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October 14, 2019 - January 27, 2020
So why do almost all cities remain viable, whereas the vast majority of companies and organisms die?
metabolic rate, which is the amount of energy needed per second to keep an organism alive; for
Second Law of Thermodynamics, which says that whenever energy is transformed into a useful form, it also produces “useless” energy as a degraded by-product: “unintended consequences” in the form of inaccessible disorganized heat or unusable products are inevitable.
This fundamental, universal property resulting from how all things interact by interchanging energy and resources was called entropy by the German physicist Rudolf Clausius in 1855.
The battle to combat entropy by continually having to supply more energy for growth, innovation, maintenance, and repair, which becomes increasingly more challenging as the system ages, underlies any serious discussion of aging, mortality, resilience, and sustainability, whether for organisms, companies, or societies.
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.
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.
You are a complex system par excellence. In a similar fashion, a city is much more than the sum of its buildings, roads, and people, a company much more than the sum of its employees and products, and an ecosystem much more than the plants and animals that inhabit it. 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.
These simulations have given credence to the idea that 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. In many instances, the whole seems to take on a life of its own, almost dissociated from the specific characteristics of its individual building blocks. Furthermore,
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.
The Darwinian theory of natural selection is the scientific narrative that has been developed for understanding and describing how organisms and ecosystems continuously evolve and adapt to changing conditions. The study of complex
Parenthetically, 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.
Because networks determine the rates at which energy and resources are delivered to cells, they set the pace of all physiological processes. Because cells are constrained to operate systematically slower in larger organisms relative to smaller ones, the pace of life systematically decreases with increasing size. Thus, large mammals live longer, take longer to mature, have slower heart rates, and cells that don’t work as hard as those of small mammals, all to the same predictable degree. Small creatures live life in the fast lane while large ones move ponderously, though more efficiently,
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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. Indeed, the litany of such discoveries both large and small is testament to the extraordinary ingenuity of the collective human mind.
Unfortunately, however, there is another serious catch. Theory dictates that such discoveries must occur at an increasingly accelerating pace; the time between successive innovations must systematically and inextricably get shorter and shorter. For instance, the time between the “Computer Age” and the “Information and Digital Age” was perhaps twenty years, in contrast to the thousands of years between the Stone, Bronze, and Iron ages. If we therefore insist on continuo...
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two parts: a geometrical argument showing how areas and volumes associated with any object scale as its size increases (Figure 5) and a structural argument showing that the strength of pillars holding up buildings, limbs supporting animals, or trunks supporting trees is proportional to their cross-sectional areas (Figure 6).
That’s why builders, architects, and engineers involved in construction classify wood by its cross-sectional dimensions, and why lumber yards at Home Depot and Lowe’s display them as “two-by-twos, two-by-fours, four-by-fours,” and so on.
for every order of magnitude increase in length, areas and strengths increase by two orders of magnitude, whereas volumes and weights increase by three orders of magnitude.
The reason for this vast difference in impact despite an apparently small increase in magnitude is that the Richter scale expresses size in terms of orders of magnitude. So an increase of one unit actually means an increase of one order of magnitude, so that a 6.7 earthquake is actually 10 times the size of a 5.7
The fundamental equation, which is universally known as the Navier-Stokes equation, arises from applying Newton’s laws to the motion of fluids, and by extension to the dynamics of physical objects moving through fluids, such as ships through water or airplanes through air.
Roughly speaking, the nonlinearity arises from feedback mechanisms in which water interacts with itself.
Complex systems often manifest chaotic behavior in which a small change or perturbation in one part of the system produces an exponentially enhanced response in some other part.
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. Fifty years ago, before we had access to such high-powered computation and therefore less accuracy in predicting outcomes, and before we became so concerned about fuel performance and exhaust pollution, the diversity of car design was much more varied and consequently much more interesting. Compare a 1957 Studebaker Hawk or a 1927 Rolls-Royce to a relatively boring-looking
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This concept of “universality” is the reason why the acceleration due to gravity was included in the definition of the Froude number, even though it played no explicit role in how to scale from model ships to the real thing. It turns out that the ratio of the square of the velocity to the length is not dimensionless and so depends on the units used, whereas dividing by gravity renders it dimensionless and therefore scale invariant.
Because the essence of any measurable quantity cannot depend on an arbitrary choice of units made by human beings, neither can the laws of physics. Consequently, all of these and indeed all of the laws of science must be expressible as relationships between scale-invariant dimensionless quantities, even though conventionally they are not typically written that way.
why is the sky blue? Using an elegant argument based solely on relating purely dimensionless quantities, he shows that the intensity of light waves scattered by small particles must decrease with the fourth power of their wavelength. Thus, when sunlight, which is a combination of all of the colors of the rainbow, scatters from microscopic particles suspended in the atmosphere, the shortest wavelengths, corresponding to blue light, dominate.
The search for fundamental principles that govern how the complexity of life emerges from its underlying simplicity is one of the grand challenges of twenty-first-century science.
it is natural to ask if there are “universal laws of life” that are mathematizable so that biology could also be formulated as a predictive, quantitative science much like physics.
“high energy physics” is the name of the subfield of physics concerned with fundamental questions about the elementary particles, their interactions and cosmological implications.
A necessary component of the evolutionary process is that individuals eventually die so that their offspring can propagate new combinations of genes that eventually lead to adaptation by natural selection of new traits and new variations leading to the diversity of species. We must all die so that the new can blossom, explore, adapt, and evolve. Steve Jobs put it succinctly3: No one wants to die. Even people who want to go to heaven don’t want to die to get there. And yet death is the destination we all share. No one has ever escaped it, and that is how it should be, because death is very
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Metabolism is the fire of life . . . and food, the fuel of life. Neither the neurons in your brain nor the molecules of your genes could function without being supplied by metabolic energy extracted from the food you eat.
but here’s something truly extraordinary that you should know about yourself: 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!
The rate at which the total number of these ATPs is produced is a measure of your metabolic rate.
The classic case of Newton’s laws is a standard example. Only when it was possible to probe very small distances on the atomic scale or very large velocities on the scale of the speed of light did serious deviations from the predictions from Newton’s laws become apparent. And these led to the revolutionary discovery of quantum mechanics to describe the microscopic, and to the theory of relativity to describe ultrahigh speeds comparable to the speed of light.
concept related to the idea of a toy model is that of a “zeroth order” approximation of a theory, in which simplifying assumptions are similarly made in order to give a rough approximation of the exact result. It is usually employed in a quantitative context as, for example, in the statement that “a zeroth order estimate for the population of the Chicago metropolitan area in 2013 is 10 million people.” Upon learning a little more about Chicago, one might make what could be called a “first order” estimate of its population of 9.5 million, which is more precise and closer to the actual number
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As individuals grow from newborn to adult, or as new species of varying sizes evolve, terminal units do not get reinvented nor are they significantly reconfigured or rescaled. For example, the capillaries of all mammals, whether children, adults, mice, elephants, or whales, are essentially all the same despite the enormous range and variation of body sizes.
This maximization of offspring is an expression of what is referred to as Darwinian fitness, which is the genetic contribution of an average individual to the next generation’s gene pool.
All the laws of physics can be derived from the 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.
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.
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.
direct current (DC), beloved of Edison, in which electricity flows in a continuous fashion like a river, and alternating current (AC), in which it flows in a pulsatile wave motion much like ocean waves or the blood in your arteries.
biography of Young titled The Last Man Who Knew Everything: Thomas Young, the Anonymous Polymath Who Proved Newton Wrong, Explained How We See, Cured the Sick, and Deciphered the Rosetta Stone, Among Other Feats of Genius.
The take-home message is clear. In general, it is meaningless to quote the value of a measured length without stating the scale of the resolution used to make it.