What is the mechanism of learning in the brain? Despite breathtaking advances in neuroscience, we do not seem close to an answer. We introduce PJOIN (for “predictive join”), a primitive that com- bines and extends the operations of JOIN and LINK that are the basis of Valiant’s computational theory of cortex. We show that PJOIN can be implemented naturally in Valiant’s neuroidal model, a conservative formal model of cortical computation. Using PJOIN — and almost nothing else — we give a simple algorithm for unsupervised learning of arbitrary ensembles of binary patterns. This algorithm relies crucially on prediction, and entails significant downward traffic (“feedback”) while parsing stimuli. Prediction and feedback are well-known features of neural cognition and, as far as we know, this is the first theoretical prediction of their essential role in learning.