Motivated by a basic problem in information theory, David Blackwell posed
an apparently innocent question in a 1957 conference paper: does the
conditional distribution of an ergodic hidden Markov chain possess a
unique invariant measure?  To the best of my knowledge Blackwell never
worked on this topic again, but the question has been revisited several
times in different contexts in the ensuing 50+ years and has proved to   
be surprisingly elusive.  In this talk, I will aim to give an overview   
of the different strands of this story.  In the process, we will return
again and again to seemingly unrelated papers by David Blackwell.