This article discusses the use of proximal deictic expressions to designate distal entities, focusing on the use of the present tense to designate past events. Cognitive approaches to this issue assume that such usages presuppose a special conceptual construal, in which the spatio-temporal distance between the ground and the designated event space is bridged in some way. In this paper, I argue that there are two distinct ways in which this may be accomplished. One is through mentally displacing the ground (...) to the distal space, so that the designated events become proximal in relation to this alternative ground. The other involves bringing the distal space into the ground in the form of a representation. I describe the distinctive characteristics of the two scenarios, showing both where they converge and at what point the difference becomes relevant for linguistic analysis. (shrink)