  We argue that a (slightly) curved space-time probed with a finite resolution,
equivalently a finite minimal length, is effectively described by a flat
non-commutative space-time. More precisely, a small cosmological constant (so a
constant curvature) leads the kappa-deformed Poincar\'e flat space-time of
deformed special relativity (DSR) theories. This point of view eventually helps
understanding some puzzling features of DSR. It also explains how DSR can be
considered as an effective flat (low energy) limit of a (true) quantum gravity
theory. This point of view leads us to consider a possible generalization of
DSR to arbitrary curvature in momentum space and to speculate about a possible
formulation of an effective quantum gravity model in these terms. It also leads
us to suggest a {\it doubly deformed special relativity} framework for
describing particle kinematics in an effective low energy description of
quantum gravity.
