  We present herewith certain thoughts on the important subject of nowadays
physics, pertaining to the so-called ``singularities'', that emanated from
looking at the theme in terms of ADG (: abstract differential geometry). Thus,
according to the latter perspective, we can involve ``singularities'' in our
arguments, while still employing fundamental differential-geometric notions
such as connections, curvature, metric and the like, retaining also the form of
standard important relations of the classical theory (e.g. Einstein and/or
Yang-Mills equations, in vacuum), even within that generalized context of ADG.
To wind up, we can extend (in point of fact, {calculate) over singularities
classical differential-geometric relations/equations, without altering their
forms and/or changing the standard arguments; the change concerns thus only the
way, we employ the usual differential geometry of smooth manifolds, so that the
base ``space'' acquires now quite a secondary role, not contributing at all (!)
to the differential-geometric technique/mechanism that we apply. Thus, the
latter by definition refers directly to the objects being involved--the objects
that ``live on that space'', which by themselves are not, of course, ipso facto
``singular''!
