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the average number of heartbeats in the lifetime of any mammal is roughly the same, even though small ones like mice live for just a few years whereas big ones like whales can live for a hundred years or more.
scaling relationships that quantitatively describe how almost any measurable characteristic of animals, plants, ecosystems, cities, and companies scales with size.
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.”
the remarkably similar ways in which cities, companies, tumors, and our bodies work, and how each of them represents a variation on a general theme manifesting surprisingly systematic regularities and similarities in their organization, structure, and dynamics.
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.
The future of humanity and the long-term sustainability of the planet are inextricably linked to the fate of our cities. Cities are the crucible of civilization, the hubs of innovation, the engines of wealth creation and centers of power, the magnets that attract creative individuals, and the stimulant for ideas, growth, and innovation. But they also have a dark side: they are the prime locus of crime, pollution, poverty, disease, and the consumption of energy and resources.
The open-ended exponential growth of cities stands in marked contrast to what we see in biology: most organisms, like us, grow rapidly when young but then slow down, cease growing, and eventually die. Most companies follow a similar pattern, with almost all of them eventually disappearing, whereas most cities don’t.
Cities are remarkably resilient and the vast majority persist.
metabolic rate, which is the amount of energy needed per second to keep an organism alive; for us it’s about 2,000 food calories a day,
the amount of energy needed to support an average person living in the United States has risen to an astounding 11,000 watts. This social metabolic rate is equivalent to the entire needs of about a dozen elephants.
Whenever energy is used or processed in order to make or maintain order within a closed system, some degree of disorder is inevitable—entropy always increases.
Dissipative forces, analogous to the production of disorganized heat by friction, are continually and inextricably at work leading to the degradation of all systems.
To maintain order and structure in an evolving system requires the continual supply and use of energy whose by-product is disorder.
Scaling simply refers, in its most elemental form, to how a system responds when its size changes.
huge resources are spent each year on investigating cancer in mice, yet a typical mouse develops many more tumors per gram of tissue per year than we do, whereas whales get almost none, begging the question as to the relevance of such research for humans.
metropolitan Los Angeles, which is indeed ten times larger than Oklahoma City with 12 million inhabitants, has a GDP that is actually more than $700 billion, which is more than 15 percent larger than the “predicted” value obtained by the linear extrapolation implicit in using a per capita measure.
GDP, like almost any other quantifiable characteristic of a city, or indeed of almost any complex system, typically scales nonlinearly
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.
Surprisingly, an animal that is twice the size of another, and therefore composed of about twice as many cells, requires only about 75 percent more food and energy each day, rather than 100 percent more, as might naively have been expected from a linear extrapolation.
This systematic savings with increasing size is known as an economy of scale. Put succinctly, this states that the bigger you are, the less you need per capita (or, in the case of animals, per cell or per gram of tissue) to stay alive.
I think the next century will be the century of complexity.
Stephen Hawking
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.
The economic output, the buzz, the creativity and culture of a city or a company all result from the nonlinear nature of the multiple feedback mechanisms embodied in the interactions between its inhabitants, their infrastructure, and the environment.
Ant colonies are built without forethought and without the aid of any single mind or any group discussion or consultation. There is no blueprint or master plan.
This feat is accomplished by each individual ant obeying just a few simple rules mediated by chemical cues and other signals, resulting in an extraordinarily coherent collective output.
computer simulations of such processes have successfully modeled this kind of outcome in which complex behavior emerges from a continuous iteration of very simple rules operating between individual agents.
the bewildering dynamics and organization of highly complex systems have their origin in very simple rules governing the interaction between their individual constituents.
In general, then, a universal characteristic of a complex system is that the whole is greater than, and often significantly different from, the simple linear sum of its parts.
This collective outcome, in which a system manifests significantly different characteristics from those resulting from simply adding up all of the contributions of its individual constituent parts, is called an emergent behavior
in many such systems there is no central control. So, for example, in building an ant colony, no individual ant has any sense of the grand enterprise to which he is contributing.
self-organization. It is an emergent behavior in which the constituents themselves agglomerate to form the emergent whole,
another critical characteristic of many complex systems, namely their ability to adapt and evolve in response to changing external conditions. The quintessential example of such a complex adaptive system is, of course, life itself in all of its extraordinary manifestations from cells to cities
while it is not generally possible to make detailed predictions about such systems, it is sometimes possible to derive a coarse-grained quantitative description for the average salient features of the system. For example, although we will never be able to predict precisely when a particular person will die, we ought to be able to predict why the life span of human beings is on the order of one hundred years.
Scaling up from the small to the large is often accompanied by an evolution from simplicity to complexity while maintaining basic elements or building blocks of the system unchanged or conserved.
fundamental building blocks like cells, mitochondria, capillaries, and even leaves do not appreciably change with body size or increasing complexity of the class of systems in which they are embedded.
“metabolic rate scales as a power law whose exponent is very close to the number ¾.”
similar scaling laws hold for essentially all physiological quantities and life-history events, including growth rate, heart rate, evolutionary rate, genome length, mitochondrial density, gray matter in the brain, life span, the height of trees and even the number of their leaves.
They are all “power laws” and are typically governed by an exponent (the slope of the graph), which is a simple multiple of ¼, the classic example being the ¾ for metabolic rate.
The number 4 therefore plays a fundamental and almost magically universal role in all of life.
The universality and predominance of ¼ power scaling strongly suggests that natural selection has been constrained by other general physical principles that transcend specific design.
It is the generic physical, geometric, and mathematical properties of these network systems that underlie the origin of these scaling laws, including the prevalence of the one-quarter exponent.
Growth can be viewed as a special case of a scaling phenomenon. A mature organism is essentially a nonlinearly scaled-up version of the infant—just
Growth at any stage of development is accomplished by apportioning the metabolic energy being delivered through networks to existing cells to the production of new cells that build up new tissue.
The growth theory also explains a curious paradoxical phenomenon that you might have pondered, namely, why we eventually stop growing even though we continue to eat. This turns out to be a consequence of the sublinear scaling of metabolic rate and the economies of scale embodied in the network design.
Because networks determine the rates at which energy and resources are delivered to cells, they set the pace of all physiological processes.
all mammals that have ever existed including you and me are, on average, approximately scaled versions of a single idealized mammal.
Like organisms, cities are indeed approximately scaled versions of one another, despite their different histories, geographies, and cultures,
good, the bad, and the ugly are integrated in an approximately predictable package: a person may move to a bigger city drawn by more innovation, a greater sense of “action,” and higher wages, but she can also expect to confront an equivalent increase in the prevalence of crime and disease.
a finite time singularity. In a nutshell, the problem is that the theory also predicts that unbounded growth cannot be sustained without having either infinite resources or inducing major paradigm shifts that “reset” the clock before potential collapse occurs.
We have sustained open-ended growth and avoided collapse by invoking continuous cycles of paradigm-shifting innovations such as those associated on the big scale of human history with discoveries of iron, steam, coal, computation, and, most recently, digital information technology.
