You Are Here (21 page)

Those of us who have to work in cubicle farms may find them soul destroying, and those of us who don’t might be amused by them, but the main thing is that our behavior in such work environments points up the importance of the configuration of space not just in our homes but in the larger indoor spaces of our lives—spaces in which we work, play, or educate or entertain ourselves. Just as the right kind of house can make us feel happy, thoughtful, excited, or creative, so can workplaces and other, more public spaces influence our feelings and behavior in important ways, both positive and negative.

When thinking about the spaces inside our dwellings, we are often preoccupied with the influence of space on repose. Where are the best resting or thinking places? Where do we bring company to sit? In larger buildings such as offices, schools, courthouses, government buildings, and shopping malls, we are likely to spend more of our time in motion, and the way that we move from one place to another is likely to influence the quality of our experiences or the efficiency of our workday. To understand how the organization of physical space affects our movements, we need to look beyond isovists to see how the appearance of inner spaces is influenced by movement.

Researchers interested in the technical properties of space and how those properties change for us as we move have defined new measures that are related to the isovist analyses we considered in the last chapter.
One such measure is called a visibility graph. To understand how visibility graphs are constructed, remember that the isovist represents all visible locations, as defined by both open and closed contours, from a single position in an interior such as the large family room/kitchen in my house. Isovists work well to define all that can be seen from a single point in space, but to understand how the shape of space influences movement, we need to consider the connections between isovists.

The isovist that is available to me changes as I walk across a room, from one side to the other. A visibility graph is a symbolic way of representing such changes using the concept of intervisibility. Two locations in a space are said to be intervisible if an observer standing at one of the two points could see the other. Imagine a complex space, such as an irregularly shaped room in an art gallery, filled with an orderly grid of points, where each point represented a potential viewing position. At each viewing position, some of the other points would be visible and others would not. A visibility graph for this space would show all of the intervisible points. This type of representation is interesting because it shows how our perceptions of space change as we walk about. Just as an isovist can be used to characterize the size and shape of a piece of space from a single viewpoint, a visibility graph can be used to do much the same kind of thing, except that it reflects the way that the appearance of the space changes with our movements.
²

For example, the “stability” of a space is a measure of how the number of intervisible locations varies in different parts of a space. A bland, rectangular space with no visual occlusions, such as a large great room in a modern suburban home, would be a very stable space. A more jagged arrangement with lots of walls and barriers jutting out, a spiky space in other words, would be much less stable. Another spatial measure that can be derived from the visibility graph is something called the mean shortest path length. To calculate this, we measure the shortest distance from each point in our grid to every other point and
then we calculate the average. This value will depend very much on the overall shape of the space as well as on any barriers to movement that might be within it, such as pieces of furniture in a home or desks in a workspace. A measure like mean shortest path length is different from isovist measures because it reflects not only the shape of a space but also its possibilities for movement. I may be able to see the window from behind the outer edge of my cubicle wall, but if I decide to walk to the window I need to walk around another row of cubicles.

If visibility graphs were just another cool toy for mathematicians interested in space, they would not be worth our trouble here, but there are intriguing indications that such graphs, and many other related tools for analyzing space, can make surprisingly accurate predictions about how we move through and spend our time in a complex configuration of space. The Space Syntax Laboratory, a part of the Bartlett School of Planning at University College, London, has had marked success in predicting how people move through spaces on the basis of the graphical tools I have been describing.
³
Because most of the work of this group is concerned with the influence of spatial configuration in larger urban settings, we will deal with it more extensively in the next chapter, on city space, but many of the principles used to steer urban planning apply equally well to interior spaces.

For example, an analysis of intervisibility and shortest path length values for the Tate Gallery in London has been used successfully to predict where visitors will congregate in the gallery. The Space Syntax Laboratory has used these kinds of analyses to advise the gallery on the effective placement of exhibits to encourage the flow of people and avoid pedestrian gridlock. What is most remarkable about the success of these analyses is that they work well even when little or no account is taken of what kinds of objects will actually be in the space. Analyses of space can be based on the raw configuration of space—its shape rather than its contents.

Predicting where people will congregate in a space based on its shape can be a useful tool for planners. A gallery owner wishing to draw maximal attention to a particular work of art could use visibility graphs to determine where best to place the work. A designer of shopping malls could engineer a space so as to steer people to some locations and away from others. A committee of workers trying to design an efficient workspace could use a basic understanding of space to facilitate a particular group dynamic by engineering the manner in which people interact in the space. Sometimes, such strategies can be explicit and obvious and don’t require any mathematical measures at all. For example, most people are aware of explicit spatial strategies used by grocery stores to ensure maximal traffic, such as placing the dairy case as far as possible from the entry door so that customers dashing in for a carton of milk must navigate many aisles of products they didn’t set out to buy. In other cases, much more subtle methods can be used. To understand a few more of these subtleties, we must take our analyses of the shapes of space just a little further.

Apart from making predictions about how people will move through space and where they might congregate, mathematical analyses of the shape of space can help us to understand how well we can find our way around a building. We all know that some buildings seem intrinsically more difficult to navigate than others, but it isn’t always clear why this might be.

As legend has it, the building where I work, the psychology building at the University of Waterloo, in Ontario, was designed so that its shape corresponds roughly to the shape of a brain. Many visitors or even longtime students complain that they have difficulty finding their way about because of the lack of distinguishable landmarks in the corridors. Each hallway is the same size and shape,
and the whole building can seem like a beehive of identical orange office and laboratory doors. Other reasons for the poor navigability of my building have to do with the way that spaces are connected. The connections between spaces can be captured using a slightly different technique, referred to as space syntax. In space syntax analysis, we try to use a simple graphical method to describe the way that different regions of space are connected to one another, just as we might use the linguistic form of syntax to understand how a sentence is constructed.

To begin, we draw a diagram in which each room is reduced to a single point, and then draw lines connecting all the points that are directly accessible to one another, a “point-and-stick” representation. Such lines would most commonly represent hallways, but when two rooms are directly adjacent to one another, the doorway between the rooms could also be represented by a line. The diagrams below show an example, using the ground floor of my own house. Figure 8 shows the actual layout of the rooms, and Figure 9 shows the floor plan reduced to points and lines.

Figure 8
: The ground floor of my house, shown as a standard floor plan

Figure 9
: The ground floor of my house, shown using space syntax analysis

If we formalize space in this manner we can obtain some simple measures by calculating things like the average number of steps (where a step is a hop from one point to another, connected point)
required to get from anywhere in the space to anywhere else in the space. Diagrams such as Figures 8 and 9 are so simple it would hardly seem worthwhile to carry out these kinds of arithmetic operations, but for more complex spaces in larger buildings, such analyses can be revealing.

One such measure, referred to as intelligibility, characterizes the degree to which the shape of any small part of a space reflects the shape of the whole space. Think of this as a kind of correlation between the spatial characteristics of the whole building and the characteristics of any small part of the space. An intelligible building is one in which the hallways that one needs to use most often to get from one place to another are also the ones that intersect with many other hallways. It isn’t hard to imagine an unintelligible building: it could be one in which a hallway intersecting many other hallways leads exactly nowhere, or one in which a small area with very few connections must be navigated to get almost anywhere else in the building. A building that contained a regular grid of hallways would also be considered unintelligible because all hallways would appear to be more or less equivalent. They would all present a similar appearance and they would all be equally connected to one another. Certain types of spatial puzzles, such as hedgerow mazes, are often designed explicitly to have very low intelligibility. As was the case with visibility graphs, the marvelous thing about intelligibility in this formal sense is that it correlates very well with behavior. People get lost in spatially unintelligible spaces much more often than they do in intelligible ones.

It might seem strange at first that these simple diagrammatic representations of space, in which shape and volume are reduced to nothing more than dots and sticks, work so well to predict our movements in a building. The success of space syntax has to do with the manner
in which our mind deals with problems of space and navigation, as we saw in the first half of this book. For one thing, many types of space syntax analysis completely disregard the metrics of space. Simple diagrams of rooms and hallways like Figure 8 collapse all information about the sizes of the rooms that are represented by the dots, or the lengths of the hallways that are represented by the lines, yet they can make highly accurate predictions about how people will explore the spaces and how well they will be able to locate themselves. This flagrant disregard for size and shape should remind you of some of Barbara Tversky’s findings regarding the schematization of space. By asking research participants a series of simple questions about geography, Tversky was able to show that we straighten curves, simplify geometry, and reduce complex spaces to a simple series of points and lines. Just as our mind represents space as a kind of dimensionless topology, formal models of that topology can predict our movements through space with surprising accuracy.

What is perhaps even more surprising than our apparent disregard of distance when wayfinding is that our behavior inside buildings can be simulated to a high degree of accuracy by replacing us with “agents”—simple bits of computer code that are designed to behave according to a small number of rules, the most important of which is “always move in the direction that is the most ‘open.’” If a computer simulation is drawn to approximate the layout of a real building, and a few such agents are unleashed on the simulation, like tiny Pac-Men that chomp down the hallways guided only by simple rules, the agents have problems where humans would get lost and spend the most time where humans would spend the most time in the real building.
⁴
This finding draws a direct line from the point-and-stick representations of the syntax of built space, through our ability to quickly recognize the size and shape of spatial isovists, to our specialized brain, heavily biased toward the visual sense and an understanding of layout,
landscape, and vista but less sophisticated when it comes to understanding the connections between the seen and the unseen.