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Cities obey the laws of living things

Cities obey the laws of living things

9 comments

·September 7, 2025

0xcafefood

It's not mentioned in this article, but Geoffrey West's book "Scale: The Universal Laws of Life, Growth, and Death in Organisms, Cities, and Companies" give a fascinating and approachable overview of similar ideas.

One of the ideas presented is the "quantization" of the exponents observed in power laws relating various biometrics. E.g. it's known that the larger a species' average mass, the longer it lives, and that this relationship is expressed as a power law. What West found is that the exponents in many of these relationships are integer multiples of 1/4! This book, and West's research, uncover the origin of that phenomenon, relating it back to the efficient distribution of material throughout the organism (certain branching laws of cardiovascular networks, or phloem in plants, etc.)

It's not hard to see how that could apply to things like cities and companies as well.

ajmurmann

Fabulous book. I cannot recommend it strongly enough. It's impossible to unsee the two scaling laws he lays out for cities once you know about them:

Infrastructure scales with 0.85: "It may not come as such a big surprise to learn that larger cities require fewer gas stations per capita than smaller ones, but what is surprising is that this economy of scale is so systematic: it is approximately the same across all of these countries, obeying the same mathematical scaling law with a similar exponent of around 0.85. What is even more surprising is that other infrastructural quantities associated with transport and supply networks, such as the total length of electrical lines, roads, water and gas lines, all scale in much the same way with approximately the same value of the exponent, namely about 0.85." - West, Geoffrey. Scale: The Universal Laws of Life, Growth, and Death in Organisms, Cities, and Companies (pp. 272-273).

Social effects scale with 1.15: "However, of even greater significance was the surprising discovery that the data also reveal that socioeconomic quantities with no analog in biology such as average wages, the number of professional people, the number of patents produced, the amount of crime, the number of restaurants, and the gross urban domestic product (GDP) also scale in a surprisingly regular and systematic fashion, as illustrated in Figures 34–38. Also clearly manifested in these graphs is the equally surprising result that all of the slopes of these various quantities have approximately the same value, clustering around 1.15. Thus these metrics not only scale in an extremely simple fashion following classic power law behavior, but they all do it in approximately the same way with a similar exponent of approximately 1.15 regardless of the urban system." - (p. 275).

araes

Kind of neat, especially with a bit of skepticism toward the bigger is always better claim. Lot of "really" large animals, not actually that successful.

Elephants, Rhinos, Tigers, not especially successful. Start to become really high value targets with limited ability to defend against threats from every direction, and almost every nearby animal is "red circle", including humans. The Asian elephant is Endangered, the African savanna elephant is Endangered, while the African forest elephant is Critically Endangered. The the black, Javan, and Sumatran rhinos are Critically Endangered. Tigers are Endangered at 5% of historic range.

Dinosaur replenishment rates became negative in the Late Cretaceous, even before the Cretaceous–Paleogene extinction event. More species were going extinct than new ones were evolving with a decrease in the development of new traits or adaptive strategies. It all started stagnating, and then they could not cope with sharp changes.

A lot of cities are similar. Paralysis, stagnation, difficulty dealing with threats and changes, and almost every member of human society views them as a high value target. Why target podunk nowhere for pocket change, when a single success swindling New York or Los Angeles is millions. Politics targets them constantly. Now they're even drawing federal military responses.

Bigger's definitely got issues.

abdullahkhalids

The paper in question [1].

Their big results seems to be that on a log-log scale CO2 emissions are linear with respect to population with a slope of 1.12.

[1] https://www.pnas.org/doi/full/10.1073/pnas.2501224122

OgsyedIE

I'm not fluent in this topic. Is there much overlap between these scaling laws and dissipative structures in thermodynamics and/or systems theory?

dredmorbius

Yes.

See: <https://news.ycombinator.com/item?id=45188686> (Geoffrey West / Santa Fe Institute).

markstock

Let's be a little more clear: these are not "laws" as much as they are scaling relationships, this is not "new math" (see Ziph and others), and central planning has always had an impact on city development. Nevertheless, I appreciate this line of inquiry.

markstock

Just a few volumes from my bookshelf related to this:

Network Analysis in Geography, Haggett and Chorley

Cities and Complexity, Batty

Urban Grids, Busquets et al