2 Creativity as Theory Construction

A machine may solve a difficult problem without creating the conceptual world in which future problems become easy to state. The distinction is visible in mathematics: proving an isolated theorem is an achievement, but introducing objects such as prime numbers, Fourier series, or Lie groups creates a durable language of objects, operations, laws, examples, and questions. The latter is the phenomenon this book calls theory construction.

Chapter 1 supplied the starting point: a provisional sketch, a current realization typed by it, and the provenance and uncertainty of its declarations. The present chapter asks what can happen after that acquisition. Improving a model of the sketch is one achievement; changing the sketch so that new kinds of model, explanation, or experiment become expressible is another. This distinction turns initialization into the first state of a creative process rather than an unexplained precondition.

The source-bearing sketch is an input to that process, not automatically a creative artifact. Creativity begins when the learner constructs and admits a novel composite, consequence, or theory change relative to what its acquisition channels already supplied. Provenance is what makes that relative claim auditable.

Feynman’s atomic-hypothesis thought experiment gives the scientific analogue. Its achievement is not that a sentence has a short code. The hypothesis declares a small ontology of particles, motion, and interaction from which a large family of observable consequences follows [ Feynman et al. , 1963 , Section 1–2 ] . The desired economy is therefore generative compression: a compact theory whose compositional structure supports reconstruction, explanation, intervention, and extension.

. The shortest description of existing data need not be the most creative theory. A synthetic theory earns its economy by exposing reusable objects and laws that generate consequences beyond the observations from which it was constructed.

¹1. A theory is persistent when it can be communicated, reused, criticized, and extended by reasoners other than its originator. Novel output alone does not meet this standard. ↩

Chapter 0 supplied the working categorical language for representing such structure. The preceding books develop that language and learning from failures of compositionality in greater depth [ Mahadevan , 2026b , 2026e ] . We do not rederive those foundations here. Our concern is what happens when repair of the current realization is no longer sufficient. The surviving proposal may revise another component of the maintained package, or it may make the stronger move of changing the objects, arrows, equations, or generative language of the theory presentation.

. Synthetic creativity is the broader program of constructing novel, persistent, and admissible conceptual extensions. Infinitesimal creativity is its governing architecture: use interacting local repairs to diagnose where a maintained package is inadequate, then state the creative jump as a finite, typed package comparison. A change of presentation or generative language is the special case of theory extension, in which new answers, predictions, and experiments become expressible.