Scale summary

Crowds go wild for mega monsters in movies like Godzilla. But could such beasts actually exist in real life?

Most people would tell you such an idea is pure science fiction and, in the seventeenth century, the Italian physicist and mathematician Galileo Galelei already knew they were right. After all, scaling laws rarely work in a linear fashion.

By now, we know how the relationship between the metabolic rate and body mass of nearly all animals abides by a simple scaling law.

However, we can be even more precise. We can also say that an increase of body mass by the factor 10⁴, or by four orders of magnitude, will result in an increase of the metabolic rate by a factor of 10³, or three orders of magnitude.

If you look closely at the mathematical details behind scaling laws, there’s yet another surprise to be discovered: in most cases, biological scaling factors involve the numbers ¼ or ¾.

For instance, the number of leaves taken as a function of a plant’s mass increases by a factor of 2 to the power of ¾. So, what explains the mysterious prevalence of the number four?

Consider the cities of New York, Paris and São Paulo. They might not appear to have much in common; after all, they’re in disparate corners of the world and are homes to highly divergent cultures.

Even so, there are a number of hidden similarities in these metropolises, and scaling relationships can make them plain to see.

Modern life has become so tied to the city that the author feels a new human era is upon us. In his opinion, it began with the Industrial Revolution of the late-eighteenth century and can be called the Urbanocene. So, what can scaling laws tell us about this new period in human history?

Well, in biology, the pace of life slows down as size increases. For instance, an elephant metabolizes energy much more slowly than a mouse and also lives for a much longer time. In cities, however, life appears to accelerate with size.

You just learned how the number and diversity of businesses scales relative to city size. But what about the scaling that occurs within a business itself? How do sales, expenses and profits scale with size?

Actually, there are surprisingly common scaling patterns for all of these metrics. For instance, net income, gross profit, total assets and sales all scale up with incredible regularity relative to company size as measured by the number of employees.

You’ve learned a number of rules of scale and how they correspond to all manner of circumstances. But what do these laws mean for human life in general?

Well, they can tell us a great deal about the human population. For instance, since the Industrial Revolution, the world’s population has been growing at an incredible rate. This boom has marked an unforeseen shift since, for 2 million years, the human population had been growing at a steady, albeit much slower, rate.

So, the human population exploded with the Industrial Revolution and has been increasing exponentially ever since. People have been warning about the impacts this sustained growth will have and it’s becoming increasingly clear that such growth is straining the relationship between human society and nature.

This begs the question: Can we sustain a global population of over 10 billion and continue increasing levels of consumption without destroying the biosphere?