Re: [EXTERNAL] Some braille references

Hi Bill,

Luckily (for me), Neil is overly optimistic on exactly the part you're
happy to support, so I can contradict you both in tandem. The claim:
"as an mfrac with linethickness=0, there is no problem understanding
that it is a binomial to a software translator"

is only accurate if you've decided this is all you're going to support
in your software. And especially in cases using "\atop", rather than
"\binom", because - as the name suggests - there is no semantic
commitment even in the latex macro, let alone the presentation MathML.

As is customary, some freshly collected counter-examples from arXiv:
 -- ( · \atop · ) is used for a column vector;
   - (C.4) in https://arxiv.org/pdf/0906.3743.pdf
   - (1,1), Theorem 2.4, (2.21),... in https://arxiv.org/pdf/0906.2242.pdf
   - page 4, in https://arxiv.org/pdf/math/0607411.pdf
   - (52), (53) in https://arxiv.org/pdf/cond-mat/0609580.pdf
   - with fractional values, bottom of page 8 in
https://arxiv.org/pdf/1112.5353.pdf
   - (2.9) in https://arxiv.org/pdf/hep-th/0607092.pdf
   - "spin part" of the wave function after (4) in
https://arxiv.org/pdf/cond-mat/0009028.pdf
   - figure 4 in https://arxiv.org/pdf/1909.07663.pdf
   - "bispinor", (20) in https://arxiv.org/pdf/1205.6983.pdf
--  ( · \atop · ) used to classify Einstein equations:
   - start of Appendix A, page 12 in https://arxiv.org/pdf/1302.4875.pdf

-- {pmatrix} used to write binomials:
   - page 3 of https://arxiv.org/pdf/math/0506006.pdf
   - specifically: \begin{pmatrix}n\\ i\end{pmatrix} and
\begin{pmatrix}m\\ i\end{pmatrix}

I of course also spotted a couple of binomial uses of \atop along the
way (such as https://arxiv.org/pdf/cond-mat/0011360.pdf ), in support
of Murray's use.

I am happy to repeat this point (with examples) as many times as
needed. Namely, an assumption that any mathematical notation (i.e.
presentation tree) has a *unique* implied meaning is bound to be
demonstrably false, when compared against the full body of
mathematical writing. It can be a correct assumption if contained to a
specific area of writing, such as "K-14 western educational
materials". And then we can explicitly enumerate exactly what we mean,
with explicit tests and selector patterns. We've discussed such an
approach as part of a "Default Intent" effort.

As to adding "minimal semantic information available in presentation
MathML", we first need to answer "serving which applications?". For
the accessibility-oriented ones, the discussions about Intent
annotations have been making some progress, and it is a good design
choice to think of parallel attributes on top/on the side of the
presentation tree. As a baseline, communicating exactly what is
written has the great benefit of not making false claims about what
was meant.

So, to conclude. "an mfrac with linethickness=0" is clearly ambiguous
in arXiv, and can't be defaulted to any one meaning, as far as that
corpus is concerned.

P.S. Side-remark: sometimes an article uses notation so exotic that
even knowing that *some* uses of \atop are binomials, still leaves an
unsuspecting reader guessing if *all* uses of \atop are binomials, or
instead get overloaded for some other purpose. I stumbled on one such
document. "Example 21" in it is not for the faint of heart, even if
you are fully sighted and prepared to tackle arXiv. Enjoy:
https://arxiv.org/pdf/1512.05937.pdf

Greetings,
Deyan

On Thu, Jul 8, 2021 at 9:37 PM Hammond, William F <whammond@albany.edu> wrote:
>
> (I may be in a top-posting dungeon for a while.  Sorry.)
>
> Neil writes:
>
> If the binomial is represented as an mfrac with linethickness=0, there is no problem understanding that it is a binomial to a software translator. But if it is represented using mtable, then there is nothing to distinguish the two in the presentation MathML.
>
>
> Notice that Neil is saying that there is value in having minimal semantic information available in presentation MathML.  (I've said this before regarding the removal of <mfenced>.)
>
>            -- Bill
>
>
>
> ________________________________
> From: Neil Soiffer <soiffer@alum.mit.edu>
> Sent: Thursday, July 8, 2021 5:57 PM
> To: Noble, Stephen <steve.noble@pearson.com>
> Cc: Murray Sargent <murrays@exchange.microsoft.com>; deyan.ginev@gmail.com <deyan.ginev@gmail.com>; ljmaher03@outlook.com <ljmaher03@outlook.com>; www-math@w3.org <www-math@w3.org>
> Subject: Re: [EXTERNAL] Some braille references
>
> I heard back from Susan Osterhaus. Her reply was basically that transcribers typically don't know math well so Nemeth code is designed so that it only reflects the symbols on the page, not the interpretation of them since that is beyond what transcribers typically know. That reminded me of what Dr. Nemeth said of MathSpeak (the way to speak math that resembles Nemeth). His readers didn't typically know much math, so he just wanted them to tell him what was on the page so he could write it in (Nemeth) braille on his braille writer and be able to review it.
>
> I did come up with one notation where someone needs to make a semantic determination: binomial vs 2x1 column matrix. In Nemeth, a binomial is represented with an open paren,  top part, a "directly under" symbol, followed by the bottom part, and finally a close paren; a matrix would occupy two lines. There might be a single line way of doing a matrix for braille displays, but I didn't see it mentioned.  If the binomial is represented as an mfrac with linethickness=0, there is no problem understanding that it is a binomial to a software translator. But if it is represented using mtable, then there is nothing to distinguish the two in the presentation MathML. Typically the subject area would make it obvious, but in isolation, some hint from the author is needed. The same is true for a sighted reader. Many WYSIWYG editors use the mtable form for binomials, so this is not a theoretical problem, but one that is common in MathML usage.
>
> Susan Jolly sent me email and reminded me that Nemeth was very thoughtful in his choice of dot patterns so that they would be more intuitive. For example, here is a fraction (recall a braille cell is 3x2 dots):
> ⠹⠆⠌⠒⠼
>
> There are five braille cells in the expression. The first and last cells are the start and end fraction symbols and the middle cell is the 2D  "/". The full column for the start/end is like a fence for fingers and the middle symbol resembles the slash, so this can be easily(?) recognized as a fraction. FYI: the numerator is a '2' (a "dropped" b ['b' starts in the first row, not the second]) and the denominator is a 3 (a dropped c). Another example of an encoding choice that resembles the print form is '=' which has the two character braille representation "⠀⠨⠅⠀" ("that is a "⠨" and a "⠅" character with a blank before and after it). That's your braille lesson for today :-)
>
>     Neil

Received on Friday, 9 July 2021 04:22:12 UTC