http://arxiv.org/abs/gr-qc/0505052 Authors: Rodolfo Gambini, Jorge Pullin Comments: 8 pages, one figure, fifth prize of the Gravity Research Foundation 2005 essay competition Report-no: LSU-REL-051105 We argue that recent developments in discretizations of classical and quantum gravity imply a new paradigm for doing research in these areas. The paradigm consists in discretizing the theory in such a way that the resulting discrete theory has no constraints. This solves many of the hard conceptual problems of quantum gravity. It also appears as a useful tool in some numerical simulations of interest in classical relativity. We outline some of the salient aspects and results of this new framework.