  We study the effects of projection of three-dimensional (3D) data onto the
plane of the sky by means of numerical simulations of turbulence in the
interstellar medium including the magnetic field, parameterized cooling and
diffuse and stellar heating, self-gravity and rotation. We compare the
physical-space density and velocity distributions with their representation in
position-position-velocity (PPV) space (``channel maps''), noting that the
latter can be interpreted in two ways: either as maps of the column density's
spatial distribution (at a given line-of-sight (LOS) velocity), or as maps of
the spatial distribution of a given value of the LOS velocity (weighted by
density). This ambivalence appears related to the fact that the spatial and PPV
representations of the data give significantly different views. First, the
morphology in the channel maps more closely resembles that of the spatial
distribution of the LOS velocity component than that of the density field, as
measured by pixel-to-pixel correlations between images. Second, the channel
maps contain more small-scale structure than 3D slices of the density and
velocity fields, a fact evident both in subjective appearance and in the power
spectra of the images. This effect may be due to a pseudo-random sampling
(along the LOS) of the gas contributing to the structure in a channel map: the
positions sampled along the LOS (chosen by their LOS velocity) may vary
significantly from one position in the channel map to the next.
