Re: Arguments for supporting Motion P1788/0023.01:NoMidRad
Ralph Baker Kearfott wrote:
Actually, if there were only one way of doing something or constructing
something, would there be a need for standardizing it?
A need for standardizing exists only if different versions are so
widely used that lack of standardization impedes progress.
This is not the case for midrad arithmeitc. In this case,
standardization by elimination of one of the options would even
be unwise, since different midrad operation definitions have
different uses.
Should (2+-1)*(2+-1) be 4+-5 or 5+-4?
Both are correct and both are most useful in the right circumstances.
The proper choice depends on which use one wants to make of the
operation. The first choice is the only choice that is suitable
for vectorizing interval linear algebra. But the second choice has
the desirable attribute of being tightest, which is the most
critical requirement when a significant uncertainty io present.
So one would have to standardize at least two different midrad
arithmetics.
Putting midrad into the standard thus heavily multiplies the work
to be done by the committee. It will give a nightmare in many respects,
dissipating lots of energy and delay completion of the standard
-- for a very questionable gain.
Note that I am neither against midrad nor against Kaucher intervals.
In particular, I have made constructive use of both in my work.
But I am strongly against _standardizing_ it, because there hasn't
been enough theroetical and practical work with it to support the
decisions to be made and be aware of all the possible pitfalls,
and because designing for it well very much complicates the standard,
and makes decisions very difficult without further support by research.
I am aware of many pitfalls and pointed out the most dangerous ones.
But I have no idea whther my list is complete, or what else could
go wrong.
It requires much more research and experience before one can
confidently say that making design decisions regarding midrad or
Kaucher arithmetic has no ill-understood side effects.
It makes only sense to standardize something that has been used a lot,
so that all design tradeoffs are known and well-understood. This is
the case for infsup arithmetic on intervals defined as closed and
connected sets, but not for the other options.
Standardizing something too early is likely to introduce bad design
features that are hard to eliminate later, and stifles exploration
of the best possibilities.
Thus I believe that even those promoting midrad and Kaucher arithmetic
in this forum will be better off not having a standardized -- hence
rigid and for a long time incorrigible -- framework, to which they are
forced to stick to be standard compliant.
But with the present motion passed, they have all the freedom they need,
and are compliant as long as the infsup part of their implementation
(without which no interval implementation is of general use) conforms
to the standard and a few useful and natural conversion rules are
obeyed.
Arnold Neumaier
On 9/16/2010 02:42, Arnold Neumaier wrote:
Paul Zimmermann wrote:
I strongly advise to include mid-rad in P1788, at least to clarify
how to
correctly represent a mid-rad interval, and how to correctly compute
with it.
There is no single correct way of computing with midrad intervals.
Several things depend on which judgment is made, already in exact
arithmetic, and different choices have different advantages and
disatvantages.