But, from what 1 have explained in earlier chapters, a high center of projection should pose no problem: The robustness of perspective should take care of correcting for distortions caused by viewing the fresco from a vantage point that does not coincide with the center of projection. The Last Supper does, however, pose a problem, for Leonardo was not content to leave robust enough alone. He did not just produce a space that is internally consistent; he created a space that suggests architectural continuity with the refectory, an illusionistic architecture along the lines we have discussed in Chapter 4. Unfortunately, no one has taken a photograph of the fresco from the center of projection. To get a feel for how well the fresco meshes with the line defined by the feet of the liernes that define the ten bays, consider the photograph shown in Figure 9.12, taken from approximately the height of the center of projection, somewhat too far to the left of the refectory, and about 25 m (roughly 82 ft.) too far.12 The tops of the tapestries represented on the right wall of the room in which the Last Supper is taking place cry out to be aligned with the feet of the liernes on the side wall of the refectory. In Figure 9.13, which is a simulation of the view of the fresco from the height of the center of projection, and looking straight on at the vanishing point, but still somewhat too far away, the alignment of the feet of the liernes in the refectory with the tops of the tapestries in the fresco is quite close.
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Fig.9.13 Franz Fischnaller's reconstruction of the relationship between the real architecture of the refectory and the painted architecture by Leonardo by the feet
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Assuming that a viewer standing at the center of projection sees the virtual space in which the Last Supper takes place aligned with the real space of the refectory, we have an interesting problem. To judge from his writings, Leonardo seems at one point to have not believed in the robustness of perspective. As we saw in Chapter 5, he recommended that paintings be viewed from the center of projection or that the center of projection be "at least twenty times as far off as the greatest width or height of the objects represented" (Leonardo da Vinci, 1970, §544, pp. 325-6). In his Last Supper, he created a painting that no one, under normal circumstances, would see from the center of projection. Had he created a virtual space that did not suggest itself as an extension of the real space of the refectory, the robustness of perspective would have ensured that no distortions would be perceptible. But in addition to defining an elevated vantage point, he designed the architectural background of the Last Supper to mesh with the refectory in a way that could produce its illusionistic effect only when seen from the inaccessible center of projection. If this line of reasoning is correct, then this masterpiece further enriches the dialectical tension between the observer's station point and the center of projection of the painting. Because there is a suggestion of continuity between the real and the virtual architecture (very much as in Pozzo's ceiling), the inconsistency between them "pushes" you away from the low vantage point to which your body confines you, and "pulls" you up toward the center of projection, which resolves the tension. At the same time, the inconsistency helps you adopt a non-corrective way of looking at the fresco, one in which the you can pay attention to the rather jarring discrepancies between the virtual and real architecture. In this respect, Leonardo created a "difficult" work of art, one that forces you to engage in mental work to overcome the obstacles Leonardo has placed in your way to achieving an illusion of depth via perspective.
In fact, Leonardo did even more to make the work difficult. You will remember that Pedretti's measurements give a figure of 46 by 26° for the angular extent of the fresco when seen from the center of projection. You will also recall that rectangular objects seen under an angle greater than 37° are likely to appear distorted (Chapter 7). Nevertheless, none of the representations of right angles (be they visible or implicit) violate Perkins's laws. And yet something is wrong. The shape of the virtual room represented in the fresco does not appear to be rectangular, but trapezoidal. To quote Steinberg:
To one who can read a simple perspective, the suggestion that Leonardo's space is meant to be experienced as if on a trapezoidal plan comes as an affront - as though one didn't know how to read. The literate eye wants to interpret the waning width of the room as an illusion - not what is "really there." [We omit here an interesting footnote by Steinberg.] If the side walls seem bent on closing in behind Christ, our educated intelligence knows that such mere appearance must be discounted. (1973, p. 376)
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Fig.9.14 Cropped version of Leonardo's Last Supper
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Steinberg claims that this impression is caused by the failure of certain key features in the fresco (the upper edges of the hanging tapestries) to align with corresponding features in the refectory when the fresco is seen by a person standing on its floor. But even when the fresco is reproduced so that the walls of the refectory are invisible (Figure 9.9), that is, under conditions that allow the robustness of perspective to come into play, the impression of accelerated convergence remains. I believe that the impression is caused by Leonardo's unusual cropping of the upper part of the picture. If the ceiling had been allowed to extend to its intersection with the picture plane, I believe there would have been no tendency to perceive the plan of the virtual room as being trapezoidal. In the absence of such an uncropped picture, we can make a similar point by cropping the picture into conformity with more standard representations. In Figure 9.14 I have cropped the sides of the fresco. As a result, the impression of looking into a trapezoidal space is greatly diminished. The reason for the change is that, although none of the intersections that are part of the perspective construction violate Perkins's laws, the points at which the upper boundary of the picture intersects the ceiling-wall orthogonal is (to use the terminology introduced in Figure 7.17) a tee, and therefore cannot represent a rectangular corner. If, as we argued in Chapter 7 the presence of such local features affects our perception even though their component lines are not intended to be interpreted as belonging to one trihedral angle, then the walls should have a tendency to be perceived as being in the same plane as the ceiling. Indeed, if one crops the bottom of the fresco, as in Figure 9.15 , there is little to suggest that the light regions on either side of the coffered ceiling represent walls
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Fig.9.15 Cropped version of Leonardo's Last Supper, showing top part only
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Was Leonardo aware of all these effects when he designed this painting? We shall never be certain. There is no question, as his notebook entry (quoted in Chapter ) shows, that he was acutely aware of the problem of distortions caused by moving the eye away from the center of projection, and so it is extremely unlikely that any feature that we have discovered in this work escaped Leonardo's notice. Steinberg asked himself this question, and his answer serves us perfectly: "It is methodologically unsound to imagine Leonardo insensitive to the implications of his inventions" (1973, p. 369). There is one passage in Leonardo's late writings (Atlantic Codex, folio III, v-b in the Ambrosian Library of Milan, written at least twenty years after he painted The Last Supper), that suggests that Leonardo may have understood the way in which perspective can induce an experience of elevation in the spectator:
And the figure painted when seen below from above will always appear as though seen below from above, although the eye of the beholder may be lower than the picture itself. (Emphasis supplied. Quoted by Pedretti, 1978, p. 39, footnote I)
Let us recapitulate the lengthy argument of this chapter. We started with two general answers to the question why the Brunelleschi peephole was abandoned, namely, that peepholes are gimmicky and that, because of the robustness of perspective, peepholes are not necessary to achieve a compelling illusion of depth. In the latter part of this chapter, we discussed two masterpieces in which perspective was exploited to achieve effects that could not be achieved by any other means. Mantegna used perspective to produce a discrepancy between the direction of the spectator's gaze (upward) and the direction implicit in the orientation of the picture plane (horizontal). The result is a vibrantly tense work full of foreboding. Leonardo used perspective to elevate the viewer to an extraordinarily high center of projection, thus achieving a feeling of spiritual elevation. At the same time, the odd cropping of the top of the picture tends to destroy the rectangularity of the room in which the Last Supper is taking place. As a result, there is an indefiniteness, an ambiguity, about the place, most befitting to the locale of an event so critical to the spiritual life of the church.
