The Khovanov homology groups of torus knots T(n,m) are known to stabilize as m goes to infinity with n fixed. In this talk, we make the observation that when n = 2, the stable limit happens to be isomorphic to the homology of the free loop space of the 2-sphere. Our main result suggests that this is not merely a coincidence: we prove that the k-colored sl(N) homology of T(2,m) stabilizes to the homology of the free loop space of the complex Grassmannian Gr(k,N). We also relate the space of closed geodesics on the Grassmannian to the k-colored sl(N) homologies of the individual torus knots T(2,m).