I think you are criss-crossing two conversations here. China's population is NOT growing "like crazy" because they still have the 1 child policy. But their economy is certainly growing like crazy.
And have you ever asked yourself WHY an industrialized nation's population levels off? The answer is a) birth control, and b) women being freely empowered with the right to decide their own reproductive destinies. Women in Arabia have no say in birth control, and so the birth rate in that nation is a runaway train.
One more thing I'd like you to consider is "the exponential function." Are you aware of the dynamic and ever-upwardly-escalating numbers that result from exponential growth? And of the ramifications to human population when the exponential function is applied to human birth rates?
Yes, exponential growth will be stopped by something or other. Any ecosystem can only support so much life, and once there's a saturation point, there's either equilibrium, or cycles of growth and dying out. Fish in a lake is an example.
Even with space travel and unlimited resources, exponential growth of human population will reach a limit - even expanding in all directions at the speed of light (an algebraic function, volume expanding with the cube of time), mathematically exponential growth will eventually catch up to fill the volume, and then it WILL slow down.
The question isn't whether exponential growth of human population will stop, but when and how.
I hope we can sort out some sort of carbon nanotube space elevator to get round that. But - and I am asking seriously and not rhetorically, honest - what's so great about the asteroid belt? I mean, with a massive amount of investment we could pick up a whole bunch of minerals, but is that actually going to a) pay for itself b) do any good other than giving us a whole bunch of minerals>
Actually, the asteroid belt is a bit out of the way, orbit-wise, and it'll take a lot of energy to get that stuff into Earth orbit or wherever. There's enough little chunks of asteroids in near-Earth orbit that we could get first, as well as take chunks out of the Moon. We'll have plenty of time to get to the Asteroid belt.
As for what we'll do with it, presumably nanotechnology will have advanced to where the main need is atoms of the right elements to be able to make just about any physical product needed by humankind.
Dare I ask how one checks such growth?
You ask people pretty please to stop having so many babies.
When they don't. you feed them as best you can, knowing that not everyone will get enough to eat.
Or perhaps (I think likely) agriculture will continue to improve (perhaps we'll grow wheat in orbit or, ahem, on the Moon) and we WILL be able to feed mayne 20 billion people on Earth, but with warnings that we won't be able to feed 25 billion or 30 billion, and the big moral dilemma will be whether to add birth control chemicals to the food we're giving to those billions of people relying totally on the technology and generosity of first-world nations to eat.
