Re: Friendly amendment to Motion 25
> From: "Nate Hayes" <nh@xxxxxxxxxxxxxxxxx>
> To: "P-1788" <stds-1788@xxxxxxxxxxxxxxxxx>
> Subject: Friendly amendment to Motion 25
> Date: Sat, 28 May 2011 12:25:11 -0500
>
>
> P1788,
>
> In light of recent discussions, I submit the attached PDF as a friendly
> amendment to Motion 25.
>
> Since there appears to be strong agreement between myself, John and Arnold
> on the treatment of the min and max operations, I have moved this out of the
> rationale and into the motion text.
>
> To capture other ground which appears to have been gained, I also added a
> new section in the rationale entitled "Towards a Foundation of Decorations"
> that I hope people will consider.
>
> Sincerely,
>
> Nate Hayes
>
Nate,
In future it might be nice if you 'decorated' such friendly
amendments with the changes from the original motion. Or,
at least, tell us what the differences are. As best I can
tell the only differences are in the new section 2.4 & a
new section 3.3 discussing FTDIA.
No matter.
In section 2.4 you state that the domain for min & max shall
be the same as for add. Indeed, I am fairly sure that the
domain for min & max must be strictly LARGER than that for
add. Min & max must be defined for empty operands & non-
empty results whereas add is not. That is, min & max of a
non-empty operand together with an empty operand must be the
non-empty operand. So min & max return results in a domain
where add would return empty. Min & max of both empty
operands is empty just as it is in add. I'll leave it to
your sense of parsimony of definition to decide whether that
case is outside the domain of min & max or inside it &
defined to be empty.
You make no mention of it but it must be true that union &
intersection also differ from add in their domains of
validity.
The continuous you describe in definition 1 is C0 continuous.
This must be so if, as you state later:
S(sqrt,[0,4]) = D3.
Definition 3 only applies to functions for which having one
of their operands empty is OUTSIDE their domain. Min & max
are counter examples as may be other functions.
The entries in the table in section 3 contain all possible
examples of a decoration crossed with an empty or non-empty
result. And yet for many of the entries I cannot think of
an example that applies. Can you provide representative
examples for each entry please?
Many of the entries seem contradictory or, at least,
confusing without examples to guide me. In particular,
decoration = D0, result = non-empty seems to describe a
function that manages to return a non-empty result even
though the cross product of its operands is entirely
OUTSIDE its domain of definition. Other entries have
similar conceptual problems for me.
Whether your philosophy is tracking or static the one
fundamental property we need to prove an FTDIA is the subset
property. That is, if xx \subset yy then we must have
S(f,xx) >= S(f,yy) FOR ALL xx, yy, & f.
And yet you permit (in so many words on page 2):
S(sqrt,[0,4]) = D3
S(sqrt,[-1,2]) = D1
S(sqrt,[-3,-1]) = D0
Thus, were I to have xx = [-3,-1] & yy = [-3,2] we would
have xx \subset yy but S(sqrt,xx) < S(sqrt,yy).
You use the word Tracking when you describe your approach
but this is neither tracking nor static behavior. And not
consistent with FTDIA as I have come to understand it.
And we still have no decoration for 'ill'.
Yours,
Dan