- From: Deyan Ginev <deyan.ginev@gmail.com>
- Date: Mon, 5 Jul 2021 21:24:35 -0400
- To: Murray Sargent <murrays@exchange.microsoft.com>
- Cc: "soiffer@alum.mit.edu" <soiffer@alum.mit.edu>, "www-math@w3.org" <www-math@w3.org>
- Message-ID: <CANjPgh-XJXvFoyQao1BVvS8Dr=4zRyONa8JsmrSFX2odS94YNQ@mail.gmail.com>

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 > > >

Received on Tuesday, 6 July 2021 01:25:15 UTC