  We prove that suitable weak solutions of the Navier-Stokes equations exhibit
Type I singularities if and only if there exists a non-trivial mild bounded
ancient solution satisfying a Type I decay condition. The main novelty is in
the reverse direction, which is based on the idea of zooming out on a regular
solution to generate a singularity. By similar methods, we prove a Liouville
theorem for ancient solutions of the Navier-Stokes equations bounded in $L^3$
along a backward sequence of times.
