  A taming symplectic structure provides an upper bound on the area of an
approximately pseudoholomorphic curve in terms of its homology class. We prove
that, conversely, an almost complex manifold with such an area bound admits a
taming symplectic structure. This confirms a speculation by Gromov. We also
characterize the cone of taming symplectic structures numerically, prove that
complex 2-cycles can be approximated by coarsely holomorphic curves, and
provide a lower energy bound for such curves.
