杏吧原创

鈥淗ow in the image of material man, at once his glory and his menace, is this thing we call a city,鈥� said the architect Frank Lloyd Wright in a 1904 speech. He proceeded to elaborate on his metaphor of a city as a living organism:

鈥淭housands of acres of cellular tissue, the city鈥檚 flesh, outspreads layer upon layer, enmeshed by an intricate network of veins and arteries radiating into the gloom, and in them, with muffled, persistent roar, circulating as the blood circulates in your veins, is the almost ceaseless beat of the activity to whose necessities it all conforms鈥︹��

Do cities actually work like biological entities? In his rather Gothic description, Wright emphasised the physical functions of a city: distributing goods, conveying people and removing waste. It鈥檚 the same view that economists traditionally take to explain our insatiable desire to live in the same place as everybody else. Cities evolve, the theory goes, because they benefit from economies of scale and manage resources more efficiently than decentralised communities. Biology works similarly: large animals expend energy more efficiently than small ones, so the metabolism of an elephant is slower than that of a mouse.

A new view of cities is emerging, however, which goes beyond conventional economics or biology. Cities are where ideas are born, say Luis Bettencourt of the Los Alamos National Laboratory and Geoffrey West of the Santa Fe Institute, both in New Mexico 鈥� and that is a far more powerful growth stimulant than economies of scale. 鈥淭he presence of qualified professions and entrepreneurs constitutes a reason for a place to grow,鈥� says Bettencourt. 鈥淚f you can create a place that is exciting intellectually, that tends to attract more people.鈥�

The findings are surprising because they suggest that cities follow growth trajectories that have no biological counterpart. This year, for the first time, more people will live in cities than in rural areas, according to UN projections. At this tipping point in human history, it is worth trying to understand the mechanisms behind urbanisation and where it is headed.

鈥淭his year, for the first time, more people will live in cities than in rural areas, according to UN projections鈥�

Cities have fascinated social scientists for more than a century. The English economist Alfred Marshall is often credited with being the first to study cities from an economic point of view. In his 1890 book he wrote: 鈥淭he large towns and especially London absorb the very best blood from all the rest of England; the most enterprising, the most highly gifted, those with the highest physique and the strongest characters go there to find scope for their abilities.鈥�

During the 20th century, many researchers studying urban growth focused on economies of scale and their effect on wages. In 1974, Vernon Henderson of Brown University in Rhode Island proposed that cities reach an optimal size by growing until their workers鈥� per capita income reaches a maximum; when it starts to decline, workers leave for other cities. More recently, researchers including West have tried to identify deeper mechanisms behind these societal patterns. Though West is a physicist by training, his reputation stems mostly from his pioneering and controversial work on scaling laws in biology 鈥� how things change with size.

What is all the fuss about scaling laws? 鈥淧hysicists are used to thinking about extremely large systems of identical particles,鈥� says Steven Strogatz, a mathematician at Cornell University in Ithaca, New York. Take a piece of iron: at high temperatures, the spins of the particles jiggle around in random directions. If you gradually lower the temperature, the spins stay random until you reach a critical point 鈥� then they suddenly line up, and you have a ferromagnet.

This switch from disorder to order is called a phase transition. In the 1960s, physicists noticed that phase transitions follow certain universal patterns, called power laws, even if they have nothing in common physically. Kenneth Wilson of Cornell showed in the 1970s that these power laws come about through the growth of fractal structures, work which won him the . Since then, Strogatz says, 鈥淲hen physicists see a power law, they think in terms of phase transitions, and they smell Nobel prizes. They are like sharks with blood in the water.鈥�

鈥淚n 1974, Vernon Henderson proposed that cities reach an optimal size by growing until their workers鈥� per capita income reaches a maximum鈥�

Biologists, meanwhile, had known about a mysterious power law for decades. In 1932, the Swiss physiologist Max Kleiber showed that the amount of metabolic energy used by animals increases with size, as the three-quarters power of their body weight: so for example, a dog that is 16 times as large as a rat will use only about eight times as much energy. Alternatively, an animal鈥檚 metabolism per kilogram slows down in proportion to the one-quarter power of its weight. That is why a mouse has to eat half its body weight in food every day, while humans can get by on a far smaller proportion of theirs.

When he heard about Kleiber鈥檚 law, West thought about it as a physicist. Was there a fractal structure involved? Well, yes, an animal鈥檚 circulatory network has branches upon branches upon branches. Was there a large assembly of identical units? Yes, the capillaries are more or less the same size in an elephant as in a mouse.

In 1997, West鈥檚 team showed that the quarter-power law follows from these observations, along with an assumption that the circulatory network optimises the use of energy (). By working out the properties of the network, they derived the power law for metabolic rate and also showed that other quantities such as the size of blood vessels and the length of an animal鈥檚 life scale with body size according to power laws. West鈥檚 team has since extended these ideas to natural ecosystems (New 杏吧原创, 1 May 2004, p 38). Their model, however, is still not widely accepted by biologists (see 鈥淧ower struggle鈥�).

Undaunted, West set his sights on another large system of identical units 鈥� the modern city. In particular, he wanted to know whether the imagery of a city as a living organism could be backed up by quantitative data. 鈥淢y first strategy was to ask the same question that had been answered in biology: are there scaling laws? Surprisingly, for cities in particular, no one had looked at this question.鈥�

With help from their collaborators at Arizona State University, Tempe, and Dresden University of Technology in Germany, West and Bettencourt tracked down all sorts of information about the 鈥渕etabolism鈥� of cities, including the number of gasoline stations and laundries, electrical power usage and the total wages earned. Their database, assembled with the aid of the internet from hundreds of cities across the US, Europe and China, is the first important outcome of the project. 鈥淭he type of data they obtained would not have been possible to get 20 years ago,鈥� says Sidney Redner, a physicist from Boston University who has written on migration to and from cities.

The team plotted each variable versus city population and looked for an overarching pattern. 鈥淲hen I started, I thought everything would be like biology,鈥� says West. If cities followed biological laws, he reasoned, their metabolism per capita ought to slow down as they get bigger, and the scaling should follow a power law. 鈥淗ad we seen quarter powers, we would have said, 鈥楩antastic! Cities are just big biological organisms鈥�,鈥� West says. 鈥淏ut it just wasn鈥檛 true.鈥�

Instead, they found that the variables fell into two distinct groups (). Quantities related to a city鈥檚 infrastructure, such as the number of gas stations and the length of paved roads, did scale 鈥渟ublinearly鈥�, meaning that the larger the city, the less of these were required per capita. But measures of economic output and innovation 鈥� the number of patents, total wages, GDP, even the pace of walking 鈥� scaled 鈥渟uperlinearly鈥�, showing increasing returns with size (see Graphs). 鈥淭he scaling laws say that on average, as a city grows you can predict its output and input, its energy consumption, its wealth creation, its level of crime,鈥� says Bettencourt.

The results suggest that bigger cities have a faster pace of life, fuelled by wealth and new ideas. It鈥檚 a phenomenon that has no biological counterpart, says West, but it fits with the common perception of the big city. What鈥檚 more, the consequences for growth over time are clear. While biological organisms have a built-in mechanism for keeping their size under control, cities may not, which means their growth can accelerate out of control. Indeed, Bettencourt and West鈥檚 work strongly suggests that there is no maximum per capita income; big cities just get richer, and rich cities get bigger.

This has major implications for urban sustainability. The researchers have shown in their models that if sublinear growth dominates, a city鈥檚 population will gradually approach its optimum size and then stabilise. By contrast, a city growing superlinearly has no maximum size, so in theory its population can keep growing infinitely. Of course, no real city can sustain such growth, so any superlinear boom must be followed by a bust.

New York is a perfect example. Throughout its history, West says, the city has experienced waves of accelerating growth: from 1800 to 1850, from 1860 to 1890, from 1900 to 1920, from 1930 to 1940 and from 1950 to 1960. (After 1960, the pattern is harder to discern.) Each boom was followed by a bust, and the cycles are getting shorter; in fact, they are getting too short for the decennial census to track (see Graph).

That is no accident. 鈥淪uperlinear scaling gives a natural explanation for why the cycles have to get tighter,鈥� says West. In his models, if you reset superlinear growth at the time of a bust, the duration until the population would grow infinite again gets shorter. As West points out, examples of this are all around us. 鈥淭he timescale of an innovation, as measured by a product lifetime, is now significantly less than a human lifespan. That鈥檚 a new phenomenon,鈥� he says. For instance, pen and ink lasted for hundreds of years. The typewriter, a few generations. The personal computer, one generation. Now we have iPods, cellphones and other mobile devices. Will they even last one generation?

Urban organism

鈥淚f you take it to its logical conclusion, you鈥檒l need a major innovation every year, or every few months,鈥� says West. 鈥淭hat is obviously not sustainable. What is the nature of the end stage? We certainly do not have an answer.鈥�

Richard Florida, an economic geographer at George Mason University in Fairfax, Virginia, echoes West鈥檚 concerns. 鈥淚 worry if we push the speed of the urban organism past that of the human organism,鈥� he says. 鈥淎lready we鈥檙e hiring personal trainers and coaches to keep us going, and boosting our memory with computers.鈥� He adds that as cities continue to get larger, the contrast between the 鈥渢alent-attracting haves鈥� and the 鈥渢alent-exporting have-nots鈥� will increase, and the fault lines will not run between the developed and developing world, as they used to, but will split countries internally.

The picture is not very encouraging for the have-nots either. Take the US cities of Buffalo, Pittsburgh and Cleveland, whose populations have been steadily diminishing since 1960. 鈥淭hese are cities that stopped growing because they haven鈥檛 found the next innovation cycle, and were left with something stagnant or collapsing,鈥� Bettencourt says.

So what is the lesson for urban development? Is there a third choice besides stagnation or increasingly frantic cycles of boom and bust? As a matter of fact, there is. You can invest the fruits of the city鈥檚 economy in something other than growth, says Bettencourt. 鈥淭he assumption of our paper is that as you create resources, you put them back into the city to create more population,鈥� he says. 鈥淭hat鈥檚 not necessarily true. You can use them to change the shape of the city, to add infrastructure or to change the type of economic activity.鈥�

The next step is to explain why an idea-based economy scales superlinearly. It might have to do with the network of contacts between people. If a city has n inventors, the number of contacts between inventors can grow roughly as fast as n². The power of 2 represents a superlinear growth rate, whereas a power of 1 would be linear. From the data it looks as if the actual power is neither 1 nor 2, but around 1.2. The researchers hope that by working with Strogatz, an expert on networks, they will flesh out an explanation.

Bettencourt and West admit that their quest for an underlying theory has only just begun. One can hope that a final model of how cities work will be as vivid as Wright鈥檚 original description: 鈥淭he poisonous waste is drawn from the system of this gigantic creature by infinitely ramifying, thread-like ducts, gathering at their sensitive terminals matter destructive of its life, hurrying it to millions of small intestines to be collected in turn by larger, flowing to the great sewers, on to the drainage canal, and finally to the ocean.鈥�