Re: [EXTERNAL] Some braille references

Dear Neil and Murray,

Thank you. I have allotted some time to study up on Braille, since I'm
completely ignorant on the technicalities of the topic at the moment, so
these resources help a lot.

I've also found (at a cursory glance) several introductory overviews on
youtube, which I also like exploring. There is a lot of high quality
educational STEM content on video streaming sites nowadays. One of them
linked to a fantastic resource by Pearson called "the Nemeth Symbol
Library", which has a wonderfully broad list of examples:

https://accessibility.pearson.com/resources/nemeth-curriculum/nemeth
-symbol-library/index.php

Another practical bit I liked from that talk was a short description of
"common issues in Nemeth code transcriptions" from a practitioner writing
such materials, as seen here:
https://youtu.be/_I3TQFOqbhc?t=1991

Lots to learn! Curious to see further pointers and discussion as to where
our "mathml intent" prototypes need to be extra-mindful of the Braille
serialization.

Deyan


On Sun, Jul 4, 2021 at 6:19 PM Murray Sargent <
murrays@exchange.microsoft.com> wrote:

> As Neil points out, UEB math braille is more verbose than Nemeth math
> braille due to the need for the numeric indicator to disambiguate 1-9 0
> from a-j. The post Braille for Math Zones
> <https://docs.microsoft.com/en-us/archive/blogs/murrays/braille-for-math-zones>
> discusses this and related considerations further. Nemeth has a number of
> other advantages, notably its productive rules for constructing braille for
> math symbols. I’ve used the rules to greatly extend the number of Unicode
> math symbols in Nemeth braille beyond those appearing in the official
> Nemeth standard. Another advantage is that so long as the math braille is
> inside math-zone delimiters (corresponding to TeX’s $’s or MathML’s <math>
> and </math>), it’s quite globalized, that is, it can work in many different
> languages without localization. In UEB, the math-zone start delimiter is
> ⠸⠩ and the end delimiter is ⠸⠱.
>
>
>
> As Neil also points out, Nemeth math braille is presentation oriented.
> Hopefully Sam Dooley will chime in with any non-presentation oriented
> examples. Off hand, I don’t think of any.
>
>
>
> Happy math brailling 😊
>
> Murray
>
>
>
> *From:* Neil Soiffer <soiffer@alum.mit.edu>
> *Sent:* Sunday, July 4, 2021 2:43 PM
> *To:* www-math@w3.org
> *Subject:* [EXTERNAL] Some braille references
>
>
>
> I've had a few people ask about braille math codes. For a long time in the
> US and many other places (including some non-English speaking countries),
> the Nemeth Braille code has been the most common braille code used. That
> code was designed by Abraham Nemeth, a blind mathematician, who came up
> with it for his own use. He then formalized it for use by others. The
> primary reference is often called the "green book" due to its stark green
> cover. It is online at
> https://nfb.org/images/nfb/documents/pdf/nemeth_1972.pdf
> <https://nam06.safelinks.protection.outlook.com/?url=https%3A%2F%2Fnfb.org%2Fimages%2Fnfb%2Fdocuments%2Fpdf%2Fnemeth_1972.pdf&data=04%7C01%7Cmurrays%40exchange.microsoft.com%7Cba5f4ada4f85482f582708d93f34e036%7C72f988bf86f141af91ab2d7cd011db47%7C0%7C0%7C637610319508427232%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=bkVI4wXqnRsywMSwBL0D21zWs3Op%2B94xX%2FF3d9%2F9JgY%3D&reserved=0>
> .
>
>
>
> Recently, a number of English countries unified the math braille code with
> the rest of the braille code used for literary text in Unified English
> Braille. UEB uses the same dot patterns for 0-9 and a-i and therefore
> requires a numeric prefix to say "now this means a digit" (Nemeth code
> numbers are a-j lowered down one dot). Needless to say, a numeric indicator
> makes math more verbose. I've seen estimates that UEB math uses ~40% more
> space to represent math. A tutorial on UEB math is
> https://uebmath.aphtech.org/
> <https://nam06.safelinks.protection.outlook.com/?url=https%3A%2F%2Fuebmath.aphtech.org%2F&data=04%7C01%7Cmurrays%40exchange.microsoft.com%7Cba5f4ada4f85482f582708d93f34e036%7C72f988bf86f141af91ab2d7cd011db47%7C0%7C0%7C637610319508437179%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=848MnSF82A6ogPXFRXHe1%2FVQnc54sI8Qr6opOQPbGEY%3D&reserved=0>.
> The tradeoff for the verbosity is that braille readers don't need to learn
> different patterns for 0-9 and some other characters such as "+" and "-".
> UEB provides a way to include Nemeth code in UEB literary code via
> start/end markers.
>
>
>
> The use of UEB math vs Nemeth is hugely controversial. Both math codes are
> very much oriented towards describing what is displayed and I don't think
> MathML favors either one. I do not think it is appropriate for any of our
> spec work to advocate for either standard. It would be good to learn for
> internationalization efforts whether any braille codes encode semantics
> (see below). Braille codes for languages based on the Roman alphabet have
> somewhat standardized on the patterns used for letters and some indicators
> (capital, number), but there is less commonality outside of those dot
> options (standard braille is 2x3 dots, hence 2^6=64 chars; there are some
> 2x4 versions). I have no knowledge of how braille is done in countries that
> don't have a small alphabet/letters.
>
>
>
> If some braille codes do make use of semantics, that could potentially
> affect our intent discussions. There are some people in the group who know
> Nemeth better than I do, so I hope they chime in and can give examples
> where Nemeth or some other braille code is not purely syntactic.
>
>
>
> A few other notes:
>
>
>
> Louis Braille was French and he developed the first braille code after losing
> his sight as a child
> <https://nam06.safelinks.protection.outlook.com/?url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FLouis_Braille&data=04%7C01%7Cmurrays%40exchange.microsoft.com%7Cba5f4ada4f85482f582708d93f34e036%7C72f988bf86f141af91ab2d7cd011db47%7C0%7C0%7C637610319508437179%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=h9sSmxKJJ%2BYxhycWBtCPbregIYeXy%2BLLz%2FH9cwzrKYI%3D&reserved=0>
> (it's a terrible story and not one to read if you are a new parent). Hence,
> the original braille code was French and there have been several revisions
> to the code since. One of the later changes is to add "dot 6" to the
> symbols a-i to indicate a number. This document
> <https://nam06.safelinks.protection.outlook.com/?url=https%3A%2F%2Fchezdom.net%2Fmathematicalbraillecodes%2F&data=04%7C01%7Cmurrays%40exchange.microsoft.com%7Cba5f4ada4f85482f582708d93f34e036%7C72f988bf86f141af91ab2d7cd011db47%7C0%7C0%7C637610319508447138%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=xRqZkgAdHJrfp3RPT4LYe5CvYUxHpkFNreHLZWswQJo%3D&reserved=0>
> summarizes some other braille codes used in other countries and has some
> references.
>
>
>
> DotsPlus
> <https://nam06.safelinks.protection.outlook.com/?url=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DnutFACIkIR0C%26pg%3DPA1219%26lpg%3DPA1219%26dq%3Ddotsplus%2Bmath%26source%3Dbl%26ots%3DERWYIi8WGz%26sig%3DACfU3U2tlFn70QN-WeD1sWkwZkPDAzk8IA%26hl%3Den%26sa%3DX%26ved%3D2ahUKEwjcz4m3rMrxAhUWip4KHTdIBYAQ6AEwBXoECA8QAw%23v%3Donepage%26q%3Ddotsplus%2520math%26f%3Dfalse&data=04%7C01%7Cmurrays%40exchange.microsoft.com%7Cba5f4ada4f85482f582708d93f34e036%7C72f988bf86f141af91ab2d7cd011db47%7C0%7C0%7C637610319508447138%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=Mx1oWhrfihPaWqorUbkPv7s5JM%2FqvtkrClFiwRY2%2F5U%3D&reserved=0>is
> a system for displaying braille math on a braille embosser developed by
> John Gardner. DotsPlus only requires knowledge of braille letters and
> numbers. All other symbols are displayed graphically. A major problem with
> DotsPlus is that it can't be written by a person easily (could use swell
> paper, but it would be difficult). A less major problem is that the
> vertical motion required to read it is unfamiliar to braille readers.
>
>
>
> A version of braille maybe used by the Dutch (introduced in 2009)
> linearizes the math first into a calculator-like notation with parens and
> some notations replaced by standard abbreviations (e.g, "sqrt(...)").
> Having linearlized and reduced the problem to text, standard braille can be
> used. Some schools in (I think) German speaking countries have pushed
> learning LaTeX for math and so they too use a linearization of the math
> that doesn't require a new code.
>
>
>
> Nemeth code translation requires some context when generating it. For
> example, nested fractions/radicals indicate the amount of nesting when they
> start/end ('start fraction start fraction ... end fraction end fraction'
> for a simple nesting). It also indicates the current level of scripts (e.g,
> 'super super script' for a second level script) and has a braille indicator
> for indicating "baseline" when a script has ended and is back to the
> baseline.
>
>
>
> Hopefully this sheds a little light on braille math. I strongly encourage
> others with more knowledge to elaborate on some points and/or correct
> things I wrote.
>
>
>
>     Neil
>
>
>