  The recent sample of 21 detached eclipsing binaries in the Small Magellanic
Cloud (Harries et al. 2003, Hilditch et al. 2005) provides a valuable test of
the binary mass function for massive stars. We show that 50% of detached
binaries have companions with very similar masses, q=M_2/M_1 > 0.87, where M_1,
M_2 denote the masses of the two binary components, M_1 > M_2. A Salpeter
relative mass function for the secondary is very strongly excluded, and the
data is consistent with a flat mass function containing 55% of the systems and
a ``twin'' population with q>0.95 containing the remainder. We also survey the
vast existing literature discussing the mass ratio in binaries and conclude
that a significant twin population (of more than 20-25%) exists in binaries
that are likely to interact across a broad range of stellar masses and
metallicity. Interactions involving nearly equal mass stars have distinctly
different properties than those involving stars of unequal mass; the
secondaries will tend to be evolved and the common envelope evolution is
qualitatively different. The implications of such a population for both binary
interactions and star formation are substantial, and we present some examples.
We argue that twin systems may provide a natural stellar population to explain
the recently proposed prompt channel for type Ia SN, and the presence of a twin
population dramatically reduces the maximum inferred NS+BH merger rate relative
to the NS+NS merger rate. Twins may also be important for understanding the
tendency of WD and NS binaries to be nearly equal in mass, and inclusion of
twins in population studies will boost the blue straggler production rate.
