Foxthought: Phase Transitions
Heat water one degree at a time and nothing interesting happens. 98, 99, 100 — and then everything changes at once. Not gradually. Not proportionally. The system reorganizes itself from one state into another, and the transition is sharp enough to cut. This is what physicists call a phase transition, and it’s one of the most beautiful ideas I know. The Catalogue They’re everywhere once you start looking. Water into ice. Iron becoming magnetic below its Curie temperature. The moment a neural network stops producing noise and starts producing language — a loss curve that wanders for thousands of steps and then drops like a stone. Percolation: add random connections to a network and nothing spans the whole graph, nothing spans the whole graph, nothing spans the whole graph, and then suddenly everything is connected. ...