What is the minimum number of people you need in order to maintain (not necessarily to extend) our current level of technological civilization?
Some loose thoughts.
(1) This is a badly formed question, for two reasons. First, we can't talk about minimum numbers to maintain anything unless we know for how long. A generation or two? Then it might not be much. A thousand generations? Indefinitely?
Second, there is no such thing as a "level of technological civilization". You see some of the absurdity of the notion in some of the commenters on the post, who take 'level of technological civilization' to be something that improves with every upgrade of Windows and every new improvement in cell phones and video game consoles. There is no single "level of technological civilization"; rather, there are levels of advancement for different technological fields. Civilization, even considered purely in terms of its artifacts (which is what we are doing when we are talking about 'technological civilization'), is an immensely complex thing even in very simple societies. When one artifactual lineage is progressing, another may be degenerating, and yet another may be static. Indeed, that's exactly what we have in any civilization. If you are talking basic, important for living at all technologies, you're talking a fairly limited set of things: many of the basic tools -- hammers and screwdrivers and running water and gardening implements -- haven't changed their basic forms for quite some time now because they already do exactly what you need them to do, and could be had even in a fairly primitive society if the raw materials and the know-how were available. Some of these would be perfectly serviceable in more primitive forms, with the difference only being noticeable in unusual circumstances or when it comes to very specialized tasks. We could have cars with steam engines instead of gasoline combustion engines; they would have quirks arising from the use of steam engines, but they would do what cars do. If everyone has access to walkie talkies with good range and to public phones, how often are they likely to feel the lack of a cell phone? And we see things like this on a smaller scale even in our own society: the toys of Manhattan that rural farm boys in some backwoods Podunk Hollow mostly only hear and read about, and the perfectly serviceable farm technology of Podunk Hollow that no one ever uses in Manhattan, are all part of the same 'technological culture'. Manhattan might have flat screens and Podunk might have boxy cathode ray tubes; they are the same technological civiliztion. Manhattan might have cable internet and Podunk might have dial-up; they are the same technological civilization. Podunk may have the technology to sustain itself agriculturally from here to the end of time while Manhattan need to pray that it never has to try; they are still the same technological civilization. At least, if you're going to say that they're not, you are committed to saying that there is no such thing as 'our' technological civilization, and that the Joneses have a different level of technological civilization entirely: after all, they just bought the latest cell phone. And if you are measuring civilizations by whether they have iPads or not, you might take time explicitly to reflect whether this is actually an appropriate metric for entire civilizations.
I was going to say that there were three reasons why the question wasn't well-formed, but I spent so much time on the second that I forgot what the third one was.
(2) But even badly formed questions can raise good questions. It does seem that there would be minimum populations needed to sustain particular technologies from one generation to the next. Obviously you'd need enough people for a breeding population: to carry anything over to the next generation you need the next generation. And there is a very good argument to be made that as the population involved in learning goes down the chances that the population's overall ability to learn and use what the prior generation did decreases sharply. Large populations allow for lots of redundant learning; redundant learning increases the chances that the next generation will learn the particular thing that needs to be learned as well. Smaller populations of students increase the risk of loss through accident, stupidity, or laziness. And if the population of students is too small, it might well be impossible for the students, even if very bright and diligent, to learn even most of the relevant and important things that a larger population of teachers knows. Some technologies are labor-intensive: it just takes a lot of people to make them, handle them, maintain them, period.
I actually have a fairly strong interest in this on the ideas side: in particular, what minimum conditions are needed for the kinds of social learning that carry philosophical ideas from generation to generation in societies with various kinds of educational institutions. A very tough set of questions to answer.
(3) Stross tries to extend the reasoning to colonization, but colonization by its very nature is a different story, for a number of reasons. (a) The colonies that belong to any technological civilization are, by their very nature, closer to the Podunks than the Manhattans. They would represent the same civilization as it operates under colonial conditions, which are vastly more restrictive. They can't be Manhattans, which draw on a whole society over a long history; they are starter kits rather than cities relying on full-blown, built-up-over-the-centuries infrastructure. Trying to colonize in such a way that all one's colonies are Manhattans is an insane idea: building a Manhattan on Mars all at once is prohibitively more difficult than building a Manhattan on Earth over three centuries. (b) Colonies are not completely isolated from their sources; even if it takes years of travel to get to the colony, any sane colonization plan would involve stocking up the colony as much as possible with useful technology from earth, and then following with at least occasional waves of resources until sustainability could be achieved. Full autonomy of a colony will be a long way off, yes, but full autonomy is hard to achieve even on Earth; relative autonomy does just fine for most purposes. You don't need to supply yourself if you can find some way to barter and trade, and obviously that would be one of the first thoughts of any plan for colonization. (c) Why in the world would you care whether the colonies have the same technologies as long as they have what they need to survive? People on Mars would not be one whit worse off if they couldn't play Wii or drive Ford Fusions or use Windows Vista. They would probably be just fine if they all had landlines instead of cell phones, and they might be so rebellious as to refuse to go extinct for lack of WiFi.