When I look back over my long, relatively eclectic career, complex systems have been a common theme in all the activities I’ve been involved in. It started in the 1960s, when I was an undergraduate and graduate student at the University of Chicago majoring in physics, - the study of complex natural systems. The research for my thesis was focused on the highly complex world of atoms and molecules.
After finishing my studies, I joined IBM Research in 1970 and switched to computer sciences. My main research interests were centered on large computer systems, including mainframes, supercomputers and distributed systems. In the 1990s, my work was focused on the kinds of complex systems and applications made possible by the advent of the Internet, World Wide Web and e-business.
Then, around ten years ago, I became very interested in the applications of technology to market-facing, people oriented complex systems, especially systems involving services. Over the past few years, I have also become increasingly interested in economic systems.
In addition, I started to notice that a number of the concepts and principles I learned many years ago as a physics student seem to apply to these new kind of complex organizational systems I was now interested in. Let me explain.
But, once you start dealing with atoms, molecules and exotic subatomic particles, you find yourself in a whole different world, with counter-intuitive, somewhat bizarre behaviors which are governed by the laws of quantum mechanics. The orderly, deterministic world of classical physics gives way to a world of wave functions, probability distributions, uncertainty principles, and wave-particle dualities.
But, the worlds of the very small, as well as the very large, - which are governed by the rules of special and general relativity, - are not the only ones with counter-intuitive, bizarre behaviors. So is the world of highly complex systems, especially those systems whose components and interrelationships are themselves quite complex, as is the case with systems biology, evolutionary biology, as well as with organizational and sociotechnical systems whose main components are people.
In such systems, the dynamic nature of the components, as well as their intricate interrelationships renders them increasingly unpredictable and accounts for their emergent behavior. New terms, like long tails, Freakonomics and black swan theory, - every bit as fanciful as quarks, charm and strangeness, - have begun to enter our lexicon.
The study of such complex systems as a scientific discipline is relatively new. A couple of weeks ago I watched one of the most exciting and clearest explanations I have seen of what this young discipline might be all about. Why Cities Keep Growing, Corporations and People Always Die, and Life Gets Faster, is a fascinating 51 minute video based on a conversation with physicist Geoffrey West. Geoffrey West is Distinguished Professor and Past President of the Santa Fe Institute, a non-profit research institute dedicated to the study complex systems. Prior to joining the Santa Fe Institute in 2003, he was the leader and founder of the high energy physics group at Los Alamos National Lab.
Dr. West starts out his conversation by talking about his background:
“I spent most of my career doing high-energy physics, Quarks, dark matter, string theory and so on. Between ten and fifteen years ago I started to get interested in the question of whether you can take some of the powerful techniques, ideas, and paradigms developed in physics over into the biological and social sciences. And of course, some of that has obviously been done with spectacular success. But the question was, in a bigger picture, to what extent can biology and social organization (which are both quintessential complex adaptive systems) be put in a more quantitative, analytic, mathematizable, predictive framework so that we can understand them in the way that we understand "simple physical systems"?”
In the 1990s, Dr. West’s attention 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?
“The great thing about scaling is that if you observe scaling (that is, how the various characteristics of a system change when you change its size) and if you see regularity over several orders of magnitude, that typically means that there are underlying generic principles, that it is not an accident. If you see that in a system, it is opening a window onto some underlying, let's use the word, "universal principle".”
“The remarkable thing in biology that got me excited and has led to all of my present work (which has now gone beyond biology and into social organizations, cities, and companies) is that there was data, quite old and fundamental to all biological processes, about metabolism: Here is maybe the most complex physical chemical process possibly in the universe, and when you ask how it is scaled with size across mammals (as an example to keep it simple) you find that there is an extraordinary regularity.”
Dr. West was referring to Kleiber’s Law, named after biologist Max Kleiber who in the 1930s observed that for the vast majority of animals, their metabolic rate, that is, the amount of energy expended by the animal is proportional to its mass M raised to the ¾ power, that is M¾. Kleiber’s law applies to an amazing range of sizes, from bacteria to blue whales.
Because the scaling is sublinear, that is, the exponents are less than 1, it means that 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. In addition, 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. Moreover, 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.
Dr. West and his collaborators at the Santa Fe Institute 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 1930s.
Once he understood the origin of the scaling laws in biology, Dr. West started to turn his attention from biological organisms to social organizations. Could you view cities and companies as a kind of extensions of biology, 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? 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?”
Geoffrey West’s work on cities was the basis for a December, 2010 article in the New York Times Magazine, A Physicist Solves the City.
“[West] wanted to invent urban science . . . this first meant trying to gather as much urban data as possible,” writes Lehrer. “Along with [Luis Bettencourt], another theoretical physicist who had abandoned conventional physics, and a team of disparate researchers, West began scouring libraries and government Web sites for relevant statistics. . .”
“After two years of analysis, West and Bettencourt discovered that all of these urban variables could be described by a few exquisitely simple equations. For example, if they know the population of a metropolitan area in a given country, they can estimate, with approximately 85 percent accuracy, its average income and the dimensions of its sewer system. These are the laws, they say, that automatically emerge whenever people “agglomerate,” cramming themselves into apartment buildings and subway cars. It doesn’t matter if the place is Manhattan or Manhattan, Kan.: the urban patterns remain the same.”
In the aforementioned video conversation, Dr. West says:
“ . . . we found that cities scaled. . . Not only do they scale, but also there's universality to their scaling. . . . One of the first results was a very simple one - the number of gas stations as a function of city size in European cities. What was discovered was that they behaved sort of like biology. You found that they scaled beautifully, and it scaled as a power law, and the power law was less than one, indicating an economy of scale. Not surprisingly, the bigger the city, the less gas stations you need per capital. There is an economy of scale.”
“ . . . But then, we discovered two things later that were quite remarkable. First, every infrastructural quantity you looked at from total length of roadways to the length of electrical lines to the length of gas lines, all the kinds of infrastructural things that are networked throughout a city, scaled in the same way as the number of gas stations. Namely, systematically, as you increase city size, I can tell you, roughly speaking, how many gas stations there are, what is the total length of roads, electrical lines, et cetera, et cetera. And it's the same scaling in Europe, the United States, Japan and so on. It is quite similar to biology. The exponent, instead of being three quarters was more like .85. So it's a different exponent, but similar. But it's an economy of scale.”
“The truly remarkable result was when we looked at quantities that I will call “socioeconomic”. That is, quantities that have no analog in biology. These are quantities, phenomena that did not exist until about 10,000 years ago when men and women started talking to one another and working together and forming serious communities leading to what we now call cities, i.e. things like wages, the number of educational institutions, the number of patents produced, et cetera. Things that have no analog in biology, things we invented.
“And if you ask, first of all, do they scale? The answer is yes, in a regular way. Then, how do they scale? And this was the surprise to me; I'm embarrassed to say. It should have been obvious prior, but they scaled in what we called a super linear fashion. Instead of being an exponent less than one, indicating economies of scale, the exponent was bigger than one, indicating what economists call increasing returns to scale.”
“What does that say? That says that systematically, the bigger the city, the more wages you can expect, the more educational institutions in principle, more cultural events, more patents are produced, it's more innovative and so on. Remarkably, all to the same degree. There was a universal exponent which turned out to be approximately 1.15 which translated to English says something like the following: If you double the size of a city from 50,000 to a hundred thousand, a million to two million, five million to ten million, it doesn't matter what, systematically, you get a roughly 15 percent increase in productivity, patents, the number of research institutions, wages and so on, and you get systematically a 15 percent saving in length of roads and general infrastructure.”
“However, some bad and ugly come with it. And the bad and ugly are things like a systematic increase in crime and various diseases, like AIDS, flu and so on. Interestingly enough, it scales all to the same 15 percent, if you double the size. Or put slightly differently, another way of saying it is, if you have a city of a million people and you broke it down into ten cities of a hundred thousand, you would require for that ten cities of a hundred thousand, 30 to 40 percent more roads, and 30 to 40 percent general infrastructure. And you would get a systematic decrease in wages and productivity and invention. Amazing. But you'd also get a decrease in crime, pollution and disease, systematically. So there are these trade-offs.”
In summary, the infrastructure and resource requirements of cities scale sublinearly, just like in biological organisms. That means that cities give us economies of scale. They are real centers of sustainability, consuming less resources than smaller towns.
But, arguably more important, cities facilitate human interactions. They are centers of creativity and innovation. And, every measure associated with those human interactions increases superlinearly. The bigger the city, the more productive and wealthier it is by approximately 15 percent per capita. But, along with the positive consequences of human interactions, come the negatives. Crime, diseases and traffic congestion go up superlinearly by the same 15 percent per capita.
Dr. West’s findings in both biology and cities are quite preliminary, raising more questions than they answer. A number of biologists and urban experts disagree with his conclusions. We will find that some of his results are wrong, to be corrected by future researchers. In the end, his main contribution is to challenge us all to not just analyze and classify mountains of data, but to try to make sense of it all by looking for the kind of elegant hidden laws and common principles that have worked so well in physics. This is the way science always works, and hopefully will do so again as we learn how to best think about complex systems.