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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.

O
n 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.

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.
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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.
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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 people 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!
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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.

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.
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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.