation ensues.55

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Or could it be that this seeming universalism obscures a deeper truth: that different viewpoints are assumed no longer to be different; that the other side is no longer even a side in the sense of a clear position but simply a section of a sphere, an aspect of a circular argument? Have the alternatives reduced themselves to something as peripheral as a different lens which we put on our camera whereby the angle is changed but the same world is recorded? One is reminded of the seemingly endless channels on cable television which give one a superficial impression of endless points of view, but then look frighteningly alike. We can change channels but the same filter on reality remains.56 Do the alternative methods both on painted canvas and on electronic screens really open up new worlds, new realities in the way that Christianity created visions of earth, hell and heaven? There is also a very different way of seeing these developments, as new explorations in the complexity of personal perception and interpretation, and as part of a larger trend towards visualization. This, for instance, is the view of Buckminster Fuller who, in his Critical Path, emphasizes the value of a sphere as a way of getting beyond primitive polarities of up and down.57 His Dymaxion map, which unfolds the surface of the spherical earth onto an icosahedron is an attempt to make all the views of a sphere sides visible at once.58 This map and his Geoscope59 are but two examples of a conscious strategy to expand the range of the visible. Here again we can trace a well established European tradition in this direction, particularly in using instruments and graphs to visualize temperature, pressure and other fundamental features of our environment as Marey60 (1878) documented so marvelously in his classic study more than a century ago; a trend which has been greatly enhanced in the past decades through developments in photography.61 But Buckminster Fuller's vision, which relates to Mandelbrot's in terms of fractals,62 is concerned with much more than seeing hitherto invisible sections of the spectrum. There is a commitment to recording and rendering visible processes in time, which occur so slowly that they are imperceptible in everyday life, phenomena ranging from short term events such as patterns in the the movement of clouds or the growth of fingernails; to longer processes such as the growth of trees and long term changes such as the shifts in continental plates. In this view, space and time are integrally connected. Progress can be measured in terms of the extent to which we make visible these interdependencies between space and time. Nor is this seen as merely an intellectual game. Fuller sees this as a tool for seeing how best to use our limited natural resources, establish more effective communications and optimize the realties of demogaphics and potentials of mass production. In this view Termes' explorations can be seen as a personal expression of a universal tendency which is helping our long term survival on the planet. 5.I.A. vs. A.I. It is instructive to compare these artistic experiments with other developments in technology. In the 1970's, there was a great emphasis on artificial intelligence (AI); the assumption being that computers could potentially do everything faster and better than humans. One merely needed to imitate the structure of the brain electronically and all would be well. Many promises were made: few were kept. Two schools developed: one rule based, the other knowledge based. In the meantime some researchers at the frontiers make clear distinctions between some tasks in which computers far excel human capacity and other tasks where human abilities remain paramount. Hence, Frederick Brooks63 has, for instance, developed strategies which combine human faculties and electronic components in order to extend capacities of the senses, for which he has coined a new term intelligence amplification or augmentation (IA). Rather than replacing humans the new quest is to extend their capacity.

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A similar quest has long been connected with technology in the European tradition where machines have literally been used as extensions of human capacities. In many cases these were simple physical extensions of limbs: a crane for instance permitted a person to lift heavier things higher than with one's unaided limbs. In some cases these extensions were also sensory as in the case of telescopes and microscopes. The American innovations64 are fourfold. First they apply the notion of extension to electronic machines. Second they create new interplays between limbs and senses. Third they deal with scale in a novel way. Fourth they introduce the principle of sensory transducers. All but the first of these innovations require explanation. The most famous application of these initiatives has, of course, been the development of head mounted displays which produce a sensation of virtual reality (VR). The mass media have tended to see this largely as some kind of new toy, emphasizing its potential entertainment value or dramatizing the principle of being able to have the sensation of touching someone not actually present, even speculating wildly on new possibilities of making love at a distance. However both the concerns of those at the frontiers and the implications of their work are rather more serious. The idea of the head mounted display itself is not new. Its immediate predecessors65 are Morton Heilig's experience theatre (1955) and his sensorama simulator (1962) and its roots can be traced via the quests for stereoscopic vision that began seriously with Wheatsone (1832), back to the eighteenth century fascination with dioramas and panoramas. But whereas these early attempts at recreating the visual environment involved enormous rooms, the head mounted display requires only two miniature television screens positioned directly in front of each eye. Interestingly enough these images involve a type of spherical perspective which the eye perceives as rectilinear, just as optical researchers since the time of Helmholtz have been insisting.66 It will be noted that there are curious parallels between this pragmatic use and the aesthetic applications of spherical methods by the artists discussed earlier. Both multiply ways of looking at an object or a scene. The difference is that the head mounted display can be linked with a touch sensitive glove or with a forced feedback arm, such that one can touch as well as see these objects. Instead of just seeing a model of molecules, this new extension of sight and touch allows one to feel how molecular docking works in a model. In September 1991, one of the pioneers in this field, Warren Robinett at Chapel Hill, North Carolina, decided to take these principles one step further by linking the head mounted display and force feedback arm directly with an electron scanning tunneling microscope. This will make it possible to touch and manipulate real atoms and will illustrate dramatically new interplays between limbs and senses, the second innovation referred to above. A third innovation is scale. If one is in a diorama, one needs to change the physical size of the room in order to alter its scale. Building alterations are difficult. They also have definite structural limits.67 One can make a room twice, or even ten times as large, but not five hundred or five thousand times. In the case of the head mounted display one simply needs to adjust the size of the images projected onto the tiny screens and the problem of structural limitations no longer obtains. A room with walls an inch high can be altered almost instantaneously to a room ten times, one thousand or even one million times as large. This means one can move from a viewpoint where one is looking at the exterior walls of a room to a viewpoint where one sees the interior walls of the same room without changing one's own position. It will be noted that this experience, although it explores different aspects of ambiguities between inner and outer, is again related to that of the termespheres. There are also interesting differences. The termespheres can be

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rotated to display a series of viewpoints and changing relations of space in time, but the temporal scenes remain episodes. By contrast a head mounted display introduces a continuum, a dynamic interplay of viewpoints, one dramatic step closer to a virtually real environment. European scientists have traditionally been concerned with rendering visible phenomena which are not perceptible to the naked eye as in the case of infra-red and ultra-violet rays in the spectrum. Sensory transducers, the fourth innovation mentioned above, will translate into visual terms sensations linked with other senses: i.e. hearing, touch, taste and smell. Hence it will theoretically become possible to translate auditory information acquired through ultra-sound techniques such that one can effectively see what one hears. Similarly one will be able to see what one tastes or smells in a new way. Thus far researchers have focussed attention on the practical consequences of these innovations. For instance, the remote action potentials of virtual reality will enable one to operate robots at a distance with all the sensitivity as if one were actually there oneself. Hence if there were a future Chernobyl, one could pilot a robot into the radioactive trouble spot and repair the damage without risk of human lives. Given the potentials of changes in scale, trips through arteries of the human body which were the subject of the science-fiction film Fantastic Voyage two decades ago, could soon become a reality. If termespheres can introduce a whole new range of perceptual puns, games, puzzles and mysteries, imagine what aesthetic consequences these innovations could bring. Ironically after Europeans claimed that perspective was a phenomenon that began and ended with the Renaissance, North America is reminding us that perspective is still very much alive and that even today many of its potential complexities remain unexplored. Some hint of this has recently come from an unexpected quarter: fractals. 6. Fractals. Some persons have remained very critical of the inability of fractals to simulate convincingly visible objects in Nature. A reason for this can be suggested. One of the basic assumptions underlying perspective is the inverse size-distance law which states that if the distance of an object is doubled, its size on the picture plane is one half; if the distance is trebled, its size on the picture plane is one third and so on. Hence size is a function of distance. Mandelbrot's68 (1967) article about the size of the coastline of Britain implicitly challenged this basic premise. Mandelbrot pointed out that if one measured the coastline with a measuring stick one kilometer long, the coast would have a certain amount of corners and a certain length. If, however, one measured the same coast with a scale of one centimeter the same coast would have many more corners and be much longer. The basic assumption underlying Renaissance perspective was that size and shape is simply a function of distance. Mandelbrot's observations call for a modification whereby size and shape is now a function of both scale and distance. Ironically fractals which brought this problem into focus have offered no solution. Their underlying principle of iteration ignores the issue. Iteration assumes that a given shape will remain constant as its scale changes. But if shape and size are independent of scale then they remain a function of distance as they were in the Renaissance. This helps explain why fractals are particularly effective in terms of ornamental patterns and why fractal versions of the natural world look more like fractured imitations of Nature. Meanwhile perspectival rules which take into account both scale and distance have yet to be found.

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Notwithstanding this limitation of fractals in dealing with objects in the everyday visible world, there is serious evidence to suggest that their iterations are helping scientists to recognize new order in what had hitherto been dismissed as random patterns of chaos in nature.69 So fractals can be seen as another dimension of the generalized quest for visualization of which the spheres and polyhedra of Dick Termes, the dymaxion map and geospheres of Buckminster Fuller and developments in virtual reality are all examples; different manifestations of sensory augmentation and ultimately intelligence amplification (IA). 7.Space and Ahistorical Timelessness. Views of outer space also evidence aspects of perception, perspective and representation in North America.70 Sometimes there are clear parallels between terrestial and celestial art (figs. 16-17). For instance, there has been a trend among twentieth century artists to show views from skyscrapers, airplanes or from some undefined aerial view. Occasionally these are dramatic views looking straight down (di su in sotto). Frequently they include a panoramic view that streches to an horizon that is shown as curved. It is striking that a disproportionate amount of space art chooses a similar viewpoint allowing us to look to the curving horizon of a planet, comet, or other object hurtling through space. In 1932 Jobin suggested that the experience of seeing skyscrapers and aeroplanes from the ground necessitated the introduction of curved perspectival features. In retrospect, it was rather the experience of viewing the ground from the heights of skycrapers, aeroplanes and more recently satellites that inspired the ever growing attentiveness to spherical dimensions of perspective. Theoretically space art should introduce us to remarkable new worlds. But in this respect the North American examples are less interesting than we might have hoped. Once we recognize the view from above as a topos we discover that even the clouds from supposedly far off worlds are merely the earthly clouds seen from a different viewpoint. In some cases we are able to trace with some precision how an earthly landscape is transformed into an alien vista as in an English view of a Fault Valley on Mars by Hardy (1989). He began with a drawing of a fault valley at Thingvellir in Wales. This he reversed, expanded the size of the valley floor, exaggerated features of the cliff and changed the colours. Artists from the United States employ a similar process using Death Valley as a model for their extra-terrestial drawings. Frequently these space paintings juxtapose objects in radically different scales: a familiar piece of rock in the unfamiliar scale of hundreds of miles high just as it is colliding with a very familiar earth. Quite often, for no apparent reason, historical monuments become a part of space phantasies. Hence we see Egyptian pyramids or Roman monumental arches hovering in space or standing etched against a barren rockscape. Sir Ernst Gombrich, whose Art and Illusion was the starting point of this paper has offered psychological reasons for the limitations of all human art in terms of his concept of schemata. Individuals get caught up in drawing that with which they are familiar. To continue the earlier theme of devil's advocate one could ask whether there is not another danger evident in American examples, particularly in their space art, namely a tendency to impose a stamp of the present on everything, a stamp which assumes that every other is somehow a copy or iteration of their sameness? Some would say that the concept of foreigner does not really exist in the United States: that persons from other countries are aliens, if unfriendly they are enemy aliens. According to this view even aliens are assumed to be poor copies of persons from the United States, almost a racial version of the neo-Platonic, Plotinian and Manichaean assumptions about the informing of spirit in imperfect matter, iterations that did not quite work. Is it a coincidence that fractals, in

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which the theme of iteration is central, have been used most successfully to envisage alien worlds in films such as Star Wars? Attitudes to time are closely related to this mentality. The stamp of the present allows time to be a great concern but only in terms of everyday experience. History exists theoretically as a subject but not as a reality in the way that it confronts one constantly in Europe. The past is finished.71 What counts is the frontier. In the nineteenth century that increasingly meant some point further west. Once California had been reached some looked to Hawaii, and one wonders if the present day love-hate relationship with Japan and China is not a logical extension of this mentality for some. For others the frontier has evidently become outer space, where history loses, while wild open spaces take on, all meaning; such that space and ahistorical timelessness become keys to perception and representation. But this again is not the whole story. When I sent a draft of this paper to my friend Eric Dobbs he argued that the tradition of becoming a Yankie, a citizen of the United States, often described in terms of a melting pot of cultures, has led to such a mash that everyone feels themselves an alien and sees their country as a nation of proud misfits who had the courage to break away from the conformities and strictures of European culture. In this view the tradition has mixed the cultures so thoroughly that individuals are "simply inundated by an incomprehensible array of cultural variety". They are trained not to see differences and hence are shocked to discover that their inability to distinguish subtle local customs in Europe, which they see as a positive act of not discriminating one culture against another, is often perceived by Europeans as simple lack of discrimination and even as a calculated insensitivity to their traditions. In this view the frontier tradition, with its explorers, adventurers, trappers and dreamers, has been dominated by individuals who saw the New World literally as that, or as the individual in the film, Blade Runner puts it, as "a chance to begin again in a golden land of opportunity and adventure". This provides quite a different context for space-art and for the competition between celluloid reality and live experience which so often puzzles Europeans:

Space-art can be classified among a range of fantastic genres: science-fiction, fantasy, horror, superheroism, action/adventure and maybe to a lesser degree mystery. Each genre appears in painting, movies, television, literature, video-games, sculpture and role-playing games. The variety is mind boggling. And yet all of them in every media have at least one essential characteristic in common: they must be realistic. The audience will enter into the illusions, "Once upon a time...."; "A long, long, time ago in a galaxy far away...." or whatever other device is used such as the closet in the Tales of Narnia or the time machine in Back to the Future, but always there must be a convincing explanation for the fantasies. This phenomenon of earthly artifacts in unearthly places may be related to the need for realism, rather than just an imposition of now on then or there. And at the same time there must be some recognition that our images of past and future otherwheres do resemble our own here.72

Persons of the Old World will find something ironic in this analysis, which reveals that the country which set out to reject the ancient beliefs, superstitions and myths of the European tradition has fallen back into a more universal framework of the mythical-- no wonder Jung is becoming of ever greater interest in the United States. But they must also recognize that there is something very profound in the quest for phantasy and imagination and more recently virtual reality which Europeans too often dismiss as undue attention to Hollywood films and movies. But then Europeans also frequently dismiss

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comics, especially the frivolous types personified by Mickey Mouse, forgetting that this comical figure was invented in the same decade that Hitler used realistic films of rats to characterize the ills of Europe and that in the end comical mice were a healthier alternative to realistic rats. 8. Conclusions. There is a description of America by a witty Englishman as the place " where nothing is so old as the new" and one is tempted to add "where nothing is so similar as the other". The devil's advocate would suggest that perhaps these phenomena are integrally connected, such that a country which has no genuine sense of its own otherness in a temporal scale, cannot understand otherness spatially. In business, other companies are competition which increasingly means that they must be absorbed or simply eliminated. If companies in Japan or Germany have excellent products they are combatted with trade wars either to be destroyed or be made the same. In culture, other countries are perceived as underdeveloped versions of oneself, rather than as places with independent traditions of their own. Hence even the frontiers of space become a copy of the familiar. Is it a coincidence that the concept of the paradigm in the sense of Kuhn was coined in the United States; a concept which incidentally is accepted equally by proponents of both the perceptual and the conceptual schools? In the electronic realm, the United States, more so than any other country, has programmed rules for computer software. These programmes are immensely powerful and very useful. But they also impose an orthodoxy, as Stephen Bingham, the president of the Canadian firm, Alias, calls it. This orthodoxy is not limited to computer programmes: it is weakening, rendering suspect, and even threatening to eliminate entirely the very meaning of other. This is an international problem. Some individuals in Canada are at least conscious of standing in the shadow of a country that sees itself as a shining light. Europe alas is unconsciously absorbing the rhetoric that the world outside of America is underdeveloped, and is adopting as a model precisely those American symptoms which are least interesting: propagation of the stereotype, institutionalization of alternative lifestyles such that only one model remains and the proponents even forget that it is only a model. For some citizens of the United States this is the normal, the truth and nothing but the truth: there is no other. Such individuals would probably not be surprised to find one of the pioneers of virtual reality admitting that: "we seek to eliminate the unexpected by anticipating as much as we can because what we fear most is novel experience".73 Perhaps we need a new approach to others that bridges the extremes. In the United States there is a tendency either to overlook differences of others, or assume that because all are different the problem is not worth individual study, but at least there is a general acceptance. In Europe there are exquisite distinctions in the definitions of others, not just in the special connotations of Viennese philosophical circles74 who draw on their inheritance of Fichte's ideas, but these too often use other to exclude others. We need a new ways of recognizing, acknowledging, representing difference and otherness as instruments of understanding, rather than as tools of exclusion. We need to study multiple viewpoints simultaneously to appreciate differences and to recognize our common humanity. It is perhaps telling that Alfred Schutz, one of the fathers of modern sociology, began his theories of comparative perspectival viewpoints in Vienna and developed it in the United States.75 Our discussion began with a survey of some of the major schools of perception in the United States. We noted their European roots. On the surface these debates are less bitter than in Europe.76 In the United States a member of the conceptual school may happily speak with an opponent in the perceptual school and even treat them as a variant of their

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own party.77 The devil's advocate would suggest that this is because they are unable to appreciate the deeper meaning of other schools and would ask whether there be, moreover, a connection between this new relativism of philosophical viewpoints and the enormous rise of alternative methods of perspective, methods which multiply the number of viewpoints but have no clear side; methods which use mathematics to seem objective but are in fact new studies in the psychology of pictorial representation; new externalizations of inner worlds; attempts to objectify the subjective? Are these methods linked with the American emphasis on psychology78, which has glorified Freud, Jung and their followers in ways that Europe never dreamed?79 Or is this paradoxical quest for multiple individual viewpoints which remain impersonal another manifestation of what Lasch has called the American culture of narcissism?80 In the world of illness there is a trend toward multiple personalities. Are these multiple viewpoints the positive aesthetic equivalents? But even the devil's advocate should recall the dangers of gross generalizations. The European who associates America with the supposed evils of technology, often forgets that technology itself is neutral, and that the same the United States of America also produced the wisdom of Zen and the Art of Motorcycle Maintenance. During the Reagan era there was an attempt in the United Sates to characterize the Soviet Union as the evil empire, as a metaphor for the enemy. The European who speaks of Americans (thus lumping together indiscriminately citizens from South America, Central America, the United States and Canada) is in danger of the same mistake, using America as a metaphor for all the ills of the world and all their fears and ills. In earlier centuries hell offered a convenient cubbyhole for the gamut of negative impulses and troubles. Today, while congratulating ourselves that we have become liberated from such conceptual illusions we are in danger of transposing our spiritual and psychological fears onto material places, dismissing them when in fact, we should be recalling the lines in the preface to Baudelaire's Fleurs du Mal: "Hypocrite lecteur, mon semblable, mon frère". The context of that phrase, it will be recalled, was Baudelaire's claim that the real monster which we have to fight is boredom and indifference (Ennui), the legendary nothing against which Ende's Unending Story was launched and against which the games, comics, videos, films, and other realities however virtual from the United States have thus far provided our most important defence. There are clearly many unanswered questions with respect to these new methods which had their origins in European mirrors five centuries ago. If we look at the positive dimensions of these new spherical and multi-perspectival experiments, they offer extraordinary new examples of non-dogmatic approaches which take into account individual diversity, new interplays of space, time and experience. Europe has its own equivalents. Blind imitation would clearly be wrong. Yet perhaps these experiments can suggest new ways for Europe to keep open and multiply its own viewpoints. In so doing can it keep alive the deeper meanings of other? Is history the secret? If so what mirrors does it need to reflect the secrets it so often hides? Acknowledgments. I am grateful to the Social Sciences and Humanities Research Council of Canada for a Canada Research Fellowship which has given me the time for quiet research and to the Department of External Affairs of the Government of Canada for a travel grant which made it possible to give the lecture version of this paper in Sansepolcro, the ideas for which have emerged in the past years in discussions with my student, Barbara Keyser and friends, Professor Deirdre Vincent, Sergio Sismondo, John Orme Mills, Udo Jauernig and Warren Robinett, each of whom I thank. I am particularly grateful to Eric Dobbs and to Professor Robert Hansen whose detailed comments have been incorporated into the final version.

16

List of Illlustrations

17

1. 1. Maurits Escher, Hand with reflecting mirror, lithograph, 1935.

18

2

3

3 2. Dick Termes, Escher 3, 1983. 3. Ibid.

19

5

4. Maurits Escher, Saint Bavo (Haarlem), black ink, 1920. 5. Ibid., Detail of reflecting surface on chandelier.

20

6

7

6. Dick Termes, God's eye view, 1988. 7. Ibid., Other view of same.

21

8

9

9. Ibid., Pieces of the whole, 1984. 9. Ibid., Other view of same.

22

10.

11

10. Ibid., Detail of figure 8. 11. Ibid., Detail of figure 9.

23

12

13

12. Ibid, Flat-flat sphere, 1968. 13. Ibid., Total photo of the Pantheon.

24

14

15

14. Ibid., Termesspheres. 15. Ibid. Total photos.

25

16

17

16. Gary Meyer, View of Manhatten. 17. Donald E. Davis, The moon's south pole, c. 1980.

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Notes 1 Julian E. Hochberg, "Nativism and Empiricism in Perception" in: Psychology in the Making, ed. Leo Postman, New York: Alfred A. Knopf, 1963, pp. 255-330. 2 Maurice Pirenne, "The Scientific Basis of Leonardo da Vinci's Theory of Perspective", The British Journal for Philosophy of Science, Edinburgh, 3, 1952, pp. 169-185. 3 Sir E. H. Gombrich, Art and Illusion, Princeton: Princeton University Press, 1960. Cf. pp. 131, 247. 4 Nelson Goodman, Languages of Art, London: Oxford University Press, 1969, p.15. 5 Pavel Florenskij, La prospettiva rovesciata e altri scritti, ed. Nicoletta Misler, Rome: Casa del libro editrice, 1983. 6 L. F. Shegin, Die Sprache des Bildes, Dresden: Verlag der Kunst, 1982 (translated from the Russian original of 1970). 7 B. Uspensky, A Poetics of Composition, Berkeley: University of California Press, 1973. 8 Ernst Mach, Wozu hat der Mensch zwei Augen, Leipzig: J. A. Barth 1896. (Populär-wissenschaftliche Vorlesungen). 9 Sir E. H. Gombrich, "The What and the How: Perspective Representation and the Phenomenal World", Logic and Art. Essays in Honor of Nelson Goodman, ed. R. Rudner and I Scheffler, New York: Bobbs Merrill, pp. 19-149. 10 E.g. J. J. Gibson, "On the Information Available in Pictures", Leonardo, Oxford, vol. 4, 1971, pp. 27-25. 11 Cf. Sir E. H. Gombrich, "Mirror and Map: Theories of Pictorial Representation", Philosophical Transactions of the Royal Society of London, London, vol. 270, no. 903, 1975, pp. 119-149. 12 Cf. J. J. Gibson, The Ecological Approach to Visual Perception, Boston: Houghton Miffin, 1979, pp.112-120. 13 Cf. Ernst Mach, The Analysis of Sensations, New York: Dover, 1959 (translated from the original German, Analyse der Empfindungen, Jena: Fischer, 1886). 14 J. J. Gibson, as in note 11, p.112. 15 Rudolf Arnheim, Visual Thinking, Berkeley: University of California Press, 1969, Cover. 16 Suzi Gablik, Progress in Art, London: Thames and Hudson, 1976. 17 Cf. Jean Piaget and Bärbel Inhelder, The Child's Conception of Space, London: Routledge and Kegan Paul, 1956 (translated from the French, La représentation de l'espace chez l'enfant, Paris: Presses universitaires de France, 1948). 18 Sidney J. Blatt in collaboration with Ethel S. Blatt, Continuity and Change in Art: The Development of Modes of Representation, Hillsdale: Erlbaum, 1984, p.39. 19 Parallel with this has been the rise of computer technology which has brought with it a distinction between traditional analogue images and the new digital images. Digital image technology has helped the notion of images being conceptual and there are even tendencies to attempt to read back the roots of this in the nineteenth century. For instance, Jonathan Crary, Techniques of the Observer, Cambridge: MIT Press, 1990, p. 2 asks: "What is the relation between the dematerialized digital imagery of the present and the so-called age of mechanical reproduction?" While disclaiming that his book will engage this question directly, he nonetheless argues that the early nineteenth century introduced a radical break with traditional concepts of images.

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20 Cf. the author's Leonardo da Vinci Studies I, Munich: Deutscher Kunstverlag, 1986, pp. 155ff. 21 On this problem see: L. Dalrymple Henderson, The Fourth Dimension and Non-Euclidean Geometry in Modern Art, Princeton: Princeton University Press, 1983. 22 Cf. M. Pirenne, Optics, Painting and Photography, Cambridge: Cambridge University Press, 1975, p. 146. 23 Guido Hauck, Die Subjektive Perspektive und die horizontalen Curvaturen des Dorischen Styls, Stuttgart: Wittwer, 1879. 24 For a survey of these developments see the author's: "Panofsky's Perspective a Half Century Later", La Prospettiva Rinascimentale, ed.M. Dalai-Emilaini, Florence: Centro Di, 1980, pp. 565-584. 25 W. Blumenfeld, "Untersuchungen über die scheinbare Grösse im Sehraume", Zeitschrift zur Psychologie der Physiologischen Sinnesorgane, Leipzig, Abt 1, Bd. 65, S.241-404. 26 See: A. E. Ames, C. A. Proctor, B. Ames, "Vision and the technique of the eye", Proceedings of the American Academy of Sciences, vol. 58, no.1, February 1923, pp.4-84. This was the same Ames who developed the Ames room and whose student W. H. Ittelson in Visual Space Peception, New York: Springer, 1960, developed what was known as transaction(al)ist psychology. Their initial premise was that perception cannot be studied in isolation. "It can only be studied as part of the situation in which it operates" (p. 13). Ironically, the situations which this group produced, distorted rooms, elongated chairs seen from very carefully controlled single points of view, had very little to do with real life experience which usually permits us to examine objects from various points of view as we move past them. But as my colleague Hansen pointed out these experiments "had everything to do with traditional pictures which are invariably ,monocular and static views." As a result what appeared to them as proofs of the arbitrariness of perspective now appear more useful as entertaining displays in science museums rather than serious challenges to the objectivity of perspective which, in the case of ambiguous objects has recourse to four or six viewpoints rather than just one. 27 A. Ames, Jr. and C. A. Proctor, "Dioptrics of the Eye", Journal of the Optical Society of America, Philadelphia, vol. 5., 1921, pp. 22-844. The quote is from p. 22. 28 Ibid., p.22. 29 Ibid., p. 83. 30 Rudolf K. Luneburg, "The Metric of Binocular Visual Space", Journal of the Optical Society of America, Philadelphia, vol. 440, no. 10, 1950, pp. 627-642. The quote is from p. 627. 31 A. A. Blank, "The Luneburg Theory of Binocular Vision", Psychology : A Study of Science, Vol. 1, Sensory, Perceptual and Physiological Formulations, ed. S. Koch, New York: McGraw Hill, 1962, pp. 395-426. 32 C. H. Graham, "Visual Perception", Handbook of Experimental Psychology, ed. Stevens, New York: Wiley, 1951, pp. 868-920. 33 K. N. Ogle, "The Optical Space Sense", The Eye, ed. H. Davson, New York: Academic Press, vol. 44, 1962, pp. 211-417. 34 M. Pirenne, as in note 21 above, p. 147.

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35 Patrick A. Heelan, Space Perception and the Philosophy of Science, Berkeley: University of California Press, 1983, pp.49-51. 36 Ivan Jobin, Ligne droite ou ligne courbe? Cone ou sphère optique? Montreal: Albert Levesque, 1932. 37 Armand Cassagne, Traité de Perspective pratique, Paris: Fourault, 1897. 38 Jobin, as in note 35, p. 30. 39 For an introduction to this literature see the Foreword by Robert Hansen to his translation of Albert Flocon, André Barre, Curvilinear Perspective, Berkeley: University of California Press, 1987. There will be a more detailed survey in the author's own Literature of Perspective. 40 Robert Hansen, ". This Curving World. Hyperbolic Linear Perspective", Journal of Aesthetics and Art Criticism, Philadelphia, Vol. XXXII, no.2, Winter 1973, pp.147-161. 41 Rudolf Arnheim, "On Hansen's Curved Perspective", Journal of Aesthetics and Art Criticism, Philadelphia, Vol. XXXIII, no.1, Spring 1974, p.424. 42 Alan Turner, "Constructions Based on a Curved Perspective", Leonardo, Oxford, vol.9, 1976, pp. 275-278. 43 H. C. Reggini, "Perspective Using Curved Projection Rays and its Computer Application", Leonardo, Oxford, vol. 8, 1975, p. 307. 44 Michael Moose, "Guidelines for Constructing a Fisheye Perspective", Leonardo, Oxford, vol. 19, no. 1, 1986, pp. 61-64. 45 Marcia Clark, ed., The World is Round, Contemporary Panoramas, New York: The Hudson River Museum, 1987. 46 Tomas Garcia Salgado, Manual de perspectiva modular, Mexico: Trillas, 1988. For an English version see his "A Modular Network Perspective Model vs. Vectorial Models", Leonardo, Oxford, vol. 21, no. 3, 1988, pp. 277-284. 47 For Escher's work see: J. L. Loscher, ed., Leben und Werk M.C. Escher, Eltville am Rhein: Rheingauer Verlagsgesellschaft, 1984. 48 For an analysis of these see Rob Ruurs, Saenredam, Amsterdam: Benjamins, 1987. For colour photographs and schemes of which views the artist used see Gary Schwartz and Marten Jan Bok, Pieter Saenredam. The Painter and his Times, New York: Abbeville Press, 1989. 49 This church designed by Brunelleschi (c.1434) just over a decade after his first perspective demonstrations (c. 1415-1425) is said to have been one of the earliest conscious applications of perspectival effects to physical as opposed to represented architecture. 50 U.S. Patent 4,214,821 on 29 July 1980. 51 Kenneth R. Adams, "Tetraconic Perspective for a Complete Sphere of Vision", Leonardo, Oxford, Vol. 9., 1976, pp. 289-291. 52 See Philippe Comar et Nöel Blotti, Stenopé. La représentation de l'espace, Paris:" Cité des sciences et de l'industrie, 1987. 53 David Hockney, Keynote Address, Society for Photographic Education Conference, State University of New York, College at New Paltz, 1985. Cited in Marcia Clark as in note 43. 54 Buckminster Fuller, Ideas and Integrities, Toronto: Prentice Hall, 1963, p. 26. A more detailed and daunting definition is given on p. 9:

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By "teleologic" I mean: the subjective-to-objective, intermittent, only spontaneous, borderline-conscious, and within-self communicating system that distills equatable principles-characterizing relative behavior patterns- from out pluralities of matching experiences; and reintegrates selections of those net generalized principles into unique experimental control patterns -physically detached from self- as instruments, tools or other devices admitting to increased technical advantage of man over environmental circumstance, and consciously designed to permit his modification of forward experiences in preferred ways. 55 For a thought provoking dscription of recent developments see: Walter Truett Anderson, Reality Isn't What It Used to Be, New York: Harper and Row, 1990, particularly pp. 79-102: "The Meanings of Literature". 56 One important reason is corporate sponsorship which ensures that everything has a stereotyped acceptability. See: Herbert I. Schiller, "Corporate Sponsorhip. Institutionalized Censorship of the Cultural Realm", Art Journal, New York, Vol. 50, no. 3 , Fall 1991, pp. 56-59. 57 Buckminster Fuller, The Critical Path, New York: St. Martins Press, 1981, pp. 544-58. 58 Ibid, pp. 164- 169. 59 Ibid, pp. 161-197, particularly 170-184. 60 E. J. Marey, La méthode graphique dans les sciences expérimentales, Paris: G. Masson, 1878. 61 See for instance, Alex Pomansanoff, The Invisible World. Sights Beyond the Limits of the Naked Eye, London: Secker and Warburg, 1981, and John Darius, Beyond Vision, Oxford: Oxford University Press, 1984. 62 See: Benoit B. Mandelbrot, The Fractal Geometry of Nature, New York: W. H. Freeman and Co. 1977, pp. 21-22. He is consciously going against a strand of modern science which has assumed that visualization was something one needed to get beyond or forget as one came closer to abstract truth. Cf. Arthur I. Miller, Imagery in Scientific Thought, Cambridge, Mass.: MIT Press, 1984. 63 See: Howard Rheingold, Virtual Reality, New York: Summit Books, 1991. 64 Cf. Warren Robinett, "Electronic Expansion of Human Perception", Whole Earth Review, Sausalito, Fall 1991, pp. 16-21; Warren Robinett, Artificial Reality at UNC Chapel Hill, 10 minute Videotape, August 1990, included in SIGGRAPH '90 Video Review; Cf. J. C. Chung, M. R. Harris, F. P. Brooks, H. Fuchs, M.T. Kelley, J. Hughes, M. Ouh-Young, C. Cheung, R. L. Holloway, M. Pique, "Exploring Virtual Worlds with Head-Mounted Displays", Proceedings of SPIE: Non Holographic True Three-Dimensional Displays, vol. 1083, January 1989, pp. 42-52. 65 See Rheingold, as in note 48, pp. 449 ff. 66 Does this mean that Pirenne was wrong and that the conventionalists are right? No. Pirenne's claims about the objectivity of perspective were rooted in the mathematical relation between an original object and its image on a picture plane. Under regular conditions of vision we are certainly not aware of either the concave surface of the retina or the convex form of the outer eye. However in cases where objects are unusually close to the eye the distance from the surface apparently does play a role and hence appears to transform rectilinear lines into curvilinear ones.

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67 See D'Arcy Wentworth Thompson, On Growth and Form, Cambridge: Cambridge University Press, 1917. 68 B. B. Mandelbrot, "How long is the coast of Britain? Statistical Self-Similarity and Fractional Dimension", Science, London, Vol. 155, 1967, pp. 636-638. 69 See: James Gleick, Chaos. Making of a New Science, New York: Penguin Books, 1987. 70 Cf. David A Hardy, Visions of Space, Toronto: McLelland and Stewart, 1990. 71 This attitude is strikingly illustrated in the title of a recent article by Michael Hammer," Reengineering Work: Don't Automate, Obliterate", Harvard Business Review, Cambridge, Mass., July-August 1990, pp. 104-112. 72 Eric R. Dobbs, Personal Communication, 2 November 1991. 73 Myron Krueger, Artificial Reality II, New York: Addision Wesley, 1990, p. 189. Cf. p. 205 where there is a discussion of mainstreaming children as a part of their education. 74 Cf.Alfred Schutz, Collected Papers I. The Problem of Social Reality, ed. Maurice Natanson, Hague: Nijhoff, 1973, pp. 18-19, 25, 31ff.,5, 60, 117,121, 123, 125ff., 133ff., 141, 147, 156, 158ff., 160, 166ff., 170ff, 180ff., 1944ff., 218ff., 244, 2544, 258, 266, , 312, 313,ff., 316ff., 320, 326ff., 328, 353. 75 Ibid., pp. 315 ff.: The general thesis of the reciprocity of perspectives. In a footnote (no. 33) Schutz acknowledges : "The term was coined by Charles H. Cooley, Social Organization, New York, 1909, Chaps III-V, but used in a different sense. We designate by it merely a purely formal aspect of social relationship". This appraoch has evolved into a whole new field of perspective taking of which one example is Diane Thimme Marsh, The Impact of Perspective-Taking Training on Interpersonal Problem Solving, PhD, University of Pittsburgh, 1977. A more thorough study of these trends is being made in the present author's Literature on Perspective. 76 In Europe to be a follower of Professor X can mean that one is not allowed to talk with Professor Y who belongs to a different school, religion or political party. 77 This, of course, is not only an American tendency. The Professor of comparative religion at Oxford, Richard Zaehner used to be criticized for transforming the most exotic of eastern religions into proto-Christian variants. Our point would be that this tendency is even more visible in an American such as Joseph Campbell. 78 There is of course an important nineteenth century context for the pyschological treatment of the senses which emerges via Schopenhauer and Helmholtz. Cf. P.F.H. Lauxtermann, "Five Decisive Years: Schopenhauer's Epistemology as Reflected in his Theory of Colour", Studies in the History and Philosophy of Science, Oxford, vol. 18, no. 3, 1987, pp. 271-291. I am grateful to Barbara Keyser for this reference. 79 For a fascinating study of the larger context for this development see: John Seeley, The Americanization of the Unconscious, New York: Universal Science publishers, 1967. I thank Francesco Battisti for this reference. 80 Christopher Lasch, The Culture of Narcissism, New York: Warner Books, 1979.