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F. Scott Fitzgerald once wrote that one sign of a "first-rate intelligence" is the ability "to hold two opposing ideas in mind at the same time and still retain the ability to function." According to Roger Martin, a sure sign of a first-rate business intelligence is the ability to recognize two diametrically opposing ideas and meld them into a new model that is superior to either.

In his new book, The Opposable Mind: How Successful Leaders Win Through Integrative Thinking, which the Harvard Business School Press is due to publish in December, Martin sketches out the process by which innovators as varied as Procter & Gamble chief AG Lafley, choreographer Martha Graham, and Red Hat co-founder Bob Young used the constructive tension from two conflicting ideas to "think [their] way through to a new and superior idea."

Martin holds that design thinking is a critical component of integrative thinking. In a phone interview, he argued that designers often engage in abductive reasoning: they imagine what might be and act on that insight—even though they can't prove it. This was the first step that Isadore Sharp took when he imagined a new model for a luxury hotel—a model that gave birth to the Four Seasons Hotels and Resorts Ltd.

As Martin tells it, in the early 1970s, there were two dominant business models for would-be hoteliers: small motels offering a few homey frills at modest prices and large, downtown hotels with expensive amenities that catered to business travelers. Rather than follow the lead of most business strategists, which is to look at a decision as a series of "either-or" propositions and settle for the choice with the fewest downsides, Sharp held the two opposing models in his head, stared into the mystery of how to imagine a third way, and hit upon a design that would "combine the best of the small hotel with the best of a large hotel."

Sharp's new model for Four Seasons replicated the "at-home" feeling of the small hotel by being the first to offer shampoo in the shower, 24-hour room service, dry cleaning, and the like. Four Seasons replicated the efficiency of the office by being the first to install two-line phones and well-lighted desks in every room and 24-hours business centers. Sharp essentially redefined luxury as a service that temporarily filled in for both the home and the workplace. "By offering guests a distinctly different kind of service," says Martin, "Four Seasons could charge a substantial price premium."

Sharp couldn't prove that his new model would succeed until he actually built it—a key reason why many executives dislike talk of "design thinking." After all, it's a lot easier and safer to run a billion-dollar business than it is to invent one. And yet today, Four Seasons, with 73 hotels, is considerably larger than the next biggest luxury hotelier, Ritz-Carlton, with 59 hotels.

Successful designers often speak of having a "creative breakthrough." Perhaps what they're really describing is integrative thinking: creatively resolving the tension between two opposing ideas, as Isadore Sharp did more than 30 years ago.