Braille for Math Zones

Mathematical text in modern technical documents appears in math zones. This is true for LaTeX, Microsoft Office math, MathType, Open Office, HTML5, etc. The main reason is that the typography of mathematical text differs from that for ordinary text (see, for example, User Spaces in Math Zones) and has special layout constructs such as square roots, stacked fractions and multilevel subscripts and superscripts. Nevertheless, the two math braille standards, Nemeth and Unified English Braille (UEB), were designed without math zones in mind. This lack led to unnecessarily complicated syntaxes since concepts such as natural language contractions needed to be disambiguated from math symbols. Furthermore, the standards are defined for English, while math braille can be used unchanged with most natural languages.

The most obvious simplification of relegating math to math zones is that it nearly eliminates the need for the Nemeth braille numeric indicator ⠼ in math zones since contractions aren’t used in math zones. In fact, the only need for the numeric indicator in a math zone is in the very rare case that the math style changes inside a number as in 1234. The code ⠼ is also used to end fractions, but that use never was ambiguous since contractions aren’t allowed in fractions and Nemeth digit codes represent digits inside fractions.

One common scenario for which ⠼ can be omitted is when a digit follows a space in a math zone. Relational operators like = and → are always surrounded by spaces in the Nemeth standard. For example, the limit

is officially written in Nemeth braille as

⠐⠇⠊⠍⠩⠭⠀⠫⠒⠒⠕⠀⠼⠴⠻⠀⠹⠎⠊⠝⠀⠭⠌⠭⠼⠀⠨⠅⠀⠼⠂

Here, the Nemeth standard specifies that since the 0 (⠴) and 1 (⠂) follow a space, they should be preceded by a ⠼. But in a math zone no ambiguity exists if the ⠼ is omitted, resulting in more efficient input and simplified braille display.

The numeric indicator must precede all numbers for UEB math braille in math zones and elsewhere, since UEB uses the same codes (⠁⠃⠉⠙⠑⠋⠛⠓⠊⠚) for 1-9, 0 as for the letters a through j, respectively. The Nemeth digits use those codes shifted down a row (⠂⠆⠒⠲⠢⠖⠶⠦⠔⠴) which don’t overlap letters or other symbols. The Nemeth digit codes appear as parts of some mathematical symbols, such as ⠫⠲ for □. This choice is mnemonic since a square has 4 (⠲) sides. No ambiguity there either. Some digit codes are used in common punctuation, such as 4 (⠲) in ⠸⠲ for period (as distinguished from decimal point). This use isn't ambiguous since the ⠲ is preceded by the punctuation indicator⠸.

In conclusion, it seems that the most efficient braille for math zones is Nemeth math braille minus the use of the numeric indicator except in the rare switching of numeric styles as in abcd. Such math braille is international except where natural language words are inserted such as “if”. In contrast, the text surrounding math zones is in a specific natural language. UEB is the obvious choice for English text. When Nemeth math zones are embedded in UEB, they start with ⠸⠩ and end with ⠸⠱ in accord with Using the Nemeth Code within UEB contexts. Other languages may be able to embed Nemeth math zones with these codes too. Math braille isn’t simple, but in modern documents it’s simpler than you may have thought ☺.