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  It is difficult to imagine that anyone hearing these accounts of scurrying rats, soaring bees, or industrious food-caching birds could harbor any lingering doubts about whether such feats of wayfinding prove the existence of mental maps, yet in some quarters debate still rages. To find one’s way from any location to any other, it is necessary to compute both distances and angles. In other words, the bee, bird, and rat maps that I have described to you work properly only if they are based on the same kind of geometry that we use to design street maps of cities. Not everyone agrees that animals such as birds, bees, and rats possess such maps. Indeed, many argue that in trying to find convincing evidence for such maps in the minds of animals, we are simply asking the wrong questions. What would be more fruitful, they say, would be to understand what sense animals need to make of space to maintain their habits of life, and then to do the experiments necessary to see how such spatial sense is constructed.

  Strangely, fewer of us find reason to doubt that there are maps in the heads of human beings. We will see in the next chapter that such maps are peculiar kinds of things that cut close to the heart of the unique human connection with physical space.

  CHAPTER 6

  MUDDLED MAPS IN HUMAN MINDS

  THE PECULIAR NATURE OF OUR MENTAL MAPS AND

  WHAT IT SAYS ABOUT HOW WE UNDERSTAND SPACE

  I see nothing in space as promising

  as the view from a Ferris wheel.

  E.B.WHITE

  On one level, it seems strange to doubt the hard realities of space and time. If I want to know how long it will take me to drive to Chicago, or whether there’s still time to walk to work, the relevant calculations are straightforward and are based on equations that have been well understood since ancient times. The same basic mathematics transported tiny capsules full of men across the vast reaches of space to the moon. As he stepped onto the dusty surface, nobody heard Neil Armstrong ruminate on the possibility that the massive Saturn V boosters that had pushed him and his shipmates across the void had been a figment of their minds. The beautiful blue planet they looked back on from their lonely vantage point in space was no invention. It was real and it was a long way off. Doubting any of this seems a regressive step.

  Yet think of the everyday phenomena of your own lived space. If space is nothing more than an infinite expanse of pure geometric nothingness, then how can the distance from home when departing so often feel longer than the distance to home when returning? Walkers gauge the distance between two points based on the number of turns they have made along the way rather than the distance they have walked or the time spent walking. When placing new furniture in our home, why are we so often surprised by what does and doesn’t fit into spaces that can be almost as familiar to us as parts of our own body? In earlier times, we might have attributed such strangeness to the mystical power of place. Now that we see places more as objective locations studding cold space than as powerful entities brimming with their own special kind of life, we turn inward for answers to such questions. We seek answers in our own psychologies.

  Given the oddities of the psychology of space that I’ve just listed, along with many others that I’m sure you can think of from your own life, we should be prepared for the possibility that whatever mental maps we might possess may have features not predicted by the impressive wayfinding feats of the birds and the bees. Not only can we expect our cognitive maps to be inaccurate but at times they may turn the world into a place that defies the laws of physics (or geography at least) in ways that are downright weird. In spite of this weirdness, such maps often seem to work. The sketch maps that we draw to help guide visitors to our house may have the faintest of resemblances to real geography, but what is most important about such maps, mental or otherwise, is that they serve the purpose for which they are designed. Provided that they work, there may even be some advantages to constructing maps that make only weak connections with physical reality. They may be easier for us to remember, or they may leave out details that might confuse us. It may even be that our ability to play fast and loose mental games with space is what underlies many of our most dazzling cognitive feats, especially those that free us from the bounds of real spaces to allow us to inhabit those made of electrons. The maps that we imagine and draw may provide useful signposts to the organization of our own spatial mind. When we sketch a map, what we include and what we leave out may have much to teach us about the cartography of our own inner mental spaces.

  THE ORIGINS OF HUMAN MAPS

  Archaeological evidence suggests that the production of primitive maps predates written text and numbers by several thousand years. In a way, this is not surprising, as there seems to be something deep and universal about our desire to find ways to represent spaces to each other. Though children need some instruction in order to understand how to use a map, it is relatively easy for them to grasp the basic idea that a drawing is related to a physical space in an orderly way. Such a cognitive leap is much simpler than, for example, coming to terms with the idea that text—long lines of abstract squiggles on a page—may convey meaning. The cognitive building blocks that children need to appreciate the connection between topological aspects of real space (what is connected to what) and map topology emerges at an early age, certainly in the preschool years. An ability to use maps to solve metric problems, such as deciding on the shortest route from one location to another, arises much later in life, if at all. Much evidence suggests that for most of us the ability to represent space with metric accuracy may never develop fully.1

  The earliest known maps, scratched into stone about 40,000 years ago, were simple depictions of natural objects, having more in common with prehistoric rock art than with topographic maps. Though some of these depictions look as though they may have been maps, we know little about their function, so it can be difficult to be certain that they are maps at all. For something to be a map as conventionally understood, it must have an intended use that relates to either understanding or moving through geographic space. For example, if I drew a picture of my neighbor’s face, it would be true to say that the picture was a “map” of her face in the mathematical sense, but that is hardly what we are thinking of when we use the word map.

  Some early carvings found in parts of Europe and North Africa portray scenes of animals and a few stylized figures that may or may not represent parts of the spatial context in which the animals were found. Later carvings are much less ambiguous and show two of the common hallmarks of modern maps. One is a system in which repeated use of a symbol is made to stand for some feature of an environment. The symbols are thought to represent dwellings, individual people, and sometimes animals. The other cartographic hallmark of these very early drawings is that some of them show survey, or overhead, views of the environment. In some cases, perspectives are mixed up so that some figures are shown in profile while others are shown from overhead.2

  Children’s drawings also show such mixtures of perspectives, as do certain styles of modern art—cubism for one. Children may mix perspectives because they are unable to put together accurate maps of spaces from viewpoints that they cannot adopt themselves, whereas visual artists using cubist techniques are motivated by the desire to show objects from unusual, impossible, or multiple perspectives. We have no way of knowing what prompted our ancient ancestors to use such multiple perspectives in their drawings. Is it possible that in such mixed perspectives we are witnessing an early struggle to break free of what can be seen directly in favor of the spaces of imagination?

  There is much that we can never know about the drawing skills, the cognitive toolbox, or the motivations of early primitive artists, but we can certainly see the beginnings of the struggle to comprehend and capture on stone the properties of large-scale geographic spaces. Survey drawings of prehistoric environments suggest that some early humans were capable of adopting a perspective that may have been impossible for them to have seen with their own eyes.

  Much later, there can be little doubt that pe
ople produced drawings that were meant to be appreciated from a bird’s-eye view. One of the most famous examples of such representations was made by the Nazca of Peru. The famous Nazca lines, carved out of the ground more than 2,000 years ago, portray a variety of objects and animals on such a grand scale that they can be viewed in their entirety only from a great height above the ground. Although it seems likely that these drawings were meant to be observed by deities, a number of other theories have been entertained, such as that the drawings were giant calendars, irrigation channels, even landing pads for extraterrestrial spacecraft!3 These depictions were not maps, but they illustrate an increasing facility with the geometry of geographic space.

  One thing that makes it so hard to know whether some of these early graphics were real maps is that we rarely have any idea how the maps related to the physical landscape as it appeared at the time the maps were drawn. The spans of time involved are so long that much would have changed between the time the lines and marks were hammered into stone and the time they were unearthed by modern scientists. And even if these drawings were meant to represent the physical landscape, it isn’t clear that they would have been used as aids for navigation. Some may have had symbolic or religious functions in the lives of those who created them. The detailed maps of what seem to be agricultural fields drawn by some cultures may have served as a kind of amulet designed to fulfill a superstitious belief that representing the plots of crops would help to ensure a successful harvest.

  Though we have to be guarded in our interpretations of their meanings and uses, ancient maps provide an important window into the origins of human representations of space. Regardless of the many questions about these maps that we will never be able to answer fully, these artifacts leave little doubt that an important hallmark of the unique human engagement with space consists of this basic tendency for us to construct mental models of the stuff. Though these models can have all kinds of uses, it is only in rare cases that they have anything like metric accuracy. Much modern research has been devoted to exploring why this might be.

  GEOGRAPHY LESSONS

  Time for a pop quiz:

  1. Which city is farther north: Seattle or Montreal?

  2. Which city is farther west: Los Angeles or Reno?

  3. Imagine the map of North and South America. Which North American city lines up with the west coast of South America: Vancouver or Chicago?

  Before I give you the answers, think about how you imagined geographic space. The questions deal with areas of land that are too large to have been visualized all in one go (unless you happen to be an astronaut), so your images would have been based on maps that you have seen rather than from direct personal experience. In a way, these questions might seem to have less to do with the way we find our way through space using mental maps and more to do with how we imagine the space and geometry contained in simple pictures. Perhaps it doesn’t even matter that the images happen to be maps at all. As you’ll see, though, there are some interesting connections between the ways that we imagine the kinds of pictures conjured by memories of maps we’ve seen many times since childhood and the ways that we try to use our own cognitive maps to navigate through space.

  And now the answers, which may hold one or two surprises for you:

  1. Seattle is farther north than Montreal.

  2. Reno is farther west than Los Angeles.

  3. Chicago, and not Vancouver, lines up with the west coast of South America.

  If you’re like many of the participants in studies of how we form cognitive maps, then at least one of these answers is likely to send you off to find the nearest atlas to check the facts, but I can assure you that you will find no errors.

  Barbara Tversky, a cognitive psychologist, carried out groundbreaking studies on cognitive mapping at Stanford University in the 1980s.4 These studies showed some of the key differences between mental maps and the physical spaces they represent. One such difference arises from what Tversky calls alignment. The idea is a simple one. Our mind’s eye tends to shy away from the diagonal, the oblique, the slanted, in favor of horizontals and verticals. Hence, when we represent a line or surface with such irregularities, we tend to straighten it out. This accounts for our tendency to align the edges of North and South America when we imagine them on a map, so that we are surprised when we are told that the western edge of South America aligns with a city in the eastern half of North America.

  It isn’t just our impression of large-scale geographic space that is influenced by alignment, but also the smaller spaces that we traverse every day. Erik Jonsson, a retired engineer with a lifelong interest in navigation, conducted an informal study of drivers stopping at a rest station on an interstate highway in the United States. Though most drivers knew where they had come from and where they were going, few of them could tell Jonsson their compass bearing just before they had pulled off the highway. They had straightened out all the curves in the road.5

  Tversky conducted another study in which she asked Stanford students questions about locations close to the campus. Just as we rotate whole continents in our heads to make them line up, the students tended to align local bodies of water with north-south and east-west compass headings. This tendency was so pronounced that the hapless students ended up making considerable errors in judging the relative positions of local landmarks and communities that they visited every day.

  What causes us to rearrange our maps of space to conform to tidy horizontal and vertical lines that exist only in our imagination? Tversky argues that one part of the answer has to do with the natural axes of symmetry of our bodies, and the fact that we are upright beings who spend much of our waking lives orienting ourselves to the force of gravity. We tend to line up the world with the horizontal and vertical because two of the most salient benchmarks against which to compare all spatial attributes are the force of gravity and the appearance of the horizon. It is certainly true that preference for the vertical and horizontal is written into everything from our mythologies of space and the design of our street maps to the basic operation of our visual system.

  Noted geographer Yi-fu Tuan describes a deeply rooted tendency for human beings to categorize the cardinal directions of space according to the axes of the body.6 Most cultures make clear distinctions between the meanings of “in front” and “behind” as they refer to the orientation of the body. The various cultural connotations of “left” and “right” are reasonably well known. In most cultures, the left side is inferior to the right. We shake with our right hands; we eat with our right hand in cultures where utensils are eschewed. Our most valued assistant is our right-hand man. The left hand is still referred to in the scientific literature as the sinistral hand, in contrast to the right, dextral hand, with the modern word sinister taking its root from an early designation of left-handedness. One interesting exception to the low status of the left is found in Asian cultures, in which the primary cardinal direction is the south (the main entrance to the Forbidden City is on its south side, for instance). This being the case, left is the side of the rising sun, and so is afforded privileged status.

  In the ancient Asian science of feng shui, the orientation of buildings and cities with respect to the cardinal directions was considered to be critical to the health and success of the built environment. Streets and buildings were aligned carefully with such directions, and the human body can be seen in microcosm in some applications of feng shui principles. As our straight, two-legged posture pushes our heads up against the force of gravity, it is a cultural universal that physical height correlates with the direction from which human power emanates. Palaces tower over landscapes for reasons that transcend military strategy. The city of Beijing is built on largely flat terrain, yet the Forbidden City, the ancient throne and power center of the old city, is considered to be at the peak, with the surrounding regions arrayed below it like a set of virtual terraces.

  Architecture’s embodiment of power structures, equating height with might, did not end
with the decline of palaces, royalty, and feudal systems of governance. It takes only a quick glimpse at the skylines of the Manhattans of the world to be convinced of this. Gigantic, geometrically perfect towers of trade and commerce jut above the horizon, fierce and warlike. It is beyond coincidence that the modernist World Trade Center was the target of a vicious terrorist attack in 2001. Mohammed Atta, the apparent mastermind of the murderous assault, was trained as an architect and worked as an urban planner. One report suggests that he was driven into the arms of the jihad in reaction to the architectural westernization of parts of Cairo. Atta, more than many others, would have understood and resented the symbolic significance of the towers.

  At the much more mundane level of the everyday operation of our sense of vision, it has long been known that we are more sensitive to vertical and horizontal lines than to oblique ones. Sensitive vision tests using fine grids of lines show that we are better able to see spaces between lines when they are oriented either vertically or horizontally than when they are presented at oblique angles. This sensitivity bias for aligned stimuli has to do with a preponderance of neurons in our visual brain that are tuned to the horizontal and the vertical. Nobody knows the origin of this bias, but it is likely to be related to the orientation of our bodies with respect to gravity.

  Not only are we more sensitive to horizontal and vertical lines but we also seem to prefer them in images. Visual artists such as Piet Mondrian certainly understood such preferences. His paintings, mostly consisting of grids of colored blocks, were devoid of the oblique. Mondrian was a member of an artistic group known as the de Stijl group that tried to place aesthetics on a scientific basis. An explicit part of the artistic manifesto of the de Stijl group was the dictum that oblique lines must be avoided at all costs. Modern psychological experiments have confirmed the intuitions of these artists. When participants in an experiment were asked to judge the pleasantness of a series of Mondrian paintings presented either as the artist had intended or tilted to oblique angles, they preferred Mondrian’s horizontals and verticals.