A pair of identical particles swapping places sounds like a small move. In quantum physics, it is a defining one. In everyday three-dimensional space, that swap only comes in two flavors. Either the system looks exactly the same after the exchange, or it flips sign in a way that forces the particles to avoid sharing a state. Those two outcomes sit at the heart of the boson and fermion divide that organizes the Standard Model. Lower the number of dimensions, and that clean split starts to fray. Physicists have predicted since the 1970s that a middle ground should exist: anyons, particles that are neither bosons nor fermions. In 2020, experiments observed anyons at the interface of supercooled, strongly magnetized, one-atom-thick semiconductors, a two-dimensional setting. Now two joint papers in Physical Review A describe a one-dimensional system where anyons can exist, and spell out what their behavior should look like. (a) Bosonic-anyon–fermionic-anyon mapping that connects Ψ+, Ψ−, Ψα,+, and Ψα,−. (b) Momentum distributions (top) nα,+(k) and (bottom) nα,−(k) for three identical free-space bosonic anyons and fermionic …