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Is there anything harder to define—but as easy to spot—as cool? In Cool Rules: Anatomy of an Attitude, co-authors Dick Pountain and David Robins propose a definition as good as any: “Cool” is “a permanent state of private rebellion.” The National Portrait Gallery gamely takes a crack at this ephemeral notion in a new show, “American Cool,” that opens today. The exhibit includes portraits of everyone from Miles Davis, Billie Holiday, and Elvis Presley to Joan Didion and Jay Z, captured at their most stylish by such photographic giants as Henri Cartier-Bresson, Annie Leibovitz, Richard Avedon, and Diane Arbus. Of all the art venues in town, the National Portrait Gallery hardly seems like the hippest, so maybe we should chalk it up to a bid for geek chic. Or perhaps a case of overcompensation. The exhibition is on view daily 11:30 a.m. to 7 p.m. to Sept. 7 at the National Portrait Gallery, 8th and F streets NW. Free. (202) 633-8300. npg.si.edu.