  This essay constitutes a review of the information geometric approach to
renormalization developed in the recent works of B\'eny and Osborne as well as
a detailed work-through of some of their contents. A noncommutative
generalization of information geometry allows one to treat quantum state
distinguishability in geometric terms with an intuitive empirical
interpretation, allowing for an information theoretic prescription of
renormalization which incorporates both the condensed matter and quantum field
theoretic approaches.
