The degenerate special Lagrangian equation governs geodesics in the space of positive Lagrangians. Existence of such geodesics has implications for uniqueness and existence of special Lagrangians. It also yields lower bounds on the cardinality of Lagrangian intersec- tions related to the strong Arnold conjecture. An overview of what is known about the existence problem will be given. The talk is based on joint work with A. Yuval and with Y. Rubinstein.[-]