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If we give them optimal conditions and the sole purpose of multiplying, it'd still take at least 400 years. 8 billion is a big number, but once it gets going, they multiply fast
It's an interesting idea, because it shows that the crazy ideas that Hitler had about breeding would not work. All the people outside the experiment would easily outbreed them, simply because there's more to begin with.
The same for populating Mars by breeding. Not going to happen. Earth could easily outnumber the Martians by sending a single ship in that timeframe. Whatever purpose colonizing Mars has, it'd be a waste of time trying to breed humans there.
Same thing for the fearmongering about Muslims outbreeding the European populations. Not happening. Whatever cultural differences we have today will be far gone by the time that the genetics of either group outbreed the other. It's like complaining about half the current population being descendants of Ghengis Khan. It makes no difference.
Um... 400 years is rather low. Even for optimal. But realistic is more like 1000's.
Hitlers idea was to keep killing the people with the wrong genetics for as long as it took. Hand him nukes and he could clear people a lot faster at the cost of getting some of those he wanted to keep. I bet he would have been willing to trade. Mars... no idea what you are talking about. No one has ever suggested mars could outbreed earth. Muslims... the fearmongering I hear is that they will pollute the culture by bringing their own. Don't need to outbreed for that. And mixing of cultures is a good thing, not a bad one. That is the real reason those people are wrong.
For most of history, people were dying of bullshit about as fast as they were made, especially the kids. OP didn't specify if that comes back, and a few hundred is what a premodern birth rate gives you without it. Relatedly, 15% of everyone who's ever lived is still alive, because growth has been so fast since we figured out how to stop, like, plagues.