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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.

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.
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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 unique 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.

But it isn’t just the construction of our minds that has enabled us to slip off the mantle of the geometry of space. Our soaring ability to harness energy and technology has allowed us to construct our physical environment in almost any way we please. Hand in glove with our spatial mind, we have used our abilities as toolmakers to
design environments that support and extend our mental penchant to transcend physical space. Everything from architectural design through urban planning to modern light-speed communication technologies has been designed to reflect, support, and extend our mastery of physical space.

A
n old mentor of mine, something of a father figure, once told me that the two numbers that have the most impact on our economic future are the starting salary of our first job and the price that we pay for our first house. At the time, I had no reason to believe that I would ever have a job or a house, so I just nodded politely without paying much attention. When I finally bought a house, I had little idea what it was really worth and, within days of moving into it, less of an idea what had made me buy this particular house. A small river ran through the basement. The floors were so uneven that a baseball placed on the kitchen floor would roll quickly to the other side of the room. The “yard” consisted of
about a half acre of prime wetland—not much good for gardening and requiring some vigilance on my part to ensure that neither children nor dog were sucked into the bog. What I did know about that old house, though, was that I loved it from the moment I set foot in it, even as the hungry fleas from the previous owner’s dog leapt out of dormancy in the old carpets to attack my ankles for a fresh meal.

Years later, when I was selling that house, I still understood very little about what made people buy houses. I placed all my trust in the hands of a realtor, who handed me tip sheets filled with nuggets of wisdom for prospective sellers. Most potential buyers, I was told, have made a decision within eight seconds of getting to the front door. Hence, I was advised to polish the doorknob to a high gloss and to make the entranceway immaculate. At open houses, one of the most commonly inspected areas is the inside of the air exhaust fan over the stove, I read. I had no idea why one would stick one’s head into such a nasty little space, but I dutifully scoured my exhaust fan for all I was worth. Not only this, but when looking for a house to buy, I developed a new habit of peering up under stoves, always wondering what surprises might be in store for me.

The new trend in the house-selling business is what is called fluffing or staging. Teams of experts, self-described design gurus and fashion divas, descend upon one’s house, sometimes removing all the contents and replacing them with what amounts to a Hollywood stage set. Though it is difficult to get one’s hands on meaningful statistics with enough detail to allow a scientific opinion, the consensus among real estate professionals is that such staging reaps enough additional profit for the seller that it would be worthwhile at twice its cost. (Though the price of a good fluff can be modest if one is willing to do much of the labor oneself, a full going-over on a large estate can easily cost tens of thousands of dollars.)
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Much of the fluffing effort is devoted to obvious cosmetic concerns such as decluttering, euthanasia for the garage-sale armchairs that lurk in family rooms, and sometimes a fresh coat of paint in a neutral tone. But some of the staging effort consists of a deliberate attempt to sculpt the perceptions of the potential buyer with respect to the configuration of the interior spaces of the house. By artfully placing a few good pieces of furniture, not only can one exert a strong impression on the viewer’s assessment of the size and shape of a space but one can manipulate the manner in which a space is explored and scrutinized.