Read this article trying to estimate the minimum population necessary to maintain a society at our current level of technology. It does require a great deal of labour and expertise; almost everything manufactured today has computers in them, and someone has to have the knowledge of how to produce and calibrate every one of them, not to mention manufacturing the rest of the product. In addition to the labour and expertise necessary to manufacture everything, you must maintain that level of education across generations, so teaching the next generation requires labourers in education in a proportion to the current population. The article also points out that we can provide all the food we need with less than 1% of our population. (This is probably the most significant change in human society ever, since it frees up about 98% of our population for non-agricultural purposes)
The estimate is based on the current population of industrial nations. It basically says, "The population of the EU plus the US plus Japan is X, and they are roughly self-sufficient, so that's roughly what's necessary to perpetuate the technology level." The article ended with bounds of 100 million to 1 billion people, with a surprise ending insisting that any Martian colony must have at least 100 million to survive at our current level of technology.
This is wrong for several reasons. First of all, any Martian colony will exist with an Earth capable of communicating with it. With modern developments in telecommunications, automation, and manufacturing from digital instructions, the vast majority of intellectual processes could be off-shored to administrators back home. The article completely ignores the benefits of communications with another society. To meet the author on his own terms, I'll do the same for the remainder of the article. (I'll also ignore assumptions like the idea that there will be a 1:10 staff:student ratio in this theoretical society, there's no reason that it must be 1:10 instead of 1:20.*)
The central problem is his theory that the current population of the industrial world reflects (in some ratio) what is necessary to maintain the technology level**. This ignores the fact that the vast majority of human labour is unnecessary.
We live in a surplus economy, everything is produced in numbers grossly more than needed. Things aren't just produced in too-large numbers, they're also produced in too-large varieties. Our society only requires about 3-5 non-industrial automobile designs, (Small car, large car, SUV type car, truck for hauling things, etc.) but we have thousands. All this waste produces huge inefficiencies, which means that the persons responsible for producing those products could be removed from society with no harm to the technology level. We don't need people designing a new model of car every year, and we don't need people manufacturing a car for each person on the planet. If we put an emphasis on producing things that lasted as long as possible, and recycled materials aggressively, we could save labour than I can imagine.
So a large fraction of industry could be eliminated, but this is nothing compared to the vast swathes of our society that produce nothing at all. First, let's kill all the lawyers. Not really, but let's get rid of most of them in our theoretical society. Also into the dustbin of history can go products of fiction, like advertising, "alternative" medicine, real medicine that deals with superficial ailments, most people in the "news entertainment" industry, self-important bloggers, art, and any product that serves as a status symbol.
Even larger than our producers of nothing are our producers of marginalia. There are endless products in our society that technically serve a function, but could be effortlessly removed without a loss to society or technology. A glance around any room in America should confirm that thought instantly.
Inefficiencies are rife in our society. The article cites the civil aviation industry as requiring half a million persons to maintain. This ignores the fact that a well planned society wouldn't need one, and even if it needed some aviation, it certainly wouldn't need as much as we have now. All transport of persons in planes is unnecessary. Eliminate all personal transport from the aviation industry, and I think you'll find it doesn't need anywhere close to 500.000 people to maintain. Additionally, on Earth, planes may, arguably, be necessary to transport rare materials to manufacturing centers, but of course there are no oceans to cross on Mars, and rail could reach any place on the planet with equal ease.
I could go on about how our urban sprawl and distributed manufacturing centers create waste at every level of society, but this post is already too long and boring.
Instead, check out this reaction to the same article.*** It seems to be against reducing the world's population, but doesn't summon up much of an argument, "If 85% of the world's population disappeared, leaving only 5 million Nigerians, but everything else in the world's economy society was exactly the same, Nigeria wouldn't have as good an economy to export minerals to the industrial world!" This is a bad argument for two major reasons. First, it's absurd to assume that trade with other nations would be the same despite a world population drop of 85%. Second, Nigeria isn't a very good example of a "very poor nation" It has a "middle income status" according to the Worldbank, and has many industries and exports****. If you want to find an economy that wouldn't suffer from reduced population, try anywhere that has subsistence farming, like Europe before and after the Black Death.
Before the Bubonic Plague, Europe's population was so large that labour was incredibly cheap, which meant that no one would bother to invest in technologies to make labour was more efficient. Inefficient farming meant that farmers couldn't produce much more than enough to feed themselves, and farms had to spread into marginal territories, where farms were even less productive. With the death of 1/3 of the population, it was no longer necessary to cultivate marginal farmland, and the value of labour increased to the point where improved ploughs and farming techniques were rapidly adopted. This enormous loss of life resulted in an unprecedented improvement of every measure of well-being for the succeeding generations.
*Come to think of it, that 1:10 faculty:student ratio is a big variable. Of the 100.000.000 people in this minimum society, about one in eight will be a student in K-10, which means that one in 80 will be educating them, not to mention college level education. Tweaking this number even a little creates huge changes.
**After writing this, I looked back at the article to discover that the lower bound, 100 million, has no justification whatsoever. Only an allusion to the number of people necessary to maintain a civil aviation industry. I can't hope to rebut an argument through assertion, but I'll leave the rest of the article up, since our society is still worthy of analysis.
***An interesting detail about this article, it jumps from "maintaining our level of technology" to "maintaining our standard of living". Of course, they're not even close to being equivalent. After all, we could eliminate all subsistence farmers from the planet without harming our level of technology, and resulting in a net increase to our standard of living. To be fair, he may be changing the subject, not saying that they are the same thing. Also, "standards of living" and "quality of life" often are treated as the equivalent to "money spent on my benefit". So long as you're out of crushing poverty, money has very little relationship to happiness.