  In quantum mechanics, each observable is assigned a collection of
projections. Two observables are compatible (can be measured simultaneously) if
and only if any two projections that are assigned to them commute. This led to
the study of noncommuting sets of idempotents which further led to the skew
lattice theory that was founded and explored by Jonathan Leech. In the present
paper we shall see how noncommuting projections can be regarded as generators
of a skew lattice.
