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

This paper considers the relationships among meaning generation, selection, and the dynamics of discourse from a variety of perspectives ranging from information theory and biology to sociology. Following Husserl’s idea of a horizon of meaning in intersubjective communication, we propose a way in which, using Shannon’s equations, the generation and selection of meanings from a horizon of possibilities can be considered probabilistically. The information-theoretical dynamics we articulate considers a process of meaning generation within cultural evolution: information is imbued with meaning, and through this process, the number of options for the selection of meaning in discourse proliferates. The redundancy of possible meanings contributes to a codification of expectations within the discourse. Unlike hard-wired DNA, the codes of non-biological systems can co-evolve with the variations. Spanning horizons of meaning, the codes structure the communications as selection environments that shape discourses. Discursive knowledge can be considered as meta-coded communication which enables us to translate among differently coded communications. The dynamics of discursive knowledge production can thus infuse the historical dynamics with a cultural evolution by adding options, that is, by increasing redundancy. A calculus of redundancy is presented as an indicator whereby these dynamics of discourse and meaning may be explored empirically.

💡 Research Summary

This paper, “Toward a Calculus of Redundancy,” presents a novel theoretical framework that integrates Shannon’s information theory with phenomenological and sociological concepts to analyze the dynamics of meaning generation, selection, and discourse in cultural evolution. The authors argue for a fundamental dualism between information processing and meaning processing, proposing “redundancy” as the key conceptual link and quantitative indicator for studying their interaction.

The core argument begins by strictly distinguishing between three dynamics: (1) information processing, defined as Shannon-type probabilistic entropy (H), which follows the second law of thermodynamics and increases over time; (2) meaning processing, which is the reflexive assignment of significance to information, expanding the set of conceivable options; and (3) the codification of communication, where symbolically generalized codes (e.g., in law, science, art) structure discourse as selection environments. The paper’s pivotal move is to reinterpret Shannon’s redundancy (R = 1 - H_system/H_max) not merely as repetition or error-correcting surplus, but as the reservoir of “not-yet-realized possibilities” generated by the act of meaning-making.

When meaning is assigned to information, it multiplies the number of potential states a system can be in. Formally, if N represents the number of informational options and M the possible meanings attached, the maximum entropy of the system becomes log(M*N), not just log(N). This expansion of the option pool is the source of redundancy. Crucially, while information processing follows the “arrow of time” (recursion), meaning processing can operate through feedback loops that work “against the arrow of time” (hyper-incursion), thereby capable of increasing or decreasing redundancy.

The authors contrast biological evolution, constrained by hard-wired DNA, with cultural evolution. In cultural systems, codes are not fixed but socially constructed and can co-evolve with variations. These codes span “horizons of meaning” (Husserl) and structure communications. Discursive knowledge acts as a “meta-code,” enabling translation between differently coded communications (e.g., between scientific disciplines). Thus, cultural evolution is driven by the dynamics of discursive knowledge production, which injects historical developments with new options—that is, by increasing systemic redundancy.

The paper reviews and critiques conflations of information and meaning in works by Bateson, Luhmann, Floridi, and others, insisting on their analytical separation. It draws on biological theories (Brooks & Wiley, Kauffman’s “adjacent possible”) but emphasizes that cultural and technological evolution can rupture historical constraints on possibilities by orders of magnitude, fundamentally resetting the boundary of what is possible.

In conclusion, the authors propose developing a “calculus of redundancy” as an empirical research program. This calculus would aim to quantify the trade-off between uncertainty generation (information) and uncertainty reduction through meaning codification, offering a measurable indicator to explore the complex, non-linear dynamics of discourse and meaning in knowledge-based, culturally evolving systems. The framework positions redundancy not as a given but as a constructed and dynamic space of potentiality, central to understanding innovation and change in human societies.