  We discuss a problem of Arnold, whether every function is stably equivalent
to one which is non-degenerate for its Newton diagram. We argue that the answer
is negative. We describe a method to make functions non-degenerate after
stabilisation and give examples of singularities where this method does not
work. We conjecture that they are in fact stably degenerate, that is not stably
equivalent to non-degenerate functions. We review the various non-degeneracy
concepts in the literature. For finite characteristic we conjecture that there
are nowild vanishing cycles for non-degenerate singularities. This implies that
the simplest example of singularities with finite Milnor number, $x^p+x^q$ in
characteristic $p$, is not stably equivalent to a non-degenerate function. We
argue that irreducible plane curves with an arbitrary number of Puiseux pairs
(in characteristic zero) are stably non-degenerate. As the stabilisation
involves many variables, it becomes very difficult to determine the Newton
diagram in general, but the form of the equations indicates that the defining
functions are non-degenerate.
