I think it highly depends how big you make the thing &indeed what are the living conditions. If the people living on the thing can go one with their life withou much hardship they might not mind - even here on Earth most people just go on with their life and are happy.

Yeah, right we are 300 hundred years from the target but & 500 years on the way but so what ? You go for somo zero-g polo, do some cooking and pottery classes with firends, maybe learn machining so you can help with ship maintenance and so on.

It is the same on Earth - you go on with your life knowing you will propabably not live long enough to see some far future projects to be complete, like the final form of the Hagia Sophia Catthedral or Half Life 3 release. And thats mostly fine ?

Even with enough space and great living conditions, there will be greedy people who will try to gain power by gating resources. There will be factions forming, there will be conflict, and fighting. You need too many people for all to feel like one cohesive social unit for 1000 generations, humans just aren't built that way.

And that's just conflict. What if an early generation decides to target a planet that's less useful re/ metals etc., but that's much better suited for human life? How can you guarantee they won't decide to change course as a gift to their descendants, without draconian measures against such ideas?

> Also as for changing course - that is in many cases impossible, at least unless you want to make it 100% certain that you will die alone in the coldness of space. Just too much energy needed to signficantly change the trajectory & starts, at least in our part of the Galaxy, being too far apart.

Sure, the later generations wouldn't have that choice, but the first few definitely would. You need to bring a ton of fuel anyway to slow down, and 1000 generations is plenty of time to increase fuel efficiency a little. So a minor change e.g. at generation 5 seems very much doable, unless you have concrete examples that prove otherwise.

> It is the same on Earth - you go on with your life knowing you will propabably not live long enough to see some far future projects to be complete, like the final form of the Hagia Sophia Catthedral or Half Life 3 release. And thats mostly fine ?

I'm not forced to live my entire life working towards the Hagia Sophia or HL3, with the choice to do otherwise being taken away from myself AND from 1000 generations of my descendants.

If I was on that ship, I'd vote to blow it up, just so those responsible won't get away with it.