  Since Baade's photographic study of M32 in the mid 1940s, it has been
accepted as an established fact that M32 is a compact dwarf satellite of M31.
The purpose of this paper is to report on the findings of our investigation
into the nature of the existing evidence. We find that the case for M32 being a
satellite of M31 rests upon Hubble Space Telescope (HST) based stellar
population studies which have resolved red-giant branch (RGB) and red clump
stars in M32 as well as other nearby galaxies. Taken in isolation, this recent
evidence could be considered to be conclusive in favour of the existing view.
However, the conventional scenario does not explain M32's anomalously high
central velocity dispersion for a dwarf galaxy (several times that of either
NGC 147, NGC 185 or NGC 205) or existing planetary nebula observations (which
suggest that M32 is more than twice as distant as M31) and also requires an
elaborate physical explanation for M32's inferred compactness. Conversely, we
find that the case for M32 being a normal galaxy, of the order of three times
as distant as M31, is supported by: (1) a central velocity dispersion typical
of intermediate galaxies, (2) the published planetary nebula observations, and
(3) known scaling relationships for normal early-type galaxies. However, this
novel scenario cannot account for the high apparent luminosities of the RGB
stars resolved in the M32 direction by HST observations. We are therefore left
with two apparently irreconcilable scenarios, only one of which can be correct,
but both of which suffer from potentially fatal evidence to the contrary. This
suggests that current understanding of some relevant fields is still very far
from adequate.
