  We review a simple mechanism for the formation of plateaux in the fractional
quantum Hall effect. It arises from a map of the microscopic Hamiltonian in the
thin torus limit to a lattice gas model, solved by Hubbard. The map suggests a
Devil's staircase pattern, and explains the observed asymmetries in the widths.
Each plateau is a new ground state of the system: a periodic Slater state in
the thin torus limit. We provide the unitary operator that maps such limit
states to the full, effective ground states with same filling fraction. These
Jack polynomials generalise Laughlin's ansatz, and are exact eigenstates of the
Laplace-Beltrami operator. Why are Jacks sitting on the Devil's staircase? This
is yet an intriguing problem.
