RE: [EXTERNAL] Some braille references

Good feedback. Note that Nemeth distinguishes between a binomial and a 2×1 column matrix. The binomial {n\atop k} is ⠷⠝⠩⠅⠾ and the nearly identically looking (inline) parenthesized 2×1 column matrix \pmatrix{n\\k\\} is ⠷⠠⠷⠝⠠⠾⠠⠷⠅⠠⠾⠾
Thanks,
Murray

From: Neil Soiffer <soiffer@alum.mit.edu>
Sent: Thursday, July 8, 2021 5:58 PM
To: Noble, Stephen <steve.noble@pearson.com>
Cc: Murray Sargent <murrays@exchange.microsoft.com>; deyan.ginev@gmail.com; ljmaher03@outlook.com; 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