^ Yeah, the generation ship would have to be nothing but frozen embryos, because no group of people can be cooped up that long and not go nuts, and since the first or second generation would realize that it's 20 or 30 years back to Earth, and 4000 years if they don't turn around, they'll turn around, or at least stop (if reaction mass is only sufficient for one start and one stop), radio back, and await rescue.
The reason is that the early generation of people will look around and realize that for 4,000 years they can't expand. They can't really modify much. They can't go anywhere, they just exist. Their only purpose is to reproduce, die, and get recycled. Their children's only purpose is the same, ad naseum. It's too much for a human to face day in and day out, especially human parents.