Let me remind the reader how the question of finding the center of projection came up: We were inquiring why the surface of the picture had to be perceptible for perspective to be robust; in the geometric analysis just concluded, we saw that to find the center of projection we have to construct a perpendicular to the picture plane. Now to erect a perpendicular to the surface of the picture, that surface must be visible. If we assume that the visual system performs an analysis that is analogous to these geometric constructions, then we should not be surprised to observe that when the surface is not visible, as in Pozzo's ceiling, the robustness of perspective is lost. If you do not look at the ceiling from the yellow disk that tells you where to stand for your eye to be at the center of projection, the painted architecture looks lopsided and about to tumble. Pirenne summarizes this point in the following words:

When the shape and the position of the picture surface can be seen, an unconscious psychological process of compensation takes place, which restores the correct view when the picture is viewed from the wrong position. In the case of Pozzo's ceilings, on the other hand, the painted surface is `invisible' and striking deformations are seen. (1970, p. 99)^3.

		Fig.7.3 If magic lantern will not come to body's eye, mind's eye must go to magic lantern. (a) When a transparency is projected onto a plane not parallel to plane of transparency, it will look distorted from all vantage points. (b) When a transparency is projected onto a plane parallel to plane of transparency, it will not look distorted from any vantage point (except very extreme ones).

Further evidence on the crucial role of the perception of the texture of the picture plane in making possible the robustness of perspective can be obtained by carrying out a very simple experiment. Suppose you want to show slides to an audience, and you are forced to place the projector on one side of the room. How should you place the screen: Should you have the screen face the people in the middle of the room, or should you set up the screen to face the projector? The intuitive solution to this problem is the former. We are uncomfortable in turning the screen away from the spectators; we feel we are not giving them the best possible chance to see the pictures, for, we think, they will look distorted. However, the correct solution is the nonintuitive one: Always set up the screen to be perpendicular to the projector; otherwise the picture will look distorted to everyone in the audience. The explanation for this surprising rule of thumb is simple (see Figure 7.3): We have argued that viewers normally feel that their mind's eye is on a perpendicular to the picture plane, erected at the foot of the principal ray. Let us assume, for the sake of simplicity, that a photograph of a natural scene is being projected. Under optimal viewing conditions, the screen is at a right angle to the optical axis of the projector, and the spectator is very close to the optical axis of the projector. Because most slides are not cropped, the center of the slide can be taken as the center of projection; on that point, a line perpendicular to the picture plane is erected and the viewer feels that his or her mind's eye is on that line, which happens to coincide with the optical axis of the projector, and hence no distortion is experienced. In fact, as long as the optical axis of the projector remains at right angles to the screen, the mind's eye will fall on that axis. However, if the screen is tilted relative to the optical axis of the projector, the viewer will locate his or her mind's eye at a point away from the optical axis of the projector and will perceive a distorted picture.

		Fig.7.4 Photograph of a photograph (Time, March 29, 1968).

The account I have given of our preference for the positioning of projectors also holds for a phenomenon pointed out by Pirenne (1970, pp. 96-9): If we look at a photograph of a scene that has a photograph in it (such as Figure 7.4), the scene will not appear to be distorted regardless of the point from which we look at the photograph. But unless the photograph in the scene is parallel to the picture plane, it will appear to be flat and distorted from all points of view. It will be seen only as a picture and it will not have the vividness of depth that the scene it belongs to may have. This is an example of the operation of a mechanism of compensation for the viewer's position in space vis-à-vis the picture's center of projection: It suggests that the compensation requires the viewer to be able to perceive the surface of the picture. But in what sense does one not perceive the surface of the photograph in the photograph? In Figure 7.4, we can immediately see that we would have to move our viewpoint to the right in order to see the poster of Nixon frontally. Thus, strictly speaking, we can see the orientation of the surface of the distorted photograph. Why then is it distorted? I believe there are two reasons for this.

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³ This theory was developed by Pirenne on the basis of a suggestion made by Albert Einstein in a letter written in 1955.