  Star formation in molecular clouds is intimately linked to their internal
mass distribution. We present an unprecedentedly detailed analysis of the
column density structure of a high-mass, filamentary molecular cloud, namely
IRDC G11.11-0.12 (G11). We use two novel column density mapping techniques:
high-resolution (FWHM=2", or ~0.035 pc) dust extinction mapping in near- and
mid-infrared, and dust emission mapping with the Herschel satellite. These two
completely independent techniques yield a strikingly good agreement,
highlighting their complementarity and robustness. We first analyze the dense
gas mass fraction and linear mass density of G11. We show that G11 has a top
heavy mass distribution and has a linear mass density (M_l ~ 600 Msun pc^{-1})
that greatly exceeds the critical value of a self-gravitating, non-turbulent
cylinder. These properties make G11 analogous to the Orion A cloud, despite its
low star-forming activity. This suggests that the amount of dense gas in
molecular clouds is more closely connected to environmental parameters or
global processes than to the star-forming efficiency of the cloud. We then
examine hierarchical fragmentation in G11 over a wide range of size-scales and
densities. We show that at scales 0.5 pc > l > 8 pc, the fragmentation of G11
is in agreement with that of a self-gravitating cylinder. At scales smaller
than l < 0.5 pc, the results agree better with spherical Jeans' fragmentation.
One possible explanation for the change in fragmentation characteristics is the
size-scale-dependent collapse time-scale that results from the finite size of
real molecular clouds: at scales l < 0.5 pc, fragmentation becomes sufficiently
rapid to be unaffected by global instabilities.
