The Illusion in the Picture

The Illusions in the Picture

Robert Hopkins' theory of depiction in Picture, Image and Experience, 1998, broke new ground in the prominence it accorded to an interesting range of discrepancies between what is depicted and what is seen in a depiction. His development of this idea in Ch. 6 is named the “Separation account.” (128) In pictures to which the account applies what is seen in the picture diverges from what is recognized as the subject depicted. By invoking Separation (as he calls it) Hopkins aims to reconcile his experiential theory of depiction, which makes experienced resemblance of “outline shape” between the motif in a depiction and what is seen in the picture the norm, (1) with apparent counterexamples in which the outline shapes of the two are strikingly different. Stick figures are an extreme example (2) but abstract (e.g., cubist) representations or free sketches are of far more artistic moment. Hopkins uses a sketch by Alfred Stevens as an example.

The subtleties of Hopkins ' text concerning what is seen in pictures featuring Separation (3) need careful interpretation. He does not say that viewers always see an anomalous figure in a sketch such as Stevens'. Only that they can and typically do so. He imagines a viewer who sees in a sketch by Alfred Stevens “a man of an outline shape as determinate as that she sees the drawing as having.(4) That man is semi-transparent, especially at the top of his leg and headpiece. His nose and mouth blur indistinctly into the rest of his face. Across his upper arm and midriff run parallel curving strands of something. The little finger of his left hand seems malformed.” (139) However, such a viewer if competent will know that certain aspects of this figure cannot represent properties of the subject, for her competence as a viewer incorporates practical knowledge of a number of constraints normal to any known pictorial practice. To wit: (1) Depiction-interpretations are in general limited to the kinds of things there are in the world; (2) Unreal subjects are validly ascribed only to the extent that the ascriptions are underwritten by shared human interests; (3) Depiction-interpretations are conditioned by recognition of the limitations of verisimilitude achievable within a given medium and also by knowledge of competing artistic aims, e.g., expressive graphic or painterly technique. An artist may employ rapid, free-hand strokes, sacrificing accuracy for the sake of verve.(5) This clearly plays a part in Stevens' sketch.

This understanding of depiction practice, Hopkins says, will convince the viewer that the artist did not intend her to take a partly semi-transparent man to be depicted, but rather a (roughly) normal man who is, however, indeterminately depicted. In some cases this knowledge may lead her to tailor her seeing-in (6) experience to bring it into line with the pictorial content, confining what is seen in the drawing to what is underwritten by such resemblance of outline shapes as exists between the two. But if not, at least her knowledge will induce her to regard her unamended seeing-in experience as “eccentric.” (139)

A similar maneuver is applicable to the case of a stick figure. We see, in this case without eccentricity, an impossibly straggly, bulbous-headed human form in the picture on the basis of resemblance of outline shapes. It is hard to see how it could be otherwise with the stick figure, since (according to Hopkins ) it isn't clear what resemblance of outline shapes could exist given the radical indetermination of the subject. (7) As Hopkins carries his account of depiction forward, seeing-in remains a constant component of pictorial experience but one that must be supplemented or interpreted by a number of constraints, including artistic convention, in order to provide an explanation comprehensive enough to handle the diversity of types of depiction. (8)

Hopkins is vague as to how prevalent “eccentric” seeing-in is and what positive role it can play in pictorial experience of cases like the Stevens' drawing. His overriding aim is to explain how the content of some pictures is (in some respects) indeterminate because of the over-determinateness of the surface features. The precise experiential character and the utility of eccentric seeing-in are of less moment for him.

Another demurrer is this: whatever the precise character and scope of experiential seeing-in may be, the Separation Account need not claim that bona fide cases of depiction are ever such as to resist a more idiomatic use of the ‘seeing in' locution. For the phrase is often used for an experience of seeing a picture as being of a given subject without concern for what is seen-in it in the somewhat technical sense that holds center stage in the Separation Account. There is no reason to cavil at this popular use. It is only necessary to avoid confusing it with the more technical sense.

For my purposes the main value of Hopkins' concept of Separation is the opening it provides for a more radical affirmation of the Separation entailed by pictures – especially by pictures whose pictorial space is fairly well differentiated (9) -- and by means of that, for a better account than has been so far given of the phenomenology of seeing-in. I believe that progress in this endeavor can be made by pushing the idea Hopkins introduces further than he does.

Wherever the Separation phenomenon crops up, what is seen in the depiction is to some extent “divorced” from the depiction subject. That means that either the depiction subject is not seen in the picture, though it is ascribed to it as the subject; or else there are two different things seen in the picture, the true subject and something that takes on more determinations of the surface design than characterize the subject. In these cases seeing P as a picture of O involves three items: the picture, the subject and the non-subject. Since the last is seen in the picture in a particularly immediate way I will call it the “visually ostensible subject.” “Subject” deserves scare quotes here, for these ostensible subjects are not subjects, any more than counterfeit dollars are dollars. They are only as-if subjects.

Hopkins represents the Separation phenomenon as arising in cases where the experienced resemblance of outline shapes is problematic, as in stick figures, caricatures, sketches, and abstract representations. But I believe that a Separation phenomenon is at least latent in all attentive picture viewing where the picture possesses substantial pictorial or optical depth. All such pictures, viewed correctly, have a visually ostensible subject in some way and to some degree distinct from their true subjects. I also believe that it is not contrary to the intention of the artist that we see in the picture these “eccentric” ostensible subjects. To the contrary it is something that an artist typically desires, requires, cherishes. It is, explicitly or implicitly, part of the depiction endeavor. Appreciation of the picture as a picture requires it, art criticism could hardly proceed without recognizing it, and in general the charm of pictures would not be half of what it is without visually ostensible subjects being intended and recognized (and the intention being recognized in a Gricean sequence). I will call the first of these propositions the ubiquity claim and the second the aesthetic significance claim.

With regard to ubiquity, let us consider a finely textured full-color painting such as Ghirlandaio's Portrait of Giovanna Tornabuoni (10) (1488). For all its fidelity of color and texture to the intended subject (which is the sitter idealized), the flesh is presented as somewhat wooden and the hair as somewhat artificially stiff, as Vasari complained of the paintings of this period. The subject is not to be taken as wooden and stiff in these particulars. Nor is the lustrous gown to be taken as precisely like the real gown. Even if we cannot precisely specify the intention, we know it cannot be exactly this. No gown sleeve could present precisely that combination of clarity and confusion. Overall the painter subtly stylizes, combines a precision with a muted glow that confuses the detail of the sleeve. There is also the barely noticeable brushwork that textures the neck in an unfleshlike way that the painter is not able to avoid.

You may say, yes, but the viewer is supposed to overlook the discrepancies, to see Giovanna's unstreaked flesh right through the brushwork, her silky hair through the two un-silky-stranded buns, and the tangible stitchwork through the complications on the sleeve. But I submit that no such “seeing through” is possible; or, to the extent that it is, it is either counter-artistic (naïve or negligent) or else impure. By impure I mean that the “eccentric” ostensible woodenness never is expelled from the experience but persists like a veil or double-image. Perhaps you can visualize the subject full-fleshed, etc. You can imagine that your seeing the parts of the surface is seeing these properties of the subject. But there is a more perspicuous experience of the work that involves perceptual awareness of what is more immediately presented than the subject. One is tempted to say that the true subject, truly propertied, is referred to, not presented. Or that we can access it only by make-believe, not by an immediate visual impression.

With regard to the aesthetic significance claim, it seems equally certain that Ghirlandaio intended viewers to see the anomalous properties of the visually ostensible subject, though not intending to impute those properties to the subject. He certainly saw them, and there is good reason to think that what the artist sees the viewer should also see. Our appreciation of Ghirlandaio's distinctive style depends on not only seeing the surface marks as surface marks but also seeing surface marks as if they were object- and scene-defining, that is, seeing a visually ostensible subject in the picture which is significantly different from the picture's depiction-subject.

The reason seems plain enough. The depiction-tradition governing pictures of this sort invites us to do a number of things: (a) to use our general capacity to see things in the surface, bringing as many marks into the experience as fall within the normal (or supranormal) repertoire; (b) to discriminate between ensembles of marks that are literally subject-descriptive and those that are auxiliary in one way or another, or are simply visual noise useful only as marking the surface as a surface; the Separation phenomenon foregrounds the difference between those that are literally subject-specifying and those with other functions; (c) to navigate among the auxiliaries in appropriate ways, appreciating how they enrich (or alternatively, detract from) the total depiction-experience.

So far the Separation phenomenon has been confined to what is “eccentrically” seen in the picture when viewed from the point of view that the picture itself implies is the correct one, as a result of the overdetermined “facture”of the picture. But there is another aspect of Separation altogether. Consider Michelangelo's drawing of one of the nudes from the Sistine ceiling. What position of the legs do we see in the picture?

Seen from the correct viewing station the legs are seen extending out toward the viewer at a roughly 45º angle. But as we well know, seen from an oblique angle the effect is different. Then (from the left) the legs swing closer to 90º or (from the right) closer to the picture plane. Manet's dead matador notoriously swings similarly to right and left as the viewer moves laterally. What legs do, eyes do also. If they are ever directed toward the viewer they follow her as she moves laterally. More generally the pictorial space seen in the picture undergoes striking contortions, expansions, and compressions as the picture is viewed from different stations. (11) Yet the depicted subject does none of these things. These anomalies are a direct consequence of the discrepancy of dimensions (two vs. three) and the fact that vision is irremediably perspectival. Even if the anomalies are not always noticed consciously, there is no question but that they are available and that they operate at a preconscious level. If they did not we would experience a full illusion (of an unchanging subject) or else would be incapable of seeing a subject in a picture (would see the picture only as a surface).(12)

Thus Separation operates not just at the level of facture (13) but also at the level of spatial relations however naturalistic the drawing may be. This strengthens the ubiquity thesis, but also introduces some confusion. For what does it imply about what we see in the picture? Does it imply that we see a different visually ostensible subject from the different viewing stations, or the same object undergoing contortions? And what aesthetic or artistic benefit can there be in such anomalies? Unlike the earlier, facture-based, anomalies, these reveal nothing about the artist's technique or style. They do not tease us with specific visual metaphors or fantastic possibilities. They are not under the artist's control, being consequences of the only visual processes of which we are capable.

As to the one-or-many question, I prefer the one: the visually ostensible subject passes through states of expansion, contraction, and contortion with changes in the point of view. But the state of greatest relevance is the one with the properties it has when seen from the appropriate viewing station. Call this the canonical state of the visually ostensible subject.

As to significance, two facts are to be noted. First the canonical state of what is seen in the picture depends on the artist's choice of implied point of view. The variations available to the artist are lateral, vertical and in depth. Thus in Dutch architectural painting the correct point of view may be laterally off-center as well as higher or lower, or closer or farther off, than is usual. Seen head-on from the usual height and distance, the state of the virtual subject is decidedly non-canonical. Further, where there is more than one implied horizon, a not at all infrequent occurrence, different parts of the virtual subject will be presented non-canonically from any of the standard points of view. Much good can come from these “eccentric” artistic choices. For the viewer to enjoy that artistic good depends on her seeing the visually ostensible subject canonically.

The artist has no control over the variability of the state of the visually ostensible subject. But that does not mean that this general aspect of Separation has no effect upon our experience of the visually ostensible or real depiction subject. What rubs off on the visually ostensible subject is a quality of inherent insubstantiality. Since the least shift discomposes it, it cannot be real. It is as merely “optical” as is the doubling of a finger held close when one's focus reaches far beyond it. That virtuality also gives a distinctive flavor to the underlying fictive character of the actual depiction subject (or the subject as depicted), different from what a sculpture, for instance, confers upon its subject. Both subjects are distanced, both are changeless (anachronistic), but the pictorial subject can reveal only one view of itself.(14)

The flatness of the picture, which is essential to the volatility just mentioned, contributes in other ways too, notably by leveling the focal differences proper to any viewing of an actual subject, and in so doing making available fluctuations or ambivalences in the visually ostensible subject. Its efficacy in this respect is reinforced when the suppression of virtually all modeling of forms in the picture weakens the illusion of definite spatial relations, as happens for instance in Matisse's The Egyptian Curtain. To pick but one example, the leaf-shapes in the curtain at the right are reduced to contours standing out against the untextured black expanse of the curtain.

The contours are freed from the curtain to twist and turn in space. Thus the green leaf-form can be seen to curve along the rounding of the curtain but also, with equal force, to extend out from the curtain like a scimitar. In so doing it links up with the pattern of protrusive palm fronds, turning a broad, downward arch into a jaunty upturned, aggressively protrusive blade. Other anomalies are resident in the pattern, comparable to the scimitar, giving the picture a richly sportive suggestiveness. That same green leaf can also be seen (without forcing, without fault) as curling broadside to the viewer's gaze. Each of the gambits, so to speak, is immediately presented in depth, is seen depth-wise, as the eye plays with the pattern. Without perceived flatness of the surface and painterly flattening of the curtain that particular palimpsest of conflicting appearances could not occur. The conflicting “readings” replace one another as naturally as do the changing but entirely compatible visual impressions in sensory experience of actual scenes, and leave a residual presence behind. This is possible because the flatness and the flattening greatly level the force exercised by any single reading. None can elbow the others off stage for long, and those upstaged often merely retreat to the margins.

The Matisse example makes plain how various are the things that can be seen in a picture to good effect. (It is equally obvious that in many cases what is seeable counts against the efficacy of the depiction, as when colors that should stay in their proper depth refuse to do so, a complaint commonly levied in 17 th and 18 th century academies.) This calls attention to another fundamental trait of seeing-in. What is seeable in a picture is a class of diverse visually ostensible subjects. Call this the diversity thesis .(15) An immediate consequence is that a proper theory of depiction must explain which ways of seeing are correct or appropriate as ways of seeing-in, and which are not. In the case of the Matisse, I think it is evident not merely that a number of visually ostensible subjects are correctly (appropriately) seen in the picture, but that in familiarizing ourselves with this diversity, our experience develops in the direction of simultaneous awareness of discrepant visually ostensible subjects intermixed with continuing but varied awareness of the surface. Call this the complexity thesis .(16), (17)

Can introspection of these seeing-in experiences shed any light on the nature of seeing-in in relation to perception of real subjects? I think it can. First, I think we can appreciate features of the experience that enable it to be quasi-illusory in spite of the fact that there can be neither stereopsis (18) nor any sliding of focus in or out relative to the visually ostensible depth. Introspection suggests, to me at least, that what greases the skids is the phenomenal resemblance between out-of-focus and peripheral blurring. When one's focus lights upon a part of a picture, say the knee of Michelangelo's ignudo, the thigh is somewhat blurry, aping the blurring that would occur if it were actually recessive, as in a sculptural equivalent. Given this resemblance it cannot be surprising that our recognitional capacity for the 3D aspect is activated, though its functioning in pictures is, in my view, non-veridical.(19) The result is a variably strong or weak misimpression of actual depth. At the same time our experience provides us with a vital contrary impression, an awareness of the first impression's non-veridicality, stemming from equally apparent indications in the visually ostensible subject: our flatness-recognitional capacities are also activated. As a result the virtual object is extended in a frail and insubstantial – unreal, merely virtual -- depth.

Intimately related to this is our well-grounded confidence that moving our gaze to the thigh will create a comparable effect on the knee, resembling the experience of an ocular shift in perception of an actual knee. Given this confidence it is hardly surprising that the visually ostensible subject is (i.e., seems) convincingly, but unstably, extended in depth.

There is one other idea that I wish to insert before the time runs out. That is that seeing the visually ostensible subject in the picture is always done from the viewer's point of view. That is why what I have called the canonical state of the visually ostensible object proper to the picture can be fully experienced only when the viewer's point of view is coordinated with the point of view implied by the design. This is fully consistent with the fact that we can see what subject is depicted from what point of view even when we move away from the correct point of view, and with the possibility that sometimes we can tell what state of the visually ostensible subject it will present from that point of view. (20) Those insights, I believe, are better regarded as cases of perceptual knowledge of these aspects rather than full-scale seeing-in experiences of them.

I am keenly aware of how much I have not covered in this brief paper. More is consigned to endnotes, and more yet is yet to be worked out. I hope some of the problems and perhaps even some solutions will come out in the discussion.(21), (22)

Footnotes

1. Hopkins ' explanation of outline shape has a number of obscurities, especially his reference to a “solid angle”. In a later article (Hopkins 2003) he explains the concept more fully, citing Reid's account of visible figure . The visible figure of an object is defined in terms “of the directions of its various parts from a point in its environment.” In the appended figure the visible figure of the face of the pyramid seen from PP1 is the set of angles formed by the rays from PP1 to the edges of the pyramid at aebcfa and all points in between). The visible figure of the pyramid from PP2 consists of the set of angles formed by the rays from that point to the edges of the pyramid at aebcdga and all points in between with the addition of an internal division running cfa. Thus understood the visible figure is “solid” because the angles are three-dimensional, even though from PP1/PP2 the figure shows as a two-dimensional silhouette, as is shown by the figure on the picture plane (PL 1 and PL 2 in the diagram). Hopkins' outline shape is hence an abstraction from the traditional idea of a “visual pyramid”of rays in a rectilinear projection of an object to a point, as in the diagram. I find it helpful to locate it within this larger picture. The base of the visual pyramid with apex PP1 is flat but slanted, since it conforms to the face of the Egyptian pyramid relative to PP1. The base of the visual pyramid with apex PP2 is more complex, since it conforms to two slanted sides of the object. This schematization results in more substantial “visual shapes” – three-dimensional ones that more fully represent both the object and our visual data, allowing for depth of focus. The projection of the motif on PL1/PL2 is a cross section of the visual rays. While it is flat (providing the picture plane is flat), it possesses a dimension of depth defined by the length of the visual rays from the projection point to their terminations on the plane. Thus a change in the position or orientation of the picture plane will alter the shape of the projection, even though the change would not be visible from the projection point.

2. Stick figures are peripheral in my account, since there is virtually no 3D pictorial or optical space in such figures. For more discussion of this, see note 7 following.

3. I follow Hopkins in using the upper case “S” to indicate that this is a technical usage.

4. Note how extreme this is: every surface mark seen by the viewer is seen in terms of a property of the anomalous “man” seen in the drawing. All that is necessary for Separation is for some marks that are not subject-indicating to be seen as visually ostensible subject-indicating. There are obviously degrees of Separation.

5. The artist may produce a line which displays the speed of the stroke rather than depict the subject determinately. (138, 144)

6. At this point I use “seeing-in” in a general sense, without reference to any particular account of it, e.g., either of those given by Wollheim.

7. Given the stick figure provided by Hopkins (123) it is, as he says, not particularly easy to see the intended subject in it, at least according to the meaning Hopkins gives to that expression. Why? The actual reasons, I think, differ somewhat from the ones he gives. It can hardly be that the (normal) subject is too indeterminate to resemble the shape of the figure in any respect. The subject is a standing human with arms hanging more or less straight down from the shoulders. That much is clearly based on resemblance to the lengths, directions and junctures within the motif. Other aspects of the motif (thickness of lines, e.g.) are not depiction-relevant. (This is roughly Budd's line.) More significantly, I think, there is virtually nothing visually suggestive of pictorial (or optical) depth in the image. Given that absence, there is no clear sense of a point of view, and hence no outline shape, since that by definition must be relative to a point of view. (This could be relaxed so as to allow for a direction of view, to cover cases of parallel projection, but we may set that detail aside to keep things simple.) So Hopkins ' criterion of something being seen-in the motif cannot be satisfied. By that standard the viewer sees nothing in the motif, though (normally) sees it as representing a standing human. If depicting requires seeing something relevant in the motif, nothing is depicted by the motif. However, in the hands of a clever artist, even stick figures can be given far more specific human qualities, especially of posture and gesture. They can dance, cavort, strut, creep, race, etc., thereby conferring these properties on the depiction-subject. Such determinations of the motif carry with them effects of spatial depth and point of view. Hopkins ' stick figure in contrast is entirely bereft of such suggestions because the drawing is careless and therefore clueless. The result is that Separation is not exemplified by the stick figure in Hopkins ' text, though it would be exemplified if that figure were enriched so as to suggest spatial depth.

8. These are: (i) depictions have a minimum depiction content, (ii) depictions are always from a point of view, (iii) the depictable is always visible, (iv) misrepresentation is possible only within limits, (v-vi) general depiction-competence plus knowledge of the appearance of the subject is necessary and sufficient to understand pictures of that subject. Various refinements of these are made as the discussion proceeds.

9. In my view the Separation Account applies also to non-figurative visual works such as the classic works of Pollock, Rothko and countless others where there is fairly robust optical space, as well as designs of all sorts that meet the same condition. In my lexicon “design” is the generic term for works visual works on a flat surface and “picture” is reserved for designs which have indicators of the absolute magnitude of the represented spatial relations. The current promiscuous use of “picture” to cover all paintings and drawings seems to me seriously ill-advised.

10. Domenico Ghirlandaio, Portrait of Giovanna Tornabuoni , 1488. tempera on panel, 77 x 49 cm. Museo Thyssen-Bornemisza , Madrid .

11. Anyone in doubt as to the perceptual impact of these distortions is invited to walk back and forth in front of the oversized photographs of Jeff Wall currently on exhibit at the Museum of Modern Art in New York . The architectural features of the interior scenes are particularly subject to distortion, as are landscape features such as roadways and ditches depicted as orthogonal to the picture plane. Viewed up close the space seen in the photographs becomes radically compressed in depth, and so forth. Viewers who miss these deformations are not attending closely to what is there to be seen in the works.

12. I am aware that this flies in the face of the alleged perceptual constancy of the pictorial effect (Kubovy calls it robustness). But the effect of constancy obtains only when pictures are viewed with less than scrupulous attention and with the assistance of clear indications of the orientation of the surface, such as the rhomboidal projection of its format to the viewer, almost always reinforced by other environmental markers, or where viewed from so great a distance that the alterations in our visual field of the format and environment are slight. Not all features are as robust as others. I find, for example that viewing pictures on a slanted surface more readily results in an apparent shortening of the image than does the impression of parallel sides of the format yields to an apparent non-rectangularity.

13. By this term I mean to cover drawing, coloring, and texture, the latter including line quality and texture in a more idiomatic sense. All picture-relevant properties of the motifs come under “facture.” Or again, everything that falls within the artist's control.

14. This is too bald a formulation, of course. It is nearer the truth to say a picture can never reveal as much of the spatial form of its subject as can a sculpture in the round.

15. I am distinguishing visually ostensible subjects whenever a difference can be found in any of their properties. Alternatively one could speak of the same visually ostensible subject with different properties.

16. Various visually ostensible subjects carry different weights, i.e., different degrees of importance in a full and perspicuous viewing. Generally there is one that deserves to be called the principal virtual subject. In perspectivally consistent pictures this is the one from the correct point of view.

17. Complexity is meant to supersede twofoldness. The protracted debates about the exact relation among different experiential elements in twofoldness seem to me out of touch with my actual experience and what I presume to be that of specialists who comment enlighteningly about artistic effects.

18. A key component of this is the parallax that occurs when an unchanging three-dimensional scene is viewed from changing points of view, resulting in a changing occlusion pattern. Another is the doubling of images in binocular perception when near objects are interposed between the eyes and a distant object on which the eyes are focusing.

19. On this I differ from Lopes. I do not believe pictures are or can be “transparent,” and in seeing the visually ostensible subject our “recognition” of its fictive properties is certainly not veridical. “Recognition,” like other terms for perception has both a success-use and a presumption-use. Of course our recognition of depiction-subject as a depiction-subject can be veridical even where the recognition of the visually ostensible object is not. (Note that in one respect the recognition is non-veridical even when the subject is correctly identified, since our person-recognizing capability is exercised toward a picture of a person, not an actual person.)

20. Thus we can tell from viewing a portrait from a considerable variety of points of view that the subject's eyes will follow us as we move from side to side.

21. Does the experiential account, as modified herein, hold for depictions in other drawing systems than perspective? This is a question that arises for Hopkins ' account but which he does not explicitly consider. My limitation to pictures with depth-rich pictorial space might seem to exclude such pictures as the following, which is in oblique projection rather than perspective.

This projection has nothing to do with a point, even an indeterminate point. There is only the direction of projection (each point of the picture's motif is projected in the same direction) and the angle at which the projection intercepts the picture plane. There is plainly a correspondence between the motif and the subject. This could be called an outline shape if the definition of that were loosened to allow for such a shape being relative not to a point but to a direction of projection and an angle of interception by the plane.

Two things are to be noted about this in relation to Hopkins's account.(1) The outline shape of depiction and subject are exactly silhouette-resemblant but neither is silhouette-resemblant to the outline shape we perceive of the subject, since we perceive in perspective. (2) Still, we do (or can) see a visually ostensible subject extended into space, and we are intended to do this. It is anomalous both in being subject to distortions when seen from “odd” angles and in respect of the forms and their spatial relations regardless of the viewing station. The receding sides of the individual houses spread as they recede, are smaller in the foreground than in the background, and the ground tilts up. This is of course a consequence of the nature of our vision. Yet we not only recognize the intent of the depiction to present rectangular forms of equal size in a rectangular array on a flat ground. We also appreciate that the intended forms can be verified far more easily by measurement than can the forms in the corresponding perspectival image. And we may also appreciate the accessibility of the comparatively distant houses, and the much greater accessibility of the ground areas not occluded by the houses. Here is the somewhat abridged perspectival rendering of the same scene. In it the farthest plane is hugely extensive but at a sacrifice of accessibility of the ground beyond the near houses, even from this high elevation.

We can certainly see in this something very like the subject in the perspectival rendering. Can we do the same in the oblique rendering? Not in the same intuitively natural way, i.e., not in a way that fits easily into ordinary perception. Parallel projection depictions are artificial (“conceptual”) relative to perception, which is necessarily perspectival. Hence no depiction tradition represents complete scenes in pure parallel projection of any variety, only scene slices (e.g., silhouettes), or single objects or small groups abstracted from an environment, or as in the present case, a quite limited chunk of environment. In actual pictorial systems, if an extensive scene is depicted, primitive perspective always intrudes into a dominantly parallel projection because without it the farthest plane can embrace no more breadth than the nearest and the desired scene cannot be contained in the depiction. See further note 22 below.

22. This is not the place to survey the manifold types of hybrid depictions. However, a few comments may help. Typically classical Chinese paintings combine oblique projection with perspective, and in these cases the principal visually ostensible subject is seen from a given angular direction and a sliding sequence of levels of view, distance also varying stepwise with level. The “textural” facture properties are also quite distinct from subject properties. The tension between experience of all this and any possible face to face experience of the depiction subject is very great. The masters are ingenious in (a) diverting the viewer's attention from this tension, and (b) turning it to good account. A discussion of a representative example from classical Chinese painting is available in “Digital Technology in the Service of Aesthetic Analysis and Theory ” at www.philosophy.umd.edu/Faculty/jhbrown.

Endnotes

1. No account of depiction can be right that does not explain the allure of pictures. In spite of the venerable legends of the magic of pictures being their approximation to perfect verisimilitude, no one today would deny, I think, that such allure as they have depends absolutely on the perceptible discrepancies between the properties of surface, visual field representation of surface, etc. and subject. Wollheim's acknowledgment of this can be taken as canonical: "...the artist...exploits twofoldness to build up analogies and correspondences between medium and the object of representation...[and] constantly seeks an ever more intimate rapport between the two experiences..." (1980, 224) Without the virtual object there seems to me no way to explain how the experiences of surface and something three-dimensional can be combined in such a vital way.

Furthermore, it is not just the analogies and correspondences that are cherished. It is the unreality that attracts. Look at any of Matisse's paintings where pictorial depth is robust and ask whether you want to recover from the picture the countless features that are not shown, or resolve the pervasive indeterminacies in the depiction. I think the answer will be not at all. We prefer, vastly prefer, the virtual object with its anomalies to what we think of as the real subject. It is almost as if the real subject is banished as unworthy of concern. By the real subject here I mean any physically possible subject. It is precisely the physical impossibility of the subject's virtual stand-in that entrances us. Complicating their relationship is the fact that the subject the viewer entertains is something that draws on both the virtual object and the "real" subject. I do not pretend to have gotten to the bottom of this.

2. Pictures that have lack a substantial depth effect are possible, even common. Architectural plans and elevations are obvious examples. Absent shadows they lack depth markers even where the viewer understands that a recess or protrusion is meant. Likewise stick figure drawings typically have no depth effect even though the heads are understood to be globular, the necks farther back than the chins, and so forth. The strength of the depth effect depends on how numerous and well-coordinated are the depth markers. Non-figurative paintings such as Hans Hoffman's or Jackson Pollock's classic works have plenty of depth but do not count in my book as pictures (though that's nothing against them!). Pictures have to depict spaces capable of containing coherent objects. I suggest we call such space "material." This is not true of non-figurative spaces, which cannot be material precisely because they cannot contain coherent objects. A key factor in the immateriality of optical space is the absence of any indication of the size of anything in that space, neither the size of the positive forms nor the size of spaces between them.

3. Non-perspectival pictures, for instance traditional Chinese paintings which are dominantly in parallel projection, and even technical drawings in pure parallel projection, generate a virtual object with all the basic anomalies found in perspectival cases. Even though there is no single point of view from which to view them, their virtual objects undergo comparable alterations with change of viewing position. The same is true of reverse perspective. However, there is an additional anomaly in all these cases: the virtual objects generated by non-perspectival projections are geometrically different from the subjects they refer to from every viewing position.

4. Reversible figures, which are typically in parallel projection, generate alternative virtual objects, one for each shift, as in the well-known Necker cubes. The objects differ not only in orientation but also in shape, since the side farthest back is larger than the one in front.

5. Does my notion of the virtual subject imply any special ontology? I think not. It is merely a visual experience as of a three-dimensional volume occupied by various elements. The objects, or the scene, have no independent existence. They are artifacts of one's perceptual engagement with the surface. Mechanisms at a preconscious level presumably cause some marks to seem to lie behind others. Selective attention helps since what lies in the periphery of my vision is malleable: thus when I focus on the knee of Michelangelo's ignudo the parts above are more easily able to slide back into depth than they would be if my awareness of the surface grain of those parts were sharp. So far as I am able to gauge it, the virtual object is highly sensitive to ocular fixations. All that militates decisively, in my view, against it being any sort of independent existent. For my purposes it does not need to be. All that matters is the character of the perceptual experience, which is ostensibly that of an object (scene). A necessary feature of this ostensible objecthood is that its manifold instabilities are reversible. We can always regain any of its states by looking at it in the right way.

6. What of trompe l'oeil pictures where one (supposedly) cannot see the surface? Do I suppose there is a virtual object even there, where not even twofoldness persists? Well, does twofoldness lapse? That depends on how perspicuous a viewer one is. Trompe l'oeil works that include rounded motifs (ducks, rabbits, flowers, a bugle) are readily seen through from the correct viewing positions under favorable lighting conditions and display the anomalies associated with the virtual object. Even those actual examples known to me that consist entirely of flat and nearly flat motifs (Peto's letter board) are visually distinguishable from the real thing even from the correct viewing position under favorable lighting and easily from closer up. The artist's project requires there to be some represented depth, in the curl or fold of a letter or dollar bill or in a ribbon crossing over an envelope. The trick is to represent depth super-faithfully, which requires that the appearance of depth be part of the art. The more depth is seemlessly portrayed in such a project, the greater the accomplishment. But with every instance of represented depth there is necessarily a give-away. Change of viewing position will smoke it. And no facture is so minutely perfect as to be visually undetectable. So minimal difference, sufficient for a virtual object, is present.

I find it somewhat curious that trompe l'oeil cases are described as ones where the surface cannot be seen, only the subject. One may as well say that seeing the subject is seeing the surface, that one can't see any difference. But my observations convince me that the claim of visual indistinguishability is false. What is true is that the difference isn't so apparent as in the typical picture. Nothing momentous follows from that! Well, there is another truth that should be noted, namely that one way of appreciating such a picture is to imagine that the difference is visually undetectable. But that's not the best way to appreciate the picture. And yet another truth: the extreme trompe l'oeil genre is a limited one that foregoes a large part of the powers of depiction. It accepts limits in subject-matter, in facture, in style, and in expressiveness. No wonder its virtual objects are less typical than those of other genres.

The literature on these paintings is considerable. A recent article by Susan Feagin (2001) takes the trompe l'oeil project to be merely deception. Accordingly complete success entails entire unawareness of the surface, and partial success is graded by the degree to which the surface is unapprehended. But she also includes faux marbre finishes in the genre. These, however, are intended to present the surface bodily, only the material being other than it seems. While I freely grant that dictionaries of art lump imitation surfaces with trompe l'oeil paintings, I think we ought not presume in the least upon such classifications of convenience. Taken by themselves imitation surfaces are not paintings at all in the relevant sense, hence they pertain to the present subject only by way of contrast. To be sure parts of the surfaces of architectural trompe l'oeil paintings may consist of imitation surfaces. Their context is what makes them parts of paintings, not their traits by themselves. An architectural painting becomes such by incorporating them into a pictorial space created by representations of objects in depth, whereupon the imitation surfaces are also situated in their place. Without that they are spaceless and unless made into an abstract design worthy of being called a painting remain mere imitation surfaces. (Painting is only their mode of production.) Thus imitation gold mosaics in ceiling coffers do not count as paintings, merely as decorated surfaces whose context is not pictorial but actual three-dimensional architecture, whereas in Raphael's Stanze ceilings exactly the same surfaces stand in a pictorial space and the ceiling as a whole is a painting. Thus to see one of these surfaces properly one must take in its context. It will not do to judge it as a detached segment where its pictoriality or nonpictoriality cannot be seen. When that is appreciated the main thrust of Feagin's argument is turned aside. My way of putting the counter-thesis to hers would be that trompe l'oeil paintings are never imitation surfaces. Therefore there is always twofoldness in the optimal experience of a trompe l'oeil painting.

7. As best I can make out Kenneth Clark (Cf. Lopes 1996, p. 41) is trying to see where the dominantly surface impression gives way to the dominantly subject impression. His aspiration is misconceived. He fails to realize that the full-blown subject, all its visually available content made present, is never able to be directly seen in the picture. The subject is recognized from the picture, but what is directly presented is the virtual object with the relevant surface marks included. Even up close where the virtual object is only partially realized and the physical textures and painterly qualities are dominant, the virtual object comes through in part. There is no such thing as seeing only the surface properties if one takes in all that is present to one, even up fairly close - certainly if one is near the point where one might hope to have the subject soon take over. I invite any skeptic to try it. Even where the one's foveal area of sharp vision is quite small, say eight inches across, some graphic elements will lie in front of others, a virtual space will open up revealing some object, a hand, a dog's ear, a bit of lace, a patch of smoky atmosphere (I am thinking of Las Meninas but the point can be made for any of Velazquez's works).

8. The pictures cited as counterexamples to perceived likeness theories of depiction, e.g. by Lopes, are ones whose visual field representations (or outline shapes, etc.) cannot be seen as resembling as a whole any single visual field representation in actual perception. For example the Australian aboriginal bark paintings of kangaroos where the skeleton and other internal features appear within the outline of the animal. So far as I can see these have to be regarded as "superimposition" pictures (sometimes called x-ray pictures), where visual aspects which cannot appear simultaneously or under the same conditions are combined by being superimposed on each other. Superimposition applies not only to internal features being combined with external form but particular surface features being superimposed on a part of the outer form that does not carry them, for instance both eyes shown on the same side of the head of a kangaroo. Presumably the subject is also divided: it is both the kangaroo's exterior and certain of its external and internal features. As Budd emphasizes, in such cases there is still ample perceived resemblance of design-elements to subject-elements. This is not, however, to say that the resemblances are actually perceived, as opposed to being perceptible, prior to recognition of the design as a picture, or that there is any general rule as to what sort of resemblance suffices for depiction.

Since both exterior and interior are presented in a planar way there is sometimes no depth effect, but more characteristically there is a shallow fictive depth, optical or material. Hence a kangaroo and kangaroo skeleton are sometimes seen-in the picture only in the sense of the representation being seen as located within the format, not in the sense of anything kangaroo-like being seen as residing in fictive (material) depth. Other times a flat kangaroo (or fish or turtle) shape stands out in front of textured surfaces in optical space; still other pictures place figures in material depth of a generally shallow and ill-defined sort. Different sorts of pictures call for different spatial interpretations. There is much material for close analysis in the variety of depictions.

Budd, Malcolm 1993. “How Pictures Look,” in Knowles and Skorupski, eds. Virtue and Taste ( Oxford : Oxford University Press).

____________, 1995. Values of Art Pictures, Poetry and Music , ( London : Penguin).

Susan Feagin, 2001. “Presentation or Representation” in the Journal of Aesthetics and Art Criticism , 56: 234-240, reprinted in Rob van Gerwen 2001.

Gombrich, Ernst, 1960/1988. Art and Illusion: A Study in the Psychology of Pictorial Representation . ( Oxford : Oxford University Press).

Hagen, Margaret A., 1986. Varieties of Realism: Geometries of Pictorial Representation . ( Cambridge : Cambridge University Press).

Hopkins, Robert 1997. Review of Lopes 1996, British Journal of Aesthetics, 37, 3.

_____________ 1998. Picture, Image and Experience ( Cambridge : Cambridge University Press).

_____________ 2003a. "What makes representational painting truly visual?" Proceedings of the Arisotelian Society Supplement 77 (2003) 149-167.

_____________2003b. "Pictures, phenomenology and cognitive science," Monist 86 (2003).

Kubovy, Michael 1986. The psychology of perspective and Renaissance art . Cambridge : Cambridge University Press.

Lopes, Dominic 1992. “Pictures, Styles, and Purposes,” British Journal of Aesthetics 32.

_____________ 1995. “Pictorial Realism,” Journal of Aesthetics and Art Criticism , 53 (1995).

_____________ 1996. Understanding Pictures ( Oxford : Oxford University Press).

_____________ 2005. Sight and Sensibility: evaluating pictures ( Oxford , Clarendon Press).

Peacocke, Christopher 1983. Sense and Content ( Oxford : Oxford University Press).

__________________ 1987. “Depiction,” Philosophical Review xcvi, 3 (July 1987).

Podro, Michael, 1998 . Depiction . ( New Haven and London : Yale University Press).

Schier, Flint , Deeper into Pictures , 1986. ( Cambridge : Cambridge University Press).

Van Gerwen, Rob 2001. Richard Wollheim on the Art of Painting: art as representation and expression , ed. Rob van Gerwen, Cambridge : Cambridge University Press, 2001.

Walton, Kendall, 1990. Mimesis as Make-Believe . Cambridge : Harvard University Press.

_____________, 1987. 'Looking at Pictures and Looking at Things,' in Andrew Harrison (ed.), Philosophy and the Visual Arts . The Hague : D. Reidel.

Wollheim, Richard 1980. Art and Its Objects ( Cambridge : Cambridge University Press).

_______________ 1987. Painting as an Art (Princeton: Princeton University Press).

________________2001a, “On pictorial representation,” in Rob van Gerwen 2001.

Hopkins' outline shape is hence an abstraction from the traditional idea of a “visual pyramid”of rays in a rectilinear projection of an object to a point, as in the diagram. I find it helpful to locate it within this larger picture. The base of the visual pyramid with apex PP1 is flat but slanted, since it conforms to the face of the Egyptian pyramid relative to PP1. The base of the visual pyramid with apex PP2 is more complex, since it conforms to two slanted sides of the object. This schematization results in more substantial “visual shapes” – three-dimensional ones that more fully represent both the object and our visual data, allowing for depth of focus. The projection of the motif on PL1/PL2 is a cross section of the visual rays. While it is flat (providing the picture plane is flat), it possesses a dimension of depth defined by the length of the visual rays from the projection point to their terminations on the plane. Thus a change in the position or orientation of the picture plane will alter the shape of the projection, even though the change would not be visible from the projection point.

2. Stick figures are peripheral in my account, since there is virtually no 3D pictorial or optical space in such figures. For more discussion of this, see note 7 following.

3. I follow Hopkins in using the upper case “S” to indicate that this is a technical usage.

4. Note how extreme this is: every surface mark seen by the viewer is seen in terms of a property of the anomalous “man” seen in the drawing. All that is necessary for Separation is for some marks that are not subject-indicating to be seen as visually ostensible subject-indicating. There are obviously degrees of Separation.

5. The artist may produce a line which displays the speed of the stroke rather than depict the subject determinately. (138, 144)

6. At this point I use “seeing-in” in a general sense, without reference to any particular account of it, e.g., either of those given by Wollheim.

10. Domenico Ghirlandaio, Portrait of Giovanna Tornabuoni , 1488. tempera on panel, 77 x 49 cm. Museo Thyssen-Bornemisza , Madrid .

12. I am aware that this flies in the face of the alleged perceptual constancy of the pictorial effect (Kubovy calls it robustness). But the effect of constancy obtains only when pictures are viewed with less than scrupulous attention and with the assistance of clear indications of the orientation of the surface, such as the rhomboidal projection of its format to the viewer, almost always reinforced by other environmental markers, or where viewed from so great a distance that the alterations in our visual field of the format and environment are slight. Not all features are as robust as others. I find, for example, that in viewing pictures on a slightly inclined surface the height of the figures is more readily seen as shortened than the sides of the format are seen as convergent.

14. This is too bald a formulation, of course. It is nearer the truth to say a picture can never reveal as much of the spatial form of its subject as can a sculpture in the round.

20. Thus we can tell from viewing a portrait from a considerable variety of points of view that the subject's eyes will follow us as we move from side to side.