Toward a Calculus of Redundancy: The feedback arrow of expectations in knowledge-based systems

Whereas the generation of Shannon-type information is coupled to the second law of thermodynamics, redundancy—that is, the complement of information to the maximum entropy—can be increased by further distinctions: new options can discursively be generated. The dynamics of discursive knowledge production thus infuse the historical dynamics with a cultural evolution based on expectations (as different from observations). We distinguish among (i) the communication of information, (ii) the sharing of meaning, and (iii) discursive knowledge. Meaning is provided from the perspective of hindsight as feedback on the entropy flow and thus generates redundancy. Specific meanings can selectively be codified as discursive knowledge; knowledge-based reconstructions enable us to specify expectations about future states which can be invoked in the present. The cycling among the dynamics of information, meaning, and knowledge in feedback and feedforward loops can be evaluated empirically: When mutual redundancy prevails over mutual information, the sign of the resulting information is negative indicating reduction of uncertainty because of new options available for realization; innovation can then be expected to flourish. When historical realizations prevail, innovation may be lockedin because of insufficient options for further development.