Marshaling stories and studies, an expert advises us to stop worrying—to free our minds and conquer problems by approaching them from opposing angles.

It’s Not About the Shark: How to Solve Unsolvable Problems. David Niven. 240 pages. St. Martin’s Press.

David Niven has come up with an Alfred E. Neuman-esque solution to solving “unsolvable problems.” In the 10 crisp, interwoven chapters of It’s Not About the Shark, Niven cites data and draws analogies that show confronting a problem head-on, absorbing it and focusing intensely on it, makes the problem overwhelming and more difficult to solve. Instead, seeming to channel Mad magazine’s “what me worry?” cover boy, Niven advocates stepping back from the problem, ignoring it even, freeing one’s mind of it and coming at it from opposing angles.

Niven defines a problem as “a barrier. You have to bring it down, or it will bring you down.” After presenting dozens of examples to support his theme, he says: “When you have a problem, it plops down right in front of you. It’s so easy to see that it almost demands we look at it. But if your mind is open to opposites, that means you can be simultaneously flummoxed by a problem and yet maintain the belief that the problem can be solved. You can see the problem right in front of you but also see around it to what is next.”

The title’s shark refers to young Steven Spielberg’s struggles with his mechanical great white in the movie Jaws. Few remember that the mechanical shark was a dud, breaking down constantly, costing the studio bundles and wasting precious time on fruitless repairs.

The railway turned the nuisance water into a subsidiary that makes $75 million a year.

When the director analyzed his problem, he didn’t like his options but began to see another way of telling his story. It would be a movie where scenes implied the shark and didn’t show it. Thus Spielberg turned the problem inside out and found his solution, and the suspenseful movie about a killer shark you hardly see became a classic.

Indeed, Niven finds that opposites are big components of taking down a problem. He cites the work of psychologist Albert Rothenberg, who tested creative and non-creative people in word associations. He found that creative people responded often with words that were directly opposite of the test words. The creative group responded with opposites 25 percent more often than the non-creative group and gave answers 12 percent faster.

Niven tells another story about Japanese railway engineers trying to waterproof a tunnel through the treacherous Mt. Tanigawa. They could find no civil or mechanical solution that would not be off the charts fiscally. Then a thirsty mechanic made the serendipitous discovery that water burbling from the tunnel was incredibly delicious. The railway turned the nuisance water into a subsidiary that makes $75 million a year. Harvesting the water keeps the tunnel navigable. He writes: “The best-paid minds in the company furrowed their brows and closely studied the situation. But when you start with a problem at the center of your thoughts, you don’t consider the best possible answers—you fixate on the worst and most obvious obstacle.”

Niven’s formula for achieving solutions will be familiar to writers: Get down a first draft reflecting the knowledge you can quickly gather and then ultimately build on that base until subsequent drafts find the solution. In Spielberg’s instance, the first draft was the use of an incompetent killer shark that, had he deployed it, could have turned his masterpiece thriller into a campy screwball comedy. In its second draft, the piece became a shark movie without a shark. This notion was never found in the first draft’s “pile of first available thoughts.”

Similarly “Frank Sinatra Has a Cold,” Gay Talese’s Esquire profile of Frank Sinatra, contains few quotations from Sinatra because the difficult, often truculent star wouldn’t grant Talese an interview. So instead, Talese observed the crooner and his entourage at various settings while Sinatra was suffering from the title’s malady. His final draft captured Sinatra’s complexity and became a high point of New Journalism.

Niven’s mini-profile of Linus Pauling, who was lauded for integrating organic and inorganic chemistry with quantum mechanics and molecular biology, recounts the scientist’s belief that working nonstop on any project—a common approach to problem-solving—limited insights. To free his mind, Pauling liked to get away from the lab and office, and he recommended that others do this. His best thinking came in his bed as he drifted off to sleep.

Among numerous other case studies, Niven sketches the FBI’s search for Whitey Bulger and the elusiveness of the murderous Dr. Michael Swango to illustrate how overconfidence can be a detriment to solving problems.

Niven’s previous books, among them 100 Simple Secrets of Happy People, contain a strong dose of self-help. In this latest volume, each chapter closes with “The Takeaway,” a summary that connects the chapter’s points, and “Two for the Road,” suggested activities to help a reader improve problem-solving.

Anyone in the clutches of a big decision or problem or recalling such a time and hoping to learn from it will find It’s Not About the Shark informative and likely liberating.