This is a really interesting concept that I encountered over the weekend. An "Out of Context Problem" is one that we encounter without any possible preparation of forewarning. For example, the Aztec Empire was at the height of its power, literally the strongest nation in their world, when the Spanish arrived. The Spanish had technology so far beyond the Aztecs that they could never have predicted or prepared to combat it. We've seen many versions of this particular brand of "Out of Context Problem" throughout history; the Romans versus the Teutons, American Colonists versus Native Americans, even the atomic bomb dropped on Japan.
In the late 90's there were a bunch of popular "apocalypse" movies that played off of the Out of Context Problem. Armageddon, for example, was a very popular story in which scientists discovered an asteroid that would destroy the Earth within some very brief time period (I think a couple of weeks). There was no plan in place for this possibility because it was not even considered a realistic possibility. A lot of sci-fi uses this idea; most alien invasion stories use it in some way or another. In Star Trek: The Next Generation the arrival of the Borg is a problem like this. In the real world, I think the September 11th attacks are a pretty decent example.
What I've been thinking about is how we can prepare for the arrival of an Out of Context Problem. Given the unpredictable nature of the problem (something so far out of our paradigm that we simply can't see it) it would be wasteful to attempt projections of possible problems, since we already do this as a society and the types of things we predict, no matter how far-fetched, are unlikely to be the problem we will face. Worst-case scenario preparation seems more viable, like the CDC releasing a zombie apocalypse preparation guide to teach people to plan for a variety of serious disaster situations. The problem is that there is only so much planning that we can do, and worst-case scenario preparation usually focuses on basic, day-to-day, and, most of all, temporary survival needs.
It seems to me that the one thing we can do to prepare for an Out of Context Problem is to become better problem solvers in general. This might seem a little obvious, but hear me out. Whatever the problem that comes up, it is going to be outside the realm of anyone's expertise, so we become more analytic and generalized learners and problem solvers. I'm not just talking about challenging problems though: asking a mathematician to solve highly complex calculus problems isn't an Out of Context Problem. Asking an English Teach to solve the same problem is closer to being out of context.
Being able to analyze information across diverse fields and use it to solve problems is a highly valuable skill that our very specialized education system seems to ignore. The people we will need to solve the problems we aren't even qualified to dream up yet are those who will not balk at the challenge of new concepts and ideas beyond the scope of their own experience and education.