On Gibson's and Goodman's Accounts of Depiction

Leonardo

On Gibson's and Goodman's Accounts of DepictionAuthor(s): Dennis CouzinSource: Leonardo, Vol. 6, No. 3 (Summer, 1973), pp. 233-235Published by: The MIT PressStable URL: http://www.jstor.org/stable/1572642 .

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Leonardo, Vol. 6, pp. 233-235. Pergamon Press 1973. Printed in Great Britain.

ON GIBSON'S AND GOODMAN'S ACCOUNTS OF DEPICTION Dennis Couzin*

Four years ago Nelson Goodman proposed an account of depiction as part of an elaborate theory of symbol systems in his book Languages of Art [1]. J. J. Gibson then radically revised his own long-developing account of depiction in an article entitled 'The Information Available in Pictures' [2] but he was vague about the relation between his and Goodman's accounts. Goodman however published a rejoinder to Gibson [3]. In Part 1, below, I shall discuss a claim by Gibson and its denial by Goodman. In Part 2, I shall show how Gibson's claim is superfluous to his account but that other of Goodman's criticisms do point to important differences between the two accounts of depiction.

1.

Gibson stated that 'no rule or canon of inverse perspective could possibly be systematic, that is, it could not be consistently applied in the practice of projecting a layout of surfaces on a picture-plane' [4]. He gave no reasons for this claim. Is it correct ?

For objects that are spatially limited, there is a simple and systematic way of depicting them in inverted perspective. As in Fig. 1, one projects from a point behind the object to a picture-plane in front of it and, when more than one object-point projects into one picture-point, one makes the one farthest from the projection-point occlude the others. But for objects that are not spatially limited, one cannot take projection-points behind them and so this method will not work. Choosing the point at infinity gives orthogonal, not inverted, perspective.

Goodman disputed Gibson's claim and offered two examples of pictures in inverted perspective [3]. Normally, no number of examples would count against a claim of non-systematicity but Goodman has sketched rectangular boxes in inverted perspective and, although he does not say it, he must believe that if he can depict a rectangular box in inverted perspective, then he can depict anything in inverted perspective. It would seem that given one cube depicted in inverted perspective one can add cubes until one has constructed a complete coordinate system for depicting all the points beyond the given cube. This happens to be false.

Perhaps the easiest way to see this is to let the given cube-picture be the projection of cube A onto

* Department of Philosophy, University of Illinois at Chicago Circle, Chicago, IL 60680, U.S.A. (Received 15 November 1972.)

the picture-plane in Fig. 1. Conditions of recti- linearity require that when one constructs onto the given cube-picture a picture of a second cube directly behind it, one arrives at exactly the same cube-picture as given in Fig. 1 of the cube B behind cube A. And so on. However, one cannot do this indefinitely because after a finite number of steps a cube in Fig. 1 reaches the projection point, so it has an infinite projection on the picture-plane. Thus, there is no system of inverted perspective for depicting the contents of unlimited spaces. For all the hundreds of examples of inverted perspective depictions of things and interiors, there are none of landscapes.

What is to count as a system of perspective ? Such a system must determine how a region of the world is to be depicted in a flat finite picture. There must be a 'rule of location' that determines for all the points of the region corresponding points in the picture. In standard perspective and in the above limited inverted perspective this is a simple projection. But the rule need not be this and it need not even be one that may be applied point-by-point. Also, there must be a 'rule of occlusion', so that, if the rule of location assigns the same picture-point to two world-points, one knows which world-point shows in the depiction (i.e. one knows which color to make the picture-point). In standard perspective and in the limited inverted perspective, the two rules are unified but they need not be. Also, there is typically in a perspective system a sense-of-view of the world entering as a parameter in the rules. In standard perspective, this sense is specified by a viewing-point and viewing-direction, and in the limited inverted

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Fig. 1. A limited system of inverted perspective.

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Dennis Couzin

perspective by just a viewing-line but it could be quite differently specified. There may also be conditions for viewing the pictures but I am unsure whether these are legitimate parts of a perspective system.

With all this apparatus, a region of the world, which may broadly be described as 'what is before one', is depicted. The standard system depicts the contents of an infinitely extended solid angle. A system of perspective need not depictjust such a tract but it is clear that inverted perspective schemes do not depict any tract that may be described as 'what is before one', at least when one is out-of-doors. It is just for this reason that I agree with Gibson's statement that inverted perspective is not a perspective system [5].

Gibson seems to argue that, since a particular scheme of perspective (viz. the inverted) cannot underlie a faithful pictorial system, the choice of which scheme can underlie a faithful pictorial system is not one of convention. This argument is invalid. Surely there are other non-standard schemes of perspective that are systematic and so one may still ask whether choice among these schemes is one of convention. I believe Gibson has an answer to this question and it is a sort of answer that shows that inverted perspective could not be chosen even if it were a proper system. This will be considered in the next part.

2.

Gibson defines a picture thus: 'A picture is a surface so treated that a delimited optic array to a point of observation is made available that contains the same kind of information that is found in the ambient optic arrays of an ordinary environment' [6].

Goodman, in his second criticism [3], tries to establish the circularity of the definition but he bases this on misunderstandings [7]. Instead of being empty, this definition is a Pandora's box. If one looks, one finds the difficult technical notions it rests on, the seeming conflation of depiction with faithful depiction, the unclear status of the object of depiction and hope.

Gibson's definition of depiction is couched in terms of his ecological optics. It is not clear whether this new optics will breed new systems of perspective, couched in terms of optic arrays and their structures. It is clear that Gibson's characterization of depiction establishes new conditions of adequacy for the old systems of perspective. None of the old systems, including the standard system, will be adequate for all depictions, while some of the old systems, including the standard system, will be adequate for some depictions. Taken together, the resulting hotchpotch of acceptable perspective techniques probably will not constitute a system. Gibson would claim that inverted perspective will have no place even in this hotchpotch. The reason is that inverted perspective renderings cannot convey the appropriate information.

It is at this point that Goodman's third criticism arises. Goodman wonders why one cannot read the appropriate information off the appropriate inverted perspective picture. Of course one can. But reading or otherwise milking information from an optic array is not at all what Gibson has in mind when he speaks of an optic array providing information. The objection, raised by Goodman, that Gibson fails to specify the system of information interpretation, is based on a misunderstanding, because Gibson clearly intends a particular system, the human perceptual system. So a picture in inverted perspective will not provide the same information as, say, a topologically equivalent picture in standard perspective for the reason that may be stated crudely as: one cannot see that way. This is an empirical claim. Goodman's ultimate objection is that one must not restrict oneself, in explicating depiction, to this one system. He con- cludes his note by stating that 'a symbol may inform in as many different ways as there are contexts and systems of interpretation'.

There is a great gulf separating the accounts of depiction of Gibson and Goodman. Though Gibson does not seem to realize it, his account still requires that a picture must necessarily resemble the object depicted. He is emphatic that 'perceiving what is represented can [n]ever be exactly like perceiving it in the world' [8]. However, this is only to say that a perfect resemblance is not the goal of faithful depiction. Perceptions for Gibson are information pickups and picture and object, on Gibson's account, share a certain salient subset of available optical information. This guarantees a likeness in the perceptions of both. It does not guarantee that the more faithful the depiction the greater the resemblance. This is because shared information must be salient in one way for faithful- ness, and, perhaps, in another way for resemblance. Thus, if one renders a good caricature of a face less extreme, one may obtain a picture that better resembles the face, while being a less faithful depiction of it! Still, a good caricature does resemble the face.

Goodman's account of depiction has always been in terms of the syntax and semantics of the pictorial system, and, on this account, a picture's resembling its object is at best an accident. We have seen how Gibson demerits and Goodman merits the inverted 'system' of perspective. In Languages of Art, Goodman considers a pictorial system where the perspective and the color are reversed (i.e. comple- mentary colors) [9]. Again, Goodman finds the information all there and, again, Gibson would claim a loss in perceptual information. But in this example, too, there is no tendency to say that the inverted pictures are not pictures at all, although there may be disagreement about what they depict. It is curious that although Goodman declares that 'almost any picture may represent almost anything' [10], this doubly inverted pictorial system should be the wildest example in his book. Why stop? Consider the pictorial system in which a brown dog

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On Gibson's and Goodman's Accounts of Depiction

is depicted by what is a 'standard' picture of a blue butterfly and a blue butterfly is depicted by a red letter 'G' on a grey ground. We can construct such a system to satisfy the syntactic and semantic conditions imposed by Goodman's account.

Common sense reels at such examples, which do not seem to be examples of depiction at all. While in this state, one notes two things: first, Gibson's analysis, having conflated the questions of fidelity and of depiction, cannot help one to explain the plunge in following Goodman's analysis. Second, even if one prefers Gibson's kind of analysis, a correct syntactic/semantic analysis is still needed. How else could one hope to handle genuine cases of depiction by non-pictures ?

REFERENCES AND NOTES

1. N. Goodman, Languages of Art (Indianapolis and New York: Bobbs-Merrill, 1968).

2. J. J. Gibson, The Information Available in Pictures, Leonardo 4, 27 (1971).

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

4. Cf. Ref. 2, p. 30. 5. Purported systems of perspective may fail of

systematicity in many ways. Perhaps the worst failure in the literature is the system that has evolved from G. Hauck through E. Panofsky to be

6. 7.

8. 9.

10.

dubbed 'synthetic perspective' by J. White in The Birth and Rebirth of Pictorial Space (London: Faber & Faber, 1957) Chap. X. There cannot be a rule of location for synthetic perspective. Cf. Ref. 2, p. 31. First, he incorrectly transcribes Gibson's 'the ambient optic arrays' as the singular 'an optic array'. Second, he supposes that for Gibson the information in an optic array is identifiable with invariant distinctive features of objects. This is to confuse perceptual input with perceptual output. The struc- tural invariants that constitute an optic array's information are features of the array that are of sorts that must (barring trick environments) be pre- sent in neighboring arrays. Thus, the information in two well separated optic arrays for one object may be different, which is just what makes Gibson's definition (before transcription) so interesting. Where later Gibson refers to the naive percipient noticing the invariant distinctive features of objects, he does not mean features the information for which is contained in every optic array. To the contrary, he means features such as size, the information for which may be contained in no one optic array but which is correctly perceived from every point of view. The perceptual system must integrate non-size information from many optic arrays to achieve this. Cf. Ref. 2, p. 33. Cf. Ref. 1, p. 35. Cf. Ref. 1, p. 38.

Editor's note: for J. J. Gibson's reply to these comments see page 284 (Letters, Leonardo 6, 281 (1973)).

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Documents

On Gibson's and Goodman's Accounts of Depiction