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A scaling law: Simple mathematical laws that govern the properties of cities, Physicist Geoffrey West at TEDTalks November 14, 2014

Posted by OromianEconomist in cross industry agglomeration (urbanization), The Mathematics of Cities.
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Our theory suggests we will face something mathematicians call a “finite time singularity.” Equations with superlinear behavior, rather than leveling out like the sublinear ones in biology, go to infinity in a finite time. But that’s impossible, because you’re going to run out of finite resources. The equations tell us that when you reach this point, the system stagnates and collapses.

Geoffrey West @ http://discovermagazine.com/2012/oct/21-geoffrey-west-finds-physical-laws-in-cities

 

 

 

 

http://www.ted.com Physicist Geoffrey West has found that simple, mathematical laws govern the properties of cities — that wealth, crime rate, walking speed and many other aspects of a city can be deduced from a single number: the city’s population. In this mind-bending talk from TEDGlobal he shows how it works and how similar laws hold for organisms and corporations.

“What we do is, as we grow and we approach the collapse, a major innovation takes place and we start over again, and we start over again as we approach the next one, and so on. So there’s this continuous cycle of innovation that is necessary in order to sustain growth and avoid collapse. The catch, however, to this is that you have to innovate faster and faster and faster. So the image is that we’re not only on a treadmill that’s going faster, but we have to change the treadmill faster and faster. We have to accelerate on a continuous basis. And the question is: Can we, as socio-economic beings, avoid a heart attack?”

 

A scaling law basically represents how various measurements in a system—say, the bodies of mammals—change proportionally as size changes. The first and most famous scaling law is something called Kleiber’s law, which describes how metabolic rate, the amount of energy you need per day to stay alive, is related to an organism’s size. It turns out that metabolic rate [r] is just the mass [M] of the organism raised to the three-quarters power [r ≈ M¾]. A whale, for instance, weighs about 100 million times more than a shrew. You might expect its metabolic rate to be 100 million times greater, too. But it’s only a million times bigger, because metabolic rate scales as mass to the three-quarters [100,000,000¾ is 1,000,000]. The pattern holds with very few exceptions across all organisms.

Cities are obvious metaphors for life. We call roads “arteries” and so forth. But more importantly, they are our unique creations. Santa Fe feels unique, New York City feels unique. They have their own culture, history, and geography. They have their own planners, politicians, and architects. Yet when my collaborators and I looked at tremendous amounts of data about cities, we found universal scaling laws again. Each city is not so unique after all. If you look at any infrastructural quantity—the number of gas stations, the surface area of the roads, the length of electric cables—it always scales as the population of the city raised to approximately the 0.85 power.
The bigger the city is, the less infrastructure you need per capita. That law seems to be the same in all of the data we can get at. It is a really interesting relationship, and it’s very reminiscent of scaling laws in biology. However, when we looked at socioeconomic quantities—quantities that have no analogue in biology, like wages, patents produced, crime, number of police, et cetera—we found that unlike everything we’d seen in biology, cities scale in a superlinear fashion: The exponent was bigger than 1, about 1.15. That means that when you double the size of the city, you get more than double the amount of both good and bad socioeconomic quantities—patents, aids cases, wages, crime, and so on.

I believe that part of what has made life on Earth so unbelievably resilient—able to evolve and survive across billions of years—is the fact that its growth is generally sublinear, with the exponents smaller than 1. Because of that, organisms evolve over generations rather than within their own lifetimes, and such gradual change is incredibly stable. But human population growth and our use of resources are both growing superlinearly, and that is potentially unstable.
Our theory suggests we will face something mathematicians call a “finite time singularity.” Equations with superlinear behavior, rather than leveling out like the sublinear ones in biology, go to infinity in a finite time. But that’s impossible, because you’re going to run out of finite resources. The equations tell us that when you reach this point, the system stagnates and collapses.

The growth equation was derived with certain conditions that are determined by the cultural innovation that dominates each historic period: iron, computers, whatever it is. An innovation that changes everything—like a new fuel—resets the clock, so you can avoid the singularity a bit longer. But the theory says that to avoid the singularity, these innovations have to keep coming faster and faster.
I think the biggest stresses are clearly going to be on energy, food, and clean water. A lot of people are going to be denied these basics across the globe. If there is a collapse—and I hope I’m wrong—it will almost certainly come from social unrest starting in the most deprived areas, which will spread to the developed world.
We need to seriously rethink our socioeconomic framework. It will be a huge social and political challenge, but we have to move to an economy based on no growth or limited growth. And we need to bring together economists, scientists, and politicians to devise a strategy for doing what has to be done. I think there is a way out of this, but I’m afraid we might not have time to find it.

Read more @ http://discovermagazine.com/2012/oct/21-geoffrey-west-finds-physical-laws-in-cities

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