Exploration, recombination, and acceleration: a multi-scale theory of discovery dynamics

Understanding how novelty emerges within complex systems is a fundamental scientific challenge across cultural, scientific, linguistic, and technological domains. This thesis develops a unified theoretical and quantitative framework to describe how new elements and combinations arise, interact, and accelerate across scales. Building upon the theory of the adjacent possible, it integrates stochastic, network-based, and combinatorial models to connect the microscopic dynamics of discovery with the macroscopic laws of innovation. The first part introduces a generalised notion of novelty that includes higher-order events, defined as new combinations of previously known elements. Analyses of large-scale linguistic, cultural, and technological data reveal that such higher-order novelties follow distinct scaling laws, exposing the multi-level structure of innovation. To account for these patterns, the Edge-Reinforced Random Walk with Triggering (ERRWT) is proposed as a stochastic model unifying reinforcement, triggering, and recombination within a single formulation. The second part extends urn-based discovery models to capture temporal heterogeneity. The Time-Dependent Urn Model with Triggering (TUMT) introduces a dynamic rate of expansion of the adjacent possible, reproducing both stationary and non-stationary regimes and explaining phenomena such as the coexistence of core and peripheral vocabularies in language and the changing pace of novelty production over time. The third part links microscopic and macroscopic descriptions by introducing collective exploration as the bridge between individual discovery and large-scale acceleration. In a multi-explorer extension of the urn model, concurrent discoveries generate an accelerating expansion of possibilities, giving rise to the super-exponential dynamics described by the Theory of the Adjacent Possible (TAP). Altogether, the thesis establishes a coherent, multi-scale theory of the new, showing that the same principles of reinforcement, recombination, and expansion govern novelty at both the individual and collective level. It contributes to the quantitative foundations of the science of discovery and to a general understanding of how the recursive growth of possibilities drives creativity, evolution, and change.