7.3 Assimilation and accommodation

Piaget’s distinction cuts across Boden’s. If \(X\), \(Y\), their interface, and their mode of composition already belong to \(\mathfrak R_{\mathrm{diff}}\), then forming and testing the composite is assimilatory. The learner has used the current schema to organize a new case. The result can be large, surprising, and historically important while remaining assimilatory at the chosen level of description.

Proto-accommodation begins when the proposed combination requires a change to what can be represented or composed. This may involve adding an interface object, splitting an overloaded type, introducing a new conversion, or revising an equation that previously prohibited the interaction. Schematically,

records that the combination became legal only in an extended presentation. The episode is combinational in Boden’s sense because of how its ingredients are joined, but proto-accommodative in Piagetian terms because it changes the maintained schema. It becomes an accommodation only if the interface extension and its composite are independently admitted.

This cross-classification prevents a common mistake. Combining concepts from two fields does not automatically constitute transformational creativity. Conversely, an apparently modest bridge can be transformational if it creates a new sort of object or a new law of composition that persists in later work.