Dana McKenzie writing in the New Scientist:
"How in the image of material man, at once his glory and his menace,
is this thing we call a city," said the architect Frank Lloyd Wright in
a 1904 speech. He proceeded to elaborate on his metaphor of a city as a
living organism: "Thousands of acres of cellular tissue, the
city’s 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…" Do cities actually work like biological entities?
The rest after the jump.
In his rather Gothic
description, Wright emphasised the physical functions of a city:
distributing goods, conveying people and removing waste. It’s 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 – and that
is a far more powerful growth stimulant than economies of scale. "The
presence of qualified professions and entrepreneurs constitutes a
reason for a place to grow," says Bettencourt. "If you can create a
place that is exciting intellectually, that tends to attract more
people."
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.
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 Principles of Economics he
wrote: "The 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."
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’ 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 – how things change with
size.
What is all the fuss about scaling laws? "Physicists are
used to thinking about extremely large systems of identical particles,"
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
- 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 Nobel prize in 1982. Since then, Strogatz says,
"When 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."
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’s 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.
Undaunted, West set his sights on another
large system of identical units – 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. "My 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."
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
"metabolism" 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. "The type of data they obtained would not have been
possible to get 20 years ago," 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. "When I started, I thought everything would be
like biology," 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. "Had we seen quarter
powers, we would have said, ‘Fantastic! Cities are just big biological
organisms’," West says. "But it just wasn’t true."
Instead, they
found that the variables fell into two distinct groups (Proceedings of
the National Academy of Sciences, vol 104, p 7301). Quantities related
to a city’s infrastructure, such as the number of gas stations and the
length of paved roads, did scale "sublinearly", meaning that the larger
the city, the less of these were required per capita. But measures of
economic output and innovation – the number of patents, total wages,
GDP, even the pace of walking – scaled "superlinearly", showing
increasing returns with size (see Graphs). "The 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," says
Bettencourt.
The results suggest that bigger cities have a
faster pace of life, fuelled by wealth and new ideas. It’s a phenomenon
that has no biological counterpart, says West, but it fits with the
common perception of the big city. What’s 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’s 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’s
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. "Superlinear
scaling gives a natural explanation for why the cycles have to get
tighter," 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. "The timescale of an innovation, as measured by a
product lifetime, is now significantly less than a human lifespan.
That’s a new phenomenon," 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?
"If you take
it to its logical conclusion, you’ll need a major innovation every
year, or every few months," says West. "That is obviously not
sustainable. What is the nature of the end stage? We certainly do not
have an answer."
Richard Florida, an economic geographer at
George Mason University in Fairfax, Virginia, echoes West’s concerns.
"I worry if we push the speed of the urban organism past that of the
human organism," he says. "Already we’re hiring personal trainers and
coaches to keep us going, and boosting our memory with computers." He
adds that as cities continue to get larger, the contrast between the
"talent-attracting haves" and the "talent-exporting have-nots" 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. "These are cities that stopped
growing because they haven’t found the next innovation cycle, and were
left with something stagnant or collapsing," 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’s
economy in something other than growth, says Bettencourt. "The
assumption of our paper is that as you create resources, you put them
back into the city to create more population," he says. "That’s 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."
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’s original
description: "The 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."
