  Singularities appear in numerous important mathematical models used in
Physics. And in most of such cases singularities are involved in essentially
nonlinear contexts. For more than four decades, general enough nonlinear
theories of singularities have been developed. A critically important related
feature is that, above certain levels in singularities, the operation of
multiplication, and in general, nonlinear operations on such singularities do
inevitably branch in infinitely many ways, without the possibility for the
existence of some unique natural or canonical way such nonlinear operations may
be performed. Consequently, the choice in such branchings has to come from
extraneous considerations.
