Often, the Second-Biggest City Is About Half the Size of the Biggest
The same math describes words in books, incomes in crowds, and dolphin calls, which suggests cities emerge from nature, not just planning.
Wendover Productions · Why Cities ExistIn many countries, the second biggest city has about half the people of the biggest, the third has about a third, and so on. It is a rule about how sizes spread out, often called Zipf's law after linguist George Zipf, that also covers things that have nothing to do with cities.
In the United States, New York has 8.5 million people and Los Angeles has about 4 million. In Germany, Berlin has 3.5 million and Hamburg has 1.8 million. Most cities fit closely. Munich, at 1.4 million, is well above the roughly 1.2 million a one-third share would give.
London was Europe's largest city in 1800 and still is, with Paris second in both years. Ranks tend to shift only after shocks, such as government in Washington or gold in San Francisco.
The same spread appears for words in a book, people in a stadium by income, and dolphin sounds by frequency, a hint that cities emerge more from nature than from planning.
Questions people ask
Does it work perfectly in every country?
No. Most cities fit closely, but there are anomalies. Anomalies are mostly in countries with recent rapid population growth.
Why would dolphin sounds and cities follow the same rule?
Researchers do not think dolphins are copying cities, or vice versa. Both are examples of systems where many small choices add up to a lopsided outcome with a few very common items and many rare ones, a pattern mathematicians call a power law.
Why do city rankings stay so stable?
Large cities tend to stay large without outside influence. Businesses cluster in cities to share workers and work with nearby firms, which helps big places hold their lead. Ranks change when something outside changes, like government arriving in Washington or gold being found near San Francisco.