This review was recommended by one of the commenters on Izabella Kaminska's last posting at FT Alphaville which we linked in "UPDATED—A Map of Every City (plus Izabella Kaminska does a drive-by)".
And speaking of Ms Kaminska, why haven't the tech boffins at the Financial Times come up with a robo-Izzy until her return?
Finally, Professor Dyson takes a dimmer view of Complexity 'science' than many sci-guys but still writes well enough that I am not going to attribute the crotchety bits to the aches and pains of his being 94 years old. Something actually bugs him about the topic.
From the New York Review of Books, May 10, 2018 Issue:
by Geoffrey West
Penguin, 479 pp., $30.00
Geoffrey West spent most of his life as a research scientist and administrator at the Los Alamos National Laboratory, running programs concerned not with nuclear weapons but with peaceful physics. After retiring from Los Alamos, he became director of the nearby Santa Fe Institute, where he switched from physics to a broader interdisciplinary program known as complexity science. The Santa Fe Institute is leading the world in complexity science, with a mixed group of physicists, biologists, economists, political scientists, computer experts, and mathematicians working together. Their aim is to reach a deep understanding of the complexities of the natural environment and of human society, using the methods of science.
Scale is a progress report, summarizing the insights that West and his colleagues at Santa Fe have achieved. West does remarkably well as a writer, making a complicated world seem simple. He uses pictures and diagrams to explain the facts, with a leisurely text to put the facts into their proper setting, and no equations. There are many digressions, expressing personal opinions and telling stories that give a commonsense meaning to scientific conclusions. The text and the pictures could probably be understood and enjoyed by a bright ten-year-old or by a not-so-bright grandparent.
The title, Scale, needs some clarification. To explain what his book is about, West added the subtitle “The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life in Organisms, Cities, Economies, and Companies.” The title tells us that the universal laws the book lays down are scaling laws. The word “scale” is a verb meaning “vary together.” Each scaling law says that two measurable quantities vary together in a particular way.
We suppose that the variation of each quantity is expressed as a percentage rate of increase or decrease. The scaling law then says that the percentage rate for quantity A is a fixed number k times the percentage rate for quantity B. The number k is called the power of the scaling law. Since the percentage changes of A and B accumulate with compound interest, the scaling law says that A varies with the kth power of B, where now the word “power” has its usual mathematical meaning. For example, if a body is falling without air resistance, the scaling law between distance fallen and time has k=2. The distance varies with the square of time. You fall 16 feet in one second, 64 feet in two seconds, 144 feet in three seconds, and so on.
Another classic example of a scaling law is the third law of planetary motion, discovered by the astronomer Johannes Kepler in 1618. Kepler found by careful observation that the time it takes for a planet to orbit the sun scales with the three-halves power of the diameter of its orbit. That means that the square of the time is proportional to the cube of the distance. Kepler measured the periods and diameters of the orbits of the six planets known in his time, and found that they followed the scaling law precisely. Fifty-nine years later, Isaac Newton explained Kepler’s laws of planetary motion as consequences of a mathematical theory of universal gravitation. Kepler’s laws gave Newton the essential clues that led to the theoretical understanding of the physical universe.
There is a scaling law in biology as important as Kepler’s third law in astronomy. It ought to have the name of Motoo Kimura attached to it, since he was the first to understand its importance, but instead it is known as the law of genetic drift. Genetic drift is one of the two great driving forces of evolution, the other being natural selection. Darwin is rightly honored for his understanding of natural selection as a main cause of evolution, but he failed to include genetic drift in his picture because he knew nothing about genes.Genetic drift is the change in the average composition of a population due to random mutations of individual genes. Genetic drift causes species to evolve even in the absence of selection. Genetic drift and natural selection work together to drive evolution, selection being dominant when populations are large, genetic drift being dominant when populations are small.
Genetic drift is particularly important for the formation of new species, when populations may remain small for a long time. The predominance of genetic drift for small populations is due to a simple scaling law. Genetic drift scales with the inverse square root of population. This means that genetic drift is ten times faster for a population of ten thousand than for a population of a million. The scaling is the same for any kind of random mutations. If we observe any measurable quantity such as height, running speed, age at puberty, or intelligence test score, the average drift will vary with the inverse square root of population. The square root results from the statistical averaging of random events.
West is now making a huge claim: that scaling laws similar to Kepler’s law and the genetic drift law will lead us to a theoretical understanding of biology, sociology, economics, and commerce. To justify this claim he has to state the scaling laws, display the evidence that they are true, and show how they lead to understanding. He does well with the first and second tasks, not so well with the third. The greater part of the book is occupied with stating the laws and showing the evidence. Little space is left over for explaining. The Santa Fe observers know how to play the part of a modern-day Kepler, but they do not come close to being a modern-day Newton.
The history of each branch of science can be divided into three phases. The first phase is exploration, to see what nature is doing. The second phase is precise observation and measurement, to describe nature accurately. The third phase is explanation, to build theories that enable us to understand nature. Physics reached the second phase with Kepler, the third phase with Newton. Complexity science as West defines it, including economics and sociology, remained in the first phase until about the year 2000, when the era of big data began. The era started abruptly when information became cheaper to store in electronic form than to discard. Storing information can be an automatic process, while discarding it usually requires human judgment. The cost of information storage has decreased rapidly while the cost of information discard has decreased slowly. Since 2000, the world has been inundated with big data. In every science as well as in business and government, databases have been storing immense quantities of information. Information now accumulates much faster than our ability to understand it.
Complexity science at the Santa Fe Institute is driven by big data, providing abundant information about ecological and human affairs. Humans can visualize big data most easily when it is presented in the form of scaling laws—hence the main theme of West’s book. But a collection of scaling laws is not a theory. A theory of complexity would give us answers to deeper questions. Why are there ten thousand species of birds on this planet but only five thousand species of mammals? Why are there warm-blooded animals but no warm-blooded plants? Why are human societies so often engaged in deadly quarrels? What is the destiny of our species? These are questions that big data may illuminate but cannot answer. If complexity science ever moves into the third phase, some of these old questions will be answered, and new questions will arise.
West’s first chapter, “The Big Picture,” sets the stage for the detailed discussions that follow, with a section called “Energy, Metabolism, and Entropy,” explaining how one of the basic laws of physics, the second law of thermodynamics, makes life precarious and survival difficult. Entropy is disorder. The second law states that entropy inexorably increases in any closed system. West comments, “Like death, taxes, and the Sword of Damocles, the Second Law of Thermodynamics hangs over all of us and everything around us…. Entropy kills.” His big picture is seriously one-sided. He does not mention the other side of the picture, the paradox of order and disorder—the fact that, in the real worlds of astronomy and biology, ordered structures emerge spontaneously from disorder. The solar system, in which planets move in an orderly fashion around the sun, emerged from a disordered cloud of gas and dust. The fearful symmetry of the tiger and the beauty of the peacock emerge from a dead and disordered planet.
The astronomer Fang Lizhi published with his wife, Li Shuxian, a popular book, Creation of the Universe (1989), which includes the best explanation that I have seen of the paradox of order and disorder.1 The explanation lies in the peculiar behavior of gravity in the physical world. On the balance sheet of energy accounting, gravitational energy is a deficit. When you are close to a massive object, your gravitational energy is minus the amount of energy it would take to get away from the mass all the way to infinity. When you walk up a hill on the earth, your gravitational energy is becoming less negative, but never gets up to zero. Any object whose motions are dominated by gravity will have energy decreasing as temperature increases and energy increasing as temperature decreases.As a consequence of the second law of thermodynamics, when energy flows from one such object to another, the hot object will grow hotter and the cold object will grow colder. That is why the sun grew hotter and the planets grew cooler as the solar system evolved. In every situation where gravity is dominant, the second law causes local contrasts to increase together with entropy. This is true for astronomical objects like the sun, and also for large terrestrial objects such as thunderstorms and hurricanes. The diversity of astronomical and terrestrial objects, including living creatures, tends to increase with time, in spite of the second law. The evolution of natural ecologies and of human societies is a part of this pattern. West is evidently unaware of Fang and Li’s insight.
The factual substance of West’s book is contained in eighty-one numerical diagrams, displaying a large number of scaling laws obeyed by various observed quantities. The first diagram, concerning the metabolic rate of animals, shows twenty-eight dots, each labeled with the name of a warm-blooded animal species, beginning with mouse and ending with elephant. The dots are displayed on a square graph, the horizontal position of the dot showing the average body mass of the species and the vertical position showing its average rate of consumption of energy. The diagram shows the twenty-eight points lying with amazing accuracy on a single straight line. The slope of the line on the page demonstrates the scaling law relating energy consumption to mass. Energy consumption scales with the three-quarters power of mass. The fourth power of energy consumption scales with the cube of mass. This scaling law holds accurately for mammals and birds. Cold-blooded animals such as fish and reptiles are excluded because they have no fixed body temperature. Their consumption of energy varies with their temperature, and their temperature varies with the weather.
Similar diagrams display similar scaling laws obeyed by other quantities. These laws are generally most accurate for anatomy and physiology of animals, less accurate for social institutions such as cities and companies. Figure 10 shows heart rates of mammals scaling inversely with the one-quarter power of mass. Figure 35 shows the number of patents awarded in the United States scaling with the 1.15 power of the size of the population. Figure 36 shows the number of crimes reported in cities in Japan scaling with the 1.2 power of population. Figure 75 shows that commercial companies in the United States have a constant death rate independent of age—the life expectancy of a company at any age is about ten years. The short lifetime of companies is an essential feature of capitalist economics, with good and bad consequences. The good effect is to get rid of failed enterprises, which in socialist economies are difficult to kill and continue to eat up resources. The bad effect is to remove incentives for foresight and long-range planning.
The closest that West comes to a theory of complexity is his discussion of fractals. A fractal is a structure with big and small branches that look similar at all sizes, like a tree or the blood-vessels of a mammal. When you magnify a picture of a small piece of it, the result looks like the whole thing. The mathematician Benoit Mandelbrot began the study of fractals in the 1960s and called attention to the ubiquity of fractals in nature. Since fractal structure is independent of scale, it leads naturally to scaling laws. West discusses in detail the example of the mammalian blood-vessel system, whose fractal branching evolved to optimize the distribution of nutrients through one-dimensional vessels in three-dimensional tissues. Optimal branching results in the observed scaling law, the total blood flow scaling with the three-quarters power of the mass. Most of the scaling laws in biology can be understood in a similar way as resulting from the fractal structure of tissues....MUCH MORE