Let's just put this out there. If you have heard the whole Synchronicity album, you know that there is a song called "Synchronicity I". Both that song and this one were written by Sting, and he has refused to reveal the connection between the two.
This song was a worldwide single for The Police, hitting the Top 20 in both the US and UK. While the video was somewhat post-apocalyptic, the song itself is rooted in Carl Jung;'s theory of (guess what) synchronicity - which rejects chaos and seeks connection between unrelated events. It remains my favorite Police song, possibly because it is so unlike anything else they ever did.