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6.4 Assimilation and accommodation across the landscape

Chapters 2 and 3 introduced the Piagetian distinction and its differential realization. This survey does not define that machinery again. It uses only the resulting diagnostic question: does a process work inside a maintained representation, or does it propose a change to the representation, its observers, its generative operations, or its admission rules? The first is assimilatory. The second is proto-accommodative until independent evidence admits it. A revised admission rule cannot, by itself, certify the revision that introduced it.

This axis resembles Boden’s distinction between exploratory and transformational creativity, but the two classifications are not identical. Boden classifies how a conceptual space is used or transformed. The Piagetian reading additionally emphasizes why reorganization occurs, how the old scheme is related to the new one, and whether the change restores a viable equilibrium with experience. Combinational and exploratory work is often assimilatory, while transformational work often begins with a candidate extension; neither implication is automatic.

Tradition	Assimilatory reading	Accommodative reading
Information and surprise	Update probabilities or locate novelty inside a fixed repertoire.	Change the variables, contexts, repertoire, or sample space that makes surprise measurable.
Heuristic discovery	Search with registered primitives and heuristics, as in many BACON-style law-recovery tasks.	Introduce a missing variable, concept, operator, or discovery heuristic and transport prior results.
Computational creativity	Generate and appraise artifacts under a fixed grammar and value model.	Revise the grammar, inspiring set, evaluator, or ontology of admissible artifacts.
Imagination and world models	Simulate counterfactual variation inside a maintained world model.	Repair the state ontology or transition laws when imagined and observed consequences cannot be reconciled.
Cellular automata and evolution	Explore trajectories, initial conditions, or inherited variations under a fixed constructor.	Introduce a macroscopic ontology or alter the effective constructor–variation system.
Symbolic regression	Recover expressions in a registered language.	Extend the language with latent quantities, coordinates, operations, or factorization principles.
Automated and LLM-guided science	Optimize hypotheses and experiments inside a supplied scientific world.	Revise the objects, mechanisms, admissible interventions, or theory language that defines that world.

Table 6.2 A Piagetian reading of computational-creativity traditions. Assimilation and accommodation are relative to the maintained representational package, not intrinsic labels attached permanently to an algorithm or artifact.

Three cautions prevent the distinction from becoming rhetorical. First, assimilation is not synonymous with a small parameter update. A long proof, large search, or extensive experimental campaign can remain inside the same representation. Second, accommodation is not synonymous with textual or architectural novelty. A renamed primitive, redundant feature, or Morita-equivalent presentation may leave the model content unchanged. Third, an accommodative proposal is not yet cognitive or scientific progress. Only independent admission can establish that the revised package explains the obstruction while retaining the warranted achievements of its predecessor.

Thus the table is a crosswalk, not a second formalization of DIAL. Later chapters evaluate the two loops directly: exploration and repair within a declared representation, followed—when necessary—by minimal typed extension, transport of prior competence, and independent admission.