In a celebrated scene from the 1987 movie The Princess Bride, a fierce battle of wits takes place between the evil Vizzini (Wallace Shawn) and the masked hero, Wesley (Cary Elwes).

Boasting how smart he is ("You've heard of Plato, Aristotle, Socrates? ... Morons!"), Vizzini is convinced he can logically figure out which of two goblets of wine carries the deadly toxin iocaine.

Brimming with confidence, Vizzini takes Wesley through his reasoning process: A clever man would put the poison in his own goblet, because he would know that only a fool would reach for what he is given. But Wesley would know that Vizzini could figure that out, and would therefore choose the goblet in front of him. On the other hand...

After continuing the argument for several minutes, Vizzini triumphantly snatches the goblet in front of his antagonist and drinks, as does Wesley. While boasting about how clever he's been, however, Vizzini drops dead. Wesley had poisoned both goblets. He had spent several years building up resistance to iocaine, and thus remains completely unaffected by it.

Wesley's stratagem is a classic illustration of smart-world thinking trumping analytical reasoning. Vizzini, for all his logic, never even considers the possibility of creating immunity to the poison. It isn't even on his radar.

Business has been well served by analytical reasoning. It lies behind everything from ERP and CRM systems to strategic decision algorithms to the "rational choice" model that supposedly explains the behavior of homo economicus.

But as I point out in

Smart World: Breakthrough Creativity and the New Science of Ideas

(Harvard Business School Press, 2007), as the knowledge economy morphs into the creative economy, and the digital infrastructure of our "flat" world rapidly accelerates the pace at which innovation happens, leaders badly need to master more inventive forms of thinking.

Whether it's a matter of stimulating entrepreneurial teams to create the Next Big Thing, figuring out how to exploit an emergent opportunity, or visualizing future developments that could help or seriously hurt the company, leaders can no longer rely on analytical/quantitative methods that try to predict the future by extrapolating logically from the past.

When we look at examples of scientific, technological, commercial and artistic breakthroughs -- the discovery of DNA, the rise of the personal computer, Barbie, supersizing, Frank Gehry's architecture -- we typically find the same set of mental capacities: intelligence, imagination, intuition and insight, or what I call "the 4i's."

Mattel executives, for example, fiercely resisted Ruth Handler's initial concept of an 11-inch adult doll. Market analysis showed that what little girls wanted to do was play mommy -- hence the huge market for chubby baby dolls.

But Handler, watching her daughter play with paper dolls, intuited that girls also liked to fantasize about their future life as adults. Intuition turned to insight when she encountered a quasi-pornographic German doll and realized that sex, in the form of a curvaceous figure and glamorous outfits, would be an irresistible sales factor. She was right, of course. Barbie is now a $3.4 billion global industry with brand recognition on a par with Coca-Cola.

The stumbling block for leaders who'd like to think more creatively -- more like Wesley and less like Vizzini -- has partly been a misleading conception of reality. The value of analytical reasoning is based on the assumption that it reliably reveals -- and predicts -- the objective structure of a rationally organized world that we all equally share.

But the teenagers who flocked to MySpace and YouTube were responding to novel, emergent idea-spaces -- user-generated content, social networking and digitally-driven popularity enhancement -- whose convergence was largely confined to their world.

Recognition of the patterns of social intelligence -- collective ways of knowing and behaving -- embedded in these spaces demanded of entrepreneurs and early adopters alike not logical extensions of the familiar, but imaginative, insightful embracing of the radically new.

We live in a smart world, or rather a series of such worlds, each embedded with its own unique patterns of social intelligence. Whether we're entrepreneurs bent on creating a breakthrough or leaders anxious to avoid getting blindsided by an unanticipated development, the key to success lies in thinking based on the 4i's rather than on rational analysis and quantitative prediction.

The reason is simple: Apprehending and insightfully exploiting patterns of social intelligence requires holistic rather than analytical modes of thinking, and that's exactly what the 4i's do.

Fortunately, a new science is coming to our aid. Patterns of social intelligence linked to the invention, development and consumer uptake of breakthrough products and services can be interpreted as interconnected webs whose dynamics follow well-established laws and principles of network science.

The creation -- and success -- of the iPod, YouTube and Nintendo's Wii game console, to name just a few recent examples of breakthrough creativity, can all be understood in terms of various interactions of the laws of fitness, hot spots and tipping points.

In all, I identify nine principles of networking in

Smart World

that govern creative breakthroughs.

In today's creative economy, relying solely on conventional analytical reasoning could be the equivalent of drinking from a poisoned chalice.

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Richard Ogle is the author of "Smart World: Breakthrough Creativity and the New Science of Ideas." (Harvard Business School Press, 2007). He can be reached

here.