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March 15 - August 1, 2023
the amount of energy needed to support an average person living in the United States has risen to an astounding 11,000 watts.
the bigger you are, the more there is per capita, whereas for economies of scale, the bigger you are, the less there is per capita. This kind of scaling is referred to as sublinear scaling.
indicating a systematic economy of scale but with an exponent of about 0.85 rather than 0.75. So, for example, across the globe, fewer roads and electrical cables are needed per capita the bigger the city.
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.
relative strength systematically increases as size decreases.
broad similarity extends to almost every aspect of your physiology and life history. So much so in fact that when I talk about “we” being approximately scaled versions of one another, I will mean not just all human beings, but all mammals and, to varying degrees, all of life.
body weight should increase as the square of height, which seems to be seriously at odds with our earlier discussion of Galileo’s work where we concluded that body weight should increase much faster as the cube of height.
If this is so, then BMI, as defined, would not be an invariant quantity but would instead increase linearly with height, thereby consistently overdiagnosing taller people as overweight while underdiagnosing shorter ones. Indeed, there is evidence that tall people have uncharacteristically high values compared with their actual body fat content.
The crucial point recognized by Froude was that because the underlying physics remains the same, objects of different sizes moving at different speeds behave in the same way if their Froude numbers have the same value.
Rayleigh wrote a provocative and highly influential paper in the journal Nature titled “The Principle of Similitude.”16 This was his term for what we have been calling scaling theory.
the ratio of the circumference of a circle to its diameter. This has no units,
The extraordinary scale of life from complex molecules and microbes to whales and sequoias in relation to galactic and subatomic scales.
The energy flow hierarchy of life beginning with respiratory complexes (top left) that produce our energy up through mitochondria and cells (middle and top right) to multicellular organisms and community structures. From this perspective, cities are ultimately powered and sustained by the ATP produced in our respiratory complexes. Although each of these looks quite different with very different engineered structures, energy is distributed through each of them by space-filling hierarchical networks having similar properties.
Examples of biological networks, counterclockwise from the top left-hand corner: the circulatory system of the brain; microtubial and mitochondrial networks inside cells; the white and gray matter of the brain; a parasite that lives inside elephants; a tree; and our cardiovascular system.
principle of least action which, roughly speaking, states that, of all the possible configurations that a system can have or that it can follow as it evolves in time, the one that is physically realized is the one that minimizes its action.
self-similar fashion, decreasing by a constant factor of the square root of two (√2) with each successive branching. This so-called area-preserving branching
(Above) A schematic of the hierarchical branching pipe structure of mammals (left) and the fiber bundle structure of the vasculature of plants and trees (right); the sequential “unraveling” of fibers forms their physical branch structure. In both cases cutting across any level of branching and adding up the cross-sectional areas results in the same value throughout the network. (Left) A page from da Vinci’s notebooks showing that he understood the area-preserving branching of trees.
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.
organisms operate as if they were in four dimensions, rather than the canonical three.
Thus, by analogy with the Richter scale, the Richardson scale begins with zero for a single individual murder and ends with a magnitude of almost eight for the two world wars (eight orders of magnitude would represent a hundred million deaths). In between, a small riot with ten victims would have magnitude one, a skirmish in which one hundred combatants were killed would be two, and so on.
Measuring the lengths of coastline using different resolutions (Britain in the example). (13) The lengths increase systematically with resolution following a power law as indicated by the examples in the graph. (14) The slope gives the fractal dimension for the coastline: the more squiggly it is, the steeper the slope.
In general, it is meaningless to quote the value of a measured length without stating the scale of the resolution used to make it.
The reason that being healthy and robust equates with greater variance and larger fluctuations, and therefore a larger fractal dimension as in an EKG, is closely related to the resilience of such systems.
minimizing energy loss, natural selection has also led to a maximization of metabolic capacity because metabolism produces the energy and materials required to sustain and reproduce life.
sublinear scaling and the associated economies of scale arising from optimizing network performance lead to bounded growth and the systematic slowing of the pace of life.
Here: (23) The exponential scaling of embryonic development times with temperature for eggs of birds and aquatic ectotherms (measured in centigrade), rescaled according to the ¼ power scaling law to remove their mass dependence (see text). These “mass adjusted” times are plotted logarithmically on the vertical axis against the temperature plotted linearly on the horizontal one. On such a semilogarithmic plot exponentials appear as straight lines, as observed. (24) Similar “mass adjusted” plot showing the exponential dependence of life spans of various invertebrates on temperature. Notice that
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(25) Human survivorship curves showing the rapid shift from classic exponential decay (constant mortality rate) prior to the early nineteenth century toward an increasingly more rectangular shape as the average life span progressively increased due to major changes indicated on the graph. Regardless of this progress, maximum life span has remained at about 125 years. (26) Major causes of mortality at various ages.
Change in various organ functions with age: percentage of maximal capacity plotted against age. Notice the rapid rise during growth, reaching the maximum around age twenty, after which there is a steady linear decline. Despite this steady decline, a healthy, active life is still possible until late into old age.
The spirit and substance of the Second Law of Thermodynamics and its manifestation in terms of entropy production represent the dark side of open-ended exponential growth. Independent of how superbly innovative we are, ultimately everything is driven and processed by the use of energy, and the processing of energy has inevitable deleterious consequences.
rom 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
The arguments of those like Malthus, Paul Ehrlich, and the Club of Rome may be flawed, but their conclusions and implications may well have validity.
Greed is the pejorative image of this insatiable desire for more,
but it also has an extremely important, positive flip side. Metaphorically, it is the social analog of the evolutionary biological drive of animals, including us, to maximize their metabolic power relative to their size.
A schematic of the sequence of Dunbar’s numbers reflecting a fractal-like hierarchy in the modular structure of social interactions: note that the interaction strength decreases inversely with the size of the modular group.
Zipf’s law actually predates Zipf. Much earlier it had been discovered by the influential Italian economist Vilfredo Pareto, who expressed it as a frequency distribution of incomes in a population rather than in terms of their ranking.
effective speeding up of time is an emergent phenomenon generated by the continuous positive feedback mechanisms inherent in social networks in which social interactions beget ever more interactions, ideas stimulate yet more ideas, and wealth creates more wealth as size increases.
Thus even though some people travel faster, some by car or train, some by bus or subway, and some much slower by bicycling or walking, on average all of us spend up to an hour or so traveling to and from work.
Almost twice as many people have access to cell phones in the world as they do to toilets—an
number of visitors should scale inversely as the square of both the distance traveled and the frequency of visitation.
if the distance traveled multiplied by the frequency of visits to any specific location is kept the same, then the number of people visiting also remains the same
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.
In contrast to the inherent universal properties of cities that are manifested in the scaling laws, these rank-size distributions of business types reflect the individuality and distinctive characteristics of each specific city as exhibited by the composition of its economic activities.
preferential attachment, cumulative advantage, the rich get richer, or the Yule-Simon process. It is based on a positive feedback mechanism in which new elements of the system (business types in this case) are added with a probability proportional to the abundances of how many are already there.
often conveniently forgotten that Jesus was actually referring to knowledge of the mysteries of the kingdom of heaven and not to material wealth. He was expressing a spiritual version of the very essence of diligent study, knowledge accumulation, and research and education as expressed by the ancient rabbis: He who does not increase his knowledge decreases it.
On the supply side, metabolic rate in organisms scales sublinearly with the number of cells (following the generic ¾ power exponent derived from network constraints) while the demand increases approximately linearly.
Lewis Mumford13: The chief function of the city is to convert power into form, energy into culture, dead matter into the living symbols of art, biological reproduction into social creativity.
