  Homotopy probability theory is a version of probability theory in which the
vector space of random variables is replaced with a chain complex. A natural
example extends ordinary probability theory on a finite volume Riemannian
manifold M. In this example, initial conditions for fluid flow on M are
identified with collections of homotopy random variables and solutions to the
Euler equation are identified with homotopies between collections of homotopy
random variables. Several ideas about using homotopy probability theory to
study fluid flow are introduced.
