# intellectual vanities… about close to everything

## Of Mice and Cities

‘Large Is Smart’ When It Comes To Cities
Despite the complexity of life, simplicity can manifest itself in nature as a scaling phenomenon, what Geoffrey West called the “universal scaling laws in biology.” Given biological attributes in the small-scale, these laws can be used to predict those attributes in the large-scale. This was demonstrated by taking data on the metabolic rate and body mass of animals, and then plotting that data on a logarithmic scale. The result of the plot is a relatively straight line with a slope of 3/4. Repeating this mapping exercise with various mammals and birds results in a similar line, which demonstrates Kleiber’s Law of metabolic rate being equal to body mass raised to the 3/4th power. This general formula can be used to determine an animal’s metabolic rate based on its body mass, and vice-versa. This equation allows scaling in an extraordinarily simple way, and also demonstrates economies of scale in biology: One gram of mouse muscle is 1/3 as powerful as 1g of dog muscle, and is 1/9 as powerful as 1g of elephant muscle. In biology at least, small may be beautiful but large is more efficient.

By plotting data comparing different attributes (number of gasoline stations, amount of road surface, the speed at which citizen’s walk etc.) to a city’s population, similar straight lines appear when the data is plotted on a logarithmic scale. When we compare biological and social systems, a “beta” coefficient accounts for a radical difference between their behaviours. Biological systems always have a coefficient less than one; for social systems, beta is always greater than one.

A coefficient less than one, found in biological systems, promotes economies of scale. It is driven by efficiency optimization, and results in a sigmoidal growth curve when mass is charted over time. In contrast, social organizations, having a coefficient greater than one, are driven by creation of information, wealth and resources. Its growth curve is exponential and tends towards infinity over time. Having a coefficient greater than one drives growth in a city, but what are the consequences for social organizations? When population growth is mapped against natural resource use, the growth curve tends towards infinity, as natural resource use increases exponentially over time. In the worst case, reaching resource limits would result in the collapse of a city.

Resource depletion can be delayed via technological innovation, which in effect shifts the curve in time and delays depletion to a later point in time. But avoiding collapse while at the same time demanding continuous growth requires continuous innovation, with ever-shorter “reprieves” as the innovation cycle must speed up as resource use increases. To generalize the resulting behaviour based on the beta coefficient, we see that a coefficient less than one results in a slowdown in the pace of (biological) life as size increases. For a coefficient greater than one, the pace of (social) life increases with increasing size.

Now a team of researchers, including an economist from Arizona State University, have studied the growth of cities in different parts of the world and have come up with general equations that can foretell their consumption of resources and their contributions to society. The work has debunked the notion that cities act like biological organisms, that once they start they grow, and consume and contribute at predictable linear rates.

“It’s true that large cities have more problems, they are more congested, they create more pollution and they have more crime,” said Jose Lobo, and ASU economist in the School of Sustainability. “But also because of their size, cities are more innovative and create more wealth. Large cities are the source of their problems and they are the source of the solutions to their problems.”

“Humanity has just crossed a major landmark in its history with the majority of people now living in cities,” the researchers state. “The inexorable trend toward urbanization worldwide presents an urgent challenge for predictive, quantitative theory of urban organization and sustainable development.”

This will require thinking about cities in new ways, they add. The old way of thinking about cities is as if they are an organism, which consumes resources and grows in size. Oftentimes, cities are referred to as its own ecosystem and many use the metaphor of it acting like a biological organism, Lobo said. But the team found that this was a false metaphor.

“The one thing that we know about organisms whether it be elephants or sharks or frogs, is that as they get large, they slow down,” Lobo said. “They use less energy, they don’t move as fast. That is a very important point for biological scaling.”

“In the case of cities, it is actually the opposite,” he added. “As cities get larger they create more wealth and they are more innovative at a faster rate. There is no counterpart to that in biology.”

In fact, Lobo said, the larger the city the greater return on investment. The researchers base their findings on data on the growth of cities (large urban areas) in the U.S., Europe and China over the past 150 years. They measured cities consumption of resources, (such as water usage), requirements for infrastructure (roads, transportation, lengths of electrical cable) and then measured the creative output of these areas (patents issued, “super creative jobs” generated, R&D employment, total wages). The size of the cities were determined by population.

What they found were some general correlations of size and resource consumption that more or less fit the biological organism metaphor, meaning as the city grew in size it required less energy (resources) to sustain it in a proportion called sublinear scaling. What was surprising to the team was when they measured creative output (jobs, wealth generated, innovation) as cities grew, the scaling of this output was not sublinear, but superlinear, meaning as the city grew its creative output grew faster and faster.

“It isn’t like if you double the size of a city you double its creative output,” Lobo said. “The increase you get in wealth creation is greater than the increase in size of the city.”

That ratio can range from 1.13:1 when measuring the gross domestic product in Germany, to 1.34:1 when measuring private R&D employment in the U.S.

“We are not saying that any large city is assured of prosperity forever, but if you look at the collection of cities, large cities have managed to out run their problems,” Lobo added. “Large is smart.”

All of this points to the need of rethinking large cities, both in how they are managed and what they contribute to the greater good. This is especially true today, as cities are on the brink explosive growth. Today a little more than half of the world’s population live in large urban areas. By 2030, it is estimated to be two-thirds of the world’s population will be living in urban areas. “Cities are really one of the most important innovations in humans history,” Lobo said. “We need to think of them as being very human entities and as engines of creation. We need a different perspective about cities, one that is away from thinking of large cities as a source of problems but as possible sources of solutions.”

“The practical application of this work is that the problem is not large cities, the problem is the conditions in which some of the people live in large cities,” Lobo added. “Policies should be directed to making large cities more livable not making them smaller.”

The researchers working with Lobo — Luis Bettencourt of Los Alamos National Laboratory, Los Alamos, New Mex.; Dirk Helbing and Christian Kuhnert of Dresden University of Technology, Germany; and Geoffrey West of the Santa Fe Institute, Santa Fe, New Mex. — detailed their findings in the article “Growth, innovation, scaling and the pace of life in cities,” in the current issue of the Proceedings of the National Academy of Sciences.

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