The preceding analysis shows how
wrong this viewpoint is. The contrast between Leonardo's geometric expectations
and our experience is the very issue at hand, the issue we wish to understand.
No one has claimed that "the fact observers are not consciously aware of
distortions in virtual space" implies "that the nature of virtual
space is unregistered by the visual system." On the contrary, most theoreticians
of picture perception (including Rosinski and Farber) believe that observers
are not aware of distortions in virtual space because a part of the visual system
(whose workings are unconscious) registers both the nature of the virtual space
and the orientation of the surface of the picture, and corrects the former in
the light of the latter.
Rosinski and Farber oversimplifywhen they say that "to comment on whether a picture seems distorted is to assess the correspondence between virtual and environmental space." We have seen that evaluating whether a picture seems distorted entails a far richer implicit cognitive process: One must first mentally reconstruct the scene that the painter had in mind and then assess whether within the conventions of the genre - the representation is correct. Take, for example, the exercise in perspective by the early seventeenth-century designer of architectural and ornamental pattern books Jan Vredeman de Vries (1968) shown in Figure 5.2.
Although technically in accord with the rules of central projection, the stele on the left and right are clearly seen as distorted under typical viewing conditions. We know this without ever having seen the architectural structures depicted because we reconstruct the virtual space defined by the outlines and assess the shapes to be sheared outwards rather than symmetrical pyramids. Two sources of information guide our assessment that the shapes are distorted. One is our past experience with monumental architecture, which leads us to expect the stele to rise symmetrically from a square cross-section (rather than rising obliquely from a diamond-shaped cross-section. The other is the repetitive structure of the courtyard; the forms of the stele are sufficiently similar that we expect them all to have the same shape rather than splaying out obliquely, allowing us to sense distortion from the same shape template. Both factors ultimately derive from past experience, but one is specific to known shape while the other is simply based on similarity among shapes. The deviation of the perceived shape from our expectations is experienced as distortion. If the same structure was depicting flower petals rather than a ring of stele, we would not experience them as distorted because we would expect them to splay out, and all degrees of splay are equally prevalent in the environment.
We may ask why the stele appear distorted when the perspective construction is geometrically accurate in all details. The answer is, as emphasized by Alberti, that for the image to be perceived correctly it should be viewed from the location in space for which it was constructed. We have seen that there is substantial tolerance to deviations from this viewing position, but this picture is an extreme example that goes beyond the limits of this tolerance. To be seen without distortion, the required viewing distance is about half the picture height, or 3 cm, which is at least ten times closer than the viewing distance of a typical reader. This is such an extreme deviation that objects around the edge of the picture cannot be adjusted to their expected shapes, generating what are commonly called "marginal distortions". These "distortions" are part of the required geometry of perspective when viewed from the original construction distance, but are perceived as such for large deviations from that distance.
Returning to Leonardo's recommendation to artists, we can say that on the whole his worries were well founded. In general, it is necessary to view a picture from somewhere close to the center of projection to see an undistorted version of the scene it represents. Although there is a substantial range away from this location for which the scene is perceived without distortion, it is nevertheless] true (as we will see later in this chapter) that certain types of objects seen under certain special points of view (such as eyes looking at the viewer, and the barrel of a gun or a finger pointing at the viewer) seem to follow us when we move in front of the picture, these violations of the robustness of perspective are special cases that are typically avoided by the artists of the Renaissance.
We are fortunate to know about these conditions because they provide us with a clue to understanding what makes the robustness of perspective possible under most circumstances. The robustness of perspective fails when "the spectator is unable to see the painted surface, qua surface" (Pirenne, 1970, p. 84); for example, in Pozzo's ceiling discussed in Chapter 4. Here is Pirenne's description:
If the spectator walks away from the yellow disk, thus departing from the centre of projection, the illusion of depth does remain, but the scene represented, still seen in 3D, becomes deformed. The columns, for instance, look no longer vertical, and they may look curved. This deformation continually varies as one walks about in the church. The impression one gets is that the whole structure, which no longer appears in line with the actual church as an extension of it upward, would be about to collapse if it were real.3