In this talk, we introduce a canonical geodesic current K_X​ for each X∈Tg​, representing a randomly selected simple closed geodesic on X. The map X↦KX​ defines a proper embedding of Teichmüller space Tg​ into the space of geodesic currents. This embedding naturally leads to a compactification of Tg​ that is distinct from Thurston's compactification. We will explore the construction of KX​ and its geometric properties. This is a joint work with Curt McMullen.