The scaling properties of the surface of a three-dimensional rice pile are studied. In time, the pile surface exhibits multi-scaling, where the exponents decrease with increasing moment. This is connected to the fact that the pile is in a self-organized critical state, where the dynamics of the steady state is influenced by transient properties, leading to multi-scaling. In contrast, when studying the transient properties directly, generic scaling is observed, as there is only one relevant cut-off. Similarly in space, multi-scaling is absent and within experimental error, the same scaling is observed for all moments. Again, this is connected to the properties of the critical state.