Using the language of Lines 135 Ambiguity and Reversibility Words and sentences can have many meanings. "Bow" can mean a ribbon, a part of a ship, or a posture. In "They are cooking Chapter Eight apples," the word "cooking" can be a verb or an adjective. Similarly, an individual line can depict any of the basic features of the visible environment. Usually the pattern around the line determines what is referent is, just as the phrase around "bow" limits it to "the colorful bow in someone's hair," or "the proud bow of a courtier." Using the One can ask what meaning the word "bow" could have on its own. And, similarly, one can take a simple line pattern and ask what it could depict. A circle can depict a hoop, ball, or coin, a fact that Language of Lines suggests depiction is a matter of will and choice. But closer examination leads to a different conclusion. When a hoop is de- picted, the line forming the circle depicts a wire. When a ball is depicted, the line depicts an occluding bound. To depict a coin, the line depicts the occluding edge of a disc. Notice that the referents are part of the language of outline. A highly detailed drawing may be unambiguous in its refer- ent, just as a full sentence around the word "bow" restricts the To claim that light and pictures can referent of the word. Ambiguity in perception results when only a be informative is not to deny that light and pictures can puzzle, too. few elements are considered, be they words or lines. And the In this chapter I will try to account for some of the puzzles and perceiver then selects from a set of possible referents. In the case of trickery in pictures. I will pry into ambiguity and into the workings language, the possible referents are an arbitrarily chosen set. In the of "reversible" displays, and I will try to explain "impossible" pic- case of lines, the referents are drawn from a language of outline tures yet show that the language of outlines is not violated by am- depiction that is not arbitrary, for training is not necessary for biguity, reversibility, and impossibility. Just as verbal language is recognition. It may be necessary to have some experience with de- systematic and yet capable of puzzling ambiguity, so is light and tailed, high-fidelity pictures before one can treat simple drawings as outline drawing. pictures of many possible things; discovering ambiguities in figure- Probing into the comparison between language and pictur- ground drawings is a skill that increases with age, and it is more ing, this chapter will consider whether the language of outline is developed in more intelligent children (Elkind and Scott, 1962). But restricted to vision. Experiments on touch with blind subjects will the skill makes use of the language of outlines and does not show what meanings outlines can have for the hand as well as the introduce completely new referents. In this vein, consider the dis- eye. plays that demonstrate one-sided shaping effects. 134 At first, the incomplete letters in Fig. 40 are not seen. Shapes are visible, but not the shapes that could form parts of letters. 136 A Psychology of Picture Perception Using the Language of Lines 137 Meaningless blocks are seen at first. With a hint, one can reverse the figure. Then the lines no longer shape only the blocks; one notices the shapes on the other side of the lines. At first, the spaces between blocks seem like distant background behind occluding edges of Fig.40 surfaces. The enclosed areas seem like flat foreground surfaces, and the lines depict the edges of surfaces. When reversed, with letters visible, the lines still depict edges, but the flat foreground areas are now on the other side of the lines. In sum, the side where surface seems to be alternates in Fig. 40, yielding blocks or letters. Another case of reversibility, one of the most famous, is Rubin's vase faces figure (Fig. 41). As a vase, the left and right lines represent rounded surfaces-that is, occluding bounds-with the bounded surface enclosed by the lines. The top line represents an occluding edge with surface below the line, and the bottom line Fig. 41 depicts an occluding edge with surface above the line. As a face, Fig. 42 each of the two sides again depict occluding bounds, but now they are occluding in the reverse direction. The top and bottom lines are FIGURE 40. After a few moments, incomplete letters become irrelevant to the faces, and do not depict at all; that is, they are seen visible. simply as lines on paper. FIGURE 41. A figure can be Seen as a vase or as two faces. This The figure-ground reversibility of Figs. 40 and 41 involves was used by Rubin to demonstrate figure-ground reversibility. reversing the direction of occlusion. A circle depicting a disc at one FIGURE 42. The lines in this figure can be seen as depicting a moment and a window at the next involves the same kind of billowing sail, or as a kite, symmetrical about a diagonal axis. reversibility. However, if the circle depicts first a disc and then later figure giving rise to remarkable orientation reversals is a triangle a ball, it is not the direction of occlusion that changes. Instead, the like that in Fig. 44, which can be taken as a depiction of an isosceles line depicts first an occluding edge and later an occluding bound, a triangle in depth. The orientation of the depicted triangle can be demonstration that reversals need not interchange figure and ground, switched radically. The Necker cube is more complicated than the the sides where shape is. triangle. In the cube, there is change of occlusion as well as change A beautiful example of a reversal that does not affect figure- of orientation. The wires "in front" where two lines cross usually ground is Fig. 42. At first the lines depict a billowing sail--and the switch as the obliques reorient. The ""in front" changes reveal sail may bow into the page or out of the page. With a switch of important aspects of depicting wires by lines. Usually, when a wire attention the lines can depict a kite, symmetrical about a diagonal is depicted by a single line, features of wires are omitted, like axis. The figure is almost unrecognizably different as a sail and a information for their rounded cylindrical shape and their surface kite, a reversal that is not figure-ground in type. textures. (Similarly, the triangle is depicted without information for Yet another reversal, pointed out by Necker in 1832, is its orientation, and a circular line seen as a depiction of a hole does evident in depictions of wire objects or transparent objects. A not provide information for the depth in the hole.) In some ways, the Necker cube (Fig. 43) reverses so that its front face and its back face results of omission control Necker cube reversal. Where the wires alternate. Its oblique lines reorient as the figure reverses. Another overlap, it is not evident which line is "in front." But if the cube is 138 A Psychology of Picture Perception Using the Language of Lines 139 al cubes made of real wires at the same rate (about twenty-two times per minute in a period of two and a half minutes). Even making the front face a different color (black) than the back face (grey, as in Fig. 46) did not affect the rates of reversals. Similarly, Pandina, Zeller, and Lawson (1971) found a three-dimensional cube reversed as often as did a pictured cube. It seems that information for occlusion or depth is unimportant once reversals have begun. Only in the period before reversals have started--before the reversed appearance is discovered--is such information significant. Fig. 43 Fig. 44 Fig. Fig.46 45 FIGURE 43. A Necker cube, which reverses so that the FIGURE 45. A cube drawn as though made of thick wire, oblique lines reorient, and different lines appear to be to the front. each side of the wire depicted by a line, revealing clearly which faces of the cube are in front. With a little practice, FIGURE 44. This simple triangle can be seen oriented in even this cube can be reversed quite readily. the plane of the paper on which it is printed, or slanting first FIGURE 46. A wire cube made of wires of different one way and then another. shades. redrawn (Fig. 45) as though made of thick wire, each side depicted Kennedy and Brust's finding makes sense if one thinks of by single lines, the cube is not so reversible. Information about reversals as involving a kind of attention, where the subject takes which wire is in front is presented in Fig. 45. In general, the more the display as depicting one thing and then another. Seeing some- information for which line is in front, the longer it will take for a thing as a depiction involves a kind of attention, found in its purest wire cube to reverse (Howard, 1961). form in looking at a simple figure like a circle and taking it to be a It is not impossible to make Fig. 45 reverse. With a little picture of a hoop. There is nothing about the circle that specifies a effort, the left side can be seen depicting either a near face or a far hoop rather than a hole, so it requires a special kind of pictorial face of the cube.