4.8 Boden’s modes as changes of control geometry

The construction provides a common language for Boden’s three modes without collapsing their differences.

Combinational creativity.

Registered scripts or skill sections are composed. Their bracket reveals whether ordering introduces a genuinely new effect.

Exploratory creativity.

Sections and their parameters are optimized inside a fixed \((M,A,\rho )\), Markdown grammar, and semantic compiler.

Transformational creativity.

The system changes the grammar or compiler, enlarges the admissible skill bundle, or proposes a finite base change \(M\to M^+\). Chapter 3’s comparison maps must then explain how old probes and skills transport to the new world.

This classification draws the decisive boundary. Optimizing a workflow inside a fixed skill geometry is exploratory, even when the resulting theorem or mechanism is novel. Changing what counts as a legal skill or a meaningful theory state is transformational. A Markdown revision can do either; its creativity mode is determined by its semantics, not by the number of edited tokens.