PUNTO DE EQUILIBRIO

Obliqueness, we noted, creates depth when it is perceived as a deviation from the vertical-horizontal framework because tension can be reduced and simplicity increased when the frontal obliqueness straightens out in the third dimension. For our next step we must treat obliqueness as a special case of an even broader perceptual feature, by asserting that obliqueness creates depth because it is a gradient. When we relate an oblique visual object to the stan dard coordinates (Figure

204a)

we observe that the distance from the vertical or horizontal increases or decreases gradually. If the principle of convergence is employed, e.g., in central perspective, an additional size gradient, a tapering from broader to narrower shape, obtains in the figure itself (Figure

204b).

S P A C E

Figure 204

in space and time. James

J.

Gibson was the first to draw attention to the depth creating power of gradients. He emphasized texture gradients, such as the gradually changing density of grain or shading, the coarser texture being correlated with nearness, the finer with distance. Although he realized that gradients create depth in line figures as well, he thought of these as "ghostly abstractions" of what is observed in daily experience. Since he assumed that

gradients create depth in pictures because they do so in the perception of the physical world, he believed that the most realistic texture gradients, e.g., in the photograph of a pebbly beach, create depth most efficiently. Actually, the opposite is more nearly correct. Purely geometrical line drawings such as con verging checkerboard floors or the highly abstract constructions of the painter Vasarely contain most powerful depth gradients. This is so because the ef

fectiveness of a perceptual gradient depends on the visual articulation of the pattern. The more explicitly the gradient is presented in shape, color, or move ment, the more compelling is the depth effect. Fide lity to the physical world is not a crucial variable.

When in an animated film a small disk expands, perception has to choose between keeping the distance constant and recording a change of size, or keeping the size constant and changing the distance. In weighing these sim plicity factors against each other, perception opts for the latter alternative. It transforms the projective gradient of size into a gradient of distance. Any

�

eptual feature at all can serve to form gradients. Figure 205 schematically 111d1cates a few of them: distance from the horizontal-vertical framework, size of objects, size of intervals. Since in this example they all act in the same di rection, they reinforce one another. Such gradients are the principal cause of our seeing rows of telegraph poles, fences, trees, or columns recede into depth.

S P ACE 277

Figure205

The more regular the gradient, the stronger its effect.

A

row of equal cardboard squares produces a convincing gradient, in the manner of Figure

:205. If, however, the squares are made to vary in size irregularly, there will be

confusion between size due to projection and size due to the physical measure ments of the objects, and therefore the gradient will be impaired or even destroyed or reversed. (One can experiment with a row of squares whose physical size grows more quickly than their projective size diminishes.) A field strewn with rocks of varying size may produce this sort of partial gradient, whereas Van Gogh's two chairs in Figure

206

display a strong depth effect because they vary in nothing but size and location.

278 S P A C E

The size gradient is one of the early devices to represent depth in pictures. Children soon learn that when figures arc made larger they look closer. This device, together with a height gradient that correlates depth with vertical dis tance from the base line of the picture, goes a long way toward satisfying spa tial needs. Georges Seurat in his best-known painting,

An Afternoon on the

Grande f att

e, organizes the distance dimension by distributing figures of de creasing size over the entire field. These figures are not ordered in rows but spread irregularly across the surface. The various sizes are represented rather comprehensively, however, so that a continuous scale leads from the front to the back.

Gradients create depth because they give unequal things a chance to look equal. If the gradients in Figure 205 are completely successful, we see squares of equal size lined up at cquai intervals. Furthermore, by creating depth the gradients transform the oblique slope of the row into a more stable arrange ment on a horizontal plane. Thus there is a great gain in visual simplicity.

The steepness of the gradient determines the range of perceived depth: if

we construct two equally long rows of squares, the one in which the size

difference between the first and last squares is the greater will produce the deeper vista. As we shall see, steep gradients were preferred by Baroque artists such as Piranesi. Optically, they can be obtained in photography and film with the help of short-focus lenses.

Whenever size changes at a constant rate, the observer sees a correspond ingly steady increase in depth. Thus, Figure 207a can be seen as a straight-line fence. However, when the rate of the gradient changes, the rate of increasing distance changes accordingly. In Figure

207b

the gradient Battens out and results perceptually in a curved fence (even though in these figures the neglect of all other gradients, such as the thickness of the bars, the intervals between them, and the orientation in space, militates against the depth effect).

Similarly, as James J. Gibson has shown, a sudden change in rate will

I I I _I

I I I _{II I}

Figure 207

S P A C E 279 create an edge between two surfaces of different inclination, and a gap in the continuum of the gradient will create a hiatus or leap in the depth dimension. Some painters and photographers prefer a fairly dense continuum of space, leading without interruption from the front to the back. They thereby obtain a steady recession in an obliquely oriented composition. Others, with a greater stake in frontality, employ large leaps-for exampl�, between foreground and background-thereby retaining the simple duality of figure and ground. In traditional portraits, such as Leonardo's

Mona Lisa,

the eye must jump from the frontal figure directly to the distant landscape.

We noted that gradients support constancy of size. If there are gaps in the gradient, constancy tends to break down since it does not come about by itself but must be created by visual factors. The figures in a distant landscape do not look the same size as the person portrayed in the foreground; and when

we peer down from a tower or airplane things are by no means their natural

size. "A little cloud out of the sea, like a man's hand,'' says the Bible.

What· has been shown for size gradients holds true for other perceptual factors as well, e.g. for motion gradients. Just as the spatial intervals between the squares or telegraph poles diminish, so the speed of an object in an ani mated film must diminish if the object is to be seen as moving away at a constant speed. A motion gradient also adds to the depth effect in a landscape as we observe it from a car. Buildings and trees in the foreground race past us much faster than distant ones, and the difference in apparent speed correlates with our distance from what we see.

Aerial perspective relies on gradients of brightness, saturation, sharpness, texture, and to some extent of hue. In nature, the phenomenon is due to the increasing body of air through which objects are seen. However, aerial per spective is effective in painting not mainly because we know that it indicates distant expanses in nature. On the contrary, those vistas in nature are so deep because of the perceptual gradients they produce. Photographers know that the focus scale from blur to sharp image shapes the volume of an object con vincingly even though the zoom lenses of our eyes have prepared us for no such experience. In portraits, for example, the relief of the head may be heightened when the eyes of the sitter are in focus but his ears and the tip of his nose arc slightly blurred.

Not all gradients create depth. In the paintings of Rembrandt one can see that a scale of light, leading from the brightness near the source to complete darkness will not produce its usual strong depth effect when it extends like a halo in all directions around a center. In such a case the frontal pattern is not seen as the projection of a simpler one in depth. The same is true, for example,