"Inverted Perspective in Visual Art and Controversy: A History of a Critical Concept from the Past Century" (In Swedish), 303pp, + 90pp pictures (Uppsala University, 2001) SUMMARY (continued) Back to first page List of Illustrations The Journal of Leonardo has been a vital forum for discussions on matters of perspective, and James J. Gibson's article "The Information Available in Pictures" (1971) resulted in more than one hundred different entries. According to Gibson, optics differs from the system of perspective, because the eye is not a fixed point of projection, but rather a moving point of observation, and the artist making a picture selects a sample of the information available in the ambient optical array. As caricature enhances the information in the picture, compared to photographic representation, it provides a middle ground, where the picture might be true to visual perception, but not to perspective understood as central projection. The theory of perspective seems to lack a way of sorting out constancy phenomenon peculiar to pictures from those in everyday vision. In most perspective pictures, the perceived depth is also lesser than what is given in the ground-plan of the perspective construction. In Leonardo, Kenneth R. Adams (1972) set out to show that flattened space in perspective pictures is parallel to geometrical characteristics of ellipses. His argument was articulated further by Kim H. Veltman (1986), who argued that the tiled floor in perspective paintings like The Flagellation by Piero della Francecsa seems compressed, and looks more like squares when seen from an oblique position than to a correctly placed viewer. The same year, Michael Kubovy wrote in The Psychology of Perspective and Renaissance Art: "Whatever is prescribed by the geometry of central projection is tested against its acceptability to perception." This is qualified by the diverging results of the examples given by Kubovy and Veltman. Kubovy mentioned Raphael, who in The School of Athens used circles to represent spheres avoiding ellipses as marginal distortions, while Piero, according to Veltman, used a diametrically opposed way to obtain the effect of an illusory sphere, painting an egg-form over the head of the Virgin in the Brera Altarpiece. (picture 25b) What is acceptable to perception seems to provide no unambiguous rules, neither in the Renaissance nor in 1986. Kubovy did not observe that Paolo Uccello, representing a horse and its basement in different perspective, produced an inverted perspective zone, where the horse is broken off from the base, but held that it reduced the distorting effects of an oblique viewpoint in the representation of the statue. (picture 26a) Neither did Gombrich, commenting on an artist's awareness of natural reflection, notice that the bottle in a Pompeii painting was represented with a straight standing line, showing its opening as an ellipsis turned towards the observer, with the reflections in the surface of water determining an intermediate ellipsis. (picture 26e) When this same opposition between aspects composed together occurred in a mosaic representing a dog, Gombrich denounced the possibility of a compositional intention, declaring it to be the result of a "clumsy execution". (picture 26d) The constancy phenomenon of ellipses seems to provide a middle ground, where perspective passes into reversed perspective without coming into the focus of interest. In actual uses of the term "perspective", this middle ground is included, and the concept is blurred by this fact to the extent that no line of demarcation is possible between "perspective" and "inverted perspective". This brings the discussion back to its starting point in Goodman's review of Art and Illusion from 1960. "If we are told truly", Goodman wrote, "that in a picture, receding lines like the track of a railroad are represented diverging instead of converging with increasing distance, the information will be the same as in an ordinary picture". Rudolf Arnheim reviewed the history of inverted perspective in Leonardo (1972). He pointed out Glaser's false examples of inverted perspective as resulting from constancy, and eventually denounced the concept of an inverted perspective explaining it in terms of composition on the flat picture surface. Constancy, then, might be understood as correcting or distorting the visual impression, but Gibson would deny that the phenomenal object is a "mere phantasm" resulting from brain activity. Taking his departure in classical optics understood as a science of vision, Vasco Ronchi argued that intense studies of the mechanism of vision lead to the conclusion that "the apparent world is very different from the real world". A spectator tends to underestimate magnitude when it is far away, and constancy works as a corrective only in the range of 20 meters. Gibson's reference to the horizon as a mathematical invariant seems to make it possible to reconcile these diverging opinions. It is quite normal to experience a house or a barn on a field some hundred meters away with reversed convergence of receding lines. Perspective foreshortening plays little role at this distance for a fairy large object like a house, but the road dwindling towards the horizon still might be an apparent triangle as the landscape far away tends to appear to rise vertically. Like the apparent convergence of the roadsides, the apparent divergence in the receding lines of the house seems to signal that the distance is misjudged. Perspective then seems to contain information, disregarding whether it is normal or reversed. Gibson, although he regarded the talk of a system of inverted perspective as nonsense, never claimed that objects or single pictures could not be represented with diverging receding lines. Goodman, on the other hand, argued that a cube represented in reversed perspective could provide more information than a picture in perspective, understood in the context of a relevant symbol system. Gibson seems to be in agreement with Goodman, on the opinion that an object represented in reversed perspective would provide different information than the same object set in standard perspective, but because "one cannot see that way". This was questioned by John L. Ward (1976) in Leonardo. Awareness may have three different focuses in picture perception, he stated. It might concentrate on the material surface of the picture, on space depicted, or one might be trained to see space as depicted on a surface. When seen from an oblique position, pictures in perspective may disturb our capacity to observe form constancy, resulting in the impression of instability of form in the faces of cubical objects. Distortions can lead to the impressions of inverted recession of parallels, but those "will be normally seen as caused and will prompt the viewer to stand at a better position". The awareness of these phenomena is not involuntary, you see the effect only when you are looking for it. In several entries in Leonardo , the Russian engineer Boris Rauschenbach elaborated on a perceptual perspective, which would be truer to perception than Renaissance perspective, and allow for inverted perspective in representations of objects. Constancy in the near range could compensate for the foreshortening in perspective, to the effect that perspective might occur as divergent. "Many persons to whom I demonstrated this possibility now can recognize seeing nearby objects in inverted perspective; they are simply surprised that they have not noticed it before", Rauschenbach wrote in 1983. His perceptual perspective meant modifying Renaissance perspective by introducing a mathematical factor that is dependent on a function defining the effect of constancy. (picture 28b) (picture 28d) Rauschenbach thus provided an attractive analogy. An artistic style might result in, as well as from, the personal transmission of this special awareness. In an essay dedicated to Nelson Goodman, Marx Wartofsky (1972) argued that we see ellipses more or less as circles, depending on our acquaintance with a style, rather than due to natural factors. As late as 1978, Gibson stated that one can learn to see in perspective, observing the natural facts of occlusion, and a picture produced according to the principles of occlusion may induce an "awareness of being in the world", which contrary to being an illusion, might be the only legitimate goal of a depiction. Compared to the occlusion in natural perspective, the representation in reversed perspective diminishes the objects in the foreground. If no further information is included in the picture, this procedure would leave parts of the picture plane empty. Filling out the lacunas might be done by adding information from successive visual acts, so that what is hidden by the near range objects in ordinary perspective may be completed through a slight movement of the head. The picture no longer takes an illusory place in a continuum of geometrical optics, but has to be composed from more or less discrete elements. Panofsky observed in Abraham with Angels and the Sacrifice of Isaac, at San Vitale in Ravenna, an almost palpable example of decomposition of ancient perspective. (picture 3b) The landscape is no longer seen as through a framing window, but the picture is a part of the flat wall under the vault. The tree depicted is not occluded by the frame but is bending in an unnatural way to conform to the curve of the architectural border. This reduction is unfortunate as it tends to be contradicted by the composition itself, which bears witness of an unreluctant use of occlusions. A hut at the far left is occluded by the frame, and the angels are sitting behind an occluding table, their feet being nested, through paradoxical occlusion, with the lathes of the table legs, as remarked by Willats. The humble bending of the tree crown might be understood, in comparison to the vista of the neighbouring absidal conch, as a device designed to give an illusion of vaulting to the flat pictorial field. Gibson commented on another aspect of the problem: "The margins of a picture, the frame, could never be mistaken for the occluding edges of a window", he stated, perhaps focusing on parallax as a possible invariant, resulting from binocular vision or a moving point of observation. Willats (1996) applied new principles adapted from the theory of artificial intelligence in the analysis of pictures. Line junctions, for example, are understood as picture primitives denoting scene primitives, such as corners, occluding contours, and even impossible figures. Configurations, when denoting figures impossible to understand as scene primitives, tend to flatten out the picture by directing focus to the material plane of the picture, he stated. In analysis, these features might provide evidence for stylistic family resemblances between pictures from the traditions of imperial miniatures of Medieval Europe, Russian Orthodox icons, and modernist abstract painting. Willats understood inverted perspective as a distinct projection system, but based on secondary geometry departing from the picture plane. He made a critical point of the lack of understanding for inverted perspective in Margaret Hagen's 1986 study on geometries used in representation. Hagen's commitment to the ideas of Bunim as well as Gibson lead her eventually to disregard examples of reversed perspective as comparable to experiments made by children and uneducated adults. Her attitude was unfortunate, so much more as her comprehensive study in many cases could be applied even to pictures that, under analysis, could be understood as examples of inverted perspective. This enhanced possibility of appreciating the spatial setting take effect when the Adoration of the Magi in a 12th century gospel book from Hardehausen is completed with its counterpart representing Virgin Mary and the Child. (picture 18a) (picture 18b) The latter is spatially set in inverted perspective, originally placed on the opposite side to the picture with the kings. The king, protruding from the picture plane then, pointed out by Hagen as modifying the flatness stated by Bunim, is reaching out to the opposite page in the spatial niche created between the sides, when the book is not fully opened. This is another effect of the same constancy that Gombrich referred to in Ptolemy's Optics, which was known in a contemporary translation into Latin. It creates a solution to the overcutting of the feet, placing the king in front of, but in the same space as the others, without effecting the flatness that disturbed Bunim. Gezenius ten Doesschate tried to show that imaginary space is in conformity with perspective in a naturalistic picture, by letting a person with a single eye observe an illusionist imitation of an occluded room which was partly visible through a doorway. (picture 31d) In binocular vision the situation is changed. Misalignment in the observed horizon, for example, might follow from the combination of two observational points in the case of occlusion, if the head is not held horizontally. The occluding object can become invisible or deformed due to the same reasons. Thus, some of the most disturbing features of Medieval, Byzantine and Orthodox representation of pictorial space might be explained, either from the assumption of an artist deliberately using paradoxical denotation, playing with the possibilities of opposing picture plane to scene space, or from optical effects of a dual observational point. Some of the runic inscriptions in Uppland show strong stylistic affinity with their contemporaries in European painting, when the anomalies in the interlacing of the ornamental snakes are systematically observed. An illuminating example is "U 898" consisting of a rune animal and an interlacing ornamental snake. (Foto ATA, picture 32c) Here the body contour of the snake forms false attachments with runes in several places, and the interlacing is transparent or semi transparent, accordingly, in three places. Misalignments caused by occlusion, sometimes effecting false attachments between inner and outer body contour, create spatial contradictions, without disturbing the splendid composition and rhythmic play. Characteristically, many critics of the twentieth century have declared these traits to be marks of decline, carelessness or clumsy execution. It is possible for a modern artist to work in a pictorial idiom where inverted perspective occurs naturally. Birgit Ståhl-Nyberg was educated at The Royal University College of Fine Arts in Sweden, and later became a teacher at Konstfack in the faculty for Art Teacher Training. In one of her last large works, reversed perspective seems to play an important role for the composition and the narrative. (picture 39c) A red book, in the right hand foreground, is represented with its sides receding in inverted perspective. Alerted by this visual signal, the critic might become sensitive to other deviations from normal pictorial logic in the picture. The thumb overcutting the side of the book causes a misalignment in its contour, analogous to the broken horizon behind the banner. The lower left corner of the book further has an angle matching a corner of a pentagram or a pentagon. All these traits are well integrated in the over all composition of the scene. The Songbook of the Time thus becomes an ambiguous sign, representing the red road to a socialist society, trodden by the youngsters of the socialist party, portrayed from an old photography. It is problematic to talk about the use of inverted perspective in paintings by Ståhl-Nyberg, as she did not work in the manner of a traditional perspective, but used a conception of pictorial space borrowed from Leger, and early Modernism. Reversed perspective necessarily refers to a convention of normal perspective, which cannot be taken for granted in the Modernist tradition. The other aspect of the concept of inverted perspective is its critical usefulness to point out the close affinity between Ståhl-Nyberg's painting, executed almost in the Socialist Realism manner, and a Byzantine wall decoration from the Chora chapel of fourteenth century Constantinople. (picture 7b) It seems possible that the modern artist consciously tried to use a similar pictorial language for her own artistic and political ends. The artist's declared intention was to make the beholder work out the meaning of the painting starting from reflection over deviant details. A parallel composition in a Portrait of St. Luke from a thirteenth century Byzantine Gospel illuminates the possibilities and conditions for interpretation. (picture 22a) The bow in the back of the armchair can be understood as a segment of an ellipsis or a parable, which might be confirmed if the composition is analysed thoroughly. (picture 40f) But this interpretation is extremely strained if you are not tuned in to an excited sensitivity for this kind of compositional play. This might be a reason why the book in Ståhl-Nyberg's picture is hardly recognised as optically deviant even when pointed at. More generally, inverted perspective is often overlooked by critics lacking an appropriate framework. This investigation of the origin of inverted perspective, then, might be understood, in the tradition of Ernst Cassirer, as a search for a framework consisting in prevailing basic operations of perspective analysis, reasonably termed "inverted perspective". Back to first page List of illustrations 1c) Manuskript; folio 89r, Yttersta Domen, Kosmas Indikopleustes Kristen Topografi Vatic. gr. 699, Biblioteca Vaticana, Rom. (Efter Ainalov 1961, fig. 17) 3b) Mosaikutsmyckning på norra bågfältet i koret av San Vitale i Ravenna, Abraham med änglarna och Isakoffret. Efter Demus 1948, fig. 41. 3e) Mosaikutsmyckning i absiden till Torcellokateralen; Apostlar (Efter Demus 1948, fig. 22) 3f) Mosaikutsmyckning i absiden till Torcellokateralen; Apostlar (Detalj av Demus 1948, fig. 2) 4d) Manuskript; Josefs historia, Ashburnham Pentatyken, Bibliothèque Nationale, Paris. Foto Ecole des Haute Etudes (Efter André Grabar, 1968, bild 222). 5f) Manuskript; Faraos dröm och Josefs drömtydning, Wiener Genesis. (Efter Wulff 1907 Abb. 1) 7b) Mosaik; Överräckandet av purpurgarnet, Chorakyrkan i Istanbul (Efter Michelis 1955, fig. 114). 7f) Detalj av barnteckning; Omvänt perspektiv på gatuscen (Efter Wulff 1927, Abb.155) 7g) Fresk; Bröllopet i Kana, Giotto, c.a 1305 i Arenakapellet, Padua (Efter John White 1987 bild 16a). 10b) Väggmålning; Persikor och glaskärl ca 50 e. Kr. Herculaneum, Rom, Nationalmuseum, Neapel (Efter Janson 1991 Färgpl. 23). 12a) Landskap; Mio no Matsubara, Noami (Efter Glaser 1920, Abb.22) 12c) Scen ur Genji-monogatari, Takayoshi Tosa, 1100-tal. (Efter Glaser 1908, Abb. 1) 13f) Wundt, Pseudoskopisk ringfigur. (Efter Wundt 1923, 30) 15a ) Ikon; Den Heliga Treenigheten, Andrej Rubljew. (Efter Willats 1997, Färgpl. 1) 16a) Mosaik: Jungfru Marie födelse, Daphneklostrets kyrka, (Efter Michelis 1955, bild 105. 7c) Detalj av barnteckning; Tunnor (Efter Wulff 1927, Abb.117) 18a-b) Manuskript; Konungarnas tillbedjan, Evangeliarium från Hardehausen, 1100-tal, Kassel Landesbibliothek, teol. fol. 59 r. v. Foto Bätß, Trier (Efter Swarzenski 1931, 60f). 19c) Väggmålning; Korsets träd och Nattvarden, Taddeo Gaddi, Museo dell'Opera di Santa Croce, Florens. (Efter Borsock 1960, pl.13) 19d) Väggmålning; Nattvarden,Uppståndelsen, Korsfästelsen och Gravsättningen, Andrea Castagno, Santa Apollonia, Florence. (Efter Borsock 1960, Pl. 58) 21e) Väggmålning; Petrus helar den lame, Cimabue, San Francesco i Assissi (Efter White 1987, bild. 1a). 25b) Pannå: Madonnan och barnet, sex Helgon, fyra Änglar och greve Federico II da Montefeltro, Piero della Francesca. Altarstycke, Brera , 1472-4. Pinacoteca di Brera. (Efter Kubovy 1986, Fig. 1.5) 26a) Fresk överförd på duk; Sir John Hawkwood, Paolo Uccello 1436, Santa Maria delle Fiore, Florens. (Efter Kubovy 1986, Fig. 7.12) 26d) Mosaik; Cave Canem, Pompeij, Museo Nazionale, Neapel. (Efter Gombrich 1982, Fig. 120). 28e) Diagram över hur visuell perception kan resultera i omvänt perspektiv, figur till artikeln "On My Concept of Perceptual Perspective". (Efter Leonardo 16 1983, s. 29) 28f) Tre sätt att avbilda en stol, figur av Rauschenbach. (Efter Leonardo 16 1983, s. 30) 31d) Doesshates schematiska framställning av experimentet för jämförande av bildrum med perceptuellt rum. (Efter Doesschate 1964, s. 65) 32c) Runristningen U898, Uppland, Norby, Bondkyrko socken. Foto ATA, B21:146. 34a) Föremål som står på mitten av ett bord förskjuts mot betraktaren. a) Den kluvna betraktarpositionen. b)Den sammanfattade inställningen. c) föremålen rycker fram mot betraktaren. (Efter Shegin 1982, Zeichnung 9) 39c)Triptyk i olja; Vägen till frihet och bröd 2, Birgit Ståhl-Nyberg, 157x200cm; den socialdemokratiska ungdomsklubbens utflykt till Gravasund 1928, 1979 (Efter Rusningstid 1992, sidan före 33). 40f) Geometrisk bearbetning av författaren; Ellipskonstruktion i bilden av Evangelisten Lukas, Sturtzenbecker-evangeliariet,1200-tal, MS Gr. 9. Back to first page List of Illustrations