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So, given the following assumptions and starting criteria:

  • The colony ship comes from a human culture that is about 100 years advanced from the present.
  • The amount of initial colonists are around 5,000 people.
  • They bring with them many specialists and libraries of information about known technology.
  • They have enough supplies like clothes and food, and heavy equipment to bootstrap a town and provide it with the essential facilities like clinics, schools, farms, governments, labs, simple manufacturing, etc.
  • They have power sources with long-term fuel sources, such as fusion and solar, that will last for ~100 years before they have to build their own electrical source.
  • They have survey equipment to begin mapping out resources.
  • They have two satellites to help them find resources.
  • Their form of transportation for supplies are heavy ground vehicles.
  • All vehicles are electrical.
  • The relative spread of resources is similar to Earth, but let's say that their landing zone was selected due to a relative abundance of basic metals and farmland.
  • There is no resupply from Earth.

...how long might it take this colony to become fully self-sustaining such that they could create their own vehicles, supplies and technology on the level of the stuff that they brought with them and perhaps even build their own ships to begin exploring the stars?

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    $\begingroup$ I'm not sure your question is answerable (yet i'm curious about the results!) One thing to note, though, is that an existing infrastructure can be a hindrance to progress, so i think the one limiting factor is how fast can they be enough people. $\endgroup$ – Burki Jan 25 '18 at 16:59
  • $\begingroup$ What kind of extraction equipment do they start with? $\endgroup$ – Ash Jan 25 '18 at 17:02
  • $\begingroup$ @Burki That makes sense. Children have to grow up and receive education and apprenticeships. Population growth might not be linear, unless there are some agreements that people are going to make babies (or it's supplemented with some kind of Brave New World-esque lab babies.) $\endgroup$ – zazen Jan 25 '18 at 17:04
  • $\begingroup$ why on earth would htey wait 100 years to build their own electrical source water wheels or solar collectors can be built relatively easily. $\endgroup$ – John Jan 25 '18 at 17:06
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    $\begingroup$ The minimum is the time needed to reach a population of about 100 million; a population much smaller than 100 million cannot have technological parity with Earth as it is now, much less as it will be in the next century. Technology is made up of very many very complex very specialized fields, and for technological parity you need to have true experts in all of them. Note that currently there is no country on Earth which has technological parity with the entire human civilization. $\endgroup$ – AlexP Jan 25 '18 at 17:14
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~1,000 years

By modern technology I am assuming you mean enough to support a full space program, which means you need a very large country worth or people, which is a lot of infrastructure. Building and maintaining modern technology requires tens of millions to hundreds of millions of people, many of them simply maintaining the other people. That is really going to be the limiting factor, the number of people and specialized labor you have.

Human populations can grow at about 2% a year under ideal conditions (max ever recorded) so using A=Pe^(rt) you are looking at 380 - 500 years at minimum.

But realistically you are looking at 1,000 year as a safe minimum because growth will be anything but ideal without modern infrastructure. Plus this assumes a single mindedness you will never achieve with humans, the population estimate should probably be larger since people will tend to form factions which will create a lot of redundancy.

handy compound interest calculator to put in your own numbers.

EDIT : had to recalculate, the online calculator is using "R" and not "r" which makes a big difference.

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  • $\begingroup$ This seems like a long time. Maybe the idea of technological parity is too broad—specifically perhaps just being able to (with pre-existing scientific research, and after building an infrastructure to create electronics, metal alloys, etc.) re-create the technology that they know about. They will have brought records of and some experts in existing technologies and can teach those things to their children. They wouldn't necessarily need figure it all again from scratch. $\endgroup$ – zazen Jan 25 '18 at 17:30
  • $\begingroup$ I am actually assuming they do not have to discover anything and just need the requisite labor force. consider how many specialists it takes to build one MRI machine then how many it takes to support one technician, then consider you need many of them, and that is just one isolated piece of tech. Technology is reliant on large populations. $\endgroup$ – John Jan 25 '18 at 17:36
  • $\begingroup$ This is why I linked the calculator so people who want to try different end populations sizes can and I recommend growth factors around 1-1.4%. $\endgroup$ – John Jan 25 '18 at 17:41
  • $\begingroup$ Maybe there's a point where the population and the technological needs are more balanced? So, on Earth, we need that a high level of population to support technology because we have a global civilization. We also have a lot of areas of specialization because there's no focus. Maybe with this civilization, if they specialize with technological aim to eventually reach the stars again, maybe they will have less branches and items of technology to maintain. With the interest calculator (if I'm using it right), there could be ~1.2MM people in 500 years at a 1.1% growth rate. $\endgroup$ – zazen Jan 25 '18 at 17:57
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    $\begingroup$ This is the right answer with the wrong scale. The tech mountain does require an obscene number of people to support the luxury of high technology. However, that 2% is under "normal" circumstances where breeding isn't culturally maximized. My A to another Q suggests 1/4 Mil after 100 years. A memory inefficiency won't let me run it past 115 years and I'm too lazy to fix it, but it suggests more than enough people in less than 1,000 years. $\endgroup$ – JBH Jan 25 '18 at 18:19
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It depends, but approximately 350 years is a good estimate

As @Burki mentioned in a comment, the big hindrance will be how long before they have enough people. They will also need time to set up infrastructure and simply build things up, but with technology 100 years more advanced than ours and without many of the current problems built into our world that are slowing us down in some ways that will be child's play next to simply getting enough people.

While an approximate, I will say that "enough" is roughly 100,000. That is somewhat arbitrary of course, but that is enough to constitute a genuine city with diversified labor and a full culture and enough they could readily spare another 5,000 to go to another planet and repeat the process.

There are many factors that go into population growth rates, but if we assume they are similar to current earth rates, we can expect the population to double roughly every 70 years. More details on the math as well factors that could influence are here among other places.

For 5,000 people to grow to approximately 100,000 - 120,000 at current growth rates would take roughly 5 doublings or 350 years.

This obviously is doing a lot of rounding and making a lot of assumptions, the biggest ones are:

  • That there are no enormous obstacles they need to overcome before getting down to really building civilization. If they need to really terraform an inhospitable world first it will be very different.
  • Their population grows at roughly current earth population. If they decide to put effort as a society specifically into population growth it could go substantially faster. Conversely if they decide to deliberately limit population growth for sustainability reasons or other reasons it might take much longer.
  • That 100 years worth of technological advances from today is enough to give them the necessary space travel and make building infrastructure somewhat easier than current, but not enough to radically change their capabilities from current standards in a relevant way.
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  • $\begingroup$ Interested to see if there are other perspective, but this makes sense to me. My gut feeling is 300-500 years, but I know that this is a complex question that would probably require a systems theorist and way more data to get a better guess. It's a story idea though, so I just want it not to have gaping irregularities. The population issue was not as clear to me before, so thanks to you and @Burki. $\endgroup$ – zazen Jan 25 '18 at 17:38
  • $\begingroup$ In this case the time scale is right but the population estimate is wrong. In my A to another Q I simplify the number of jobs that must be filled just to colonize, much less sustain a high technology. To put it simply, people forget the number of farmers, loggers, miners, and common laborers needed to run a society from the top of the tech pyramid. $\endgroup$ – JBH Jan 25 '18 at 18:23
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The answer really depends on two things, in my opinion at least; one how much extra-planetary material are they extracting? Two what kind of extraction equipment are they starting with?

The first can give a colony access to materials that are relatively scarce on planet and also may allow them to import material to planet in quantities that are impossible to mine efficiently. The example that is always bandied about is a moderately large Iron Type asteroid AKA a cubic mile of iron-nickel alloy, bringing that into orbit and chopping it down as needed could supply a colony with all the raw metal it needs for decades.

With the second point, extraction equipment, this is a case of the quality (meaning type) of equipment rather than how much they brought along. There are two types of mining machine "pickaxes" and "nanotech". In this case "pickaxe" refers to any piece of equipment that need human labour to produce and human labour to maintain, no colony is going to have the numbers and secondary equipment to support such equipment over the long (generational) term, nanotech is any extraction equipment that can take raw rock and produce finished goods without any human intervention, so called "Cornucopia Machines". Cornucopia Machines are self-repairing and self-replicating.

If you're talking Cornucopia type extraction then the day the colonists land they're already fully self-sustaining and have access to any form of technological artifact in the machine's database, which is probably everything invented before they left, and possibly in-flight updates. Barring elemental bottlenecks (where a particular substance is very scarce relative to industrial demand, like Neodymium in Lost in Transmission) you can have anything you want or need at the press of a button.

On the other hand if you're talking about hardrock mining their resources with existing, and irreplaceable, "pickaxe" equipment brought from home then they may never reach the level of their homeworld because they're going to wear that gear out before they have the labour pool and production equipment to replicate it and they'll never have the resources to do the work. They'll have to fall back on older methods, possibly as far as the stone age, and then progress anew. This is because, as has been mentioned in comments and answers, below a certain level of population the specialisation and division of labour to maintain and advance technological material culture breaks down. When it does cultures don't stand still, they revert, one of the ways around this in fiction is reduce the entire production chain from raw ore to finished consumer goods to the domain of a single, generally small, device divorced from human labour. Those devices are the Cornucopia Machines.

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  • $\begingroup$ Thank you for this answer. This makes a lot of sense. I hadn't considered a cornucopia machine. That gives me an idea for maybe a limited cornucopia device that could help take some, but not all, of the burden off of the colonists. I do want there to be an element of time for this colony of at least a few centuries, but not so incomprehensibly long that the culture might begin to look alien. At least not in this current iteration of the story idea. $\endgroup$ – zazen Jan 25 '18 at 20:32
  • $\begingroup$ @zazen If you went for nanotech resource extraction but human labour processing you would still need the population run-up but you avoid much of the risk of reversion due to insufficient population, you'd have materials on-tap to make anything that the population could maintain that way. $\endgroup$ – Ash Jan 26 '18 at 14:31
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It can be 500 years, or it can be 5

The big unknown here is how our technological level would advance in the next 100 years towards the beginning of the story.

At present, the major limiting factor is colony's population. To achieve a full technological cycle, a colony would need to implement extraction of raw materials, their processing, manufacturing, and possibly recycling. And, to get somewhat to the parity with Earth, it has to be done in dozens of industries. Even if the colony has all parts and materials to build mines and factories for everything - from iron to computer chips, it wouldn't have manpower, even closely, to operate all of those facilities. It would need a population of at least 1 million to cover all the bases, and, without resorting to cloning, it would take a couple of hundred years to get there. Consider then that they, realistically, are not going to have all parts and materials to build their infrastructure - thus they would have to build everything from scratch - and my estimate is doubled to 400 years. And then, the Earth would not likely stand still for 400 years, so the colony would need to catch up to the new advances, which make the whole process even longer, so I would look at 500 years.

However, it does not have to be that way if AI/robots can come to the rescue. Imagine that starting tech level is high enough that we don't need a single live human to operate a factory. In that case, population is no longer a limiting factor. The colony can build any facilities at will, and have them operational in no time. So, if they can put robotic builders at work, in a few years the colony would have a full spectrum of mines and factories, all working with minimal supervision. Mission accomplished.

P.S. My minimum estimate of "1 million" assumes that the colony is run military-style rather than as a free economy. Also the assumption is that 5,000 starting colonists are all in working and childbearing age, and generally are in good health.

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It heavily depends on the evolution of the social stratification and relationships with motherland.

A colony such as the one envisioned is bound to have a very different development compared with "classic" colonies (e.g.: Greek colonies or European "conquests" in New World).

Main differences are:

  • Long distances might mean low-to-nil contact with motherland.
  • No "aboriginal" population to trade/submit.
  • Much easier settlement due to modern building technology.
  • Possible unanticipated problems with local flora/fauna/chemical composition...
  • Better beforehand planning.
  • Lower fertility rate.
  • Higher health security and thus longer life expectancy.

What follows is in the hypothesis of an almost completely isolated colony.

In this condition it is highly likely the colony will start up working like a single "corporation", with a trustee board, and a strict hierarchical control structure.

This structure is bound to break apart sooner or later, as colony grows, giving rise to (almost) separate entities. The exact moment and mode of the breakdown will determine if and when the colony will be able to match motherland technological level.

Best scenario is:

  • Corporation holds together for several generations.
  • It starts several far-located sub-colonies.
  • Mother corporation grants complete independence to sub-colonies as soon as they can manage it.
  • Trade is encouraged on an equality basis.

This (somewhat) resembles political structure of Magna Grecia colonies. In this scenario it's likely the Colony should be in position to start R&D "departments" within a few generations and thus be able to "keep up" (somewhat) with motherland. Stabilization could be achieved in very few centuries.

OTOH worst scenario (barring utter colonization failure) is:

  • Original Corporation tries to keep everything under strict control.
  • Sub colonies are set-up as dependent branches with no autonomy.
  • Violent rebellion ensues with collapse of central authority and a centrifugal flight of low-tech splinters (far-west colonization).
  • Small settlements are left t their own devices wit no central coordination and little-to-no trust with "original colony".

In this scenario technology is going to fall hard and no resources for research are going to be spared for a long time (till population is in the tens of millions ballpark). This would follow our own world development model where large industries and associated technology improvements is fueled by "numbers"; i.e.: if you haven't a (very) large customer base. This might mean a couple of millenniums will pass without radical technological improvements.

Note: in the last scenario it's very likely colony will never get in par with motherland (unless communications get better) because in the meantime motherland technology would have improved and catching-up is not going to be easy.

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0 years (technology), or 350 years (industry)

The US was founded in ~1620 depending on your definition of founded. A bunch of colonies started popping up at that time. It took ~150 years for the colony to declare independence.

Meanwhile the mother country was going through an Industrial revolution. Even though the mother country was advancing quickly, the US was at least tied for second in technological advancement through the late 1700s into the 1800s. By the 1890s, you could say that the US had caught up; and by the start of WWI the US had the world's most advanced automobiles, tire rubber, steelmaking, etc. While the US never really 'passed' the mother country, it also never really lagged that far behind, technologically.

As far as industry goes; the US passed UK in population in the 1860s; and the German Empire in the 1880. Its per capita industrialization was already ahead of Germany's; and passed the UK by 1900. So it is safe to say that by around 1880; or 360 years after the first colonies arrived, the US was the foremost industrial power on Earth.

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