8.2 Assimilation as exploration

Exploratory creativity is the clearest computational analogue of Piagetian assimilation. New observations and constructions are interpreted through an existing schema. Search may update a model, add a theorem to a library, or traverse a long trajectory, but the types and legal moves used to describe that achievement remain unchanged.

Assimilation is not necessarily small. A million-step proof search and a decades-long investigation can both remain inside a fixed mathematical language. Conversely, a one-line proposal can be proto-accommodative if it adds a primitive that changes which expressions exist. Size of the trajectory and level of representational change are independent variables.

Piagetian equilibration suggests a disciplined outer control. The system first attempts to absorb a discrepancy using paths in \(\mathcal E_{\mathfrak R_{\mathrm{diff}}}(X)\). Only persistent, independently reproduced failure supplies evidence that the current space may be inadequate. Even then, failure of search is not proof of impossibility: the path may exist but be computationally inaccessible.

. Exhausting a search budget is not the same as exhausting a conceptual space. Accommodation requires evidence of representational inadequacy, not merely a timeout, a poor heuristic, or a weak proposal model.