Cities and scale: Part 1, the grand theory
Why aren’t human beings an average of nine feet tall? Isn’t size an advantage?
Robert Wadlow, 8′ 11″, died at the age of 22 of blood poisoning
For that matter, why aren’t we three feet tall? (Arthur C. Clarke once observed that for going into space, smaller people would be better, since they will need much less payload and hence much smaller rockets.)
It would change the dynamics
For that matter, why not gargantuan bugs? During the 1950’s, innumerable atrocious science fiction movies (like Them!, the best of them all) posited giant ants –
“A horror horde of crawl-and-crush giants/
clawing out of the earth’s steaming depths.”
– repeating the canard that since an ant can lift several multiples of its body weight, “if an ant were the size of a man, it could lift a car.”
And terrify your date
In fact, it couldn’t lift itself, because though size scales linearly, and strength scales with the square of size, weight scales with the cube (’square-cube law’).
The right size for an animal, therefore, is a saddle point: being the right size is a mini-max solution, as first (and best) expressed in J. B. S. Haldane in his wonderful essay, On Being the Right Size.
“There’s even a reason blackboards are the size they are.”
Haldane examines the effects of water surface tension (insignificant to a human, deadly to an insect), circulatory system and breathing, strength, speed, body warmth (small animals die in cold climates) and gravity:
To the mouse and any smaller animal it presents practically no dangers. You can drop a mouse down a thousand-yard mine shaft; and, on arriving at the bottom, it gets a slight shock and walks away, provided that the ground is fairly soft. A rat is killed, a man is broken, a horse splashes.
Thanks for the image, JBS
Haldane also mentions flying, or why angels don’t work:
An angel whose muscles developed no more power weight for weight than those of an eagle or a pigeon would require a breast projecting for about four feet to house the muscles engaged in working its wings, while to economize in weight, its legs would have to be reduced to mere stilts.
To stay aloft, you boys are gonna have to lose a lotta weight!
In light of this biological scaling optimization, might similar reasoning and imperatives influence the size of cities? Is there an ideal city size — and if so, what is it? Do cities reveal any kind of structural relationship similar to biological organisms?
That’s the question asked — and answered, at least via a mountain of statistics and regression analysis — by a fascinating new PNAS paper, Growth, innovation, scaling, and the pace of life in cities, by a quintet of authors bookended by Luis M. A. Bettencourt and Geoffrey B. West.
Luis Bettencourt, of
Geoffrey West, of the Santa Fe Institute
The authors make no bones about their interest in cities and their reasons for tackling the problem now:
Humanity has just crossed a major landmark in its history with the majority of people now living in cities. Cities have long been known to be society’s predominant engine of innovation and wealth creation, yet they are also its main source of crime, pollution, and disease.
I really like a crisp, clear expression of the challenge: cities have always been where wealth was born, yet bringing so many people together in proximity has all those negative externalities. When one vector (wealth) goes one way, and another (disease) goes the other, we want to know which (if either) will prevail, or whether they can reach a happy medium. Moreover, the problem is urgent:
The inexorable trend toward urbanization worldwide presents an urgent challenge for developing a predictive, quantitative theory of urban organization and sustainable development.
Since AHI blog posts use big words only when necessary, I’ll translate for you
You mean I don’t need a Ph. D. to enjoy this post?
Translation: It would be really nice if we had some idea what elements comprise the optimal city, and its optimal size.
Here we present empirical evidence indicating that the processes relating urbanization to economic development and knowledge creation are very general, being shared by all cities belonging to the same urban system and sustained across different nations and times.
It looks like all cities scale up and down according to mathematical laws that we can deduce.
Can we tessellate the entire globe with cities?
Many diverse properties of cities from patent production and personal income to electrical cable length are shown to be power law functions of population size with scaling exponents, 
, that fall into distinct universality classes.
Quantities reflecting wealth creation and innovation have 
1.2 > 1 (increasing returns),
As cities get bigger, people in them get richer, cleverer, and more creative.
whereas those accounting for infrastructure display 
0.8 < 1 (economies of scale).
As cities get bigger, they need less infrastructure per person.
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.
Even though animals reach optimum sizes, maybe cities don’t?
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.
As a driver of growth (and viability), economies of scale run out of gas after a while, whereas innovation and creativity have increasing returns, where the bigger is more better than the next bigger.
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.
A while back, I was privileged to hear a stimulating address by Rakesh Mohan, deputy governor of the Reserve Bank of India, whose talk on urbanization (a distillation of his many writings on globalization and urbanization) was anchored by this blunt assessment: unskilled labor is obsolete.
Rakesh Mohan, Deputy Governor, Reserve Bank of
The statement is striking — and coming from an Indian, deliberately provocative — and it resonated strongly with me. As he said then:
If the world is urbanizing, it’s because people think it’s a good idea. Yet our urban planning as a ‘third-class carriage’ mentality: I’m inside, don’t you dare come in, you’re much better off where you are. Most urban planners live in largest cities in the world, yet they complain that cities are too large. This report takes the opposite view.
It may be crowded, but I’ve got my seat, and you don’t
That’s big stuff. When we envision why cities exist, we imagine economies of scale in infrastructure — roads, electrical grids, water and sanitation, density and building. We also instinctively think of cities as speedy — life in the fast lane — versus the archetypal sleepy country village.
All that infrastructure makes for rapid transit
As the authors put it:
The increasing concentration of people in cities presents both opportunities and challenges toward future scenarios of sustainable development. On the one hand, cities make possible economies of scale in infrastructure and facilitate the optimized delivery of social services, such as education, health care, and efficient governance. 7301.
Other impacts, however, arise because of human adaptation to urban living. They can be direct, resulting from obvious changes in land use (e.g. urban heat island effects and increased greenhouse gas emissions) or indirect, following from changes in consumption and human behavior. 7301.
If the authors are right, successful urbanization hinges on our ability to make cities smarter, faster, idea factories — and to do that, we have to make everybody in the city a contributing part of the city’s collective knowledge economy.
Are they right? What’s their evidence?
We’re looking for it now
[Continued tomorrow in Part 2 .]
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