# Scale | Geoffrey West

Summary of: Scale: The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life in Organisms, Cities, Economies, and Companies

By: Geoffrey West

## Introduction

Welcome to the magical world of scaling – the fascinating patterns and phenomena that govern our complex world. In ‘Scale: The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life in Organisms, Cities, Economies, and Companies’, Geoffrey West takes you on an intriguing journey of the rules that underpin biological and socioeconomic life. From understanding the intriguing straight lines formed by plotting metabolic rates of animals to the unseen connections among New York, Paris, and São Paulo, you’ll discover scaling relationships and their implications on human existence. Navigate through this summary filled with mind-blowing information on how biological and human networks function, along with the insights into the future of our world.

## The Incredible Patterns of Life

Earth is home to numerous species and diverse cultures, which can be overwhelming to comprehend. However, behind the complexities of biological and socioeconomic life are surprising systematic patterns. Scaling relationships play a significant role and lead to incredible correlations that are not mere coincidences. For instance, there is a perfect relationship between the metabolic rate of animals and their body mass. Likewise, the total number of heartbeats in an animal’s life is also related to body mass, producing a straight line. In economics, the number of patents registered in a city scales 15 percent faster than the city’s population. Understanding this phenomenon can help to illuminate much about the world. Scientists study mice to model the way new drugs will affect the human body, which seems impossible since mice are much smaller than humans. But scaling can explain the answer. The article explores other incredible examples of scaling relationships that explain organisms, cities, and even companies in the subsequent parts.

## Scaling Laws and the Lack of Real-Life Godzilla

Learn how scaling laws explain that a creature like Godzilla cannot exist in real life and the practical implications of nonlinearity.

Godzilla might be a thrilling character in movies, but in real-life, he would not survive due to the nonlinearity of scaling laws. Though scaling laws do not work linearly, most people might dismiss the idea of nonlinearity and find the characteristics of such a giant monster purely hypothetical. In the seventeenth century, Italian physicist and mathematician, Galileo Galelei, had already demonstrated how scaling laws do not follow a linear pattern. When scaling up each side of a square foot to three feet, the area becomes nine square feet instead of three. Similarly, the volume of a three-foot cube becomes 27 cubic feet, meaning that if the cube’s sides are tripled, the volume will increase 27 times. However, length and strength only increase by the factor of nine and three times, respectively. Therefore, if Godzilla existed, it would be 60 times heavier than his bones could bear, and his bones would break instantly.

The nonlinearity of scaling laws not only explains the practical implications of Godzilla’s defeat but also extends to other sectors, such as transportation. In the 1800s, trans-Atlantic steamships were dismissed as commercially untenable due to the enormous space required for fuel. However, English engineer Isambard Kingdom Brunel demonstrated that according to the nonlinearity of scaling laws, the drag forces exerted on a ship only increase proportionally to the size of the hull, which scales by the square of the ship’s dimensions. Thus, the larger the steamship, the lesser fuel it needs to transport each ton of cargo. Therefore, nonlinearity explains why Godzilla is a hypothetical creature. Still, it can also have practical implications, like cost-saving in transportation.

## The Generality of Biological Scaling Laws

According to the author, the relationship between the metabolic rate and body mass of animals is predictable and follows a scaling law. For example, when body mass increases by a factor of 10⁴, the metabolic rate increases by a factor of 10³. The author proposes that biological scaling laws can be explained through a network-based theory. Biological systems function through networks, which transport energy, matter, or information, and these networks have three generic properties: they are space-filling, terminal units are invariant, and over time they become optimized to perform better. These general systemic properties explain the hidden regularities of biological diversity and translate into mathematical language. The author believes that these properties can provide a framework to explain the regularities observed in the world.

## The Fascinating Role of the Number Four in Biological Scaling Laws

Biological networks resemble fractals, making it necessary to extend towards the fourth dimension, which explains the prevalent use of the numbers ¼ or ¾ in scaling laws. Scaling laws dictate that the metabolic rate of an organism rises by a factor of 2 to the power of ¾, less than 2. Therefore, the demand for energy increases faster than energy can be produced, halting the growth in its tracks. The book discusses more interesting examples of scaling laws from social and economic spheres.

## The Scaling Relationship between Cities

The size of a city affects various aspects of life within a metropolis, and there is an underlying scaling law that applies to many of these traits. The growth of gas stations, pipes, roads, and electrical wires only increases by 85% if the size of a city is doubled. Furthermore, the 15-percent rule indicates that a larger city corresponds to higher wages, per capita GDP, crime rates, cases of AIDS or flu infections, number of restaurants, and patent applications. This implies that if a city with 10,000 residents and 100 restaurants doubled in population, it would have 1,150 restaurants. However, these scaling laws are only applicable to cities within the same country due to differences in affluence. Cities can also be compared to biological organisms as they function similarly and possess networked systems. Examples of such systems include the utilization of energy and resources and the production of waste and information. Moreover, urban transport networks correspond to space-filling properties as they must serve the city’s residences.