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Lets take a 60km radius island where the people have access to early XXI century technology. The whole island was planned and artificially built, so it has no mountains or otherwise bad/sterile terrain.

Since it was artificially built, there are enough rivers, lakes, and the hills /valleys were pre-planned so the freshwater from the rain makes it cycle smoothly.

Also, there is no mineral production. Assume all mineral / metal needs come from asteroid mining/magic/etc. There is little to no surplus, but no scarcity, not even rare earth minerals.

Aside from that, all the food, livestock, clothing and industrialized products and energy must be produced inside the island. They can use any technology available to an early XXI century Earth (some 20 years - 2035 - ahead at most). The industry and the society is zero-waste.

And the island has no useable ocean around. So they cannot use seawater, fish or deploy boats or aquatic vehicles. Travel to other nations is rare, and is made by air.

How large a population could this secluded island nation support?

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  • $\begingroup$ Possibly already answered in part here: How many people can you feed per sq. km. of farmland? $\endgroup$ – Serban Tanasa Mar 20 '15 at 3:34
  • $\begingroup$ @SerbanTanasa great resource, I will add that to the question. But we still have to factor in city and factory and transportation space, but I think that answer covers farmland production neatly $\endgroup$ – Mindwin Mar 20 '15 at 3:37
  • $\begingroup$ That's not that small. Larger than Hawaii, Jamaica, Gambia or Kosovo. Since Hawaii is physically remote it might be the easiest one to separate from its external commerce and use as a rough guide? $\endgroup$ – Leushenko Mar 20 '15 at 4:24
  • $\begingroup$ Related question. $\endgroup$ – Irigi Mar 20 '15 at 6:43
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Using the numbers from https://worldbuilding.stackexchange.com/a/9589/7718, each person needs approximately 1000m2 for food production. That number is already adjusted for various inefficiencies and is much larger than needed for other purposes such as living space, so is a reasonable approximation of total space needed per person.

Your island is 11 billion m2, so you can fit in 11 million people without doing anything special.

If you really want to maximize the population, go vertical. Covering the entire area with a hundred story building is well within the capabilities of 21st century engineering, and would let you squeeze in over a billion people.

You would obviously need quite a bit of energy generation since the lower levels won't be getting any sunlight. At 1300W/m2 you need 14TW. That is equivalent to approximately 2000 large nuclear power plants.

Cooling might be a problem, since we need to lose the equivalent of a 10kT nuclear bomb every three seconds. Using seawater would be easiest, but we could probably do it by bringing in air from outside the city if we really had to. The area around this island is going to be rather windy.

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    $\begingroup$ This article academia.edu/2194711/… suggests 30 sq meters/person for a 3000 cal/day vegetarian diet. The wonders of hydroponics. $\endgroup$ – WhatRoughBeast Mar 20 '15 at 5:33
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    $\begingroup$ 1000 sqm is for normal land with meat included, but since we are going for maximum population... Say 50 sqm/person so they have a bit of living space, and we get a population of 22 billion. $\endgroup$ – Quentin Clarkson Mar 20 '15 at 6:22

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