The 1870 ballet Coppélia is based on two stories by E. T. A. Hoffmann, the German Romantic writer who loved dolls and doppelgängers. The plot is simple. Franz is happily engaged to Swanhilda, yet also intrigued by the silent beauty who sits reading on the balcony of Dr. Coppélius’s house. The more she ignores him—human nature!—the more he’s attracted. But is this ideal being real? Choreographer Jean-Christophe Maillot pulls the girl-versus-doll classic into our era of artificial intelligence. —L.J.