Inside, outside and their relation

One distinction has an inside, an outside and the relation by which they differ and meet. The triad is the common grammar from which the explanation grows.

Inside means the identity or distinction currently being followed. Outside means what is other relative to that reference. Relation makes their difference and connection definite. The roles depend on the reference and belong together.

An inside can contain relations among smaller identities and be an outside for one of them. Its whole can participate in a larger relation. This lets the source connect a local explanation to its surroundings without duplicating the same identity for every viewpoint.

Three vertices give three points of reference. In the locked geometric reading, changing the reference through the turn traces a circle. Hierarchy names three primary roles plus nine internal readings; phase places that one twelve around the turn.

An engine must say which state belongs to each role and how a change in the relation affects the next state. The present phase engine implements declared coupling and return across nested phases. The roles alone do not specify every coefficient or generate an unimplemented dimension-opening law.

A cell and its surroundings, a participant and a conversation, or a module and its callers can each be examined through this grammar. The grammar asks the same structural question; the actual boundary, access rules and mechanism must be established in each domain.

Changing the observer reference can exchange what is read as inside and outside while preserving the relation being followed. A useful teaching view therefore shows both the current focus and the larger whole to which it belongs.