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  While we move about, we use a series of quick glimpses, called fixations, interleaved with rapid eye movements called saccades. The average duration of a fixation is about half a second. Though there are slight variations, all saccades take roughly the same length of time, less than one-tenth of a second, regardless of the distance the eye travels during the movement. The greater the distance, the faster the eye moves. (Indeed, saccades are the fastest movement produced by the human body.) This detail is important because it suggests that saccades are programmed before they begin. In other words, before the eye begins to move, it knows where it is going. Generally, movements that have this property, whether they are movements of the eyes or of missiles loaded with nuclear payloads, are called ballistic movements.

  These patterns of saccades and fixations have a definable structure to them, related to the actions that they accompany. Fixations vary in length depending on what they are for (locating an object, assisting in a movement such as grasping, checking something). These extraordinary patterns of fixation and movement are one illustration of the elegant pas de deux between perceiver and perceived. Our senses don’t merely take in the world. In a way, we actually make the world we live in through these kinds of interactions. In the most superficial way, our movements through space may resemble those of bacteria and slime molds, but our progress toward the buffet table is underpinned by an elegant and beautiful perceptual dance that is largely beyond the reach of consciousness. With great concentration, as in the exercise I encouraged you to try earlier, we can become aware of the occasional eye movement or head turn, but we couldn’t possibly have a genuine firsthand experience of the staccato visual sampling that underlies our stable perceptions of the visual world.

  GRASPING SPACE

  Movements such as reaching, grasping, and walking have been the subject of intense scientific scrutiny. One reason for this is that the study of such movements has much to tell us about how perception and movement work together, but another, more significant reason is the tremendous importance of our ability to grasp and manipulate objects. Everyone has heard the old saw that the main reason human beings have come to dominate the planet is our possession of an opposable thumb. Though this is a dubious claim (I would put my money on our massive cerebral cortex rather than on our thumbs), there is no doubt that our ability to coordinate our eyes and our hands to interact with the world with exquisite precision is a major hallmark of what it means to be a human being. A few other animals have impressive abilities to manipulate objects (raccoons, for example), but no other animal comes close to our combination of speed, precision, and flexibility in organizing skilled movements using visual control.

  Though we reach for objects hundreds of times a day without a second thought, the problems that must be solved to complete these movements accurately are formidable. We must transform a viewed target location into a set of muscle contractions. If this seems easy, remember that the exact muscle contractions that are required will depend not just on the location of the image of the target on the retina but also on the position of the eye in the head, the head on the body, the arm on the shoulder, and perhaps even the orientation of the torso (think of bending over and picking up an object from the ground). In order to calculate the appropriate muscle contractions, it is crucial that our brains keep careful track of the relative positions of different parts of our own bodies as well as the appearance of the visual scene in front of us. We can do some of this work by using a specialized set of sensory receptors embedded in our joints and muscles. The outputs of these so-called proprioceptors report to our brain on the position of our body. In addition, whenever our brain sends a command to our muscles to move, a copy of that command is kept at hand in a neural filing cabinet so that we can use it to keep track of the expected consequences of each movement that we make. Our brain tries to save time by predicting the consequences of a movement before it has even taken place.

  When we move our eyes, our hands, and our arms, we need only keep careful track of the relative movements of our body parts—eye relative to head, head relative to body, hand relative to shoulder, and so on. Walking changes everything. With each step, we take flight from the surface of the planet, and when we alight we are in a new location. It is no longer sufficient to measure our own muscular contractions or motor commands to determine our exact position in space. We need an entirely new set of tools.

  Carrying a full glass of beer across a crowded barroom can be tricky business. When standing still, or walking at a smooth, unchanging speed, the beer sits securely in the glass, no tidal waves of liquid threatening the floor or our clothes. But each change of direction or speed can cause the precious liquid to slosh around in the glass. Now imagine an observant and scientifically minded drinker wandering across the floor with glass in hand. She might notice that the way the beer moves in the glass is related in a very orderly way to the movements of the glass. Sudden changes of motion cause predictable reactions in the shape of the surface of the ale. In fact, a careful observer could calculate the path of the glass through space by doing nothing other than measuring and recording such changes (though she might not be the most fun person to drink beer with). To calculate accurately, she would need to note each and every movement of the surface of the fluid. If she was distracted for even a moment, or if her memory failed her, the missing data would cause her to lose track of her position completely.

  Many animals, including human beings, have a specialized set of organs that sense movement in exactly the same manner as our observant beer drinker. These structures, called the vestibular system, consist of a series of interconnected chambers and tubes within the middle ear. These wondrously shaped vestibules, looking a bit like a curvy architectural creation by Frank Gehry, are filled with a viscous fluid. Inside each of these tubes is a small chunk of gelatin, studded with tiny crystals of limestone to give it added weight. As our head accelerates and decelerates through space, the blobs of gelatin wobble around just like the beer in the glass. Tiny hairs embedded in the blobs are bent by each wobble, and these bending movements send signals to our brain.

  The vestibular system works remarkably well for controlling certain types of movement. For example, our ability to maintain fixation on a visual target as we walk around or even leap through the air is largely brought about by a precise dialogue between our vestibular system and our eye muscles. But as a device for keeping track of our movements in larger-scale space, the vestibular system has the same weakness as our beer carrier. Errors creep into the mix, and those errors accumulate over time. Without any help from other sources, the vestibular system will become lost and disoriented. One possible source of help comes from the visual system, which has specialized abilities to keep track of our position as we move through space.

  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 inventor was 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 hi
mself 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 neural circuits 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 target that can be sensed directly. As we’ve seen, these kinds of problems can be solved using nothing more than some basic sensors, a means of movement, and some biological wiring that joins the two together. For a one-celled animal seeking sustenance in a lakebed, a sowbug on its way to the dark, moist underside of a rock, or even a basic robotic device, things can be just that simple. Though we humans share these basic elements with all other animals, our guidance mechanisms are embedded in a much larger and more complicated system. Our ceaselessly moving eyes perch atop a complicated tower of flesh, flicking from one viewpoint to another in an elegant dance that helps us to put together an overall view of the world. The basic rules that get us from the street corner to the bus stop, or from the kitchen table to the front door, may not differ substantially from those used by bacteria, insects, or other simple beings, yet the detailed differences in how we use our senses to construct a sensory world will assume increasing importance as this story progresses.

  Many of the everyday challenges of space may involve nothing more than finding a way to move toward a target that is clearly visible, but this is hardly what we think of as wayfinding. More challenging and interesting tasks involve seeking out targets that cannot be seen directly. Here we enter a new realm where we find positions by using the relationships among things, rather than the very simple changes in the apparent size, shape, and strength of sensory signals that characterize our use of taxic mechanisms.

  CHAPTER 2

  LOOKING FOR LANDMARKS

  HOW WE SEARCH FOR THE INVISIBLE

  BY USING THE VISIBLE

  The philosophy of the school was quite simple— the bright boys specialized in Latin, the not so bright in science and the rest managed with geography or the like.

  AARON KLUG

  One of the worst jobs I ever had was poring through old life insurance records to discover the names and birthdates of children of policyholders so that the company I worked for could create a computer program to send out birthday cards to those children. Though the job was staggeringly dull, there was one saving grace. The office I worked in was near the top of a skyscraper on the outskirts of downtown Toronto, and from its south-facing windows, I was able to watch the construction of the CN Tower, until recently the tallest free-standing structure in the world. The highest parts of this tower were built using a magnificent Sikorsky Skycrane helicopter, an undertaking of such significance that the schedule of appearances of the machine was published in some local newspapers and broadcast on the nightly news. I had a front-row seat, free of charge, provided I could master the art of pretending to fill computer coding sheets with names and dates while watching the tower take shape.

  As a young man whiling away his hours at a boring job, I had no sense of the transformative effect the tower would eventually have on the city. The main justification for the structure was that the boom in high-rise construction in downtown Toronto had begun to impede various kinds of radio telecommunications. But the rationale clearly had as much to do with establishing a “world-class” landmark for the city, an identifiable icon of space-age advancement, as it had to do with the pragmatics of transmitting radio waves and microwaves. But as well as serving as a landmark in the more colloquial sense of the word—as a structure whose silhouette has become identifiable as a part of the Toronto skyline as readily as New York City’s Empire State Building or Seattle’s Space Needle—the CN Tower has come to serve as a true landmark in the navigational sense. Wherever you are in the core of the city, or even in the outer fringes, it doesn’t take much of an effort to find the tower and thereby to help fix your own location. (The positional fix is helped along by the fact that the tower is located near the north shore of Lake Ontario, so one is very unlikely to be south of the tower.) The tower can also be used to gauge one’s distance from the downtown core. When I drive into the city, along a highway that skirts the edge of Lake Ontario, the easiest way to judge my progress is to take a fix on the apparent size of the tower.

  Used in this way, the CN Tower is a classic navigational landmark. Though the tower itself is most often not our final destination, we can find our goal by its relationship to the tower. We have gone slightly beyond the realm of navigating toward targets that we can see. We are no longer following plumes of the delicious aromas arising from buffet tables, or flying airplanes on to clearly visible runways using tools not conceptually different from those employed by everything from the E. coli bacteria in our guts to rattlesnakes hunting down field mice. Now we are using the visible to find our way to what is invisible. To do this means to have at least an implicit understanding of the spatial relationships between things. Such abilities place us in slightly more rarefied company.

  Some of the first conclusive studies demonstrating animals’ use of landmarks for navigation were conducted by the biologist Nikolaas Tinbergen. Though he was eventually awarded the Nobel Prize for his studies of animal behavior, Tinbergen was the black sheep in his family. In contrast to his industrious brother, Jan (who also won a Nobel Prize, for economics, in 1969), “Niko” was known for spending dreamy summer vacations observing and photographing animals rather than applying himself in a rigorous manner to any of the established branches of zoology.1 What was most remarkable about Tinbergen was his flair for close observation of the behavior of animals followed by elegant and convincing field experiments that highlighted the principles underlying his observations.

  On one family vacation, Tinbergen spent some time observing digger wasps. These wasps dig small nests in the ground, which they provision with captured and paralyzed insects so th
at when their young hatch they will have a larder awaiting them. This set of behaviors requires the wasps to repeatedly leave the nest and then return to it. Tinbergen wondered how the wasps found their way back to the tiny, almost invisible entrances of their nests.

  Tinbergen’s approach was characteristically simple yet effective. Wondering whether the wasps might be using visual landmarks to locate the nest entrance, he simply removed some of the natural objects that lay scattered near the entrance, sat back, and waited to see what would happen. When the wasps returned, it was clear to him that they had become disoriented. Tinbergen’s experimental coup de grâce came from a further experiment in which he seized control of the situation by replacing the objects surrounding the nest entrance with a carefully arranged circle of pinecones. Once the wasps overcame their confusion and regained their ability to find the nest, Tinbergen shifted the ring of cones to a nearby location. When the wasps returned, they searched for the nest entrance in the center of the displaced array of cones, demonstrating that Tinbergen had correctly identified the manner in which wasps found their way home.2

  This simple, informal style of experiment has come to form the backbone of studies of landmark navigation in animals ranging from the wood ant to the human being. Today, though the sophistication of the methods used has advanced to a state that Tinbergen could not have imagined, the logic of the experiments has changed very little.

  Tom Collett, an experimental biologist at the University of Sussex in England, has spent a lifetime studying spatial navigation in insects.3 Collett’s taste in species has been democratic—he has worked with a variety of ants, bees, and wasps, so his findings generalize well. One question that preoccupies Collett is the way insects memorize configurations of landmarks. What do they look for as they try to return to the nest? Despite the small size of their brains, insects show surprisingly sophisticated cognition. When leaving a place to which they need to return, flying insects carry out highly structured orientation flights, in which they turn to face the goal and carry out a series of swooping arcs around it. Their purpose is to produce a kind of image or snapshot of the vista surrounding the goal location that can be recalled later.