Here's what it's like to have a conversation with Amelia, the nearest thing yet to a real-life version of Samantha, the artificial-intelligence operating system in the movie "Her."

"Where does Christopher Mims work?" types Ergun Ekici, the lead architect of Amelia, into her (for now) text-based interface. And then, well, there's really no other way to put this: Amelia responds like a person. She's read my bio online. She knows all about me. But her real talent isn't regurgitating information; it's solving...