theology; MAX and MIN

[gls@think.com (Guy Steele)]

   Date: Tue, 22 Aug 89 18:08:24 PDT
   From: will@cs.uoregon.edu

   Guy Steele Jr:
       Theologically or politically speaking, under the first view inexact numbers
       strive to obey laws acknowledged to be perfect, but to a greater or lesser
       degree are each in a state of sin.  Under the second view they are all
       model citizens, adhering perfectly to their own laws which, however, are
       acknowledged not to be ideal but merely the best one can do in this
       imperfect and finite world.

   In the imperfect world I live in, the supremum implied by the phrase
   "the best one can do" is even less likely to exist than in the world of
   computer arithmetic.

Touche'.  Make that "merely a pretty good thing one can do...".

   Theologically speaking, Guy's new proposal has the same problem as his old
   proposal:  It introduces two new demons to undermine a user's faith in
   exact numbers.  Only the names have changed: now the demons are called
   LARGEST and SMALLEST.  The damage done by these two procedures won't be
   ameliorated by having exactness-preserving SUP and INF as well.  For
   simplicity, I say that if MAX and MIN, by whatever names, are going to be
   exceptions to the perfect rules of exactness, then let's just acknowledge
   them as exceptions and to hell, theologically speaking, with the sinfully
   striving exactness-preserving versions.

Hm.  Mayhaps my metaphor hath become a petard.

I don't see why faith in the *exact* has been undermined, but only faith
in the *inexact* (which was probably misplaced anyway).  I think we all
agree that SUP and MAX/LARGEST would agree on exact inputs.  I think that
when you speak of "exactness-preserving" you mean "inexactness-preserving",
and similarly "perfect rules of exactness" => "perfect rules of
inexactness" which is then seen to be a contradiction in terms.

--Guy "I Haven't Had So Much Fun While Trying to Be Serious in Years" Steele