  Borel's construction of the regulator gives an injective map from the
algebraic $K$-groups of a number field to its Deligne-Beilinson cohomology
groups. This has many interesting arithmetic and geometric consequences. The
formula for the regulator is expressed in terms of the classical polyogarithm
functions. In this paper, we give a survey of the additive dilogarithm and the
several different versions of the weight two regulator in the infinitesimal
setting. We follow a historical approach which we hope will provide motivation
for the definitions and the constructions.
