MIAMI—In a gala ceremony at its Miami headquarters, the Burger King Corporation rolled out two new sandwiches that conceptually negate each other. "The new Veggie Burger, with just seven grams of fat, is a refreshing, heart-smart alternative to the usual fast-food junk," Burger King vice-president Robert Fass said. "And brace yourselves, meat lovers: The new BK Hickory Bacon Triple Stack—three juicy, big-beef patties topped with crispy bacon and slathered in a rich, smoked-cheddar sauce—is gonna blow you away." Burger theoreticians posit that the sandwiches could destroy each other if sold in a single order.