Tuesday, January 5, 2016

Scale: "Why People and Companies Die While Cities Keep Growing"

From Irving Wladawsky-Berger:
The Winter issue of strategy+business includes a very interesting article on theoretical physicist Geoffrey West, - The Fortune 500 Teller.  Dr. West is Distinguished Professor and Past President of the Santa Fe Institute (SFI), a non-profit research institute dedicated to the study of complex systems.  Prior to joining the SFI in 2003, he was the leader and founder of the high energy physics group at Los Alamos National Lab.

About 20 years ago, West got interested in whether some of the techniques and principles from the world of physics could be applied to complex biological and social systems.  In particular, he wondered if we could apply empirical, quantifiable and predictive scientific methods to help us better understand complex biological organisms and social organizations like cities and companies.
In the 1990s, his attention first turned to biology.  There are enormous variations in the characteristics of living creatures, their live spans, pulse rates, metabolism, and so on.  How do these characteristics change with body size?  Why do human beings live roughly 80 to 100 years, while mice live only two to three years.  Are there some common principles that apply to all living creatures regardless of size?  Can we find empirical mathematical models that might allow scientists to ask big questions about life, aging and death?

As it turns out, such a model was developed in the 1930s by biologist Max Kleiber.  Kleiber observed that for the vast majority of animals, their metabolic rate, the amount of energy expended by the animal, is proportional to its mass M raised to the ¾ power, that is M¾Kleiber’s Law applies to an amazing range of sizes, from bacteria to blue whales.
Because the scaling is sublinear, that is, the exponent is less than 1, larger species are more efficient than smaller ones, needing less energy per pound.  While an elephant is 10,000 times the size of a guinea pig, it needs only 1000 times as much energy.  Furthermore, the bigger the organism, the longer it lives, and the longer it takes to grow and mature, all predicted by the same sublinear power law.  This simple scaling applies to a large number of physiological variables besides metabolic rate, including how long the organism lives, how long it takes to mature, its growth rate and so on.
Along with SFI colleagues, West studied these scaling laws, and concluded that they were due to the internal structure that makes life possible, - the nutrient networks that have to reach every cell and capillary in a living organism.  They modeled such networks, assuming that evolution would arrive at the most efficient structures possible, and came up with the ¾ power scaling between metabolic rate and mass that Max Kleiber had empirically observed in the 1930.

Their theory also explained why organisms grow rapidly when young but eventually stop growing.  As the number of cells doubles, the number of capillaries rises by only 75 percent.  As the organisms grow larger, the delivery system fails to keep up with the growth in cells, so eventually the growth must stop.

He then turned his attention from biology to social organizations.  Could you view cities and companies as large-scale organisms, each with its own internal infrastructure connecting all its various components?  Do similar scaling laws apply?  “Is New York just actually, in some ways, a great big whale?  And is Microsoft a great big elephant?, he asked in a fascinating video conversation, - Why Cities Keep Growing, Corporations and People Always Die, and Life Gets Faster.  “Metaphorically we use biological terms, for example the DNA of the company or the ecology of the marketplace.  But are those just metaphors or is there some serious substance that we can quantify with those?”

West and his SFI collaborators analyzed an extensive body of data about cities around the world to explore the scaling relations between population and a wide range of attributes, including energy consumption, economic activity, demographics, infrastructure, innovation, employment, and patterns of human behavior.

They discovered that the measurable infrastructure of cities, - e.g., the lengths of roadways and electrical lines, the number of gas stations, - scale sublinearly, just like in biological organisms, but with a scaling factor of .85.  That means that if the population of a city doubles, its infrastructure needs to only increase by a factor of 1.85.  This .85 scaling factor was true for cities of any size across the world as well as for any measurable infrastructure....MORE