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The Divine City is a truly massive piece of architecture in the shape of a cube

It is over 2000km on each edge, and has 4 sturdy walls, a thick base, and a light roof

It is densely populated, with many stories going from the base to the top of the walls

It is on Earth, and does not curve with the ground

This titanic structure would have some issues with its size. It would be extremely heavy, and it seems implausible that this structure could stand up as a regular building. But, it may be able to stand up some other way, if properly designed

Could this city realistically exist?

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    $\begingroup$ At 2000km you would have to consider the actual curvature of the earth (if this is on Earth). It would dip by 311.4km so you couldn't have it in a classic box shaped building. $\endgroup$
    – Mattna
    Commented Feb 13, 2022 at 14:19
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    $\begingroup$ Is this a huge cuboid with 2000 x 2000 x 2000 m3 structure? What about windows, doors, air, roads, sewerage, transport, lifts? $\endgroup$
    – imtaar
    Commented Feb 13, 2022 at 14:35
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    $\begingroup$ 2000km is a preposterous number for something built on the earth. I suspect such a structure will always be either (a) too light to support itself or (b) heavy enough to turn the inside into magma. $\endgroup$
    – Daron
    Commented Feb 13, 2022 at 14:47
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    $\begingroup$ Go for broke: make it 20000 km on each edge, and put Earth inside. $\endgroup$
    – Therac
    Commented Feb 14, 2022 at 7:43
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    $\begingroup$ Even if it could exist, supposing an actually flat bottom square and plumb to the curvature of the earth at it's center, gravity is going to make the edges of that platform feel like a ramp drawing you back towards the center of the platform. I can't work the math right now but it should be pretty significant. $\endgroup$
    – user8827
    Commented Feb 14, 2022 at 13:16

7 Answers 7

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Not on Earth

@SeanBoddy mentioned in a comment the fact that Earth's gravity would not act "downwards" through the cube. The effect would be most significant at the bottom corners.

To calculate the magnitude of this effect, we know Earth's radius ($6,400\,km$), and we know the distance from the center of the cube's lower face to one of that face's corners is $\sqrt2 * 1,000\,km$. So we have a triangle $6.4\,Mm$ up, $1.4\,Mm$ across, which gives us an angle of a little over $12.3\,degrees$: mildly uncomfortable, but more importantly, very structurally significant, as load-bearing walls need to be vertical.

[That $\sqrt2 * 1,000\,km$ comes from assuming the cube is touching the sphere of the Earth at the center of the cube's bottom face. So the distance we want is from the center of that face, to one of its corners. We could just take the diagonal length of a unit square ($\sqrt2$), and multiply it by half the width of our square ($1000$), or we can go the long way round, using Pythagoras, taking the full diagonal of the bottom square as $\sqrt{2000^2 + 2000^2}$, or $\sqrt{8M}$, which is $\sqrt2 * 2000$; then halving that to get the distance to the center instead of from corner to corner, which again gives us $\sqrt2 * 1000$. However we get there, it's a shade over $1414\,km$ or the "$1.4\,Mm$ across" I mentioned.]

Not even in space

If this cube were formed of solid rock, it'd be a sphere, as it would be about a thousand times larger (ten times in each direction) than required to surpass the ~200km "potato radius". So even taking into account that it's not solid (there are holes for rooms), you'd most likely need something a whole lot stronger in compression and lighter than concrete for this to work even in space, let alone on Earth.

However, if, for every unit of wall/floor volume, you have a thousand of empty "room" space, then it might just work.

For each room, the Walls and floors scale with N^2 and volumes scale with N^3, so this should be possible, so long as your rooms are a thousand times wider, deeper and taller than their wall thickness.

Not really feasible unless the walls themselves are only an inch thick, or are hollow skimmed either side with half an inch of material. Seems like you're not building this cube from concrete, not even in space: you're building it from sheetrock and 2x4s, like a modern Texan house.

If it's on Earth, you may suffocate

The volume of all air on the planet, if put at sea level pressure, forms a sphere with a diameter of $1,999\,km$. So there's not enough air in the world to put in that box and allow people to live in it. If it was relying on the Earth's air, then people would only be able to live in the bottom $7\,-\,8\,km$ or less, as that's around the altitude of the "death zone" for human breathing. Alternatively, it'd need a system of locks and pumps at least every km of altitude or so, to maintain air pressure through the cube; and to bring its own air supply as Earth wouldn't have enough.

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  • $\begingroup$ I don't see where the $\sqrt{1000}$ km figure is coming from. I'm getting $\sqrt 5 \times 1000 \simeq 2236$ km. From the lower face to one of the top corners. See image. The scale is 1 unit = 1000 km. $\endgroup$
    – Daron
    Commented Feb 15, 2022 at 14:59
  • $\begingroup$ I typoed :) Instead of sqrt(1000), I should have put sqrt(2) * 1000, as that (1.4 Mm) is the value I used for the later calculation. I'll fix, and add rationale. Assuming that the cube is touching the Earth at the center of its lower face, with the face horizontal relative to Earth's gravity at that point, then the distance we want is the distance from the origin in your diagram (where gravity will be "vertical"), to the corner (where gravity will be maximally sloped). $\endgroup$ Commented Feb 15, 2022 at 19:13
  • $\begingroup$ Fixed - thanks for catching! Also used MathJax markup, rather than being lazy... thanks for poking me by example :) $\endgroup$ Commented Feb 15, 2022 at 19:28
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(Big) Space Cube

Space Cube.

THE DIVINE CITY does not curve with the Earth's surface because it is too big to fit on the Earth's surface without causing the apocalypse.

THE DIVINE CITY is 2000km wide. Nearly one hundred times the height of the largest mountain in the solar system.

THE DIVINE CITY is over half as wide as the Moon. The Moon! Imagine trying to put something that big on the planet without it tearing itself apart from any of:

(a) atmospheric effects

(b) rotational forces

(c) gravity differences at the top and bottom

(d) the inside turning to magma

(e) being too big

THE DIVINE CITY is not on the planet because it is its own planet. Or maybe it is a space station. We are not sure. None of us were around when it was created. That is part of what makes it DIVINE.

THE DIVINE CITY'S denizens are called Devas. They live in tunnels that can go a few kilometers under the surface. These people are different from the Earth people due to the weaker gravity and thinner atmosphere. Their language sounds like whistling but there are also low frequency tones that make you want to go to the bathroom.

THE DIVINE CITY has its own gravity, geology and weather. They believe the center is molten but have not been down to check in person.

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    $\begingroup$ Downvote because they have not been down to check in person. Freaklng layabout sloths! $\endgroup$
    – Willk
    Commented Feb 13, 2022 at 15:08
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    $\begingroup$ Btw that borg cube has a measly edge length of 3km. Not 2000. The moon comparison is much better. $\endgroup$
    – Bergi
    Commented Feb 13, 2022 at 23:09
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    $\begingroup$ Wouldn't it collapse under their own gravity and get spheric shaped? $\endgroup$
    – raulmd13
    Commented Feb 14, 2022 at 9:05
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    $\begingroup$ @raulmd13 That is a concern but I have not run the numbers. Give it your best shot and have it on my desk tomorrow morning. $\endgroup$
    – Daron
    Commented Feb 14, 2022 at 13:24
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    $\begingroup$ @raulmd13 Hmm. . . It seems our holy cube might collapse into a holy safety cube. $\endgroup$
    – Daron
    Commented Feb 14, 2022 at 17:22
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There's no way such a thing can stand on Earth. Maximum height of earthly mountains is a bit over 8km because anything above that would sink mantle and thus become lower (mons Olympus on Mars can be higher due to lower gravity and thicker mantle) (see this).

Anything strong enough to sustain it's own weight (if that is at all possible, which I strongly doubt) would sink in the crust like an iceberg in water.

Given the size you request it would be a problem even to keep its cubic shape even in space as it would have it's own gravity and it's well over the size where asteroid try hard to become spherical.

In space, of course, you could make it much more lightweight and thus you can have little gravity to counter. Problem with such a setup are:

  • very large cross section so virtual certainty to get incoming debris daily.
  • If orbiting in relatively low orbit large tidal effect trying hard to break structure apart (see: Roche limit).

Note that even "simply" adding a kilometer thick "protective" layer of the lightest material known today (graphene aerogel) would already have a mass (~3.8e15kg for the pure "shield", nothing inside) comparable with a fair sized asteroid like Eros.

Another "simple multiplication exercise": if you have layers 100m apart (which is a pretty high ceiling to have in all your "rooms") you will end up with 2000 * 2000 * 20000 Km2 of sheer surface. If you put a "moderately populated" (like Holland) 500person/Km2 (Singapore has >8000p/Km2 and it is not the most densely populated in THIS world) you get about 4 trillion people, giving them a mass of 80kg each you get 3.2e15Kg, more than enough to generate a fair gravity pull by themselves, without any life support equipment (or clothing).

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  • $\begingroup$ " it would be a problem even to keep its cubic shape even in space" => Not really. Asteroids are random formation of matter. No nanostructure with insane strength, no automated repair bots, no intent. The DIVINE city has all of that however. And with the significantly lower gravity, bulding high "mountains" (= the corners) wouldn't be that big of a problem $\endgroup$
    – Hobbamok
    Commented Feb 14, 2022 at 12:16
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    $\begingroup$ @Hobbamok: agreed (I also specified it in the reply), but it is something to keep in mind, You won't be able to do it with stainless steel. You can even use tidal forces to counterbalance (some of the) gravity pull, at least in one direction. $\endgroup$
    – ZioByte
    Commented Feb 14, 2022 at 12:25
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    $\begingroup$ @Hobbamok THE DIVINE CITY is much bigger than an asteroid. $\endgroup$
    – Daron
    Commented Feb 14, 2022 at 13:14
  • $\begingroup$ @ZioByte Incoming debris is a certainty but I wager THE DIVINE CITY is big enough that even if all the debris orbiting the planet hit at once it wouldn't make a dent in the overall shape. $\endgroup$
    – Daron
    Commented Feb 14, 2022 at 13:16
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    $\begingroup$ It will EVENTUALLY be spherical. A civilization that can build this can probably afford to keep reshaping it as a cube. $\endgroup$ Commented Feb 14, 2022 at 21:43
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maybe, but your satellites won’t survive

Most satellites are between 160 and 2000 km above earth. This means any of these satellites might impact the city unless they are take down. You could have them course correct, but given the size of the city that might not be possible.

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    $\begingroup$ The city wont stay that high it will sink in to the earth, and likely collapse under its own weight. $\endgroup$
    – John
    Commented Feb 13, 2022 at 23:33
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    $\begingroup$ @John yeah, I’m just pointing out even if they do stand, satellites will not work. $\endgroup$
    – user64888
    Commented Feb 14, 2022 at 1:40
  • $\begingroup$ If the city stands on a pole (and it better do, because I really don't want to imagine what a significant rotational imbalance would do to the Earth), you can still have LEO satellites in equatorial orbits. $\endgroup$ Commented Feb 14, 2022 at 13:59
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In addition to the other concerns, I'm worried about where you're going to find 2,000 meters square of flat ground to stick your city. I've done some mockups to show the size of the Divine City, to give you an idea of how big the ask is.

enter image description here

enter image description here

enter image description here

I can't help but wonder if it could possibly float. But then, it's likely it would need a draught of hundreds of kilometres at least.

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It's hard to imagine a material that could be used to build such a structure. It's likely that a structure of this size requires active support. Think space fountain but on a much larger scale. By accelerating pellets (or whatever) up a tube and then deflecting them back in a loop, you create a force that helps hold the structure up.

A Space Fountain uses a continuous stream of electromagnetically accelerated metal pellets to hold things up at extreme altitudes using the same basic physical principles that a water fountain uses to suspend a plastic ball at the top of its vertical jet of water.

Small metallic pellets by the millions would be shot up to a "deflector" station far overhead, which would use magnetic field scoops to catch the pellets, curve them back down with an electromagnetic accelerator, then shoot them back down to the ground. The ground station would in turn use a magnetic scoop to catch the pellets, curve them back up with a powerful electromagnetic accelerator, and shoot them back at the station in one continuous loop. The pressure exerted on the magnetic fields of the scoop and curved EM accelerator by the continuous stream of pellets would keep the station aloft.

ORBITAL RAILROADS: BEANSTALKS AND SPACE FOUNTAINS

I imagine that sitting this structure on your planet can only lead to Bad Things, so an orbital structure is more reasonable. I'm imagining a black hole or something in the middle to keep it all powered.

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It cannot be "flat to the ground", assuming you mean the base is a flat plane.

The distance from corner to corner, with sides 2000 km long, is 2828 km. Simplifying the Earth to a sphere, this means that if you place the center of the based on the surface of the Earth, the corners are at an altitude of approximately 155 km, aka Low Earth Orbit. If, on the other hand, the corners are on the surface and the base cuts through the Earth, that means that at the center it's 155 km deep, or well into the upper mantle. This is...problematic, and means that the excavation would result in an event that would have tectonic implications over the entire planet and probably result in a near total mass extinction event as it would create the largest volcanic event since the Earth finished forming.

This would be bad.

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