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.
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).
Yes, much of the book after that tries to get to the root of that. I'm still in the middle of that and cannot give a satisfying summary yet. He establishes the numbers based on observation and then looks for explanations
Thanks a bunch for linking this. I had similar ideas doing system architecture, quit my job after seeing those concepts at work and after some years actually started writing a presentation with the city being a single entity for my hometown. Both the article and the book are for sure some reassurance for me i wasn't abstracting into madness ;)
In my city this is kinda easy as the river is 1:1 named to the city, so any links between nature and human culture is faster to process.
Traditional engines proved unfit so i stubbornly continued working on a webgpu one allowing nestable entities for definition of laws across branches / groups in the graph. The graph is handed to compute shaders and calculates the world matrix for the scene tree per frame. Allows for portals too, etc.
Here's a demo of it doing 4D entities to animated 3D and the graph engine building a scaled universe without a fixed reference frame (dono if that's the right word, it just means there are no fixed world units or global grid, it's always derived from your position in the graph): https://krei.se/vid/demofinal.mp4
This is also halted for now as i'll go with Rust instead of TS in the future and handle the main graph logic on a central server handing out only trees to clients (similar to how ARMA and Battlespace works from what i read).
I'm not sure what i will get from the book, but if someone is poking similar ideas i'm always open for dialogue and/or wish you plenty luck and the best on this interesting journey!
Bit of a cliche but a few years ago I came back from a larger than planned acid trip and couldn’t unsee roads as arteries. Nice to see I’m not crazy and smarter people than I have formalised this to some degree :)
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.
Seems we are rediscovering concepts familiar to the Sumerians, where cities were considered as gods. Following the article, what animal (or components of an animal) would your city embody?
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.
It’d be strange if they didn’t. All human organization should be expected to behave like this, especially as rates of communication become faster.
As much as our brains seem to be evolved to delude us about it, we’re not uniquely able to resist the continuity between physics and chemistry and biology.
As self-replicating chemical and physical systems, we exist only because our atoms, molecules, cells, organs, bodies, and cultures all follow these rules naturally selecting for least action
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.
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).
Is there any insight into why it's 0.85 or 1.15, specifically?
Yes, much of the book after that tries to get to the root of that. I'm still in the middle of that and cannot give a satisfying summary yet. He establishes the numbers based on observation and then looks for explanations
Thanks a bunch for linking this. I had similar ideas doing system architecture, quit my job after seeing those concepts at work and after some years actually started writing a presentation with the city being a single entity for my hometown. Both the article and the book are for sure some reassurance for me i wasn't abstracting into madness ;)
It's an old mockup, please don't laugh - i soon hit walls and wrote my own n-dim graph engine since then: https://der-chemnitz.de/indexold.html
In my city this is kinda easy as the river is 1:1 named to the city, so any links between nature and human culture is faster to process.
Traditional engines proved unfit so i stubbornly continued working on a webgpu one allowing nestable entities for definition of laws across branches / groups in the graph. The graph is handed to compute shaders and calculates the world matrix for the scene tree per frame. Allows for portals too, etc.
Here's a demo of it doing 4D entities to animated 3D and the graph engine building a scaled universe without a fixed reference frame (dono if that's the right word, it just means there are no fixed world units or global grid, it's always derived from your position in the graph): https://krei.se/vid/demofinal.mp4
This is also halted for now as i'll go with Rust instead of TS in the future and handle the main graph logic on a central server handing out only trees to clients (similar to how ARMA and Battlespace works from what i read).
I'm not sure what i will get from the book, but if someone is poking similar ideas i'm always open for dialogue and/or wish you plenty luck and the best on this interesting journey!
Bit of a cliche but a few years ago I came back from a larger than planned acid trip and couldn’t unsee roads as arteries. Nice to see I’m not crazy and smarter people than I have formalised this to some degree :)
Some of them are literally called arterials.
Thanks for the book recommendation. Grabbing this before I forget the title.
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.
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
I'm not fluent in this topic. Is there much overlap between these scaling laws and dissipative structures in thermodynamics and/or systems theory?
Yes.
See: <https://news.ycombinator.com/item?id=45188686> (Geoffrey West / Santa Fe Institute).
Seems we are rediscovering concepts familiar to the Sumerians, where cities were considered as gods. Following the article, what animal (or components of an animal) would your city embody?
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.
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
Made me think of A City Is Not A Tree - https://www.patternlanguage.com/archive/cityisnotatree.html
It’d be strange if they didn’t. All human organization should be expected to behave like this, especially as rates of communication become faster.
As much as our brains seem to be evolved to delude us about it, we’re not uniquely able to resist the continuity between physics and chemistry and biology.
As self-replicating chemical and physical systems, we exist only because our atoms, molecules, cells, organs, bodies, and cultures all follow these rules naturally selecting for least action
Jane Jacobs: The Nature of Economies.