Quantifying the dynamics of failure across science, startups and security

Human achievements are often preceded by repeated attempts that fail, but little is known about the mechanisms that govern the dynamics of failure. Here, building on previous research relating to innovation1–7, human dynamics8–11 and learning12–17, we develop a simple one-parameter model that mimics how successful future attempts build on past efforts. Solving this model analytically suggests that a phase transition separates the dynamics of...