RE: Motion 52: final "Expressions" text for vote
My understning is that most things with decorations are well-defined, problems appear with things like NaI for which lack a good math foundations even for exact numbers, so I do not think that the ltest problems revealed a major crisis, I may have missed something
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From: Bill Walster [billwalster@xxxxxxxxx] on behalf of G. William (Bill) Walster [bill@xxxxxxxxxxx]
Sent: Friday, November 22, 2013 12:15 PM
To: Kreinovich, Vladik; Michel Hack; stds-1788
Subject: Re: Motion 52: final "Expressions" text for vote
Sure, Vladik.
Any standard for how to implement computing with mathematically defined
objects will be ambiguous unless the definition of the objects and the
results of operations on, and functions of them are unambiguously
defined. It has been clear, at least to me, from the outset that the
current P1788 effort was doomed because such a mathematical foundation
has yet to be developed. Such a foundation must be completely
independent of any implementation considerations.
Instead of concentrating on the mathematical foundation, what has been
attempted is to define the mathematics and its implementation
simultaneously. This is extremely difficult because existing hardware
and languages impose constraints on any implementation that then become
imposed on the mathematics. This causes confusion, misunderstandings,
and results in an extremely unclear, ambiguous, and baroque draft
standard, which in my opinion is what exists.
As evidenced by many discussions including the recent ones on Motion 52,
I believe without a clear mathematically sound foundation on which to
base any interval implementation, we will only hurt our credibility in
the larger mathematical and scientific communities by continuing on the
current P1788 path.
A way to put computing with intervals on a solid mathematical foundation
is to wait to consider implementation details, including language syntax
and semantics, until the mathematical foundation for its implementation
is published in "Mathematics of Computation."
<http://www.ams.org/publications/journals/journalsframework/mcom>
This is my motion and the reason for it.
Cheers,
Bill
On 11/22/13 10:43 AM, Kreinovich, Vladik wrote:
> Can you please explain what you mean?
>
> ________________________________________
> From: stds-1788@xxxxxxxx [stds-1788@xxxxxxxx] on behalf of G. William (Bill) Walster [bill@xxxxxxxxxxx]
> Sent: Friday, November 22, 2013 10:24 AM
> To: Michel Hack; stds-1788
> Subject: Re: Motion 52: final "Expressions" text for vote
>
> How can a standard for computing with intervals be constructed if the
> result of evaluating any given numerical expression that contains
> intervals is ambiguous? I do not believe it can, and therefore, I
> believe such a construction is premature. As evidence of this fact, I
> the recent discussion concerning the content of Motion 52 is more than
> sufficient proof.
>
> Therefore, I move that all work on a standard for computing with
> intervals be suspended until such an unambiguous interval mathematical
> foundation is developed and published in "The Mathematics of Computation."
>