You Are Here (10 page)

Findings such as these suggest that these animals hang on to their sense of place with great tenacity. Draconian disorientation procedures, including incarceration in dark boxes and on spinning turntables, can affect performance in some types of tasks, but even
here one of the most peculiar things is that animals, rather than falling back on other sources of information not affected by such procedures (such as landmarks), will sometimes behave as though, having been robbed of their primal attachment to the earth, they cannot make proper sense of these other beacons of navigation.

Do human beings use the same strong sense of direction in solving navigation problems? Edward Atkinson’s experience in an Antarctic blizzard, the many anecdotal accounts of people becoming lost in wilderness, and our own tendency to become lost in relatively simple environments like shopping malls and office buildings suggest that we are built differently. Now we should see what the scientific studies have to say.

As a young woman is ushered into a psychology laboratory, she is asked to don a pair of opaque goggles to occlude her vision and a set of headphones to muffle ambient sounds. She communicates with the experimenter via a tiny earbud speaker. The woman is led about the room to one invisible target after another and is allowed to touch each one in turn. At the conclusion of this learning phase, she is led to a starting position and directed to walk to a specified target. Except for the fact that she is in a completely unfamiliar environment, this woman is in similar circumstances to the hapless cottage owner stumbling about looking for the light switch, or the exhausted mother trying to find her way out of a dark bedroom to the sounds of a crying infant. In experimental psychology labs, we can measure with great precision the extent to which people in such circumstances can find their way around, and the results are interesting, to say the least.

In one of the first such studies conducted in my laboratory, we had participants stand at one end of a standard squash court, take
a good look around, and then let us lead them from place to place while they wore opaque goggles. We led participants to a series of different objects, one at a time, and then we led them back to the starting position and asked them to strike out by themselves to find the objects. One of the first odd things we noticed was that even though the participants had had a good look at the size and shape of the room, they would raise their hands before them so as to avoid collisions with the walls, even though in many cases the nearest obstacle was at least five meters away from them. Discussions with participants both during and after our procedures soon made it clear that they had very little idea where they were. Our formal measurements of their performance in simple tasks designed to test their knowledge of their own positions revealed that they were performing at levels barely distinguishable from chance. In these initial studies we made no deliberate attempt to disorient them—no lightproof carts or spinning turntables were required for our participants to become completely disoriented. The differences in behavior between people and other animals could not have been more striking.
¹²

Through years of experience, we have learned many tricks that have helped us to extract reasonable performance from participants in experiments such as these, but there is still a massive contrast between the performances of non-humans in our laboratory and those of the people who volunteer for our studies. With animals, the challenge is usually to find a way to make them forget about the larger spatial context of the labyrinth of laboratory rooms so that we can be sure we’re controlling how our critters use space. With people, the challenge is to provide them with enough support that they can find their way across an ordinary rectangular room without banging their heads into the walls. Why do such differences exist? Though there’s still much that we don’t understand about this, there are some important clues.

In very simple situations, we can find our way to a target with reasonable accuracy. For example, imagine a task in which you are able to take a long look at a target that is lying on the ground some distance in front of you—say about 10 meters. Then, with eyes closed, you are asked to walk to the target. Provided that you are allowed to walk immediately after you close your eyes, you should be able to land within a few centimeters of the target. As you read these words, you may be very skeptical that you could perform well in such a “blindwalking” task. When you have a chance, try it out (ideally in a large, flat, outdoor space like a sports field). You will almost certainly be surprised by your accuracy.

When walking tasks like these are made slightly more complex, human performance unravels quickly. On a triangle-completion task, blindfolded people are walked along a path of a few meters and then, after changing direction, they are led along a second path. Their task is to complete the triangle by walking back to their starting point. There are two main differences between the triangle-completion task and the blindwalking task, both probably important. First, the triangle task does not contain an explicit visual preview of the target or of the stopping points (the corners of the triangle). We need to plan our homing route entirely on the basis of bodily information that we receive while walking (vestibular information, feedback from the muscles used in walking, and so on). Second, the triangle-completion task involves measuring both a pair of walked distances and the angle between them—considerably more complex than just estimating a visual distance. These two differences conspire to degrade our performance on this task sufficiently that, as ants, we would surely starve or fry in the blazing sun. In one typical study, after walking short triangles ranging in size from two to six meters, the average angular turning error in heading for home was more than 20 degrees, and the size of the distance error was around 50 percent of the distance walked.
¹³

Except when the power fails or when we’re trying to creep around darkened rooms without disturbing sleeping family members, we human beings are not very likely to find ourselves trying to navigate entirely without using our visual sense. But the fact that we become disoriented so quickly and completely when deprived of visual fixes has a greater meaning. Our inability to tap into body-based senses to keep track of location may be a deficit rooted in our biology, a loss of an ability possessed by our ancestors that has fallen into dormancy through lack of use, or, what I think most likely, a combination of the two.

If we once possessed the ability to keep track of our location using path integration, perhaps even if not to the same degree seen in ants or even in rats or geese, what has caused our increasing tendency to lose contact with position, place, and space? Has some other way of understanding space come to supplant the ancient ways of gluing us to our place on the planet? The landmarks are now in place, our route is becoming slightly clearer, and some of the answers lie directly on our path.

N
avigation using a map is a key transition from the simple kinds of tasks that I’ve been discussing thus far to the more complicated accomplishment of true wayfinding. In a wayfinding task, not only is the target invisible from the starting point but it can be found only by carrying out the correct sequence of movements based on what can be seen, heard, or felt at each point in the sequence. You don’t
need
a map to complete a wayfinding task, and you
certainly
don’t need a map for any task that is simpler than the definition I’ve just given.

When you read the word
map
, the most likely thing that will spring to your mind (unless you’re a mathematician) is the folded paper that you might find in your glove compartment. There is no
question that this is a map, albeit a very specialized one. The reason the map is taking up space in your car is that it is a useful tool for navigation, and what makes it useful is that the map is a model of the real world. A good map will contain replicas of things found in the real world that it is useful to know about, such as roads, schools, and shopping malls. Maps often have other useful features as well, such as a compass rose that allows you to orient the map properly to the real world and a scale so that you can work out the real distances between the points represented. But do all of these features have to be present for something to be called a map? To answer this question, we’ll want to stand back and take a much more general view of maps, where they come from, and how they are used.

I have a friend who has spent much of his life traveling from one country to another in search of many of life’s greatest pleasures, including fine beers. Because the consumption of fine beer is often incompatible with razor-sharp accuracy in calculations of currency conversions, my friend has learned a useful trick. He carries a card in his wallet that lists a series of dollar amounts and their equivalents in local currency. To a mathematician, this relationship of one set of values to another constitutes a map just as surely as the one in the glove compartment. The main difference between this kind of map and a road map is really only that the road map contains two dimensions whereas the currency chart contains one. Direction isn’t part of a one-dimensional map, so a compass is not required. In both cases, a scaling factor is used to relate one variable to another.

Mathematicians who are interested in different ways of mapping one quantity on to another are called topologists. The formal definition of topology is almost guaranteed to cause you to put this book down and run away screaming, so I will give only an informal
idea of what topologists do.
¹
Imagine taking a sheet of something flexible, like rubber or latex, and drawing a simple map of your neighborhood on it. Now think of all of the ways that you could distort that sheet by, for example, stretching it over your face or stepping on one side and tugging at a corner. The only things that are against the rules are ripping the sheet or gluing any of its edges together. A topologist is interested in understanding which properties are preserved by your wanton handling of this map and which ones are altered.

For mathematicians, the importance of topology is hard to overestimate. Not only does it draw links between major areas of mathematics such as algebra, geometry, and mathematical analysis but it has also led to the mathematical field called graph theory, which has been pivotal in providing the tools to help provide solutions to such practical matters as how to prevent traffic jams and how to design networks of computers. Many problems in applied mathematics involve finding the most direct and efficient routes between one place and another. One classic example of this sort is the “traveling salesman problem,” in which one has to find the most efficient route that provides one visit each to a group of randomly arranged targets. The traveling salesman problem is of interest not only to, well, salesmen but also to those who design such things as circuit boards (to minimize production costs) and robotic devices that carry out repetitive tasks.

In psychology, the field of topology has helped us to understand the ways in which maps can be used to navigate. For example, think of the last time you drew a sketch map for someone to help them find their way from one place to another. Typically, such maps contain only the bare minimum of features that you deem necessary for them to find their way without becoming lost, so the major emphasis is placed on those points where people need to make explicit
decisions (“Which way do I turn when I see the post office?”). Scale is seldom well preserved on sketch maps. A long, straight stretch of highway is likely to be compressed compared with another part of the map where a complicated cluster of intersections needs to be negotiated. So your map is a good topological map in the sense that it preserves the connectedness of places and the order in which they will be encountered, but it is not what is called a metric map because dimension and angle have not been preserved. For the most part, we expect the paper maps that we buy at gas stations to be metric in this sense. We expect there to be a proper scale to them, so that they represent accurate two-dimensional models of the real world.