More on this book
Community
Kindle Notes & Highlights
Christaller posited that urban systems, and by implication individual cities, can be represented as idealized two-dimensional crystalline geometric structures based on a highly symmetric hexagonal lattice pattern that repeats itself at smaller and smaller rescaled granularities,
it shares in common with organically evolved network structures. It is space filling and self-similar (and therefore hierarchical),
Typically, the fractal dimension of a healthy robust city steadily increases as it grows and develops, reflecting a greater complexity as more and more infrastructure is built to accommodate an expanding population engaging in more and more diverse and intricate activities.
hidden beneath the geometry even of cities with rectangular grids lurks a fractality that permeates all cities and is reflected in the universality of the scaling laws.
the interstate road network system of the United States.
the roads were planned to be as straight as possible in order to minimize distance and travel times between major cities,
it’s surprisingly regular and does not look much like a classic fractal.
Yet despite appearances, the interstate system is in fact a quintessential fractal when viewed through the lens of the actual traffic flowing on it, rather than when viewed simply as a physical road network.
the thickness of each road section represents the truck traffic flowing on it
the regular grid of the interstate that you are used to seeing on a map has been transformed into a much more interesting hierarchical fractal-like structure remarkably reminiscent of our circulatory system.
The New Science of Cities, which emphasizes the more phenomenological traditions of the social sciences, geography, and urban planning
A city is an emergent complex adaptive system resulting from the integration of the flows of energy and resources that sustain and grow both its physical infrastructure and its inhabitants with the flows and exchange of information in the social networks that interconnect all of its citizenry.
Not quite so obvious, however, is to visualize the geometry and structure of social networks and the flows of information between the people in them.
the notion of “six degrees of separation.” This was articulated by the highly imaginative social psychologist Stanley Milgram in the 1960s
small-world networks typically have an overabundance of hubs and a large degree of clustering relative to randomly connected networks.
This greater degree of clustering because of this hub structure means that small-world networks tend to contain modular subnetworks, called cliques, which themselves have high connectivity within them so that almost any two nodes are connected.
the six degrees of separation is approximately the same across all communities. Furthermore, it turns out that the modular structure is typically self-similar so that many characteristics of small-world networks satisfy power law scaling.
soldiers were traditionally told to break the regularity of their footsteps when marching across bridges. Modern bridges are designed to ensure that this sort of thing doesn’t happen.
Milgram was very much struck by the psychological harshness of life in the big city.
Milgram borrowed the term “overload” from electrical circuit and systems science theory. In big cities we are continually bombarded with so many sights, so many sounds, so many “happenings,” and so many other people at such a high rate that we are simply unable to process the entire barrage of sensory information.
Milgram suggested that the kinds of “antisocial” behaviors we perceive and experience in large cities are in fact adaptive responses for coping with the sensory onslaught of city life,
small-world networks typically manifest power law scaling reflecting underlying self-similar characteristics and a preponderance of cliques of individuals.
the evolutionary psychologist Robin Dunbar and his collaborators, who proposed that an average individual’s entire social network can be deconstructed into a hierarchical sequence of discrete nested clusters whose sizes follow a surprisingly regular pattern.
at the lowest level of the hierarchy the number of people with whom the average individual has his or her strongest relationships is, at any one time, only about five.
its defining characteristics was “the set of individuals from whom the respondent would seek personal advice or help in times of severe emotional and financial distress.”
You will notice that the sequence of numbers that quantify the magnitude of these successive levels of the group hierarchy—5, 15, 50, 150—are sequentially related to each other by an approximately constant scaling factor of about three.
There is evidence that in social networks this pattern with a branching ratio of three persists beyond the 150 level to groups having sizes of approximately 500, 1,500, and so on.
The number of around 150 represents the maximum number of individuals that a typical person can still keep track of and consider casual friends and therefore members of his or her ongoing social network.
we simply do not have the computational capacity to manage social relationships effectively beyond this size.
the group size of social primates scales with the neocortex volume of their brains as a classic power law.
Dunbar went much further by suggesting that this relationship is causal in that human intelligence evolved primarily as a response to the challenge of forming large and complex social groups rather than the usual explanation that it is a direct consequence of meeting ecological challenges.
it implies that the self-similar fractal nature of social networks is encoded in our DNA and therefore in the neural system of our brains.
this suggests that the hidden fractal nature of social networks is actually a representation of the physical structure of our brains.
we are led to the outrageous speculation that cities are effectively a scaled representation of the structure of the human brain.
a famous scaling law known as Zipf’s law for the ranking of cities in terms of their population size.
it states that the rank order of a city is inversely proportional to its population size. Thus, the largest city in an urban system should be about twice the size of the second largest, three times the size of the third largest, four times the size of the fourth largest, and so on.
He first enunciated his law in 1935, not for cities but for the frequency of word use in languages.
the most frequent word is, not surprisingly, “the,” which accounts for roughly 7 percent of all words used, while the second-place word “of” accounts for about half as many, namely 3.5 percent of all words, followed by “and” with about a third as many, namely 2.3 percent, and so on.
Even more mystifying is that this same law is valid across an astonishing array of examples, including the rank size distributions of ships, trees, sand particles, meteorites, oil fields, file sizes of Internet traffic, and many more.
Pareto’s law, or the Pareto principle, has often been loosely stated in the form of the so-called 80/20 rule, in which the richest 20 percent of a population controls 80 percent of the total income,
This asymmetry, in which there are only a very small number of very large entities but a huge number of very small ones, is characteristic of Zipf’s law.
the fact that these Zipf-like distributions are found across such a diverse set of phenomena suggests that they express some general systemic property that is independent of the character and detailed dynamics of the specific entities under consideration.
there are many more rare events than would be expected had they been random and obeyed Gaussian statistics. This difference is sometimes characterized by saying that power laws have “fat tails.”
It’s therefore not so surprising that these distributions are not Gaussian.
the number of links between people increases much faster than the increase in the number of people in the group and, to a very good approximation, is given by just one half of the square of the number of people in the group.
An obvious though subtle fundamental constraint is that all of our interactions and relationships necessarily take place in a physical setting, whether in houses, offices, theaters, stores, or on the street.
Mobility and social interaction, both so essential for the successful operation of a city, bring together the constraints of space and time—you
which interweave the structure, organization, and dynamics of social and infrastructural networks.
When these constraints on the mobility and physical interaction space of people in cities are imposed on the structure of social networks, an important and far-reaching result emerges: the number of interactions with other people in a city that an average person maintains scales inversely to the way that the degree of infrastructure scales with city size.
Consequently, the exponent controlling social interactions, and therefore all socioeconomic metrics—the universal 15 percent rule for how the good, the bad, and the ugly scale with city size—is bigger than 1 (1.15) to the same degree that the exponent controlling infrastructure and flows of energy and resources is less than 1 (0.85),
