I wonder how much people we really need to replicate, sustain and exceed present levels of technology and culture (on another planet perhaps)?
Given that we allow every person to develop their talents of contributing to the productivity of the society. Not just being a wage drone or an unemployed drone.
My guess is: as few as a few million people today, hundred thousands when we figure out robotics.
I recall a reading very fascinating comment on Reddit a few years ago on this subject: if you want to maximise for maximum biological diversity at the lowest cost, the best option would be to have a small all-female crew, and as much diverse frozen sperm as possible (which is the most compact form of proto-human we got).
Then upon reaching the intended planet, fertilise every female with a unique cell. Repeat every generation until you run out of frozen sperm. Hey presto, biological diversity for cheap.
Of course, if anything this shows the problems with optimising for one variable at the expense of ignoring of all others.
By the threshold of technology you mention (intersteller travel to habitable planets) you would certainly have the technology to grow and maintain an artificial womb. So you just stock the ship with self-replicating printing machines that can deploy artificial wombs, and have millions of frozen egg / sperm to populate them.
Really though, at that point, you might as well send the learning AI robots instead. Fleshy emotional meat bags with difficult to replicate reproduction are a liability.
I wasn't talking about diversity, rather about how much people are needed to sustain and industrial civilization. Perhaps this number is much greater than number of people you need for diversity (several hundred people populated the whole pre-Columbian americas and they didn't have terrible problems with diversity)
At the moment? Large enough that it realistically can't be done. Millions and millions. Millions of tons of equipment, too.
Emerging technologies (nanotech...) may be able to reduce this, but for the moment it's perfectly realistic to consider scenarios where new colonies usually regress to 18th/19th century technology for a few generations. This, of course, makes colonizing uninhabitable planets such as Mars... hard.
Mars we could probably do, it'd just be costly. An interstellar variant? Not likely.
Given that we allow every person to develop their talents of contributing to the productivity of the society. Not just being a wage drone or an unemployed drone.
My guess is: as few as a few million people today, hundred thousands when we figure out robotics.