What does this mean for making decisions in real life? Research suggests that neither nose-in-the-spreadsheet rationality nor pure gut inspiration is right all the time. The best approach lies somewhere between the extremes, the exact point depending on the situation. Naresh Khatri and H. Alvin Ng, of Nanyang Technological University in Singapore and Massey University in Wellington, New Zealand, surveyed nearly 300 executives in the computer, banking, and utilities industries -- meant to represent three different degrees of business stability -- and then compared what executives said about their own decision-making styles. Intuition was clearly the favored strategy for computer-industry execs. Planful approaches were the norm in the relatively staid, rules-driven utilities industry.

In a similar vein, Dave Snowden, director of IBM's new Cynefin Centre for Organisational Complexity in Wales, suggests basing your approach on the nature of the problem confronting you. Snowden breaks problems down into four types:

The problem is covered by rules. This is the domain of legal structures, standard operating procedures, practices that are proven to work. Never draw to an inside straight. Never lend to a client whose monthly payments exceed 35 percent of gross income. Never end the meeting without asking for the sale. Here, decision-making lies squarely in the realm of reason: Find the proper rule and apply it.

The situation is complicated. Here it is possible to work rationally toward a decision, but doing so requires refined judgment and expertise. Building an automobile, for example, is a complicated problem. You can diagram it; you can assemble and disassemble it; if you remove a piece, you know the consequences. This is the province of engineers, surgeons, intelligence analysts, lawyers, and other experts. Artificial intelligence copes well here: Deep Blue plays chess as if it were a complicated problem, looking at every possible sequence of moves.

The situation is complex. This sort of problem can't be resolved by rational analysis. Too much is unknowable. Complex systems -- battlefields, markets, ecosystems, corporate cultures -- are impervious to a reductionist, take-it-apart-and-see-how-it-works approach because your very actions change the situation in unpredictable ways. "Complexity is coherent only in retrospect," Snowden says. With hindsight, for example, the malevolent lines leading to 9/11 are clear, but it would have taken pure luck to see them beforehand.

The strategy is to look for patterns at every level, Snowden says. Or rather, the idea is to allow patterns to surface and trust your gut to recognize them. That's how masters play Go, a game that artificial intelligence can't seem to understand. They don't so much analyze a game as contemplate it. When a pattern or behavior emerges, they then reinforce it (if they like it) or disrupt it (if not).

In the realm of complexity, decisions come from the informed gut. Karl Wiig, a consultant who runs the Knowledge Research Institute, and Sue Stafford, who heads the philosophy department at Simmons College, saw this in action while designing systems for insurance companies. "Insurance underwriting software is good only for simple cases," Stafford says. Plug in the data -- married white male, age 30, driving this and living here -- and get a quote. Hard cases -- the diabetic actuary who skydives and teaches Sunday school -- need human underwriters, and the best all do the same thing: Dump the file and spread out the contents. "They need to see it all at once," Stafford says. They don't calculate a decision; they arrive at one.