There is a growing group of people who believe the world is over populated. I want to push back against that mentality a little bit, because we should not resign ourselves to hopeless thinking. There are plenty of things we can do to improve our situation before resorting to dramatic actions. I want to avoid "there is no other solution" like thinking. Once we stop looking for other solutions, it will become a self-fulfilling prophecy. That is what I mean by lazy and morally hazardous.
It is not lazy to try to control population growth, it is the only viable longterm solution because technology can not solve this problem. The goal must be to stop population growth or, for practical matters, increase the doubling time at least to the order of millennia. That is why I gave the example with colonizing the Milky Way, to make clear how bad the problem is and how infeasible technological solutions are.
less desirable options: uncontrolled global civilisation collapse with rapid decline in living standards and population, nuclear war, etc
more desirable options: intentionally adjusting lifestyle / affluence in western countries, non-coercive methods of population control (e.g. better healthcare, increased access to family planning, increased opportunities for women to participate in education / economic activity, etc), less focus on short-term appropriation of wealth
One could ponder whether it would make sense to use population control in addition to improved technology and development to make the ride across the world population peak smoother, to make the peak lower and happen earlier. There would almost certainly be at least some benefits to this, but given how long political debates about that would probably take, never mind implementing and enforcing the decisions, there might actually not be enough time to do this and get some noticeable impact out of it.
As long as it looks like the world population will peak around the end of the century, go for technology to make it as pleasant as possible, but if the outlook indicates that the world population does not peak or at least stabilize in the foreseeable future, then population control is really the only way or it will become pretty unpleasant as you indicated in your first scenario.
Is there a recognized exhaustable availability of resource X? Then we simply don't allow that resource to be used as a means of capitalist value extraction from a planet. The resources belong to the commons, and we must shift away from allowing profits to guide the use of raw materials.
I look at, say, the last century of the automobile, and cannot avoid wondering just how different our lives would be if we'd bypassed the idea of placing a couple tons of metals and plastics in everyone's driveways. What else might we have used those materials for, if we mandated that using them had to be done in a way that benefited a large number of people with the same material cost. This really goes for nearly every consumer product made available to the markets.
I don't think we'll be able to come up with viable long-term strategies for handling population growth, and providing a high quality of life to all members of that population, until we move beyond status-driven consumerism and the capitalist economies that create and depend on them.
I'm obviously missing something in the figures you're using to calculate here, but how exactly would we consume all the galaxy's resources in < 3,000 years? We've been doing our thing on Earth for more than 3,000 years, and there are still resources available.
I'm not disputing that we consume far too many resources in a very irresponsible fashion. That just seems to me to be a very much higher rate of resource consumption than we've seen historically. Surely, if we were to develop the ability to colonize other planets, we wouldn't reproduce the same wasteful resource consumption patterns and history, because we'd have greater technology and, more importantly, improved philosophical outlooks on how we use those resources. Are you thinking we'd move 100% of the human population to each new planet and just set up the same wasteful shop we have till we exhausted the planet? I'd expect moving a smaller portion of the population to each new place, and setting up a far less wasteful colonization effort, that itself would continue to improve (hopefully).
With a population growth rate of 1 % per year the population doubles every 70 years. 2685 years are about 39 doubling periods which means that the population will increase by a factor of 549,755,813,888 over this time and if we needed on Earth at the beginning we then need that many Earth-like planets or the entire Milky Way under my assumptions of 400 billion stars and one inhabitable Earth-like planet per star. This assumes no further or at least only negligible technology advances over those 2685 years, i.e. we do on the new planets what we did on Earth when the carrying capacity of Earth was reached, but which we assumed was the best thing possible at that point in time.
Exponential growth is really that bad and 1 % per year is a pretty high growth rate. We could never have sustained such a growth rate for extended periods. We only surpassed 1 % per year in the early 20th century, before that it was a lot lower. My entire point was to demonstrate that exponential growth with 1 % per year is so huge that it would grow beyond any realistic resource limits in pretty short time. Decreasing the growth rate by a factor of 10 to 0.1 % per year will only increase the doubling time by about a factor of 10 and we would still reach the carrying capacity of the Milky Way in relatively short 26,728 years. Stabilizing the population at some point is really the only option, exponential growth can not possibly work besides with growth rates that are essentially zero.
Which population is that? Certainly not humans.
[1] http://history.stackexchange.com/questions/17465/yearly-popu...
[2] http://faculty.econ.ucdavis.edu/faculty/gclark/210a/readings...
[0] http://news.nationalgeographic.com/news/2014/09/140918-popul...
And, because you mentioned the end of the century, there is still »The Limits to Growth« and it predictions. I am actually not sure on which side I am here. I can't really imagine a collapse of society as we know it in the second half of the century but I am also aware of the sudden and unexpected behavior of complex systems and how hard it is to counteract a system with a lot of inertia. But if the predications come true, population control may become an issue sooner than we like.
http://www.google.co.uk/search?q=human+population+growth&prm...
Except there isn't a sprawling amount of resources for an exponentially growing population. Let's say we reach the resource limit of Earth and start reaching for the stars to find new places to live. If we can colonize one Earth-like planet around every single star of the 400 billion stars in the Milky Way, we would run out of places to live after 2685 years if the human population kept growing at a rate of 1 % per year. That isn't even enough time to reach all places in the Milky Way even if we could travel at the speed of light. Actually you could barely cross 2 % of the diameter of the Milky Way in that time. Exponential growth is unsustainable. Period.