So, on contraception - you do realize that that's voluntary, right?
Now, in the United States it is voluntary, yes.
You do realize that you can't just put modern America on this ship, and have it succeed, yes? People will have to give up some of what we currently feel are rights, for the sake of the mission. You want humanity to reach another star, you have to give up a few things. If you aren't on board with that, you shouldn't be on board. We are talking less about putting just folks on here, and more about putting together a paramilitary organization, and putting it on board.
Imagine, for our purposes, that every person on this ship is a highly trained NASA astronaut - because they'd have to be. Start with that level of dedication and agreement to follow The Plan. You will have exactly zero problem finding 10,000 people who will agree to give up some of their reproductive rights for such a mission.
And, again, very few contraception methods are 100%. What are you going to do about "accidents".
Absorb them in the system. We are going to have some accidental, unexpected, unplanned deaths, too. The system will have to have wiggle room both up and down.
And, as far as innovation goes, well, show me a closed society with extremely limited resources and virtually no outside contact which has then gone on to display innovation.
You have outside contact. You're at sublight speed - radio and comm lasers will work just fine to reach the ship from Earth, and back again.
Even reaching Alpha Century means an 8 year turn around for any communication. Not going to happen.
You're not going to have personal conversations, no. But, you *are* going to get all the technical journals and design specs you want, beamed to you 24/7/365. There's probably an entire industry that grows up on Earth to design new things that ship (and, after that, the colony) might use. Labs galore doing R&D for them.
And, let's not forget, we're in a closed system with ZERO additional resources. Any resources lost cannot ever be replaced. So, how do you innovate, create, experiment, without losing resources?
You keep hammering on the fact that this is a closed environment. That means that unless you very specifically open the environment and throw things into the vacuum of space, you actually can't lose any resources. They're still in there with you! You simply have to have a method of reclaiming them - in other words, everything gets recycled. The reasons we don't do this on Earth are not technical - they are economic and cultural.
Note, on the notion of personal freedoms, I did mention upthread that if your generation ship is large enough, then my issues go away. But, even with a population of 10000, that would be extremely limited. And, frankly, if you can create a closed system for that many people, you have zero need for leaving the solar system.
It isn't like you get to dictate to me what size population "we" are talking about, dude.
No need?!? Let us be clear, there was no "need" for humans to migrate out of Africa - at the time this happened, the population pressure was not high. But we did it anyway. We expanded and explored every continent long before population pressures made it necessary. If you see no need to leave the solar system... that's your problem. I am 100% positive that, given the technical possibility, the biggest problem with finding 10,000 volunteers will be in culling down from the millions of applications you'd get.
And, by the way, if you can do this for 2000, I don't think you'll see any particular technical issues arise if you increase the population size by a factor of five. You can do 10K with just more of what you'd use for 2K, with probably a bit more economy of scale on your side for the larger group.
But, perhaps most importantly, if you are talking about colonization, then you want 10,000 on board. Not only does that make for greater genetic diversity in the breeding population (though you can overcome some of those limits with frozen gametes or embryos), but unless you posit humans gestated in tanks, your colony growth is limited by how many babies you can churn out once you arrive. With typical human population growth rates, it'll take that 2000 person population about 540 years to reach a million+. The 10K population can do it about 120 years faster.
