  The embedding of finite metrics in $\ell_1$ has become a fundamental tool for
both combinatorial optimization and large-scale data analysis. One important
application is to network flow problems in which there is close relation
between max-flow min-cut theorems and the minimal distortion embeddings of
metrics into $\ell_1$. Here we show that this theory can be generalized
considerably to encompass Steiner tree packing problems in both graphs and
hypergraphs. Instead of the theory of $\ell_1$ metrics and minimal distortion
embeddings, the parallel is the theory of diversities recently introduced by
Bryant and Tupper, and the corresponding theory of $\ell_1$ diversities and
embeddings which we develop here.
