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How big could an empire using World-War II equivalent technology become on a very large world?

Setting: Handwavium-based-artifact by a Kardashev III+ civilization, or perhaps a simworld created by AI researchers in the (not-so?) distant future. We're talking about a 1-AU-radius world (except people live on the outer not inner side of the hollow sphere), so for all intents and practical purposes (at least with WWII transport tech), a humongous and near-flat world (it would take hundreds of years to drive around at 130km/h). Let's assume that:

  • It's Earthlike in effect. The exterior surface (I'm assuming it is a hollow Dyson-like sphere, outside populated, with 20-40 km of earth and oil and rock on top of the thin handwavium layer keeping it together) is somehow kept Earth-like (1g, 1001 KPa air, habitable throughout, with each area subjected to a myriad local (small) sun-like sources orbiting in such a pattern that most areas see something like a 24 hour day-night cycle and temperate-climate-like seasons). There are geological process emulators, so there are volcanoes and tectonic plates and earthquakes, ensuring that chemical elements get cycled through properly and all Earth-like. The world has ample coal, oil, metals and other resources. Fake fossils everywhere, cunningly planted.

  • Feature granularity is Earth-like. I mean earth-sized seas and continents, very few if any size-driven impassable oceans, mountains or deserts. (i.e. the ocean or desert does not stretch in that direction for 10,000,000 km)

  • Primitive humans were seeded throughout, 20,000 years prior. Uniform distribution with several small (but genetically sustainable) bands placed in habitable areas.

  • It's big. Very big. If I did my calculations right, the total area is about 281,229,865,303,000,000 square km, that's about 500 million Earths' worth.

  • Some rare areas would be thousands of years ahead of the pack due to sheer geniuses or dramatically good conditions, so I expect some areas to reach industrial tech while others are still hunter-gatherers. I'm not sure what I want to define as areas in terms of size, but I expect them to be pretty large, since technology does tend to diffuse outwards.

Let's skip ahead to a point where there are now industrial-level civilizations on the planet, with WWII-era technology. How big could a World-War II equivalent technology empire become in such a world?

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    $\begingroup$ Question: how will these guys obtain oil? Was it "planted" for them to later find and use? Or will you give them some alternative fuel? $\endgroup$ – AndreiROM Jun 17 '16 at 17:38
  • $\begingroup$ A comment on the idea that large areas will remain in the stone age. That won't happen on anything less than island-continent granularity. Given land connectivity there will be trade which will disseminate products and know-how. Useful tech, such as the wheel or smelting iron or the arch, will move out from its point of discovery "forever" until it arrives at an impenetrable barrier such as an ocean. $\endgroup$ – nigel222 Jun 18 '16 at 10:05
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    $\begingroup$ How do you want to define an empire? We often define it by having control over large areas of land, but if we choose to define it as having a powerful influence over that land instead, we can cover a lot more area because we are willing to accept more dissention from the fringes $\endgroup$ – Cort Ammon Jun 18 '16 at 14:18
  • $\begingroup$ @AndreiROM, the oil is in there, right next to the fake dinosaur bones. $\endgroup$ – Serban Tanasa Jan 9 '17 at 15:15
  • $\begingroup$ Even with WWII tech, these people should be able to calculate the shape and curvature of their world. They would see the multiple suns when they are traveling by plane/balloon and probably be very confused. $\endgroup$ – A. C. A. C. Jul 13 '17 at 19:08
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Potentially very large.

The limits would be speed of transport and communication.

For comparison the Roman Empire was about 4,000 km across with maximum communication and transport speed of ~10 km/hr (horse or boat)

By the time of the British Empire you have spread to effectively be world wide or about 40,000 km (Earth's circumference) with speeds of travel and communication around ~40 km/hr (steam train and fast sailing ships)

WWII tech would push the land speeds up to around 100-150 km/hr, ocean speeds of ~50-60 km/hr, and the addition of air travel at speeds of ~500-1000 km/hr.

The big change was the introduction of radio communications allowing messages to travel at near the speed of light.

Assuming the transport speeds are the limiters (which would all require infrastructure to support), your empire could easily be multiple earths in size ~1,000,000+ km.

For an upper maximum size example: an ocean vessel or train line running for a lifetime (~50 years) would only go 20-40 million km so I think an empire larger than that would be very unlikely.

With radio there could be communication around the entire object (with repeater stations for line of sight issues) but I think it would be unlikely to care about a place that is so far away it would require generation ship timelines to get there.

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    $\begingroup$ Good point about transportation speed being the limiting factor. If someone's territory is even more than a few years' travel away I think nobody would care to mess with them. At that scale any governmental cooperation would consist almost entirely of "agreements" because nobody would want to travel that far to enforce anything. $\endgroup$ – thanby Jun 17 '16 at 15:59
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    $\begingroup$ Even if the "empire" does not spread across the whole area their is likely to be a cultural imperative to expand. A wave of colonists will travel out to the edges and set up camp with a radio. The tech, skills and people will spread. $\endgroup$ – Donald Hobson Jun 17 '16 at 16:09
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    $\begingroup$ At some point population is going to start restricting your ability to expand and maintain security. $\endgroup$ – AndreiROM Jun 17 '16 at 17:32
  • $\begingroup$ Mongol empire expended on more than 1 year of travel. I'd say between 1 and 3 years of horse riding.In this case (as for Alexander), it is an emperor building it's empire along his path. Of course, this kind of empire collapsed quickly $\endgroup$ – Madlozoz Feb 9 '18 at 15:49
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@JoshKing's answer addresses the main issue very well, but I want to toss in an alternative. Considering that communication around the sphere could still be achieved by radio at near-light-speed, it's theoretically possible to organize a government that spans the entire sphere.

Governments only work because of two things: (1) People generally agree what rules there should be, and to a much greater extent, (2) the government has the ability to enforce those rules. If global (spherical?) consensus could be reached on a set of laws/rules, enforcement agencies (police/military/etc) could be organized at intervals around the sphere to enforce them locally. If any one group decided to stop obeying, it would be the responsibility of the agencies adjacent to them to quell the disturbance and return the region to status-quo.

There's just a teeny-tiny sarcasm engine revving problem with this whole idea, though. Even on tiny little planet Earth we haven't managed to achieve any level of cooperation remotely close to what would be required in this scenario, so chances are it's nearly impossible for humans as we know them to accomplish. But it's at least food for thought.

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    $\begingroup$ It's not atiny problem, it's a huge one. There's no way whatsoever that a government ruling the whole sphere could be established. Too many colonies, too many cultures, too many tech levels, etc. Someone would have to enslave the whole place for generations, etc. $\endgroup$ – AndreiROM Jun 17 '16 at 17:33
  • $\begingroup$ The limiting factor isn't communication, it's your ability to get troops out to deal with an uppity governor declaring independence. Historical evidence says you can't manage an empire with a one-way travel time greater than about six months, and more than three is pushing it. $\endgroup$ – Mark Jun 17 '16 at 22:06
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    $\begingroup$ Perhaps I should have emphasized the matter more, the severe sarcasm was apparently lost in translation. $\endgroup$ – thanby Jun 18 '16 at 14:00
  • $\begingroup$ @AndreiROM that's why he said "sarcasm engine revving" $\endgroup$ – Aarthew III Jun 19 '16 at 2:59
  • $\begingroup$ @AarthewIII To be fair I didn't add that in until after I learned there was some confusion on the matter $\endgroup$ – thanby Jun 20 '16 at 11:19
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I like all answers so far, all have valuable points.
Also I may confirm OP calculations, it's 554,502,685 times larger surface.

How big it is

Larger surface means also larger possible population, 3.88151879518e+18 peoples, if we take current density, and it may be 10-100 times bigger, even ww2 tech. But let's stick with first number.

Six degrees of separation

  • Six degrees of separation is the theory that everyone and everything is six or fewer steps away, by way of introduction, from any other person in the world, so that a chain of "a friend of a friend" statements can be made to connect any two people in a maximum of six steps. It was originally set out by Frigyes Karinthy in 1929 and popularized in an eponymous 1990 play written by John Guare.

What will it mean for such large population?
It will be not Six degrees of separation but 12 degrees of separation.

  • It is result of following equation 6 * X, where X is from: Max_sphere_population=6dos_theory_populationX=average_person_connections6*X
    X=ln(Max_sphere_population)/ln(6dos_theory_population)~=ln(3.9e+18)/ln(2.5e9)

It means any chain of command will be 2 times longer then nowadays. Without internet, without computers, without databases, without terabit/sec of data channels etc. And with radio stations, and typewriters - it will be even worse to manage that population. It have not to stay long in that state - so I assume they developed proper stuff.

Population

Just a side note, how long it will take to reach such number by population. Population growth

  • Global human population growth amounts to around 75 million annually, or 1.1% per year or 1.011 times per year or 1.011^100~= 3 times per 100 years.

It depends from start number, but let say million at the begin. It will take 2600 years

So not million years, not even 10-100 thousands. If we keep health care and food production on ww2 level - we can expect even faster grow, because of fewer limiting factors like price of surface to live, wood, water etc etc - just go far enough where no body cares and all is ours - like wild west.

How far is that? I guarantee you 20000 km is far enough, more then enough not to care, even in our time with satellites and gps. Actually 1000-2000 is enough. Even less is enough, but it depends on density of population in that place.

So you may travel on your personal wood gas powered auto, wild west style but with autos.

Government efficiency

  • What actually means 12 degrees of separation instead of 6 degrees of separation.

It means command chains are 2 times longer, it means not only 2 times slower reaction, but if there is 10% chances to do something wrong, and 90% to do it right - it means with 3 times longer chain it will be 19% and 81% for fail and success, for single chain. So any imperfection of systems will grow. higher is that imperfection more impact it will have.

Or it may be depicted another way - each human from our current world is president of another world of same size. Not sure that I like to think about that.

As radio will be main source of transferring data (for OP tech level) - easier to fake transfers, to falsify data, etc. More possibility's for corruption, more possibility's to exploit.

Even with today technologies it will be a big big problem, not because of tech, but because of social factors and concept of central government as pyramid of influence.

But there is and was different approaches, sort of p2p approach, as not perfect example but some of it's kind Decentralized autonomous organization.

Our current systems capable for cases 4-5 degrees of magnitude management, which are actually power of some undefined number of peoples, in theory above I estimate it is something like 40.

This number have actually more deeper sense, connected to our biological limitations, I mean mostly with our brains. As usual with humans it is't something strict, but it makes sense.

There is so called Dunbar's number

  • Dunbar's number is a suggested cognitive limit to the number of people with whom one can maintain stable social relationships. These are relationships in which an individual knows who each person is and how each person relates to every other person. This number was first proposed in the 1990s by British anthropologist Robin Dunbar, who found a correlation between primate brain size and average social group size. By using the average human brain size and extrapolating from the results of primates, he proposed that humans can only comfortably maintain 150 stable relationships. Proponents assert that numbers larger than this generally require more restrictive rules, laws, and enforced norms to maintain a stable, cohesive group. It has been proposed to lie between 100 and 250, with a commonly used value of 150. Dunbar's number states the number of people one knows and keeps social contact with, and it does not include the number of people known personally with a ceased social relationship, nor people just generally known with a lack of persistent social relationship, a number which might be much higher and likely depends on long-term memory size.

This number may be in base of that 6 degree power, 150 makes big number 1.1390625e+13 which is still less then number of that may be achieved in that world, 340,000 times lesser, it may mean probably 340000 countries or and probably yes a bigger number of them.

Let say ambassador will have printed book, or 10 books just with names of counties. 340000 countries = 3400002 ambassadors, as example.

Depending on how well these 150 people groups overlap with other 150ppl groups - depends how strong is county identity

Everything above, are not just a big numbers, it is not linear grow complexity of all tasks, every single task that is connected to people managment's. It is at least O(n2).

It's reasonable to take current sizes of counties, in therm of peoples. Our governments systems also developing with people grow, but at any given time they are on the edge of their capabilities.

Even with perfect, state of art tech and system, human brains are limiting factor, and in given time as 300 years, it will to stay a significant limiting factor. Even with tech developing, which may substitute and extend some capabilities - it will stay major limiting factor. And that's good actually.

Notes

As note I have to say that 6dos theory is't confirmed yet, as far as I know. Because of different obstructions, complexity of task, not well defined metrics etc etc.
But interesting numbers from FB this and this

  • It had over 5.8 million users, as seen from the group's page. The average separation for all users of the application is 5.73 degrees, whereas the maximum degree of separation is 12.
  • The average distance we observe is 4.57, corresponding to 3.57 intermediaries or "degrees of separation."
  • Within the US, people are connected to each other by an average of 3.46 degrees.

So many may personally to feel difference between 6 and 3.57 degrees of separation. And 10 and 2000 friends)).

Country size estimation

  • As reasonable number of people who identify them self with particular country, and territory, I would take something between 100 and 2000 millions of peoples.

  • As territory 10 km2 average per person. Way too much, but why not if it is plenty of land there.

As result 18000-80000 km radius from metropolis with 10km per person
Or 5600-25000 km radius if 1 km2 per person. (My personal favorite)
Or 1488-6666 km radius with current 0.0695604 km2 per person.

Naval transportation

People do not forget about dirigibles it will be very useful even with, and probably with, our tech, when it comes about distant land transportation covering. Specially if there will be consistent air flows like on earth, add solar panels and with air bearings it will be sweet - never breaks never have to to refuel. It will be like dream, not fast dream but comfortable, large, which may transport you to any point on land and on sea, cheap, efficient.

As personal recommendation for OP and important moment allowing to investigate large swarms of peoples I recommend, also for any who is attracted by this question, to think about O'Neill cylinder aka space habitat. It is actually the same situation, from social point of view, with same huge amount of peoples, huge amount of surface, huge amount of space habitats, but without handwavium. And actually is possible 30 years later after stated by OP tech.

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  • $\begingroup$ +1 for having the most amount of thought out of all the answers so far. $\endgroup$ – Aarthew III Jun 19 '16 at 3:14
  • $\begingroup$ How did you arrive at 18 degrees of separaation? $\endgroup$ – hyde Jun 19 '16 at 5:02
  • $\begingroup$ @hyde very good question, calculated (maybe), but at the moment I'm not sure it's right number, will think about it tomorrow morning and fix it or explain. something like 6 * ln(3.88151879518e+18)/ln(X=1571570). Yes wrong number estimated it like we have current million people population (number with 6 zeros, 18/6, but yes we are 7e+9) have to be 11.32 (for 7e+9) or ca 12(for 3e+9 peoples) - will fix it now $\endgroup$ – MolbOrg Jun 19 '16 at 5:30
  • $\begingroup$ @hyde fixed and explained a bit, notice if it need more explanation $\endgroup$ – MolbOrg Jun 19 '16 at 14:03
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    $\begingroup$ The degrees of separation thing assumes everyone is in contact, potentially, does it not? What if there were 2 technical civs on opposite sides of the sphere, completely disconnected from each other? I don't see how that would be impossible, given the size of the thing... $\endgroup$ – Serban Tanasa Jun 20 '16 at 17:48
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To add a little to Josh King's answer, it's not just the speed of travel and the speed of communication, it's the speed of culture that really limits an empire.

If the group is united, then it could spread unchecked to surround the entire sphere.
But if there is any differences between them then different cultures will start to form, and then those will split off as they get to far from the center of culture and become something "other".

You'll see this in a small way if you look at very large cities:

enter image description here

In some ways New York is the center of culture for the U.S., and is very ethnically diverse thanks to it being one of the main points of immigration in the past.
If New York grew to consume the Earth, those neighborhoods would by and large remain, and if the Empire of New York was weak, its culture tenuous and fragmented, and it was unable to maintain control, it's likely that those neighborhoods would leave the empire to do their own thing.

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Only real way to keep distant areas under central rule is to be able to project power, in other words be able to go and remove anybody who tries to rule without approval of the central government. Another critical need for power projection is to be able to defend the edges from external threats.

Only reasonable way to project power with WW2 technology (or even today's technology) over ranges longer than range of airplanes is by naval fleets. To be able to actually keep projecting power, you need supply lines. I would estimate maximum reasonable supply line length to be... say, 100 days. Assuming cargo ship speed of 1000 km/day, that's naval distance of 100 000 km, two and half circumferences of the Earth. So depending on geography, maybe half of that as bird flies.

Any larger than that, and fringe parts of the empire will start to secede and claim independence. This happens as soon as population at edges is large enough to sustain their own army. If the central government tries to support their power projection from too far of their seat of power, well, they just gave someone means to turn that power against them and secede even more easily.

Only way to be larger than this would be by being truly good government, but I doubt that is possible. There's always corruption, inability to really care about people 100 000 000 km away etc. Central government won't be able to stay good government for the edges of the empire. So they will want independence, and they're too far away to be stopped at this distance I estimated above.

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    $\begingroup$ What if the caring is done by local counselors, only a general framework like human rights and the running of the councils are centrally controlled. It is possible to run a straight government and people won't revolt unless they are really bad. $\endgroup$ – Donald Hobson Jun 18 '16 at 18:31
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Josh King is quite right about transport and communications being the bottleneck on any civilisation, and given Earth-like political conditions that match the tech to the time as it were transport is more important and his math is probably about right.

BUT, if we pick a different political model; say ancient China or Rome after they split the empire, and scale up what you get is a civilisation that is centrally organised but realises it cannot make realtime decisions throughout it's territory. Central government makes policy but leaves the actual governance of the people in any given province to the locals. I don't know about establishing an empire using this model but once in place it could cover the whole world as round-trip communications are going to take on the order of an hour and a half to two hours. Transferring people and equipment around to respond to crises is only necessary within or at most across to a neighbouring province so transport speeds stop being a handicap.

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  • $\begingroup$ That sort of system can't last. What control does the central government use to ensure its policy is being followed? At some point someone is going to realize that aside from a sternly worded letter there's nothing the government can do if a province tells them to take their policy and shove it, because it will take years for any kind of military force to arrive to enforce governmental will. $\endgroup$ – Keith Morrison Feb 9 '18 at 16:27
  • $\begingroup$ @KeithMorrison Nothing lasts forever. The, loyalist, neighbours in the next province over can actually field an effective military force within at most days so unless the "shove it" policy is widespread order can be restored at gunpoint very efficiently and rapidly but the point of the decentralised system is that the government rules by consensus not by military might. $\endgroup$ – Ash Feb 13 '18 at 11:24
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The real issue is how do you keep them at WW 2 level of tech for longer than a few years. As soon as you have hundreds of millions of Earths linked by telegraph lines the pace of technological change will become unbelievable.

As for the max size of the empire, ancient empires seemed to max out at a few months of travel time (3 to 6? Something like that. Mesopotamia was too far to be ruled from Rome. Scale that to the speed of travel in WW 2 and you have half of an answer).

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