Arnheim's great books, this one as well as his Visual Thinking, began a revolution in the understanding of art and inspired me to make my own analysis of one artist's paintings, van Gogh, so I just wanted to make a few comments about that. (I even once received a letter from Arnheim, saying he liked my ideas). His ideas have influenced many researchers since, including myself, and I hope you don't mind if I make some further comments on that. Again, I owe Arnheim for pointing me in the right direction. So the following ideas really result from following his lead, so I hope it won't be considered too inappropriate to post them here.
As Ernst Gombrich has shown, analyzing space in a picture is an extremely complex business. The fact that even sophisticated observers sometimes form mistaken impressions of a pictorial space is itself an interesting phenomenon and illustrates an important principle of the human visual system, which is that it is not very good at evaluating precise metrical relationships. If the space is so constructed that it is at least internally consistent, it may look realistic when it is not, and the space may even seem distorted when it is not.
Considering the problem of the different recession rates for the objects in van Gogh's paintings, how do we account for these distortions? We could simply dismiss them as errors resulting from van Gogh's inability to paint perspectivally, but would be a mistake, for the following reasons:
1) The magnitude and direction of the errors in the sizes of objects are consistent with known psychophysical mechanisms of size constancy.
2) There is a strong shape constancy effect, and also (as John Ward has pointed out), such as in the two chairs and the pictures on the wall (in his Bedroom at Arles).
3) Van Gogh's failure to map out an initial, precise, major metric eliminates the most important perspective cue for object scaling and thus permits the inherent constancy-scaling effects of the human visual system to surface.
4) Although distorted perspectivally, the space is nevertheless internally consistent. This is to be expected from secondary size-constancy effects.
5) The technique of squinting to enhance one's depth of field, which van Gogh sometimes used, would reinforce cues to size constancy by essentially putting the station point behind the artist.
Points 4 and 5 require further discussion.
As noted earlier, secondary size constancy is the tendency for the sizes of objects to correlate with other perspective cues. Even in a painting with a very poorly defined or no major metric (such as in van Gogh's Bedroom), most perspective errors are not random. If they were, the errors would occur in both positive and negative directions about some mean value and would therefore average out. This is rarely the case, however. Usually the errors show a consistent trend. This is because once a given direction and magnitude of deviation has been established, other cues tend to be altered accordingly for the sake of consistency. This can be seen in van Gogh's Bedroom where different objects show similar effects. Although the objects themselves show different vanishing points, the size effect is nevertheless the same.
Van Gogh is also known to have used squinting in order to increase his depth of field. This would cause both foreground and background objects to appear simultaneously more in focus and therefore would have the effect of putting the station point artificially in back of the observer. Durer illustrated a device to accomplish this in his treatise on perspective, but simply squinting strongly can produce a powerful effect of several feet.
Schapiro, Heelan, and various other writers have commented on the sense of realism which van Gogh's paintings create in the viewer. But at this point we could ask why, if van Gogh's perspective space is in many ways so imprecise, we continue to see it as powerful and realistic? Partly it is due to the fact that although there are many spatial distortions present, the space is nevertheless consistent with psychophysical expectations and the distortions due to size constancy are of the proper psychophysical magnitude. This is perhaps to be expected given van Gogh's interest in objects and in the depiction of objects for their own sake. The result is that objects possess more autonomy in van Gogh's paintings than they would if he had taken pains to construct a unified perspective space and thus show appropriate psychophysical effects.
The main reason, however, concerns a fundamental principle of mammalian visual systems. It has been demonstrated repeatedly in experiments that the human visual system is a poor detector of the absolute values of such things as brightness and distance. On the other hand, the visual system is very good at preserving relationships and relative levels of things. Our eyes, for example, throw away information about luminous intensity but conserve and even enhance information about relative brightness and contrast borders, as in the well-known case of Mach bands. This mechanism enables us to easily detect the outlines of objects under varying levels of illumination. In fact, the visual system is such a good extractor of lines that it creates them where they don't even exist or where they are only suggested, as in the well- known case of illusory and subjective contours.
A similar phenomenon occurs in space perception. As I discussed earlier in this article, many experiments have shown that people rarely view paintings from the proper perspective point, and yet experience very little distortion in the perceived objects. This suggests that the visual system constructs an internal model which preserves the relations between the objects in a scene. When distortions occur, the visual system is capable of compensating internally for the perceived distortion. In practical terms, this means that the perspective may depart substantially, both quantitatively and qualitatively, from reality and yet be seen as realistic if it is not too greatly distorted and if the space is at least internally consistent.
What all this shows is that artists are, in essence, perceptual problem solvers, or, as Rudolph Arnheim has said, "visual thinkers." Such a view is, I believe, preferable to the idea that the artist paints from some inexplicable or mysterious talent, or from some sort of abnormal psychology or pathology.