This talk discusses a surprising (to the speaker) relationship between two different topics in string theory. The first of these is the doubled geometry approach. This involves extending the geometry of the background in order to realise a larger symmetry, which corresponds to T-duality on compactification. This is a step towards a ``duality covariant'' formulation of string theory, and towards understanding string theory backgrounds beyond supergravity. The second topic is non-relativistic string theory, where the background geometry, and symmetries, are not enlarged but restricted. I will discuss what these have to do with each other, and how the flexibility of the doubled formalism allows one to obtain results about non-relativistic limits of string theory, with a particular example being the construction of a locally worldsheet supersymmetric Newton-Cartan string as in my paper 1908.00074.
