8 Exploratory Creativity

Exploratory creativity searches a conceptual space without changing its generative rules. It includes much of theorem proving, program synthesis, symbolic regression, optimization, and evolutionary search. Optimization is one important instance, but exploration is broader: the artifact may be a proof, program, mechanism, or reachable construction rather than a minimizing parameter vector. A fixed space may contain consequences that no reasoner has encountered, and a short path to them may be extremely difficult to find.

Chapter 7 asked whether existing components could be joined through a new typed interface. Here the interface and generative language are already registered. The creative artifact is instead an admitted path, construction, or consequence within that language. Failure to find such a path is evidence about search only; it becomes evidence about the language only after the controls developed at the end of this chapter.

. Exploration is meaningful only relative to a declared space. State the objects, legal moves, observers, stopping rule, and resource budget before claiming that a system has explored rather than retrieved or improvised.