  We perform the first self-consistent, time-dependent, multi-group
calculations in two dimensions (2D) to address the consequences of using the
ray-by-ray+ transport simplification in core-collapse supernova simulations.
Such a dimensional reduction is employed by many researchers to facilitate
their resource-intensive calculations. Our new code (F{\sc{ornax}}) implements
multi-D transport, and can, by zeroing out transverse flux terms, emulate the
ray-by-ray+ scheme. Using the same microphysics, initial models, resolution,
and code, we compare the results of simulating 12-, 15-, 20-, and
25-M$_{\odot}$ progenitor models using these two transport methods. Our
findings call into question the wisdom of the pervasive use of the ray-by-ray+
approach. Employing it leads to maximum post-bounce/pre-explosion shock radii
that are almost universally larger by tens of kilometers than those derived
using the more accurate scheme, typically leaving the post-bounce matter less
bound and artificially more "explodable." In fact, for our 25-M$_{\odot}$
progenitor, the ray-by-ray+ model explodes, while the corresponding multi-D
transport model does not. Therefore, in two dimensions the combination of
ray-by-ray+ with the axial sloshing hydrodynamics that is a feature of 2D
supernova dynamics can result in quantitatively, and perhaps qualitatively,
incorrect results.
