The information in this article is based on my understanding of the April 2003 Draft copy of "The Nemeth Uniform Braille System: NUBS" [which can be downloaded from the link] by Abraham Nemeth, Ph.D. Any opinions, findings, and conclusions or recommendations expressed in this article are those of the author and do not necessarily reflect the views of Dr. Nemeth. The article assumes some familiarity with the current Nemeth code.
Executive Summary A minor modification to the Nemeth braille code has been proposed by Dr. Nemeth. The modified version is called the Nemeth Uniform Braille System (NUBS). NUBS employs explicit indicators to delineate inline or embedded mathematics from surrounding text. (The use of explicit indicators removes any possibilities for ambiguity and eliminates any need for special rules involving contractions and short-form words.) NUBS also distinguishes text, with or without embedded mathematics, from displayed mathematics.
NUBS has been carefully designed to ensure that all mathematical items are transcribed identically whether the items are embedded or displayed. This is in contrast the proposed UEB (Unified English Braille) where this is not always the case. NUBS also avoids the indicator clutter and long expressions associated with the UEB. Another advantage of NUBS mathematics is that it, like Nemeth mathematics, is more similar to print mathematics than is the UEB mathematics.
The Nemeth Uniform Braille System (NUBS) is an updated version of the Nemeth code that incorporates explicit mechanisms for distinguishing literary text from mathematics. Both the original Nemeth code and NUBS are unified codes that handle literary text and mathematics in a uniform manner.
The first version of the Nemeth code was adopted in 1952 and the final revision was made in 1972. The code has been used successfully by several generations of braille students, teachers, and transcribers in the BANA countries. Nonetheless, it has been faulted for minor ambiguities and uncertainties when mathematics is embedded in text even though most of these difficulties arise only in extremely unlikely or artificial situations. A related concern is that the absence of explicit indication of embedded mathematics complicates automated back-translation. (Back translation software uses heuristics or consults a braille dictionary to determine whether or not an item is text.)
More annoying for the braille user are the various restrictions in the Nemeth code's Rule IX—Contractions and Short-Form Words required to avoid having contractions contact various mathematical symbols and indicators. NUBS eliminates or simplifies most of these restrictions.
Three of the major difficulties in designing a braille system that handles narrative (literary) text and mathematics in a uniform manner are:
The remainder of this introductory section gives an overview of NUBS. The second section presents the same information in more technical terms.
It turns out that the first simplification in designing a uniform code is to start with the rule that mathematical items and sequences of mathematical items cannot contain contracted braille.* This rule immediately removes the need for displayed mathematics—or what is referred to in NUBS as a notational passage—to include explicit indicators for the purpose of differentiating the use of certain cells as contractions or parts of multi-cell contractions from their unrelated uses as symbols according to the rules for mathematics.
Specifying a particular unambiguous method for distinguishing displayed mathematics from other text, which may contain embedded or inline mathematics, is outside the scope of this article. There are numerous possibilities:
NUBS terminology refers to a mathematical item as a notational word. Notational words and phrases (three or more notational words in sequence) may be embedded in non-mathematical text by using the proper indicators. This is the subject of the rest of this article.
The second simplification occurs with the use of the dropped numbers rather than upper numbers. (Persons reading this article are undoubtedly familiar with this terminology; if not, the main point is that different braille cells are used for digits and for letters.) One advantage of dropped numbers is that they are distinct from the cells used for letters so that it is easy to identify a braille symbol as a digit without the need for mode indicators.
Dropped numbers or digits are, like upper numbers, examples of braille cells that can cause tactile recognition problems. Dropped numbers require a preceding dot locator when they start a line or are preceded by a space. (The exact rules for the use of the number sign in NUBS are slightly more complicated than this and are stated here.) Upper numbers would also require dot locators if the required mode indicators didn't happen to function as dot locators.
The conventional dot locator for numbers is the cell (dots 3456) or number sign which, because it has dots in both the top and bottom rows of the cell, serves as a dot locator for the braille cell that follows it.
The third simplification comes with the scheme used to distinguish embedded mathematics. The key feature of this scheme is the distinguishing of word-like mathematical items in contrast to individual mathematical symbols. In the words of Dr. Nemeth the scheme is "as unobtrusive as possible without compromising the requirement for unambiguous transcribing and reading."
Also, if the embedded mathematics is a single item, such as a number or fraction, then it only requires an indication of where it begins. On the other hand, if the embedded mathematics is a phrase of three or more items, then it is simpler for the reader if just the beginning and end of the phrase are indicated rather than each individual item.
The fourth and final simplification comes with the particular specifications for delimiters and items. The NUBS system, which was designed by Dr. Nemeth, who also designed the original Nemeth braille code, solves this problem in an especially elegant manner that requires minimal changes to the Nemeth braille code.
Note that if you are unfamiliar with braille, or more specifically, with the demands of braille mathematics, it may not be immediately obvious why the particular system described here offers the simplest and most straightforward approach to a uniform braille system. Nonetheless, it should certainly be clear how the system works.
The NUBS specification starts with a rigorous definition of delimiters. Sequences of braille symbols between a pair of delimiters are called words. NUBS recognizes three types of words: narrative (or literary), notational (or mathematical), and hybrid (or mixtures of literary and mathematical components). The need for a hybrid word is an artifact of the older rules for literary braille and its use in NUBS considerably simplfies the requirement for upward compatibility with literary braille.
NUBS delimiters are braille symbols and non-printing characters that divide sequences of braille cells into items referred to as words in the NUBS system. Words, by definition, never include delimiters. The specification for certain delimiters is context-dependent in that in some cases the same symbol is or is not a delimiter depending on its context.
NUBS specifies three types of words: narrative, notational, and hybrid. Persons familiar with the representation of mixed print texts as XHTML plus MathML will immediately realize that narrative words are those that would be reprented by XHTML while notational words are those that would be represented by MathML islands.
Narrative words include ordinary dictionary words, abbreviations, most acronyms, ordinal endings and any attached punctuation marks. From a technical standpoint it is easiest to define a narrative word as a word that doesn't meet the definition for notational word or hybrid word.
Notational words are items that represent numbers, mathematical constructs or contain mathematical symbols, i.e. any item that
Hybrid words are items that can be separated into notational parts and narrative parts. Examples of a hybrid words are 1st and twenty+.
The parts of a hybrid word must be separated in NUBS by the (dot 5) hybrid item toggle indicator. An embedded hybrid word also requires a preceding start indicator. If the hybrid word starts with a digit, then the preceding indicator is (dots 3456); otherwise the preceding indicator is (dots 56). These are the same symbols used as start indicators for embedded notational words.
Please appreciate that this overview is mainly intended to give you a general feel for the three different types of words. In practice, the three different types of words are rigorously distinguished according to the corresponding print symbols and syntax (and the official rules for contracted braille) so there can never be any ambiguity as to which type of word a particular delimited item corresponds.
As previously stated, NUBS uses explicit indicators to delineate embedded notational items in order to avoid ambiguity with contracted braille. The use of indicators is reduced if a distinction is made between notational words and notational phrases, defined as a sequence of three or more notational words. A single notational word only requires an indicator at the start of the word since the end of the word is unambiguously delineated by a delimiter. A notational phrase requires indicators at both the start and end of the phrase unless it is enclosed in a pair of grouping symbols, in which case it only requires an indicator at the start.
The cells used for NUBS digits always require a preceding dot locator for tactile readability so the number sign would be a convenient indicator before notational words. However, using a number sign before notational words that don't that begin with digits could be distracting to the braille reader and would also be less informative as far as telling the reader what is coming next. Braille users are familiar with using the letter sign (dots 56) before a single letter representing a mathematical symbol.
These considerations together with the need for different symbols to indicate the start of a notational word and the start of a notational phrase led to the choice of the following symbols as indicators for embedded mathematics.
Type of Embedded
|Start Indicator||End Indicator||Reminder|
|notational word beginning with digit||#||not used||none|
|notational word beginning with non-digit||;||not used||none|
|notational phrase where the first word begins with a digit||;#||;'||notational words other than the first which begin with a digit still require a number sign dot locator|
|notational phrase enclosed in a pair of grouping symbols||;;||not used||notational words other than the first which begin with a digit still require a number sign dot locator||notational phrase not enclosed in a pair of grouping symbols and where the first word begins with a non-digit||;;||;'||notational words other than the first which begin with a digit still require a number sign dot locator|
Note that embedded notational items appearing in notational words and phrases are transcribed in exactly the same way as when they appear in displayed notational passages.
The number sign (dots 3456) dot locator is required immediately before a digit—whether embedded or displayed—which follows any NUBS delimiter with the exception of a digit at the start of an embedded notational word or phrase which is preceded by the (dots 3456) word indicator or the (dots 56, 3456) phrase indicator, respectively. [The dot locator has no semantic significance; its only purpose is to make the braille more readable. Since the latter indicators intentionally terminate with the same braille cell (dots 3456) as the number sign, an additional explicit dot locator is not required after these two indicators.]
Note that the number sign is never used in the interior of a NUBS word.
*Displayed expressions can, of course, included uncontracted braille words.
Link to NUBS draft added 4/21/2006.
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