Leonardo

Leonardo,Vol. 6, pp. 233-235. PergamcmPress 1973. Printedin Great Britain. ON GIBSON’S AND GOODMAN’S ACCOUNTS OF DEPICTION Dennis Cowin* Four years ago Nelson Goodman proposed an account of depiction as part of an elaborate theory of symbol systems in his book Languages o f Art [l]. 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 discussa claim by Gibson and its denial by Goodman. In Part 2, I shall showhow Gibson’sclaim is superfluousto hisaccount but that otherofGoodman’scriticismsdopoint to important differencesbetween 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 reasonsfor this claim. Is it correct? For objects that are spatially limited, there is a simple and systematic way of depicting them in invertedperspective. As in Fig. 1, oneprojects from a point behind the object to a picture-planein front of it and, when more than one object-pointprojects into one picture-point, one makes the one farthest from the projection-point occlude the others. But for objectsthat are not spatiallylimited,one cannot take projection-points behind them and so this method will not work. Choosing the point at infinitygives orthogonal, not inverted,perspective. Goodman disputed Gibson’s claim and offered two examplesof picturesin 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 givencube-picturebe 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 rectilinearity 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 indefinitelybecause 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 depictingthe contents of unlimited spaces. For all the hundreds of examples of inverted perspective depictionsof things and interiors, there are none of landscapes. What isto countasa systemofperspective? Such a system must determinehow 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 locationassignsthe samepicture-pointto two world-points, one knows which world-point shows in thedepiction (i.e. one knowswhich colorto makethepicture-point). In standard perspectiveand 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-viewof the world entering as a parameter in the rules. In standard perspective,this senseis specifiedby a viewing-point and viewing-direction, and in the limited inverted Fig.1. A limited system of invertedperspective. 233 234 Dennis Couzin...