  Most of what is known about neutrino masses and mixings results from studies
of oscillation phenomena. We focus on those neutrino properties that are not
amenable to such studies: $\Sigma $, the sum of the absolute values of the
neutrino masses; $m_\beta $, the effective mass of the electron neutrino; and
$m_{\beta\beta} $, the parameter governing neutrinoless double beta decay. Each
of these is the subject of ongoing experimental or observational studies. Here
we deduce constraints on these observables resulting from any one of six {\it
ad hoc\} hypotheses that involve the three complex mass parameters $m_i$: (1)
Their product or (2) sum vanishes; (3) Their absolute values, like those of
charged leptons or quarks of either charge, do not form a triangle; (4) The
$e$-$e$ entry of the neutrino mass matrix vanishes; (5) Both the $\mu$-$\mu$
and $\tau$-$\tau$ entries vanish; (6) All three diagonal entries are equal in
magnitude. The title of this note reflects the lack of any theoretical basis
for any of these simple assertions.
