Transformational Creativity in Science: A Graphical Theory
Samuel Schapiro, Jonah Black, Lav R. Varshney
TL;DR
We formalize transformational creativity in science by modeling scientific conceptual spaces as directed acyclic graphs $S=(V,E)$, where axioms are sink nodes and edges encode constraint dependencies. The framework shows that modifying axioms yields the greatest transformative potential, linking space reconfiguration to Kuhn-style paradigm shifts, with $T^p_\text{mod}(v)=|\text{depends}(v)|$ guiding transformability and a proof that axioms maximize this potential. Historical cases—geocentrism to heliocentrism, relativity, and non-Euclidean geometry—are captured as explicit axiom changes and corresponding rule transformations, illustrating how paradigm shifts emerge from space redesign. The paper also sketches a path toward AI-assisted transformative discovery by coupling large language models with the graph-based framework to produce interpretable, transformative ideas via graph transformations.
Abstract
Creative processes are typically divided into three types: combinatorial, exploratory, and transformational. Here, we provide a graphical theory of transformational scientific creativity, synthesizing Boden's insight that transformational creativity arises from changes in the "enabling constraints" of a conceptual space and Kuhn's structure of scientific revolutions as resulting from paradigm shifts. We prove that modifications made to axioms of our graphical model have the most transformative potential and then illustrate how several historical instances of transformational creativity can be captured by our framework.