{"id":"changing-neighborhoods","title":"Becoming neighbors through a change of representation","regions":["representation","computation"],"question":"Can two structures become operationally close only after a transformation changes how their relation is represented?","formulation":"Rotation is used as an analogy for making a previously unavailable neighborhood or route accessible. Later material explicitly revisits the connection between an agent walking a manifold and learned similarity.","representations":[{"name":"Transformation followed by a neighborhood query","affords":"Separates movement from the rule that defines closeness.","loses":"A useful transformation still needs a concrete domain and cost.","epistemic_kind":"reconstruction"},{"name":"Contextual similarity relation","affords":"Allows the same pair to be near for one task and far for another.","loses":"May no longer satisfy metric assumptions.","epistemic_kind":"reconstruction"}],"tension":"Geometric proximity, semantic similarity, and compatibility of actions can diverge.","challenge":"What observable operation becomes possible after the transformation that was impossible before it?","development":"active","epistemic_kind":"reconstruction","evidence":["basis-changing-neighborhoods"],"next_move":{"text":"Use two tasks with the same items but different relevant relations; compare route quality under a fixed and a task-indexed neighborhood.","epistemic_kind":"model_proposed"},"open_questions":["Can two structures become operationally close only after a transformation changes how their relation is represented?","What observable operation becomes possible after the transformation that was impossible before it?"],"formal_status":"open_problem","version":1,"content_hash":"18848deebd95bf2dc9de1e2960c3dd92dd6cf93d1dddccab1fb0f603c5eb0db1"}