Born reciprocity is an old idea that found renewed interest in recent years the context of UV/IR mixing, and which has intriguing overlaps with T-duality, non-commutativity and meta-string theory. In this talk I show how, using tensor networks, it can be understood very simply and naturally as a global Hilbert-space phenomenon. This leads to a novel general understanding of UV/IR mixing, with implications for renormalisation and naturalness in string theory.