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Our preference for vertical alignment crops up in everyday life as well. Who among us has not felt (and perhaps succumbed to) the desire to straighten a crooked picture on a stranger’s wall? Filmmakers use a technique, pioneered by Alfred Hitchcock, in which slight camera tilts produce sensations of visceral discomfort in viewers. When lines that would normally follow the horizontal or vertical are pushed slightly toward the oblique, cinemagoers are, quite literally, put on edge.
Note what is happening here. Psychological tendencies that have their roots in the orientation of our body and the organization of our senses seem to have taken precedence over what we see and feel of the dimensions of physical space. When we try to imagine such spaces, whether by remembering pictures or by mentally replaying our movements through space, our predilection for the clean vertical and horizontal contours overrides much of our ability to represent spaces accurately. We construct spaces rather than sense them.
CHUNKS OF SPACE
Anyone who has looked at children’s drawings knows that our mind tends to simplify visual patterns. The complexity of real forms comes to be replaced by simple collections of basic shapes, organized according to schemas—sets of rules that dictate how these basic shapes must be fitted together. Such schematization of shapes results in human figures that become sticks with big round heads. Birds in flight become stylized squiggles, and the sun is represented as a yellow disk with a symmetric burst of sunbeams around it. An important part of the training of an artist consists of learning to draw what is seen rather than what is in one’s mind. In other words, artists must be taught to unlearn the routines of schematization in order to draw accurate copies of real life.
The same processes that simplify our drawings act on our conceptions of space, and the reasons are similar. Maps that simplify spaces, straighten curves, even out distances, and turn irregular clumps of land into orderly geometric shapes are much easier for us to remember than those that contain every warp and wobble of raw geographic space.
One of the best examples of this tendency to regularize space, and another of the factors responsible for the geographic illusions that I pointed out in my list of questions, is something called regionalization. To understand how regionalization works, try this exercise: as you are sitting at this moment, close your eyes and point to the location of some object that you know to be in the room with you—a lamp, window, or door, it doesn’t really matter. If you open your eyes, you’ll probably discover that you were able to point reasonably accurately to the object you chose.
Now try something different. Imagine an object again, but this time, choose something that is outside the room you’re sitting in. If you’re sitting in your home, you might try pointing to the position of an object in a room on another floor. Now try pointing to the location of your best friend’s home. What about the location of city hall, or the nearest body of water? As you go through this exercise, you’ll notice that some targets are easier to point to than others, and that completing this task for certain kinds of landmarks will involve considerable mental gymnastics. You may have noticed something else as well. When we are required to imagine the position of an object that is not currently within view, we try to reconstruct that object’s position in a series of discrete steps. I can point to the lamp across the room with no difficulty whatever, but if I then try to point to the location of the toaster in my kitchen, several rooms away, I try to reconstruct a path from where I am to the goal object, and then mentally add together all the segments of the path. Instead of trying to conjure a spatial image of the toaster from my current position, I manage the problem by first imagining the view from the threshold to my study as it opens into the hallway beyond. This orients me toward the kitchen. Then I imagine myself at the end of the hallway, looking into the kitchen. At each stopping point I imagine a view, and then I try to add all the views together to connect the beginning to the end of my path. As you can imagine, the larger the number of segments involved, the more likely we are to become inaccurate.
In one study of the psychological regionalization of space, people were taken into a small, windowless room and, after being given a chance to look around to become familiar with their surroundings, they were asked to close their eyes and point to objects in the room, much as I suggested you do a few moments ago. Participants found this task easy and generally did well at it. Next, they were taken out of the room and led on a walk around a part of the building that surrounded the experimental room. At various stopping points on their walk they were asked to point to objects inside the room they had left. Once back inside the room, they were asked to point to objects they had seen outside. Participants found both of these latter tasks to be much more difficult, presumably because they were trying to piece together views of space in the same way I did when trying to imagine my toaster. Other studies conducted with people in spaces that they had used regularly for at least two years (their offices) showed similar findings, so our difficulties in making spatial connections do not seem to have much to do with the amount of experience that we have with a part of space.7
Why do we regionalize space? One part of the answer is that regionalization is a handy way to help out our limited memory resources. Most people, when called upon to remember a long list of items, will resort to a strategy called chunking. For example, when I try to remember a grocery list, I categorize items into different groups—fruits, vegetables, meats, dairy, and so on. Then my job is to remember a small group of lists, each containing a handful of items, and this is easier than trying to remember one long list. The process of learning about spaces is similar. It is easier to memorize the locations of a series of objects within each room, and also to remember the rough layout of a set of rooms in a house, than it is to try to remember a long set of locations of objects and to place them all on one very large map.
Although this kind of hierarchical organization of space can help us to manage our memory load, it results in distortions in our maps of space. In our mental maps, the distances between points that are in different regions seem longer than distances between points within the same region. This effect is strong enough that it not only affects how we think about our lived spaces while sitting idly and reflecting but it also influences our choice of routes when walking or driving. A route that requires many changes in direction seems longer to us than one that is straight. The reason is that each turn brings into view a new set of features, and so constitutes a new region. The practical implications of these effects have drawn the interest of those who design buildings, neighborhoods, and cities because it is possible to influence how people might use a space by judiciously tinkering with its size and shape. In an urban center, if we want people to get out of their cars and walk, many clever tricks of planning will entice them to do so, but one tactic is to make interesting locations appear closer together by prudent organization of space.
Our tendency to chunk space into regions is a cornerstone of our spatial mind. Even experiments that use highly abstracted spaces show a strong effect. For example, one study showed that if research participants were asked to memorize the positions of a random array of objects on a computer screen, they did so by mentally dividing the screen into a series of regions based on the locations of the objects they saw. When they were quizzed about the distances between objects, distances within mental regions shrank compared with those that crossed regions.8 Most of us, when asked whether Seattle or Montreal is farther north, will answer by remembering that Canada is north of the United States and then assume (erroneously) that Montreal is north of Seattle. Similarly, Reno seems as though it should be east of Los Angeles because Nevada is (partly) east of California.
Mental maps, like the maps we sketch on napkins to guide our friends around town, are filled with inaccuracies, distortions, and even absurdly impossible spaces. When we begin to draw a map and we preface our effort with words such as “This is not to scale, but …,” we are implicitly acknowledging this feature of the weird spaces that
we share with one another. But beyond being a kind of graphical shorthand we use to convey the main features of geographic spaces, the maps we sketch have deep affinities with the properties of the spaces that inhabit our minds. Our minds treat distance and direction with cavalier disrespect but represent topological relationships with greater clarity. Though we don’t seem to have much of a grasp of how far away things are, nor what their angular relationships might look like (especially when they cross regions), we have a good idea of how different parts of space (roads, paths, hallways) are connected. Just as topological maps, like twisted rubber sheets, can tolerate much distortion while retaining some information about spatial relationships, so can the maps we hold in our heads help us through spaces, particularly the ones that we build for ourselves. Provided we understand how regions are connected, and what is in each one of them, we can plan routes to goals. We may not always (or even often) take the most efficient route, but we usually know which set of spatial decisions will help us get to our final destination. I might not know how far it is from the bakery to the post office, or which one of those goals is farther from my house, but I know how to get between one and the other, and I know how things will look when I get there.
Are these topological maps of space the kinds of cognitive maps that Edward Tolman had in mind in the 1940s? Are they the kinds of maps that researchers in animal behavior have fought over for the intervening sixty years? Not really. Rats solving a sunburst maze, bees interpreting a waggle dance, and pigeons solving a gradient map to find their way back to a roost need access to a map that retains some metric features. Novel shortcuts work only if we understand the real distances and angles between locations. All too often, unless we are trackers using traditional methods, or members of a culture living by our wits in barren landscapes where one wrong turn can kill us, such spatial information eludes us. Unlike other animals, which are tightly anchored, body to ground, fixed to the earth with a sureness of footing that can be almost impossible to sunder, human beings seem preternaturally prone to a kind of spatial flight of fancy in which our minds sculpt physical space to suit our needs. Though under certain circumstances and with specialized training we are capable of some prodigious feats of navigation, the more common occurrence for modern human beings is that we flounder through a highly schematized version of physical space that has only a weak relationship with the real thing. When this strategy works for us, it is often because we have designed an environment for ourselves that is replete with spatial crutches, an environment that makes heavy obeisance to the metric inadequacies of our spatial brain. But when the strategy fails, it can do so quickly and disastrously, sometimes even costing us our life. We spend much of our life being only one miscue away from complete spatial disorientation.
SPACE AS MENTAL PROJECTION
The news is not all bad for human beings. Though our mind is put together in such a way as to make accurate maps of larger-scale spaces a difficult conundrum for us, the same cognitive capacities that make us get lost walking to the corner store may underpin some of the most remarkable features of our mind, including those that set us apart from all other animals. Our ability to abstract ourselves from our current spatial context, to close our eyes and to visualize ourselves in some other space, no matter how stylized it might be, is probably a uniquely human thing. Our ability to visualize the floor plan of a building from an overhead perspective and to not only see ourselves in the building but to see what we would see from our imagined position is a capacity possessed by no other animal. Though astral projection and other out-of-body experiences may be the stuff of fantasy and science fiction, our ability to throw around our viewpoint at will is real and significant.
Jean Piaget, one of the founders of modern developmental psychology, devised a task that he called the three mountain problem. Children were shown a model of a miniature landscape containing what looked like three mountain peaks. They were asked questions about the appearance of the peaks from alternative points of view. For example, a child might be asked to describe what another child, sitting facing the first child, would be able to see from his position. Piaget found that before a certain stage of development, children had great difficulties with this task.9 In a very real sense they were locked into their own point of view. Older children can adopt these alternative views much as adults can. For me, the wonder of the three mountain problem is not that young children cannot do it but that adult human beings can do it. This means nothing less than that, for all our topological weirdness, we have found a way to free ourselves from the confines of physical space and to take flight. While my body is planted here in this chair before my computer screen, my mind can be down the hall in the kitchen, down the road on the beach, or looking down from high in the sky. From each of these vantage points, I can estimate roughly where to place my own faraway body in the picture.
No less revolutionary than our ability to picture ourselves in physical space from alternative points of view is the fact that we can picture a place that does not contain us. Even though I am no longer in the kitchen, as I was a few minutes ago (stealing one of the few remaining home-baked chocolate chip cookies before the children came home from school), I am completely confident that the kitchen still exists. Even though I have not been to the beach now for two days (sigh), I know that it is still there and that it doesn’t somehow slip off the edge of the universe when it is out of my graspable space. Though these facts might seem obvious, their implications are profound. Were it not for our ability to apprehend parts of the physical world beyond our immediate sight or grasp, we would be very different kinds of beings. An essential ingredient of self-consciousness (and here I mean not the awkward, gangly self-consciousness of a shy teenager but the objective awareness of oneself as a causal agent in the world—in other words, as a being who can make things happen) is this ability to abstract space. If we could not take a vantage point on the world that was outside our own body, we could not appreciate that the physical world endured when it was outside the range of our senses, nor could we appreciate the difference that it makes that our own body is in that world. Understanding the difference between a world that contains us and one that doesn’t is at the very heart of what it means to have a personal identity. Without the ability to take an objective perspective on space that is not centered on ourselves (understanding that the world goes on without us, in other words), it is hard to imagine that we could have much notion of the passage of time, either. Psychologically, time is inextricably bound up with movement. The horizon represents a place of the future or, if we turn around to see where we’ve been, the distant past. Without an idea of time, it is difficult to imagine being able to see oneself as an enduring being with a personal history. The self that binds all of its history into one cohesive biography can do so only by using time as the glue.
Maps can either be based on some kind of physical gradient in the world or they can be constructed mentally by careful observations of landmarks and measurements of the distances between them. Pigeons, food-caching birds, bees, and many other kinds of animals appear to navigate with stupendous accuracy by relying on one or the other of these two types of maps.
In this chapter, we have found that human map construction and use suggests that our own mental spaces are composed of a strange, rubbery substance. Though most of us can find our way home every night, we often have little cartographic insight into how we got there. We live teetering on the brink of spatial collapse, but we’re made blissfully unaware of this by a plethora of wayfinding aids offered up by architecture and modern technology. The maps of space that reside in our mind, though they are nothing like the spaces described by physicists or mathematicians, represent a kind of compromise between our need to conquer space well enough to survive and the limited capacities of our memory. What we cannot perceive directly or remember, we invent. The silver lining of this act of invention is that our ability to imagine, stylize, and transform space with our mind frees us from it in a way that is u
nique to us. This freeing of our mind from the trappings of physical space has been one of the key ingredients in an evolutionary path that has helped make us into beings unique among all living things on the planet (and perhaps in the universe) because we can both imagine ourselves being elsewhere and imagine an infinity of “elsewheres” existing without us. The same regionalization that mentally disconnects us from other spaces allows us to free ourselves from the constraints of physical space in a way that is impossible for any other animal. By inventing space, we have made it our own.
Our minds hold a strange and wonderful power over space. Unlike birds, bees, and other creatures of field and forest, we seem able to make spaces, bend them to our needs, and imagine them as things other than what geometry suggests they are. It may well be true that our ability to conjure space in this fashion has been one of the major engines that has helped to push humanity to a preeminent position as the only truly self-conscious beings on the planet. The combination of a mind predisposed to take in complex views using a highly developed sense of vision and then to join those views together in an odd amalgam based on topological connectedness has allowed us to invent and construct spaces beyond the wildest imaginings of early human beings.