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Hillier begins by characterizing urban spaces as little more than strings of beads, where the beads are two-dimensional polygons of space, and strings are the paths from one district to another. From such patterns of nodes and paths, Hillier derives a grammar of space that he refers to as space syntax. The measures Hillier describes give us a way of describing relationships between small parts of a space—a single piece of road, for instance—and the entire context in which it is found. Whereas Whyte or Jacobs could stand on the street and describe with convincing and witty prose the nature of the street life that hums in lower Manhattan, Hillier’s space syntax methods can give us a precise set of numbers describing the relationship between, say, Washington Square Park and the surrounding Greenwich Village streetscape. These numbers can be used to make solid predictions about where and how many people will be found in the park.

One of the most useful of such numbers is what Hillier calls the coefficient of integration. Each of the lines on a map of a built space can be given such a coefficient, and it represents, roughly speaking, the average number of turns that must be made to get from any one place on the map to any other. The easiest way to think about this is to imagine a neighborhood that you are familiar with, beginning with the street on which you live. Now, mentally travel from your street to the nearest convenience store, and count the number of turns that you would have to make along the way. If you repeat this exercise, but for a very large number of different destinations, then you can calculate the average number
of turns required to get from your starting point to anywhere else in a region (or a whole city if you like). The higher this average number, the less integrated your starting point and the lower the coefficient of integration.

If you calculate integration coefficients for an entire region, the numbers can be represented nicely by using the heaviness of the lines on the map to represent the integration coefficient of each street. The heaviest lines have the highest coefficients, or highest integration, in other words. Shown in Figure 12 is such a map for my own neighborhood.
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Figure 12
: A map of my neighbourhood, showing areas of highest coefficiency using heaviest lines

The most interesting thing about these maps of integration coefficients, and the reason that I’ve burdened you with the details of how they are constructed, is that they work remarkably well to predict how we behave in space. People (and cars) tend to congregate at regions of high integration. In fact, such measures work so well that Bill Hillier’s group has built a successful private consultancy that uses the principles of space syntax analysis to help cities
plan buildings, streets, and neighborhoods in ways that promote desirable traffic patterns, both pedestrian and vehicular.

You might notice that there are some similarities between the analyses of space that I’m describing here and isovists. In both cases, some simple generalizations about the shape of space are being used to describe and predict how we behave in space. Notice as well that in both cases, we don’t even need to describe
how
space is being used to make predictions about where we will find collections of people in a space. In the case of space syntax, there is a remarkable tendency for people to be found in the greatest numbers in areas of a city that have the highest integration values. The more connected an area is to the rest of the city, the busier it is likely to be.

Space syntax analyses such as these are not only useful tools for those in the business of designing city spaces. They also connect with our own mental maps of space. In one illustrative study, researchers knocked on doors in an area of London and asked respondents to draw sketch maps of their immediate neighborhood. At this point in the book, it shouldn’t surprise you to know that these sketch maps were often wildly wrong and seldom represented distance and angle with anything like metric accuracy. Our minds simply do not map large-scale space in this way. What the findings did show was that when the sketch maps were subjected to the same space syntax analyses as the real places they were supposed to represent, there were remarkable affinities between the two. Though our mental maps may resemble real spaces only in a weak sense, they share the same syntax as physical space in the manner prescribed by Hillier’s approach. Just as space syntax analysis collapses much of the metric size and shape of space to a series of nodes and lines, so does our mind put maps of space together as a series of simple viewpoints (the nodes) and the connections between them (the lines).
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Like isovist analysis, one of the most remarkable features of these studies is the finding that the reasons for our movements through a space are much less important than the bare structure of the space—the way that different areas in a space are enclosed and connected. Though knowing the functional organization of a space (where the stores are, where the washrooms are, and so on) can enhance our ability to predict movements through that space, the organization of the space is a much stronger predictor of our movements than what kinds of functions are served by the space. It might seem a little odd for me to tell you that when you jump in your car and drive into the city, or hop off the bus and start walking the streets of the urban core, I can predict exactly where you will go based on how the streets are connected together without needing to know that you have set out to, for instance, buy a pair of shoes. To make sense of this claim, remember that Hillier’s theory is really meant to account for aggregate behavior of large numbers of people in cities. Though the computer that calculates the integration values of streets in your city couldn’t possibly realize that you need new shoes, when many such trips to the city for many purposes are averaged together, the computer can do a pretty good job of predicting how such trips will be organized.

There’s another way of thinking about the relationship between the shapes and connections of city spaces and the kinds of attractions that might be found in particular places. Imagine that you are an entrepreneur and you want to establish a retail business in a city. How do you look for a site? It doesn’t take a roomful of psychologists or planners to tell you that you want to place your business in an area with lots of foot traffic, and it may be that the best way to find such a site is to use the time-honored methods of William Whyte—go and watch what happens on the street. In other words, it’s probably no accident that successful businesses that depend on walk-in traffic are located in
areas with high integration values. What is new and more interesting is that space syntax methods give us a way of predicting where such integration values will be found
before
we go looking, or even before the streets are built. These methods work so well because they mirror the ways that our mind responds to the properties of space, thus making a direct route from the way our mind works to the shapes of our cities. Our cities succeed or fail depending on how well we understand and manage this deep connection between mind and metropolis.

It may seem strange at first that space syntax takes little account of the distances between locations in a city. In our busy lives, we tend to find the shortest route from one place to another, especially as our familiarity with a city increases. Yet in Hillier’s space syntax, it is only the number of changes in direction that determines the spatial integration of a location. Because Hillier’s methods are designed to predict where people will congregate rather than to explain the wayfinding performance of individuals on single trips, the absence of distance measures in space syntax is not at all problematic in this respect. More surprising, though, is that in spite of our best efforts to plot efficient courses through the city, we are often fooled about distance in ways that are exactly consistent with the space syntax approach.

Many studies have shown that people who are led along walking or driving routes that have many changes of direction are likely to overestimate the distance that they have traveled.
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Even though we are heavily invested in finding shortcuts, our spatial mind mirrors the nodes and lines of Hillier’s spaces to such a degree that we confuse the dimensions of space in much the way that space syntax predicts. Just as we’ve seen on many occasions now, the rules of mental space often appear to be topological rather than metric, and so they are well reflected by descriptions of physical spaces based on topology.

Just as there is evidence that we have an intuition for the configuration of space given by isovists (one piece of evidence being our facility with finding locations of prospect and refuge in new spaces), there are also signs that we have a deep latent sense for areas of high integration in more complex spatial configurations.

Imagine that you’ve landed in an unknown city. You don’t speak the language or understand the signs, and must rely only on your inner navigational senses to find your way from place to place. Over time, your movements are likely to spread slowly from a home base (perhaps your hotel) to other areas of interest—the place with good coffee, the best sidewalk bench for people watching, the nearest Internet café for catching up with the news. Often what happens is that you learn the configuration of a major street first, and then slowly learn to find your bearings from this major street to a growing set of goal locations. It is as if the major street becomes a kind of backbone upon which you build a more extensive skeleton of routes. What makes this strategy so effective is that the major street is likely to be a location of high integration, well connected and intelligible. As long as you can find your way back to this street from a variety of locations, your risk of becoming unfathomably lost is reduced. And because the major street is well integrated, your chances of finding it, even if you become disoriented, are high. Even if you lose your skeleton, the shape of space encourages you to rediscover it by wandering.

Notice, as well, that it is entirely possible to use this kind of approach to navigation without having any idea how the different goals you seek in the course of the day might be related to one another. You might have no clue how to walk directly from the Internet café to the coffee joint, but you know that the two places are connected via your skeleton, and that is all that you need to know to navigate from one to the other with ease. It isn’t that the skeleton helps you to know the spatial relationship between the coffee joint and the café.

This relationship doesn’t matter so long as you know that both places connect to the spine route. It’s as if the café and the coffee joint are in two different universes, but they’re connected somehow by the skeleton. There is a resemblance here to the findings I described in the first part of the book related to what I called the regionalization of space. We have great difficulty in drawing connections between the visible and the invisible in cities, just as we do in small sets of spaces in psychology laboratories. We learn useful tricks that can guide us from one space to another, often by using idiosyncratic links between places. There may not be anything spatially pretty or efficient about the routes we choose, but they work well most of the time.
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Many people have had such experiences, even in fairly familiar surroundings, where they might discover that a route they have been taking for years and years (a drive to the office, a walk through a shopping mall) is neither the shortest nor the most efficient. We sometimes even seem to take great pleasure in engaging in lengthy debates about route choices. When meeting friends for dinner in a restaurant, the debate about how best to share the bill is often rivaled only by the one about the best way to get home.

If there were deeply felt psychological principles of space at work in the organization of cities, then one prediction would be that we could discern patterns in urban streetscapes that reflected those principles. If city plans were laid out according to the whims and wiles of wandering travelers, then I imagine that this is exactly what would happen. We could look at an aerial photograph of a city and read off the inner workings of the minds of the beings who carved streets into the earth. As everyone knows, though, this is not how cities are built. Some cities, especially those of recent vintage in the New World (Washington, D.C., for example), were planned from scratch.