The grounding of semiotics in the finiteness of cognition is extended into constructs and methods for analysis by incorporating the assumption that cognition can be similar within and between agents. After examining and formalizing cognitive similarity as an ontological commitment, the recurrence of cognitive states is examined in terms of a “cognitive set.” In the individual, the cognitive set is seen as evolving under the bidirectional, cyclical determination of thought by the historical environment. At the population level, the distributed “global” cognitive set is argued to be constrained to a manifold in which the cognition of individuals is determined only when their cognitive sets meet certain conditions in the world: a result seen as consistent with Lotman’s semiosphere.With these foundations in place, dimensional modelling of the semiosic field is inaugurated. Firstly, measures of cognitive similarity are formalized as cognitive “distance” and on this basis the concept of a semiotic vector is defined. Secondly, semiotic vectors are seen to shape a general pattern of oscillation in semiosis, and thus to imply zero points in semiosic potential. Thirdly, semiosic oscillation in individual agents is shown to be consistent with a novel diachronic or longitudinal interpretation of Greimas’ semiotic square expanded into a “semiotic pipe” in which cognition traverses an n-dimensional space structured by axes of oscillation. Finally, the expanded theory of finite semiotics is advanced as a useful basis for two new complementary disciplines: (1) a computational, mathematical science of “natural semiotic processing” (NSP) to trace and model semiotic vectors and oscillation; and (2) an ethical, rhetorical art of “technological influencing” (TI) to guide its inputs and applications.

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For semiotics the precipitous arrival of the information age and the “attention economy” suggests a new theoretical standpoint: that semiosis is a function of the finiteness of human cognition and the allocation of that resource. Proceeding on this basis, a model is presented that offers novel definitions of semiosis and semiotics. Inter-agent similarity of cognition and its mediation through artefacts are then introduced to suggest how finite cognition may be determined and equilibrated through reticular mechanisms. Finally, an explanation of how artefacts evolve to consume cognition based on Foucault’s concept of corpora of knowledge is broached.

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