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    Our understanding of how vision contributes to our perception of space and motion advanced when a newly minted researcher, James Gibson, co-opted to the U.S. Air Force during World War II, stood on a runway watching fighter planes landing. 6 Without question, landing is the most difficult part of flying—seasoned pilots will tell you that the definition of a successful landing is one that you can walk away from. In wartime, when new pilots needed to be trained quickly and in large numbers, there was a tremendous incentive to understand what made landing an aircraft so difficult. There was also great interest in developing a psychological test that might predict a person’s aptitude for flying. Both of these problems fell to Gibson. Gibson must have been acutely aware of the personal consequences of failure. One of his predecessors had presented potential pilots with brief glimpses of the silhouettes of different types of aircraft and then asked them to identify the shadows. This very difficult task was an abysmal failure in predicting flying aptitude, and its inventorwas discharged to the front lines. When John Watson, who later became an important figure in twentieth-century psychology for his theories of learning, was assigned the flying aptitude task, he found a way to pass the job along to a colleague, perhaps saving himself from the embarrassment of failure.
    James Gibson showed more perseverance than his predecessors and eventually came to realize that good pilots kept track of their direction of movement, their altitude, and their velocity by taking advantage of certain regular patterns of visual motion that were produced by a moving observer. Gibson called these patterns optic flow, and he considered them to be at least as important to our sense of our own position as the signals we received from our vestibular system. As we move forward, the images of different parts of the world sweep across our retinas, but the region of space whose image enlarges most slowly indicates our direction of motion and our target. What this means to a pilot is that as his aircraft arcs toward the ground, the part of the planet’s surface that appears to be expanding most slowly, called the focus of expansion, is his point of interception with the ground. One part of being a good pilot is developing an understanding of how such optic flow information can be used.
    The patterns of visual motion that Gibson described guide our movements all the time. While driving a car, for example, we can gauge our direction of motion using the focus of expansion. In a similar vein, as we approach a target, we can calculate when to slow down and stop in order to avoid a collision using simple calculations based on measurements of optic flow. Our ability to avoid being struck by oncoming projectiles, such as knowing when to duck to avoid being conked by a baseball, is also based on these kinds of calculations. There is even some evidence suggesting that human beings, and many other animals, possess specialized neuralcircuits for detecting and responding very rapidly to these visual motions.
    There is little doubt that Gibson was correct in his surmise that we use optic flow to complete simple orientation movements similar to those that can be observed in animals looking for light, darkness, warmth, or food. All of these patterns of visual motion, both those caused by our own movements and those caused by movements of objects in the world, could theoretically be used to compute our position and so help us to know our place in the world. As we will see later, the calculations that are involved can become enormously complicated, and it isn’t at all clear that we can carry them out very accurately, especially when our movements take us on the complicated paths of travel that characterize our everyday behavior.

    The simplest kinds of problems in navigation involve nothing more than finding a way to decrease the distance between oneself and a