Scale: The Universal Laws of Life and Death in Organisms, Cities and Companies

by Geoffrey West

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. If we tried to respond to every stimulus, our cognitive and psychological circuitry would break down and, in a word, we would blow a fuse just like an overloaded electrical circuit. And sadly, some of us do. 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, implying that without such adaptations we’d all blow our fuses.

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.

simply do not have the computational capacity to manage social relationships effectively beyond this size.

This suggests that increasing the group size beyond this number will result in significantly less social stability, coherence, and connectivity, ultimately leading to its disintegration.

The neocortex is the most sophisticated part of the brain, controlling and processing higher functions such as sensory perception, the generation of motor commands, spatial reasoning, conscious thought and language, and therefore the computational capacity to participate in complex social relationships. This presumed connection between brain size and the ability to form social groups is called the social brain hypothesis.

Furthermore, because the geometry of white and gray matter in our brains, which forms the neural circuitry responsible for all of our cognitive functions, is itself a fractal-like hierarchical network, this suggests that

the hidden fractal nature of social networks is actually a representation of the physical structure of our brains.

as Zipf’s law for the ranking of cities in terms of their population size. This is shown graphically in Figure 39. It’s an intriguing observation: in its simplest form, 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. So, for example, in the 2010 census, the biggest city in the United States was New York with a population of 8,491,079.

Human Behavior and the Principle of Least Effort,

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, which is approximately true for the entire globe. Similarly, roughly 80 percent of a company’s profits come from 20 percent of its customers, as do 80 percent of its complaints.

Fractals are often the result of an evolutionary process that tends toward optimizing specific features, such as ensuring that all cells in an organism or all people in a city are supplied by energy and information, or maximizing efficiency by minimizing transportation times or times for accomplishing tasks with minimal energy. Less obvious is what is being optimized in social networks.

the desire of all individuals and companies to maximize their assets and income—coupled with the concept of maximal filling of social space are the underlying driving forces.

total possible number of pair-wise links between people in a city is given by the total number of people in the city multiplied by the total number minus one—all divided by two.

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.

all socioeconomic metrics should scale with the square of the population size.

Dunbar number, according to which we even have difficulty sustaining any sort of meaningful relationship with more than about 150 people,

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.

Just as raising the temperature of a gas or liquid increases the rate in the number of collisions between molecules, so increasing the size of a city increases the rate and number of interactions between its citizens.

Cities are effectively machines for stimulating and integrating the continuous positive feedback dynamics between the physical and the social, each multiplicatively enhancing the other.

The strengths of social interaction and the flows of information exchange are greatest between terminal units (that is, between individuals) and systematically decrease up the hierarchy of group structures from families and other groups to increasingly larger clusters, leading to superlinear scaling, increasing returns, and an accelerating pace of life.

if we think of social networks as layered hierarchies beginning with individuals as the “invariant terminal units” and progressing systematically up through modular groupings of increasing size from families, close friends, and colleagues to acquaintances, working clusters, and organizations, then the corresponding strengths of interaction and amounts of information exchanged at each level systematically decrease, resulting in superlinear scaling.

diseases spread faster, businesses are born and die more often, commerce is transacted more rapidly, and people even walk faster, all following the 15 percent rule.

The multiplicative compounding of socioeconomic interactivity engendered by urbanization has inevitably led to the contraction of time.

Rather than being bored to death, our actual challenge is to avoid anxiety attacks, psychotic breakdowns, heart attacks, and strokes resulting from being accelerated to death.

the size of cities has to some degree been determined by the efficiency of their transportation systems for delivering people to their workplaces in not much more than half an hour’s time.

of around 1.15 regardless of the urban system. In other words, the systematic 15 percent increase in socioeconomic activity with every doubling of city size, whether in wages and patent production or crime and disease, should track a predicted 15 percent increase in the interaction between people.

In other words, the systematic 15 percent increase in socioeconomic activity with every doubling of city size, whether in wages and patent production or crime and disease, should track a predicted 15 percent increase in the interaction between people.

accelerating pace of life originates in the increasing connectivity and positive feedback enhancement in social networks as city size increases.

number of visitors should scale inversely as the square of both the distance traveled and the frequency of visitation.

the prediction of movement in cities can be restated as saying that the number of people traveling to a specific location scales with both the distance traveled and the visitation frequency as a power law whose exponent is −2.

if the distance traveled multiplied by the frequency of visits to any specific location is kept the same, then the number of people visiting also remains the same.

Galileo’s seminal insight that the strength of the limbs of animals should scale sublinearly as the 2⁄3 power of their body weight.

superlinear scaling laws whose exponents are 1.15 rather than 1.00. This approximately 15 percent increase in all socioeconomic activity with every doubling of the population size happens almost independently of administrators, politicians, planners, history, geographical location, and culture.

the total number of establishments in each city regardless of what business they conduct turns out to be linearly proportional to its population size.

The proportionality constant is 21.6, meaning that there is approximately one establishment for about every 22 people in a city, regardless of the city size.

put it slightly differently: doubling the size of a city results in doubling the total number of establishments, but only a meager 5 percent increase in new kinds of businesses.

all of this increase in diversity is reflected in a greater degree of specialization and interdependence involving larger numbers of people, both as workers and as clients.

He who does not increase his knowledge decreases it.

every city needs lawyers, doctors, shopkeepers, tradesmen, administrators, builders, et cetera. As cities grow and these basic core activities become saturated, the pace at which new functionalities are introduced slows down dramatically but never completely ceases.

Once the set of individual building blocks is large enough, the resulting combination of talents and functions is sufficient to generate novel variations that expand the business landscape, giving rise to specialized establishments such as exotic restaurants, professional sports teams, and luxury stores, leading to greater economic productivity.

that business types whose abundances scale superlinearly with population size systematically rise in their rankings, whereas those that scale sublinearly systematically decrease.

major theme running throughout this book is that nothing grows without the input and transformation of energy and resources.

Food is consumed, then digested and metabolized into a usable form that is transported through networks to supply cells, where some is allocated to the repair and maintenance of existing cells, some to replace those that have died, and some to create new ones that add to the overall biomass.

through networks to supply cells, where some is allocated to the repair and maintenance of existing cells, some to replace those that have died, and some to create new ones that add to the overall biomass. This sequence is the basic template for how all growth occurs whether for organisms, communities, cities, companies, or even economies. Roughly speaking, incoming metabolized energy and resources are apportioned between general maintenance and repair, including replacement of what’s already there and has decayed and the creation of new entities, whether cells, people, or infrastructure, that add to the system and increase its size. Thus the energy available for growth is just the difference between the rate at which energy can be supplied and the rate that is needed for maintenance.

sequence is the basic template for how all growth occurs whether for organisms, communities, cities, ...

incoming metabolized energy and resources are apportioned between general maintenance and repair, including replacement of what’s already there and has decayed and the creation of new entities, whether cells, people, or i...

energy available for growth is just the difference between the rate at which energy can be supplied and the rate...

On the supply side, metabolic rate in organisms scales sublinearly with the number of cells (following the generic 3⁄4 power exponent derived from network constraints) whi...

metabolic rate in organisms scales sublinearly with the number of cells (following the generic 3⁄4 power exponent derived from network constraints) while the demand increases approximately linearly. So as the organism increases in size, demand eventually outstrips supply because linear scaling grows faster than sublinear, with the consequence that the amount of energy availabl...