  Certain mathematical structures make a habit of reoccuring in the most
diverse list of settings. Some obvious examples exhibiting this intrusive type
of behavior include the Fibonacci numbers, the Catalan numbers, the
quaternions, and the modular group. In this article, the focus is on a lesser
known example: the noncrossing partition lattice. The focus of the article is a
gentle introduction to the lattice itself in three of its many guises: as a way
to encode parking functions, as a key part of the foundations of noncommutative
probability, and as a building block for a contractible space acted on by a
braid group. Since this article is aimed primarily at nonspecialists, each area
is briefly introduced along the way.
