Title: Scale: The Universal Laws of Life, Growth and Death in Organisms, Cities and Companies
Author: Geoffrey West
Scope: 5 stars
Readability: 3 stars
My personal rating: 4 stars
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Topic of Book
West explains how all complex objects are networks of simple objects that have evolved to work together. All these objects show a common mathematical scaling pattern. This applies to the physical world, the chemical world, the biological world and the human world.
If you would like to learn more about how complexity shaped human history, read my book From Poverty to Progress: How Humans Invented Progress, and How We Can Keep It Going.
- All large complex objects are composed of many simple objects.
- This is true for animals, plants, cities, organizations and human networks.
- Energy enables the simple to scale up into the complex. Scaling enables small objects to coalesce together to serve a specific purpose.
- All objects follow a quarter-power scaling rule internally, while producing external benefits far above that. This economy of scale means that as they grow, they become more effective at solving tasks.
Important Quotes from Book
“The examples … are just a tiny sampling of an enormous number of such scaling relationships that quantitatively describe how almost any measurable characteristic of animals, plants, ecosystems, cities, and companies scales with size. You will be seeing many more of them throughout this book. The existence of these remarkable regularities strongly suggests that there is a common conceptual framework underlying all of these very different highly complex phenomena and that the dynamics, growth, and organization of animals, plants, human social behavior, cities, and companies are, in fact, subject to similar generic “laws.”
“A common property shared by all of them is that they are highly complex and composed of enormous numbers of individual constituents, whether molecules, cells, or people, connected, interacting, and evolving via networked structures over multiple spatial and temporal scales.”
“it’s not often appreciated that without a continuous supply of energy and resources, not only can there be no manufacturing of any of these things but, perhaps more important, there can be no ideas, no innovation, no growth, and no evolution. Energy is primary. It underlies everything that we do and everything that happens around us.”
“Scaling and scalability, that is, how things change with size, and the fundamental rules and principles they obey are central themes that run throughout the book and are used as points of departure for developing almost all of the arguments presented. Viewed through this lens, cities, companies, plants, animals, our bodies, and even tumors manifest a remarkable similarity in the ways that they are organized and function. Each represents a fascinating variation on a general universal theme.”
“Scaling simply refers, in its most elemental form, to how a system responds when its size changes.”
“This reflects an essential feature of all cities, namely that social activity and economic productivity are systematically enhanced with increasing size of the population. This systematic “value-added” bonus as size increases is called increasing returns to scale by economists and social scientists, whereas physicists prefer the more sexy term superlinear scaling.”
“A typical complex system is composed of myriad individual constituents or agents that once aggregated take on collective characteristics that are usually not manifested in, nor could easily be predicted from, the properties of the individual components themselves. ”
“When humans began forming sizable communities they brought a fundamentally new dynamic to the planet. With the invention of language and the consequent exchange of information in social network space we discovered how to innovate and create wealth and ideas, ultimately manifested in superlinear scaling. In biology, network dynamics constrains the pace of life to decrease systematically with increasing size following the ¼ power scaling laws. In contrast, the dynamics of social networks underlying wealth creation and innovation leads to the opposite behavior, namely, the systematically increasing pace of life as city size increases: diseases spread faster, businesses are born and die more often, commerce is transacted more rapidly, and people even walk faster, all following the approximate 15 percent rule.”
“This way of thinking about innovation, which relates it to the drive or need to grow bigger, to expand horizons and compete in ever-larger markets with its inevitable confrontation with potential limitations imposed by physical constraints, will form the paradigm later in the book for addressing similar kinds of innovation in the larger context of biological and socioeconomic adaptive systems.”
“Metabolism is the fire of life . . . and food, the fuel of life.”
“Metabolic rate is the fundamental rate of biology, setting the pace of life for almost everything an organism does”
“Once the dust had settled, we proposed the following set of generic network properties that are presumed to have emerged as a result of the process of natural selection and which give rise to quarter-power scaling laws when translated into mathematics.”
“The idea behind the concept of space filling is simple and intuitive. Roughly speaking, it means that the tentacles of the network have to extend everywhere throughout the system that it is serving… More specifically: whatever the geometry and topology of the network is, it must service all local biologically active subunits of the organism or subsystem. ”
“the terminal units of a given network design, such as the capillaries of the circulatory system that we just discussed, all have approximately the same size and characteristics regardless of the size of the organism. Terminal units are critical elements of the network because they are points of delivery and transmission where energy and resources are exchanged.”
“The final postulate states that the continuous multiple feedback and fine-tuning mechanisms implicit in the ongoing processes of natural selection and which have been playing out over enormous periods of time have led to the network performance being “optimized…. Networks have evolved so that the energy needed to sustain an average individual’s life and perform the mundane tasks of living is minimized in order to maximize the amount of energy available for sex, reproduction, and the raising of offspring.”
“Fundamental to the conceptual framework of the theory is that, despite these completely different physical designs, both kinds of networks are constrained by the same three postulates: they are space filling, have invariant terminal units, and minimize the energy needed to pump fluid through the system.”
“The resulting magic number four emerges as an effective extension of the usual three dimensions of the volume serviced by the network by an additional dimension resulting from the fractal nature of the network.”
“organisms operate as if they were in four dimensions, rather than the canonical three. In this sense the ubiquitous number four is actually 3 + 1. More generally, it is the dimension of the space being serviced plus one.”
“Almost all of the networks that sustain life are approximately self-similar fractals.”
“Quarter-power scaling laws are perhaps as universal and as uniquely biological as the biochemical pathways of metabolism, the structure and function of the genetic code, and the process of natural selection. The vast majority of organisms exhibit scaling exponents very close to ¾ for metabolic rate and ¼ for internal times and distances. These are the maximal and minimal values, respectively, for the effective surface area and linear dimensions of a volume-filling fractal-like network.”
“In marked contrast to this, almost none of our man-made engineered artifacts and systems, whether automobiles, houses, washing machines, or television sets, invoke the power of fractals to optimize performance. To a very limited extent, electronic equipment such as computers and smart phones does, but compared with how you work they are extraordinarily primitive. On the other hand, human-engineered systems that have grown organically such as cities, and to a limited extent corporations, have unconsciously evolved self-similar fractal structures which have tended to optimize their performance.”
“The city as the engine for social change and increasing well-being is one of the truly great triumphs of our amazing ability to form social groups and collectively take advantage of economies of scale.”
“Exponential growth starts out rather slowly, even innocuously, before smoothly transitioning to what might be termed rapid growth.”
“From a scientific perspective the truly revolutionary character of the Industrial Revolution was the dramatic change from an open system where energy is supplied externally by the sun to a closed system where energy is supplied internally by fossil fuel. This is a fundamental systemic change with huge thermodynamic consequences, because in a closed system the Second Law of Thermodynamics and its requirement that entropy always increases strictly applies. We “progressed” from an external, reliable, and constant source of energy to one that is internal, unreliable, and variable.”
“So in marked contrast to infrastructure, which scales sublinearly with population size, socioeconomic quantities—the very essence of a city—scale superlinearly, thereby manifesting systematic increasing returns to scale. The larger the city, the higher the wages, the greater the GDP, the more crime, the more cases of AIDS and flu, the more restaurants, the more patents produced, and so on, all following the “15 percent rule” on a per capita basis in urban systems across the globe.”
“With the development of language, human beings acquired the capability of exchanging and communicating new kinds of information on a scale and at a rate that was unprecedented in the entire history of life. A major outcome of this revolution was the discovery of the fruits of economies of scale: by working together, we could build and accomplish more with the same amount of individual effort, or equivalently, we could complete specific tasks faster using less energy per person. Communal activities such as building, hunting, storing, and planning all evolved and benefited from the development of language and the consequential enhanced ability to communicate and think. Furthermore, we developed imagination and brought to consciousness the concept of the future and therefore the remarkable ability to plan, to think ahead and construct possible scenarios in anticipation of future challenges and events. This powerful innovation in human cerebral activity was entirely new to the planet”
“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.”
“the superlinear dynamics of social networks leads to a systematic increase in the pace of life: 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. This is the underlying scientific reason why we all sense that life is faster in a New York City than in a Santa Fe and that it has ubiquitously accelerated during our lifetimes as cities and their economies grew.”
“So the increase in transportation speed resulting from the marvelous innovations of the past couple of hundred years has not been used to reduce commuting time but instead has been used to increase commuting distances. People have taken advantage of these advancements to live farther away and simply travel longer distances to work. The conclusion is clear: 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.”
“Because walking speed is about 5 kilometers an hour, the typical extent of a “walking city” is about 5 kilometers across (about 3 miles)… There are no city walls of large, ancient cities (up to 1800), be it Rome or Persepolis, which have a diameter greater than 5km or a 2.5km radius… the size of cities could grow but, according to Marchetti, constrained by the one-hour rule.”
“the total number of contacts between people in a city over an extended period of time is plotted logarithmically versus the population size of the city. As you can see, a classic straight line is revealed for both sets of data, indicating power law scaling with the exponent in both cases having the same value very close to the predicted 1.15, in spectacular agreement with the hypothesis.”
“The size of an average individual’s modular cluster of acquaintances who interact with one another is an approximate invariant—it doesn’t change with city size… even in large cities we live in groups that are as tightly knit as those in small towns or villages. ”
“There is, however, an important qualitative difference in the nature of these modular groups in villages relative to those in large cities. In a real village we are limited to a community that is imposed on us by sheer proximity resulting from its small size, whereas in a city we are freer to choose our own “village” by taking advantage of the much greater opportunity and diversity afforded by a greater population and to seek out people whose interests, profession, ethnicity, sexual orientation, and so on are similar to our own. ”
“This critical component is captured in a different kind of metaphor such as the city as a cauldron, a crucible, a mixing bowl, or a reactor in which the churning of social interactions catalyzes social and economic activity: the people’s city, the collective city, the anthro-city.
The image of the city as a large vat in which people are being continually churned, blended, and agitated can be viscerally felt in any of the world’s great cities.”
“Perhaps the most salient feature is how relatively slowly fundamental change actually occurs. Cities that were overperforming in the 1960s, such as Bridgeport and San Jose, tend to remain rich and innovative today, whereas cities that were underperforming in the 1960s, such as Brownsville, are still near the bottom of the rankings. So even as the population has increased and the overall GDP and standard of living have risen across the entire urban system, relative individual performance hasn’t changed very much. Roughly speaking, all cities rise and fall together, or to put it bluntly: if a city was doing well in 1960 it’s likely to be doing well now, and if it was crappy then, it’s likely to be crappy still.”
“Once a city has gained an advantage, or disadvantage, relative to its scaling expectation, this tends to be preserved over decades. In this sense, either for good or for bad, cities are remarkably robust and resilient—they are hard to change and almost impossible to kill. ”
“The data reveal surprisingly simple and unexpected regularities. For instance, the total number of establishments in each city regardless of what business they conduct turns out to be linearly proportional to its population size. Double the size of a city and on average you’ll find twice as many businesses. 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. Or to put it slightly differently, on average a new workplace is created each time the population of a city increases by just 22 people, whether in a small town or a large metropolis.”
“the data also show that the total number of employees working in these establishments also scales approximately linearly with population size: on average, there are only about 8 employees for every establishment, again regardless of the size of the city.”
“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.”
“Increasing diversity is closely linked to increasing specialization, and this acts as a major driver of higher productivity following the 15 percent rule.”
“All cities exhibit the same underlying dynamics in the development of their business ecology as they grow. Initially, small cities with a limited portfolio of economic activities need to create new businesses and functionalities at a fast rate. These basic activities constitute the economic core of every city, big and small; 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.”
“at the coarsest level of the NAICS classification scheme traditional sectors such as agriculture, mining, and utilities scale sublinearly; the theory predicts that the rankings and relative abundances of these industries decrease as cities get larger. On the other hand, informational and service businesses such as professional, scientific, and technical services, and management of companies and enterprises, scale superlinearly and are consequently predicted to increase disproportionally with city size, as observed.”
“sublinear scaling and economies of scale that dominate biology lead to stable bounded growth and the slowing down of the pace of life, whereas superlinear scaling and increasing returns to scale that dominate socioeconomic activity lead to unbounded growth and to an accelerating pace of life.”
“Intriguingly, companies manifest yet another variation on this general theme by following a path that sits at the cusp between organisms and cities. Their effective metabolic rate is neither sub- nor superlinear but falls right in the middle by being linear.”
“where the overall growth of the market has been factored out, all large mature companies have stopped growing. Their growth curves when corrected for both inflation and the expansion of the market now look just like typical sigmoidal growth curves of organisms in which growth ceases at maturity,”
“After growing rapidly in their youth, almost all companies with sales over about $10 million end up floating on top of the ripples of the stock market. Of these, many operate with their metaphorical noses just above the surface. This is a precarious situation because if a big wave comes along they may well drown.”
“Taking one year as the time slice, this says that the percentage of five-year-old companies that die before they reach six years old is the same as the percentage of fifty-year-old companies that die before they reach fifty-one. In other words: the risk of a company’s dying does not depend on its age or size.”
“The fact that companies scale sublinearly, rather than superlinearly like cities, suggests that they epitomize the triumph of economies of scale over innovation and idea creation. Companies typically operate as highly constrained top-down organizations that strive to increase efficiency of production and minimize operational costs so as to maximize profits. In contrast, cities embody the triumph of innovation over the hegemony of economies of scale. Cities aren’t, of course, driven by a profit motive and have the luxury of being able to balance their books by raising taxes. They operate in a much more dis“wrong time can lead to their demise. Younger companies, which are buffered against this by an initial capital endowment, become particularly vulnerable once this initial infusion is expended if they are unable to turn a significant profit. This is sometimes referred to as the liability of adolescence.
The fact that companies scale sublinearly, rather than superlinearly like cities, suggests that they epitomize the triumph of economies of scale over innovation and idea creation. Companies typically operate as highly constrained top-down organizations that strive to increase efficiency of production and minimize operational costs so as to maximize profits. In contrast, cities embody the triumph of innovation over the hegemony of economies of scale. Cities aren’t, of course, driven by a profit motive and have the luxury of being able to balance their books by raising taxes. They operate in a much more distributed fashion, with power spread across multiple organizational structures from mayors and councils to businesses and citizen action groups. No single group has absolute control. As such, they exude an almost laissez-faire, freewheeling ambience relative to companies, taking advantage of the innovative benefits of social interactions whether good, bad, or ugly. Despite their apparent bumbling inefficiencies, cities are places of action and agents of change relative to companies, which by and large usually project an image of stasis unless they are young.
To achieve greater efficiency in the pursuit of greater market share and increased profits, companies stereotypically add more rules, regulations, protocols, and procedures at increasingly finer levels of organization, resulting in the increased bureaucratic control that is typically needed to administer, manage, and oversee their execution. This is often accomplished at the expense of innovation and R&D (research and development), which should be major components of a company’s insurance policy for its long-term future and survivability.”
“We found that the relative amount allocated to R&D systematically decreases as company size increases, suggesting that support for innovation does not keep up with bureaucratic and administrative expenses as companies expand.
The increasing accumulation of rules and constraints is often accompanied by stagnating relationships with consumers and suppliers that lead companies to become less agile and more rigid and therefore less able to respond to significant change.”
“While the dimensionality of cities is continually expanding, the dimensionality of companies typically contracts from birth through adolescence, eventually stagnating or even further contracting as they mature and move into old age.”
“The great challenge for companies is how to balance the positive feedback from market forces, which strongly encourage staying with “tried and true” products versus the long-term strategic need to develop new areas and commodities that may be risky and won’t give immediate return.
Most companies tend to be shortsighted, conservative, and not very supportive of innovative or risky ideas, happy to stay almost entirely with their major successes while the going is good because these “guarantee” short-term returns. Consequently, they tend toward becoming more and more unidimensional.”
“By the time a company realizes its condition it is often too late. Reconfiguring and reinventing become increasingly difficult and expensive. So when a large enough unanticipated fluctuation, perturbation, or shock comes along the company becomes seriously at risk and ripe for a takeover, buyout, or simply going belly-up.”
“We need a broad and more integrated scientific framework that encompasses a quantitative, predictive, mechanistic theory for understanding the relationship between human-engineered systems, both social and physical, and the “natural” environment—a framework I call a grand unified theory of sustainability. It’s time to initiate a massive international Manhattan-style project or Apollo-style program dedicated to addressing global sustainability in an integrated, systemic sense.”
“In biology, the network principles underlying economies of scale and sublinear scaling have two profound consequences. They constrain the pace of life—big animals live longer, evolve more slowly, and have slower heart rates, all to the same degree—and limit growth. In contrast, cities and economies are driven by social interactions whose feedback mechanisms lead to the opposite behavior. The pace of life systematically increases with population size: diseases spread faster, businesses are born and die more often, and people even walk faster in larger cities, all by approximately the same 15 percent rule. Moreover, the social network dynamic underlying superlinear scaling leads to open-ended growth, which is the primary assumption upon which modern cities and economies are based. Continuous adaptation, not equilibrium, is the rule.”
“theorem”: to sustain open-ended growth in light of resource limitation requires continuous cycles of paradigm-shifting innovations”
If you would like to learn more about how complexity shaped human history, read my book From Poverty to Progress: How Humans Invented Progress, and How We Can Keep It Going.