The question is,
In a world that is in chaos politically, socially and environmentally, how can the human race sustain another 100 years?Now, this is an awful broad question but it's also important, and could also taken as some sort of an inkblot test. I'd encourage everyone to actually plan out an answer, at least in their heads.
The first answer to appear was
They will live underground...which I found rather hilarious. :)
My answer, which is probably not as good as that, follows: it underwent a bare minimum of editing, for which I apologize in advance.
There is no simple answer to your question re: the next 100 years, as I'm sure you're aware. We will have to take it one step at a time. But as I see it our general strategy should be:
We need to convince the public, politicians, religions, and businesses that our species' survival is actually in doubt: there's too much inertia based on short-sighted self-interest otherwise. Perhaps a well-placed question to Ask Yahoo might generate some awareness of this issue. :)
Beyond that, we should enlist and provision our top forward-looking scientists (Lord Martin Rees and Ray Kurzweil come to mind) to chart out the least dangerous paths technology could take, and the top students of human nature to find ways to strengthen our society, to buffer it against future shock, and to find ways to give everyone- from suicide bombers to North Korea- some form of hope for a more prosperous future. The promise of a better future for one's children makes all the difference. We should also spend significant resources on innovative ways to encourage the best and brightest upcoming minds into thinking about the future.
The increasing destructive power of technology is perhaps our largest challenge, and there's no way to put the genie back in the bottle (see Kurzweil, "The Singularity is Near"). But we can do things to channel where future technology goes. A good first step is to enact well-researched, foresighted laws and procedures governing proliferation of bio- and nano-tech, and to stay ahead of the technological curve with our policies, contrary to what we do now. There are many regulatory agencies that are not well-structured for dealing with the future, and we must not blink in completely tearing them down and building better ones in their place.
I apologize for using a tired metaphor, but we should view getting ready for the future as an undertaking at least as large in scale as the Apollo Project. And as we get started preparing for the future and reversing the mistakes of the past, it'll all happen fast: to quote Al Gore, "The political system, like the environment, is nonlinear ... In 1941 it was impossible for us to build 1,000 airplanes. In 1942 it was easy. As this pattern becomes ever more clear, there will be a rising public demand for action."
The second step in channeling technology is to setup a world body to enforce the technology laws we enact, and to go along with this, build a more-or-less automated system, having many many cross-referenced inputs, to find and track any situations where people, institutions, and governments are not following our bio- and nano-tech proliferation policies. We have somewhat ham-fisted and ineffectual precursers to this in place, but we should get away from such a body being an arm of government and try to structure it more efficiently, thoughtfully, and transparently- perhaps a mashup of Google and CERN.
The third step is to increasingly augment this hypothetical proliferation tracking system with artificial intelligence and distributed sensors, because as bio- and nano-tech get easier to make, the capacity to track who can (and has) made what becomes more and more difficult. Maturing bio- and nano-tech will also make space colonization both easier and more imperative, as you have noted.
Beyond that, it's difficult to predict what will happen. A lot could go wrong- but we also can throw an unparalleled amount of resources, top talent, and cutting-edge theory and technology into making a good go at things. Once our society realizes we actually are in trouble, you'll be amazed at how much can be done so quickly. And as Lord Rees has stated, despite the dangers technology brings, "there are grounds for being a techno-optimist."
Let's not count humankind out just yet.