But now people - students, outsiders - talk about Dorchester as if it were everything south of Dudley Square. And they say, "Don't go there - Dorchester's dangerous". Dangerous?

And my wife asks about the region between Mass Ave and Melnea Cass Blvd: is it the South End or Roxbury? And what's the boundary between the South End and the Back Bay? Do these lines move with demographics: if people are black, then it's Roxbury? That's an unpleasant definition.
As it turns out, we're not alone. The Globe has an interesting article and a great map addressing the question.