  In some sense, the world is composed of shapes and words, of continuous
things and discrete things. The recognition and study of continuous objects in
the form of shapes occupies a significant part of the effort of unraveling many
geometric questions. Shapes can be rep- resented with great generality by
objects called currents. While the enormous variety and representational power
of currents is useful for representing a huge variety of phenomena, it also
leads to the problem that knowing something is a respectable current tells you
little about how nice or regular it is. In these brief notes I give an
intuitive explanation of a result that says that an important class of minimal
shape decompositions will be nice if the input shape (current) is nice. These
notes are an exposition of the paper by Ibrahim, Krishnamoorthy and Vixie which
can be found on the arXiv:1411.0882 and any reference to these notes, should
include a reference to that paper as well.
