Dr. Kim H. Veltman

III    Vision and Representation

1. Introduction
2. Independence of Perspective From Vision
3. Retinal Images
4. Geometrical Space and Visual Space
5. Gibson's Distinctions
6. Status of Perspective
7. Recent Research
8. Conclusions

1. Introduction

    The history of perspective can be seen as a story of changing relations between theory and practice of vision and representation. In Antiquity theories of vision appear to have preceded theories of representation. In Greece, the earliest treatise on representation, according to Vitruvius, was by Agatharcus, followed by those of Democritus (c. 460-370 B.C.) and Anaxagoras (c.500-428 B.C., see appendix 1).

    Theories of vision began earlier and were dealt with in terms of four disciplines: physics, i.e. meteorology, (Aristotle), philosophy (Lucretius), mathematical optics (Euclid) and medicine (Galen). There were two main theories of how visual rays function: one claimed that rays go out from the eye (extramission), another that images come to the eye (intromission). Corresponding to these alternatives were two fundamentally different frameworks for understanding vision. One, linked indelibly with Plato, claimed that knowledge was basically innate and therefore did not require acquisition of new knowledge through visual stimuli. The other approach, challenged by Aristotle, held that there was nothing in the intellect which was not previously in the sense [of vision]. These two frameworks have been linked with various opposites: idealism vs. materialism; rationalism vs. empiricism; nature vs. nurture; intuitional theory vs. empirical theory, deductive vs. introspective, nativism vs. empir(ic)ism or to use modern jargon, analogue vs. digital images. In the history of psychology all these tend to be seen as different names for a single set of opposites. As will be noted below, philosophers and historians claim that they reflect at least two different oppositions. While the two approaches associated with Plato and Aristotle are frequently reduced to simple polarities, it should be stressed that the details of each side are too easily lost in these dualities, all the more so because both sides have their own complex history in the course of which their methods become increasingly intertwined. The historiography of both sides also changes with time such that who ends up on which side also varies. By way of introduction, two examples will be cited to caution the reader that all such schematizations of the schools, including this one should be taken with a grain of salt. In the nineteenth century, for instance, when Helmholtz coined the terms empiricism and nativism to characterize these two schools he simply traced the tradition back to Kant. Subsequent authors, especially in the United States, have reversed the order of the presentation, speaking of nativism and empiricism and tracing the origins of these two schools back to Descartes and Hobbes respectively. Historically we know that Kant was an exceptional individual who set out to find a means of reconciling extreme formulations of these two sides. In the United States, where these polarities are taken more seriously, Kant, is treated as a nativist by Hagen (1980, cf. our fig. 14). We have already noted a similar approach in our discussion of Blatt (see above pp. 8-10*).

    The best survey of these terms is found in an appendix by Hatfield (1990), who noted that philosophers insisted on (271): "a sharp separation between the genesis or causal origin of a thought or idea (innate or learned) and questions about the justification of knowledge (through reason alone or by appeal to sensory experience)". Hence, philosophers distinguished two sets of debates nativism-empirism (nativistisch-empiristisch, a distinction introduced by Helmholtz) and rationalism-empiricism (Rationalismus-Empirismus, two epistemological positions which emerged in the eighteenth century). By contrast, psychologists tended to conflate these two sets of oppositions to one.

    For our purposes, debates concerning these two frameworks are of great interest for five reasons. First, they explain why some persons have recognized the independence of perspective from vision and even claimed the irrelevance of perspective for vision. Second, these debates bear on discussions whether or not the shape of the retina is significant in perception, a theme which has practical implications for artists who think that one might need to use spherical methods in order to draw correctly. Third these debates brought into focus a distinction between visual space and geometrical space, which dovetails with arguments about spherical vs. rectilinear images but also raises larger questions concerning subjective vs. objective and paradoxical trends to an objectification of the subjective especially in the United States.

    Period Empiricists Nativists 1600-1700 Hobbes, Locke Descartes 1700-1800 Berkeley Kant 1800-1850 Associationism -Hartley -Mill Sensory Physiology-Young Psychophysicism-Fechner -Mller -Helmholtz Hering 1900-1950 Ames Gestalt School -Koffka Transactionalism-Ittelson -K"hler -Werthheimer -Arnheim 1950-1960 Constructivism-Gregory Gibson 1960-1970 Perspectivism 1970-1980 Invariant Information Theory 1980-1990 Generative Theory

Fig. 14. Key figures in debates between nativists and empiricists according to Hagen (1980). Fourth, some of the complexities of this debate help us to understand why perspective has become so important for modern psychology, particularly in the school of Gibson. Fifth, there are ways in which these debates bear on the fundamental question of the status of perspective: is it merely a convention or does it represent an objective method? Each of these basic themes will be considered in turn.

2. Independence of Perspective From Vision

    In Antiquity, members of the empirical school included Heraclitus (fifth c. B.C.), Protagoras, Empedocles, Democritus, Aristotle and Epicurus. They stressed the importance of experience and that nothing could be known which had not come through the senses (nihil in intellectu quod non prius in sensu). In the seventeenth century, this idea was taken up by Hobbes (1651). In his work On Man (1658), Hobbes insisted that the analogy between vision and images on screens of camera obscuras was false and that the retinal image played no significant role in the process of vision, as Maurin (1974), noted in an article which also referred to recent debates between Ronchi and Gibson. The ideas of Hobbes were explored further by Locke (1690) who claimed that we begin life with a clean slate (tabula rasa). Sensations in the eye were, however, only the first step of a process. These were combined with their residues called images through the "laws" of association, whence the name associationists for later followers of this school. Berkeley (1709), took this approach much further by insisting that there could be no direct sense of abstract distance, perception of far objects' distances, convergence, of near objects or perception of size. A two dimensional image on the retina was insufficient to determine an object's three dimensional situation. Hence perspectival effects of distance (size perspective, linear perspective and atmospheric perspective) were effectively irrelevant for the visual process, or so it seemed. This approach was taken further by Hume (1739), the associationists, Hartley (1740) and Brown (1820) in England, and subsequently Lotze, Helmholtz, Wundt and Titchener on the Continent. Helmholtz, for instance, claimed that the shape of the retina ought not to have any effect on the shape of the image which we see (see below p. 90), and as Boring (1942) recounts he also explained (31):

how people who lived only on a spherical surface would learn that all parallel lines intersect in two points, how people on an egg shaped surface would eventually realize that circles of the same radius may have different circumferences, how men confined to a plane would never be able to get out of a square and how beings who had four dimensions at their disposal could step out of a sphere as easily as we can step out of a circle.

    The same Helmholtz did important experiments to suggest that visual space may be Riemannian and quite distinct from Euclidean space (see below). Hence, ironically, the same empiricist school which insisted that all our knowledge comes to us through the senses, provided a series of demonstrations and arguments suggesting that there could be no simple link between outside world, projected images on the retina and what we see. Since there was no easy physical explanation for vision, another explanation had to be found. This is very important because it helps us to understand how what began as an empiricist school could become linked with introspectionism.

3. Retinal Images

    Evidence to the contrary came from unexpected quarters. In the late fifteenth century, Leonardo da Vinci, had explored analogies between eye and camera obscura. Kepler (1604), developed this analogy in his Commentary on Witelo (V.2): "I say that vision takes place when the image of the whole hemisphere of the world in front of the eye and even a little more, is formed upon the concave reddish surface of the retina". This idea which was soon taken up by Jesuits such as Scheiner (1619), who used real and model eyes as camera obscuras to demonstrate the principle of inversion of images. The use of camera obscuras as aids in drawing and painting was also well established by this time, and there were even analogies between seeing and painting (cf. below pp. 122-127) and yet curiously enough, seventeenth and eighteenth century artists almost invariably assumed that they would be painting on a flat surface even though they saw on a spherical surface.

    Ironically it was the tradition, linked with innate ideas since the time of Plato and given new life in the seventeenth century by Descartes, that played a key role in emphasizing the importance of retinal images. Descartes did much to characterize animals as reflex machines and to establish the notion that the senses could be treated as purely mechanical processes. Both Leibniz (1714) and Kant (1781) whose ideas are frequently linked with the nativist camp, helped in drawing attention to the retinal image. Another nativist, the sensory physiologist, Johannes Mller, played an ambivalent role in this development. On the one hand his law of specific nerve energies stated that: "external agencies can give rise to no kind of sensation which cannot also be produced by internal causes, exciting changes in the condition of our nerves". This potentially undermined further the importance of analogue type images in the eye, because any impression made by exterior physical images on the retina could be simulated by interior nerve stimulation. On the other hand, the links which he established between surface of the retina and nerve endings gave new impetus to explore these correlations precisely, as was done by Hering and Stumpf, who were linked with both the nativists and the phenomenologists in the tradition of Goethe and Purkinje. With the development of psychophysics by Fechner in the 1850's the curved nature of the retina took on further significance. For since it was now claimed that every response was directly linked to a stimulus, one needed to account for what happened at and behind the retina, which became feasible through Ramon Y Cahal's pioneering work on histology and studies of how the retina became linked with rods and cones. The nativists and phenomenologists eventually led to the Berlin school of Gestalt psychology.

    Although it was particularly the nativists who focussed on the curved nature of the retina and the subjective aspects of vision in general, there was also interest from empiricists (cf. below p. 90*) such as Hermann von Helmholtz, whose detailed studies of the eye revealed that visual space could on occasion perceive straight lines as curved. Although he himself concluded that this had nothing directly to do with the retina, his work sparked further research. Another empiricist, who became interested in these problems through unexpected circumstances, was the artist, A. E. Ames. As he reported in a later article (1921), around 1910, he was painting with his sister and believed that (22): "if they could make an exact reproduction in form and color of a scene they would have a technically satisfactory work of art". To this end they made a set of thirty five hundred colored cards, but found that the results were "tight", "hard" and lacking in atmosphere. 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: "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".

    These themes were taken up afresh by Ames, Proctor and Ames (1923) in an article entitled Vision and the technique of art. The authors acknowledged the pioneering efforts of the artist, Birge Harrison, who had shown "that a picture in its general form should be similar to our retinal impressions" . The authors explored analogies between the eye and camera, making photographs which they believed approximated the way the eye sees. The effects of chromatic aberration, spherical aberration and irregular astigmatism on the retina were discussed, as were effects of depth of field and distortion. It was claimed that the image on the retina of a rectangular grid would be barrel shaped (pl. 47.2), which: "causes straight lines that do not pass through the axis of vision, to be bowed outward in their central portions. It also causes objects away from the object to be imaged in smaller relative size than those near the axis" .

    This led the authors to conclusions which help account for recent trends in variant perspectival perspectival methods particularly in the United States (see below 123*). It will be noted that Ames was also the inventor of the Ames room and related illusions which led to the development of transactionalism. These relied on perspective while calling into question its validity. Ames' visual experiments were carried out at Dartmouth College where Luneburg, who cited him, carried out his studies of parallel lines (see below pp. 93-94*) and came to related conclusions about the Riemannian nature of visual space. Borissalievitch (1923,1926,1950,1953,1955) used the spherical structure of the retina as a point of departure for his quest to find an optico-physiological method of perspective which he believed also accounted for various optical adjustments methods in antiquity. The assumption that the spherical surface of the retina should determine directly the methods with which we represent the world inspired various architects and artists to devise a series of spherical projection methods, including Deininger (1914), Birker (1923), Jobin (1932), M”hrle (1941), Boaga (1948), Schumacher (1952), Flocon, Barre (1963), Bouligand, Flocon, Barre (1964) and others (see below pp. 122-126*). Interestingly enough most of these practitioners have been unaware of the optical, physiological and psychological literature either on the retina in general or on specific debates concerning geometrical and visual space.

4. Geometrical Space and Visual Space

    Descartes' (1637) Discourse on Method, while explicitly concerned with applying geometry to vision, also prepared the way for a mathematical treatment of the psychical and a psychology of the unconscious. Malebranche, in his Research on Truth (1674-1675), developed this Cartesian geometrical approach to vision and established a rationalist theory of vision emphasizing its inborn, innate qualities. Descartes' study of apparent size and problems of visual space perception had intimated that there were potential discrepancies between perceptual space and objective space. Volkmann (1836), whose brother-in- law was Fechner, the founder of psycho-physics, suggested that there might indeed be discrepancies between perceptual and real space, and asked whether direction lines (Richtungsstrahlen) and visual rays (Sehstrahlen) coincided. Volkmann (1858), tried to show that they did. Hering (1862), came to very different conclusions. He claimed that visual directions (Sehrichtungen) had nothing to do with direction lines (Richtungslinien); that visual space was subjective and incommensurable with objective space, i.e. relations of outer things with the surface of the retina. His colleague, Helmholtz, linked with the empiricists and the greatest optical expert of the nineteenth century, stated this more dramatically ( ): For my part I hold it as likely that it makes no difference at all to vision what shape (Gestalt), form, or position the retina has, what distortions the image suffers on its surface, as long as it is equally sharply impressed on the entire surface and neither the shape of retina or the image changes perceptibly with time. In the natural consciousness of an observer the retina does not exist at all. This distinction between physical and visual space was restated by Mach in his Analysis of Sensations (1886):

    The space of the geometrician is a mental construction of three dimensional multiplicity, that has grown up on the basis of manual and intellectual operations. Optical space (Hering's `sight space') bears a somewhat complicated geometrical relationship to the former. The matter may be best expressed in familiar terms by saying that optical space represents geometrical space (Euclid's space) in a sort of relievo-perspective....The space of the geometrician exhibits at every point and in all directions the same properties- a quality which is by no means characteristic of physiological space . In his subsequent Knowledge and error, Mach (1905) devoted an entire chapter to the differences between physiological and geometrical space. Physiological space like tactile space, he claimed, was non- metric, finite, anisotropic and non-homogeneous. By contrast, geometrical, Euclidean space was metric, infinite, isotropic and homogeneous. Hence there was a profound difference between subjective physiological space and objective, geometrical space.

    Lambert (1774), in his treatise on perspective, had raised a related problem, whether the eye perceives painted space in the same way that it perceives physical space in the everyday world. With the rise of photography in the latter nineteenth century this question was reformulated: whether the eye perceives photographic space in the same way as physical space. In cases where a photograph was taken from a near point of view it was found that there were clear discrepancies and that a person viewing the photograph could not get his eye close enough to the picture in order to simulate the experience of the original physical space. To correct this problem, von Rohr (1905,1908), invented a special instrument (called a Verant in German) which aroused considerable attention at the time. Psychologists, notably Aster (1906) and Jaensch (1911), studied conditions under which photographs could produce optimal effects of plasticity. Not everyone was convinced, however. In Italy, for instance, Ovio (1910) studied the properties of printed images seen from oblique angles. In Germany, Rudolf Peter (1921), in a fundamental study, which began by surveying this tradition since the time of Descartes, did a series of experiments to explore how individuals observed the space of photographs of paintings. He used a painting by Vermeer as his sample. Peter claimed that spatial relations can be established in painted space (Bildraum), but that the objects therein and their spatial values involve other relations than those in regular visual space. Both Mach and Peter were important sources for the distinction between subjective and objective space made by Panofsky (see above p. 4*).

    Peter's concern whether or not visual space and depicted space coincide was taken up independently by Doesschate and Fischer (1937), who experimented with how individuals perceive perspectival drawings and found that a perspective drawing of single surfaced objects involves only a perception of space (Raumwahrnehmung) and no sensation of space (Raumempfindung). The authors concluded that one needed a three dimensional object in perspective in order to have a sensation of space. Doesschate (1951), pursued this problem in an article, On imaginary space in paintings, this time explicitly taking issue with Peter's conclusions. He cited Van Mander's anecdote that (47): "onlookers bet for high stakes whether there is a flat picture or a real object and how a German emperor often, by mistake, would pass through a garden painted by Paul Vredeman de Vries". With his friend Fischer, Doesschate designed an apparatus to solve the problem experimentally. They concluded that "it seems, though it is not proved, that normal and imaginary optical spaces are of the same origin and that they show the same structures". Doesschate (1960) returned to these themes in an article on painter's perspective. More recently Gombrich has defended this view in a lively debate with Gibson who claims that physical space and depicted space evoke very different visual experiences (see below p. 95*).

    Zanetti (1968) considered the assumption that the geometry of visual field was a non-Euclidean elliptical or a hyperbolic (Lobatchewsky-Bolyai) projection but concluded that it was a Euclidean projection in keeping with the laws of linear perspective (cf below p. 124*). The problem of visual space vs. geometrical space was also explored by Ronchi (1971, 1974), who distinguished between the apparent world and the real or geometrical world, pointing out that the "contraction of the apparent world is much smaller than the real one". He noted that classical optics had been concerned more with the geometrical world than with the actual experience of the visual world and proposed a new optics to deal with this. At the turn of the twentieth century some individuals such as Daublebsky v. Sterneck (1906, 1908), were trying to bridge the gap between this supposed opposition by insisting that every point in visual space corresponded to one in real space and pointing to the visual angles law. This led (1910) to study of real and apparent monocular directions of sight. The result of these explorations of relations between visual and objective space was a series of comparisons: objective size with apparent size; objective distance and apparent distance; apparent size and apparent distance; objective direction and apparent direction. These debates brought into focus a series of six basic problems which were, and in many cases still are, seen either to prove or disprove the links between geometrical and visual space, namely the curved nature of the retina; the moon illusion; apparent curvature of the heavens; the apparent curvature of beams from a lighthouse, moving past consecutive objects and the perception of parallel rows. The first of these has already been considered above. The rest will be considered in turn.

Moon Illusion

    Already in Antiquity, authors had noted that the apparent size of the moon is larger at the horizon than when seen above against the vault of the heavens. Both Aristotle (fourth c. B.C.) and Ptolemy (c.150) explained this in terms of refraction. Sabra (1987) has studied Alhazen's contribution to this problem.

    The best single article on the subject remains ClarapŠde (1906), who began with a review of nine basic theories concerning the apparent size of the moon:1) refraction (Aristotle, Ptolemy, Destefano 1865); 2) dilatation of the pupil (Gassendi 1642, Stroobant 1865); 3) drop of the crystalline (Schaeberle 1899); 4) comparison (attributed to Descartes by Molyneux 1687, Helmholtz 1866); 5) contrast (Lhr 1898); 6) direction of vision (Gauss 1830, Stroobant 1884, Zoth 1890, Gutmann 1903); 7) overestimation of the angles (Zehender 1899); 8) feableness of peripheral visual acuity (Bourdon 1898); 9) greater distance of the horizon which is linked with three variables 9a) interposed objects (Ptolemy, Alhazen, Witelo c.1270, R. Bacon, Kepler 1604, Descartes, Malebranche 1675, Biot 1810, Wallis 1686, Huygens, Kundt 1863); 9b) aerial perspective (Alhazen, Witelo, Berkeley 1709, Le Cat 1744, Dunn 1762, Euler 1772, Biot 1810, Helmholtz 1866); 9c) shape of the heavens (Alhazen, Witelo, Malebranche, Hobbes 1658, R. Smith 1738, Mairan 1772, Brandes 1827, C.E. Schmidt 183*, K„mtz 1836, Zeno 1862, Helmholtz, Blondel 1888, Wundt, Filehne 1894, Reimann 1902).

    ClarapŠde observed that to him, and Molyneux, the moon seemed nearer when seen above against the vault of the heavens, but since this contradicted the majority of other authors he accepted that one needed another explanation which he sought in "the impression we have that the stars at the horizon, notably the moon, are terrestial objects" . To test this idea he asked 20 individuals to compare the relative sizes of two moons (actually the same size) in a drawing, one near the horizon, the other high in the sky, and found that 14 perceived the one on the horizon as larger, five perceived the two as equal, while one saw the moon at the horizon as smaller than the one in the heavens. In a postscript, ClarapŠde noted that Bourdon (1905) in an analysis of an important study by Mayr (1904) had independently come to the same conclusions, namely that we see objects in the sky as if they were terrestrial objects when they are at the horizon. More recently the problem was taken up afresh by Kaufman and Rock (1962), who used photographs as well as drawings in their tests. Their conclusion was (268): "that the moon illusion depends on the presence of terrain and specifically on the distance effect of the terrain. Eye elevation, color and apparent brightness evidently have nothing to do with the phenomenon".

Apparent Curvature of the Heavens

    The apparent concavity of the vault of the heavens was a well known phenomenon. The Oxford English Dictionary traces English usage of the term to 1591. The astronomer Schickhardt noted that although the course of a comet appeared to be curved it was in fact rectilinear. He also suggested the implications this had for art (see below p. 122*). Filehne (1895, 307), in a significant essay which included an historical survey of the problem, traced the notion of the curvature of the heavens as a conic section back to Hobbes. He traced the competing view of the heavens as a half ellipsoid back to Smith (1755). He noted that Smith's calculations were partly adapted and partly simplified by Drobisch (1854), who was among the first to pose the problem in a way that could be experimentally tested. Fechner (1859) discussed the apparent size of the stars as an example of his so called law of pyschophysics.

    Reimann (1890-1891), made a first attempt to quantify this apparent curvature and suggested that the atmosphere was a factor in this subjective experience. Zoth (1899) suggested direction of sight played a role in both the apparent form of the heavens and the apparent size of the stars. Mach (1908) claimed to have observed luminous rays of the setting sun passing through holes in the clouds which appeared to be curved and reunite at a point opposite the sun.

    Daublebsky von Sterneck (1906), taking as his point of departure Helmholtz's descriptions concerning psychological aspects of the vault of the heavens, provided more quantitative data concerning its apparent curvature. That same year (1906) he proposed a theory of apparent distances. Two years later he also proposed a theory for the apparent curvature of the heavens and apparent size of the stars, which led (1908) to a more general theory of visual space (see next section). The same v. Sterneck (1908), challenged by Meinong's psychophysical "law", whereby differences in stimulus (Reizverschiedenheiten) were matched by differences in response (Empfindungsverschiedenheiten), constructed experiments which he believed confirmed this.

    Witte (1918), studied these questions and claimed that objects at infinity appeared to be at a distance of ten kilometers by day, whereas by night everything that was beyond 100 meters appeared to be on a curved surface (see also next two sections). Mller (1918) made the most thoroughgoing study to date of two related problems: the apparent vault of the sky by day (Referenzfl„che des Himmels) and of the stars at night (Referenzfl„che der Gestirne). He began with a review, complete with mathematical equations, of three types of apparent vault: section of a sphere; section of a paraboloid and half an ellipsoid. A review of major contributions followed including Reimann (1890, 1891), von Sicherer (1904), Figee (1906), A. Mller (1905 etc.), Ernst (1904), Nijland, Bourdon (1899) and von Sterneck (1906, 1907). With reference to the vault of the heavens he identified a series of factors: day and time of the observations, visual angle, saturation of the colour of the blue sky, kind and density of the clouds, distance of the horizon, range of visibility, direction of the heavens and characteristics of the landscape. In the case of the apparent size of stars he listed as additional factors: height, colour and intensity of the star, general condition of the air, and characteristics of the horizon: i.e. whether it be lined with trees or houses. Mller considered both physiological and psychological aspects and referred also to related experiments involving beams from a lighthouse and parallel rows. More recently Barthel (1953) has broached problems of apparent curvature of the heavens in a popular article.

Apparent Curvature of Light from a Lighthouse

    Apparent curvature of light from a lighthouse emerged as a special instance of the larger problem concerning apparent curvature of the heavens. Bernstein (1904) reported on a lighthouse on the island of Helgoland of which the electric lightbeam could be seen to the horizon. Having observed the apparent curvature of its beams under various conditions Bernstein claimed that one needed to make a distinction between the space of visible objects (Raum der sichtbaren Objekten) and the space of observation (Raum der Anschauung). As he pointed out, these findings raised questions concerning Reimann's (1890-1891) claims that atmospheric effects alone could account for the shape of the heavens. Bernstein noted that both Gauss (1880) and Zoth (1899) had mentioned direction of sight as a factor in this phenomenon and added a further complicating factor of his own. If one stands on a hill the direction of sight does not alter substantially with respect to the horizon. Nonetheless, the zenith appears closer and the heavens appear flatter whether the hill is twenty, fifty or one hundred meters high.

    Doesschate and Fischer (1939), returned to this problem citing their own experiments with the beacon at the airport in Soesterberg. They discussed the problem of apparent curvature of the heavens, cited as insufficient Dunoyer's explanation in terms of curvature of the retina and the distortion of images seen in indirect vision, and proposed instead that it was due to the reduced dimensions of optical or visual space which did not exceed 100 meters.

Moving Past Consecutive Objects

    Plateau (1880), studied consecutive images and concluded that optical space did not exceed 51 meters. Doesschate and Fischer (1939), did related experiments looking at luminous sources from a moving automobile and found the limits of visual or optical space to be between 50 and 60 meters.

Parallel Rows

    The problem of how parallel rows are perceived emerged in the seventeenth century in the planting of trees. Fabry claimed and Taquet believed he had demonstrated that one needed to plant trees in the shape of two opposing hyperbolic rows in order that they appear parallel. In the early years of the eighteenth century Monsieur Carr‚ of the French Academy brought the passage of Fabry to the attention of his colleague, Varignon (1720) who, aware also of Taquet's demonstration, offered a more general solution of the problem using the analysis of sines of various visual angles, but came to no clear conclusions. These claims were reviewed in an anonymous (1720) article on the parallelism or apparent non-parallelism of rows or alleys of trees. In England, Robert Smith (1738), in his Compleat system of optics, attributed a similar claim to his friend Martin Folkes. In France, Bouguer ([1755],1767), of photometry law fame, linked Varignon's claim with Malebranche's theories and established that two rows of the trees appear parallel if they are planted in the form of two opposing hyperbolas. He also showed how straight lines could appear curved. According to Doesschate and Fischer (1939, 105), Bouguer was thus the first to describe apparent curvature of visual space and explain it through under-estimation of distance.

    In the early twentieth century, this problem was taken up afresh by Hillebrand (1902), in his alley experiments. Rows of light points were so arranged that they appeared to be parallel and no longer seemed to converge. The resulting divergent curves were found to be comparable to an hyperbola. Sterneck (1906), also concerned with curvature of the heavens, was stimulated by Mach's (1905) distinctions between geometrical and visual space, to develop a theory of apparent distances. Citing Hillebrand's studies and a series of his own experiments, Sterneck suggested that these phenomena could be explained through a basic underestimation of distances for which he offered a formula. This led to more comprehensive psychological studies on Visual space as a result of experience (1907), in which he developed his theory of apparent distances, again showing its relation to Hillebrand's results, with a section on the apparent curvature of the heavens and apparent size of the stars, plus a section on the apparent steepness of mountains. Poppelreuter (1910) explored these problems. Blumenfeld (1913), repeated Hillebrand's experiments under better technical conditions with similar findings concerning parallel alleys. In addition, when he asked observers to set up alleys of equidistant walls, he found that in the distance alleys a) did not appear parallel and straight and b) that in the distance alleys appeared to lie outside the parallel alleys.

    These experiments, as well as the horopter experiments of Helmholtz, served as a starting point for Luneberg (1948), who distinguished clearly between visual space and physical space and attempted to express both in mathematical terms. He claimed that while physical space was Euclidean (240): "the visual space of binocular vision is a hyberbolic Riemannian space." He was careful to note that while qualitative agreement between theory and experiment was ensured, a systematic quantitative test had still to be made. Luneberg (1950), developed these ideas claiming that visual space has a uniquely determined non- Euclidean metric or psychometric distance function (627): "which varies in its numerical parameters from observer to observer. But its general form is invariant; it is the metric of the three-dimensional hyperbolic geometry". In this paper Luneburg removed the restriction on freedom of observation and for the first time introduced a "probable mathematical function involved in motion." Hardy (1949) restated the findings in more dramatic terms (560):

    The theory, then, is that visual space differs from physical space; that if the latter is Euclidean in our vicinity the former is certainly not; that the metric of visual space closely corresponds to, or is identical with, the metric of Lobatchewsky's hyperbolic geometry; that at least two and probably more, personal constants enter into this metric; that these constants (like refractive errors, aniseikonia, stereopsis, etc.) are fairly stable for a given individual but may be modified by such factors as age, correction of refraction, experience, and other factors; that they are probably also closely related to his mechanical and artistic skills and that they may eventually prove to have considerable predictive value in regard to personell selection for special tasks.

    Luneburg's student, Boeder (1957), restated these ideas in an article on the theory of visual space as did his follower, Blank (1959). Not everyone agreed. In the Netherlands a series of experiments on the perception of parallels by Doesschate and Kylstra (1955) found some surprising characteristics but noted that "no one among our subjects observed an apparent curvature of the lines". Doesschate (1959) raised the question whether Cezanne had anticipated Luneburg's claims. In the United States, Luneburg's claims were questioned by psychologists such as Graham (1951) and Ogle (1962). In England, they were challenged by Pirenne (1975). In the United States, they were subsequently proven wrong as noted by Heelan (1983). No simple mathematical formula for subjective dimensions of vision has been found. Even so, the fundamental distinction between the visual space and geometrical space is largely accepted. It is a starting point for J. J. Gibson's distinctions between visual field and visual world.

5. Gibson's Distinctions

    Gibson's (1929) published work began with an experiment on the perception of drawings. Gibson (1933) took as his point of departure Stratton's work on new space habits as a result of wearing glasses which distorted the visual field. Instead of a lens with curved surfaces, simple prisms were used. Gibson found (27) that when a curved line has been perceived for any considerable length of time, it becomes phenomenally less curved than it was at first, and also that after such a period of fixation or inspection, a straight line appears distorted with an opposite curvature. This lead him to conclude that (31): "there is a system of point to point corellations between retinal field and phenomenal field but that it is not a rigid system"

    Gibson (1950), claimed that empty space was irrelevant for the theory of space perception and proposed that the fundamental sensations of space were (367) "impressions of surface and edge". He offered a tentative list of eight essential properties in experiencing a determinate surface: 1) the property of being visually resistant or hard; 2) the qualities of extended colour; 3) the property of being illuminated or darkened; 4) the quality of slant; 5) the property of nearness or farness or distance; 6) the impression of a closed contour; 7) the quality of shape-at-a-given-slant and 8) the quality of size-at-a-given-distance. The main body of his paper focussed on the problem of texture gradients and led him to conclude (384):

    The perspective of texture, as distinguished from the perspective of rectilinear outlines, seems to be a fundamental basis for the impression of a three dimensional environment, or what has been called space. The results of this experiment suggest that the property of the slant of a surface can be assigned a correlate in retinal stimulation, and that perhaps other properties of the phenomenal environment can be similarly accounted for when an appropriate psychophysical method has been applied to them.

    This article heralded themes which Gibson (1950) developed in his first major book The perception of the visual world,themes which were important for at least two reasons. First, his emphasis on lines and contours has become one of the major themes of Gibson's student, Kennedy (see below pp.). Second, his work on texture gradients has spawned a whole subsequent literature, which has since been reviewed by Haber (1974).

    Gibson (1952) made a useful distinction between the visual field and the visual world. Boring (1952), in an important article, claimed that there is a complex way in which the entire tradition of two schools provides a larger background for Gibson's distinctions. The debate between empiricism and nativism can be seen as one between sensation and perception, between operationists (or operational behaviorists) and phenomenologists, which has its nineteenth century roots in a debate between the Leipzig school of Wundt-Titchener and the Berlin school of the Gestaltists. They disagreed about what was immediate and what was mediate. The Leipzig school held that sensations, contents and existential processes were immediate and that from these came derived entitities such as knowledge and meaning. The Berlin school claimed that objects were immediate and that sensations, contents and existential processes were derived from these by inference and abstraction. The Leipzig school focussed on the reduced, unstable space of visual geometry; the Berlin school was concerned with the unbounded, stable space of Euclidean geometry. Stated in naive terms, Leipzig was concerned with what we see: Berlin with what we know, the old debate of world of appearance and world of reality in a new guise.

    Leipzig Berlin Wundt-Titchener Gestalt School Immediate:Sensation, Contents, Existential Processes Immediate: Perception, Objects Mediate: Knowledge, Meaning Mediate:Sensation,Contents,Existential Processes Visual Field Visual World Reduced, unstable space of visual geometry Objective, stable space of Euclidean geometry

Fig. 15. Dichotomies implied by the Leipzig and Berlin schools and reflected in Gibson's work according by Boring (1952).

    According to Boring, the concerns of the Leipzig school became Gibson's visual field; those of the Berlin school were reflected in his concept of the visual world (see fig. 15). In reply to Boring, Gibson (1952) took up the example of railroad tracks extending to the horizon. In one sense they are "seen" to converge in a perspectival sense. This Gibson termed the visual field. In another sense they were "seen" not to converge. This Gibson termed the visual world. Boring had suggested that the visual field was a reduced form of the visual world. Gibson insisted that they were different, or as he later (1966) claimed, alternative ways of seeing. Boring (1952), replied that he did not understand the visual field. There were good reasons for this confusion. At this stage Gibson was only implicitly making a connection between the visual field, (traditionally termed visual space), and perspectival images made by artists. To complicate matters, he was gradually revising his definitions of both perspective and pictures. Already in his Perception of the Visual World (1950), Gibson was clear that perspective did not provide a simple stimulus, as he recalled later (1971, 28): "The perspective of surface texture is not shown, only what are called outlines. In both cases note that it is the optic array that is the stimulus, not the image".

    Gibson, Olum, and Rosenblatt (1955) identified four cues were needed to see the distance of a given object in space: binocular parallax or disparity; linear perspective; aerial perspective, superposition, shading; and motion parallax. They showed that the accepted formulation of motion parallax was insufficient, and offered a more general description in terms of motion perspective, analysed mathematically in terms of the optical flow-pattern reflected from a surface to an eye. They concluded that if these variables were stimuli for perception they (385):"can determine not only the experience of a stable tridimensional world, but provide a basis for the judgments required for the control of locomotion in that world." Gibson (1960) greatly expanded the traditional meaning of perspective:

It is possible therefore to think of perspective as a more general science than the rules of representative drawing, or the description of visual sensations or even the transformations of forms on one abstract plane to forms on another plane. It would be the geometry of the ways in which the light is reflected. Linear perspective of the classical sort would be only a small part of it, for that is merely the perspective of the edges of rectangular objects. There is also the perspective of the textures of inclined surfaces, the gradients of texture-density, the steps of density at the edges of objects, the ratios of densities in different directions and still other variables of higher order.

    Above all there is the perspective of change of position as distinguished from the perspective of position. When the station point moves, the whole structure of the optic array undergoes transformation. A new set of variables arises to confirm the information in static perspective. The parameters of transformation are specific to the motion of the station point; the invariants under transformation are specific to the permanent properties of the environment. The optical array has a unique structure for every station point in the world. And the change in structure of the array is unique for every change of station point in the world. This is essentially what is meant by saying that ambient light carries information about the world.

    As Gibson's ideas developed his concept of a picture changed also. When he wrote his Ecological optics, Gibson (1979), recorded four stages in this development. A first attempt in Gibson (1954) defined a picture as (270-271): "an array of pencils of light coming to the pupil of an eye such that each corresponds in brightness (and hue, if any) to its radiating element of the picture surface". In Gibson (1960b) this was revised to "an array of nested visual solid angles at the station point determined by steps or contrast of intensity and spectral composition of the ambient light". In Gibson (1966b) a picture was redefined as "an array considered as a stationary structure", which was then modified in Gibson (1971) to "an array of persisting invariants of structure that are nameless and formless".

    Gibson's description of the contrast between the visual field (sensation) and the visual world (perception) shifted also. In The senses considered as perceptual systems, Gibson (1968), suggested (236): "that men had not paid attention to the perspectives of things until they learned to draw and to perceive by means of drawings". Hence the making of pictures led persons to discover that they had sensations. At the same time he made bold to suggest (237):"that the data for perception, the invariants of available stimulus information, were quite independent of the data for sensation, the retinal images considered as pictures". He also     discussed two conceptions of information: one, was information about, which permits perception of, the other was information as structure, which allows perception as discrimination.

    In an article on "The Information Available in Pictures", Gibson (1971) took to task Goodman on the analogy between visual and verbal images. Gibson accepted that both pictures and language could be said to have structure and even a sort of grammar, but insisted that (34) "the informative structure of ambient light is richer and more inexhaustible than the structure of language". Gibson (1979,285) developed this distinction: "The essence of a picture is just that its information is not explicit. The invariants cannot be put into words or symbols. The depiction captures an awareness without describing it. The record has not been forced into predications and propositions".

    Gibson (1971) also claimed that there were two basic theories of pictures: a point-projection theory and a symbol theory of pictorial information, linked with the ideas of Kepes and Goodman. The point-projection theory was based on perspective and assumed that a "picture can stand for a real object or scene insofar as the rays from the picture are the same as the rays from the real object". The symbol theory claimed that pictures are symbols which one needs to learn to read much as one needs to read written speech. Gibson rejected both theories and presented his new theory based on the assumption that light can convey information about the world: "This theory makes it possible to distinguish between the pictorially mediated perception of the features of the world and direct perception of the features of the surroundings and yet understand that there is common information for the features that they have in common".

    This deserves further explanation. As we have shown there was a traditional distinction between subjective visual space and objective geometrical space. In his early writings Gibson argued that we actually see both. Hence his distinction between the (subjective) visual field and the (objective) visual world. He now argued that the visual field was irrelevant, that what we see is the visual world and that: "the basis of this direct perception is not the form sensations, or even the remembered sequence of these forms, but the formless and timeless invariants that specify the distinctive features of the object. These are the information for perception".

    He called his new theory ecological optics. In his early work Gibson had linked pictures with the visual field. His rejection of the visual field did not, however, lead him to reject pictures because he now insisted (31): "that an informative picture contains the same kind of timeless invariants that a sequence of perspectives contains". Gibson (1979), developed these ideas in Ecological optics where he claimed that: "if a picture displays the perspective of a scene it puts the viewer into the scene, but that is all. It does not enhance the reality of the scene....The advocates of perspective representation are mistaken, but those who reject perspective as a mere convention are also mistaken".

    Gibson also distinguished sharply between linear or artificial perspective as he termed it, and natural perspective of the optical array (283): "Artificial perspective leads to a set of prescriptions for producing virtual streets, buildings and interiors seen from from a fixed position and a corollary requiring that the painting be viewed with one eye at a unique station point. Natural perspective leads to ecological optics and the concept of the invariant structure in a changing optic array".

    In answer to the question: what does it mean to see in perspective? Gibson now suggested a further distinction between patchwork perspective and edge perspective. He argued that drawing in perspective requires only edge perspective "whereas patchwork perspective is a myth. One can learn to draw the former but not to see the latter". Hence line drawing could specify some invariants of surface layout (a corner, edge, occluding edge, wire, fissure, and a skyline) but not others (shading on a curved surface, penumbra of a cast shadow, texture of a surface, or reflectance of a surface). Already at an early stage, Gibson (1971), had insisted that a picture could not be a substitute for reality. This idea he now restated more dramatically (1980, 291): "A picture requires two kinds of apprehension, a direct perceiving of the picture surface along with an indirect awareness of what it depicts. This dual apprehension is inescapable under normal conditions of observation. The fooling of the eye, the illusion of reality, does not then occur".

    Gibson (1980) pursued this distinction in his last work, "A Prefatory essay on the perception of surfaces versus the perception of markings on a surface": "Surfaces have the kind of meanings that I call affordances, whereas marks on a surface can have referential meanings; that is, the marks refer to something other than the surface itself. A surface does not stand for anything". In this Socratic essay, which raised many more problems than it solved, Gibson (1980, xv-xvi) listed at least ten different meanings for the term image : 1) solid; 2) pictorial; 3) arrested; 4) mirror; 5) camera; 6) photographic; 7) retinal; 8) afterimage; 9) memory; 10) mental image. Gibson's complex work has been cited in detail because he has been central to a number of recent discussions and helps us to understand various developments: why, for instance, psychologists should have become so interested in the perception of pictures (e.g. Hagen 1980); why psychologists now emphasize textures and gradients as part of a quest for invariants and structure; why there is so much emphasis on line drawings (see below p. 139*). Gibson's work also helps us to appreciate why perspective has become so central to psychological debates. What was seen by many as a method linked only with the subjective visual field has now been linked equally with the objective visual world. As a result while Gibson's work has played a role in the development of virtual reality thus linking perspective with new realms of subjective phantasy (see below pp. 138-139), he has also shown that perspective is much more than a convention, and has helped to revive interest in the status of perspective as an objective method.

6. Status of Perspective

    In the fifteenth century, when the rules of perspective were not yet well understood, perspective had various detractors as Piero della Francesca noted in his Perspective of Painting. Nevertheless, both Piero and his younger contemporary, Leonardo da Vinci, were at pains to demonstrate that perspective was based in experience and could be demonstrated mathematically. Sixteenth century authors saw perspective as an important element in their search for causes (cf. above p. 2*). After the demonstrations of Guidobaldo del Monte, Stevin and Desargues, it was generally assumed that perspective was an objective method important for both mathematics and science. Hence the prominent role it played in an illustration of the French Academy of the Sciences and on the title page of Newton's Optics (1740). This assumption continued into the twentieth century as evidenced by Wyllie (1903, p. 195) who claimed that perspective: "is an exact science; and the majority of its rules can be demonstrated with absolute certainty, so that they can no more be disputed than the multiplication table or the propositions of Euclid".

    The development of a clear distinction between visual space and geometrical space in the nineteenth century introduced serious problems for the traditional view that linear perspective corresponds both to what we see and what is there. As we have noted (above p. 54*) Florenskij (1919) used this as a starting point for his claim that linear perspective was but one of many possible methods. Panofsky (lecture 1924-1925, published 1927), was the most famous author of the time to assume that linear perspective must correspond to geometrical space, but was then led to suggest that curvilinear perspective corresponded to visual space. Hence while he did not question the objectivity of linear perspective he brought into discussion its being but one among other methods.

    It is important to recall that a number of (now often forgotten) authors were making similar claims. Riehl (1926, 1961) in an article on "Kinds of Perspective" pointed out how Cezanne, Gauguin, Van Gogh and their followers had pushed the old perspective aside and had destroyed the notion that there was only one correct perspective. Riehl noted that there were at least four reasons why this happened: the spiritual component (geistige Anteil) in a picture; the problem of form, the making of images on the surface of a picture; opposition between painting surface and spatial depth and the problem of binocular vision. He listed a series of alternative responses to these problems ranging from the aspective methods of Egyptian art to parallel persepctive, concluding on an optimistic note that there remained unlimited new possibilities with which to experiment.

    Thouless (1930) in an article entitled The Truth about Perspective? asserted that (121): "we see objects not in the shapes demanded by the laws of perspective but as a compromise between these and the shapes we know that they have in physical reality", which provoked correspondence with Hughes and Boxsius (1930). Thouless (1970), considered another alternative (133):

an experimental situation in which the retinal image remains constant and the reality changes. What is then observed is not that the appeareance remains constant but that this changes in the same direction as does the real character of the object. This result seems to point to a "compromise" explanation rather than a "constancy" one.

    Blanch‚ (1946), ten years before Gombrich claimed that: "Linear drawing even when it is correct as far as perspective is concerned can only with difficulty pass as a manifestation of visual realism.... Drawing has the intellectual character of a schema rather than the sensible character of a copy." Blanch‚ cited examples of alternative methods in the orient: "Hence our system does not have that universality that we were tempted to accord it" ; mentioned the difficulty that children have even in recognizing perspectival rules and applying these when they learn them; distinguished between visual perspective and geometrical perspective, yet maintained that artists reproduce what they "see" while making clear that no artist sees the same, concluding: "For the artist it is not so much a question of painting what he sees as arriving at seeing something which can be painted and which is at the same tiime worthy of being painted to make for himself, in other words a visual reality that is at once delectable to the eye and transposable to the canvas" .

    Wald (1950), argued that the old analogy of eye and camera was still valuable: that both use a lens to focus an inverted image on a light sensitive surface; both possess an iris to adjust to various intensities of light, and both relied on chemical processes. Wald cited examples of optograms, images that had been photographed on the retina. This was an exceptional position. Francastel (1951,7), in an influential book, claimed that linear perspective: "is a conventional method of expression based on a certain conditions of technology, science and of the social order of the world in a given historical moment". Michel (1952), distinguished between visual, constructed and translated space (used in painting). He followed Francastel's view that perspective was a convention and took up Grabar's notion of the intellectual symbol whereby a vision of the soul destroys perspectival space. Kentzler (1954-1955), discussed the limits of perspectival construction. Bandmann (1956) believed that perspective was now only one form among many used to characterize western art from the eleventh to the nineteenth century. Zanetti (1960) attacked the views of both Benevolo (1960, 151), who had claimed that "perspective is based on an intellectual notion of reality similar to the Cartesian one of res extensa" and Francastel (1951), insisting that perspective had a basis in objectivity.

    Kentzler (1954-1955), explored parallels between optical and acoustical ratios; claimed that the limits of undistorted perspective were within an angle of 30 to 40 degrees; that the eye had a hyperbolic image, whereas perspective had a plane image. He consequently suggested combinations of cylindrical and spherical perspective to approximate effects of vision. Malecki (1961) claimed that linear perspective, with its emphasis of a single viewpoint was a particular manifestation of the Renaissance in western culture, that eastern cultures had developed parallel perspective, that the middle ages had its own variants and that twentieth century art was a rejection of the constructed position of a single viewpoint. Merleau Ponty (1961) in an article entitled "Eye and Spirit" cited Panofsky and claimed (210): "The truth is that no method of expression acquired resolves the problems of painting or transforms them into technique because no symbolic form ever functions as a stimulus....Renaissance perspective is not an infallible trick: it is but one particular case".

    Adams (1962), explored the problem of naturalistic painting. He noted how nineteenth century artists often explained this in terms of retinal images and perspective. He cited Ames (1923) as a climax of this tradition which he criticized for two errors: that painters are (35) "concerned with producing a single retinal image in the spectator" and "that the picture itself must resemble the retinal image". He therefore rejected the idea of making curved images (see below pp. 96-100* ). Adams' own explanation for naturalism was (36-39):

the more the perceptual mechanisms used in constructing the picture space operate in their normal manner, the more naturalistic will be the picture....It does not follow from our hypothesis that only one naturalistic treatment is possible for any given subject....An artist can, through his painting, select among alternative sets of cues, which would give rise to the same spatial interpretation.

    Adams (1972) explored the question of "Perspective and the viewpoint" and concluded (217): "The depth of perceived space falls short of that predicted by geometrical hypothesis. The results do not confirm current assumptions about the importance of the mode of viewing. Monocular and pinhole viewing, although they may increase the likelihood that the viewer will experience a full illusion of space, do not increase the apparent depth of that space"

    Meanwhile, Heymann (1962), asserted that three dimensionality depended on a combination of kinaesthetic, haptic and optic experiences which led to three-dimensional perception structures (Wahrnehmungsgestalten) and then to a three-dimensional imagination structure (Vorstellungsgestalt). He argued that cave paintings of France and Spain might be looked at as technical drawings made for practical purposes. Whether a painting was abstract or concrete depended on the relative optical vs. haptic- kinaesthetic components. Rzepinska (1964), took up Panofsky's question of perspective as a symbolic form. The fact that it was part of Renaissance style did not deny its objective scientific values. On the question of curvilinear perspective she asked: if scholars claimed that linear perspective was a convention why then should curvilinear perspective be an objective truth? Bartke (1974), asked rhetorically whether perspective was outdated, noting that there were many examples of contemporary art in the German Democratic Republic which confirmed its continued significance notwithstanding the rise of subjective-idealistic ideologies which had brought irrational views to art and challenged the validity of laws of perspective. He intimated that these laws changed with the advent of photography. Ronchi (1971, 1974), in his discussions of new optics noted that the contraction of the apparent world was much smaller than the real world and thus distinguished also between visual perspective and geometrical perspective. De Chapeaurouge (1975), disagreed with Novotny (1938), who had described perspective as if it had gone unquestioned from the Renaissance until the Impressionists and drew attention to an ongoing conflict between perspective and importance scale (Bedeutungsmassstab), i.e. between optical appearance, significance and truth. Trapp (1977), linked perspective with mimesis but then noted that all art is mimetic.

    In the United States, Snyder (1979-1980), took as his points of departure Gombrich (1960) and Panofsky (1927) to claim: "If there is a paradigm inherent in the invention of linear perspective, as Panofksy urges us to believe there is, it is the model of vision as picture. What Alberti accomplished was not the objectification of the subjective, but rather the externalization of the internal". Kaori Kitao (1980) examined Kepler's (1604) distinction between imago and pictura as a separation of perception from his optics and separation of his science from art. Kubovy (1986), while arguing that perspective was an invention, argued that it could not be dismissed as a convention because of the robustness of perspective, its ability to convey information even when not seen from the original vanishing point. One result of these many views was the emergence of an important debate whether perspective is a convention or an objective method.

Perspective as a Convention

    As noted earlier Florenskij (1922), citing Mach's comments concerning the limitations of linear perspective, referred to it as a symbolic form (two years before Panofsky's lecture and) five years before Panofsky published his Perspective as a Symbolic Form. Panofsky's position was complex. As was noted (p. 4*) Panofsky (1915), initially began from the assumption that perspective was the basis of objectivity and rightness in a painting. Further study, particularly the work of Blumenfeld (1913) and Peter (1921), convinced him that while linear perspective produced objective relations between object and represented image, this did not (necessarily) correspond with the subjective image seen by the eye, to which the curvilinear methods of Antiquity corresponded more closely. At the same time, Panofsky's neo-Kantian assumptions led him to believe that each era had a given world view, theory of vision and representation. He argued that the Greeks had employed a method of spherical perspective. Hence while holding that linear perspective was objective, in that it was the only method to produce an accurate mathematical link between object and representation, Panofsky (1927), implied that it was an alternative to spherical perspective and thus implicitly claimed that linear perspective was a convention rather than an absolute system. Panofsky returned to these ideas in his later writings (1938, 1940, 1943, 1953), as did Bunim (1940), and White (1949-1951, 1957) who added more confusion than clarity through his restatement (see above p. 5*).

    This idea was repeated by Sir Herbert Read (1956, 66) in a sentence which Gombrich subsequently attacked: "We do not always realize that the theory of perspective developed in the fifteenth century is a scientific convention; it is merely one way of describing space and has no absolute validity". Florenskij and his formalist circle had also developed ideas of perspective as a language (cf. above pp. 53-54*). This analogy was taken up by the structuralists and developed in the United States through Kepes (1944) and later Goodman (1968), who asserted that perspective was merely a symbol. Goodman's understanding of technical laws of perspective was minimal as when he claimed (16): "By the pictorial rules, railroad tracks running outward from the eye are drawn converging but telephone poles (or the edge of a facade) running upward from the eye are drawn parallel. By the laws of geometry they should be drawn converging". Goodman appears not to have understood that objects in the same plane as the picture plane do not change in size, (i.e. objects higher or further to the side), only objects in different planes. Nonetheless, Goodman attacked the views of Gombrich and Gibson to claim that (19): "the behavior of light sanctions neither our usual nor any other way of rendering space and perspective provides no absolute or independent standard of fidelity." In Goodman's view perspective was simply a convention.

    Goodman's work sparked a lively debate with major figures such as Gibson and Gombrich (see below) including a series of notes. For instance, Gombrich (1971) raised questions about how Gibson would have an artist deal with a panoramic alpine view. Gombrich (1979) suggested that if only Gibson had seen some German and Austrian Baroque churches or Bramante's altar in Santa Maria presso San Satiro in Milan he would not have doubted the illusionistic potentials of painting. Goodman (1979) insisted that Gibson had misunderstood his comparisons between verbal and visual images.

    Goodman also sparked a series of other commentaries. Wartofsky (1972) expressed Goodman's idea of languages of art in his own terms, claiming that the choice of perspective as a canon of fidelity "is an historical act, which involves the adoption of and interpretation of Euclidean geometrical optics as a theory of vision; and that this theory of vision is false" . Wartofsky (1978) went considerably further. Claiming to develop the ideas of Goodman, he also took up ideas of Gibson to arrive at a position that was the inverse of the theory of the constancies (see below p. ), arguing that visual space was a result of experience with representation.

    Meanwhile, Lycan (1971) drew parallels between Gombrich's duck-rabbit problem and aspects of Wittgenstein's philosophy (see below p. 130*). Couzin (1973) made comparisons between Gibson and Goodman. Hester (1976) believed that he could throw light on Goodman's claims by distinguishing between conventional (something that involves an end to be achieved and the achievement is subject to scientific verification); based on convention and mere convention. Ward (1976) believed that perspective was mainly a convention but nonetheless concluded that (288):

depicted space in perspective pictures can be seen as real without instruction but only to the extent that the information for flatness is reduced enough to be overlooked or to the extent that vieweras learn to distinguish between information for depicted depth and information for flatness. Although the ability to perceive pictorial space increases with practice, even very young children, at least in industrialized societies, seem to have little difficulty in perceiving spatially complex illusions in pictures with a high degree of accuracy.

    Jones and Hagen (1978) explored "The perceptual constraints on choosing a pictorial station point" found that (196): "young children prefer pictures drawn with considerable perspective convergence when they are situated at the station point for those pictures.This evidence lends support to Gibson's idea that pictures carry the same kind of information as the scene they represent." They suggested that experience with paintings where the station point was at least 10 times the size of the pictured object --as Leonardo and Drer had recommended, might explain why adults found strong convergence unnatural and therefore rejected Rosink's (1976) claim that geometrical equivalence necessarily leads to perceptual equivalence. Carrier (1980) returned to the debates between Goodman and Gombrich on the question whether perspective is or is not a convention, noting that a convention can be arbitrary or "the result of innate human characteristics and therefore in a sense objective". These discussions did not tackle the larger questions.

    Steer (1989) set out to explore the implications of Gibson's theories for art history, which led him to attack Bryson's notion that paintings necessarily have a semantic relationship (105-106): The `semantics' and `grammar' of any mode of communication must surely lie within its own realm and in painting they must derive from our visual and kinaesthetic experience. As regards the meanings which paintings convey, a similar point be made. Obviously, what a painting means must be affected by how it means it and since its very nature the visual mode is experiential and the linguistic mode didactic the equation of the two can only lead to confusion. Pictures are not in the least like texts and if we loosely say that we `read' them, or write of their `semantics' or `grammar', it is only because no words exist to describe adequatelly what happens when we look at them. How visual images mean things is the question that most needs exploring and in this exploration new theories of perception are likely to be a vital tool.

Perspective as an Objective Method

    Among those insisting that perspective is an objective method in the past generation, three figures have played a key role, namely, Gombrich, Gibson and Pirenne. Of these the position of Sir Ernst Gombrich is perhaps the most difficult to characterize and requires some understanding of a tradition to which he was reacting. In 1956 Gombrich gave a series of lectures on The visible world and the language of art which were subsequently published (1960) as Art and illusion. Here he attacked the notion that we paint what we see because "seeing" was a complex combination of what we recognize and what we remember. His teacher, Emmanuel Loewy, had focussed attention on the latter factor and described the artistic process in terms of creating memory images. Gombrich chose instead to speak of schema or schemata because he wished to make the point that they were not just rooted in memory. They were open to correction and improvement. Connected with this was his famous phrase: "making comes before matching". Gombrich insisted that this matching process was not simply a case of imitating or copying nature as earlier scholars had assumed. His hypothesis was to reverse the earlier claim of Hanfmann (1957) that (129): "when classical sculptors and painters discovered the character of Greek narration, they set up a chain reaction which transformed the methods of representing the human body- and indeed more than that". Hence the Greek revolution in realism was due to a new interplay between story-telling and image making and this change in function caused a change in form.

    Some of his explanations were less straightforward. Gombrich described the background of perspective in terms of Greek art but left open the question whether Renaissance perspective was a "discovery or rediscovery" (cf. 1975, 132). By not taking a clear stand on this question he left open the precise definition of what perspective is. Moreover, he referred (1960, 131) to "the tricks of illusionist art, perspective, modeling in light and shade" in Greek art, as if perspective were indeed a convention, while challenging (247) those such as Read who claimed that perspective was not an objective method. Gombrich also explored analogies (239, 361-365) between the language of art and the language of words, which through the subsequent writings of Goodman became associated with relativistic views of perspective. To complicate matters he used the example of Ames chairs to explain the principles of perspective and to claim (250) "that any number of objects can be constructed that will result in the identical aspect from the peephole" (Sources, pl. 42). Strictly speaking this is true but it applies particularly to cases where a single object or a single room is involved. It is much more unlikely in the case of an entire context. If a wider definition of perspective is taken namely one which refers to the general laws of integrating information from different planes, then there would be no reason to limit oneself to a single viewpoint and one could test the veridity of a view. By citing only the case with one viewpoint and the Ames example, Gombrich made it appear as if the principles of perspective were more fluid than they in fact are.

    Gombrich (1965), returned to these themes in an article entitled "Visual discovery through art". He now explained the artistic process in terms of recall and recognition and as schema plus correction. Gombrich returned to his claim that the purpose of art that led to perspective (21): "was not so much a general desire to imitate nature as a specific demand for the plausible narration of sacred events" and explored the paradox of inverted recognition (25): "not of reality in a painting but of a painting in reality". He argued that (19) "whatever can be coded in symbols can then be retrieved and recalled with ease" and spoke of perspective as a code. Terms such as symbol, schema and code were also used by Goodman in favour of the relativist camp. However, Gombrich now stated explicitly that code in the sense he meant it was not just a convention or (20): "a fortuitous code that differs from the way we see....A picture painted according to the laws of perspective will generally evoke instant and effortless recognition. It will do so to such an extent that it will in fact restore the feeling of reality including -and this is most important- the constancies".

    To illustrate the constancies Gombrich chose a superb example from Evans' Introduction to color (1948) showing a photograph with a row of posts in perspective (fig. ) of which the furthest one had been reproduced alongside the nearest to demonstrate how we interpret size in context. In "The Visual Image", Gombrich (1972) continued to move away from Goodman's notion of art as a language by establishing further distinctions between verbal and visual images: "We shall see that the visual image is supreme in its capacity for arousal, that its use for expressive purposes is problematic and that unaided it altogether lacks the possibility of matching the statement function of language". In response to Goodman's claim that "perspective provides no absolute or independent standard of fidelity", Gombrich (1972) proposed a distinction between the "what" and the "how" of representation. He claimed that if perspective cannot tell us how we will see a picture, its occlusion principle provides us with objective means of determining what will be seen. By way of example he correlated information from a photograph with information on a map. Gombrich also returned to the problem of the constancies. While he agreed with Gibson that there were problems in trying to link phenomenal world and picture, he noted that pictures were also part of the phenomenal world and that (141) "if the phenomenal world bends, turns and twists, so surprisingly does the perspective representation". He suggested three ways in which a perspective picture is stretched or transformed (149):

The first corresponds to the Thouless effect of the constancies and demands that objects that are drawn as tilted will appear slightly more turned to the beholder than they are really represented. The second, which should be based on the same tendency, would demand that the picture itself, frame and all, would appear less foreshortened than it is; and yet the third, which is the most important and the most interesting, is precisely based on the objective and unnoticed transformations in the plane which are due to this foreshortened view.

    In an essay in honour of Gibson, Gombrich (1974) considered the problem of the vault of heaven, suggested that there were two distinct purposes in vision: one, the practical context of everyday life; the other involving orientation, where veridical perception is irrelevant and proposed that in looking at the limits of the visual world, man might have become aware of the visual field. This led him to claim that the curvature of the heavens: "does not represent what we see, but what we really do not perceive. It marks the transition from the world of solid objects to the field we scan for orientation. These two distinct modes of perception may thus account for the existence of two warring schools in the theory of perspective".

Mach visual space geometrical space Gibson visual field visual world Gombrich optical world (mirror) physical world, experienced world (map)

Fig. 16. Comparison of basic terms in Mach, Gibson and Gombrich.

    In an essay on "Illusion and Art", Gombrich (1973) returned to the ways in which changes in viewpoint cause shifts in apparent orientation, now showing how the street in Hobbema's Avenue (London, National Gallery) tends to follow one around (like the eyes of Mona Lisa) as one moves off to the side (pl. 54.1-3) and compared painting with mirrors and maps. These comparisons were a point of departure in his review lecture at the Royal Society, where Gombrich (1975, 122), used slightly different terms than his predecessors (fig. 16):

There is a common-sense distinction between information about some feature of the physical world (such as a building) and its appearance from a given station point and under given conditions. Maps give us selective information about the physical world, pictures, like mirrors, convey to us the appearance of any aspect of that world as it varies with conditions of light and may therefore be said to give information about the optical world.

    Gombrich pointed out that although maps used conventional signs and symbols the use thereof was not arbitrary. He noted that there were links between maps and photographs, that both were based on projection, which derived from perspective. He pursued his earlier claims concerning the objectivity of perspective in terms of occlusion, the what rather than the how, and provided both an example involving a window (pl. 51.1-4) and a model (pl. 51.5). At the same time, Gombrich maintained his earlier view that perspective projections are not reversible, that a perspective projection "does not give us adequate information about the object concerned, since not one but an infinite number of related configurations would result in the same image". He thus went on to argue (133):

From a logical point of view a perspective representation, therefore, has this in common with a map that it indicates a class of objects, though a class of which only very few members would ever be known in our environment. It is even possible to formulate the problem of illusion caused by perspective representations in this way. We take one specimen of the class -the flat design on the plane in front of us- for another, the solid object over there.

    When he considered the question why pictures are so resistant to anamorphosis that they tend to right themselves he again suggested that we tend to read perspective pictures as maps and thus ignore foreshortenings that occur when they are seen from the side because we "see them as they are". He went on to suggest why appearances, i.e. the sky or distant panoramas from a mountain top, cannot be mapped. In conclusion he argued that linear perspective was more accurate than other methods, while accepting that artists might legitimately choose to explore subjective rather than objective realms of representation, visual experience rather than the physical world. In "Image and code: scope and limits of conventionalism in pictorial representation", Gombrich (1978) claimed that while meaning does not depend on likeness: "Western art would not have developed the special tricks of naturalism if it had not been found that the incorporation in the image of all the features which serve us in real life for the discovery and testing of meaning enabled the artist to do with fewer and fewer conventions". A number of these essays were reprinted in Image and the Eye (1982).

    When Gombrich (1988) returned to these problems in an article on "Western art and the perception of space", he claimed that (5) "the whole subject is in the melting pot" and in a crisis. To explain this he insisted on a clear distinction between the science of optics (concerned with the behaviour of light) and the subject of perception (concerned with visual illusions). He cited a number of classical examples of such illusions using trompe l'oeil (6): "to make it clear that they were not necessarily connected with the portrayal of individual motifs in painting. The creation of illusion and the skill of mimesis, the imitation of reality, went to some extent their own separate ways". Gombrich refused to take a stand on whether the ancients had developed perspective. He claimed that study of geometrical optics led Brunelleschi to bring these hitherto separate strands together when he made his perspective demonstrations in the fifteenth century. He described Alberti's concept of the window; noted that (8): "Part of its strength is due to the fact that it is capable of empirical verification" and went on to emphasize the window's (8) "intrinsic ambiguity. For though it is true that the level squared floor will always project on the window in the way the method predicts, it is also true it that the two-dimensional projection can never suffice to tell us that that floor out there was in fact level and composed of squares". Alberti's procedure, he stressed (8): "rests on...the assumption that we have prior knowledge of the shapes to be represented." According to Gombrich, "the infinite multiplicity of interpretations which Alberti's view through the window permits" raised further questions of psychology.

    Gombrich went on to focus on what he called the radical revolution in perceptual psychology introduced by Gibson whereby our eyes register (11) "not stationary stimuli but the flow of information as we move through the world....Seen from this biological point of view, the fact of traditional perspective that, for instance,a rectangle will project on to the retina or onto the window pane as a trapezoid is not wrong but relatively irrelevant." Indeed, the perspective of a stationary eye, as recorded in a camera "should be regarded as an oddity. Far from telling us how we really see the world, perspective has created a confusion in the mind of psychologists of perception." In the final section of his essay, Gombrich drew attention to recent developements in computer technology, concluding that they could well lead to a new art form as did scene painting in Greece and Brunelleschi's experiment in the fifteeenth century. The third and most articulate defender of the objective dimensions of perspective was Maurice Pirenne. B.A.R. Carter (personal communication) reported that soon after the appearance of White's (1951) article, Pirenne arranged for a dinner in London hosted by Carter and attended by Gombrich, Gregory and White for the purpose of discussing the question of the objectivity of perspective. Carter agreed, Gombrich half agreed, Gregory and White remained unconvinced. Pirenne (1952), in an article entitled "The scientific basis of Leonardo da Vinci's theory of perspective", explicitly challenged the views of those who suggested that perspective was merely a convention, namely, Hauck (1879), Panofsky (1927), Bunim (1940), White (1949-1951) and Pope-Hennessey (1950).

    Pirenne set out to prove that Renaissance perspective was the only natural system of perspective. "With a high degree of approximation it corresponds to the way we actually see the world around us". Pirenne pointed out that:

17. Schema of three basic aspects of vision from Margaret Livingstone, "Art, illusion and the visual system", Scientific American, New York, January 1988, p. 85. it cannot be too much emphasized that the picture drawn in perspective does not by any means aim at representing the retinal image or any pattern of nervous stimulation. Its aim is to send to the eye the same distribution of light as that which the object itself would send. It is for this reason that the problem of perspective is one merely of geometrical optics, not of neuro-physiology.

    Pirenne's key point was as simple as it was essential, namely, that linear perspective establishes an objective, geometrical relationship between an object and its image on the picture plane, which holds true whether or not there is an eye at the vanishing point. In this sense perspective is independent of vision. Pirenne (1958) returned to this claim; again in an article (1963) on "Laws of Optics and Freedom of the Artist" and in his major book, Optics, painting and photography (1970), where he explored in detail relationships between vision, representation and photography, while attempting to create a new framework for understanding the claims of Luneburg and others concerning spherical perception and representation. Evett and Pirenne (1974), produced "An experimental demonstration of the validity of scientific perspective", which was intended as a challenge to authors such as Murray and Murray (1968) who (69): "appear..to cast doubt on the adequacy of scientific perspective to give `an exact representation of physical reality'". Pirenne (1975) returned to these questions.

    Among those who agreed with Pirenne were Guillot (1975) who argued that artists had not yet explored potentials of relief effects with monocular vision; Ward (1976), who challenged the views of Goodman, and Wartofsky (286-287): "Perspective may be used according to certain conventions but perspective itself is not a convention....Pictures constructed in a uniform perspective provide viewers with as complete a correspondence to the real world as is possible on a 2-dimensional surface".

7. Recent Research

    In the past decades the work of Hubel and Wiesel and their students have greatly expanded our understanding of the visual pathways within the brain. As Livingstone (1988), reported there are three distinct pathways: one dealing with color, a second with high resolution static form pereption and a third concerned with movement and stereoscopic depth. (fig. 17). She noted that in the lateral geniculate bodies (b in fig. 18) the small cells in the parvo carry information about colour contrast and the large cells of the magno system carry information about luminance contrast (80).

    Fig. 18. Model of the human eye and location of the three basic aspects of human vision, in Livingstone, 1988, p. 80: From the magno cells information is sent to layer 4b of visual area 1 (c) and then to the thick stripes in visual area 2 (d). There the signals are analysed to give information about motion and depth. Input from the parvo system is sent to the interblobs of visual area 1 and then to the pale stripes in visual area 2, where it is analysed for information about shape. Input from both the parvo and the magno systems is combined in the blobs, where it is processed for colour and luminance. It then passes to the thin stripes of visual area 2 and from there to visual area 4.

    She identified what parts of the brain dealt with static form perception and movement, before these elements were re-integrated in forming a coherent image of the world. one of the fascinating conclusions of this research was that these three elements of vision were interdependent. Livingstone showed, for example, that a change in colour and contrast greatly changed the perspectival effect of spatial drawings such as Escher.

8. Conclusions

    It was shown that already in Antiquity there were two fundamentally different approaches to vision: one assuming that images were innate (Plato), the other relying on the experience of the senses (Aristotle). Within this Aristotelian tradition seventeenth century authors argued that there existed no simple correspondence between images on the retina and visual images as we experience them. In so doing they argued that (linear and atmospheric ) perspective was irrelevant for vision. Ironically, largely through Descartes, it was the heirs of the Platonic tradition, who explored analogies between camera obscuras and the eye, and reinstated attention to the importance of perspective for the visual process. By the nineteenth century research into the physiology of vision established conclusively that the curvilinear physical shape of images on the retina had no simple one to one corespondence with rectilinear perception of images.

    It was shown how this discovery led to a distinction between geometrical space and visual space, which served in turn as a starting point for Gibson's distinction between visual field and visual world. The development of Gibson's theories was outlined and their implications for debates on the status of perspective were assessed. It was shown that there were two dominant schools, one arguing that perspective was merely a convention, a second insisting that perspective was objective; that a major problem in these discussions lay in precision concerning which aspects were or were not objective and concluded that perhaps the most important consequence of these debates lay in how it forced art historians, historians of science, psychologists and philosophers to examine each others' methods.

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Last Update: August 4, 1998