Through the MOAT (Mother of All Tableaux"), Optimality Theoretic (OT) constraints rate entire grammars against each other within a typology, imposing a structure of order and equivalence on them. An associated geometry views grammars as regions, with properties determined at their borders, using the same data that gives rise to the MOAT. These structures delimit what can and cannot be an OT typology, how typologies can be represented in Violation Tableaux, and how grammar-regions can merge to classify concrete and abstract languages"--