What makes some representationsThus: design as value-driven representation.betterthan others?

**Semiotic morphisms** are maps of semiotic spaces that *preserve
significant* properties.

- Semiotic systems are
*theories*not models, so morphisms translate theories, not concrete signs. *Quality*of representations is measured by how well features of source space preserved.- Representations can be combined;
*blending*is special case.

E.g., book table of contents preserves structure & names of parts, but not content.

Design is massaging source & target spaces, & morphism, to achieve
*quality*, subject to constraints, plus discovering and refining
values, all done iteratively.

Design principles (all with precise mathematical formulations):

- Important subsigns map to correspondingly important subsigns in representation.
- Most important axioms also satisfied by their representations.
- Better to preserve form (i.e., structure) than content, if something must be sacrificed.

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