[caconym_]

One random (heh) thing that occurs to me reading this article is that if you are using hashing for security (e.g. password hashing, key derivation, ...) then what the author is calling "invertibility", i.e. there are few values in the input space that map to some value in the output space, is actually a good thing. All other things being equal, the more such input values there are, the more feasible collision/preimage attacks become. It seems clear that for these purposes, the information content of the output should be at least equal to that of the input.