This graph, from the Defense Advanced Research Projects Agency, shows the exponential growth in possible outcomes for a range of activities, from a simple car engine diagnosis with 100 variables to war gaming with 1 million variables (that's what the 10301,020 represents).

The point DARPA is trying to make in explaining its Real-World Reasoning Project is that computers will never be able to exhaustively examine the possible outcomes of complex activities, any more than a roomful of monkeys with typewriters would ever be able to re-create the works of Shakespeare.

But in the recently completed Phase I of the Real Project, as it's called, the agency did discover shortcuts that can tame the punishing combinatorial complexity that for decades has stymied efforts to model the real world.

Beyond brute force

Bart Selman, a computer science professor at Cornell University and one of three DARPA contractors on the project, points out that for a decade there have been automated reasoning tools that can discover defects in chip or software designs. These tools can "prove" the correctness of a specification without exhaustively testing every situation the chip or software might encounter.