Let f(x,y) define an isolated singularity at the origin. In this talk we explore a new flat metric  induced on the Milnor fiber of f by the associated complex Hamiltonian vector field. With the help of this metric we can define a spine on each Milnor fiber via the classical method of the medial axis. This spine depends on the choice of boundary for the Milnor fiber. It is subanalytic and comes equipped with a retraction from the boundary onto it. We hope to understand the geometry of the versal unfolding space via these spines. This ongoing joint work with Norbert A’Campo.