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Applying Physics to Explore Networks as Chaotic Systems

War breeds confusion. Thanks to a confused disconnect between media interest and political intrigue, following the connections, fueling factors, and original instigators of war is nearly impossible. Yet take the Syrian Civil War, run a mass of data known about it through a new program dubbed MAPPR, developed by three TED fellows to present graphical representations of mathematical relations, and you can easily obtain the motivations and desires of major world powers. What one must understand is that the true power of networks comes with the derivation of basic laws to govern the mapped connections. Geoffrey West, a “retired” theoretical physicist wanted to explore the systems that governed the world around us. Looking first at biological systems and convergent evolution, he was able to derive several laws to govern the various biological networks of animals. For instance, the metabolic rate of a creature is equivalent to its mass taken to the three-fourths power eg. an elephant consumes a tenth the energy per mass as a mouse. Additionally, the log-log plot of heart rate to mass shows a high fit linear slope of -¼ and the log-log plot of genome length to mass shows linear slope of ¼.  A simple example of how he has done so involves the mapping of the blood flow between organs in the animal’s body. The greater number of edges running out from a given organ, the larger the capillaries may be, as demonstrated by the heart. Once debate over his proposed guidelines turned into a debate over why certain crustaceans were exempt, he decided to move on.

Using his existing research, he sought to represent the multiple complex networks of interactions of cities as another predictable system governed by basic laws. Whereas in animals he mapped the network of blood flow to certain organs, he mapped the traffic flow through shopping centers and stores. This research held promise as the majority of human beings now live in locations of high urban density, such as an increasing 85% urbanization in the United States. West soon found, however, that cities are more complex than any biological system. The networks within cities that complicate them beyond biological models are the surprising effects from the dense social networks of cities. Many social scientists have proposed that living in a situation that promotes the quantity of social interactions promotes productivity, moral positivity, and continued health of the society as a whole. The challenge then became to find the equations that connected the dense social network connecting people to friends and employers with the existing financial and transit networks that display the flow of money and physical goods.

While much social research depends on human nature and social studies, West chose to draw from hard statistics from both physical and social realms to build his networks. The statistics he drew from vary between “gas stations and personal income, flu outbreaks and homicides, coffee shops and the walking speed of pedestrians”. Using these people, locations, and businesses as nodes, he was able to analyze the networks of multiple cities to obtain constant social trends. These are emergent laws, ones unintended by society but underlying every dense population center. Such laws will always come into effect as people gather in greater and greater population densities. This is a process referred to by West as “Agglomeration”.

What West found is that much like large organisms, cities have an economy of scale. Cities consume dramatically fewer resources per capita than small communities. In practice, this is shown as doubling the size of a city only consumes 85% more resources than the original city. Take a statistically average person, double the size of their city, and they’ll be 15% more productive, with society as a whole spending and banking 15% more per capita. This is possibly a result of an increased number of edges to people in their social network in real life and online, which is shown to increase productivity. Combine just those two trends and see that city growing to double its size increases output to about 230% while increasing input to only 185%.

At this point, much of West’s work may seem like data drawn from simple statistics. However, networks provide the ability to represent these statistics to see the connections and flows between consumption and production. For instance, West calculates a single person to draw off a total of 11000 watts from their resource network, a greater consumption per day than that of a blue whale. You could display this network as one edge representing the calories consumed from a local coffee shop, another edge to the power our computer draws from the grid, and yet anther for the gas driving our cars from the gas station.

Furthermore, West noticed something interesting while tracking the connections between innovation and the economy. With each major innovation, such as the internal combustion engine and recently more efficient electric motors, society builds a whole new network of profitability, just as the previous economy was beginning to slow down. On a classical map of networks, you might represent this innovation by a bridge connecting the old commercial network of goods and resources to the new one. These bridges, West argues, are necessary if humanity is to continue experiencing the positive effects of urbanization. Should they ever stop, the economy will collapse upon itself from lack of desirable resources.

The results found by West demonstrate that networks can be used to analyze and improve systems outside of straight economics and hardcore physics. Considering that social centers such as cities show no indications of disappearing, work must be done to understand them. Indeed, it would seem that in order to achieve a sustainable future, humanity must engineer cities that optimize their efficiency and build upon West’s social research.



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