We show that if the nearly-linear time solvers for Laplacian matrices and
their generalizations can be extended to solve just slightly larger families of
linear systems, then they can be used to quickly solve all systems of linear
equations over the reals. This result can be viewed either positively or
negatively: either we will develop nearly-linear time algorithms for solving
all systems of linear equations over the reals, or progress on the families we
can solve in nearly-linear time will soon halt