I find the idea increasingly compelling, that a properly constructed thesaurus supports some of the same geometric ideas as are applied to Euclidean and related spaces. Specifically the moving point in space is analogous to the topic moving in the thesaurus. The final curve that was traced by the point is analogous to the story information, told one word at a time.
This analogy continues at the local level, where different narrative structures are "best fit" to the adjacent verbiage, and used to fill in topic specific information. This mechanism is analogous to the derivatives at a point on a curve corresponding to "best fit" idealized line, circle, helix. Thus the moving frame of Frenet, Darboux, Cartan, Chern, [Pohl], ... becomes a moving local narrative for transforming local words into defined topic structures. It may seem awkward but, in this formulation, the words are parameters of the moving topic.
To round out the theory (literally) I hope to state some basic principles about connectivity and completeness of stories [Also the negatives: non-sequitur and irrelevance]. Details are coming into view.
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