Amazing megacities law

2024 Author: Seth Attwood | [email protected]. Last modified: 2023-12-16 15:55

For the past century, a mysterious mathematical phenomenon called Zipf's Law has made it possible to accurately predict the size of giant cities around the world. The thing is that no one understands how and why this law works …

Let's go back to 1949. Linguist George Zipf (Zipf) noticed a strange tendency for people to use certain words in a language. He found that a small number of words are used consistently, and the vast majority are used very rarely. When you evaluate words by popularity, a striking thing is revealed: a first-class word is always used twice as often as a second-class word and three times as often as a third-class word.

Zipf found that the same rule applies to the distribution of people's incomes in a country: the richest person has twice as much money as the next richest person, and so on.

Later it became clear that this law also works in relation to the size of cities. The city with the largest population in any country is twice the size of the next largest city, and so on. Incredibly, Zipf's law has operated in absolutely all countries of the world over the past century.

Just take a look at the list of the largest cities in the United States. So, according to the 2010 census, the population of the largest US city, New York, is 8,175,133. Number two is Los Angeles, with a population of 3,792,621. The next three cities, Chicago, Houston and Philadelphia, boast a population of 2,695,598, 2,100,263 and 1,526,006, respectively. Obviously these numbers are inaccurate, but nevertheless they are surprisingly consistent with Zipf's Law.

Paul Krugman, who wrote on the application of Zipf's law to cities, has excellently observed that economics is often accused of creating highly simplified models of complex, chaotic reality. Zipf's Law shows that everything is exactly the opposite: we use overly complex, messy models, and reality is strikingly neat and simple.

The law of power

In 1999, the economist Xavier Gabet wrote a scholarly work in which he described Zipf's law as a "law of force."

Gabe noted that this law holds true even if cities grow in a chaotic manner. But this flat structure breaks down as soon as you move to cities outside the category of megacities. Small towns with a population of about 100,000 seem to obey a different law and show a more explicable size distribution.

One may wonder what is meant by the definition of "city"? Indeed, for example, Boston and Cambridge are considered two different cities, just like San Francisco and Oakland, separated by water. Two Swedish geographers also had this question, and they began to consider the so-called "natural" cities, united by population and road links, rather than political motives. And they found that even such "natural" cities obey Zipf's Law.

Why does Zipf's law work in cities?

So what makes cities so predictable in terms of population? Nobody can explain it for sure. We know that cities are expanding due to immigration, immigrants are flocking to big cities because there are more opportunities. But immigration is not enough to explain this law.

There are also economic motives, as big cities make big money and Zipf's Law works for income distribution as well. However, this still does not give a clear answer to the question.

Last year, a team of researchers found that Zipf's Law still has exceptions: the law only works if the cities in question are connected economically. This explains why the law is valid, for example, for an individual European country, but not for the entire EU.

How cities grow

There is another strange rule that applies to cities, it has to do with the way cities consume resources when they grow. As cities grow, they become more stable. For example, if a city doubles in size, the number of gas stations it requires does not double.

The city will be quite comfortable to live in if the number of gas stations increases by about 77%. While Zipf's law follows certain social laws, this law is closer to natural ones, for example, to how animals consume energy as they grow up.

Mathematician Stephen Strogatz describes it this way:

How many calories per day does a mouse need compared to an elephant? Both of them are mammals, so it can be assumed that at the cellular level, they should not be very different. Indeed, if cells of ten different mammals are grown in a laboratory, all these cells will have the same metabolic rate, they do not remember at the genetic level how big their host is.

But if you take an elephant or a mouse as a full-fledged animal, a functioning cluster of billions of cells, then the cells of an elephant will consume much less energy for the same action than cells of a mouse. The law of metabolism, called Kleiber's law, states that the metabolic requirements of a mammal increase in proportion to its body weight by a factor of 0.74.

This 0.74 is very close to 0.77 observed in the law governing the number of gas stations in the city. Coincidence? Maybe, but most likely not.

All of this is terribly exciting, but perhaps less mysterious than Zipf's law. It is not so difficult to understand why a city, which is, in fact, an ecosystem, albeit built by people, must obey the natural laws of nature. But Zipf's law has no analogue in nature. This is a social phenomenon and it has only taken place over the past hundred years.

All we know is that Zipf's law also applies to other social systems, including economic and linguistic. So maybe there are some general social rules that create this strange law, and someday we will be able to understand them. Whoever solves this puzzle may discover the key to predicting things much more important than the growth of cities. Zipf's Law may only be a small aspect of the global rule of social dynamics that governs how we communicate, trade, form communities, and more.