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Scaling simply refers, in its most elemental form, to how a system responds when its size changes.
simple linear proportionality, implicit in using per capita measures, is almost never valid. GDP, like almost any other quantifiable characteristic of a city, or indeed of almost any complex system, typically scales nonlinearly. I
we urgently need a science of complex adaptive systems to address the host of extraordinarily challenging societal problems we face.
Momentum, energy, and temperature are classic examples of quantities that are precisely defined in physics but are used colloquially or metaphorically in everyday language.
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.
it’s worth pointing out that the subsequent decrease in the rates of cellular damage from metabolic processes underlies the greater longevity of elephants and provides the framework for understanding aging and mortality. The
The scaling law, however, is nonlinear and says that metabolic rates don’t double but, in fact, increase by only about 75 percent, representing a whopping 25 percent savings with every doubling of size.
if the size of a mammal is doubled, its heart rate decreases by about 25 percent.
The bigger the city, the more the average individual systematically owns, produces, and consumes, whether goods, resources, or ideas.
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.
companies are much more like organisms than cities. The scaling exponent for companies is around 0.9, to be compared with 0.85 for the infrastructure of cities and 0.75 for organisms.
Much of the work that my colleagues and I have been involved in and which will be elucidated in some detail in later chapters could be described as social physics, although it is not a term any of us uses with ease. Ironically, it has been picked up primarily by computer scientists, who are neither social scientists nor physicists, to describe their analysis of huge data sets on social interactions.
an alternative definition of the BMI has been suggested in which the BMI is defined as body weight divided by the cube of the height;
Isambard Kingdom Brunel, and why is he famous? Many consider him the greatest engineer of the nineteenth century, a
One of the curious unintended consequences of these advances is that almost all automobiles, for example, now look alike because all manufacturers are solving the same equations to optimize similar performance parameters.
the most famous dimensionless number is pi (π),
In terms of mass alone, the overall scale of life covers more than thirty orders of magnitude (1030) from the molecules that power metabolism and the genetic code up to ecosystems and cities.
My visceral reaction to the provocative statements concerning the diverging trajectories of physics and biology was that, yes, biology will almost certainly be the predominant science of the twenty-first century, but for it to become truly successful, it will need to embrace some of the quantitative, analytic, predictive culture that has made physics so successful.
death is very likely the single best invention of life. It’s life’s change agent. It clears out the old to make way for the new.
As a physicist I began to wonder to what extent biology was a “real” science (meaning, of course, that it was like physics!), and how it was going to dominate the twenty-first century if it wasn’t concerned with these sorts of fundamental questions. This apparent
Sir D’Arcy Wentworth Thompson in his classic book On Growth and Form,
Metabolism is the fire of life . . . and food, the fuel of life.
every day you typically make about 2 × 1026 ATP molecules—that’s two hundred trillion trillion molecules—corresponding to a mass of about 80 kilograms (about 175 lbs.). In other words, each day you produce and recycle the equivalent of your own body weight of ATP!
shall be using the terms “coarse-grained” and “zeroth order” interchangeably.
all employees of a company, viewed as terminal units, have to be supplied by resources (wages, for example) and information through multiple networks connecting them with the CEO and the management.
If outlet size was naively scaled isometrically with the height of buildings, then a typical electrical outlet in the Empire State Building would have to be more than fifty times larger than the ones in your house, which means it would be more than ten feet tall and three feet wide rather than just a few inches. And as in biology, basic terminal units, such as faucets and electrical outlets, are not reinvented every time we design a new building regardless of where or how big it is.
of the infinite number of possibilities for the architecture and dynamics of circulatory systems that could have evolved, and that are space filling with invariant terminal units, the ones that actually did evolve and are shared by all mammals minimize cardiac output. 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. This
All the laws of physics can be derived from the principle of least action
the variation among terminal units within a given design is a relatively small secondary effect.
Oxygen molecules bind to the iron-rich hemoglobin in blood cells, which act as the carriers of oxygen. It is this oxidation process that is responsible for our blood being red in much the same way that iron turns red when it oxidizes
After the blood has delivered its oxygen to the cells, it loses its red color and turns bluish, which is why veins, which are the vessels that return blood back to the heart and lungs, look blue.
the theory predicts that there will be no reflections at any branch point if the sum of the cross-sectional areas of the daughter tubes leaving the branch point is the same as the cross-sectional area of the parent tube coming into it.
You probably thought that this was for lubrication purposes but in fact it’s actually for matching impedances. Without the gel, the impedance mismatch in ultrasound detection would result in almost all of the energy being reflected back from the skin, leaving very little to go into the body to be reflected back from the organ or fetus under investigation.
But what’s really surprising is that blood pressures are also predicted to be the same across all mammals, regardless of their size.
natural selection has taken advantage of the mathematical marvels of fractal networks to optimize their distribution of energy so that 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.
Healthy hearts have relatively high fractal dimensions, reflecting more spiky and ragged EKGs, whereas diseased hearts have low values with relatively smooth EKGs.
Etruscan shrew, which is the smallest known mammal. It is only about 4 centimeters long, easily sitting on the palm of your hand. Its tiny heart beats at more than a thousand times a minute—about twenty times a second—as it pumps blood with the same pressure and speed as you do, and even more astounding, as does a blue whale. And
Likewise, although a blue whale is a hundred million times (108) heavier than a shrew, the average distance between its capillaries is only about (108)1/12 = 4.6 times larger.
sensitivity to temperature is exponential. The reason for this sensitivity is that all chemical reaction rates depend exponentially on temperature.
at a deep level, birth, growth, and death are all governed by the same underlying dynamics driven by metabolic rate and encapsulated in the dynamics and structure of networks.
If global warming induces a temperature increase of around 2°C, which it is on track to do, then the pace of almost all biological life across all scales will increase by a whopping 20 percent to 30 percent.
United States alone we spend more than $50 billion a year on various antiaging products, regimens, and drugs ranging
note that every country in the world now has a higher life expectancy than the highest life expectancy in any country in 1800.
half-life of publicly traded companies in the United States is only about ten years.
So in just fifty years (five half-lives) only (½)5 = 1/32 or about 3 percent are still posting sales.
hearts beat approximately one and a half billion times during an average lifetime. This invariance is approximately true for all mammals,
total amount of energy used in a lifetime to support a gram of tissue is approximately the same for all mammals and, more generally, for all animals within a specific taxonomic group.17 For mammals it’s about 300 food calories per gram per lifetime.
Although the detailed role and extent of oxidative damage in aging remains unclear, it has stimulated a mini-industry of antioxidant supplements such as vitamin E, fish oil, and red wine as some of those elixirs of life to combat aging.
I remind you that a modest 2°C decrease in body temperature can result in a 20 percent to 30 percent increase in life span.19 So if you were able to artificially lower your body temperature by just 1°C (that’s about 1.8°F) you could enhance your life span by about 10 percent to 15 percent.
the theory predicts that if you consistently decrease your food intake by 10 percent (a couple of hundred calories a day) you could live for up to 10 percent longer (up to ten years
