One of the most basic tools in the theory of automorphic forms is the truncation operator, first defined in [Langlands: 1966] but elaborated in later work of Jim Arthur (particularly [Arthur: 1978] and [Arthur: 1980]). In spite of its fundamental nature, there are many mysteries about it. In this article I’ll not dispel many of these, but I’ll at least motivate its definition by relating it to ...