I had a quick question about how big a city could be while still being believable, in the sense of being able to run it properly. I am writing a science fiction type story and the main setting is inside this city, which I need to be as big as possible. The city is surrounded by a very high wall and no one is allowed in or out.
Isaac Asimov's Foundation epic has a planet-sized city named Trantor.
A real-world primate city (a political geography term meaning dominating the surrounding country region in every aspect of society and culture and technology on a global scale) would involve some interchange with its hinterlands, the agricultural, industrial, and cultural production regions providing goods and services to the city. At present, the largest such city is New York. Chicago, Los Angeles, London, Paris, Berlin, Moscow, Tokyo, Bejing, Singapore, Mexico City, and Buenas Aires follow close behind and are primate cities as well.
Administrative practices create governance issues when a geopolitical entity grows so large that the center, either physically or socially or both, is too far from the peripheries to effectively maintain, control, and manage them. This was a problem for ancient Rome that influenced its decline.
Current primate cities strain to maintain law and order and provide adequate services for their denizens. Current social, cultural, and technological practices make those primate cities as large as they can practically be before the peripheries begin to break down and away from the center. That is an ever present problem for large cities, in danger of splintering at any moment and declining into chaos and disorder, like Detroit.
I seem to remember Plato's rule of thumb on the size of a empire being the distance an army can travel in a day (or week?). Using that and our current tech it might be possible for a worldwide government.
I was thinking Ba Sing Se of the Last Airbender, it's all considered one city but a large portion of it is farmland. I think this is an important thing to consider with your "no one in, no one out" policy.
The real answer to your question is it can be as big as you can convince us it could possibly be. There isn't any hard data on the size a self-sustainable city could grow because there isn't really one of those.
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