I think you’re all missing two of the most important requirements - government, and the retaining and teaching of mathematics and the scientific method.
It was these three things that really kicked off human progress. Specifically, capitalism allowed for the formation of capital and the competition amongst individuals that led to advancement. And without the scientific method, your attempts at improvement amount to just flailing around wildly hoping to hit paydirt.
I assume we can retain and teach the scientific method. Government is much more iffy. Without a capitalist government, you’re going to have a hard time convincing people to come in out of the fields and work hard on inventing things that will not be of any personal use to them (or not enough use to make up for the lost time in the fields).
There have been agrarian communities that survived for thousands of years without almost any advancement. The ancient Egyptians, for example. People need an incentive to strive for more. In many societies that incentive came from religion, and that’s why most of the great works of these civilizations were religious.
Education’s a biggie. When you are scrabbling for existance, you simply can’t afford to give your kids a higher education. The books you brought with you will deteriorate. And without solid grounding in basic math, your calculus text will just be gibberish to your kid anyway.
Then there’s the problem of creating all the incremental technologies, which I think many of you are greatly underestimating. For example, making steel is not as simple as just finding some iron ore and applying the right mix of elements. How do you make a fire hot enough? How do you contain that fire? Wood is no good - a wood fire with a bellows might get you a soft pig-iron. So now you need to find coal. And once you find it, you have to be able to mine it in quantity, without steel. Not an easy proposition.
An example: people knew how to make airplanes for perhaps 70-80 years before the Wright brothers. But they couldn’t build them, because they didn’t have an engine with a high enough power-to-weight ratio. Current engine technology used steam to drive pistons, which was just way too inefficient. Then we discovered oil, but didn’t have the alloys needed to built lightweight cylinders that could withstand the heat and pressure.
Once those technologies became available, and the first light internal combustion engines became available, airplanes were inevitable, and in fact there were at least five or six under construction when the Wright brothers flew, all of which eventually did fly. Within a few short years, airplanes were all over the place.
So, having said all that, here’s my prediction: First, I think it’s highly likely that this colony would vanish without a trace. The odds of a small group of people starting from scratch surviving and prospering is pretty small, I think. Oh, some of their children might survive, but all knowledge would be lost.
If they do thrive (let’s say we drop them in the equivalent of the Nile delta, where food is plentiful, and easily-domesticated animals are abundant), then I think there’s a good chance that they will drop technology altogether and become complacent and lose their knowledge. You have to provide an incentive to strive.
But let’s assume that they are committed to regaining their lost technology, and live where food is abundant and they are relatively safe. So they have leisure time to try and regain what they lost. How long?
At best, perhaps 300 years. At worst, perhaps 1000. That’s all it took us, really. You can’t say that it took us 12,000 years to get to this point, because the vast majority of that time was spent in relative stasis. But once the double innovation of the scientific method and capitalism kicked off the industrial revolution, we made fast advances.
So, first generation gets established, builds a community, and builds enough of an infrastructure to guarantee that their kids will be educated. Perhaps they even find enough time to search out seams of coal and some basic iron ore. By the time they die, they have iron pots, horse-drawn plows, and the first factories are opening to manufacture things like garments, powered by water wheels.
Our community might even have a sewer system made of clay aquiducts, and a ready source of fuel for lamps (required to maintain an education, because school will almost certainly be at night after the work is done).
After years of nothing, this generation will be very proud of what they accomplished, and will die happy.
The next generation will make improvements in metallurgy, perhaps to the point of making steam boilers. This might get us a bit of electricity here and there, but it will be expensive and used only for mandatory research. This generation might even have enough food storage to allow some people to become full-time scientists and engineers. The pace of improvement would really pick up, and by the time they die, we might have the odd factory mass-producing things like horseshoes, cutlery, coins, etc. I’m assuming that some kind of capitalist government will exist, or all bets are off. Remember, these factories will be literally sweatshops. There will be people whos jobs are backbreaking, shovelling coal into a boiler all day, mining it, hauling it, etc. Without an incentive, they just won’t do it. I can’t stress the requirement of good government enough.
And so it goes - many improvements in steel are required before we can lay rails for transport, and before that you need huge factories to make locomotives, which implies a huge population and enough diversity to allow thousands of people to focus on such large-scale tasks. But until you have wide scale transport, you have a lot of duplicated effort, and very little trade, which means the economy stays very inefficient and the resources available to science and technology stay relatively small. Plus, as your population expands and relocates, they can take relatively few goods with them, which means they start from scratch. Look at the first pioneers out west - long after the people in cities in the east had electric light and trolleycars, the settlers were freezing in the dark and plowing the fields by hand. It was the advent of railroads that allowed people to bring their technology with them when civilization expanded. Until you get to that point, the pace of innovation will be very slow.
One major factor here is the size of your population. You need millions of people to sustain the diversity to make something like a train. You need experts in rubber, fuels, steel, construction, mathematics, geology, geography, you name it. This implies a huge population. So just by sheer numbers you’re looking at many generations into the future.
If this society breeds like rabbits and stays successful, perhaps 8 or 9 generations are required before we have that kind of population. And now government becomes even more important, because you’ll start having population pressure, and the potential for war and conflict that could stop advancement in its tracks.
Then there are the wildcards - a fire destroying critical books, floods, plagues, etc. Which is why I started by saying that the most likely result was that the colony would vanish in a couple of generations.
Fun topic!
