Typological and Topological Meaning
This line of my research investigates the relations between "meaning-by-category" vs. "meaning-by-degree", since some semiotic systems, like language (particularly its phonological, lexico-grammatical, and basic semantic resources), are specialized to construct categorial contrast relations ('typological meaning') and not very good at representing quantitatively precise degree or matters of continuous variation (e.g. in shape, color, relative position), while others, such as gesture and visual depiction are quite good at showing these more 'topological' relationships. Effective meaning-making requires that we combine semiotic resources of different kinds to make both of these general sorts of meaning coherently. Mathematics historically has evolved in large part (though not entirely) as a bridge between verbal-conceptual-categorial meaning on the one hand, and spatial-kinetic-pictorial meaning on the other.
"Typological and Topological Meaning in
Diagnostic Discourse." To appear in Discourse Processes
(special issue on Discourse in Problem-based Learning, ed. T.
Koschmann) Manuscript.
Opening Up Closure: Semiotics Across Scales. New paper on semiotics in complex dynamical systems.
Mathematics in the Middle: Measure, Picture, Gesture, Sign, and Word. New paper on semiotics and mathematics.
"Teaching All the Languages of Science: Words, Symbols, Images, and Actions" -- Relevant section
See also discussion in Multiplying Meaning paper. This takes a while to download since it incorporate numerous figures, but it is probably worth the wait.