Yes, that makes sense to me: we don't have a formal, precise way of discussing (measuring) information content when faced with the kind of "hierarchical structu

Yes, that makes sense to me: we don't have a formal, precise way of discussing (measuring) information content when faced with the kind of "hierarchical structure that is robust to loss" that is prevalent in natural high dimensional data. (FWIW, I don't like the term "hierarchical structure" that much, but cannot think of a more appropriate term. It's as if there's no good terminology for discussing these issues, at least not yet.)