Modeling problem-solving dynamics and creativity: the interplay between virtualization and actualization

This study develops a theoretical framework for creative problem solving as a cyclical interplay between virtualization and actualization. Virtualization refers to internal representational restructuring, whereas actualization refers to the external implementation and testing of candidate solutions. Drawing on analogies from fluid dynamics, these processes are formalized using coupled differential equations that yield an oscillatory trajectory, integrating insights from representational change theory, divergent thinking, and search-based approaches into a recursive mathematical framework. The model implies that creative problem solving depends on the coordinated coupling between representational transformation and concrete implementation, and on an adaptive balance between the amplitude and speed of the virtualization–actualization cycle. It also yields a difficulty-dependent implication: rapid cycling should become increasingly important as task difficulty increases. We provide a preliminary proxy-based empirical illustration using behavioral data from a T-puzzle experiment involving 462 participants and 3429 participant–game observations. Entropy, Trial Count, their interaction, and Mean Response Time were used as coarse behavioral proxies for virtualization-like exploration, actualization, trajectory expansion, and transition speed. The results were broadly consistent with selected implications of the framework: Entropy and Trial Count were negatively associated with task success, whereas their interaction was positive and statistically significant. Mean Response Time was negatively associated with success. However, the analysis does not directly observe the model’s latent state variables, estimate the full dynamical system, or test the difficulty-dependent component. The main contribution is theoretical, with the empirical analysis serving as an initial operational illustration.