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must be repeated here that, before stereopsis is actually experienced by the patient, there is nothing one can do or say which will adequately explain to him the actual sensation experienced.”

It is not possible for most scientists and doctors to experience both a normal and strabismic view of the world. Ophthalmologists, for example, must have excellent vision to operate on their patients’ eyes. Yet, Brock seemed to have an uncanny understanding of how I once saw and how my vision had changed. Curious, I delved deeper into his writings and found out why. Frederick Brock was a strabismic. The first patient he had treated was himself.

7

WHEN TWO EYES SEE AS ONE

I want the unobtainable. Other artists paint a bridge, a house, a

boat, and that’s the end. They are finished. I want to paint the

air which surrounds the bridge, the house, the boat, the beauty

of the air in which these objects are located, and that is nothing

short of impossible.

—Claude Monet

Two days after my first stereo experience, I was pulling clothes out of the dryer and noticed something quite odd. I happened to glance up at the collection of winter coats suspended from pegs fixed to a wall located about ten feet away from me. One of the coat sleeves was popping out toward me, capturing and defining a layer of space that I had never seen before. The folds and creases in the coats stood out in striking clarity and detail. The scene reminded me of a painting by Jean Auguste Dominique Ingres of the

Princess Albert de Broglie (Figure 7.1). I had always liked the portrait but used to think that the pleats and grooves in the princess’s clothes were painted in an exaggerated manner. No one, I thought, really saw the texture of the gown in that kind of depth and detail.

While our family’s coats lacked the grandeur and eloquence of the royal gown, their wrinkles and folds were now as captivating to me as the painting of the princess and her beautiful dress. I walked up to the coats and rearranged them, punching down the quilted material in some places, puffing it up in others, then walked away to see how they looked. I walked back and ran my hands along the material to see if the sense of three dimensions that I saw from ten feet away matched the threedimensional feel and shape of the garments. I was reminded of my children when they were little babies, of how they found the wrapping paper around a gift to be more appealing than the gift itself. I also realized that I was calibrating my newfound stereopsis with my former ways of inferring depth.

FIGURE 7.1: Princess Albert de Broglie, née Joséphine- Eléonore-Marie-Paulinede Galard de Brassac de Béarn, by Jean Auguste Dominique Ingres (1780-1867). (Image copyright © The Metropolitan Museum of Art/Art Resource, New York)

Three-dimensional objects cast their images on our retinas, which are made up of flat sheets of cells. We construct a 3D view of the world from these 2D images using a combination of depth cues. With stereopsis, we compare the position of the images on the two retinas to construct a vivid sense of three dimensions. We also use cues that can be seen with just one eye. These are the same cues that painters like Ingres use to evoke a realistic sense of three dimensions on a flat canvas. In fact, by discovering and exploiting these cues, the artists of the past were in many ways vision scientists.

Imagine that you are a new, perhaps reluctant, student in a beginning art class, and your teacher hands you a lump of clay. She asks you to sculpt a ping-pong ball. You rub the clay between your two palms until its surface is smooth and round. Then, you paint the clay ball white. This proves to be no problem at all. You have created a three-dimensional sculpture to represent a three-dimensional object. So far, art class is a piece of cake.

Now, the teacher gives you a new assignment. You must draw the ping-pong ball. Again, you think that this will be

ridiculously easy. You confidently draw a circle on a piece of paper.

But the picture you’ve drawn looks more like a flat, white disk. It could represent a cylinder seen from the top end or, perhaps, the bottom of a white, semicircular mound. Since you’re trying to represent a three-dimensional object on a two-dimensional piece of paper, your picture is ambiguous.

FIGURE 7.2

As you puzzle over how to make your circle look spherical (Figure 7.2), the art teacher suggests that you place your ping-pong ball below a small lamp. When light strikes the ping-pong ball from above, the upper surface

appears bright, while the lower surface is in shadow. Since we normally see the world with light from above (from sunlight or from overhead lights in a room), we interpret a circular object that is bright on top and dark below as a sphere. So, you try making the top surface brighter than the bottom to represent this shading difference, and notice that your flat circle looks more 3D (Figure 7.3). This is one of the tricks Ingres used in his portrait of the princess. With shading, her gown looks so solid and real that you feel you can almost reach out and touch it.

FIGURE 7.3. (© Julia Wagner)

If your lamp light hits the ping-pong ball from above but at a slight angle, the ball will cast a shadow—which it wouldn’t

do if it were a disk lying flat on the ground. So, you redraw the ping-pong ball with a shadow as if it were illuminated from above at an angle, and now your drawing looks convincingly like a sphere (Figure 7.4).

FIGURE 7.4. (© Julia Wagner)

The art teacher then shows you many additional tricks for suggesting depth, the same depth-perception cues that you unconsciously use in real life. If, for example, a tree in real life or in a painting breaks up a view of a fence, then you infer that the tree is standing in front of the fence. This cue is referred to as object occlusion. An artist can use this cue not only to suggest depth but to create an optical illusion, as

M. C. Escher often did. In the Escher-like drawing in Figure 7.5, the artist has used the principle of object occlusion to confuse us. Both wheels are blocking parts of each other, so you cannot figure out their position in relation to each other.

FIGURE 7.5: Which wheel is blocking which? (© Margaret C. Nelson)