Follies of the perspective theorists, 1: Nelson Goodman and Languages of Art

In his book Languages of Art of 1976, the American philosopher Nelson Goodman considers how systems of symbols work in the arts; not just in literature, but in those fields that use non-verbal symbols like painting, music, dance, and architecture.[1] He opens his first chapter with a discussion of realistic pictures made in perspective. The book was very influential on the rise of cultural relativism in the humanities; in particular the revival of the old idea, going back to the 1920s and Erwin Panofsky’s essay on Perspective as Symbolic Form, that linear perspective is an arbitrary cultural convention.[2]

The conventional wisdom, Goodman says, is that “An artist may choose his means of rendering motion, intensity of light, quality of atmosphere, vibrancy of color, but if he wants to reproduce space correctly, he must… obey the laws of perspective.” These laws, as introduced in the Renaissance, “… are supposed to provide absolute standards of fidelity that override differences in style of seeing and picturing.” The definition of a picture in correct perspective is that it presents, to an eye, a bundle of light rays that corresponds geometrically to the bundle of rays which that eye would receive directly from the scene depicted. As Alberti and Leonardo said, a picture in perspective is like a view through a window, drawn on the glass. Seen from the viewpoint, the lines on the glass follow the lines in the scene.

Goodman will have none of this. His aim is to ‘assail common sense’. He marshals a series of arguments, all of which seem to me false. First, he cites Ernst Gombrich’s case in Art and Illusion that “there is no innocent eye”. A person looking at a picture comes with preconceptions. “Not only how but what [the mind] sees is regulated by need and prejudice.” So, according to Goodman, it is not possible for a picture to convey the real appearance of its subject. This is surely misconceived.

We have three entities: the picture, the real scene, and the viewer. The viewer brings his or her prejudices and prior knowledge both to the picture and to reality. This does not affect the perspective relationship between the picture and the scene. The perspective will be correct or not, irrespective of who looks at it or what they think. An artist does not have to adjust his or her work to accommodate the preconceptions of the public. Not all people who look at realistic pictures will consciously understand or appreciate their perspective structure; but those who do, will be able to recognise the correspondence of the picture to the scene.

Goodman’s second argument is that, in any case, the laws of perspective are not true. The assumption that a picture will “deliver a bundle of rays matching that delivered by the scene itself”, he says, is “plainly false”. He gives an example. “By the pictorial rules, railroad tracks running outward from the eye are drawn converging, but telephone poles (or the edges of a facade) running upwards from the eye are drawn parallel. By the ‘laws of geometry’ the poles should also be drawn converging. But so drawn, they look as wrong as railroad tracks drawn parallel.”

This is a basic misunderstanding, about the angle at which the poles are viewed, either in direct vision or in a perspective picture. If a person looks straight ahead at a row of telephone poles - that is to say, his or her eyes are directed horizontally - then the poles will indeed appear vertical. The same is true of a frontal perspective with a central axis that is horizontal. However, supposing the observer looks upwards at two adjacent poles, then they will appear to slope inwards towards each other. The same applies in a perspective whose axis is angled upwards. If the lines of the poles in such a perspective image were continued, they would meet in a vanishing point above the picture. Goodman assumes that the central axes of perspectives are, or should be, always horizontal. If not, the result ‘looks wrong’. He is thinking about people looking at pictures hanging on walls at eye level. He worries that a picture of telephone poles may have a perspective axis tilted upwards, but is being viewed by an observer looking straight ahead.

The issue, admittedly, is psychologically complex. It is a curious historical fact, which probably misled Goodman, that theorists of perspective, and artists, have been reluctant to discuss this convergence of verticals, or depict it in paintings of buildings. In the past such pictures have indeed seemed wrong to many observers. (I discuss this in a separate essay, ‘Looking up’.) It is arguable that the experience of tipping one’s head back to look at very tall buildings and photographing them in the nineteenth century provoked a reassessment of how they should be represented. Today I think most people are familiar with the effect from photographs and are not disturbed. The important point is that, however viewers might feel about pictures in which verticals converge, they do not break the laws of perspective.

Goodman ends his discussion with an illustration that, as he believes, clinches his general argument.[3] But there are troubles here, again having to do with what happens when people look up. Goodman imagines a person looking at a tall tower. His diagram is complex, so I have decomposed it into several parts, and simplified his argument somewhat without losing the essential points. In the first part, the person’s eye is at a. He looks towards the point f on the tower. His axis of vision af is angled upwards. So he sees the sides of the tower converging upwards, as in my thumbnail sketch (Figure 1). A perspective made at the picture plane indicated by the heavy line would be similar.

Now Goodman considers a picture of the tower made from a much higher viewpoint m. The observer’s axis of vision mf is horizontal. Here the sides of the tower in the view or in a perspective picture will be vertical, as in my second thumbnail (Figure 2). Goodman imagines the observer looking at this image at ground level from the viewpoint a, as though it was a conventional picture hanging on a wall. He is triumphant about the fact that the picture does not match the view looking up. (Of course it does not. For the picture to correspond to the view it would have to be made with the axis of vision angled upwards and the picture plane tilted back, as in Figure 1.)

Goodman imagines two ways in which the picture of Figure 2 could be made to resemble the view by moving it to different positions. The first way is to hang the picture high up above the observer so that he sees it from below (Figure 3). My diagram shows the picture at the right, and what the viewer would see at the left. In the picture the walls are vertical, but from this viewing position both the image of the tower and the frame of the picture would appear to converge. Goodman’s second way of hanging the picture is to set it directly in front of the observer but at an extreme tilt, so that again the verticals in the picture, and its frame, would be seen to converge (Figure 4). But as Goodman comments: “We do not usually hang pictures far above eye level, or tilt them drastically bottom towards us.”

What is the trouble here? First, as mentioned, Goodman is focussed on pictures that are hung vertically on walls in front of viewers who look horizontally at them. Second, he makes the basic assumption that we must always look at a picture in perspective from its theoretical viewpoint (and very strictly, look with one eye only, through a peephole). This is necessary, however, only if the artist is seeking to deceive the viewer into believing that he or she sees, not a picture, but the real scene.

In other circumstances, people can look at pictures in perspective without problem from many positions and angles. The mind is capable of allowing for the fact that these positions are well away from the theoretical viewpoint. The perspective does not appear wrong unless the picture is viewed from a very extreme lateral position. We are also quite capable of imagining ourselves, in front of a picture, to be looking from somewhere quite other than where we are actually standing. We can look at a bird’s eye view of a city in a book or on the wall before us and imagine ourselves up in the sky looking down. We can look at a painting of a skyscraper by Georgia O’Keeffe directly in front of us and imagine that we are craning our heads upwards.

Branko Mitrovic analysed these geometrical fallacies in Goodman’s argument, in a paper given in 2012. [4] Extraordinarily, his was the first such critique.