Re: Constructors motion
Dear Dan and colleagues,
Sorry to catch up the discussion so late.
> Please forgive a naive question but can someone tell me
> why Kaucher intervals are excluded?
Although I see several scientific and technical reasons why we should
not include Kaucher intervals in the standard: We already had this
discussion more than one year ago, so I am surprised to hear Mr. Hayes
now saying that it is not complex to include Kaucher intervals in the
standard! For exemple, Kaucher interval arithmetic is not defined for
unbounded intervals, there is no empty Kaucher interval, there is no
clear definition of the evaluation of a function for Kaucher intervals
that are outside its domain, there no way to interleave Kaucher
intervals arithmetic and reverse operations, etc.
I think the right question is why would we actually include them in
the standard?
Mr. Hayes owns several patents on modal intervals, so his reasons for
including modal intervals in the standard are clear. Another reason
could be that Kaucher intervals are useful to solve some important
problems. I read later in the discussion
> Our users are going
> to need some flavor of non-standard intervals to aid
> them in solving equations.
Why do you think that Dan? My personal experience shown me that
classical interval can do everything that Kaucher intervals do, even
better. There are some exceptions, like solving equations in the space
of intervals, but I think actual applications of Kaucher arithmetic
are not at all among the interests of Mr. Hayes.
If I remember well, Mr. Hayes has been arguing in last year
discussions that modal interval can be quicker on some very specific
problems. But I did not see anything concrete, although Arnold
Neumaier has spent lot of energy to try clarifying this question!
From a non scientific point of view, I don't think more than 10 people
worldwide do know well this theory, among which some disagree on key
points of the theory. Is it reasonable to try include such a non
mature theory in the standard? There is still a lot of work for
obtaining a good standard for classical interval, should not we better
spend our time on these issues? Finally, I think having Kaucher
intervals included in the standard will make it harder to use to
people not familiar with interval arithmetic, which could not help
spreading the standard.
> OK, let's decide NOW whether or not we want Kauchers
> to be part of the standard, extension or not.
I agree with you Dan, let's not loose more time on this question ! I
think this would be a critical error to include Kaucher intervals in
the standard, that could even lead to its failure. But this is only my
personal opinion.
Kind regards,
Alexandre
--
Dr. Alexandre Goldsztejn
CNRS - Laboratoire d'Informatique de Nantes Atlantique
Office : +33 2 51 12 58 37 Mobile : +33 6 78 04 94 87
Web: www.goldsztejn.com
Email: alexandre.goldsztejn@xxxxxxxxxxxxxx