Angelina Jolie has never lacked for influence. When she adopted a baby from Ethiopia, inquiries at U.S. adoption agencies about other Ethiopian orphans doubled. When she named other children Vivienne or Maddox, those names shot up the popularity charts for American newborns. So this week, when a woman known for her powerfully iconic beauty announced that she had undergone an elective double mastectomy to reduce her genetically high risk of breast cancer, it was a cultural and medical earthquake — a revelation so arresting it became the subject of TIME’s newest cover story, which will publish to TIME.com Thursday morning, before hitting newsstands Friday