8 Characterizing Communicative Processes
Being able to precisely characterize a particular communication system allows
one to compare communication systems, including deciding whether two systems
are equivalent, as well as providing a method by which one can rank communication
systems based on their characterization. One may also characterize a system
by naming or describing it, based upon its content. The Minimum Description
Length (MDL) for a system is the shortest length that can describe and differentiate
one process from others in the domain of possible processes [Ris89, WF87].
The Minimal Description (MD) characterizes what makes up a system, and thus
identifies what is complex and special about each system. A system which is
easy to describe has a relatively short description and a small MDL, while a very
complex system, approaching randomness, would have a relatively large MDL.
We are describing only the two informative processes defining the communication
system. If we have two processes, and there are many other processes
below them on the hierarchy, we may compute the MDL by considering only
the complexity of the two informative processes, with no attention being paid to
processes below. We might, however, choose to view the world as containing
larger processes, e.g., you as a process and me as a process, in which case the
MDL would be computed for me or for you and might or might not include this
medium. Because the reader differs from the author, the reader function is not a
perfect inverse of the writer function, making the MDL much larger than if the
author were writing for himself, the reader then being a near-perfect inverse of the
writer. The ordering of systems, from simple to complex, can be accomplished by
listing the systems in order of their MDL value, e.g.