A first-principles mathematical model integrates the disparate timescales of human learning

Lifelong learning occurs on timescales ranging from moments to decades. People can lose themselves in a new skill, practice for hours until exhausted, and pursue mastery intermittently over decades. A full understanding of learning requires an account that integrates these timescales. Here, in response to calls for more formal theory in the psychological sciences, we present a parsimonious mathematical model that unifies the nested timescales of learning. Our model recovers well-established patterns of skill acquisition, and explains how these patterns can emerge from short-timescale dynamics of motivation, fatigue, and effort. Conversely, the model explains how patterns in these short-timescale dynamics are shaped by longer-term dynamics of skill selection, mastery, and abandonment. We use this model to explore the theoretical benefits and pitfalls of a variety of training regimes. Our model connects disparate timescales—and the subdisciplines that typically study each timescale in isolation—to offer a unified, multiscale account of skill acquisition.