[std-interval] Interval comparison operators
Dr John Pryce
j.d.pryce at ntlworld.com
Mon Jun 5 00:04:43 PDT 2006
Lee, and participants in this group
At 19:12 04/06/06, R. Baker Kearfott wrote:
>My view is that, if there is a hopeless lack of consensus, it may
>indicate that there isn't a single "right" way, but choosing
>a particular way and having a standard is better than having none.
>However, we should strive to maximize the utility of the language
>in the standard.
Like Baker, I feel optimistic that a consensus will emerge. I
STRONGLY agree with Baker's paragraph above.
Lee, you have written eloquently of the Principal Value (PV) model
that you have been working on. If it is as different in
concept/philosophy/goals (I don't know enough about it to know which
of those words are most appropriate) from the "classical interval
model" as you say, then certainly it needs a different standard from
one that supports the classical model. Therefore, I do not see you as
in conflict with the classical intervallers, but as complementary.
However I speak as the principal author of containment set (cset)
theory for the last few years. Csets are NOT the most widely held
view of classical intervals, and when I started working on them for
Bill Walster under contract to Sun around 2001 they were generally
seen as an eccentricity that would soon die out.
Evaluation of cset theory by the interval community was delayed
slightly by commercial confidentiality. That prohibited putting some
aspects of csets in the public domain - mainly Sun's implementation
detail. The main reason for delay was that Bill and I had serious
disagreement, not over what a cset-based interval implementation
should do, but about what the results *meant*. I believed, and still
do, that Bill's philosophy of csets at that time was mathematically
inconsistent. As a result we could not agree on a paper to submit to
the open literature. We spoke at conferences etc, but some of the
assertions we made were incompatible, which was not good for credibility.
Maybe it was a blessing in disguise, because then I joined the ISL
project steering committee, and working with 3 guys who have jointly
over 50 years interval programming experience, plus a professional
software engineer, widened my outlook so that the paper I eventually
wrote, Pryce and Corliss "Interval arithmetic with containment sets"
(2006), submitted to "Computing", see
http://homepage.ntlworld.com/j.d.pryce/isloct05/IntvlArithCsets.pdf
was far clearer and more concise than it would otherwise have been.
And, to my surprise, my ISL colleagues decided of their own accord
that a cset-based interval system was the one they preferred, though
the well-known packages they had up to then used, and in one case
written, were based on what I call the Simple System.
How did this come about? I believe it was because I had been able to
write an account that showed such a system is
- rock-solid mathematically,
- actually useful.
Both are necessary conditions for acceptance in this corner of
scientific computing (sadly, not sufficient). I urge you to move the
task of writing up what PV intervals are all about to near the top of
your priorities, if not the actual top. And get it into the open
literature so that people can pull your ideas to pieces (as my cset
ideas have been for several years), force you to refine them, and
eventually be convinced you are making sense.
I find many things you write very weird or downright false (e.g.
distinctions between line segments and sets, and tests on the empty
set). That is because I am matching it against my model, which is
firmly based on classical set theory. You have work to do to convince
me, but my mind is open. As I am a mathematician, the "rock-solid
mathematically" interests me more, initially, than the "actually
useful". I think many people with more interval experience and/or
more influence in the scientific world than I would agree with me.
PV intervals must be mathematically consistent, or they will die. But
there is more than that. You must have an underlying purpose for
them, or philosophy about them, that explains why this consistent bit
of mathematics actually helps humans solve real life problems. From
what you write, you are a fair way towards having both, but you won't
convince the world unless you WRITE IT UP for public evaluation.
Best wishes for that project.
John Pryce
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