Yes, they are losing population, but not drastically. In the past decade, Japan has dropped from 127.8 million, to 126.8 million. That's less than one percent (it is 0.7% or so of the population, over an entire decade). In the long run, yes, you'd want to correct for it, but it isn't a situation to call for *forcing* people to have babies.
Expectations in Japan is that by 2050, Japan will be down to 60 million people. These predictions are being taken so seriously that Japan is currently changing its immigration laws to make it easier for foreign workers to work here. They are predicting massive worker shortages in very short order.
IOW, Japan is facing a very serious problem. And, one that a generation ship couldn't fix with immigration.
Do you mena that you dont read all of the sci-fi books about the ships that explode in space or get destroyed when they crash land on a planet? They usually have one great action scene at the start but I have to admit not much character development after that.
Ok, this? This was funny.
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As far as "no romance" goes. If all you're doing is exploring, there are far, far cheaper, more effective, and safer ways of exploring the universe than a generation ship. Again, no society invests a significant portion of its resources on exploration just for the sake of exploration. Expecting the people of the Earth to invest a significant portion of the entire planet's resources for a significant length of time, just so a tiny handful of people will get to explore the universe is just not going to happen.
And, again, if we're talking 5 billion years in the future when our sun begins to expand, well, at that point we're into Dyson Sphere territory. Heck, by that time, you could probably harness the sun itself as your propulsion system, creating a Dyson sphere around the sun to house a virtually infinite number of people (yes, it's not infinite but, a Dyson Sphere with a diameter of, say, Venus's orbit, would have a surface area of a (not a mathematician) crap ton of Earths. IOW, it might not be infinite but, it could at least wave at infinity in the distance.
