NEW YORK—In 1980, Douglas Hofstadter, an obscure young computer science professor at Indiana University, won a Pulitzer Prize for his first book, Gödel, Escher, Bach: An Eternal Golden Braid. Equal parts brain-straining, witty, and epiphanic, “GEB”—as its devotees call it—leveraged math, art, and music to illuminate a remarkable feature of reality. Though systems may appear solid and self-sustaining, they also may contain contradictions that they can never resolve from within.