Abstract: In this informal talk, I will outline new work using elementary ideas by means of which an algebraic analogue of the usual KZ equation is exhibited. This difference equation arises via the introduction of Hurwitz polyzeta functions and suitable regularizations. A difference equation analogue of the notion of connection will also be presented, built around the algebraic KZ equation, for which a generating series for Hurwitz polyzeta functions is a "flat section". Also, the algebraic independence of the Hurwitz polyzeta functions will be demonstrated, along with a construction of regularizations of polyzeta functions using limits.