Perspective as a Convention: On the Views of Nelson Goodman and Ernst Gombrich

Leonardo

Perspective as a Convention: On the Views of Nelson Goodman and Ernst GombrichAuthor(s): David CarrierSource: Leonardo, Vol. 13, No. 4 (Autumn, 1980), pp. 283-287Published by: The MIT PressStable URL: http://www.jstor.org/stable/1578105 .

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Leonardo, Vol. 13, pp. 283-287. Pergamon Press 1980. Printed in Great Britain

PERSPECTIVE AS A CONVENTION: ON THE VIEWS OF NELSON GOODMAN AND ERNST GOMBRICH

David Carrier* Abstract-Nelson Goodman's claim that the method of geometric perspective is a convention is contrasted with E. H. Gombrich's view that the method possesses objective validity. The status of those compensations made when viewingperspectivepicturesfrom 'incorrect 'positions is discussed in relation to Gombrich's distinction between the 'how' and 'what' of visual perception. After arguing that accounts of compensation cannot distinguish between perspective pictures and nonperspective pictures or verbal descriptions of the depicted scenes, the author analyzes the concept of convention. He notes that conventions may be thought of in two different ways. Either a convention is arbitrary or it is the result of innate human characteristics and, therefore, in a sense, objective. He suggests that Gombrich 's writings may support the claim that perspective is an objective method of representation. He places this particular debate within the context of Gombrich's general view of art history.

I.

Although many art historians and aestheticians have written about the method of geometric perspective as a convention, the dispute between Nel- son Goodman and E. H. Gombrich best illustrates the issues at stake. Goodman's assertion that perspective is only a convention contrasts dramatically with Gombrich's claim that perspective is objectively valid. And, as Gombrich indicates, only if perspective is more than a convention can his claim be sustained that figurative painting from Giotto to the impressionists is a progressive refinement of methods of pictorial representation.

I will not repeat accounts of the characteristics of geometrical perspective. Carter's compact sum- mary article [1] and John White's book on the history of perspective [2] I find are excellent. My concern is with certain issues that I do not find have been analyzed adequately.

I shall call perspective the geometrical method of pictorial representation, highly developed in the Renaissance, and nonperspective any other method. Usually, even Renaissance perspective pictures do not strictly use a central vanishing point. Nonperspective aspects of such pictures will not be considered, as this analysis is concerned only with aspects of pictures that obey the rules of geometrical perspective.

For perspective pictures, there is only one viewing point from which, when seen with one eye, they present a view corresponding to that of the real scene they depict. I call this the correct viewing point and others incorrect viewing points.

*Dept. of History and Philosophy, Carnegie-Mellon Uni- versity, Schenley Park, Pittsburgh, PA 15213, U.S.A. (Received 28 May 1979).

II.

In this dispute about perspective's being a conventional or an objective method of depiction a number of relatively minor points obscure the central disagreements. I shall begin by dealing with these points.

First, Goodman says that a depiction will soon disappear if one looks at a perspective picture from the correct position [3]. 'Experiment has shown that the eye cannot see normally without moving relative to what it sees.' Two kinds of eye movement are possible: moving the position of the eyes by moving the head, and involuntary scanning or voluntary eye movements with the head held still. Goodman's second reference to experimental work on this topic describes how the eye goes blind when a motionless depiction is placed on the retina by using a special kind of contact lens. Only when both kinds of eye movement are prevented does the eye go blind. Looking at a perspective picture from the correct position through a peephole prevents only head movements. The eye movements still taking place do move the eye away from a focus on the center of the picture. But in practice this distortion will be small.

Second, Goodman presents an objection to at- tempting to make a perspective picture indis- tinguishable from what it depicts [3, pp. 14-15]. 'Even where both the light rays and the momentary external conditions are the same, the preceding train of visual experience, together with information gathered from all sources, can make a vast difference in what is seen.' Some psychologists of visual perception have denied this claim [4]. But since Gombrich does not [5], this is not an objection to his account of perspective.

Third, Goodman claims that 'the assumption ...

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that a picture drawn according to the standard pictorial rules will ... deliver a bundle of light rays matching that delivered by the scene portrayed' is mistaken. But his counter-example is ambiguous as given. 'Railroad tracks running outward from the eye are drawn converging, but telephone poles ... are drawn parallel. By the "laws of geometry" the poles should also be drawn converging. But so drawn, they look... wrong...' [3, p. 16]. If the eyes are at track level, and the head is tilted upward, then, since for each pole its top is further away from the eyes than its bottom, the poles will appear to converge. Standing at some height and viewing the poles with the line of sight parallel to the tracks is the more usual viewing position. Then the poles will be perpendicular to a line from the viewer's eyes and so should be drawn as vertical parallels.

III.

Gombrich and Goodman agree that one does not usually view perspective pictures from the correct position. Goodman concludes [3, p. 13] that perspective is only a convention. Gombrich argues [6] that one must consider how one compensates for seeing these pictures from incorrect positions. Others have discussed these compensations [7]; I will not do so. Apparently these compensations can be discussed independently from questions about the objectivity of perspective. For Goodman that one can learn to see perspective pictures as looking correct from incorrect positions does not demon- strate that perspective is objective. Different sorts of nonperspective pictures would look correct after enough experience [3, p. 36]. A system of representation is somewhat analogous to language in this respect. To the English the grammar of French may seem 'unnatural', not objective. This does not mean that French is based on conventions and English is not. This is a complex matter. Pirenne [7, pp. 216] and Carter [1, p. 848] discuss the globe depicted on the right-hand side of Raphael's 'School of Athens'. They believe that according to perspective the globe should be drawn as an ellipsoid. Is that correct? Gombrich [5, pp. 145-146] says: 'Unlike spheres, circular wire hoops parallel to the picture plane would not project as ovals but as circles.'

Gombrich's distinction between 'what' and 'how' in perception deals with this problem. He discusses this distinction in several of his writings [8]. The essential point is: 'Perspective aims at a correct equation: it wants the image to appear like the object. ... Having achieved this aim, it retires. It does not claim to show how things appear to us, for it is hard to see what such a claim should mean' [9]. That distant objects have a smaller apparent size is the 'objective' part of the 'what' of perception. 'How' they appear smaller is 'subjective'.

This 'objective-subjective' distinction raises deep problems about visual perception. Goodman pro- bably has reason to reject it on 'metaphysical' grounds [10]. My concerns are more practical. How is this distinction related to Gombrich's general

account of perception? In Art and Illusion and elsewhere he argues that all perspective representations are ambiguous. An infinite number of different 'gates' or 3-dimensional configurations correspond to any single geometrical perspective projection onto a flat surface. So to say what one sees of some object from a viewing point is to give one possible interpretation of what one sees. Since 'what' one sees depends upon a subjective interpretation of the gate, the 'what/how' distinction is not the same as the distinction 'what object one sees'/'how one interprets its appearance'.

Here a discussion of Gombrich's account of what is seen from a certain viewing point in the Alps is helpful [11]. He describes how he determined that he was close to, but slightly lower than, the position where a photographer stood when taking a photo- graphic perspective picture of the scene. Determin- ing one's position in this way also could be estab- lished by reference to a verbal description. Take the description: 'From where I am standing, a small forester's hut on the mountain close to me on my left stands in an apparent position just to the left of the peak in the distance.'

Such a verbal description provides one with the information one can obtain from a perspective picture. The verbal description can be converted into a perspective picture and vice versa. Why then should the perspective picture have a privileged status? Gombrich suggests that a verbal description provides a poorer account than such a picture: 'One is taken out of oneself.. . . The viewer sees himself in the environment. . .' [12]. Looking at a picture is a very different experience from reading a description. But Goodman's account of the difference between pictorial and verbal denotations describes this difference without reference to the special status of perspective pictures. This is not an obvious point. J. J. Gibson seems to misunderstand it in one of his Leonardo articles [11, p. 30]. Is reading a description a less vivid experience than seeing a picture as Gombrich seems to suggest? That question is difficult to answer. 'Death in Venice' by Thomas Mana may seem much more vivid than Visconti's cinema film based on the novel. And a verbal description might provide more information about a scene than any single picture. For example, such a description could tell how the scene changes with the seasons and describe what is not visible from one viewing point.

The same points could be made in contrasting perspective to nonperspective pictures. The information provided in a perspective picture could also be recorded in nonperspective pictures. Goodman's example of reverse perspective [13] may be mislead- ing. Although a single object can be drawn using that system of representation, a painting like Constable's 'Wivenhoe Park' is almost inconceiv- able. The further the viewing point from the picture plane of a perspective picture, the larger is the pyramidal section of space included within the space depicted in the picture. Conversely, the further one places oneself from the picture plane in

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the pictorial space of a reverse perspective picture, the smaller the space within the pictorial space. So, although distant objects that are visible in reverse perspective pictures appear large-their size is directly proportional to their distance from the picture plane, while in perspective pictures their size is inversely proportional to their distance-few such distant objects will appear within the picture. That is why reverse perspective is typically used only in portions of pictures. But there are other nonperspective systems of depiction. Consider pictures presented partly in reverse perspective. Such nonperspective pictures could provide the information contained in perspective ones [14].

So, the 'what/how' distinction seems not to tell one whether perspective is 'objective'. To describe the objective character of perception is to tell one what can be seen from a given viewing point. But no appeal to that 'what' can answer Gombrich's question: how do perspective pictures look when seen from incorrect viewing points? Some art historians [15] have felt that these difficulties are insurmount- able. If so, a proof that perspective is 'objective' cannot be provided. Here, a new approach to the difficulties seems to me to be needed.

IV.

Recognizing that one does not usually see perspective pictures from the correct viewing point, Gombrich offers a sophisticated account of how they appear from other viewing points. Goodman can agree with his account and still believe that geometric perspective is only a convention.

Part of the difficulty, I believe, is that the concept of convention needs further discussion. Marcus Hester says that a method is a convention if either 'it is imprecise or... there exists a more precise system that is not habitually used' [16]. I find his account confused. Speaking a language and obeying auto- mobile traffic regulations are good examples of human conventions. But to ask whether dog in English or pes in Czech is a better way of denoting that animal or whether stopping on a red light is more precise than stopping on a green one is meaningless.

Conventions can be thought of in two different ways. One may emphasize the contrast between what is conventional and what is arbitrary. A red traffic light signifying 'stop' is an arbitrary signifier, as is the English word dog. Or one may contrast conventions to what is 'natural'. Perhaps humans have an inborn disposition to learn some codes. Labelling hot water taps 'red' and cold water taps 'blue' might, Gombrich suggests, be more 'natural' than the converse. By 'natural' he means innate in humans; that is, given by their brain structure.

Could geometric perspective be an arbitrary but 'natural' or innate method of depiction? Three different arguments might support this position.

First, I shall sketch the 'evolutionist' argument. Many different nonperspective methods of pictorial representation are found in the world. But people

using these methods tend to abandon them after seeing geometric perspective representations. So, 'perspective is not a mere convention ... but has a basis in reality, even though the evolution of perspective took considerable time' [17].

Unfortunately, it is easy to think of alternative explanations for the adoption of geometric perspective. Perhaps the Japanese [6, p. 148] and others adopted it for the same reasons they adopted Western 20th-century clothing; because industrial and military power gave prestige to Western culture. And, that a practice is widely adopted by societies does not prove that the practice is more than convention. A practice might have been adopted only because it was most convenient or even essential to have everyone follow the same practice [18]. Gombrich's general view of art history is consistent with the 'evolutionist' argument only if certain qualifications are added to it. For him, the history of representational art ends with the aban- donment of geometric perspective in Cubism. A simple 'evolutionist' account would assert that, since Cubism follows Impressionism, Cubism must be a superior representational pictorial system [19].

A second argument refers to the simplicity of perspective representations. Martin Kemp writes: 'The amazing complexity of our visual, perceptual and intellectual structures is ultimately directed towards a kind of cognitive simplicity and stability. Linear geometric perspective is such a system of cognitive simplicity' [20].

Noting that different rules are conventions is consistent with noticing that some rules are simpler than others. A language in which there was a rule that the shortest allowable sentence must have one million words would be clearly useless. But to conclude that perspective is the simplest method of pictorial representation is difficult. Gombrich's own account suggests that for some purposes a map of a scene is simpler than a perspective picture of it.

A third argument takes seriously the suggestion that arbitrary conventions are contrasted to what is innate in humans. Describing Goodman's analysis of induction is helpful. Objects may be classified by the colors green and blue. But, the definitions grue = 'green if examined before time t, blue otherwise', and bleen = 'blue if examined before time t, green otherwise' are understandable [21]. The green/blue distinction seems innate, while the grue/bleen distinction seems artificial. I have found no satisfactory explanation for this common opi- nion. Perhaps, as Goodman suggests, green and blue rather than grue and bleen just happen 'to belong to ordinary language' [10, p. 403, 409]. But conceivably, as he also allows, there may be an explanation for the preferred distinctions in terms of 'some essential features of the human organism'. Perhaps extraterrestrial intelligent beings would think the grue/bleen distinction and nonperspective pictures are 'natural', because their brains are different. Personally, I do not believe that conventions can be explained in terms of innate characteristics of the human organism.

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Sometimes this third argument is based upon the studies of peoples who have not seen perspective pictures, but the results are difficult to interpret [7, Ward, p. 286-7; 17]. Suppose learning to see de- pictions in perspective was easier generally than learning to see nonperspective pictures. Would that show geometric perspective was an objective method of representation?

Gombrich outlines such an argument: 'Lines converging towards the vanishing point ... are understood to be at a right angle to the picture plane, and the orientation of other foreshortened objects of known shape is seen in relation to this system' [6, p. 144]. Nonperspective pictures change appearance with viewing point in more complicated ways than perspective ones, implying that the perspective ones utilize a simpler method and that understanding them might be innate.

Goodman talks about the concept of simplicity in a different way [10, pp. 275-355]. He notes that a mathematical proof is regarded as superior if it has fewer axioms than an alternate one and that a scientific theory is chosen that explains the evidence with the fewest assumptions. Even if one assumes that extraterrestrial intelligent beings would do the same, they might not agree that perspective is the simplest form of pictorial representation. N. Chomsky makes an analogous point in claiming that human languages have nontrivial features in common that make natural languages the simplest to learn. Goodman does not agree with him [22].

In Part III, I suggest that discussions about how one compensates for seeing perspective pictures from incorrect viewing points are irrelevant to the debate about perspective as a convention. These discussions by other researchers supported my conclusion. But my account of conventions shows why that suggestion may be mistaken. Any analysis of how perspective pictures look correct from incorrect viewing points could be matched by an account of how one compensates for seeing nonperspective pictures from different viewing points. But, if the account of how one compensates when viewing perspective pictures is simpler, then one would have reason to believe that perspective is an innate and objective method of representation.

There is one crucial difference between perspective and nonperspective pictures. It makes sense to speak only of compensating for not seeing perspective pictures from the correct viewing point. One can describe how nonperspective pictures look from different viewing points, but there is no correct viewing point for them. According to the argument sketched in this part, then, the special status of perspective depends on two facts: (1) With perspective pictures, the compensations from incorrect viewing points are relatively simple; (2) the effect of the compensations is that one sees the picture as if one were seeing it from the correct viewing point. I have considered only how one successfully compensates for perspective distortions when looking from incorrect viewing points. At least some aspects of perspective pictures are not compensated for, as I

pointed out in Part III. This is a way the dispute about perspective might

be resolved. Even if Gombrich's arguments that perspective is 'natural' or nonconventional are not entirely resolved, providing support for them would be important.

V.

I claimed above that Gombrich's analysis of perspective can be understood only in relation to his general view of art history, which requires justification.

His objections to Panofsky's 'perspective as sym- bolic form' are instructive. Panofsky states: 'The retinal image ... shows the shapes of things pro- jected not on a plane but on a concave surface... the eye actually projects not on a plane but on the inner surface of a sphere' [23]. Hence, perspective cannot be precise, since 'the surface of a sphere cannot be unrolled on a plane'. But, one cannot see the surfaces of one's retinas. So the fact that the retinas are curved tells one nothing about whether perspective is a convention.

Panofsky concludes that perspective can 'only be understood as arising from an entirely distinct and even specifically modern sense of space or ... as a fixing and systematizing of the external world and as an extension of the ego's sphere'. Gombrich criticizes such historicism in some of his published works [24]. He finds Panofsky's view of perspective perplexing: 'Much ... has been written about perspective and the claim... that this new style reflects the ... new Weltanschauung, centered on man and on a national conception of space. But cannot Occam's Razor be applied to these entities? Can it not be argued that perspective is ... a method of representing... any scene as it would be seen from a certain vantage point? If it does, Brunelleschi's perspective represents an objectively valid inven- tion' [25].

The general aim of historicism is to eliminate the notion that there is objective truth. Each hypothesis is taken to be an attempt to explain how the 'truth' of the world is understood by humans in a specific historical period.

Often the claim that perspective is only a convention is linked to historicism. Perspective is often thought of as the way of depicting visual aspects of the world that reflect the mode of depiction used by many of the artists of the Renaissance [23]. But, although Goodman does think that perspective is only a convention, he is not an historicist. I shall not discuss the way his view of art history differs from that of Gombrich.

Gombrich's plea for pluralism offers a statement of his position. 'If reasoned criticism of fundamen- tals [of intellectual history] will again be en- couraged, the process of trial and error should result in a real advance' [26]. Giving up belief in the objective character of perspective and of other science-like aspects of visual art would end the tradition of Western art. Most artists in this tradi-

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tion 'have felt involved with the solution of problems rather than with the expression of their personality' [27]. Ending the tradition of problem- solving may lead to work like Duchamp's found object 'Fountain' (a commercial urinal) [28]. Gom- brich says: 'I think the glorification of this kind of schoolboy joke and the role it has ... in debates about art is one of the most degrading things that has happened to art since its very beginning...'. He describes himself as 'an unrepentent parochial' [29]. 'The evolutionary series of Greek and Renaissance paintings differ from other evolutions precisely through the admixture of science'. An important part of that admixture is geometrical perspective. He believes that a proof that such perspective is conventional would deny to European painting its special status [30].

REFERENCES AND NOTES

1. B. A. R. Carter, Perspective, in H. Osborne ed., The Oxford Companion to Art, (Oxford: Clarendon Press, 1970) pp. 840-861. See also M. D. Emiliani, La Question de la perspective, translated by J. C. Vegliante, in E. Panofsky, La Perspective commeforme symbolique, translated by G. Ballange (Paris: Editions de Minuit, 1975) pp. 7-35.

2. J. White, The Birth and Rebirth of Pictorial Space (London: Faber and Faber, 1957).

3. N. Goodman, Languages of Art (Indianapolis: Hackett, 1976) p. 12.

4. J. J. Gibson, Pictures, Perspective, and Perception, Dae- dalus 89, 216 (1960) p. 221.

5. E. H. Gombrich, Mirror and Map: Theories of Pictorial Representation, Phil. Trans. R. Soc. London B 270, 119 (1975) p. 140.

6. E. H. Gombrich, The 'What' and the 'How': Perspective Representation and the Phenomenal World, in R. Rudner and I. Scheffler eds., Logic and Art (New York: Bobbs- Merrill, 1972) pp. 141-2.

7. M. H. Pirenne, review of D. Gioseffi, Prospettiva Arti- ficialis, The Art Bulletin 41, 213 (1959); R. Arnheim, Perception of Perspective Pictorial Space from Different Viewing Points, Leonardo 10, 283 (1977). J. L. Ward, The Perception of Pictorial Space in Perspective Pictures, Leonardo 9, 279 (1976).

8. E. H. Gombrich, Means and Ends (London: Thames and Hudson, 1976) p. 16 and Ref. 6.

9. E. H. Gombrich, Art and Illusion (Princeton: Princeton Univ. Press, 1961) pp. 252-3.

10. N. Goodman, The Way the World Is, in his Problems and Projects (New York: Bobbs-Merrill, 1972) pp. 24-32.

11. Ref. 6, p. 130. See also E. H. Gombrich's letters in Leo- nardo 4, 195 (1971) and 4, 308 (1971) on J. J. Gibson's article Information Available in Pictures, Leonardo 4, 27 (1971).

12. J. J. Gibson, The Ecological Approach to the Visual Perception of Pictures, Leonardo 11, 227 (1978) p. 232.

13. N. Goodman, On J. J. Gibson's New Perspective, Leonardo 4, 359, (1971).

14. See R. Arnheim, Inverted Perspective in Art: Display and Expression, Leonardo 5, 125 (1972) and D. R. Topper, On Interpreting Pictorial Art: Reflections on J. J. Gibson's Invariants Hypothesis, Leonardo 10, 295 (1977) p. 300, note 10.

15. R. Klein, Pomponius Gauricus on Perspective, Art Bulletin 43, 211 (1961) p. 226.

16. M. B. Hester, Conventionality and Perspective, Leonardo 9, 217 (1976) p. 217.

17. J. B. Deregowski, Illusion and Culture, in R. L. Gregory and E. H. Gombrich eds., Illusion in Art and Nature (London: Duckworth, 1973) p. 188.

18. D. K. Lewis, Convention: A Philosophical Analysis (Cam- bridge, Mass.: Harvard Univ. Press, 1969).

19. S. Gablik, Progress in Art (New York: Rizzoli, 1977). Gombrich states: 'I must reject the blanket assertion that I "dislike modern art"' in The Sense of Order: An Exchange, The New York Review of Books, p. 60, No. 14, (1979). His catalogue Introductions to Kokoschka (London: Victoria and Albert Museum, 1971) pp. 6-9 and Kokoschka (Lon- don: The Arts Council, 1962) pp. 10-15 suggest that what facinates him about Kokoschka is how this artist rejects the major ideas behind much of contemporary painting in the West.

20. M. Kemp, Science, Non-science and Nonsense: The In- terpretation of Brunelleschi's Perspective, Art History 1, 134 (1978) p. 157.

21. N. Goodman, Fact, Fiction, and Forecast (New York: Bobbs-Merrill, 1968).

22. N. Chomsky, Language and Mind (New York: Harcourt Brace Jovanovich, 1972) pp. 172-9 contains his reply to Goodman's criticism, Ref. 10, pp. 69-79.

23. E. Panofsky, Die Perspective als symbolische Form, (V6r- trdge der Bibliothek Warburg, 1924-1925). I quote from an anonymous unpublished translation; hence no page references are given.

24. E. H. Gombrich, In Search of Cultural History (New York: Oxford Univ. Press, 1969) and Art History and the Social Sciences (Oxford: The Clarendon Press, 1975).

25. E. H. Gombrich, The Heritage ofApelles (Oxford: Phaidon, 1976) p. 107.

26. E. H. Gombrich, A Plea for Pluralism, The American Art J. 4, 83 (1972) p. 87.

27. E. H. Gombrich, Art and Self-Transcendence, in A. Tiselius and S. Nilsson eds., The Place of Value in a World of Facts (Stockholm: Almquist and Wiksell, 1970) pp. 127-8.

28. E. H. Gombrich, History as a Critical Tool: A Dialogue, in T. F. Rugh and E. R. Silva, eds., History as a Tool in Critical Interpretation (Provo, Utah: Brigham Young Univ. Press, 1978) p. 52.

29. E. H. Gombrich, Visual Discovery through Art, in J. Hogg ed., Psychology and the Visual Arts (Harmondsworth, Middlesex: Penguin, 1969) p. 227.

30. The editor of Leonardo and one of the Journal's reviewers, also Mark Roskill and E. H. Gombrich made many helpful suggestions on my analysis and drew my attention to many important references. I have included some of Gombrich's suggestions made in his correspondence with me. I am most thankful for his aid. How I have used the suggestions I have been offered is, of course, my own responsibility.

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Perspective as a Convention: On the Views of Nelson Goodman and Ernst Gombrich