In
mathematics,
singularity theory studies spaces that are almost
manifolds, but not quite. A string can serve as an example of a one-dimensional manifold, if one neglects its thickness. A singularity can be made by balling it up,
dropping it on the floor, and flattening it. In some places the flat
string will cross itself in an approximate
X shape. The points on the
floor where it does this are one kind of singularity, the double point: one
bit of the floor corresponds to
more than one bit of string. Perhaps the string will also touch itself without crossing, like an underlined '
U'. This is another kind of singularity. Unlike the double point, it is not
stable, in the sense that a small push will lift the bottom of the 'U' away from the 'underline'.