Oscar Wilde said that an artist has succeeded if people don't understand his work but they still like it. By that standard, the Police were a huge success. Their songs are universal — they're part of all of our lives. You hear them on both pop and classic-rock stations, and they'll be played on the radio in Germany 100 years from now. At the same time, everything they did was really smart and worked on a few levels; you could love a particular song, then realize a year later that you had totally missed the meaning.

Take "Every Breath You Take." It's a great trick — it's impossibly catchy,...