Introduction
A common science-fictional scenario is the post-apocalyptic story, in which some war or disaster has destroyed civilization and the human race must rebuild from a low-tech foundation. And in real history, we see abundant evidence that civilizations are mortal: Toynbee (
http://en.wikipedia.org/wiki/Arnold_J._Toynbee) made a famous study of their life cycles.
This has led to a theory that humanity can never engage in the long-term colonization of any region (such as the Moon or the sea floor) which we could not survive in without an "advanced technology." The obvious analogy is made with the Greenland colony of the Vikings, which perished when Greenland became too cold for medieval European farming technology.
However, if one looks at actual history, one will see that the actual loss of a technology, especially in the sense of it being lost to all humanity, is very rare. For instance, while the technology of civil engineering definitely declined in the post 5th-century AD Roman West, in what became Western Europe, it remained in practice in the East. As Robert Wright points out in Nonzero, it is rare for anything important to be forgotten by the human extended mind (
http://en.wikipedia.org/wiki/Nonzero:_The_Logic_of_Human_Destiny).
Why is this?
Knowledge As Self-Replicator
Technology is a form of knowledge, and knowledge is a self-replicator, whose habitat is the mind. A useful piece of technology -- such as the principle of the wheel or how to smelt and forge iron into tools -- unless it fails to spread at inception -- will be passed on to many other minds, and thus spread so widely that it is very difficult to exterminate.
This is why, as we observe the passage of centuries, we see a steady rise in human technology. This rise is independent of the occurrence of "dark ages" -- in fact, since a "dark age" is the early springtime of a new civilization, a period in which the cold restraints of the winter of the last civilization have been slipped, technological progress may actually accelerate in a dark age, as happened to agricultural technology in the Western Dark Age of the early medieval period. It is easily noted that each civilization starts from a higher level of technology than did its predecessor (compare Europe in the 7th-10th centuries AD to Greece in the 10th-7th centuries BC) and rises to greater heights (compare the Classical Greco-Roman world of the 1st century BC to the American-Anglosphere-European world of the 21st century AD).
The Technological Ratchet Effect, and Cultural Competition
This is because any human culture is based upon certain technologies, which for this reason are important to that culture. These technologies will be strongly embedded in customs which ensure that they are taught to the next generations, and hence cannot be forgotten. What is more, because "human culture" is composed of numerous "sub-cultures" (or will fragment into such given protracted political breakdown), if by horrid mischance some human culture manages to forget an important technology, it will simply be outcompeted and displaced by other human cultures which have retained that piece of technology.
The important point here is to realize that we speak of humanity as a whole, and in terms of centuries or even millennia. It is quite possible for an important piece of technology (such as the construction of aqueducts) to be lost locally (as it was in Northwestern Europe following the fall of the Roman Empire) for centuries. But note that building aqueducts is only important if one wishes to build large cities, and it was precisely in Northwestern Europe that cities were of only minor importance for everything save imperial administration. In Southeastern Europe and the Levant, the technology was never lost, in fact was taken further with wind and water-mills -- and eventually spread back into Northwestern Europe, to aid in the rebirth of the cities in the High Middle Ages and Renaissance. The modern West builds water supply systems which are far more sophisticated and extensive than anything Rome managed at her height.
Think of this as a "ratchet" effect. A ratchet gear permits motion in only one direction: it is easy to push forward, but extremely difficult to push backward. The technological ratchet is somewhat less reliable than the mechanical one, but it makes forgetting a technology extremely difficult. In general, once anything important to a civilization at a time is discovered, it will not be forgotten.
Failed Colonies
But what of failed colonies? We can point to examples in which attempts to implant higher civilization failed: Late Classical Britain, Viking Greenland, and the like. Surely this could happen to humanity if we attempt to plant colonies on other worlds?
Yes, it could. But locally, temporarily, and only to a limited extent.
First, note that Late Classical Britain succumbed not to natural cultural decay (the withdrawal of Roman authority led to political fragmentation but not technological decline) but rather to a barbarian invasion (that of the Angles and Saxons). As for Viking Greenland, the problem there was a change in the climate: medieval Viking technology would have sufficed indefinitely to permit organized survival in the Greenland of the Medieval Climatic Optimum, but survival in the Greenland of the Little Ice Age was a much tougher proposition.
(Incidentally, climate change might have also been a factor in the fall of Roman Britain; note the extreme cold snap of 535-536, as described in
http://en.wikipedia.org/wiki/Extreme_weather_events_of_535%E2%80%93536. There was also a barbarian invasion in the case of Greenland, in the form of the arrival of the Eskimos).
Secondly, note that neither Britain nor Greenland remained permanently barred to civilization. The modern West has recolonized both territories, in the case of Britain producing a brilliant culture which proved highly-influential in the spread of the West worldwide; in the case of Greenland, at least rejoining it to the wider cultural sphere.
Finally, note that in each case the catastrophes were local. The fall of Roman Britain into darkness did not mean the fall of the Classical legacy everywhere; its survival in Italy, Gaul and Ireland, in fact, proved decisive in eventual the restoration of civilization in Britain. The fall of Greenland did not mean the collapse of all Scandinavian-derived cultures, nor even of Norse seafaring. Because the technologies survived elsewhere in the mass human memory, they could eventually replicate back into the regions from which they had been extirpated.
A Spacefaring Analogy
Imagine that, in the far future, humanity has colonized a star system possessing no planets habitable to unprotected higher Earthlife, such that the maintenance of artificial habs is vital to human survival. Assume that there are at some point six cultural zones in this system; call them Alpha, Beta, Gamma, Delta, Epsilon and Zeta. Each of these zones exploits various local resources, and trades them with the other habs.
Suddenly the star suffers a nova flare, causing great damage to the human civilization in that system. Alpha is caught directly in the flare and vaporized; Beta takes lethal thermal effects, and computers are scrambled throughout the system so that Gamma, Delta, Epsilon and Zeta all suffer losses of some of their knowledge. On Gamma and Delta the loss of knowledge is so extreme that people no longer know how to run the hab life support systems very well, and over the ensuing decades, most of the people in these colonies also perish. Epsilon manages to preserve life support knowledge through embedding in cultural ritual, and on Zeta they used superior hardened computers and hence very little knowlege is lost -- but with only limited trade from Epsilon and no trade from Alpha, Beta, Gamma and Delta, the Zetans are impoverished.
Now, what are the effects of what has happened?
Well, to begin with, the surviving cultures, Epsilon and Zeta, are clearly not going to be vulnerable to further nova flares of similar magnitude. They have already survived the worst, and learned to buffer their cultures against the deletrious consequences of such a nova.
Secondly, Zeta has both a clear motive and opportunity to attempt the recolonization of Alpha, Beta, Gamma and Delta. This may be slow due to limited resources, and of course in the case of Alpha there is a lack of infrastructure and Beta perhaps a lack of optimism about operations so close to a lethally-variable star, but such recolonization is inevitable barring an immediate recurrence of the catastrophe.
Thirdly, though the knowledge on Epsilon may be limited to bare-bones survival tech, it won't stay that way for long. The technologies lost to the nova flare will return, in the form of copies carried by Zetan traders; this is inevitable even if the Zetans don't want it to happen, because people will accidentally say too much, or deliberately defect: and in any case, the Epsilonians will be shown by example what is possible.
On Gamma and Delta, small populations may survive. We may suppose for the sake of argument that the population of Gamma completely fails (a "Greenland colony"), while on Delta ("Iceland") a small population persists using less-than-optimum life support techniques in straitened circumstances.
Eventually, the culture of Zeta becomes decadent and inward-looking, but not before the Epsilonians have learned Zetan technologies, perhaps from ambitious Zetan engineers who seek opportunities no longer available in their moribund society. Their culture reborn by the influx of Zetan ideas, the Epsilonians trade with both Delta and Zeta, recolonize Beta and Gamma, and eventually not only build new habitats in the long-lost Alpha region, but go on to found new colonies at Eta, Theta, Iota, Kappa and Lambda! And the new civilization, aware of the nova peril, hardens all its habs from the start, so that future novae will do far less damage to their economy.
How long does this take?
Who knows? Decades, centuries, millennia. The point is that something like this is fairly inevitable. And if things went worse in this system (call it Aleph), no doubt it would have been colonized from Systems Beth or Gimel. This or that pocket of a self-replicator may be extirpated, but extermination is far more difficult.
Conclusion
Science marches on. Technological progress is irreversible. Catastrophes are local, and recovery inevitable. Assuming that the human race is not annihilated, we have nowhere to go but up.