THE SPATIALITY OF SEEING AND THE SPATIALITY OF PICTURING

To return to Willats‟s theory, we might now conjecture that since he borrows his understanding of vision from Marr, he can make no allowance for these further computational steps or how they bear on the process of picture production. And so, this extended account of seeing might have two implications for his schema which are in line with the amendments we made to Marr‟s account. First, if the representational language of pictures is parasitic on the early stages of vision (as, for instance, optical denotation systems are said to be on the primal sketch, or line drawings are on the 2½D sketch)182 then this might mean that they equally serve „depiction for perception‟ or „depiction for action‟. And second, if object- centred descriptions proffer the pictorial means for making shapes recognisable they might also allow for an imagery which we experience as graspable too. All in all, therefore, the structural elements of pictures and certain of their concatenations may just as well underpin the recognitional content of a work as they do its embodied effects. Accordingly, this might give us a loose explanation for the incongruity of Picasso‟s Rue-de-Bois: that is, why it could at once be seen as a landscape and as a collection of manipulable objects.

182

But this will not be the end of the story since vision does not culminate in object-centred descriptions, but with outputs which are distinct and more informationally replete. And so in this respect, it seems necessary to consider the divergent spatiality of the visual percept and the visuomotor representation. Can these differently inflect the spatiality of pictures? And more specifically, can they be identified with different classes of drawing system and the distinct set of mapping rules on which these depend?

In Art and Representation, Willats suggests that drawing systems can be parasitic on two stages of vision which Marr identifies as fundamentally distinct. On the one hand, they can be associated with internal visual descriptions (such as the primal and 2½ D sketch) which encode information about shape in relation to a particular point of view. Or, on the other hand, they can be related to the later stages of visual processing whereby constant features of shape are presented in a view-invariant format. So, for example, Willats proposes that it is likely (although not irrefutable) that Vermeer‟s The Music Lesson (fig. 31) is derived from a view, while Andrei Rublev‟s The Holy Trinity (fig. 32) (and more interestingly for our purposes, most Cubist pictures) are structurally related to object-centred descriptions.183

However, there is a slight complication here since if any of these are to underpin „effective‟ representations, they must approximate to the projective geometry of possible views (which is where „anomalous‟ systems such as

183

For Willats‟s discussion of Vermeer see ibid, pp. 59 – 61; for his discussion of inverted perspective (the dominant system in Rublev‟s picture) and its dependency on object-centred descriptions see pp. 65 – 69.

inverted perspective miss out).184 What Willats therefore believes to be fortuitous for most of the common drawing systems is that they can both be described in terms of primary geometry (that is, with respect to the projective geometry of possible views) and in terms of a secondary geometry (that is, with respect to the two-dimensional geometry of the picture surface).185 Thus, the crucial claim of his account is that, insofar as the rules for mapping in secondary geometry are determined by the structure of object-centred descriptions, they can be naturally generated rather than having to be consciously learned.186

If this hypothesis is sound then children and adults who have not received formal training in art should generally produce pictures which are mapped from object-centred descriptions.187 According to Willats, this is most evident in the drawings of young children. For instance, in an experiment devised by the author, a group of children aged six to twelve were asked to draw a die presented at eye level so that two of its sides could be simultaneously seen.188 Interestingly, some of the younger children produced drawings such as the one shown below (fig. K) in which all the spots – including those which were not visible in the view – cohabit a single region. It may therefore be, as Willats suggests, that these children intend the region to stand for the whole volume of the die and are thus deriving their drawings from an object-centred description. And so, in a more typical example such as figure J, the child may be using lines to denote long

184

As was discussed in a previous chapter, the second criterion for an effective shape representation is that it is depicted from a general position. See ibid, pp. 23 – 24; for a consideration of the lawful concatenation of lines and line junctions see pp. 207 – 214.

185

Ibid, pp. 37 – 69.

186

For Willats‟s most explicit statement to this effect, see ibid, pp. 317 – 19.

187

For Willat‟s discussion of children‟s drawing development see ibid, pp. 287 – 319. For his discussion of the use of object-centred drawing systems in adult‟s pictures see pp. 186 – 190.

188

volumes such as arms and round regions to denote spherical volumes such as the figures‟ heads.

Figure K. Child‟s drawing of a die. From Willats (1997)

Figure J. Drawing of My Familyby a three-year old girl

If we take this claim in conjunction with the argument I have been developing then it seems that any drawing system which derives its mapping rules from object-centred descriptions may transform information about shape from visual percepts or from visuomotor representations. But either way, it is hard to see how this process would amount to a spatially coherent depiction (that is, one in which a congruity between distinct parts gives rise to a unified appearance) unless the representation were simply of one discrete object. The reason for this is that object-centred descriptions converge uniquely on one single item and thus do not allow for a global or comparative mapping of

space.189 For Willats, who is of course talking about representation as a function of what can be recognised in a picture, it is the drawing system‟s adjustment to, or fortuitous coincidence with, a view which allows it to pattern this global coherence. Thus on his account, most pictures are derived from object-centred descriptions but these are adjusted to views by monitoring spatial relations as they emerge within the picture. He states, for example, that:

[The rules of secondary geometry are] applied to an object-centred description. Once this has been done […] a view of a scene begins to emerge, and the artist or draughtsman can then continue the picture by adding further details in accordance with the coordinate system set up within this pictorial view.190

But while this recursive process may form a substantial part of picture production, one might wonder whether the allocentric and egocentric frames of reference can also inform the artist‟s construction of space. Now, it seems that the latter, insofar as it only encodes the position of one individuated item in relation to the body, can have no more influence on the global mapping of space than was said of the object-centred description. Therefore, if it does underpin certain compositional schemata (as I shall argue in a following section), then it may be that these are worked out by meditating on the phenomenology of vision

189

While Marr proposes that volumetric primitives can decompose the principle axes of an object so that the 3-D model description may capture „the geometry of shape to an arbitrary level of detail‟, and thus while it may be that these descriptions can specify structural relationships between the parts of a perceived item, if this modular organisation is always local to the object‟s own axes, then it will make no allowances for the spatial intervals between it and other elements in the scene. Vision, p. 306.

190

and by monitoring the progress of the picture191 so that it is both internally consistent and able to evoke the physicality of sight. However, any spatial coherence that this affords cannot be drawn from the structure of visuomotor representations since, due to their contingency on egocentric coordinates, they do not proffer the relevant cues.192