The Media Theory book is done and sent to the publishers. Which makes, I think, a good excuse to say a little of what it's about.

In short, a medium is a system of states and tokens that act on the states, like a deterministic finite state machine but without the complication of initial and final states, and with some extra axioms that the state transitions must satisfy. Because of these axioms, media can be shown to be equivalent in theory to partial cube graphs, but the automata-theoretic viewpoint leads to a different emphasis of topics.

There is plenty of material in the book about the sorts of things you'd expect me to be interested in: graph theory, geometry (particularly hyperplane arrangements, the regions and region adjacencies of which form media), graph drawing, and the design and analysis of algorithms. But my coauthors Falmagne and Ovchinnikov are, respectively, a cognitive scientist and mathematician, so the book also has plenty of foundational material on how to define and characterize media, how to use them to model important concepts from order theory (total orders, partial orders, weak orders, interval orders, etc), and how these concepts can be applied in the social sciences.


I'm not sure I entirely follow what it's about from this short description, but it definitely sounds fascinating!