Human population of hundreds of billions

Wild Speculations
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Armin asked:

Humanity numbering into the dozens or even hundreds of billions on earth without harming the ecosphere is impossible due to constraints in food supply, settlement area and inner conflicts. But these hurdles could be overcome by technology and cultural development. Is there a good and not-naive story about that which does not involve colonisation of space in a large scale?

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Heather Hile answered:

In The Caves of Steel by Issac Asimov, everyone lives in giant mega cities, to fit the population. But they did harm the environment, and grow vat protein etc. to feed everyone. There are limited space colonies in the story, but the novel takes place only on Earth.