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February 2 - February 21, 2019
You need to eat to stay alive and maintain and service the highly organized functionality of your mind and body. But after you’ve eaten, sooner or later you will have to go to the bathroom.
The word entropy, by the way, is the literal Greek translation of “transformation” or “evolution.”
Scaling simply refers, in its most elemental form, to how a system responds when its size changes.
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.
The second is a well-known quote from the eminent U.S. Supreme Court justice Potter Stewart, who when discussing the concept of pornography and its relationship to free speech in a landmark decision of 1964 made the following marvelous comment: I shall not today attempt further to define the kinds of material I understand to be embraced within that shorthand description [“hard-core pornography”]; and perhaps I could never succeed in intelligibly doing so. But I know it when I see it. Just substitute the word “complexity” for “hard-core pornography” and that’s pretty much what many of us would
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Unfortunately, however, while “knowing it when we see it” may be good enough for the U.S. Supreme Court, it’s not considered good enough for science.
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.
The 3⁄4 power scaling law says that, despite having 10,000 times as many cells to support, the metabolic rate of an elephant (that is, the amount of energy needed to keep it alive) is only 1,000 times (three orders of magnitude, 103) larger than a rat’s; note the ratio of 3:4 in the powers of ten.
They are all “power laws” and are typically governed by an exponent (the slope of the graph), which is a simple multiple of 1⁄4, the classic example being the 3⁄4 for metabolic rate. So, for example, if the size of a mammal is doubled, its heart rate decreases by about 25 percent. The number 4 therefore plays a fundamental and almost magically universal role in all of life.
Remarkably, analyses of such data show that, as a function of population size, city infrastructure—such as the length of roads, electrical cables, water pipes, and the number of gas stations—scales in the same way whether in the United States, China, Japan, Europe, or Latin America.
Socioeconomic quantities such as wages, wealth, patents, AIDS cases, crime, and educational institutions, which have no analog in biology and did not exist on the planet before humans invented cities ten thousand years ago, also scale with population size but with a superlinear (meaning bigger than one) exponent of approximately 1.15.
Amazingly, the answer to this is yes, as can be seen from Figure 4: like organisms and cities, companies also scale as simple power laws. Equally surprising is that they scale sublinearly as functions of their size, rather than superlinearly like socioeconomic metrics in cities. In this sense, 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.
Cities, on the other hand, become increasingly multidimensional as they grow in size. Indeed, in stark contrast to almost all companies, the diversity of cities, as measured by the number of different kinds of jobs and businesses that comprise their economic landscape, continually and systematically increases in a predictable way with increasing city size.
Galileo is also famous for perfecting the telescope and discovering the moons of Jupiter, which convinced him of the Copernican view of the solar system.
Elephants, for example, have solved this challenge by evolving disproportionately large ears to significantly increase their surface area so as to dissipate more heat.
To emphasize this point, consider increasing the height of a building or tree by a factor of 10 keeping its shape the same; then the weight needed to be supported increases a thousandfold (103) whereas the strength of the pillar or trunk holding it up increases by only a hundredfold (102
as Galileo so graphically put it: “the smaller the body the greater its relative strength. Thus a small dog could probably carry on his back two or three dogs of his own size; but I believe that a horse could not carry even one of his own size.”
In other words, from the egalitarian level playing field perspective of a physicist, the strongest man in the world in 1956 was actually the middleweight champion because he was overperforming relative to his weight. Ironically, the weakest of all of the champions from this scientific scaling perspective is the heavyweight, despite the fact that he lifted more than anyone else.
A classic example of some of the challenges and pitfalls is an early study investigating the potentially therapeutic effects of LSD on humans. Although the term “psychedelic” was already coined by 1957, the drug was almost unknown outside of a specialized psychiatric community in 1962,
West and his collaborators speculated that this bizarre and often destructive behavior, known as musth, was triggered by the autoproduction of LSD in elephants’ brains. So the idea was to see if LSD would induce this curious condition and, if so, thereby gain insight into LSD’s effects on humans from studying how they react. Pretty weird, but maybe not entirely unreasonable.
Tusko weighed about 3,000 kilograms, so using the number known to be safe for cats, they estimated that a safe and appropriate dose for Tusko would be about 0.1 milligram per kilogram multiplied by 3,000 kilograms, which comes out to 300 milligrams of LSD. The amount they actually injected was 297 milligrams.
The results on Tusko were dramatic and catastrophic. To quote directly from their paper: “Five minutes after the injection he [the elephant] trumpeted, collapsed, fell heavily onto his right side, defecated, and went into status epilepticus.” Poor old Tusko died an hour and forty minutes later.
A simple calculation using the 2⁄3 scaling rule for areas as a function of weight shows that a more appropriate dose for elephants should be closer to a few milligrams of LSD rather than the several hundred that were actually administered. Had this been done, Tusko would no doubt have lived and a vastly different conclusion about the effects of LSD would have been drawn.
Lest you think this was some fringe piece of research, the paper on elephants and LSD was published in one of the world’s most highly regarded and prestigious journals, namely Science.
Until the 1970s and the rise of its popularity, the BMI was actually known as the Quetelet index.
He found, though sometimes he merely assumed, that these variances mostly followed a so-called normal, or Gaussian, distribution, popularly known as the bell curve.
As they characterize it: “Social Physics is a new way of understanding human behavior based on analysis of Big Data.”8 While this body of research is very interesting, it is probably safe to say that few physicists would recognize it as “physics,” primarily because it does not focus on underlying principles, general laws, mathematical analyses, and mechanistic explanations.
The BMI is therefore presumed to be approximately invariant across idealized healthy individuals, meaning that it has roughly the same value regardless of body weight and height. However, this implies that 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.
Unlike the cubic scaling law, the conventional definition of the BMI has no theoretical or conceptual underpinning and is therefore of dubious statistical significance.
Remarkably, arched stone bridges go back more than three thousand years to the Greek Bronze Age (thirteenth century BC), with some still in use today.
In 2002 the BBC conducted a nationwide poll to select the “100 Greatest Britons.” Perhaps predictably, Winston Churchill came in first with Princess Diana third (she had only been dead for five years at that time), followed by Charles Darwin, William Shakespeare, and Isaac Newton, a pretty impressive triumvirate. But who was second? None other than the remarkable Isambard Kingdom Brunel!
Thames Tunnel at Rotherhithe in East London. It was a pedestrian tunnel that became a major tourist attraction with almost two million visitors a year paying a penny apiece to traverse it. Like many such underground walkways it sadly became the haunt of the homeless, muggers, and prostitutes and in 1869 was eventually transformed into a railway tunnel, becoming part of the London Underground system still in use to this day.
Brunel subsequently became the chief engineer and designer for what was considered the finest railway of its time, the Great Western Railway, running from London to Bristol and beyond.
Brunel formulated a grand vision of a seamless transition between the Great Western Railway and his newly formed Great Western Steamship Company so that a passenger could buy a ticket at Paddington Station in London and get off in New York City, powered the entire way by steam.
The Great Eastern ended up as a floating music hall and advertising billboard in Liverpool before being broken up in 1889. Such was the sad ending to a glorious vision. A bizarre footnote to this tale that is probably of interest only to ardent soccer fans is that in 1891 when the famous British football club Liverpool was being founded, they searched for a flagpole for their new stadium and purchased the top mast of the Great Eastern for that purpose. It still proudly stands there today.
Small errors resulting from simple extrapolation from what had worked before to the new situation usually had a relatively small impact.
Unfortunately, the shipwrights did not have the scientific knowledge to know how to correctly scale up a ship by such a large amount. In fact, they didn’t have the scientific knowledge to know how to correctly scale up a ship by a small amount either, but this hardly mattered. Consequently, the ship ended up being too narrow and too top-heavy so that even a light breeze was sufficient to capsize her
The field of hydrodynamics was first formalized independently by the French engineer Claude-Louis Navier and the great Irish mathematical physicist George Stokes.
Although the Navier-Stokes equation describes fluid motion under essentially any conditions it is extremely difficult, and in almost all cases impossible, to solve exactly because it is inherently nonlinear.
He realized that the primary quantity that determined the character of their relative motion was something that later became known as the Froude number. It is defined as the square of the ship’s velocity divided by its length multiplied by the acceleration due to gravity.
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.
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.
Not quite so obvious is how it enters into the motion of ships, because the buoyancy of water balances gravity (remember Archimedes’ principle).
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.
Even the most arrogant hard-nosed physicist had a hard time disagreeing with the sentiment that biology would very likely eclipse physics as the dominant science of the twenty-first century.
There have, of course, been several physicists who made extremely successful forays into biology, the most spectacular of which was probably Francis Crick, who with James Watson determined the structure of DNA, which revolutionized our understanding of the genome.
Another is the great physicist Erwin Schrödinger, one of the founders of quantum mechanics, whose marvelous little book titled What Is Life?, published in 1944, had a huge influence on biology.
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.
Because the range of animals in Figure 1 spans well over five orders of magnitude (a factor of more than 100,000), from a little mouse weighing only 20 grams (0.02 kg) to a huge elephant weighing almost 10,000 kilograms, we are forced to plot the data logarithmically, meaning that the scales on both axes increase by successive factors of ten.
Causality not right we use log becausr of nature of relatonship
