At a CCC Council meeting last week, a common theme emerged. The Army is "swimming with sensors and drowning in data". Biologists are considering trashing some of the DNA sequences they have already acquired because it will likely be cheaper to resequence in the future maintain the current data. We've been collecting tons of information, what should we do with it and if we don't have the tools yet to deal with all this data, should we bother keep it?
This reminds me of one of my favorite homework problems in complexity: Given two log-space computable functions f and g (the read-only input tape and write-only output tape don't count for space), show that the composition f(g(x)) is also log-space computable. The direct approach doesn't work for you don't have the space to store g(x).
The solution is to recompute the bits of g(x) as you need them. The lesson: When storage is expensive, it is cheaper to recompute what you've already computed. And that's the world we now live in: Storage is pretty cheap but data acquisition and computation are even cheaper.
So who says complexity has nothing to say about the real world?