We show that large N matrix models (where the matrices depend only on time) have an exact boson description in 1+1 dimensions where space is naturally a lattice of spacing ~ 1/N embedded in a geometry dictated by the potential of the matrix model. We then show that the result can be extended to the c=1 matrix model, in which N is taken to infinity with a second parameter taken to zero with the product  \mu held fixed. The exact boson description now has a short distance cutoff proportional to 1/\mu. This bosonic description explains the uv finiteness of entanglement entropy and correlation functions of the c=1 matrix model. We compare this finiteness with 2D string theory. Generalisation of these ideas to matrix models in zero dimensions and to the theory of giant gravitons is discussed at the end. The first part is based on: "Exact lattice bosonization of finite N matrix quantum mechanics and c = 1", Ajay Mohan and GM,  e-Print: 2406.07629 [hep-th]