Re: Motion 31 draft text V04.4, extra notes
John Pryce wrote:
On 6 Apr 2012, at 17:13, Nate Hayes wrote:
But I believe we also want to support intervals as ranges, e.g. for
constraint propagation. In that case it is essential to provide for
unbounded intervals at Level 1.
Folks, I apologize in advance for being pedantic but someone needs to
explain this to me:
Why is it "essential"?
Specifically: what is a concrete example of a computer algorithm that can
produce more meaningful results with unbounded Level 1 intervals as
opposed
to "overflown" intervals at Level 2?
This question has both a theological and a practical aspect...
...
of these would be dragged off by someone with horns, a red cloak and a
trident.
John, thank you for the colorful philosophy lesson.
I'm not sure what to make of it all.
Infinities aren't "essential", but they sure are "useful". I know as well
as you, Nate, that one can't compute meaningful results at Level 2 for
numbers beyond the largest representable, REALMAX. But that does NOT imply
(1) X= [a,oo] actually *means* [a,B] for some large finite B; nor
(2) it is always computationally useful to replace X by [a, REALMAX].
It appears to me you have changed the subject. Neither (1) nor (2) are
relevant to what I'm talking about or the question I've asked.... I've
certainly never advocated (2). So I'm not sure what any of this has to do
with anything, or why you even bring it up.
I'd note that "overflown" intervals at Level 2 still involve the notion of
infinity, since an "overflown" interval is related to a familiy of intervals
with an infinite number of elements. So if you've switched the topic away
from unbounded intervals to "infinites", I wouldn't disagree that infinites
are useful. But my point is how the infinites relate to the Level 1 and
Level 2 models in terms of unbounded vs. "overflown" intervals. I still have
no clue what point (if any) you are trying to make on that topic.
We COULD do banking without negative numbers: probably we used to, with
two separate books, one for credit and one for debit balances. We COULD do
electrical engineering without complex numbers. We COULD write Maxwell's
equations as Maxwell did, without vector notation. We COULD do without oo.
But let's do things conveniently. What's the big deal?
Well, that's my point! As far as I can see, "overflown" intervals do
everything P1788 requires. Compared to unbounded intervals, they also make
my life much more simpler and convenient. I believe it will do the same for
others.
In my view, unbounded intervals are an overly-complicated and unnecessary
aspect of the Level 1 model, and I see this complication trickles down to
Level 2 and below into the implementations. I believe Motion 3 was the right
thing to do at the time, but over the years of listening to P1788
discussions I've come to the conclusion the standard Level 1 model should be
restricted to bounded intervals, with the notion of "overflown" intervals
then introduced at Level 2.
This is all separate from the issue of whether 1788 should give a way to
*distinguish* a genuinely unbounded interval from an "overflowed" one that
is known to be bounded but has a bound outside the representable range.
I think P1788 just needs to pick one or the other: ubounded or "overlown"
intervals. I see absolutely no reason for both, since I have been asking the
question for years "what is an example of any algorithm that requires both"
and no one has ever answered that question, either!!
Nate