Affordable Housing Institute : US

[Continued from yesterday’s Part 1.]

Yesterday we put up the remarkable — and if true, very important — hypothesis that city scaling behaves power laws analogous to those that influence biological scaling:

 

Animal body mass and metabolism scale

 

The thesis is put forward in a new PNAS paper, Growth, innovation, scaling, and the pace of life in cities:

 

We predict that the pace of social life in the city increases with population size, in quantitative agreement with data, and we discuss how cities are similar to, and differ from, biological organisms, for which  < 1.

 

Finally, we explore possible consequences of these scaling relations by deriving growth equations, which quantify the dramatic difference between growth fueled by innovation versus that driven by economies of scale. 

 

This difference suggests that, as population grows, major innovation cycles must be generated at a continually accelerating rate to sustain growth and avoid stagnation or collapse.

 

Their policy implication is this: cities succeed only if they are eternal laboratories.

 

Now let’s examine the evidence:

 

Just look at the pictures

 

In this work, we show that the social organization and dynamics relating urbanization to economic development and knowledge creation, among other social activities, are very general and appear as non-trivial quantitative regularities common to all cities, across urban systems. 

 

AHI translation: When we went looking for data, we found it, and we can measure the numbers.

 

We present an extensive body of empirical evidence showing that important demographic, socio-economic, and behavioral urban indicators are, on average, scaling functions of city size that are quantitatively consistent across different nations and times.  7301-7302.  [Page numbers refer to the PNAS text.]

 

It didn’t matter what decade, what continent, or what city: we found that scale activities changed at roughly the same rates all around the globe, suggesting these are the demographic equivalent of Planck’s Constant.

 

You determine h only by measuring

 

Cities as consumers of energy and resources and producers of artifacts, information, and waste have often been compared with biological entities, in both classical studies in urban sociology and in recent research concerned with urban ecosystems and sustainable development.  Recent analogies include cities as ‘living systems’ or ‘organisms’ and notions of urban ‘ecosystems’ and urban ‘metabolism.’  Are these terms just qualitative metaphors, or is there quantitative and predictive substance in the implication that social organizations are extensions of biology, satisfying similar principles and constraints?  7302.

 

We haven’t read AHI’s writings about housing finance ecosystems, but if we had, we’d agree.

 

Despite its amazing diversity and complexity, life manifests an extraordinary simplicity and universality in how key structural and dynamical processes scale across a broad spectrum of phenomena and an immense range of energy and mass scales covering >20 orders of magnitude.  7302.

 

Since one order of magnitude is a 10x, twenty orders of magnitude is 100,000,000,000,000,000,000 [twenty zeroes — Ed.]

 

In biology, the lightest and heaviest animals both obey power-law scaling, so we’re pretty confident it’s right when applied to biology.

 

The biggest mammal

 

The smallest insect?

 

Highly complex, self-sustaining structures, whether cells, organisms, or cities, require close integration of enormous numbers of constituent units that need efficient servicing.  7302.

 

Since both organisms and cities are big complicated interdependent operating systems, we have at least a plausible basis for looking at the data.

 

Before turning to the city-as-metabolic-body analogy, the authors — both of them are physicists by training — start by observing that since animals are biological, they are bounded by physical constraints like body size:

 

Remarkably, almost all physiological characteristics of biological organisms scale with body mass, M, as a power law whose exponent is typically a multiple of ¼ (which generalizes to 1/ (d+1) in d-dimensions).  For example, metabolic rate scales as B x M ^¾.  Because metabolic rate per unit of mass decreases with body size, this relationship implies an economy of scale in energy consumption: larger organisms consume less energy per unit time and per unit mass.   7303.

 

Because strength varies as the square and mass as the cube, larger organisms have more internal organs and core processes, and an ever-greater share of the energy is devoted to keeping the beast alive and mobile.  Big things move more slowly, and reach a natural size limit.

 

Don’t expect him to hop

 

An elephant is approximately a blown-up gorilla, which is itself a blow-up mouse, all scaled in an appropriately non-linear, predictable way.  This concept means that dynamically and organizationally, all mammals are, on the average, scaled manifestations of a single idealized mammal, whose properties are determined as a function of its size.

 

The power-law scaling principles also apply to those two great human inventions, bureaucracy and self-organizing networks.   Bureaucracy reaches a natural limit because the bureaucracy’s ability to react slows down (inferior OODA loop); networks (such as capital markets) are smarter than people because their power to organize information rapidly.

 

From this perspective, it is natural to ask whether social organizations also display universal power law scaling for variables reflecting key structural and dynamical characteristics. 

 

Cities, however, are not animate — they are comprised of animate cells (called people) and inanimate skeleton (called municipal infrastructure) and cartilage (buildings and businesses).  So they need not adhere to the laws of physics:

 

In what sense, if any, are small, medium and large cities scaled versions of one another, thereby implying that they are manifestations of the same average idealized city?  In this way, urban scaling laws, to exist, may provide fundamental quantitative insights and predictability into underlying social processes, responsible for flows of resources, information, and innovation.  7302.

 

How closely can we approximate the ideal city?

 

Enough with the overture — what did they find?

 

We find robust and commensurate scaling exponents across different nations, economic systems, levels of development, and recent time periods for a wide variety of indicators.  This finding implies that, in terms of these quantities, cities that are superficially quite different in form and location, for example, are in fact, on the average, scaled versions of one another, in a very specific but universal fashion prescribed by the scaling laws of Table 1.  7303.

 

This finding, if it stands up, would be little short of revolutionary, because it says that future characteristics of a larger city can be extrapolated precisely from its current size and characteristics.

 

Who we are when small holds the essence of who we will be when large

 

For reference, let’s include this important table in its entirety:

 

 

The authors divide the scalars into three groups: those that go linearly with population, those that rise faster (increasing returns from networking effects), and those that rise slower (economies of scale).

 

Despite the ubiquity of power-law scaling, there is no simple analogue to the universal quarter-powers observed in biology.  Nevertheless, Table 1 reveals a taxonomic universality whereby exponents fall into three categories defined by ß = 1 (linear), ß < 1 (sublinear), and ß > 1 (superlinear), with ß in each case clustering around similar values:

 

ß ˜ 1 is usually associated with individual human needs (job, house, household water consumption)

 

ß ˜ 0.8 < 1 characterizes material quantities displaying economies of scale associated with infrastructure, analogous to similar quantities in biology.

 

ß ˜ 1.2 > 1 signifies increasing returns with population size and is manifested by quantities related to social currencies, such as information, innovation or wealth, associated with the intrinsically social nature of cities.    7303.

 

Because the table condenses down its data into a power-law variable beta, a bit of explanation may help.  When the authors speak of an increasing beta, they’re measuring the rate of growth in the quantity as a city gets larger (measured in number of people). 

 

 

Thus, if a Small city has a patent rate of 1x, when the city becomes Medium sized (growing to 3x its original), it will be producing 35% more patents per capita.  It’ll be 35% more competitive.  If it makes the leap to a Large city (10x the Small size), its patent rate will be 86% higher.  Bigger cities are smarter.

 

 

Wages too rise faster than the rate of population.  Bigger cities are richer.  Move to a city 10x your current one and your earnings will probably rise 32%.  (So too will your housing prices!)

 

To achieve both, send your kid to the city

 

Big cities may be richer and smarter, but they’re also sicker (AIDS rates rise 70% in a 10x city), more dangerous (crime rates up 45% in a 10x). 

 

Conversely, big cities need less hardware: 41% fewer gas stations per capita, 38% less roads, 25% less wiring.

 

The evidence, in short, is impressive.

 

What are the policy implications?

 

[Concluded tomorrow in Part 3.]

Send post as PDF to