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This is probably a loaded question but nevertheless an interesting topic. Take this picture from Star Trek for example. In it, you can see what must be a super massive structure that occupies so much of the horizon and at that distance! I am aware of arcologies so I suppose if we have such a huge and growing population we have no choice but to grow up ;) ? But even then, would planetary colonization technologies be potentially developed before arcological technologies thus potentially rendering arcologies impractical? What do you think?

I don't want to limit this question to the topic of arcologies. The image below also has an industrial "feel" so perhaps other types of structures may warrant such a size.

Scene from Star Trek

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  • $\begingroup$ for food production, if mean plant grow, but not nutrient paste machine. For production, combine technology cycles in one big structure, eliminate demand hauling parts back and forth, clean waste, but needs 100% automation or teleoperation. Packing huge mounts of peoples if they need interact with each other, 3D structure have more surface area then 2D, less time of travel. $\endgroup$ – MolbOrg Oct 5 '16 at 22:10
  • $\begingroup$ Space-elevator and/or orbital defense cannon $\endgroup$ – Marky Oct 5 '16 at 22:17
  • $\begingroup$ This is a good place to start: "Ecumenopolises" youtube.com/watch?v=XAJeYe-abUA $\endgroup$ – Thucydides Oct 5 '16 at 22:38
  • $\begingroup$ Water storage facility with built in water treatment system because clean water is difficult to come by especially inland and prolong drought. $\endgroup$ – user6760 Oct 6 '16 at 0:46
  • $\begingroup$ @user6760 1x1x1km storage will be enough to maybe 100 million people. But it is not huge and not much needed and it is without recycling and cleaning. So what u talking about? $\endgroup$ – MolbOrg Oct 6 '16 at 3:09
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An enormous structure like that has several benefits for a potential future civilization.

For a highly egalitarian/eco-friendly civilization (Like Star Trek), the taller you make a structure, the less impact it has on the surrounding wildlife. With everyone concentrated into a small area, no one is chopping down forests, draining wetlands, damming rivers, and carving up mountains to make space.

For authoritarian governments, concentrating people and industry into a smaller area provides easier control, and in the event of a revolt, easier destruction.

In simple economic terms (For industrial buildings and such), the closer together the facilities for extraction, processing, refining, and manufacturing the more efficient the manufacturing process is.

There may also be applications which require enormous amounts of power or resources, such as a defense laser, wormhole generator, or planetary shield. Depending on technology levels, these things could require enormous reactors, heatsinks, and support machinery.

Whether or not colonization would render arcology irrelevant depends on a couple of things. Food is heavy and inefficient to transport. It would require enormous amounts of interstellar infrastructure to effectively transport a meaningful amount of food back home. In a universe where interstellar travel is cheap (due to space elevators, fusion rockets, probably some form of ftl travel), this is feasible. It is more likely though, that colonies will not only take hundreds of years to get the kind of agricultural base to support such a large population, but also won;t be able to effectively transport resources back home.

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The real reason would be artistic, to show the viewer that they're not in the Kansas they know any more. Within the setting, how about this:

In the long historical trend, industrial facilities have grown larger

A charcoal clamp, an iron furnace, and a smithy from the iron age were all smallish structures. A Bessemer converter was larger. Industrial electric arc furnaces are larger still. The Wright brothers built their airplane in a bicycle workshop. Compare the Boeing plant in World War 2, or the assembly lines for modern airliners.

Before the reboot, we knew about things like the Utopia Planitia yards on Mars and in Mars orbit.

We can easily assume that some parts of the reboot-era Enterprise were manufactured on Earth, that those parts are large, and that the most efficient way to build them requires even larger assembly lines.

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The closer to a cube your living space is the less time and energy will be spent on transit. That is why you have skyscrapers in the cores of cities.

However, tall buildings come with a cost that now in the age of electronic communications is generally not considered worth it as much less physical transit is needed.

Given Trek-level tech I suspect the situation flips again. The cost of building tall will drop, the value of people's time goes up. Obviously, in the Trek-verse the lines have once again crossed and the value of being close to anyplace you want to go is greater than the cost of building tall.

(Note that to get the true transit benefit of building tall you must have connections at many levels. If I have to go down a thousand stories, cross the street and go back up a thousand stories it's not going to work very well.)

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