This talk is about how reproducing kernels and certain rearrangements of finite dimensional subspaces of two variable polynomials can reprove several interesting results. These include recent results of Geronimo and Woerdeman on orthogonal polynomials on the two dimensional torus as well as Ando's inequality (and its close relative, Pick interpolation theorem on the bidisk). Considerable time will be spent on one variable in order to make the ideas clear.