The spectacular results achieved in machine learning, including the recent advances in generative AI, rely on large data collections. On the opposite, intelligent processes in nature arises without the need for such collections, but simply by on-line processing of the environmental information. In particular, natural learning processes rely on mechanisms where data representation and learning are intertwined in such a way to respect spatiotemporal locality. This paper shows that such a feature arises from a pre-algorithmic view of learning that is inspired by related studies in Theoretical Physics. We show that the algorithmic interpretation of the derived “laws of learning”, which takes the structure of Hamiltonian equations, reduces to Backpropagation when the speed of propagation goes to infinity. This opens the doors to machine learning studies based on full on-line information processing that are based on the replacement of Backpropagation with the proposed spatiotemporal local algorithm.