Although the visual shape of an object is largely determined by its outer boundaries, the boundaries cannot be said to
be
the shape. When a man in the street is asked to take· the route indicated in Figure 71a: "Walk two blocks, turn left, walk two more blocks, turn right, walk one block . . . . " he will end up back where he started. This will probably surprise him. Although he hasmoved along the entire contour, his experience is unlikely to have contained
the essentials of the image he will suddenly form in his mind when he grasps the cross shape he covered on his walk (Figure 71
b).
The pair of axes, although not coincident with the actual physical boundaries, determines the character and identity of the shape. Similarly, in Figure 67 it was possible to present the basic compositional theme of Brueghel's painting by means of straight lines,Figure 71
S H A P E 93
which in no way resembled the actual outlines of the figures. We conclude that in speaking of "shape" we refer to two quite different properties of visual ob jects: (
r)
the actual boundaries produced by the artist: the lines, masses, volumes, and (2) the structural skeleton created in perception by these material shapes, but rarely coinciding with them.
Delacroix said that in drawing an object, the first thing to grasp about it is the contrast of its principal lines: "one must be well aware of this before one sets pencil to paper." All through a piece of work, the artist must bear in mind the structural skeleton he is shaping while at the same time paying attention to the quite different contours, surfaces, volumes, he is actually making. By necessity, human handiwork proceeds in sequence; what shall be seen as a whole in the final work is created piece by piece. The guiding image in the artist's mind is not so much a faithful preview of what the completed painting or sculpture will look like, but mainly the structural skeleton, the configura tion of visual forces that determines the character of the visual object. When
ever that guiding image is lost sight of, the hand goes astray.
A similar discrepancy between physical action and physical shape on the one side, and the image obtained on the other, exists in what the viewer does when he looks at an object. In recent years, exact recordings of eye movements have shown which parts of a picture observers look at, how often and how long they fixate each place, and in what time sequence. Not surprisingly, fix ations are found to cluster in the areas of greatest interest to the viewer. Other
wise, however, there is little relation between the tracks and directions of eye
movements and the perceptual structure of the final image that emerges from the scanning. The structural skeleton is no more due to the movements of the viewer's eyes than it is to those of the artist's hands.
Different triangles have distinctly different visual charatters, which can not be inferred from their actual shape, but only from the structural skeleton their shape creates by induction. The five triangles in Figure 72 are obtained by vertically displacing one corner point while leaving the other two constant.
94 S H A P E
Wertheimer noted that as the moving point continuously slides downward, chances occur in the triangle that are not continuous. Rather, there is a series of transformations culminating in the five shapes shown. Although caused by changes in the contour, the structural differences between the triangles cannot be described in terms of their contour.
Triangle a (Figure 73) is characterized by a main vertical and a secondary
Figure 73
horizontal axis, which meet at right angles. In b the main axis is slanted to the right and divides the whole into two symmetrical halves. The edge to the left, although objectively still a vertical, now looks hardly vertical at all. It has become an oblique deviation from the main axis of the pattern. In c the obliqueness of the whole has disappeared, but now the shorter, horizontal axis has become dominant because it is the center of a new symmetrical division. Triangle
d
reverts to obliqueness, and so on.The structural skeleton of each triangle derives from its contours through the law of simplicity: the resulting skeleton is the simplest structure obtainable with the given shape. It takes a distinct effort to visualize less simple struc tures-for example, c as an irregular oblique triangle or
d
as a deviation fromthe right-angled type e (Figure 74). Symmetry is used wherever it is available
I�
Figure 74
S H A P E 95
(b, c, d): in a and
e
rightangularity provides the simplest available pattern.The structural skeleton consists primarily of the framework of axes, and the axes create characteristic correspondences. For instance, in the three isos celes triangles of Figure 72, the two equal edges correspond to each other; they become the "legs," whereas the third is seen as the base. In the other two triangles the right angle makes for a correspondence between the two sides that oppose the hypotenuse.
From what has been said it follows, first, that the same structural skeleton can be embodied by a great variety of shapes. Looking ahead to Figure 95, we see three of the innumerable versions of the human figure produced by artists of different cultures. One is surprisingly ready to recognize the human body in the most primitive stick figure or the most elaborate paraphrase-if only the basic axes and correspondences are respected.
It follows second that if a given visual pattern can yield two different structural skeletons, it may be perceived as two totally different objects. Lud wig Wittgenstein's discussion of the famous duck-rabbit, a drawing that can be seen as the head of a duck looking to the left or as that of a rabbit looking to the right, shows what puzzles one must face if one assumes that the actual outlines on paper contain everything there is to the percept. This particular drawing allows for two contradictory, but equally applicable structural skele tons, pointing in opposite directions. Wittgenstein, an acute observer, realized that this was not a matter of two different interpretations applied to one per cept, but of two percepts. That two percepts could derive from one stimulus struck him as a cause of wonder.