For the four-hundredth anniversary of Shakespeare's death, Gregory Doran, the artistic director of the Royal Shakespeare Company, wanted to dazzle. He turned to "The Tempest," the late romance that includes flying spirits, a shipwreck, a vanishing banquet, and a masque-like pageant that the magician Prospero stages to celebrate his daughter's marriage. "The Tempest" was performed at the court of King James I, and it may have been intended in part to showcase the multimedia marvels of Jacobean court masques. "Shakespeare was touching on that new form of theatre," Doran told me recently, over the phone. "So we wanted to think about what the cutting-edge technology is today that Shakespeare, if he were alive now, would be saying, 'Let's use some of that.' " The politics behind Shakespeare and stage illusion are more fraught than usual these days.