> [!summary] Progressive Summary # Structured Notes ## Definitions allometric scaling law - coin terms by Julian Huxley to describe the general situation where shapes and morphology change as body size increases and different dimensions scale differently effective metabolic rate - the amount of energy we consume through our machines, infrastructure, technology, etc homeotherms - animals whose body temperature remains constant isometric scaling - body shape and geometry do not change (eg in the famous proof by Galileo) logarithmic - quantities that increase by the product of their base orders of magnitude - successive powers of 10; eg $10^6$ is six orders of magnitude superlinear scaling (increasing returns to scale) - a nonlinear behaviour in which an attribute (eg per capita GDP) increases at a faster rate than size sublinear scaling (economies of scale)- a nonlinear behaviour in which an attribute (eg energy required) grows at a slower rate than size toy model – a physicist's first step in understanding a system, by abstracting its essential components as represented by a small number of variables; a classic example is the 19th-century model of a gas as made up of molecules that are like hard billiard balls, helping to explain variables such as temperature pressure, etc (the kinetic theory of gases proposed independently by Maxwell and Boltzmann) zeroth order – a rough approximation of a given quantity that can be improved over time with first, second, third, etc orders, each subsequent order offering a finer resolution ## Chapter Summaries ### Chapter 1 - The Big Picture An interesting question that is asked in this chapter is why are cities so resilient, when no human being has lived more than 125 years, and most companies disappear after 10 years. Even cities like Hiroshima and Nagasaki, which had atomic bombs dropped on them, are thriving today. It was only when computers became powerful enough to model complex systems that we saw how complex behaviour could emerge from agents following simple rules. That's when we started thinking that it was possible to develop a quantitative science of complexity. Kleiber's law - Metabolic rate scales as a power law whose exponent is very close to the number 3/4 - based on his work in the 1930s - it was previously assumed that the scaling exponent was 2/3, because it was thought that heat was generated by the mass of the body, but dissipated through the surface area The number 4 has a universal role in scaling laws. Most biological scaling laws are "power laws"(ie can be plotted logarithmically) and use an exponent which is a multiple of 1/4. This suggests that all complex, self-sustaining structures (such as organisms, ecosystems, cities or corporations) grow fractally through a branching network that is constrained by feedback mechanisms that optimise for efficient energy use. All mammals are approximately (80-90 percent) scaled versions of a single idealized mammal. A whale is an approximation of a scaled-up elephant, an elephant is a scaled-up dog, a dog is a scaled-up mouse, etc. Same can be said for cities. Components of cities, such as roads and plumbing, display sublinear scaling of 0.85. This holds true regardless of geographic or cultural location. Socioeconomic quantities such as AIDS, crime and education, show superlinear scaling of 1.15. Ie costs and benefits of cities balance each other out at 15% relative to growth of a city. Whereas organisms slow down when they get bigger, cities speed up when they get bigger. Organisms are characterised by bounded growth, and cities by unbounded growth. Because resources and energy are needed for growth, the unboundedness of city growth cannot be sustained without infinite resources, or a paradigm shift that "resets" the clock. Historically, we have achieved paradigm shifts through discoveries of iron, steam, coal, computation, AI, etc. However, every time we shift paradigms, the pace of innovation that is required for the next paradigm shift gets quicker. The time elapsed between the Computer Age and the Information Age is about 20 years, compared to the thousands of years between the Stone, Bronze and Iron ages. We are approaching a "finite time singularity". > It's as if we are on a succession of accelerating treadmills and have to jump from one to another at an ever-increasing rate. > [!Comment] Makes me think of the Michael Meade quote: "You think you need more time. You actually need more experiences of the timeless." And I'm thinking of the time flowers in Momo. They are the opposite of the treadmill. Companies, like organisms and cities, are also scaled versions of each other. Like organisms, they scale sublinearly. Their scaling exponent is around 0.9. ### Chapter 2 - The Measure of All Things Scale of life covers more than thirty orders of magnitude ($10^{30}$), from single cells up to ecosystems and cities. This is more than the size of the Earth relative to the Milky Way galaxy, which only covers 18 orders of magnitude. Over this scale, life uses the same building blocks and processes to build a variety of forms, functions and dynamic behaviours. > All of life functions by transforming energy from physical or chemical sources into organic molecules that are metabolized to build, maintain and reproduce complex, highly organized systems. Galileo was one of the first scientists to make an argument about scale. He reasoned that the strength of any structure increases more slowly than its weight. The strength of any structure is its cross-sectional area, whereas its weight is determined by its volume. And volumes increase faster than areas. Relative strength increases when size decreases, so ants are stronger relative to their size than dogs, and dogs stronger relative to their size than humans. In 1956, chemist H.M. Lietzke came up with a simple confirmation of Galileo's prediction by comparing strengths of different weightlifters: - [Lietzke 1956-09-14 - Relation between Weight-Lifting Totals and Body Weight](zotero://select/items/1_6DAZ3FZZ) In more technical language, for every order of magnitude increase in length, areas (and therefore strengths) increase by 2 orders of magnitude, and volume (and therefore weights) increase by 3 orders of magnitude. For every order of magnitude increase in area, volumes increase by 3/2. Earthquakes are measured in orders of magnitude. So an earthquake that is 6 on the Richter scale is 10 times stronger than one that is 5. Logarithmic scales are used so that we can represent a massive range of phenomenon on a single sheet of paper. Quantities that are invariant to scale are blood pressure and body temperature. ### Chapter 3 - The Simplicity, Unity and Complexity of Life All life involves the interaction of 2 types of system: information processing (eg genetics), and processing of energy and resources (eg metabolic system). > The field of physics is concerned with fundamental principles and concepts at all levels of organization that are quantifiable and mathematizable (meaning amenable to computation), and can consequently lead to precise predictions that can be tested by experiment and observation. > Metabolism is *the fire of life* ... and food, *the fuel of life*. > Metabolic rate is *the* fundamental rate of biology, setting the pace of life for almost everything an organism does, from the biochemical reactions within its cells to the time it takes to reach maturity, and from the rate of uptake of carbon dioxide in a forest to the rate at which its litter breaks down. > To varying degrees, fractality, scale invariance, and self-similarity are ubiquitous across nature from galaxies and clouds to your cells, your brain, the Internet, companies, and cities. There are about 50 scaling laws that we know of, covering quantities such as growth rates ($3/4$), genome lengths ($1/4$), lengths of aortas ($1/4$), tree heights ($1/4$), cross-sectional areas of *both* aortas *and* tree trunks ($3/4$), the amount of cerebral white and gray matter in the brain ($5/4$), evolutionary rates (minus $1/4$), and life spans ($1/4$). Their exponents are close to multiples of $1/4$. > If you tell me the size of a mammal, I can use the scaling laws to tell you almost everything about the average values of its measurable characteristics: how much food it needs to eat each day, what its heart rate is, how long it will take to mature, the length and radius of its aorta, its life span, how many offspring it will have, and so on. Scaling laws were known to biologists such as Julian Huxley, J.B.S. Haldane and [[D'Arcy Thompson]]. Julian Huxley was the grandson of the biologist Thomas Huxley (famous for championing Charles Darwin), and the brother of Aldous Huxley. He replaced the term *race* with *ethnic group*. He also coined the term *allometric*. In the 1980s, several books were written covering all the research on allometry. There were unanimous findings on quarter-power scaling across all of biology. But there were no ideas on where they came from, or the connection with Darwinian natural selection. Our bodies contain about a hundred trillion cells ($10^{14}$). All these cells, their mitochondria, and the respiratory complexes on the mitochondria form an "interconnected multilevel dynamic structure" that "has to be sufficiently robust and resilient to continue functioning for up to one hundred years!" > This hugely multifaceted, multidimensional process that constitutes life is manifested and replicated in myriad forms across an enormous scale ranging over more than twenty orders of magntitude in mass. A huge number of dynamical agents span and interconnect the vast hierarchy ranging from respiratory complexes and mitochondria to cells and multicellular organisms and up to community structures. The fact that this has persisted and remained so robust, resilient, and sustainable for more than a billion years suggests that *effective laws that govern their behavior must have emerged at all scales.* > All of these organisms ranging from the smallest, simplest bacterium to the largest plants and animals depend for their maintenance and reproduction on the close integration of numerous subunits – molecules, organelles, and cells – and these microscopic components need to be serviced in a relatively "democratic" and efficient fashion in order to supply metabolic substrates, remove waste products, and regulate activity. > > Natural selection has solved this challenge in perhaps the simplest possible way by evolving hierarchical branching *networks* that distribute energy and materials between macroscopic reservoirs and microscopic sites. The main principles of this branching network are: 1. Space Filling - the network must service all local biologically active subunits of the organism or subsystem (capillaries must service all cells, infrastructure must service all buildings in a city, wages must reach all employees in a company) 2. Invariance of Terminal Units - As the system grows, the terminal units do not get reinvented, reconfigured or rescaled. Capillaries of all mammals, whether children, adults, mice, elephants or whales, are all the same size, despite the differences in body size. Electical outlets remain basically the same, whether the building is a house or a skyscraper. 3. Optimization - all the laws of physics can be derived from the *principle of least action*, where an action is a quantity that is loosely related to energy. Similarly, all networks that form life tend to minimize the energy needed to pump fluid through the system. > Power law scaling is the mathematical expression of self-similarity and fractality. ### Chapter 4 - The Fourth Dimension of Life > Quarter-power scaling laws are perhaps as universal and as uniquely biological as the biochemical pathways of metabolism, the structure and function of the genetic code, and the process of natural selection. > 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. 0.65 electron volts (eV) is the average energy needed to produce an ATP molecule. A 10ºC rise in temperature causes a doubling of ATP production, ie the metabolic rate doubles. Global warming is on track to produce a 2ºC rise in temperature, which will lead to a 20 -30 percent change in growth and mortality rates. This will wreak havoc in ecosystems and agriculture. Global life expectancy was about 30 years prior to 1870, rose to 34 around 1913, and to 70 years by 2011. ### Chapter 5 - From the Anthropocene to the Urbanoscene It took 300 years from 1500 to 1800 for the population to double from 500 million to a billion. It took 120 years to double to 2 billion. And another 45 years to double to 4 billion. --- Manchester was the world's first industrial city. Its population grew from 20,000 in 1771 to 120,000 in 1831, growing 6-fold in just 60 years. Its population was over 2 million by the end of the century. --- In 1830 it took about 300 hours of labour to grow one hundred bushels of wheat. By 1890, this was down to 50 hours. Today, it is less than a few hours. --- Globally, we use about 150 trillion kilowatt-hours of energy a year. We need 2000 calories a day to stay alive. This is equivalent to about 100 wattts, the power of a lightbulb. As biological organisms, we are extremely energy efficient compared to something that is man-made. A dishwasher requires more than 10 times more energy per second than we do to wash dishes. A car takes 1000 times more energy than we do to move around. The average human uses 30 times more energy than its body requires. Around 10,000 years ago, with the agricultural revolution, our effective metabolic rate started climbing from a few hundred watts (where it stayed for hundreds of thousands of years) to more than 3000 watts today. In the US, this is about 11,000 watts, more than 100 times the natural biological value. This is equivalent to the metabolic rate of a blue whale, which is 1000 times larger in mass than we are. The average human uses more than 30 times more energy than it biologically requires. It is as if we are living with a population 30 times larger, in excess of 200 billion people. If our population rises to 10 billion, and each person lived the lifestyle of an American, the effective population would exceed one trillion. 30 percent of our annual energy consumption goes to waste. Only 20 percent of the gasoline in a car actually goes to moving it. --- The truly revolutionary nature of the Industrial Revolution is that we went from an open energy system (where energy is supplied by the sun) to a closed energy system (where energy is supplied by fossil fuels). In a closed system, the 2nd Law of Thermodynamics, which says that entropy always increases, strictly applies. We progressed from an energy source that was external, reliable and constant, to one that is internal, unreliable and variable. Compared to the energy we get from the sun, our annual global needs are only about 0.015 percent of that. More energy is provided by the sun in a single hour than we use in a year. --- Weather and other life processes are exponentially sensitive to changes in temperature. A 2 degrees rise in temperature leads to a 20 percent change in these effects. --- In 1897, American engineer Frank Shuman built a proof of principle device for harnessing energy from the sun by showing that it could power a small steam engine. He patented it in 1912. In 1913, he constructed the world's first solar thermal energy power plant which was built in Egypt. It generated about 50 kilowatts (65 horsepower) and pumped more than 5000 gallons of water a minute (22,000 litres per minute) from the Nile onto adjacent cotton fields. He wrote in the New York Times in 1916: > We have proved the commercial profit of sun power . . . and have more particularly proved that after our stores of oil and coal are exhausted the human race can receive unlimited power from the rays of the sun. The discovery of cheap oil in the 1930s discouraged the advancement of solar energy. It was not to be picked up again until the energy crises of the 1970s. ### Chapter 6 - Prelude to a Science of Cities > cities are emergent complex adaptive social network systems resulting from the continuous interactions among their inhabitants, enhanced and facilitated by the feedback mechanisms provided by urban life. # Other References Good history of the research into scaling laws: - https://www.scientificamerican.com/article/lifes-added-dimensions/ # Quotes