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So, If I'm trying to make a borderline-isekai (trapped in an MMORPG world anime) setting, I might as well just make the game mechanics more real, like invisible walls, everywhere.

The world of Underdown used to be a nice place until... something happened. Now everyone has to live under 200 meters of graphene-reinforced UHMWPE and SAM2x5-630 composite plates, crammed into the elaborate cavern system, known as the Underdown (roll credits).

Such a nice location has many disadvantages, especially when used as the last beacon of civilization (sorry, that's 4chan). Today, I wanted to focus on the basic question of Underdown's size.

But first, basic information about the tech-level and the Barrier:

The Barrier:

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  • Nanomachines in the stratosphere (slightly above the ozone layer) collect all the sunshine with a 40% efficiency and send it to Underdown, so we dodged the Second Law of Thermodynamics.

The technology:

  • Despite looking high-medieval, the society actually has access to modern day (and slightly better) technology.
  • Magic is also a form of technology, which should explain why it's so inept and can only shine in terms of healing (complete regeneration, hyper-effective disinfectant), infiltration, sabotage, intel-gathering, manufacture, and Megumin-grade explosions, given time (and propane).
  • Food can also be easily be produced using magic.

Now, let's name the factors we need to consider in Underdown's size:

  • Population: Cramming the entire Pathfinder Bestiary 1 into a tiny cave, and trying to provide the preferred habitat (swamps, jungles, a bloody lava lake) for them is hard.

Let's assume 1 million individuals, who all have the same needs as an average adult human (Why? I put a hard cap on living creatures, both in terms of size and resilience to the elements, and dragons, with the size of Big Jake, are the maximum in both terms, but still, fail to outperform polar bears). Remember, this is a permanent home for them, let it be at least a bit comfy.

  • Construction materials: I'm more forgiving with that, after all, the absolute madman who built the place started using boron carbide and alumina instead of concrete halfway through. And because MMCs are widespread in this world.

So how big would Underdown (area and height (because the birds)) have to be to meet all the criteria, given the best construction materials, and all the energy in the planet? Of course, only if it can be built at all.

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  • $\begingroup$ Currently this query is slated for closure due to it being unclear exactly what you're asking. Can you please pare down your query to just the actual question plus directly pertinent background? There's a lot of irrelevant stuff about the setting that, while interesting, may be serving to cloud your point rather than clarify. $\endgroup$ – elemtilas Oct 8 '18 at 19:43
  • $\begingroup$ @elemtilas Gimme a second $\endgroup$ – Mephistopheles Oct 8 '18 at 19:44
  • $\begingroup$ If the birds are not migratory, even a couple hundred feet high should be the minimum height that birds can live with. $\endgroup$ – ShadoCat Oct 8 '18 at 19:56
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    $\begingroup$ You seem to hand-wave away a lot of the constraints on the size of this place – food is produced magically, so I assume it needs no space; energy production is not an issue either – such that the only sensible answer seems to be 'make it as big as you want it to be'. If you are asking for a minimum size, you need to decide how much space individuals enjoy in private and public spaces. Use a city of 1m pop as a guide. $\endgroup$ – John Oct 8 '18 at 21:21
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    $\begingroup$ " the Walled City had a population density of approximately 1,255,000 inhabitants per square kilometre (3,250,000/sq mi) in 1987" - if all you are asking is permanent home that is a tiny bit comfy, this plus some rudimentary math will be your answer. If you want swamps, forests etc, then we need more detail about what do you need from them. $\endgroup$ – Mołot Oct 8 '18 at 21:44
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There is more to a society than simply living space, and volumetric area.

For your society to prosper it needs production. Economy - factories and consumers.

Although the 1 million individual target is fine as a starting point, let's look at Adelaide Australia - one of many Australian cities voted very liveable. Adelaide has a population of 1,120,000. It is 3250 sqm area, which is roughly 60km x 60km. Height need only be high enough for a bird and a person to survive, but keep in mind you mentioned comfort. We really need it to be at least the height of Adelaides CBD being 132m, otherwise people could feel claustrophobic.

However having said this, this is simply the metropolitan area. People need to eat. They need resources to consume. They need economies to be a part of. If you take this criteria, it is difficult to determine a sustainable size. This is because the world is so interconnected now, cities are linked to so much activity not just in their vicinity but worldwide, that to sustain our level of technology, society and stability we really need more than one city, but dozens.

We also need lots of farm area to support each individual. Australians require 9300 sqm per person. So really you need an area at least 100km x 100km to support your 60km city simply for food.

If you can accomplish this than your city will still need to contend with heat. Without a way to expel heat, your city will cook, as we and any process within the city will make heat. We need light, we need power and energy. And water.

Then there is waste. Produce waste, water waste, sewerage. There are many very large issues to overcome.

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