  We consider the application of the multiple point criticality principle to
the pure Standard Model, with a desert up to the Planck scale. According to
this principle, Nature should choose coupling constant values such that the
vacuum can exist in degenerate phases. Furthermore we require a strongly first
order phase transition between the two vacua, in order that the dynamical
mechanism be relevant. Thus we impose the constraint that the effective Higgs
potential should have two degenerate minima, one of which should have a vacuum
expectation value of order unity in Planck units. In this way we predict a top
quark mass of 173 +/- 4 GeV and a Higgs particle mass of 135 +/- 9 GeV. A
possible model to explain the multiple point criticality principle is the lack
of locality in quantum gravity and the effects of baby universes which, on
general grounds, are expected to make coupling constants dynamical.
