Deictic (or pointing) gestures are traditionally known to have a simple function: to supply something as the referent of a demonstrative linguistic expression. I argue that deixis can have a more complex function. A deictic gesture can be used to _say something_ in conversation and can thereby become a full discourse move in its own right. To capture this phenomenon, which I call _rich demonstration_, I present an update semantics on which deictic gestures can indicate situations from a conversation’s context (...) and those situations coherently connect to prior discourse to generate information. (shrink)