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The study of inter-human communication requires a more complex framework thanShannon's (1948) mathematical theory of communication because "information" isdefined in the latter case as meaningless uncertainty. Assuming that meaningcannot be communicated, we extend Shannon's theory by defining mutualredundancy as a positional counterpart of the relational communication ofinformation. Mutual redundancy indicates the surplus of meanings that can beprovided to the exchanges in reflexive communications. The information isredundant because based on "pure sets," that is, without subtraction of mutualinformation in the overlaps. We show that in the three-dimensional case (e.g.,of a Triple Helix of university-industry-government relations), mutualredundancy is equal to mutual information (Rxyz = Txyz); but when thedimensionality is even, the sign is different. We generalize to the measurementin N dimensions and proceed to the interpretation. Using Luhmann'ssocial-systems theory and/or Giddens' structuration theory, mutual redundancycan be provided with an interpretation in the sociological case: differentmeaning-processing structures code and decode with other algorithms. A surplusof ("absent") options can then be generated that add to the redundancy.Luhmann's "functional (sub)systems" of expectations or Giddens' "rule-resourcesets" are positioned mutually, but coupled operationally in events or"instantiated" in actions. Shannon-type information is generated by themediation, but the "structures" are (re-)positioned towards one another as setsof (potentially counterfactual) expectations. The structural differences amongthe coding and decoding algorithms provide a source of additional options inreflexive and anticipatory communications.

Mutual Redundancies in Inter-human Communication Systems: Steps Towards a Calculus of Processing Meaning