Mutual Redundancies in Inter-human Communication Systems: Steps Towards a Calculus of Processing Meaning
The study of inter-human communication requires a more complex framework than Shannon’s (1948) mathematical theory of communication because “information” is defined in the latter case as meaningless uncertainty. The conference theme of “acting, learning, understanding” adds a reflexive layer of meaning processing to Shannon’s linear scheme of “sending, channel, receiving.” This reflexive layer operates non-linearly; meaning can be provided to the information from the perspective of hindsight, and with reference to other possible meanings. “A difference that makes a difference” to a system of reference presumes the systems of reference to be differently positioned in addition to being related in the Shannon-type communication. Providing information with meaning may also reduce the uncertainty that prevails.
Assuming that meaning cannot be communicated, we extend Shannon’s theory by defining mutual redundancy as a positional counterpart of the relational communication of information. Mutual redundancy indicates the surplus of meanings that can be provided to the exchanges in reflexive communications. The information is redundant because based on “pure sets,” that is, without subtraction of mutual information in the overlaps. We show that in the three-dimensional case (e.g., of a Triple Helix of university-industry-government relations), mutual redundancy is equal to mutual information (Rxyz = Txyz); but when the dimensionality is even, the sign is different. We generalize to the measurement in N dimensions and proceed to the interpretation.
Using Luhmann’s social-systems theory and/or Giddens’ structuration theory, mutual redundancy can be provided with an interpretation in the sociological case: different meaning-processing structures code and decode with other algorithms. A surplus of (“absent”) options can then be generated that add to the redundancy. Luhmann’s “functional (sub)systems” of expectations or Giddens’ “rule-resource sets” are positioned mutually, but coupled operationally in events or “instantiated” in actions. Shannon-type information is generated by the mediation, but the “structures” are (re-)positioned towards one another as sets of (potentially counterfactual) expectations. The positional differences among the coding and decoding algorithms provide a source of additional options in reflexive and anticipatory communications.