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481 pages, Hardcover
First published May 16, 2017
As Einstein wrote, "we followers of Spinoza see our God in the wonderful order and lawfulness of all that exists and in its soul as it reveals itself in man and animal". Regardless of one's belief system, there is something supremely grand and reassuring when one perceives even a tiny piece of the mystifyingly chaotic world around us conforming to regularities and principles that transcend its awesome complexity and seeming meaninglessness. As I argued earlier, analytic models such as the growth theory are deliberate oversimplifications of a more complex reality. Their utility depends on the extent to which they capture some fundamental essence of how nature works, the extent to which their assumptions are reasonable, their logic sound, and their simplicity or explanatory power and internal consistency in agreement with observations. (page 172)
Science at its best is the search for commonalities, regularities, principles, and universalities that transcend and underlie the structure and behavior of any particular individual constituent. [...] And it is at its very best when it can do that in a quantitative, mathematically computational, predictive framework. (page 269)
100^(3 / 4) = 31.6227766 � 32The above relationship is called Kleiber's law and can be expressed more universally as follows:
Y = bx^α,It turns out that there are many different growth coefficients and curiously, the number 4 keeps showing up in the exponent.
where Y = mass of the organ,
x = mass of the organism,
α = growth coefficient of the organ,
b = a constant.
There are probably well over fifty such scaling laws and another big surprise is their corresponding exponents the analog of the three quarters in Kleiber's law are invariably very close to simple multiples of one quarter.Geoffrey West provides an evaluation of these quantities and explains how the ratios are the result of biological evolution finding the most efficient size or quantity for these parameters, and that these scaling ratios could have been predicted on that basis.
For example, the exponent for growth rates is very close to 3/4, for lengths of aortas and genomes it's 1/4, the heights of trees 1/4, the cross-sectional areas of both aortas and tree trunks 3/4, for brain sizes 3/4, for cerebral white and gray matter 5/4, for heart rates minus 1/4, for mitochondrial densities in cells minus 1/4, for rates of evolution minus 1/4, for diffusion rates across membranes minus 1/4, for life spans 1/4 . . . and many, many more. The "minus" here simply indicates that the corresponding quantity decreases with size rather than increases, so, for instance, heart rates decrease with increasing body size following the 1/4 power law . . .
It is the mathematical interplay between the cube root scaling law for lengths and the square root scaling law for radii, constrained by the linear scaling of blood volume and the invariance of the terminal units, that leads to quarter-power allometric exponents across organisms.Geoffrey West then takes a look at cities and considers their similarity to biological life. In the case of biological life the terminal (i.e.smallest) unit is the cell. For a city the terminal unit is a person. He proceeds to show evidence that cities become more efficient at the dissemination of information and the utilization of energy in proportion to their size at ratios (a.k.a. growth coefficients) that reflect those of biological beings.
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. . . . . . . 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. More generally, it is the dimension of the space being serviced plus one.
Given the special, unique role of cities as the originators of many of our present problems and their continuing role as the superexponential driver toward potential disaster, understanding their dynamics, growth, and evolution in a scientifically predictable, quantitative framework is crucial to achieving long-term sustainability on the planet. Perhaps of even greater importance for the immediate future is to develop such a theory within the context of a grand unified theory of sustainability by bringing together the multiple studies, simulations, databases, models, theories, and speculations concerning global warming, the environment, financial markets, risk, economies, health care, social conflict, and the myriad other characteristics of man as a social being interacting with his environment.The book contains multiple graphs and charts which I found helpful. Many of the graphs in the book use logarithmic scaling which the books explains in excruciating detail.
I have met scant few economists who do not automatically dismiss traditional Malthusian-like ideas of eventual or imminent collapse as naive, simplistic, or just plain wrong. On the other hand, I have met scant few physicists or ecologists who think it's nuts to believe otherwise. The late maverick economist Kenneth Boulding perhaps best summed it up when testifying before the U.S. Congress, declaring that "anyone who believes exponential growth can go on forever in a finite world is either a madman or an economist."An interesting fact that I learned from the book:
"As such, [cities] exude an almost laissez-faire, free wheeling ambience relative to companies, taking advantage of the innovative benefits of social interactions whether good, bad or ugly. Despite their bumbling efficiencies, 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" pg 408i.e. cities are more important agents of economic change rather than corporations. This might explain the solid economic growth achieved by the Soviet Union before the 1970s. In the absence of corporations as we know them, maybe it was a consequence of moving the population into cities. This certainly correlates with the history of industrialisation in Great Britain and in the People's Republic of China. Again no mechanisms are offered, though he does admit that mechanistic research is necessary.