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1-Page Summary of Scale

Overview

Imagine a cube with sides measuring 10 cm. Now imagine another cube next to it, with sides measuring 20 cm. The volume of the second cube is greater than that of the first one, right? Wrong. It’s actually eight times greater!

In this post, I’ll discuss why our intuition about size is often wrong and how we can counter that by studying scaling laws.

The following are some of the key points in this book. You will learn why Godzilla can’t exist, steamships were considered unprofitable in the early 1800s and what scaling laws can tell us about our future on Earth.

Big Idea #1: A hidden pattern sustains all life and culture.

Earth is home to over 8 million species, from microscopic bacteria to enormous blue whales. On top of that, there are different cultures and traditions around the world. It can be overwhelming to think about all this diversity. However, if you look at a graph of animal metabolic rates against their body mass (the amount of energy they spend per unit time), you’ll see a perfectly straight line across many species.

The metabolic rate of an animal is fixed relative to its body mass. If you substitute the total number of heartbeats in an animal’s life for the metabolic rate, then you’ll get another straight line.

However, there is one trick. The scales need to be logarithmic, which means that the units on each axis increase by factors of ten (1-10-100)

In economics, if you plot out the number of patents registered in a city against that city’s population, you’ll find that the number of patents will increase 15 percent faster than the population.

Are these coincidences or are they scaling relationships? These phenomena can be explained with the concept of scaling. For example, new drugs are tested on mice to see how they will impact humans. However, mice and humans differ in size – so how can scientists draw conclusions about humans from tests on rodents? Well, that’s where scaling comes into play. In this article you’ll learn about other ways that scaling explains organisms, cities and even companies.

Big Idea #2: Scaling laws are rarely linear, and this has important implications.

When you watch a movie like “Godzilla,” it’s easy to think that such creatures could exist in real life. But most people would say that’s just science fiction, and Galileo already knew why. Scaling laws don’t work linearly (for example, if you scale up the size of one square foot by three times, the area will increase by nine).

Similarly, if you double the length of each side of a cube, it will have eight times as much volume.

In other words, length and area are not proportional to each other.

The size of Godzilla is 60 times bigger than a human. His volume would be 60³, and the average person’s weight is 1⁄60 th of that. However, his bones are only 3,600 times stronger than the average human. Therefore, he would be 216,000 times heavier than his bones could handle before they break.

So, nonlinearity can explain why Godzilla isn’t real. However, it also has practical implications. For example, at the start of the 1800s, steamships weren’t economically viable because they required too much space for fuel storage.

However, there is one thing that doesn’t scale with size: drag forces. So the bigger the ship, the less fuel it needs to carry each ton of cargo.

Big Idea #3: Biological scaling laws can be explained by a network-based theory.

By now, we know that the metabolic rate of animals scales with their body mass. We can also say that an increase in body mass by four orders of magnitude results in a tenfold increase in metabolic rate. What we haven’t explained is how such relationships are virtually identical for all life forms. The author has a theory about this. He believes that networks can explain biological scaling laws, which means they have three generic properties: space filling, where the tentacles reach every part of the system; redundancy (the ability to withstand damage); and modularity (components within modules work together). These network characteristics could even explain why biological diversity is so similar despite different species having very different traits.