Right behind it — at the center of the gallery, and the library building itself — is an oversize handwritten copy of the Bill of Rights, one of 14 that George Washington ordered made during the debate over ratification. It lists 12 amendments, rather than the 10 that were approved.“This shows that history isn’t set in stone,” said Anthony Marx, the library’s president, who had popped down to show off a few items. “It’s something that’s always being debated and argued, even as it’s being imagined.”The exhibition, which is free but requires timed admission tickets, includes cases dedicated to exploration, religion, performance, childhood, visual arts, social activism and other themes, whose contents will rotate regularly. There are striking juxtapositions and surprising sightlines, and objects that tell different stories depending on the angle you look from.Look through a display of the conductor Arturo Toscanini’s batons, suspended in space, and you catch a glimpse of a spotlighted case across the room holding “Political Prisoner,” a 1971 cedar sculpture by the African American artist Elizabeth Catlett. From the front, the figure — a woman with a Pan-African flag cut into her torso — looks exhilarated, regal. From behind, you see that her hands are chained.The library, Kiely said, is really a “collections of collections,” whose own history is traced through the show. The core sections are heavy on treasures donated by the 19th-century philanthropist James Lenox, like an early 16th-century copper globe that includes one of the earliest cartographic representations of the Americas. (It’s also one of only two surviving Renaissance or medieval maps with the inscription “Here be dragons.”) And about that Gutenberg Bible: The Morgan Library, a few blocks away, may have three copies, Kiely said with a laugh, but the New York Public Library’s, another Lenox gift, is “special,” since it was the first to come to America, in 1847.