If one wishes to gauge the intensity of an experience of depth induced by a picture, it is best to compare it to the most effective technique available: the stereoscope. Figure 4.1 shows a stereoscopic pair of drawings prepared by Sir Charles Wheatstone in 1831 to demonstrate his discovery of the basis of stereoscopic vision to the Royal Society (Wheatstone, 1838). If you look at them as instructed in the caption, only one picture will be seen by each eye, and you will experience the full strength of the effect. To understand the effect, hold an object in your hand and look at it first with one eye and then with the other. Because each eye sees the object from a slightly different vantage point, the object casts a somewhat different image on the retina of each eye. Each of the lines of the drawing projects a slightly different image (in orientation or position) to the two eyes. Moreover the difference between the images depends on what you're looking at in the picture. Nevertheless, when both eyes are open we see only one object; we do not see double as we might naively expect. Of course, the visual system cannot fuse two images that are very different. To see how limited is our ability to fuse disparate images, hold up your two hands, side by side, a few inches apart, their backs facing your eyes, index fingers pointing up, about half a foot before your nose, and focus on one of your fingers. Make sure that you can see both fingers clearly. If you can't, move them closer to each other. Now slowly move the hand at which you were looking closer or further away. Over a short distance, both fingers will remain in focus, but after your hand has moved about an inch you will notice that the finger at rest looks double. This is because the visual system can only fuse the two disparate images that a single object casts on the two retinæ if the so-called retinal disparity between these two images is not too large. The retinal disparity of the finger you were looking at remained zero while the retinal disparity of the other finger grew as you moved it away. Wheatstone demonstrated that if retinal disparity is small the two images not only fuse but also give rise to a most compelling experience of depth, called stereopsis.¹

What is the function of stereoscopic vision? It gives us the ability to accurately gauge and compare distances in our environment, over the range of a mile or more away. For instance, you will find it extremely difficult - indeed almost impossible - to perform a task requiring fine perceptual motor coordination at close range (such as threading a needle) with one eye closed. Given the critical role played by stereoscopic vision in the performance of such perceptual-motor skills, and given the range over which stereoscopic vision can operate, one might think that the world would appear flat when seen through one eye. The truth is that one-eyed people are not at all handicapped when it comes to visually-controlled tasks, such as throwing a ball or landing an airplane, which draw upon many types of depth information other than stereoscopic vision. From our ability to gauge depth with one eye, we might predict that a monocularly viewed picture that projects onto the retina the same image as might be projected by a three-dimensional scene would be seen in depth, because the picture would then be a projective surrogate for the scene. A projective surrogate was considered by Gibson (1954) to be a special case of the