The Objective II Committee gratefully acknowledges the general good guidance, encouragement and technical assistance provided by Mrs. Darleen Bogart, chairman of the Unified English Braille Code Research Project Committee (our parent committee), by the other members of that committee, by other participants in this project, by the officers of the International Council on English Braille and persons associated with its constituent national braille authorities, and by many braille readers and people everywhere who care about braille. This widespread good will and interest has positively inspired us with a sense of hope that important changes are possible, even as we all share a commitment to the stability of English Braille.
This report is the summary to date of the work of the Objective II Committee (commonly called "Committee 2"), which was originally charged with defining the basic methodology for extending the base literary code (English Braille), as the first technical step towards a Unified English Braille Code (UEBC or, more simply, UEB), a research project of the International Council on English Braille (ICEB). In 1993, Committee 2's charge was expanded to include the carrying out of the UEB code extensions to mathematics, computer science, and other technical fields.
This report supersedes any of the previous reports of this committee, including the "final" reports of November 1992 and March 1995 (Ref. 95a), the interim report of March 1994, and the supplementary report of October 1999 (Ref. 99a). It also includes the symbols introduced in the joint report (with the Objective IV Committee) of February 2001 (Ref. 2001a), although that report also remains substantially current as only one of its recommendations has been subsequently reconsidered by Committee 2 (see section 3.23 herein).
As a committee report, this should be regarded as a recommendation only, still subject to approval and acceptance by the UEBC Project Committee, by the ICEB, and by the ICEB's constituent national authorities. However, to keep the wording simple, UEB is described herein as if it were already an adopted code.
It is also described as if it were "finished," but of course that has never been true of any braille code, and UEB is no exception.
This document does not include extensive examples, using them
only to provide
immediate clarifications in some cases. Several
UEB example sets
do exist and are available on the ICEB web
site
(http://www.iceb.org).
This report departs from its predecessors in that it attempts to keep the language of the body of the report as nontechnical as possible, speaking directly to those who would potentially read and write UEB. Technical jargon and formalities (none all that deep, actually) have been relegated to the appendices.
Wherever we refer to "current English Braille" or simply "EB" herein, we mean the official literary code currently used in English-speaking countries, without regard to the minor differences that exist in the practical implementation of that code in different places (Refs. 91a, 92a).
Respectfully submitted,
The Objective II Committee:
The following people have also served as members, either regular or pro-tem, and have therefore participated in the work reported upon here:
At the time of this report, as at the time the UEB project was launched in 1992, the braille codes defined by the Braille Authority of North America (BANA) are divided according to subject area. Other than music, which follows an internationally accepted standard, those areas can be broadly described as (a) general literature not involving specialist notation, (b) math and those sciences employing similar notation, including chemistry, and (c) computer science.
For its first year, when it was strictly a BANA project, the objective of UEB was to bring those three distinct American braille codes into a unified system so that, for just one widely used example, one would not have to learn three different braille representations for the dollar sign.
As work progressed, interest grew in other English-speaking countries, including those where the codes defined by the Braille Authority of the United Kingdom (BAUK), or slight variations thereof, are used. BAUK also defined three distinct codes split along the same functional lines as BANA, although the BAUK math code, especially at the lower levels, can be regarded as an extension of the general literary code. But in any case, while the BANA and BAUK literary codes are close enough to be regarded as variants of the same code, the same is not true of the technical codes: both the math codes and the computer codes are very different in the two jurisdictions. Consequently, when the UEB project was internationalized in 1993, the concept of unification came to be applied to geographical as well as subject-matter divisions.
Within the UEB project, Committee 2 was given the job of defining just how the unification would take place, starting with an assumed "base" code that would be as much like the current general literary code, namely English Braille (EB), as possible.
For more details regarding the specific charges and guidelines given to Committee 2, and our interpretations thereof, see Appendix A.
In order to carry out its charge, Committee 2 sought to define very precisely how symbols are represented in literary braille, remaining faithful to current literary practice as much as possible while providing a basis for extension to technical notation — because in technical material especially, precise knowledge of the represented symbols and their relationships is essential to proper understanding.
That is, we considered that the basic units of written communication are symbols, such as letters, digits, punctuation marks and so on. In order to read, you, the reader, must not only recognize these symbols one by one but must also assemble them into larger units such as words and mathematical expressions, and then into even larger units such as sentences and paragraphs — in short, you must make sense of them.
But while the extraction of sense is your human task — and privilege and reward — you have a right to expect that the elementary symbols that you use as a starting-point will be clear and complete. In other words, it is the task of any symbol representation system, whether it be print or braille or anything else, to be capable of expressing any and all necessary symbols with complete accuracy — that is, unambiguously.
UEB provides such a system. Notice that, in UEB, we do not regard braille as representing print or as secondary or "slavish" to print in any way. Rather, we regard braille and print as parallel systems for representing symbols, and have designed UEB to do that job of representation just as well as print — that is, with the same expressiveness and accuracy.
If you would like to learn more about this philosophy and the other design principles that underlie UEB, together with related technical definitions and other details, consult Appendix B. In the main body of this report, we will present UEB in as nontechnical a way as possible, with the intention that you will learn how to read UEB — in other words, that you will learn "the reader rules." (And yes, the double meaning in that phrase is intentional, because readers have governed the process of UEB development throughout.) If you already know English Braille, you will find much of this to be obvious and familiar, since, as already stated, UEB was designed to depart as little as possible from current EB. (In fact, if you are reading this in English and in braille, and the parentheses around this sentence are among just a few unfamiliar symbols that you have encountered, you are already reading UEB — it is that easy.)
There are only 64 distinct patterns, including the space, that can be expressed with a single 6-dot braille "cell." Since the number of symbols that must be represented is many times that number, it is necessary for UEB to employ multi-cell symbols. A natural question arises: If you have a series of symbols, all run together, and some of them are or could be multi-cell symbols, how do you tell where one symbol ends and another begins? For UEB, the answer lies in a principle of symbol construction known as "prefix-root."
To explain the prefix-root concept, we first divide the 63 distinct braille cells (excluding the space) into two groups, prefixes and roots. Prefixes are the patterns having only right-hand dots plus the traditional numeric prefix, dots 3456. The roots are all the other dot patterns. Assuming that you know where a symbol begins, the rules for telling where it ends can then be given as follows:
1. If the first symbol is a root, or the space, that's also the end — in other words, it's a one-cell symbol. For example, all the following are complete symbols, and have the basic (grade 1) meanings indicated:
2. If the first symbol is a prefix, then continue until a root or a space is encountered. In the former case, the root completes the multi-cell symbol and is included in it. The vast majority of UEB symbols are of this type. In the latter case, the symbol being read stops short of the space, and therefore comprises only prefixes. Such prefix-only symbols may only occur before spaces and so have very limited application, namely to certain braille indicators that make sense only at spaces. (An indicator is a symbol that does not in itself directly represent a concrete or "printable" character, but that tells you something about one or more nearby symbols — what they mean or how they are formatted, for example.) Examples of symbols that could be read following this rule are the following:
3. To avoid major departure from prevailing custom, there are a very small number of exceptional symbols that do not fit within these simple rules (or, if you prefer, they fit within a somewhat more complex set of rules as given in Appendix B). There aren't many of these exceptional symbols that have been assigned, and it's unlikely that many more will be, and so the easiest way to deal with them is simply to list them:
These are recognized on a longest-first basis. For example, dots 56, 56 followed by something else would always be considered a grade 1 word indicator, not two instances of a grade 1 symbol indicator.
Note that all of these exceptional symbols are indicators, and comprise only prefix cells. However, unlike other prefix-only symbols, these symbols may be and typically are used before symbols other than space. Even so, by virtue of transcribing and symbol-assignment rules that are spelled out in detail in Appendix B, the existence of these prefix-only symbols do not give rise to symbol-boundary ambiguities no matter what symbols may follow them. A proof of this fact is given in Appendix C.
So, with these simple rules in mind, you can always tell where one symbol ends and another begins in UEB, even in those cases where you encounter a symbol that is new to you and need to look it up. At least you know what to look up!
All that remains, then, is to list the symbols that have been assigned. That is done by category in the next section, and in "braille order" in Appendix G.
In this section we consider the assignments of symbols, all formed in accordance with the structural rules given in the preceding section, to specific meanings — graphic symbols (i.e. those that correspond to a sign that would appear physically in print) or indicators (i.e. those that do not directly correspond to concrete print signs, but that affect the meaning of nearby symbols in braille). The assignments are listed in groups according to the nature of the symbol.
Some indicators apply only to the immediately following symbol, while others initiate "modes" that extend over several symbols or even multiple words, until the mode is terminated. The mode of termination will vary with the indicator; it may be implicit (e.g. at a space) or explicit (that is, at a terminating indicator), but in any event the terminating condition should always be precisely defined.
Modes that persist indefinitely, that is until an explicit terminator is encountered, are sometimes referred to as "passages." In most instances, the extent of passages (other than passages in foreign languages or other non-UEB braille codes) should be confined to a section of text that is normally read as a unit — that is, a single paragraph, a single heading at any level, a single line of an outline, a stanza of a poem, or other comparable unit. (That last phrase is not perfectly precise, nor does it have to be; the intention is to limit "passages" to natural units of reasonable size, so that readers entering a text in the middle need not search too far back to be sure that all applicable indicators have been seen.) "Pages" and "lines" in the physical sense, that is those that are created simply as an accident of print formatting, are not natural units for the purpose of this definition.
Apart from the meanings that are limited to specific modes, such as the digits when in "numeric" mode, the meanings that are listed in this section are the basic (or "grade 1" or "uncontracted") meanings of the symbols. In those materials where contractions are used, that is in most materials, any symbols that can stand for contractions and that are located in such a way that the contraction meaning is allowed are to be read as contractions. For example, dots 2346 is listed here as meaning the mathematical "integral sign" (3.14), but in most contexts it would mean the letter-group "the". It would mean "integral sign" only when one of the grade 1 indicators (see section 3.2) applies, or in materials entirely in grade 1. Similarly, dots 235 would generally mean "ff" whenever it appeared in the designated context (between letters) in contracted materials; it would mean "exclamation mark" when not in that context and in any instance where a grade 1 indicator is applied to it.
In the braille edition of the listings, each braille symbol is preceded by a two-cell "dot locator," dots 46, 123456, that is not part of the symbol itself but is there to make the precise dot configuration clear, e.g. to distinguish dots 145 from the similar pattern dots 256.
The basic idea behind these indicators is that certain symbols
may have both a "grade
1 meaning" and one or more "contraction meanings" or a "numeric
meaning". Whenever the
grade 1 meaning of such a symbol occurs in a context such that it
could be misread as one of
the other meanings, then a grade 1 indicator is used to establish
the grade 1 meaning. For
example,
As in EB, dots 56 is often referred to as the "letter sign," even though its use in UEB is somewhat broader.
Grade 1 mode is established for the next symbol only by the single letter sign; up to the next space or grade 1 termination indicator, whichever comes first, by the double letter sign; and up to the grade 1 termination indicator by the triple letter sign.
Note that according to the more technical symbol construction
rules given in
Appendix B, the terminator is a sequence of two symbols, not a
single symbol; thus its use for
this kind of purpose is something of an exception. That use is
justified primarily by the
parallel with certain other terminations, such as for capitals,
and causes no conflict in
meaning because the apostrophe symbol
In general, numeric mode and other modes described below may be used within grade 1 mode. Likewise grade 1 mode may be used within other modes in any instance where a grade 2 or numeric meaning might otherwise be implied. Grade 1 is implicit immediately following numbers, as defined in more detail under "Numeric Indicators" below.
Grade 1 mode is the chief means by which braille symbols that can represent contractions can also be used for special symbols such as those needed in mathematics. It is a straightforward generalization of the familiar EB letter sign, with that concept both expanded and more precisely defined.
All of the assignments given throughout this section 3, except for the numeric meanings discussed under "Numeric Indicators" and the symbols defined for use only within special modes such as arrows, are grade 1 meanings.
The grade 1 indicator, also called the letter sign, should henceforth be used only for indicating grade 1 mode, and no longer for such EB uses as distinguishing the letter "a", "i" or "o" when used "as a letter" versus "as a word". Such distinctions are impossible to automate and have no interpretive value for the reader, since those letters cannot stand for contractions. Of course a letter sign should still precede the letters a through j, though not the other letters, immediately following a number.
The transcriber guidelines for use and non-use of extended (word- and passage-length) grade 1 modes are discussed in section 5.2.
Either of the two symbols that establish capitals mode may occur immediately before the first affected letter or accent modifier to a letter. All letters up until the termination condition are then understood to be capitalized.
The double capital symbol affects only the letters that follow. Its effect is terminated by the first symbol that is not a letter nor an accent or ligature modifier to a letter. The terminators thus include any indicators other than accent or ligature modifiers, including of course the capitals mode terminator, and punctuation marks such as apostrophe, hyphen, slash, etc.
The triple capital symbol affects all letters up to the next capitals mode terminator. The interpretation of any nonletter that may occur within a capitals passage is not affected.
Note that dot 6 does not appear here as a single-symbol
capital indicator, because
technically there is no such symbol. Rather, a single dot 6
before nonspace is regarded as the
prefix portion of a single symbol. Many such symbols stand for
capital letters, and some are
just ordinary symbols for which the concept of capitalization is
not applicable. The dash (
Apart from the addition of the passage indicator, these rules for the most part only confirm existing EB practice, except that the effect of a double capital indicator is not understood to continue through a hyphen. That is partly for simplicity, to avoid having to distinguish various kinds of punctuation marks; partly because the existing rules are somewhat contradictory in that respect (hyphen being commonly used as an informal equivalent to the capitals terminator); and lastly so that, when a hyphen between fully capitalized words is used to break a line, the capitals for the second part are already present and need not be introduced exceptionally.
Since a lower-h (dots 236) can mean either a question mark or an opening quote, and moreover can mean the contraction "his" in when located suitably in grade 2, it is necessary to specify exactly when each meaning is implied. The following rules cover all the cases, even unlikely ones:
1. In grade 2 context dots 236 has the meaning "his" if and only if it is both followed by a space and also preceded directly by a space or separated from the preceding space only by capitalization or typeform indicators, or any combination thereof.
2. In cases where the contraction "his" does not apply, dots 236 means an opening nonspecific quotation if and only if it immediately follows a space, hyphen or dash or otherwise satisfies the left context conditions for sequences or symbols "standing alone" as given in section 4.2 [that is, only symbol(s) as defined in list (1) of that definition intervene between the space, hyphen or dash and the dots 236].
3. In all other cases, dots 236 means a question mark.
Mostly the above rules simply go along with existing EB usage and the commonsense idea that dots 236 means "his" when it's more or less alone, means opening quote at the beginning of a word, and means question mark elsewhere — but they also give very precise definitions to those concepts and clarify unusual cases. For example, two lower-h's
In a similar way and for the same reasons, dots 6, 236 in grade 2 context would mean "His" if and only if it is both followed by a space and also preceded directly by a space or separated from the preceding space only by typeform indicators. In all other circumstances, it would be an opening single quotation mark.
The nonspecific quotes, that is those that are not distinguished as to whether they are "double" or "single" or "Italian", should be used for the predominant quotes in all instances where the specific form of quotation marks has no technical significance (that is, in the great majority of cases).
When non-specific quotes are used in a document, their use should include all instances of that form of quote that meet the criteria of the previous paragraph, e.g. both outer quotes and second-level inner quotes.
When practical, it is desirable to provide nonintrusive means by which the braille reader can determine the original form of quotes, even in nontechnical cases. Transcriber's notes, inclusion on special symbols pages, or any other such means of providing the information are encouraged, as permitted by the production context.
Despite the normal preference for the nonspecific form, the nonspecific opening quote symbol may be used only where it would not be read as a question mark or as the contraction "his", as detailed in the rules given above. When the location would cause the nonspecific opening quote to be read incorrectly, the specific "double" or "single" or "Italian" quote mark would be used.
"Nondirectional" quotes other than apostrophes, that is quotes without any slant or curl to convey "opening" or "closing", are to be used only in those relatively rare cases when such quotes are distinguished from directional ones (as in a discourse on typography), are otherwise clearly intended (as in an ASCII listing), or there is no way to infer directionality from context. Otherwise, directional quotes, as determined by context and according to the foregoing rules, are to be used.
More specific reasons for some of these assignments and rules are as follows:
The roots (dots 236 and 356) in the quotation group are obviously motivated by the current signs. The dot 6 prefix for single quotes is also current practice for the opening quote, and has a single dot suggesting the print sign. The two dots in the 45 prefix also suggests the print sign.
The question mark is also just the current English question mark, with dot 56 used for clarity when needed to assure that it cannot be confused with the nonspecific opening quote mark nor with the "his" contraction.
In the parentheses group, the 126 root is mainly to keep all these signs fairly light, and is consistent with British maths. The dot-5 prefix for round parentheses is mainly to keep the most common sign lightest of all; in fact it has only 4 dots, the same as the lower-g used in current EB. It also suggests a distinctive feature of the print sign, namely the bulge in the middle. Following that idea, the 46 prefix for square brackets suggests the tabs at the top and bottom of the print sign, and the 456 for curly brace the points at top, bottom, and middle of the print sign. Finally, this group is consistent with the assignments (dots 4, 126 ... 4, 345) for the angular brackets (which are also the "less-than" and "greater-than" symbols).
For practical application, though not incorporated into the rules, the following further guidelines on quotes and apostrophes summarize the prevailing thinking of the committee:
Many quotation marks in print are actually "nondirectional", that is they are typographically indistinguishable as to whether they are opening or closing. Material prepared on ordinary typewriters or simpler (especially older) ASCII-based word processors, for example, tend to have only nondirectional quotes. Furthermore, apostrophes and single quotes are usually the same print character in such material — which includes the vast majority of current computer programs. The committee's decision to retain a distinct apostrophe in braille, and the directionality of quotes, was based mostly on the desire to continue a long-standing tradition that has not been shown to be overly burdensome for transcribers, nor to lead to meaningful ambiguities for readers. To a lesser degree, the decision was also based on a sense that it could be moving backwards if we ceased making distinctions that we are already making in braille at the very time when, due to advancing desktop printing technology, those same distinctions are actually becoming more common in print — and could, conceivably, become technically meaningful in some cases.
Accordingly, in all normal cases, quotes would be rendered directional, and distinguished from apostrophes, in the same way that they are now, that is on the basis of usage, primarily positioning, with typography giving only secondary clues. For strange character sequences, such as might occur in computer programs, the following guidelines were offered: (1) When in doubt as to whether a mark is an apostrophe or single quotation mark, treat it as an apostrophe. (Rationale: If it's that strangely placed, it's probably not a quote, and marks such as mathematical "primes" are most naturally treated as apostrophes. [But note that true primes, when distinguished from apostrophes, are distinguished also in braille.]) (2) When in doubt as to whether a quotation mark is opening or closing, treat it as closing. (Rationale: That way, the reader is not psychologically conditioned to expect a closing quote. Also, most pseudo-quotes that really mean something else, such as the symbols for feet, inches, minutes and seconds, occur just after the associated numbers, positioned as closing quotes.)
Note that each of the twelve initiating ("set numeric") symbols is both a graphic and an indicator; that is, they not only stand for certain print symbols but also affect succeeding symbols. Specifically, they cause the braille symbols a through j to be interpreted as 1 through 0, a mode which persists through all such symbols and also the period/decimal point (dots 256), comma (dot 2), numeric separator spaces (i.e. the defined "space-digit" symbols), and a simple numeric fraction line (defined in later section 3.9) — that is, until some other symbol occurs, including the case of a letter a through j governed by a grade 1 indicator.
Strictly speaking, the period and comma are not included within the numeric mode unless they are actually followed by another numeric symbol, i.e. a digit or the numeric fraction line. This fine point has no practical effect in ordinary cases, but could enter into the treatment of certain indices.
The twenty symbols designated "in numeric mode only" are not general grade 1 assignments, but are limited to numeric mode.
If an extended grade 1 mode is in effect at the beginning of a number, then its effect is suspended in the number itself, and then resumed after the number. If grade 1 mode is not in effect at the beginning, then any of the initiating symbols establishes "grade 1 word" mode as well as numeric mode, which practically speaking means that contractions may not follow a number until after a space or a grade 1 termination (dots 56, 3). This is to reflect the fact that letters immediately following numbers are usually not words but rather designators typical of part numbers and such. (Of course, it is possible to terminate the grade 1 mode in those exceptional cases where it is desirable to express an attached English word in its ordinary form.)
As with capitals, these rules yield braille that is quite consistent with existing EB practice, except for the change of the decimal point to use the same symbol as the period, the fact that numeric mode does not continue after a hyphen, and the treatment of separating spaces as described below. The first of these two changes is motivated in part by the desire to use just one symbol where one is used in print, whereas in current EB, the BAUK codes use dot 2 to represent the decimal point and the BANA codes use dots 46 for the same purpose. Moreover, the dots 46 character, being a prefix, can no longer stand alone as a symbol except before a space. The second change, i.e. terminating numeric mode at a hyphen, parallels the similar change for double capitals, and is motivated by similar reasons.
The "spaced numeric mode indicator" does nothing more than
allow one or more
spaces to intervene between the numeric prefix and certain roots
that would normally follow
immediately, namely the digits
Taking that idea a step further, all instances of a the
symbols
The ten symbols of the form
The usage rule is: spaces should be represented in this way when and only when they are clearly used as separators within a single number, not for spaces between distinct numbers, such as in a list of numbers or numbers in distinct columns. For that purpose, a number generally considered as a single unit should be treated as such, even though it may comprise distinct parts, e.g. a single telephone number would be considered as one number, even though it includes country, city, and exchange codes as parts.
It would seem that, more simply, we could just say that dot 5, when occurring between digits within a number, represents a separating space in print. However, the assignments and rule are phrased as they are in order to assign meanings only to properly formed UEB symbols; dot 5 by itself, except before space, is not a complete symbol.
Without this special representation of numeric separator spaces, each such space would interrupt the numeric mode and then the number sign would need to be repeated after the space. The combination of the space and a new number sign was regarded as a stronger break than the mere space in the print, possibly suggesting to the reader that a new number is beginning, not just a continuation of the same number. This special representation avoids that problem.
The main disadvantage of a special representation of separator spaces is that, in the print to braille direction, it introduces the element of judgment as to whether a given space is being used as a separator within a number or is simply a regular space between different numbers. However, practical cases where this would be a real difficulty for a human transcriber were regarded as unlikely, and if there are any cases where real doubt would exist, the rule would simply call for treatment as an ordinary space. Along these lines, a further objection could be that computer programs are ill-equipped to make such judgments. When it comes to certain kinds of input, e.g. scanned input or simple-ASCII files where the spaces might not be distinguished, that objection has merit. However, in files prepared (or edited from scanned input) on typical word processors, separator spaces would most likely be entered as special "hard" (also called "non-breaking") spaces, so that the components of the number could not possibly be broken at a line ending. In that case, the discrimination would be quite easy for programs.
In summary, while the element of judgment is always something we would prefer to avoid, the burden in this case seemed light, and easily outweighed by the benefit to the reader.
1. A telephone number, 508 555 7549:
2. Decimal equivalent of 2 to the negative 17 power (as presented in "Handbook of Mathematical Functions", National Bureau of Standards 1964, p. 1016):
The symbols establishing typeforms follow a consistent prefix-root pattern, wherein the prefix designates the specific typeform and the root determines the extent. Most of the prefixes used have an historical association in English Braille or some other mnemonic basis, e.g.: dots 46 for italics from EB, 456 for underlining (or "right-hand letter l"), 45 for bold (a right-hand "b" — also has fewer dots than for underlining, which is less common).
Motivations for the specific extent assignments were: the dot 2 for word extent is the lightest symbol, dots 2356 for passage extent the heaviest, which is consistent with both perceived frequency of use and the size of the extent itself, and dots 23 for the single-symbol has a mnemonic basis as a "left-hand letter sign".
The "word" extent covers all symbols up to the next space, even if some characters that could not be meaningfully affected by the mode intervene. (For example, there is no such thing as an "italic period," but a period in the middle of an italic word would not terminate the effect of the italic-word indicator.)
The single-symbol indicators, when applied to a contraction symbol, are understood to affect only the first letter of the contraction.
The transcriber-assigned symbol sets are in a series that can be extended indefinitely, as needed, for any meaningful print distinctions not covered by the fixed assignments. (For example, colors might be used to flag various parts of speech in a grammar text.)
It bears restating that these indicators are not intended to be used necessarily wherever the corresponding typeform is used in print, but only where such usage conveys a meaningful distinction, such as to show emphasis, or the difference between computer input and output, or the class of a variable in mathematics. The "script" indicator, for example, would normally be used only when variation from some other prevailing letter form is intentional and meaningful, not just to show that the original text happened to be in script. Likewise, any typeform used simply as part of the formatting style, for example boldface used in all main headings, should normally be ignored in the transcription.
When a typeform extends over several paragraphs, it is preferable that the intermediate closing indicators (all but the last) be omitted, even though the opening indicator be repeated at the beginning of each new paragraph.
The basic rule, naturally, is that indicators should be placed so that no incorrect information is given — that is, so that any symbols that could be affected by the indicator are within the scope of the indicator if, and only if, they in fact have the typeform in question. However, since some typeforms are irrelevant to some symbols (e.g. the aforementioned "italic" and "period"), there is often some latitude in placement for the sake of readability. Among other factors, nesting of typeforms (i.e. closing them in reverse order to opening) is generally to be preferred, when possible given other requirements. For transcribers, more guidance on the optimal placement of typeform indicators is given in section 5.3.
Dots 36 is to be used for both minus sign and hyphen if they are not distinguished in print. However, when a minus sign is actually distinguished as such in print, it must be represented as dots 5, 36. This is because well-printed mathematics texts normally do show the symbols differently, and the distinction is helpful and in certain cases possibly necessary to understanding. (An example of such a case would be the expression "interest-rate minus inflation-rate", with "minus" shown in print by a distinctive minus sign.)
The plus sign was chosen to be a lower sign patterned after (though not identical to) the British and certain other maths codes, and so as not to vary with grade. The viability of a two-cell plus sign was questioned, but it was noted that the British two-cell plus sign remains well accepted after many years of use, and this symbol is actually lighter by one dot.
The simple level changes occur frequently in mathematics, so it was considered important that they be single-cell symbols when already in grade 1 mode, which would be the norm in complex mathematical expressions. When used in literary context, for example to show footnote references, a grade 1 symbol indicator (i.e. letter sign) would often be needed to avoid reading "en" or "in". The "shapes" of the lower-e and lower-i symbols suggested those choices for the level change symbols themselves.
The scope of any of the four level change indicators, that is the symbol(s) affected by it, is the next "item". An item is defined as any of the following groupings, according to the symbol that immediately follows the level change indicator:
(1) If the next symbol initiates simple numeric mode, the item is the entire number. That would include any interior decimal points, commas, separator spaces, or simple numeric fraction lines, but not "final" commas or periods.
(2) If the next symbol is an opening general fraction indicator (defined below), the item is the entire general fraction, through the closing fraction indicator.
(3) If the next symbol is an opening radical indicator (defined below), the item is the entire radical, through the closing radical indicator.
(4) If the next symbol initiates an arrow (defined below), the item is the entire arrow.
(5) If the next symbol initiates an arbitrary shape (defined below), the item is the entire shape.
(6a) If the next symbol is an opening round parenthesis, the item is the entire expression through the matching closing round parenthesis. Note that other round parentheses may occur interior to the item, in balanced pairs. Other kinds of parentheses or brackets may occur interior to the item and may or may not be in balanced pairs; only the round parentheses are important in determining the closing one that matches opening one at the beginning of the item.
(6b) If the next symbol is an opening square bracket, the item is defined analogously to (6a), but with square brackets instead of round parentheses.
(6c) If the next symbol is an opening curly brace, the item is defined analogously to (6a), but with curly braces instead of round parentheses.
(7) If the next symbol is a braille grouping opening indicator, the item is the entire group of symbols through the matching braille grouping closing indicator.
(8) If none of the foregoing apply, the item is simply the next individual symbol.
For transcribers, braille grouping indicators should be used to indicate the extent of an item [form (7) in the above list] only when one of the other forms does not apply, or in other words the opening symbol would not correctly identify which of the listed cases applies. For example, in the case where a "half-open interval" such as
The braille grouping signs are never used to replace existing graphic symbols such as brackets, but are used to create a group in braille not implied by (1) to (6) above.
It is implicit in the definition of an "item" that braille grouping indicators must be used for clarity whenever more than one indicator (e.g. superscript and over-bar) can apply to the same item, and it would otherwise be unclear which indicator is to be applied first to form a larger item. See section 3.11 for a more complete discussion of this topic.
Left-displaced indices, e.g. an expression written at the subscript level and before the base symbol, are handled simply by using the corresponding ordinary index expression prior to the base symbol. (Note: In general, such "left indices" would follow a space — otherwise they would be indistinguishable from right indices applied to the symbol on the left).
If indices occur within indices, they are to be expressed in the same manner as if they were at the base level. In other words, the notation may be "nested".
This approach to indices is similar to that taken in the most recent Spanish unified mathematics code (Ref. 91c), although symbols more consistent with other UEB assignments have been selected. It is also isomorphic to the general approach taken by mathematical typesetting and content descriptive languages that are important for print purposes, namely LaTeX and certain SGML Document Type Definitions (DTD's) (Refs. 90d, 89c). Finally, in using a "relative" rather than "absolute" method of dealing with multiple index levels, it is consistent with British maths.
1. (In grade 1 passage) x squared:
2. (In grade 2) x squared:
3. (In grade 1 passage) x squared plus y cubed equals z to the fourth power:
4. (In grade 1 passage) H sub 2 end-sub O (the familiar formula for water):
5. (In grade 2) H sub 2 end-sub O:
6. (In grade 1 passage) 6 space m to the negative 2 power:
7. (In grade 1 passage) x sub 1 end-sub squared equals y sub 2 end-sub cubed:
8. (In grade 2) an area of 6 m squared in total.:
9. (In grade 2) It travelled at 60 ft s to the negative 1 power.:
10. (A footnote reference in superscript position, in grade 2:) In Smith sup 56 end-sup we find ...:
11. (In either grade:) 4 x to the 1.5 power y to the .5 power:
12. (In either grade:) 4 b to the 1.5 power c to the .5 power:
13. (In a grade 1 passage:) e to the x squared plus y squared power
14. (In a grade 1 passage:) e to the (x sub i+1 end-sub to the p sub i end-sub power space + space y sub j+1 end-sub to the q sub j end-sub) power (Note: parentheses not literally in print)
15. (In a grade 1 passage:) The sum from i=1 to n of x sub i end-sub squared (with summation limits written directly below and above a capital sigma)
16. (In a grade 1 passage:) The sum from i=1 to n of x sub i end-sub squared (with summation limits written to lower right and upper right of a capital sigma)
A simple numeric fraction line symbol is used only for a simple numeric fraction, that is one whose numerator and denominator both contain only digits, decimal points, commas, or separator spaces — in other words, symbols (other than the fraction line itself) that continue a single numeric item. In such a case, a single numeric fraction line symbol may be used within the numeric mode, between the numerator and denominator, and continues the numeric mode so that the entire fraction is regarded as a single numeric item.
The numeric fraction line would be read as a line between vertically (or near-vertically) arranged numbers only, never as a general fraction line between larger expressions, which are treated below. The numeric fraction line is also not used where the print is expressed linearly, using an ordinary slash (oblique stroke) character; in that case, the braille simply uses the corresponding symbols as the print, and in the same sequence.
The "general" indicator symbols are to allow linear representation of fractions that are written in print with numerator over the denominator, and where either the numerator or denominator is not completely numeric as defined above.
The opening and closing general symbols are therefore technically indicators, since there is no corresponding graphic in print, and must be used in symmetrically balanced pairs. After the opening indicator, the numerator expression is written, then the general fraction-line symbol, then the denominator, and finally the closing indicator. Both numerator and denominator may be any kind of expression whatever, including fractions of either simple numeric or general type.
As with level changes, fractions were considered so common in math contexts that it would be important that these symbols be single-cell in grade 1 mode, while in general literary context the added letter sign was not considered an undue burden. The beginning and ending symbols are balanced symmetrically.
1. Two and one-half cups sugar:
2. The fraction whose numerator is two and one-half and whose denominator is x plus y:
An ordinary radical, that is one with a vinculum extending over the affected expression (the radicand), is expressed in braille by using the opening symbol before the radicand and the closing symbol after. The radicand itself may be any expression whatsoever, and may therefore have radicals as well as other mathematical structures. In other words, radicals may be "nested".
The radical index, if any, is signified by a superscript expression in the standard form, immediately following the opening radical symbol.
The symbol for a radical without vinculum is used as a simple graphic symbol, corresponding to any such symbol used in print.
1. The mn-th root of xy:
2a. The square root of four (written with vinculum over the four, as would be usual in modern usage):
2b. The square root symbol followed by four (with no vinculum, which would usually mean the square root of 4, especially in older books, but in some modern contexts could be just a sequence of symbols):
3. The familiar quadratic formula (x equals the fraction: minus b plus-or-minus the square root of b squared minus four a c end-root all over two a) :
4. r equals the square root of x squared plus y squared end-root:
5. q equals the cube root of x cubed space plus y cubed space plus z cubed:
6. The square root of the fraction: 783.2 times 6.547 over 0.4628 end-fraction end-root equals 105.3:
7. 81 to the three-quarters power equals left-paren the fourth root of 81 right-paren cubed equals left-paren the square root of the square root of 81 right-paren cubed equals left-paren the square root of 9 right-paren cubed equals three cubed equals 27:
8. The [square root of sixteen-ninths] root of 81 equals the four-thirds root of 81 equals 81 to the three-quarters power equals 27:
For all of these, the term "item" is as defined in section 3.8.
1. x with bar over it
2. the expression x plus y with bar over it
3. AB with right arrow above
4. AB with right arrow below
5. not-equals
Note on the definition of "item" and precedence: that no precedence has been defined between certain indicators that apply to the next, previous, or surrounding items. So, for example (in grade 1)
A future committee could choose to adopt precedence rules, or in other words a defined order in which the indicators involving "items" are to be applied. This would be similar to the way that, in mathematics, "a plus b times c" is generally understood to mean "a plus (b times c)", not "(a plus b) times c" — because multiplication is understood to take place before addition, except as explicitly determined by parentheses. If, for example, it were defined that the "bar" indicator has precedence over the "superscript" indicator, then it would be clear in our example that the bar was first applied to the y, thereby making a new item that was then an appropriate object of the superscript.
While such precedence rules might eventually be desirable, the committee has determined that it would be better, at least until more experience is gained, simply to require that braille grouping symbols always be used in such cases. In other words, in the above example, one or the other of
These indicators introduce a special "arrow" mode that provides a systematic method for representing nonlooping arrows other than those described in section 3.11 or that may be otherwise specially defined.
A nonlooping arrow may be regarded as a line or "shaft", with definite end-points, that does not cross or close upon itself and upon which one or more "tips" are superimposed. Tips may occur at either end of the shaft and/or along the shaft.
Such an arrow is to be treated as an enclosure, much like a general shape (see section 3.19), but using specific enclosing indicators (and interior symbol assignments) appropriate to the components of arrows. The opening symbols are those listed above. The arrow termination is one of eight symbols expressing the overall orientation of the arrow, as follows:
All these terminating symbols have three dots, arranged in a consistent pattern that best describes the overall arrow orientation, that is the absolute direction of motion (in two dimensions) if one were to proceed in a straight line towards the "head" of the arrow, starting at the other end (the "tail").
The head of the arrow is decided, if possible, by examining the direction of those arrow tips that have direction, that is those that have a concave and convex side, with respect to the arrow shaft. The direction of such tips is towards the convex side. (Note that the "direction" we are speaking of for this purpose is one-dimensional, i.e. along the shaft, so only two directions are possible.) The complete rules for deciding arrow direction are:
(1) If there are directional tips, and all lead in the same direction, the head is the end that lies in that direction.
(2) If there are no directional tips, but one end has a tip and the other does not, the end with the tip is the head.
(3) In all other cases, the head of the arrow is deemed to be the end at the right, or in the case of strictly vertical arrows, at the top.
Simple arrows: The simplest arrows are those with a straight shaft of medium length, and a single full, common barbed (hence directional) tip at the head. (Note that this definition implies that the tip points outward from the shaft; otherwise that end would be the "tail" of the arrow.) In such cases, only the arrow indicator and the direction (terminator) are given. This defines sixteen symbols, each comprising either of the two arrow indicators followed by any one of the eight terminators giving overall orientation. These sixteen include the following examples:
General nonlooping arrows: Other arrows in this class employ the same enclosures, but between them the tip(s) and shaft segment(s) are transcribed, using the symbols given below. These items are expressed in logical order, that is starting with the arrow tail and progressing towards the head, even if that runs counter to the physical order (as in the case of an arrow oriented towards the left). Certain elements are omitted, corresponding to these reader rules:
(1) If no tip is transcribed, it is understood that an ordinary full barbed tip occurs at the arrow head, and there is no other tip.
(2) If no shaft is transcribed, it is understood that the shaft is a straight line of medium length. In this case, if no tip is transcribed, rule (1) also applies; if one tip is transcribed, it is at the head; if two tips are transcribed, the first is at the tail and the second at the head.
Symbols for shafts (which may be elongated by repetition) are:
Length distinctions not made in the print need not be made in the braille; i.e. "medium" length would be the normal default.
Symbols for tips are:
Some example of arrows that could be constructed would be:
Notes: As with general shapes, this approach to arrows creates, between the enclosures, a distinct "mode" wherein symbols are understood differently. The available symbols for shaft segments and tips can easily be extended, provided that the symbols for shafts, tips, and terminators are always kept distinct. It would also be possible to extend this general method to arrows that can close upon themselves or cross, if that were later found to be desirable. Finally, this general approach does not preclude the possibility of assigning shorter specific symbols to particular arrows that occur frequently. For instance, it was noted that the common symbol for a reversible reaction in chemistry (a half-barbed left arrow over a half-barbed right arrow), while constructible as two general arrows vertically composed, would be too clumsy in that form when the frequency of the symbol is taken into account, and so a specific sign has been assigned (see section 3.18).
As in the case of the hyphen and minus sign, the prime and the apostrophe are distinguished in braille only when they are distinguished in the print.
The actual setting-out of arrays into columns was regarded to be a format issue, and therefore not the specific concern of Committee II, while graphic symbols for enclosing arrays are properly a code issue.
These are just the basic symbols plus a preceding dot 6 to convey the big/multi-line condition. These symbols are to be repeated on each line spanned by the print symbol, and vertically aligned, thus defining the overall vertical extent.
While a "line sign" (see section 3.25) can sometimes be useful for indicating new lines (rows), e.g. as an option for note taking, the symbol should not be used for general presentation of arrays, because then the point and purpose of the two-dimensional arrangement would largely be lost for the braille reader.
For common shape symbols as typically used in geometry and trigonometry, see section 3.19.
The committee also recommends setting up a "transcriber-assigned symbols" series to be used for symbols that are rarely encountered in general but that occur frequently in a particular text, such as made-up symbols or symbols that have come into regional usage.
Together with other print symbols presented in previous sections, some of these symbols complete the set of characters defined in the American Standard Code for Information Interchange (ASCII), which is probably the best-known long-established standard list of characters for computers. By providing symbols for all of these, we provide for essentially all that were covered by the BANA Computer Braille Code (Ref. 87a).
The "visible space" is to be used regardless of the print device used for such purpose (e.g. delta, underline with up-tick at each end, or slashed b), or where the transcriber determines that a space is significant, in the same sense that "countable spaces" are used in BANA Computer Braille Code. It was noted that such visible spaces could not be used within radicals, since the same symbol is the radical terminator, but the committee concluded that there was no actual requirement for "visible spaces" in that circumstance.
The continuation indicators are to be used when it is technically necessary to show that a print line is continued, and to represent precisely the sequence of symbols right through the braille line break; they are not to be used when there is no need for technical precision or where formatting (such as indented runovers in poetry) effectively conveys the runover information adequately.
When a space occurs at the point of a break to be shown by a continuation indicator, its presence is conveyed by using the two-cell continuation indicator.
The cursor indicator symbol is used in the case where it is necessary to show the position of a "cursor" (a special blinking or otherwise distinctive shape, used to identify the focal point of activity on a computer screen). The placement of the cursor indicator is on a separate braille line, immediately under the symbol to which it refers (specifically the final cell thereof, in the case of a multi-cell symbol). There is no actual conflict with the horizontal juxtaposition indicator (section 3.20), since in the case of the cursor indicator the symbols on both sides would always be spaces, and that would never be true when using the horizontal juxtaposition indicator.
The ordinary single line bond uses the same symbol as the dash (section 3.4), a single electron shown as a cross uses the same symbol as the "times" cross (section 3.7), and a single electron shown as a small circle uses the same symbol as the "hollow dot" (section 3.16).
While the line bond symbols are to be used for the horizontal bonds only, they are general symbols and may be used in structure formulae where other bonds, such as vertical bonds, are represented using line-drawing symbols (see section 3.26).
The equilibrium arrow is normally to be used only for "double harpoons", the upper arrow having a half-barb on the upper side at the right end pointing right and the lower arrow having a half-barb on the lower side at the left end pointing left, both arrows being of equal length and weight. In cases where a transcriber familiar with the notation is quite certain that some variant double-arrow form has been used consistently throughout the text to have the same meaning, and the precise form itself does not appear, the transcriber may use the equilibrium arrow in braille with a transcriber's note documenting the substitution and the form of the symbol in print.
The equilibrium arrows that signify a trend to the right or left may be used when either emphasis or length or both distinguishes one of the directions as dominant. In cases where a transcriber familiar with the notation is quite certain that some variant double-arrow form has been used consistently throughout the text to have the same meaning as one of the trending arrows, and the precise form itself does not appear, the transcriber may use the trending arrow in braille with a transcriber's note documenting the substitution and the form of the symbol in print.
Unusual, ad-hoc and iconic symbols are considered in two categories: arbitrary described symbols (shapes) and combination symbols (see section 3.20). Only relatively uncommon symbols are to be treated in either category. That is, any common symbol is to be assigned a regular braille symbol in its own right, even if it would be possible to use a "shape" or "combination" treatment, and when such an assignment has been made then naturally that assignment is to be used.
After the opening indicator, the next symbol determines the manner of termination. If that symbol is the opening general enclosure (i.e. braille grouping symbol, dots 126, introduced in section 3.8), then all following symbols, which must be validly formed UEB symbols, through the next closing general enclosure (dots 345), including any space or dots 156, are part of the shape description. If the symbol following the opening indicator is not an opening general enclosure, then all following symbols through the next shape terminator (dots 156), or up to (but not including) the next space, make up the shape description. (For transcribers, this implies that a shape from the standard list would require a shape terminator if unspaced on the right.)
In accordance with our general principles (see A.2 in Appendix A), the "descriptions" for shapes are to be language-independent if possible, although it is recognized that such independence is frequently impractical, i.e. shapes will commonly be described by English words. Because the terminator symbol (dots 345 or dots 156) cannot be used within the description, grade 1 is generally to be used within the description. In fact, a common pattern will be to use a short series of initials or a single word for the sake of brevity, especially when a particular "shape" must be used frequently within a given text.
The definitions of all such symbols must be available to the reader. Shapes in the "transcriber-assigned" category would be listed in preliminary notes, according to producer custom (e.g. in a "special symbols page"). Possible examples would be
(Note: The second of these examples was drawn from Knuth's "The TEXbook" [Ref. 90c], where a curvy-road-sign symbol is used as an icon to flag passages treating difficult or tricky material.)
Shapes not in the transcriber-assigned category, i.e. without the dot 4, are to be from an official list of those shapes that are more generally encountered — but still not so frequently that a specific regular symbol is justified. The list as given was purposely brief, covering only the family of basic regular figures (though that family is open-ended, as noted). A future standing committee is envisioned as adding to that list gradually, as it becomes evident that certain shapes are useful to standardize. In many cases, adding to the list would be a matter of removing the dot 4 from a transcriber assignment that had proved useful and popular.
For filled and shaded shapes, the distinctive opening indicator should be used, and the remainder of the shape symbol composed in the same manner as for a basic or transcriber-assigned shape.
These indicators allow multiple symbols to be combined into a new single symbol. Again, only relatively uncommon symbols are to be treated by these mechanisms (see section 3.19); any specifically assigned braille symbol would always have preference.
Each of these indicators signals a combining of the item just prior with the item immediately following it, where "item" is as defined in section 3.8.
"Horizontal juxtaposition" is to be invoked only when two symbols are written in close proximity and it is clear from the usage that a new single symbol, distinct from the elementary symbols considered in sequence, is intended. Otherwise, symbols written one after the other should simply be brailled accordingly.
Likewise, "vertical juxtaposition" is to be considered only when a new single symbol is formed, and should not be confused with indices directly above or below, nor with vertical arrangements such as in columns of matrices. It was noted that these distinctions could require judgment in some instances, but that this was unavoidable and unlikely to present real problems in practice.
Bars and arrows are not normally to be treated using this mechanism; see section 3.11.
Some examples, with grade 1 presumed, would be:
These all use the dots 45 prefix to suggest something "up", which of course is the usual case with accents. The actual positioning, whether over or under, is implicit in the symbol itself, which precedes the affected letter.
The "over following capital letter" forms are so that the single dot indicating a capital comes before the accent indication, in accordance with current EB practice, while still technically observing UEB symbol structure formalities. In cases like this, it is clearly easier (especially for teaching purposes) to think of the dot 6 as if it were a distinct indicator in its own right.
These accent marks are not intended for use in those cases where foreign language passages, as defined in the current English Braille code, are to be transcribed. That case is covered separately; see later section 3.23. Rather, they are to be used only in "anglicized" words (again, relying on the current definition) or in other cases where accented letters are used in essentially English or technical context.
These symbols are to be used for linguistic accents (that is, those that express in some sense how the affected letter is pronounced), and not for modifiers in mathematics, despite the similarity of print appearance in some cases. (For example, the second derivative of the variable "u", expressed as the letter with two dots above, is visually similar to a u with umlaut.) The committee reasoned that linguistic accents are basically different from mathematical modifiers both in common human understanding and, usually, even in computer file coding (reflecting, for example, the fact that mathematical modifiers may apply to expressions larger than a single letter).
The placement of the accent before the affected letter is to provide timely warning to the reader that the pronunciation of the next letter is affected by an accent (as is conveyed in current EB, though only in a nonspecific way, by the preceding dot 4).
Some specific reasons for the symbol root assignments are: (1) The middle-c of the dieresis/umlaut symbol suggests the horizontal two-dot shape. (2) The French "c with cedilla" sign is the cedilla symbol root. (3) The dots 16 grave symbol root suggests the print shape. (4) The French "i with circumflex" sign is the circumflex symbol root. (5) The Spanish nyay sign is the root for the tilde accent symbol. (6) The dots 34 acute symbol root suggests the print shape, symmetrically to the grave symbol root.
The committee further recommends specific assignments for certain other accent marks and modifiers beyond the Western Europe-oriented ones assigned above, namely:
It was noted that Committee 4 might wish to consider the macron and breve, since those are commonly used as diacritical marks to indicate the length of vowels.
Considering the number of possible accents and diacritical marks, it was recommended that at least two "transcriber-assigned" accents be set aside for use as needed in specific texts.
The Greek symbols are based on the international standard (as in Refs. 72a, 77a and 84a) rather than upon the slightly different modern Greek alphabet (Ref. 90a). This is to be consistent with the Nemeth 1972 code, and with the intended use of these symbols in English and technical context only.
As with the accent marks, these symbols are not intended for use in those cases where actual Greek language passages, meeting the definition of "foreign language" passages as defined for current EB usage, are to be transcribed. That case is covered in a separate topic below (see section 3.23). Rather, they are to be used only in cases such as the word "microsecond" (with the "micro" written as a Greek mu), the names of fraternities and sororities, Greek letters such as pi and theta used as constants and variables in mathematics, and any other cases where Greek letters are used in essentially English or technical context.
The formation of the Greek alphabet illustrates a process that can be applied to other foreign alphabets as needed. The committee did consider several such possibilities, but no compelling candidate was put forward. (The Hebrew letters alef and bet are used in some mathematics, but in practice no other letters of that alphabet. Some Cyrillic letters may be used, but rarely. Old German [Gothic] script may be used, but that can better be as a "font", i.e. special typeform.) However, respecting the need for a future committee to assign another complete alphabet, or the needs of a specific transcription, all symbols having dots 456 prefix and an alphabetic root were reserved as a group for assignment to an alternate non-Roman alphabet.
In EB currently, even in a generally English context, a foreign language used as such is treated differently from English-language text. In American practice, the braille transcription of foreign-language material uses symbols that are mostly the same as those used in the uncontracted braille defined by speakers of that language, though some indicators and punctuation marks continue to follow English custom. In British practice, the same general concept prevails, although more of the foreign braille symbols and rules, including some contractions, may be used. In either case, the braille is thus logically connected to the braille that would be found in literature published entirely in that foreign language, which obviously benefits both those who are learning the language and those who already know it.
The only drawback to this current treatment is that the switches back and forth between English and the foreign language (or languages) are made implicitly. That is, the human brain is assumed capable of sensing which language is being written; no explicit indicators are given (except to the extent that font changes or formatting clues may be present). In some cases, this may only reflect the situation in the print, where sometimes the words of a foreign language may be distinguishable from English words only by referring to the larger context of presentation. This situation seems workable enough for human readers, but at the current state of the art (and for the foreseeable future) will inhibit automated translation, at least from braille to print. A blind teacher of foreign languages, for example, would have to "assist" the translation program in order to derive correct print from a braille file containing mixed English and foreign-language material. That is because this treatment of foreign languages inevitably introduces formal ambiguities into the braille.
For the automation of print to braille, the situation is essentially the same, at least for text that is scanned into the computer or otherwise unmarked as to language. However, the committee noted that material prepared on computers with one of the more advanced markup languages, or even with some word processors if properly used, can be annotated so that language changes are definitively indicated. (For instance, a word processor program might provide such a facility so that the correct language dictionary can be used for spell-checking.) In that case, it is relatively straightforward to automate production of braille with English and other languages intermixed.
A joint session of Committees 2 and 4 considered these matters and decided to assign symbols so that material transcribed in foreign-language braille codes (or for that matter any braille code other than UEB itself) within a general UEB context could be explicitly marked with code switching indicators (see Ref. 2001a, which remains current except for one guideline, and upon which the remainder of this section is based). (The exceptional guideline is a subsequent recommendation by Committee 2 that non-UEB passages always be explicitly closed prior to opening a new one.)
These symbols indicate text that is transcribed in a braille code other than UEB, such as Music Braille, established codes for languages other than English, historical or proposed codes, etc., when the nature and extent of the non-UEB transcription is not already clear from formatting or other context.
The first of these, i.e. the opening passage indicator, may be augmented by a short sequence of letters between the two symbols, i.e. before the dot 3, as an aid to identifying the specific braille code, when the alternate code is not obvious. For example,
When the non-UEB text occurs in the same line with UEB text, the opening non-UEB passage indicator (together with the abbreviation identifying the code, if any) immediately precedes the non-UEB text, and the closing non-UEB passage indicator immediately follows the non-UEB text, without spaces except for those that occur in the text. In displayed material, that is when the non-UEB text is deliberately presented on separate line(s), each of the passage indicators may be on a line by itself.
The effect of a non-UEB passage indicator ceases at the next instance of any of these four indicators. (Note, however, that Committee 2 has subsequently recommended that any non-UEB passage always be terminated explicitly, in effect returning to UEB, before starting another non-UEB passage.)
The opening non-UEB word indicator immediately precedes the word to which it applies, and its effect is terminated at the next space or at the next non-UEB word terminator, whichever comes first.
The non-UEB word indicator cannot be augmented by an identifying abbreviation. If not otherwise obvious, the code is understood to be the same as for the next previous non-UEB passage.
While not strictly speaking part of the usage rules, the following associated guidelines for transcribers were drafted in order to assist in understanding how the code switching indicators would best be used:
1. Use these symbols to indicate text that is transcribed in a braille code other than UEB, such as Music Braille, established codes for languages other than English, historical or proposed codes, etc., when the nature and extent of the non-UEB transcription is not already clear from formatting or other context. Preferably, do not use them when the nature and extent of the non-UEB material is quite clear, as for example in a table where one column contains English words and the corresponding words in the second column are the French equivalents, and the columns are respectively labeled "English" and "French" (or the arrangement is otherwise obvious). In borderline cases, use these non-UEB indicators.
2. When using the passage indicators: When the non-UEB text is to be "displayed" on one or more lines separate from the UEB text, you may place the passage indicators on separate lines by themselves. Otherwise, place the indicators at the exact point of change from UEB to non-UEB code or back, without adding any spaces not actually present in the text.
3. Use just the simple indicator symbols when the nature of the non-UEB code is obvious from context, as would almost always apply when only one non-UEB code is used within a particular text. In other cases, augment the opening passage indicator with a short mnemonic abbreviation identifying the code, e.g.:
4. In rare cases where the closing passage indicator could be misread as a symbol within the non-UEB code itself, use an opening passage indicator instead, augmented by "en" (implying that UEB is resuming) or other suitable augmentation as determined by the transcriber. Do this only when the projected misreading is a realistic concern, not when it is merely a theoretical possibility. In borderline cases, use an augmented opening symbol. Finally, if none of these methods of returning to UEB are recognizable (as a practical matter) due to the nature of the "foreign" code, then the transcriber would have to devise a safe indicator to go back to UEB.
5. In those cases where one non-UEB code is immediately followed by another non-UEB code, normally do not omit the closing passage indicator between the two. In other words, it is preferable to "return" to UEB before opening another non-UEB passage even if another non-UEB passage is to commence immediately.
6. Use the non-UEB word indicator immediately before individual words that are transcribed in a code other than UEB, when the nature of the code is obvious or the same as a non-UEB passage preceding the word within the same paragraph. In all other cases, use the opening passage indicator, even for a single word.
7. Use the non-UEB word terminator when the non-UEB transcription reverts to UEB at a point other than at a space — e.g. when a punctuation mark, transcribed in UEB, is appended immediately after a non-UEB word.
The special print symbols used to clarify pronunciation have been codified in braille (e.g. Ref. 77a), but unfortunately this is one instance where the symbol set is quite often at variance with the UEB standard symbol construction rules.
The subject of phonetics is complex enough, and the set of needed symbols large enough, that a study by a committee with the appropriate skills and interests is clearly appropriate. Pending the results of any such study, we recommend that, like foreign languages and for some of the same reasons, complex phonetics continue to be brailled according to current code, using the non-UEB indicators to make the code switches (see section 3.23).
By way of exception, when the only diacritics involved are the same as accent marks, then the accent symbols may be used.
When a "mention" dot locator is encountered, as would frequently happen in documents that discuss braille (such as the braille edition of this report) and infrequently in other contexts, it implies that the symbol following the locator is being discussed, i.e. "mentioned", and that it does not have its usual force. So if the following symbol is the grade 1 passage indicator, for instance, it does not actually switch the interpretation of the succeeding symbols to grade 1.
By contrast, when the "use" dot locator is encountered, it implies that the symbol following the locator does have its usual force and meaning. In such cases, the locator is typically present purely to assure that the next symbol is physically recognizable. For example, if it were necessary to place a colon (dots 25) far from surrounding text, a "use" locator could be used so that it could readily be distinguished from a hyphen (dots 36) or the letter "c" (dots 14). By the design of braille, such needs are uncommon, but they can arise. Probably the most common use will be to allow grade 1 passage opening and closing indicators to be isolated on lines by themselves, thus leaving the line-by-line arrangement of enclosed material (such as computer programs) aligned more naturally.
When translating braille to print, it would be natural to represent the braille symbol that follows a "mention" locator in some way in print — e.g. by dot numbers, or by showing the dot configuration using a font for "simulated braille". A "use" dot locator, on the other hand, can simply be ignored when translating to print.
The committee noted that sometimes there are various kinds of bullets used for various purposes within a text, and recommends that the existing single assignment be expanded to a "family" of related symbols to be used when distinctions are necessary.
Some of the reasons for the listed assignments are:
(1) The dollar sign suggests a "modified s", which is of course what the dollar sign is, and conveys more meaning to the braille reader in the increasingly common cases where the dollar sign is used for a special effect in place of an s in words such as "SALE" or "SAVINGS". Similarly, the other currency symbols are all "modified" basic letters — with a general preference, where possible and not in conflict with other assignments, to use dot 4 and the basic letter for currency symbols.
(2) The male and female symbols refer to the x and y chromosome, thus remaining independent of language.
(3) The degree mark suggests an elevated "zero".
The dot locator is to be used before the braille character to which it applies. Furthermore, that braille character is to be considered in its own right and not necessarily as combining, under the prefix-root rules, with any following character to form a valid UEB symbol.
The "calculator window" symbol may be used for those cases where the print directly shows a small window, typically containing some result that is being discussed in an exercise, so that it is clear to a person following the exercise that the result will actually appear in the calculator window (not just in the memory, for example). There are other such cases, e.g. "keycaps", for which similar symbols could be defined. Such symbols can be combined, using the "physical enclosure" indicator (section 3.20), to indicate the window, keycap, etc. together with its contents.
The series of transcriber-defined symbols is provided for situations where one or more symbols not defined in UEB occurs in a text, and moreover occurs so frequently in that local context that other methods provided in UEB, namely transcriber-assigned shapes and composite symbols, would yield symbols too long to be practical. In this series, the dots 3456 prefix for the multi-cell symbols, and the order of the added prefixes, is motivated by the pattern for the transcriber-assigned typeform series. Also, like that one, this series could theoretically be extended even further by adding another round of the same prefixes in the same order, though it is hard to imagine a case where such a concentration of unusual symbols would arise in practice.
In many situations, ranging from set-out long division in arithmetic to structural formulae in chemistry, it is necessary to draw "lines" in a meaningful way. The symbols and modes described in this section provide a facility for doing this using standard braille cells, in such a way that regular UEB text and diagrammatic lines can coexist, even within the same diagram, without ambiguity.
To draw a horizontal line (other than the hyphen and minus sign, which are separately defined):
(a) for horizontal lines indistinguishable from dashes as defined in section 3.4 or the lines and bonds defined in section 3.18, the symbols as provided in those sections should be used.
(b) In other cases, the horizontal line mode indicator begins
a special "horizontal line
mode". Thereafter, all nonspace UEB symbols
other than
Within horizontal line mode, the following symbols should be used where applicable:
Valid UEB symbols other than those listed
above, and
excluding
Vertical lines: Vertical line segments are drawn using any of the symbols:
While the first of these is always for a single solid line segment, the others are for variants (e.g. dotted or dashed) as needed. One or more such symbol may occur in a group, but each such group must be surrounded by spaces. This is in effect an assignment of all symbols so formed, when surrounded by spaces, to represent vertical line segments or groups of such segments.
Arrows vertically contiguous with vertical lines so constructed are deemed to be continuous with them.
Diagonal lines: Diagonal line segments are drawn using any of the symbols:
The single-cell symbols are always for single solid line segments, the others for a variant type (e.g. dotted or dashed) as needed. One or more such symbol may occur in a group, but each such group must be surrounded by spaces. This is in effect an assignment of all symbol groups so formed, when surrounded by spaces, to represent diagonal line segments or groups of such segments.
The assignments of
Arrows vertically contiguous with diagonal lines so constructed are deemed to be continuous with them.
The diagonal line symbols are to be used for vertical line segments at points where the vertical lines are crossing, or otherwise too near, diagonal lines to permit the required space between the two kinds of lines.
Because the symbols for diagonal lines also have a contraction meaning and must be spaced within the line, it is conceivable that they could be misread for those contractions in some circumstances. Consequently, it is necessary to disallow the "gh" and "ar" contractions when those fragments are surrounded by spaces, and whether capitalized or not. Since those are not real words, that restriction is deemed minor.
For the horizontal overbar in a set-out division problem, a regular horizontal line as described above may be used. For the (sometimes straight, sometimes curved) line customarily shown between the divisor and dividend in print, either a space or a spaced dots 456 (the "vertical line segment") could be used. A simple space is allowed, even when a line is present in print, because the vertical line serves little practical purpose other than as a visual cue. A space for that purpose is also customary in current British math braille.
The committee also noted that the technology for producing "real" tactile lines — for example, by using paper especially coated so that arbitrarily drawn lines can be raised by heat — is advancing rapidly. Methods are being developed that enable blind persons to compose graphics, either directly (e.g. using "pens" with heated tips) or through adapted computer-assisted drawing (CAD) programs. All this means that even better ways of doing tactile diagrams may often be available. However, there no doubt will remain many practical situations where it will be useful to employ ordinary braille cells, spaced as in regular text, for diagrammatic purposes (a view that is reflected in the BANA chemistry code, for instance). These provisions are meant to allow for that case, and by no means to discourage more advanced means of producing diagrams when they are practical.
These enclose notes written by the transcriber.
The 1995 report of this committee contained a lengthy discussion of the 189 contractions of EB and sequencing (omission of spaces) as symbols and symbol sequences whose special interpretation in grade 2 required careful analysis to prevent ambiguities. (See sections 3.27 through 3.40 of Ref. 95a, and also Appendix B of this report, which repeats some of the more fundamental reasoning from Ref. 95a with respect to contractions.) It was recommended that sequencing and several contractions be discontinued, and that the usage of some others and in particular short-form words be restricted, recommendations that for the most part have been accepted by the Project Committee or that are still under consideration. In any event, since around the time of that report the primary work on contractions has been assigned to a separate committee, Committee 3, and consequently Committee 2 has not further considered matters related to contractions except for those discussed in sections 4.2 through 4.4 below, which needed resolving because they also impact upon the "basic" (grade 1) sphere within UEB.
Many symbols and sequences have a grade 2 meaning that depends upon the condition of "standing alone," a term that requires precise definition in order to avoid ambiguity. This definition has been modified slightly since the 1995 report (section 3.41 of Ref. 95a); it now reads:
A letter, or unbroken sequence of letters, or sequence of letters broken only by embedded single apostrophe(s), regarding contractions as equivalent to letter sequences, is standing alone if the symbols before and after the letter or sequence are spaces, hyphens, dashes, or any combination, or if on both sides the only intervening symbols between the letter or sequence and the space, hyphen or dash are common literary punctuation or indicator symbols, defined as:
(1) Before the letter or sequence: Any opening round parenthesis, square bracket or curly brace, opening quote of any kind, nondirectional quote or apostrophe, opening typeform or capitalization indicator, or any combination of these.
(2) After the letter or sequence: Any closing round parenthesis, square bracket or curly brace, closing quote of any kind, nondirectional quote or apostrophe, closing typeform or capitalization indicator, comma, semicolon, colon, period, question mark, exclamation mark or any combination of these.
(end of definition)
The extent of a capitalized word indicator (double dot 6) was changed to include only the actual letters immediately following the indicator (section 3.3), which in the case of a contraction would mean the letters in the expanded (fully spelled-out) form. This means that the apostrophe now terminates the effect of the double dot 6, which in turn means that the formerly natural rendering
Grade 1 is no longer implied immediately prior to a number, though it is implied for the remainder of a word immediately following a number (section 3.5).
The focus of Committee 2, and hence this report, is primarily "reader rules" — that is, how to understand clearly what symbols are represented by a given text in UEB braille. Nevertheless, we have inevitably considered the other direction, i.e. the "transcriber rules" whereby braille is written or transcribed, from time to time — because the practicality of that process must be considered, because readability might lead us to prefer one UEB rendering over another when more than one is possible, and sometimes simply as one way to understand the reader rules more completely. Many of those considerations have already been included in the appropriate subsections of section 3; other more general issues are discussed below. In any event, the development of transcriber rules is the responsibility and province of a separate committee, Committee 6, and so all our recommendations in that area should be regarded as recommendations only, subject to further consideration by Committee 6 (and of course the Project Committee).
The most fundamental transcriber rule is that the resulting braille, when read according to the reader rules, must accurately represent the desired sequence of symbols. However, there is often more than one way to produce an accurate result according this definition, and that is where guidelines for more "readable" braille come into play.
As implied by UEB principles, there should never be any confusion, or need to rely on contextually determined "meaning", for the reader to sort out whether a given braille symbol is being used as a grade 2 contraction or as a grade 1 symbol.
In a work entirely in grade 1, which might be produced for teaching purposes or for other reasons as determined by producer policy, this issue does not arise and so no grade 1 indicators need ever be used (except as required for other reasons, e.g. for the letters a-j immediately following digits). Large sections of works, prefaced by a transcriber note according to producer custom, may also be so treated.
In ordinary, i.e. grade 2, works, the grade 1 indicators (section 3.2) must be used whenever a symbol could, taking into account its position among other symbols, be read as a contraction. There are three such indicators, which respectively allow a single symbol, a whole group of symbols surrounded by spaces (or "the rest of" the word, if used in the middle), or a whole passage to be marked as in grade 1. The latter two possibilities are called extended grade 1 modes, and a fully developed set of guidelines would give some advice as to when to use them, as opposed to simply marking each individual symbol that could otherwise be misread as a contraction.
The committee stopped short of developing such a complete set of guidelines, but has noted that the motivation for such guidelines could be grounded in certain desirable properties of the resulting braille, namely:
(1) the number of indicators is minimized;
(2) the number of cells is minimized;
(3) the number of switches between modes, e.g. between grades, is minimized;
(4) to the extent possible, English words appear in familiar form, i.e. contracted, for easy recognition.
Recognizing that those properties can easily be in conflict in certain circumstances that are difficult to envision in the abstract, the committee at one time advanced some preliminary ideas (see section 3.42 of Ref. 95a) as a starting-point only, but basically observed that more practical experience with the system as a whole would be necessary before hard-and-fast rules could be devised for the use and non-use of extended grade 1 modes.
Since that time the subject has not been formally revisited, but as more symbols have been assigned and more work done with practice texts, it has been found that extended grade 1 modes seem not to be needed nearly as frequently as originally envisioned. That is, the option of staying in grade 2, not using any extended grade 1 modes but simply using the grade 1 symbol indicator as needed, is often a reasonable strategy with material that contains fragments of technical notation, such as email addresses, web site URLs, simple math formulas and the like.
It remains necessary to explore this issue further.
Typeform indicators could, in principle, be placed so that initiating indicators precede the first character that has the indicated attribute as closely as possible, and any terminating indicators follow the last character with the indicated attribute as closely as possible. But that would often mean, for example, that a closing italic passage indicator would come between the last letter of a sentence and the period at the end, because a period cannot really be "italic." Such a placement, the committee felt, would not read as naturally as placement of the terminator after the period — and the latter would not be misleading, since the period could not be affected.
A suggested procedure was devised that yielded "nice" placements in a series of examples:
The idea is that you "home in" on where to place the terminator by applying the criteria in sequence. I.e. rule 1 will give you a range where the terminator can be placed, then you apply rule 2 to that range to get a smaller range, etc., eventually reaching a definite position. You start with the assumption that the passage extends over indefinite characters (in the sense of point 1), though a rule would be needed not to include an initial capital of a new word following a passage in full capitals, for example.
1. The terminator should be placed somewhere after the last character definitely with the relevant attribute, and before the next following character definitely without that attribute (or the end of the text). [Note that parentheses, period (full stop), comma, quote mark etc. neither definitely have, nor do not have, the attribute of capitals; a period neither definitely has, nor does not have, the attribute of italics.]
If this does not determine the position, then:
2. The terminator should satisfy nesting of other indicators or naturally paired characters (e.g. parentheses, brackets, quotes).
If this does not determine the position, then:
3. The terminator should be placed before the first space, hyphen or dash, if it exists, in the range. [The end of a paragraph is counted as a space in this regard.]
If 3 does not apply, then:
4. The terminator should be placed immediately after the last character which definitely has that attribute.
The committee considered simplified forms of the above procedure but did not arrive at one that yielded results that were as good in all considered cases.
The UEB Research Project has as its goal the development of a single braille code providing notation for mathematics, computer science, and other scientific and engineering disciplines as well as general English literature. The unified code is not to depart in major ways from the English Braille (EB) system, which is currently used mainly for general literature (Refs. 91a, 92a). Objective II is to define basic methodology for the extension process, so that the code remains consistent and unambiguous throughout the work of subsequent committees, and moreover actually to carry out such an extension for technical fields such as mathematics and computer programming.
Project Guidelines: Certain technical guidelines of the UEB Research Project are relevant to the work of this committee, and so are restated here for the convenience of the reader (though without any of the reasoning behind these guidelines, which has been amply developed elsewhere). There are six objectives, namely that the Unified Code shall:
(a) use a 6-dot braille cell;
(b) encompass Grade I and Grade II braille without making any major changes to the contractions of Grade II braille;
(c) be usable by both beginning and advanced braille readers;
(d) be computable to the greatest degree possible, without detriment to readability, from print to braille to print and employing an unambiguous braille representation of each print symbol;
(e) imbed textbook, mathematics, computer and other technical codes (excluding the music code);
(f) consider all submitted English Braille codes in its formulation (Refs. 72a, 72b, 77a, 87a, 87b, 88a, 89a, 89b, 90e, 90f, 91a, 92a, 96a, and 97a).
Committee Charge: The above guidelines were incorporated by reference in the charge to our committee, which included the following further technical specifics:
(g) to develop a general method for extending the basic literary code so that it can encompass the symbologies employed in various scientific and technical disciplines;
(h) to define the terms used;
(i) to determine the extent of symbols — print and indicators;
(j) to ensure that new symbols allowed by an extension will be unambiguous and will permit the same general form of expression in braille as in print;
(k) to ensure symbols in the Basic Code will not be altered except to bring about parallel forms in braille and print.
To this list was added, in June 1993, the task of carrying out the code extension to mathematics, computer programming and other technical disciplines.
General Interpretation of Guidelines and Charge: From the outset, it was apparent that the above set of guidelines were to be understood as a whole, and not individually as absolute strictures, or the task as defined would have presented impossible contradictions. For example, since the letter-group "gg" and a parenthesis are, when immediately surrounded by letters, indistinguishable in current English Braille (American usage), it was clear that some change would be necessary either to the contraction system or to fundamental symbol usage, if ambiguity was to be eliminated. In particular, we understood guideline (b) as generally restricting us from adding new contractions or changing the definition of any of the existing 189 contractions; we did not consider that well-reasoned changes to the rules of usage, even to the extent that a few contractions might no longer be used, were excluded from our consideration.
Further, despite the fact that precision and computability were obviously at the very heart of our charge, we did not interpret these to mean "slavish adherence to print". We understood our commitment to print practices to extend only to the point where essential information is retained in the braille transcript, while print format and style used only for ornamentation is ignored, as is current practice. For example, if all headings at a certain level are embellished in print as underlined bold, the transcription should ignore those attributes in braille while faithfully retaining uppercase letters, spaces, and similar information-bearing details, and of course following the braille formatting rules governing headings at that level.
Basis of Work from June 1993 Onward: Since the expansion of the committee's task and membership in June 1993 (see Appendix F), the general basis of the committee's work, in the sense of a point of departure, has been the original committee's report of November 1992. Nevertheless, all recommendations of that report have been considered open to possible change, and indeed some have been changed.
Other General Principles: The committee has endeavored to avoid symbol assignments and rules that conflict with internationally accepted braille conventions, or the braille conventions of sister languages, and in general to define symbols that do not unnecessarily rely on English as a mnemonic basis, to the extent that is possible while devising a code for existing readers of English Braille, and respecting the traditions of that system. For example, we have usually avoided such devices as using the letter "s" in the braille symbol for a square, because that would depend on awareness of the English word.
Kinds of Rules Considered: The rules for current English Braille are stated primarily in terms of how print is to be converted into braille. In other words the current rules are oriented towards the task faced by transcribers or computer programs translating in the print-to-braille direction. This is understandable, considering that obviously most actual media conversion is in that direction. Nevertheless, our committee observed early that there are really three kinds of rules to be considered, and that for our purposes transcribing rules were best considered as derived from the others rather than the other way around. The three kinds are:
Reading Rules: The committee felt that a braille code should be considered primarily from the point of view of the reader, who must understand precisely what symbols are being expressed by a given braille text. (That viewpoint does not change when considering a person who is writing originally in braille, who must not only understand but be able to control those symbols, with precision.) For literary material, the requirement of precision comes down to the ability to determine unambiguously how the corresponding print is spelled and punctuated, which is not unimportant, especially in many educational and professional contexts. For technical material, precise representation of symbols is even more important — often it is indispensable to any useful access to the text.
That consideration leads to the conclusion that UEB should, to the maximum feasible degree, be unambiguous in the direction that we may loosely call "braille-to-print". This does not necessarily refer to actual conversion, either by man or computer (though the issues are closely related), but rather to the preciseness with which braille represents print symbols. In fact, it would be even more correct to say that both print and braille, in parallel and equal fashion, are systems for the representation of "abstract symbols" — and our concern is that braille be at least as accurate as print in representing such abstract symbols, and their sequences and relationships.
Going the other way, it is less critical that there be only
one braille representation of a
given print text, even though it is of course desirable that
there be only one. For example, the
print text "ABC" can be represented in braille
either as
Transcribing Rules: Nothing in the preceding paragraph is meant to disparage the eventual importance of transcribing rules, under which the great majority of braille is created. However, it is meant to clarify why we considered that the definition of a braille code is primarily in terms of reading rules. From that point of view, the fundamental and most important transcribing rule becomes: to produce braille that, when the reading rules are applied, yields precisely the original print text (apart from purely ornamental aspects).
Designing Rules: The designing of various aspects of a braille code, that is in general the making up of the reading and transcribing rules and in particular the assignment of symbols, is itself an activity that needs to be subject to rules if the code is to maintain direction and coherence over time. Thus the drawing up of such designing rules is the essence of the original task assigned to our committee, and those rules should continue to apply — or be modified only after careful consideration — by any future committee concerned with the maintenance of UEB. In this report, such rules are primarily found in Appendices A and B.
A very early priority of the committee was that of defining symbols and usage rules in such a way that the extent of any symbol, that is its physical beginning and end, could always be determined no matter what symbols were placed next to it. Clarifying the extent of symbols was not only directly listed in the charge to the committee, but also is clearly necessary to provide a secure basis for an extendable code. In this section we develop a construction system that completely provides such clarification and security.
It is important to understand that here we are not, for the most part, concerned with the "meaning" of the symbols discussed; that is the distinct matter of symbol assignments. Rather, we are concerned primarily with the manner in which symbols are formed from braille characters — that is, their "structure". There are inevitable references to meaning, however, in the discussions on the space symbol and the capitalization and grade 1 (letter sign) indicators, because in those cases the meaning plays a role in the structural rules.
In this topic, we undertake to define some basic terms that are used in a precise way in this report.
Print Character: A print character is a single letter, digit, punctuation mark, or other print sign customarily used as an elementary unit of text.
This definition of a print character relies, in effect, on common understanding as to the way text based on western-alphabet languages is formed, and it knowingly avoids, at least for the moment, the surprisingly complex issues that arise when virtually every kind of expressive mark ever made by man must be considered. (See section 2, "General Principles of the Unicode Standard," in Ref. 91b.) A definition like this rather clearly considers the semicolon to be a single character, even though two distinct marks are made in forming the character. On the other hand it is less clear as to whether an accented letter is one character or two; ultimately such a choice is likely to come down to a practical consideration, such as the actual frequency of accented letters, and thus be made differently for, say, English and French.
Print Symbol: The terms "print symbol" and "print character" are used interchangeably.
Braille Character: A braille character is any one of the 64 possible combinations of the 6 dots, including the space.
Braille Character Categories: The 64 braille characters are categorized as follows:
1. 1 space.
2. 8 prefixes, subdivided as follows:
2a. 6 general prefixes:
2b. 2 special prefixes:
3. 55 roots, subdivided as follows:
3a. 12 lower roots:
3b. 26 alphabetic roots:
3c. 17 strong roots:
Prefix characters are those characters that, in current customary braille, even beyond English, are quite often associated with the characters that follow them. For all the prefixes except the number sign, their use for that purpose follows from the fact that they have only right-hand dots, and thus are most easily read when they are up against something on the right. In the case of the number sign, usage as a precursor to numbers is the universal long-standing custom. The reason for distinguishing "general" and "special" prefixes will become evident as the structural rules are developed.
Root characters are those that more commonly have a direct meaning in themselves, or that complete the symbol when following a prefix. The subdivision of roots into three smaller classes plays no role in the symbol construction rules of this section; these distinctions are descriptive and made in anticipation of possible use for other purposes only. "Strong" roots are so named because they all have dots in the top and bottom row of the braille cell and in the left and right columns, and thus are physically unambiguous — that is, they can be positively identified even when not near other braille cells.
Braille Symbol: A braille symbol is one or more consecutive braille characters that, as a unit, either (1) stand for a single print character or (2) indicate how subsequent braille symbol(s) are to be interpreted. Symbols of the first kind are called "graphic symbols"; those of the second kind are called "indicator symbols". Herein, the unqualified word "symbol" normally means a braille symbol, unless the context makes it clear that the print is intended.
Mode: The term "mode" is used to describe the effect of an indicator symbol on subsequent symbols. If, for example, an indicator causes all the letters of a word to be interpreted as capitals, then "capitals mode" may be said to be in effect over that word.
As noted above regarding prefixes and roots, a great many current braille symbols are either simple roots, or combinations of a prefix followed by a root. This suggests the following natural generalization: Let all symbols be either a single root character or a series of prefixes terminated by a root character. Mathematically, one could reduce this to: A symbol consists of zero or more prefixes terminated by a root. The extent of symbols constructed in this way would always be readily perceived when reading, regardless of the order in which the symbols appeared, because the root character would always mark the end of each symbol and therefore the beginning of the next. Moreover, this prefix-root notion would be well grounded in current usage.
Unfortunately, despite the simplicity and appeal of this concept, there are a few symbols of current English Braille — such as the double capital sign and the letter sign — that do not fit the mold, and which the committee felt should not be changed. In the end, therefore, the structural rules that were derived are necessarily a little more complex than this basic idea, though they are based upon it, as will be evident.
Symbols consisting only of prefixes, such as the double capital sign, may be called "pure-prefix symbols". Consulting current usage, and the fact that prefixes convey a sense of affecting subsequent characters, the committee felt that such symbols should never be used for graphic symbols, but only for indicators. On the other hand, symbols terminated by roots can be used both for graphic symbols and for indicators.
These are primarily worded as "reading rules" that permit the reader, starting at a braille character that is known to be the beginning of a symbol, to determine unambiguously where the symbol ends. The rules are based on the form of the symbol alone, not its meaning, since the reader may not know the meaning on first encounter and thus may need to isolate the symbol as a first step to discovering that meaning.
The rules are to be simple, yet insofar as possible encompass the symbols of current English Braille. Beginning braille readers will undoubtedly not learn these rules at the outset, but by the time they are ready to benefit from having them stated explicitly, the rules should be natural and almost obvious.
The several rules give rise to corresponding categories of braille symbols, which are considered in order, starting with the space.
The braille space symbol is simply a braille space character. In other words, in the case of braille space, "character" and "symbol" may be considered interchangeable terms, for the braille space character never combines with other braille characters to form a larger symbol.
The space symbol stands for some amount of "white space" in print, including line endings, and may itself be sensed as the end of a line. Thus all white space in print corresponds to white space in braille, and vice versa, so that the braille reader always remains completely and directly aware of this important print device. However, the braille spacing is not intended to provide a measurement of the "amount" of white space in print, which is rarely important in itself. That is, the braille reader cannot determine, from the amount of space encountered in the braille text, just how much space is present in the print text. This is because in some cases any amount of print space is represented by a single space in braille, and in other cases the number of spaces appearing in the braille text is governed by braille formatting rules, such as in the alignment of items in an outline or table.
Because some printing techniques can leave varying amounts of white space, a useful transcriber rule would be: if you have a reasonable doubt as to whether a space is present, presume that one is present.
If space is present in the print, it must be so represented in the braille. This implies that the practice of "sequencing", by which certain words may under some circumstances be written together in braille despite being spaced in print, must not be employed in UEB. For the ambiguity that would be created by sequencing ("fora" being indistinguishable from "for a", for instance), though it might not seem important in typical literary context, could seriously affect technical material, where the presence or absence of a space is often meaningful. (See also section 3.29 in Ref. 95a.)
The elimination of sequencing would have the beneficial side-effect of ending the ongoing controversy over contracting across "natural pauses".
Spaces used as separators within numbers are treated specially; see section 3.5.
Reading Rules:
(1) If a symbol begins with a root character, then that is the entire symbol (called a "simple root").
(2) If a symbol begins with a general prefix, continue to read succeeding characters, including prefixes of either type, until either a root or a space is encountered. If terminated by a root, that root is part of the symbol; if by a space, it is not part of the symbol.
The following are examples of general symbols usable in any context.
(Note: The braille sequence dots 46, 123456 that begins each entry in the braille edition of the following list of general symbols is not a part of the symbol. It is a "dot locator" whose presence enables precise determination of the following character's cell position.)
Of course some of these, particularly the last, would be unlikely candidates for actual assignment in the code; but all obey the rules for general symbols.
The following are examples of general symbols that may be used only before space:
Because these symbols consist of prefixes only, they must be used only for indicators. Moreover, because these symbols may be used only before space, or in other words at the end of a nonspace sequence, they are best assigned only to the role of "closing" indicators for modes established for entire passages. In any case, any assignment of such symbols for use must specify that they can be positioned only before a space, without exception.
General symbols terminated by a root are intended to be used for all kinds of symbols in braille, both indicators and graphic symbols; hence the adjective "general" both for the class of symbols and for the kind of prefix that begins them when they aren't simple roots. The only restriction is that, when an alphabetic print symbol has both a lowercase form and an uppercase form, then the lowercase form should be assigned to this class, and designated as such, with the associated uppercase form assigned to a corresponding augmented general symbol, that is to a symbol consisting of the same characters preceded by a dot 6 character. (The augmented symbols are described next.)
Reading Rules:
(1) If a symbol begins with a dot 6, and the next character is a space, then the dot 6 is the entire symbol.
(2) If the character after the dot 6 is a root or a general prefix, then the remainder of the symbol is read just as for a general symbol, described in the preceding topic.
The following are examples of augmented general symbols usable in any context:
The following are examples of augmented general symbols that may be used only before space:
The same restrictions apply to the use of these before-space-only symbols as were recited for the similar subcategory under "General Symbols" above.
There is an important restriction on designers for assignment
to symbols of this class.
It must not be sensible for augmented general symbols ever to
follow the dot 6 special
symbols (see topic below), for in such a case the dot 6 sequence
would appear to include the
initial dot 6 character of the augmented symbol. This could lead,
for example, to a "word
capital" indicator being read as a "passage capital" indicator.
Because all the dot 6 special
symbols establish capitalization, and differ only as to extent,
this restriction on augmented
general symbols will be met if each such symbol cannot be
capitalized. In turn this condition
will be met if the symbol is either already a capital (as with
the
For example, the two final-letter contractions "ation" and "ally" are symbols of this class (see section 3.37 of Ref. 95a).
Reading Rules: If a symbol begins with dot 6 followed by another special prefix, or with dots 5-6 in any case, the extent of the symbol is determined by reading to the right until one of the following events occurs:
(a) A space, root, or general prefix braille character is encountered. In that case the symbol is terminated just before that braille character.
(b) Another special prefix character, with highest dot lower than the highest dot of the preceding character, is encountered. In that case the symbol is terminated just before that "lower" braille character. (Put another way, symbol breaks would occur before dot 6 following dots 5-6, and not otherwise as long as only special prefixes are encountered. This rule could be summarized as "when the dots drop, stop".)
If we consider for the moment only symbols up to three characters in length, the above reading rules imply that there are exactly 8 viable special symbols, listed in the table below in a "lowest-to-highest" order, with rightmost character varying most rapidly, an ordering that is important as will be apparent. Next to each symbol is a symbol number for reference, and in some cases an assignment that will be discussed more fully in the body (sections 3.2 and 3.3) of this report.
Note that the limitation to three characters per symbol is arbitrary and for purposes of the above listing and this discussion only. If a future designer finds it useful for certain rarely-used modes, special symbols of any size may be defined, as long as the rules of formation and usage follow the same pattern as described here.
Because these symbols all lack terminating roots and are
therefore usable only for
indicators, that is in connection with modes, it is always
possible without loss of generality to
impose a rule upon the order of indicator presentation when
several modes must commence at
once. To avoid conflict, in keeping with our reading rule,
transcribers must always put
sequences of special symbols in descending numeric order as
listed above. Thus to indicate a
grade 1 passage beginning with a fully capitalized word, one
would use symbol 8,
Code designers must also be careful that, within each of the two groupings defined by repetitions of the same character, they do not define any modes that sensibly may need to be juxtaposed. In the above list, those groups are: symbols 1-2 ("dot 6 special symbols") and 6-8 ("dots 5-6 special symbols"). (The middle group, symbols 3-5, could be called "dots 6, 5-6 special symbols.) Moreover no mode may be defined for any of the dot 6 special symbols that may be needed before any augmented general symbol. These restrictions are necessary to avoid obvious overlap problems, and they are easily reduced to two simple rules:
(1) All the dot 6 special symbols must establish (or cancel) capitalization and differ only as to extent, and
(2) All the dots 5-6 special symbols must establish (or cancel) grade 1 mode and differ only as to extent.
The dots 6, 5-6 special symbols currently remain unassigned. As they are ineligible for graphics symbols, a possible future use would be for indicators establishing special mode(s).
Note that certain contractions of current English Braille, namely the final-letter contractions "ence", "ong", "ful", "tion", "ness", "ment", and "ity", must all be regarded as two-symbol sequences under this rule, and moreover require special consideration to interpret (see section 3.38 of Ref. 95a.)
(1) This system assures that all symbols, regardless of context and regardless of the reader's familiarity with meaning, are unambiguously recognizable as to their extent (boundaries) (see Appendix C).
(2) The system allows code designers henceforth always to think in terms of braille symbols as the fundamental units rather than individual braille characters, and to assign meanings to those symbols in natural mnemonic groups without concern about the possibility that chance juxtapositions could cause recognition problems in actual use.
(3) The system encompasses the symbols used in current English Braille to a remarkable degree, as will be apparent in the next section. It also does well representing many symbols from other codes of interest to the UEB Research Project, such as the 1972 Nemeth code (Ref. 72a).
(4) The system provides an orderly, efficient and suitably rich basis for future expansion. On this last point, we first note that the number of potentially available symbols is without limit in principle. If an arbitrary target limit of 3 cells is adopted for practicality's sake, we may further calculate the number of available root-terminated general and augmented symbols within that limit to be 3,410, certainly an adequate number for a broad range of notation.
This proof merely formalizes what may already be obvious, namely that the various classes of symbols and symbol ordering rules are defined in such a way that it is always possible to discern the boundary between two adjacent symbols. To put it another way: if one knows where the current symbol starts, it is always possible to tell where it ends, and therefore where the next one starts, even if one does not know the "meaning" of either symbol.
The proof is easily constructed and followed, although it is a bit tedious, like most proofs of the "enumerate all the cases" variety. Still, we think it worth spelling out, for in the process our symbol construction rules, and the reasons behind them, are likely to be further clarified.
We begin by listing the various classes of symbols defined by the reading rules. To minimize verbosity in the proof itself, we assign a 2-letter name to each class. The list follows, and for information purposes a count of the symbols with three or fewer characters is given in parentheses for each class (but note that the number of symbols in every class except space is actually unlimited, because the symbols can be arbitrarily long):
Since there are 8 classes, there are in principle 64 possible 2-symbol sequences to consider.
However, since the space symbol is complete in itself, and moreover not part of symbols in any other class, all combinations involving space as either the first or second symbol need no further consideration. That leaves the 49 combinations involving the other 7 symbol classes.
But further, since the symbols of class gw and aw can only be followed by space, none of the other combinations commencing with either of those two classes are allowed. Moreover, classes ge and au are both self-delimiting, because by definition they are terminated by the root character, and so the boundary is determined regardless of the class to the right.
The only remaining cases, then, are the 21 combinations formed by one of the classes sc, sm or sl on the left and one of the seven nonspace classes on the right. Even many of those could be grouped, but at this point it is just as easy to enumerate them and do the grouping by reference:
1. sc ge: By definition any special symbol is terminated just before a root or general prefix, and by definition a ge or gw always begins with such a character, defining the boundary.
2. sc gw: The reasoning is the same as case 1.
3. sc au: This case should not occur, because the rules for code designers forbid assigning to class au any symbol that might need capitalizing, and the transcriber rules require any capitalization indicators to immediately precede the first affected symbol.
4. sc aw: The reasoning is similar to case 3.
5. sc sc: This case cannot occur, as the rules for code designers require that 2 symbols both in class sc (or both in class sl) should never need to be juxtaposed. This is fulfilled by having the various symbols within each class indicate different extents of the same modes; it would never be meaningful, much less necessary, to initiate two different extents at the same time.
6. sc sm: This case cannot occur by the transcriber symbol-ordering rules; two indicators in those classes should always be written in the order sm sc.
7. sc sl: The reasoning is similar to case 6.
8. sm ge: The reasoning is the same as case 1.
9. sm gw: The reasoning is the same as case 1.
10. sm au: Because class sm symbols always end with at least one dots 5-6 character, and class au always begin with a dot 6, the "stop when the dots drop" rule would terminate the sm symbol at the proper point.
11. sm aw: The reasoning is similar to case 10.
12. sm sc: The reasoning is similar to case 10.
13. sm sm: The reasoning is similar to case 10.
14. sm sl: The reasoning is similar to case 6.
15. sl ge: The reasoning is the same as case 1.
16. sl gw: The reasoning is the same as case 1.
17. sl au: The reasoning is similar to case 10.
18. sl aw: The reasoning is similar to case 10.
19. sl sc: The reasoning is similar to case 10.
20. sl sm: The reasoning is similar to case 10.
21. sl sl: The reasoning is the same as case 5.
The committees working on the UEB Research Project are required to give reasons for every recommendation, and we have endeavored to do that throughout the main presentation. Sometimes those reasons mention alternatives that were rejected in favor of the recommendation, but those tend to be the minor alternatives that are still easily related to a particular decision that simply went the other way. However, in the case of certain major courses of action that were considered, the effect of choosing a particular course has been so pervasive that it is difficult to put the reasons for the choice next to any particular recommendation, and so we put them here.
These are only summaries, as it would be impractical to try to
cover all the points
made in debates that were sometimes quite spirited and
protracted. Persons interested in
tracing the details of debates should consult the committee
archives, which may be accessed
through the ICEB web site at
http://www.iceb.org.
British Maths: The British mathematics code (Ref. 89a) is a well-developed system that is regarded as integrated with EB. Even to the original (BANA) committee, therefore, an obvious first idea was simply to adopt that code, together with the literary code, as UEB. However, upon an examination of the British maths code, it became quickly apparent that the code was designed with goals and assumptions that differed greatly from those that, by reason of the charge to the committee, we had to live by. For example:
(1) The British maths code does not adhere to a single-symbol concept as it sometimes has numbers "up" and sometimes "down" (a topic in itself that is discussed further below).
(2) It artificially alters spacing (as do most math braille codes, because usually spacing is not significant to mathematical meaning).
(3) It lacks any apparent basic plan to assure symbol extent recognition (as again is true of most codes prior to UEB).
(4) It uses the letter sign with certain lower signs for common mathematical operators, whereas we wanted those combinations to reassert the "grade 1" meaning of those signs as punctuation marks.
(5) It reuses symbols that have other meanings, relying on human sensing of the mathematical context to resolve the ambiguity; for example, the "much greater than" symbol (two greater-than signs in print) is formally indistinguishable from "oo".
None of these observations is meant to fault the design of the British maths code, which is clearly based on the assumptions that intelligent human beings, with knowledge of the subject matter and a sense of the context, are doing both the transcribing and the reading. Those are reasonable assumptions for a prior period of time, and they underlie all of the older math codes; they do not, however, square with the needs of automated bidirectional translation nor with several of the other goals of the UEB Research Project, and so it was necessary to set aside the possibility of simply adopting the British code. However, many valuable concepts were drawn from that code, as well as from the Nemeth code and other existing braille technical codes.
Lower Numbers: In a purely mathematical context, there are cogent reasons for preferring to have the ten digits represented by configurations in the lower cell instead of the upper cell as is customary in literary braille. This is particularly the case in contexts where literary punctuation is unlikely and digits and letters are likely to be juxtaposed, as in algebraic expressions involving the implicit multiplication of numeric constants and letters standing for variables. In such cases, use of the lower cell can allow both numeric indicators and letter signs to be omitted, resulting in a more compact representation in braille. For mathematics, compactness is somewhat more strongly related to readability and overall usefulness, because mental and/or written computation, that is manipulation of the symbols, is involved. For those reasons, the 1972 Nemeth code uses lowered numbers, and both the British and the Russian math codes (Refs. 89a and 75a respectively) use them in some circumstances, e.g. in subscripts and superscripts, where punctuation marks are particularly unlikely.
The original (BANA) committee therefore carefully considered the possibility of "lowering" the digits, despite the concern that this might be perceived as a "major" change to literary braille and therefore beyond our charter. In fact, a small informal survey of braille readers suggested that only about half of the North American readership felt strongly opposed to lowering the digits as an issue in itself. The opposition stiffened, however, and in the end our own opinion was formed, when the additional consequences of lowering the digits were considered. Principally, this would have involved either changes to all the common punctuation marks, or the introduction of indicators to deal with cases where numbers abut punctuation marks. We found, in a small survey of literature with a generally scientific orientation (Scientific American magazines), that numbers were much more likely to abut punctuation, even apart from the obvious decimal points and commas, than they were to abut letters. Those facts convinced us that the overall best solution for a Unified Code lay with the existing English Braille and indeed worldwide custom of representing the digits in the "up" position. (See more on this subject under "dot-6 numbers," below.)
Dot-6 Numbers: There is another form of numbers, first used by Prof. Antoine in France around 1920, that remains popular, at least in parts of Europe, for technical uses. In the Antoine system, digits other than 0 use the same configuration as the upper numbers, except that dot 6 is also included. Thus 1 is dots 1-6, 2 is dots 1-2-6, etc. Zero (0) must be specially assigned, because otherwise it would be the same as the letter &+w. Various dot-6 systems differ as to the choice for zero.
The original (BANA) committee had not seriously considered a dot-6 system, mostly because such a system had never been used in any BANA codes and so seemed to be disqualified by the requirement not to make radical changes. However, the expanded committee did consider their use, eventually debating at length a proposal to use dot-6 numbers (with dots 3-4-6 for zero) normally in grade 1, except when grade 1 is used as a teaching subset of grade 2. This change was partly because the expanded scope of the UEB Research Project now included one code, viz. the BAUK computer code (Ref. 96a), that already employed dot-6 numbers, partly because of a desire to explore every possible approach to efficiency in technical expressions, and partly because, surprisingly, some North American support for dot-6 numbers had materialized.
The UEB Research Project Committee agreed that dot-6 numbers were not too radical to consider within Committee 2's charge, and so the number system generally, this time with three viable possibilities, was debated extensively once again. All three systems found advocates, and none proved to be without flaw, as summarized below:
(1) Upper numbers, i.e. the current English braille system and the one recommended in the November 1992 report: Strengths: This is the original, traditional and internationally accepted braille number system. Ordinary quantitative numbers in ordinary contexts, i.e. in sentences with punctuation, never need special indicators. Numbers, like most words, stand in an upper position and thus generally contrast with punctuation, which traditionally is put slightly "out of the way", in a lower position. Weaknesses: Since the upper numbers clash with the letters a-j, there is inefficiency and "indicator clutter" in certain alphanumeric cases, such as part numbers and postal codes. A worst-case example would be that of numbers with bases higher than 10, such as the hexadecimal (base 16) numbers used in computer work, arranged for subtraction or addition: digits would not align, unless forced to by artificial spacing rules. (See section 3.26 for the eventual resolution of the alignment issue.)
(2) Lower numbers. Strengths: The problem of juxtaposition with letters would be solved. Also, the digits would retain their "shape" despite the displacement, and so would be easily read by persons already familiar with upper numbers. Weaknesses: Since lower numbers clash with common punctuation marks, then when numbers and punctuation are juxtaposed, indicators would be required to signal each switch in meaning, and as noted in the November 1992 report, these digit-punctuation juxtapositions occur more frequently and more pervasively than digit-letter juxtapositions. The traditional notion of numbers and words being in the primary upper position, with punctuation down and out of the way, would be disturbed. Also, the number sign would continue to be needed in most cases, because otherwise isolated lower numbers could be easily misread as letters. Finally, they would not be traditional, even though they have been used in some technical codes and so can't be dismissed as untried.
(3) Dot-6 numbers. Strengths: Juxtapositions of digits with both letters and punctuation marks would be handled without excessive indicators. In an extended grade 1 context, which (depending on transcriber rules) could characterize certain intensive technical notation, numbers could be arbitrarily intermixed with letters and punctuation marks without any indicators at all, not even a numeric indicator. Thus, in such cases, dot-6 numbers would be the most efficient and indicator-free of the three systems. Also, whether in grade 1 or grade 2 context, and no matter how isolated, digits would always be readable unambiguously. Weaknesses: Many people report that they find dot-6 numbers somewhat slower to read, at least at first. The reason seems to be either the change of "shape" induced by the dot 6, or the increase in the overall number of dots, or both. In any event it seems clear that an initial slowdown would be widely experienced, and thus greatly impact acceptance of UEB; it is less clear whether or not such a slowdown would be permanent. Also, dot-6 digits would take up ten "strong" symbols that could be used for other purposes. Finally, they would not be traditional, even though they have been used in some technical codes and so can't be dismissed as untried.
After intense debate, mostly along these lines although of course much more fully developed, the relative merits of the standard upper number system were judged more important, especially for the general reader, and so that system was confirmed for all purposes.
Nums-lock: We were at considerable pains to make the representation of numbers, and mathematical symbols generally, more efficient. For a time, the original committee considered a system called "nums-lock", whereby a double number sign would introduce a mode wherein a numeric prefix would be understood as governing each symbol, much as capitals mode in effect prefixes a dot 6 to the letters over its domain. This idea was eventually supplanted by the grade 1 mode, which accomplishes almost all of the same goals by a method that is more easily related to an existing one (grade 1), and that employs a familiar symbol (the letter sign). The suppression of the number sign being still obviously desirable for, say, dense collections of arithmetic exercises, the committee later defined the concept of a "numeric passage," initiated by a double number sign.
More and Fewer Prefixes: There was never any question that the seven braille characters that have only right-hand dots would be classified as prefixes, but there was some controversy over the inclusion of the number sign, which of course has a left-hand dot and therefore could have played a role as a "strong root". There were three main reasons for including the number sign among the prefixes:
(1) Within a particular symbol length, such as the three characters we have generally been using, the number of available symbols is greatly increased by having more prefixes even at the expense of roots (at least up to a theoretical optimum number, which in any event is too large to consider because it would too greatly affect the braille system).
(2) We judged that the term "prefix" need not imply just right-hand dots, but rather an historical use of the symbol in a precursor capacity, which is certainly true of the number sign.
(3) There is essentially no loss of traditional symbols by classifying the number sign as a prefix; even the "ble" contraction would have needed changes anyway to avoid ambiguity problems.
On the other side, reason (1) from the above paragraph caused us to consider adding other symbols to the list of prefixes, but in the end every one seemed to have an existing or better use as a root. Since we judged that the number of available symbols was at an adequate level, we stopped at the eight listed.
Compatibility with an 8-dot code: During the committee's work on the 6-dot UEB, two colleagues, Profs. Gardner and Salinas, made known to us their work in designing an 8-dot braille code that corresponds via mapping rules to an associated 6-dot code. The question was raised, to what extent Committee 2 itself should attempt to maintain compatibility with this work, or with 8-dot codes generally. In considering this question, the committee noted the following: (1) The committee's charge is to design a 6-dot publishing code, which is difficult enough within all the other stated constraints, and that an enforced connection to an 8-dot code could further limit the possibilities for the best realization of its main task. (2) When an assignment has been based on "shape" as a mnemonic aid, that characteristic would usually be lost in the mapping to the other kind of code. (3) 8-dot codes are even more subject to physical ambiguity issues (e.g. the distinguishing of an isolated "i" from an isolated "in" sign) than are 6-dot codes. (4) ISO is working on an 8-dot code standard or standards (possibly different ones for math and computer work). (5) There are already several 8-dot codes, although the 6-dot subset is fairly stable and the committee would probably want to consider that as it makes its assignments. (6) Although 8-dot codes are popular on one- and two-line braille displays, they are less attractive for full-page braille publishing because the vertical space taken by each line results in fewer lines per page. (7) Even on displays, the extra row for the two added dots is frequently switched to other uses, such as showing the cursor or highlighting, and that in turn affects the viability of code assignments involving those dots. In view of these considerations, the committee elected to continue its 6-dot focus, while welcoming information on parallel 8-dot efforts and allowing that 8-dot compatibility was a positive value in symbol assignments, among the other values that we must consider. (The Gardner-Salinas work, coincidentally, has compatibility with UEB as one of its goals, and therefore would merit an even closer look, if and when the 6-dot UEB is established.)
This table associates each of the 95 printable ASCII characters with a single one of the 64 possible six-dot braille cell configurations. Conversely, each of the 64 braille cells is associated with at least one ASCII character, and in some cases more than one because there are more printable ASCII characters than unique six-dot braille cell patterns. This kind of code is mainly useful for machine-to-machine communication and storage, e.g. for braille display devices and fonts, especially in those cases where there is likely to be some direct human involvement with the code and therefore it is desirable that the code be related to one or more transcription codes so that it can easily be memorized by people who are familiar with those codes. Such a code should not itself be considered a transcription code, however. At present, probably the most widely used code of this type is North American ASCII-Braille, also known as North American Braille Computer Code (NABCC) or as "MIT Code" after the Massachusetts Institute of Technology, where it was first defined and used. MIT Code is related to current EB and the current North American (BANA) technical transcription codes.
In its October 1999 supplementary report (Ref. 99a), Committee 2 defined an "alignment mode" of UEB that made use of this table, which is of course based upon UEB. The committee later decided to remove alignment mode from UEB, but noted that the table itself remains useful for other purposes such as those described in the foregoing paragraph; and so it is reproduced here.
The table is listed in ASCII character order. While the main reasons for assignments were compatibility with UEB, sometimes there were other reasons as noted in parentheses:
Committee Membership: The UEB Research Project having started as a project of the Braille Authority of North America (BANA), the original four members — T. V. (Tim) Cranmer, Emerson Foulke, Abraham Nemeth and Joseph Sullivan, Chairman — were naturally from the region served by BANA. It was that committee, working mainly from July through October of 1992, that produced the November 1992 report. In December 1992, the Braille Authority of the United Kingdom (BAUK) responded favorably to BANA's invitation to work cooperatively, and Stephen Phippen effectively joined the committee as BAUK's representative. In June 1993, the International Council on English Braille (ICEB) accepted the UEB as an experimental project under its worldwide auspices. Correspondingly, the membership of Committee 2 was expanded to include three additional members: Bruce Maguire from Australia, Connie Aucamp (pro tem) from South Africa, and Terry Small from New Zealand.
In August 1993, Christo de Klerk was named as permanent representative from South Africa, replacing Connie Aucamp, who as a member of the UEB Research Project Committee had asked to serve only on a temporary basis.
In September 1993, the committee was greatly saddened by the death of Terry Small, who had suffered a stroke a few days earlier. His loss was felt both personally and professionally, as he had been an early resource of encouragement and insight to the entire UEB Research Project, and instrumental in raising its horizons to the international level.
Thereafter, Raeleen Smith, a member of the UEB Research Project Committee, served pro tem as the representative from New Zealand, and ultimately Margaret Salt was named as permanent representative.
The resulting 8-person committee worked steadily until December 1997, when again one of its members died: Emerson Foulke, a professor of psychology internationally known for his work on haptic perception and valued contributor to the committee's understanding of what "readability" really means.
Still another member of the committee, Tim Cranmer, died in November 2001. Tim was widely known throughout the blindness community for many technical innovations, and had chaired the committee that had developed BANA's Computer Braille Code. With Emerson Foulke, he had contributed enormously to the basic philosophy and evolution of UEB. Both Emerson and Tim were also known as gentlemen of good humor, kindness and insight; they are greatly missed.
In January 2002, at the interim meeting of the ICEB's Executive Committee, William Poole of the UK was assigned to the committee. Shortly thereafter, Frank Chennells of Canada was also appointed.
In August 2003, Margaret Salt retired from the committee after long and valued service, and Maria Stevens of New Zealand was named to take her place.
Voting basis: Each member of the committee voted individually. However, noting that five members of the expanded committee were from countries that generally follow BANA codes while only three were from countries served by BAUK, and to be sure that the BANA tradition was not unintentionally given extra weight simply by reason of people's natural tendency to fall back on the familiar, a special rule was adopted whereby the three votes from the BAUK countries, if all cast against a motion, were considered a veto. As it happened, there was never any need to invoke that rule in any actual decision.
Activities and Methods: The original four-member committee held two conventional meetings (Charlotte, North Carolina, July 1992, and Southfield, Michigan, September 1992), had three additional meetings by conference telephone call, and otherwise communicated regularly through an electronic bulletin board (BBS). The BBS enabled any member to post a message, in the form of a computer file, for later retrieval by the other members. Besides this collection and distribution function, the BBS also served as a repository for archiving all committee communications and reference documents. The BBS mechanism proved to be an effective way for persons to work together who cannot practically meet often, although it still has an economic burden in that each member must make a direct long-distance telephone call in order to send a message or even to check whether any new messages have been posted.
From June 1993 onward, the committee having been expanded both numerically and geographically, neither conference calling nor a BBS was judged to be a practical method for regular communication, and so the committee turned to the Internet for that purpose, although the BBS continued to be used for archiving. To facilitate decision-making as well as information-sharing, Robert's Rules of Order (Ref. 90b), a codification of parliamentary procedure long established and commonly used in the United States, was adapted so that motions, votes &c. could be placed by email, much as they would be at an ordinary meeting. This process has worked quite well, and even has some advantages in that several motions can be considered simultaneously (provided they do not conflict), and members can take longer to prepare their submissions than would be possible at a direct meeting, which contributes to the quality of the debate. However, face-to-face and telephone conference meetings still excel for directness of interaction and faster overall pace, and so two conventional meetings (Costa Mesa, California, April 1994, and London, England, January 1995) and one telephone conference meeting (September, 2003) have interrupted the otherwise continuous "electronic meeting".
Archives of the committee's deliberations, including every
BBS and email message and minutes of the other
meetings, may be found through the
ICEB web site at
http://www.iceb.org.
Observers: In one of its first decisions, the expanded committee voted unanimously to continue the original committee's acceptance of observers, that is to allow interested persons (subject to approval by the national representative to the UEB Research Project Committee) to listen in to the messages sent to the committee as a whole.
The committee took this action mainly to acknowledge its responsibility, consistent with UEB Research Project policy, to remain open in its workings — despite some concerns that such openness might inhibit the highly informal and speculative thinking that is typically part and parcel of good technical work. In practice, the members have not seemed to be overly inhibited, but have joined in lively debate that has only been enriched by contributions from observers (usually via side communications, but also directly, at designated times). As an additional benefit to all concerned, those who have observed the committee's struggles with imperfect choices seem to be more understanding of the conclusions reached, even if those conclusions are not always the ones that they may favor.
In these lists, the order is the customary one for braille characters, i.e. as the characters would be read in the standard seven-line table.
In the braille edition of these lists, each entry begins with a two-cell "dot locator", dots 46, 123456, which is there to assure that the position of the dots is always clear when read in real braille; it is not part of the symbol being listed.
Sighted readers who do not see a pattern
in simulated braille at the beginning of each line should download
and install the "SimBraille" font from the free downloads page of
Duxbury Systems' web site at
http://www.duxburysystems.com.
If your browser can make use
of such fonts, you should then see the simulated braille properly.
Persons who are reading this list in real braille need to be sure that their viewing device is set for "North American ASCII-Braille"; if some other device code is in effect, some of the braille characters will be incorrect.
This list presents the basic symbols of UEB for grade 1 and numeric mode, including vertical and diagonal line segments, and all directly assigned shape symbols. Valid single-cell UEB symbols that have no grade 1 assignment are also included, and noted as not assigned. Any symbol listed here may also be used freely in grade 2 when that symbol has no grade 2 definition or the context does not allow for its interpretation as a grade 2 symbol (contraction). Contractions themselves are listed in a separate report within the UEB project.
Symbols defined and used only within "arrow mode" and "horizontal line mode" are listed separately below (see G.2 and G.3). Note also that only specifically assigned shapes are listed here, whereas made-up shape descriptions are permitted as described in section 3.19.
Relevant section numbers are given in square brackets
"n/e" in the print and Unicode columns means that there appears to be no equivalent corresponding Unicode character at the time this is written. "n/a" means that Unicode correspondence is not applicable; this is typical of braille indicators.
The appearance of the characters in the "print" column
will depend on the font in use, and some fonts do not support all
Unicode characters. For definitive information about the normal form
of the character
corresponding to a given Unicode value, see the code pages at
http://www.unicode.org.
The correspondence listed for each symbol is based primarily upon the normal print form of that symbol as considered by Committee 2, and secondarily upon its "meaning" as so considered, and consequently the meaning or name listed may or may not agree with the name given in a Unicode listing. In general, especially for technical symbols, meanings and usages can vary widely from one work to the next.
Also, because of redundancy in Unicode, it should not be assumed that the value given is necessarily the only suitable one. For example, the "dot multiplication" symbol, listed as corresponding to Unicode 22c5 ("dot operator"), corresponds just as well to 00b7 ("middle dot"). Similarities such as this can be found by examining the information associated with each code on the Unicode web site mentioned above.
| Braille | Unicode | Description | |
|---|---|---|---|
| (space) | 0020 | (no dots) space [2.6] | |
| a | 0061 | letter a [3.4] or (in numeric mode) digit 1 [3.5] | |
| b | 0062 | letter b [3.4] or (in numeric mode) digit 2 [3.5] | |
| c | 0063 | letter c [3.4] or (in numeric mode) digit 3 [3.5] | |
| d | 0064 | letter d [3.4] or (in numeric mode) digit 4 [3.5] | |
| e | 0065 | letter e [3.4] or (in numeric mode) digit 5 [3.5] | |
| f | 0066 | letter f [3.4] or (in numeric mode) digit 6 [3.5] | |
| g | 0067 | letter g [3.4] or (in numeric mode) digit 7 [3.5] | |
| h | 0068 | letter h [3.4] or (in numeric mode) digit 8 [3.5] | |
| i | 0069 | letter i [3.4] or (in numeric mode) digit 9 [3.5] | |
| j | 006a | letter j [3.4] or (in numeric mode) digit 0 [3.5] | |
| k | 006b | letter k [3.4] | |
| l | 006c | letter l [3.4] | |
| m | 006d | letter m [3.4] | |
| n | 006e | letter n [3.4] | |
| o | 006f | letter o [3.4] | |
| p | 0070 | letter p [3.4] | |
| q | 0071 | letter q [3.4] | |
| r | 0072 | letter r [3.4] | |
| s | 0073 | letter s [3.4] | |
| t | 0074 | letter t [3.4] | |
| u | 0075 | letter u [3.4] | |
| v | 0076 | letter v [3.4] | |
| x | 0078 | letter x [3.4] | |
| y | 0079 | letter y [3.4] | |
| z | 007a | letter z [3.4] | |
| n/a | n/a | superposition indicator [3.20] | |
| n/a | n/a | 1. (on a line by itself) cursor indicator [3.17] | |
| n/a | n/a | 2. horizontal juxtaposition indicator [3.20] | |
| n/a | n/a | general fraction open [3.9] | |
| ∫ | 222b | integral sign [3.14] | |
| n/a | n/a | general fraction close [3.9] | |
| n/a | n/a | unassigned in grade 1 | |
| n/a | n/a | 1. when surrounded by spaces/other d'l segments, diagonal line segment [3.26] | |
| n/a | n/a | 2. when followed by nonspace, braille grouping open [3.8] [3.26] | |
| n/a | n/a | radical open [3.10] | |
| n/a | n/a | first transcriber-defined symbol [3.25] | |
| n/a | n/a | bar over previous item (also can terminate shapes) [3.11] [3.19] | |
| n/a | n/a | shape indicator [3.19] | |
| ○ | 25cb | circle [assigned shape] [3.19] | |
| n/e | n/e | regular undecagon [assigned shape] [3.19] | |
| n/e | n/e | regular dodecagon (etc. for all regular polygons) [assigned shape] [3.19] | |
| n/e | n/e | regular decagon [assigned shape] [3.19] | |
| △ | 25b3 | regular (equilateral) triangle [assigned shape] [3.19] | |
| □ | 25a1 | square [assigned shape] [3.19] | |
| n/e | n/e | regular pentagon [assigned shape] [3.19] | |
| n/e | n/e | regular hexagon [assigned shape] [3.19] | |
| n/e | n/e | regular heptagon [assigned shape] [3.19] | |
| n/e | n/e | regular octagon [assigned shape] [3.19] | |
| n/e | n/e | regular nonagon [assigned shape] [3.19] | |
| n/a | n/a | vertical juxtaposition indicator [3.20] | |
| n/a | n/a | arrow indicator [3.12] | |
| n/a | n/a | physical enclosure indicator [3.20] | |
| w | 0077 | letter w [3.4] | |
| , | 002c | comma [3.4] | |
| ; | 003b | semicolon [3.4] | |
| : | 003a | colon [3.4] | |
| . | 002e | period (full stop) or decimal [3.4] | |
| n/a | n/a | level change down (subscript) [3.8] | |
| ! | 0021 | exclamation mark [3.4] | |
| ′ | 2032 | prime (when distinguished from apostrophe in print) [3.14] | |
| ? | 003f | question mark, opening nonspecific (double/single) quote [3.4] [3.4] | |
| n/a | n/a | level change up (superscript or exponent) [3.8] | |
| n/a | n/a | closing nonspecific (double/single) quote [3.4] [3.4] | |
| n/a | n/a | simple numeric fraction (in numeric mode) [3.9] | |
| n/a | n/a | 1. radical close [3.10] | |
| ␢ | 2422 | 2. "visible space" [3.17] | |
| n/a | n/a | (before space) spaced numeric indicator [3.5] | |
| 1 | 0031 | digit 1 & set numeric & grade 1 word modes [3.5] | |
| 2 | 0032 | digit 2 & set numeric & grade 1 word modes [3.5] | |
| 3 | 0033 | digit 3 & set numeric & grade 1 word modes [3.5] | |
| 4 | 0034 | digit 4 & set numeric & grade 1 word modes [3.5] | |
| 5 | 0035 | digit 5 & set numeric & grade 1 word modes [3.5] | |
| 6 | 0036 | digit 6 & set numeric & grade 1 word modes [3.5] | |
| 7 | 0037 | digit 7 & set numeric & grade 1 word modes [3.5] | |
| 8 | 0038 | digit 8 & set numeric & grade 1 word modes [3.5] | |
| 9 | 0039 | digit 9 & set numeric & grade 1 word modes [3.5] | |
| 0 | 0030 | digit 0 & set numeric & grade 1 word modes [3.5] | |
| ∥ | 2225 | parallel to [3.16] | |
| ∞ | 221e | infinity sign [3.16] | |
| n/a | n/a | second transcriber-defined symbol [3.25] | |
| , | 002c | comma & set numeric & grade 1 word modes [3.5] | |
| . | 002e | dot (decimal point) & set numeric & grade 1 word modes [3.5] | |
| n/a | n/a | (before space) initiates numeric passage [3.5] | |
| n/a | n/a | terminates numeric passage [3.5] | |
| ⊥ | 22a5 | up tack (= perpendicular) [3.16] | |
| ⊾ | 22be | right angle with arc (or similar figure with "squared off" arc) [3.16] | |
| n/a | n/a | 1. when surrounded by spaces/other d'l segments, diagonal line segment [3.26] | |
| n/a | n/a | 2. when followed by nonspace, braille grouping close [3.8] [3.26] | |
| ' | 0027 | apostrophe, nondirectional single quote, "foot" or "minute" sign [3.4] | |
| - | 002d | hyphen, minus when not distinguished from hyphen [3.4] | |
| @ | 0040 | at-sign [3.17] | |
| ¢ | 00a2 | cent sign [3.25] | |
| ∂ | 2202 | partial derivative (curly d or delta) [3.14] | |
| € | 20ac | Euro currency sign [3.25] | |
| ₣ | 20a3 | franc [3.25] | |
| ∅ | 2205 | null set (slashed zero) [3.13] | |
| £ | 00a3 | British pound sign [3.25] | |
| ₦ | 20a6 | Naira (Nigerian) currency sign [3.25] | |
| $ | 0024 | dollar sign [3.25] | |
| ¥ | 00a5 | yen sign [3.25] | |
| & | 0026 | ampersand [3.4] | |
| ∮ | 222e | closed line integral [3.14] | |
| < | 003c | less-than or opening angle bracket [3.7] | |
| ¬ | 00ac | "not" sign (line horizontal, then down at right) [3.13] | |
| n/a | n/a | line through previous item (cancellation, "not") [3.11] | |
| n/a | n/a | transcriber-assigned shape indicator [3.19] | |
| n/a | n/a | script word indicator [3.6] | |
| n/a | n/a | script symbol indicator [3.6] | |
| ^ | 005e | caret [3.17] | |
| ∨ | 2228 | or (upright v shape) [3.13] | |
| n/a | n/a | script passage indicator [3.6] | |
| ∧ | 2227 | and (inverted v shape) [3.13] | |
| ~ | 007e | tilde [3.17] | |
| ∵ | 2235 | "since" (three dots in inverted pyramid) [3.13] | |
| n/a | n/a | third transcriber-defined symbol [3.25] | |
| n/a | n/a | first transcriber-defined typeform word indicator [3.6] | |
| n/a | n/a | first transcriber-defined typeform symbol indicator [3.6] | |
| n/a | n/a | first transcriber-defined typeform passage indicator [3.6] | |
| n/a | n/a | first transcriber-defined typeform terminator [3.6] | |
| > | 003e | greater-than or closing angle bracket [3.7] | |
| n/a | n/a | script terminator [3.6] | |
| ∋ | 220b | reverse element (reverse variant epsilon) [3.13] | |
| ⊲ | 22b2 | is a normal subgroup of (closed "less than") [3.16] | |
| n/a | n/a | transcriber-assigned filled (solid) shape indicator [3.19] | |
| ⊣ | 22a3 | reverse assertion ("T" lying on right side) [3.13] | |
| n/e | n/e | equilibrium arrow, trend to the left [3.18] | |
| ⊳ | 22b3 | inverse "is normal subgroup" (closed "greater than") [3.16] | |
| n/e | n/e | quadruple dot for bond or electrons [3.18] | |
| n/e | n/e | quadruple dashed line [3.18] | |
| n/e | n/e | quadruple cross for electrons [3.18] | |
| n/e | n/e | quadruple small circle for electrons [3.18] | |
| n/e | n/e | quadruple line bond [3.18] | |
| æ | 00e6 | ae diphthong (lowercase) [3.25] | |
| © | 00a9 | copyright (circled C) [3.25] | |
| œ | 0153 | oe diphthong (lowercase) [3.25] | |
| ® | 00ae | registered trademark (circled R) [3.25] | |
| ™ | 2122 | trademark (superscript or circled TM) [3.25] [See note 2] | |
| n/a | n/a | opening transcriber's note indicator [3.27] | |
| n/a | n/a | transcriber-assigned shaded shape indicator [3.19] | |
| n/a | n/a | closing transcriber's note indicator [3.27] | |
| † | 2020 | dagger [3.25] | |
| ‡ | 2021 | double dagger [3.25] | |
| n/a | n/a | when surrounded by spaces/other v'l segments, vertical nonsolid line segment [3.26] | |
| ∀ | 2200 | "for all" (inverted A) [3.13] | |
| ∇ | 2207 | del, nabla (inverted capital delta) [3.14] | |
| ∈ | 2208 | is an element of (variant epsilon) [3.13] | |
| ° | 00b0 | degree sign [3.25] | |
| ¶ | 00b6 | paragraph symbol [3.25] | |
| § | 00a7 | section mark [3.25] | |
| ♀ | 2640 | female or "Venus" symbol [3.25] | |
| ♂ | 2642 | male or "Mars" symbol [3.25] | |
| n/a | n/a | cedilla under following letter symbol [3.21] | |
| n/a | n/a | non-UEB word indicator [3.23] | |
| n/a | n/a | non-UEB word terminator [3.23] | |
| n/a | n/a | grave over following letter symbol [3.21] | |
| ⊂ | 2282 | contained in, is a subset of (U open to right) [3.13] | |
| n/a | n/a | circumflex over following letter symbol [3.21] | |
| n/a | n/a | simple right-pointing arrow over previous item [3.11] | |
| n/a | n/a | circle above following letter symbol [3.21] | |
| n/a | n/a | tilde as in nyay over following letter symbol [3.21] | |
| n/a | n/a | bold arrow indicator [3.12] | |
| n/a | n/a | window [3.25] | |
| n/a | n/a | boldface word indicator [3.6] | |
| n/a | n/a | boldface symbol indicator [3.6] | |
| n/a | n/a | dieresis/umlaut over following letter symbol [3.21] | |
| n/a | n/a | dot over previous item [3.11] | |
| ∃ | 2203 | "there exists" (reverse E) [3.13] | |
| n/a | n/a | ligature indicator, placed between letters when, and only when, the ligature has meaning [3.21] | |
| n/a | n/a | boldface passage indicator [3.6] | |
| “ | 201c | opening double quote [3.4] | |
| ≈ | 2248 | double tilde (approximately equal) [3.16] | |
| ” | 201d | closing double quote [3.4] | |
| n/a | n/a | acute over following letter symbol [3.21] | |
| n/a | n/a | fourth transcriber-defined symbol [3.25] | |
| n/a | n/a | second transcriber-defined typeform word indicator [3.6] | |
| n/a | n/a | second transcriber-defined typeform symbol indicator [3.6] | |
| n/a | n/a | second transcriber-defined typeform passage indicator [3.6] | |
| n/a | n/a | second transcriber-defined typeform terminator [3.6] | |
| ⊃ | 2283 | contains, is a superset of (U open to left) [3.13] | |
| n/a | n/a | boldface terminator [3.6] | |
| ⊨ | 22a8 | "is valid" sign (assertion with double stem on "T") [3.13] | |
| ⇌ | 21cc | equilibrium arrow (harpoons) [3.18] | |
| ≏ | 224f | difference between [3.16] | |
| ¡ | 00a1 | inverted exclamation mark [3.4] | |
| ¿ | 00bf | inverted question mark [3.4] | |
| n/a | n/a | 1. when surrounded by spaces/other v'l segments, vertical solid line segment [3.26] | |
| n/a | n/a | 2. (unspaced before, followed by space) line sign, as in poetry [3.25] | |
| n/a | n/a | reserved non-Roman letter (lowercase) [3.22] | |
| n/a | n/a | reserved non-Roman letter (lowercase) [3.22] | |
| n/a | n/a | reserved non-Roman letter (lowercase) [3.22] | |
| n/a | n/a | reserved non-Roman letter (lowercase) [3.22] | |
| n/a | n/a | reserved non-Roman letter (lowercase) [3.22] | |
| n/a | n/a | reserved non-Roman letter (lowercase) [3.22] | |
| n/a | n/a | reserved non-Roman letter (lowercase) [3.22] | |
| n/a | n/a | reserved non-Roman letter (lowercase) [3.22] | |
| n/a | n/a | reserved non-Roman letter (lowercase) [3.22] | |
| n/a | n/a | reserved non-Roman letter (lowercase) [3.22] | |
| n/a | n/a | reserved non-Roman letter (lowercase) [3.22] | |
| n/a | n/a | reserved non-Roman letter (lowercase) [3.22] | |
| n/a | n/a | reserved non-Roman letter (lowercase) [3.22] | |
| n/a | n/a | reserved non-Roman letter (lowercase) [3.22] | |
| n/a | n/a | reserved non-Roman letter (lowercase) [3.22] | |
| n/a | n/a | reserved non-Roman letter (lowercase) [3.22] | |
| n/a | n/a | reserved non-Roman letter (lowercase) [3.22] | |
| n/a | n/a | reserved non-Roman letter (lowercase) [3.22] | |
| n/a | n/a | reserved non-Roman letter (lowercase) [3.22] | |
| n/a | n/a | reserved non-Roman letter (lowercase) [3.22] | |
| n/a | n/a | reserved non-Roman letter (lowercase) [3.22] | |
| n/a | n/a | reserved non-Roman letter (lowercase) [3.22] | |
| n/a | n/a | reserved non-Roman letter (lowercase) [3.22] | |
| n/a | n/a | reserved non-Roman letter (lowercase) [3.22] | |
| n/a | n/a | reserved non-Roman letter (lowercase) [3.22] | |
| ≡ | 2261 | equivalent to (three horizontal lines) [3.13] | |
| \ | 005c | backslash (opposite of the slash) [3.17] | |
| { | 007b | opening curly brace [3.4] | |
| # | 0023 | crosshatch, pound or "number" [3.17] | |
| n/a | n/a | tilde over previous item [3.11] | |
| n/a | n/a | filled (solid) shape indicator [3.19] [See note 3] | |
| | | 007c | vertical line (unbroken) (the ASCII symbol, "pipe") [3.25] [See note 1] | |
| ∠ | 2220 | angle [3.16] | |
| n/a | n/a | reserved non-Roman letter (lowercase) [3.22] | |
| n/a | n/a | underlined word indicator [3.6] | |
| n/a | n/a | underlined symbol indicator [3.6] | |
| ⊦ | 22a6 | assertion ("is a theorem" sign; "T" lying on left side) [3.13] | |
| • | 2022 | bullet [3.25] | |
| ± | 00b1 | plus-or-minus (plus over minus) [3.7] | |
| n/a | n/a | underlined passage indicator [3.6] | |
| « | 00ab | opening Italian quotes (small double angle brackets) [3.4] | |
| ≃ | 2243 | tilde (swung dash) over straight line [3.16] | |
| » | 00bb | closing Italian quotes (small double angle brackets) [3.4] | |
| / | 002f | slash (oblique stroke) [3.4] | |
| n/a | n/a | fifth transcriber-defined symbol [3.25] | |
| n/a | n/a | third transcriber-defined typeform word indicator [3.6] | |
| n/a | n/a | third transcriber-defined typeform symbol indicator [3.6] | |
| n/a | n/a | third transcriber-defined typeform passage indicator [3.6] | |
| n/a | n/a | third transcriber-defined typeform terminator [3.6] | |
| } | 007d | closing curly brace [3.4] | |
| n/a | n/a | underlining terminator [3.6] | |
| ∓ | 2213 | minus-or-plus (minus over plus) [3.7] | |
| ≤ | 2264 | is less than or equal to [3.7] | |
| ≥ | 2265 | is greater than or equal to [3.7] | |
| ⊆ | 2286 | contained in or equal to [3.13] | |
| ⊇ | 2287 | contains or equal to [3.13] | |
| ⊴ | is | normal subgroup of or equal (closed "less than" with line under) [3.16] | |
| n/a | n/a | unassigned/reserved (formerly enter alignment mode [See note 4]) | |
| ⊵ | 22b5 | inverse "normal subgroup or equal" (closed "greater than" with line under) [3.16] | |
| n/a | n/a | unassigned/reserved (formerly exit alignment mode [See note 4]) | |
| n/e | n/e | triple dot for bond or electrons [3.18] | |
| n/e | n/e | triple dashed line [3.18] | |
| ∝ | 221d | "varies as" sign [3.16] | |
| n/e | n/e | triple cross for electrons [3.18] | |
| n/e | n/e | triple small circle for electrons [3.18] | |
| n/e | n/e | triple line bond [3.18] | |
| n/a | n/a | (at end of line) continuation indicator [3.17] | |
| n/a | n/a | separator space before digit 1 (in numeric mode) [3.5] | |
| n/a | n/a | separator space before digit 2 (in numeric mode) [3.5] | |
| n/a | n/a | separator space before digit 3 (in numeric mode) [3.5] | |
| n/a | n/a | separator space before digit 4 (in numeric mode) [3.5] | |
| n/a | n/a | separator space before digit 5 (in numeric mode) [3.5] | |
| n/a | n/a | separator space before digit 6 (in numeric mode) [3.5] | |
| n/a | n/a | separator space before digit 7 (in numeric mode) [3.5] | |
| n/a | n/a | separator space before digit 8 (in numeric mode) [3.5] | |
| n/a | n/a | separator space before digit 9 (in numeric mode) [3.5] | |
| n/a | n/a | separator space before digit 0 (in numeric mode) [3.5] | |
| n/a | n/a | commences opening non-UEB passage indicator (terminated by dot 3) [3.23] | |
| ( | 0028 | opening round parenthesis [3.4] | |
| √ | 221a | radical without vinculum [3.10] | |
| n/a | n/a | hat over previous item [3.11] | |
| 〃 | 3003 | ditto [3.4] | |
| n/a | n/a | enter horizontal line mode [3.26] | |
| ⋅ | 22c5 | times (dot multiplication) [3.7] or single dot for bond or electron [3.18] | |
| n/e | n/e | single dashed line [3.18] | |
| + | 002b | plus sign [3.7] | |
| = | 003d | equals sign [3.7] | |
| × | 00d7 | times (X) [3.7] or single cross for electron [3.18] | |
| * | 002a | asterisk [3.4] | |
| ∘ | 2218 | single small circle for electron, or "hollow dot" (small circle or composition operator) [3.18] | |
| ÷ | 00f7 | divided by (horizontal line between dots) [3.7] | |
| n/a | n/a | sixth transcriber-defined symbol [3.25] | |
| n/a | n/a | fourth transcriber-defined typeform word indicator [3.6] | |
| n/a | n/a | fourth transcriber-defined typeform symbol indicator [3.6] | |
| n/a | n/a | fourth transcriber-defined typeform passage indicator [3.6] | |
| n/a | n/a | fourth transcriber-defined typeform terminator [3.6] | |
| ) | 0029 | closing round parenthesis [3.4] | |
| − | 2212 | minus (when distinguished from hyphen) [3.7] | |
| n/e | n/e | equilibrium arrow, trend to the right [3.18] | |
| ≅ | 2245 | tilde over equals sign [3.16] | |
| n/a | n/a | (at end of line) continuation indicator with space [3.17] | |
| n/a | n/a | dot locator for "use" [3.25] | |
| ― | 2015 | long dash [3.4] | |
| α | 03b1 | Greek alpha (lowercase) [3.22] | |
| β | 03b2 | Greek beta (lowercase) [3.22] | |
| δ | 03b4 | Greek delta (lowercase) [3.22] | |
| ε | 03b5 | Greek epsilon (lowercase) [3.22] | |
| φ | 03c6 | Greek phi (lowercase) [3.22] | |
| γ | 03b3 | Greek gamma (lowercase) [3.22] | |
| ι | 03b9 | Greek iota (lowercase) [3.22] | |
| n/e | n/e | "normal" (superscript circle crossed by horizontal line) [3.18] | |
| κ | 03ba | Greek kappa (lowercase) [3.22] | |
| λ | 03bb | Greek lambda (lowercase) [3.22] | |
| μ | 03bc | Greek mu (lowercase) [3.22] | |
| ν | 03bd | Greek nu (lowercase) [3.22] | |
| ο | 03bf | Greek omicron (lowercase) [3.22] | |
| π | 03c0 | Greek pi (lowercase) [3.22] | |
| ρ | 03c1 | Greek rho (lowercase) [3.22] | |
| σ | 03c3 | Greek sigma (lowercase) [3.22] | |
| τ | 03c4 | Greek tau (lowercase) [3.22] | |
| υ | 03c5 | Greek upsilon (lowercase) [3.22] | |
| ξ | 03be | Greek xi (lowercase) [3.22] | |
| ψ | 03c8 | Greek psi (lowercase) [3.22] | |
| ζ | 03b6 | Greek zeta (lowercase) [3.22] | |
| χ | 03c7 | Greek chi (lowercase) [3.22] | |
| n/a | n/a | dot locator for "mention" [3.25] [3.25] | |
| ` | 0060 | accent grave alone [3.17] | |
| [ | 005b | opening square bracket ([) [3.4] | |
| θ | 03b8 | Greek theta (lowercase) [3.22] | |
| η | 03b7 | Greek eta (lowercase) [3.22] | |
| n/a | n/a | shaded shape indicator [3.19] [See note 3] | |
| ¦ | 00a6 | broken vertical bar (not the ASCII vertical bar) [3.17] [See note 1] | |
| ω | 03c9 | Greek omega (lowercase) [3.22] | |
| n/a | n/a | italic word indicator [3.6] | |
| n/a | n/a | italic symbol indicator [3.6] | |
| n/a | n/a | subindex directly below [3.8] | |
| ∪ | 222a | union (upright U shape) [3.13] | |
| n/a | n/a | italic passage indicator [3.6] | |
| ∩ | 2229 | intersection (inverted U shape) [3.13] | |
| n/a | n/a | superindex directly above [3.8] | |
| % | 0025 | percent sign [3.7] | |
| n/a | n/a | general fraction line [3.9] | |
| n/a | n/a | seventh transcriber-defined symbol [3.25] | |
| n/a | n/a | fifth transcriber-defined typeform word indicator [3.6] | |
| n/a | n/a | fifth transcriber-defined typeform symbol indicator [3.6] | |
| n/a | n/a | fifth transcriber-defined typeform passage indicator [3.6] | |
| n/a | n/a | fifth transcriber-defined typeform terminator [3.6] | |
| ] | 005d | closing square bracket (]) [3.4] | |
| n/a | n/a | italic terminator [3.6] | |
| _ | 005f | ASCII underscore character [3.17] | |
| ≪ | 226a | is much less than [3.16] | |
| ≫ | 226b | is much greater than [3.16] | |
| ⊊ | 228a | contained in, but not equal to (proper subset) [3.13] | |
| ⊋ | 228b | contains, but is not equal to (proper superset) [3.13] | |
| n/e | n/e | normal subgroup but not equal (closed "less than: with cancelled line under) [3.16] | |
| ⌒ | 2312? | arc concave downward (shape similar to U+2312 or U+2040), over previous item [3.16] | |
| ∡ | 2221 | measured angle [3.16] | |
| ⫤ | 2ae4 | reverse "is valid" sign [3.13] | |
| n/e | n/e | inverse "normal subgroup but not equal" (closed "greater than" with cancelled line under) [3.16] | |
| n/e | n/e | double dot for bond or electrons [3.18] | |
| n/e | n/e | double dashed line [3.18] | |
| ≑ | 2251 | equals sign dotted above & below (approximately equal) [3.16] | |
| n/e | n/e | double cross for electrons [3.18] | |
| n/e | n/e | double small circle for electrons [3.18] | |
| n/e | n/e | double line bond [3.18] | |
| n/a | n/a | grade 1 symbol indicator [3.2] | |
| n/a | n/a | terminates grade 1 mode (2-symbol sequence) [3.2] | |
| n/a | n/a | grade 1 symbols-word indicator [3.2] | |
| n/a | n/a | grade 1 passage indicator [3.2] | |
| A | 0041 | capital letter A [3.4] | |
| B | 0042 | capital letter B [3.4] | |
| C | 0043 | capital letter C [3.4] | |
| D | 0044 | capital letter D [3.4] | |
| E | 0045 | capital letter E [3.4] | |
| F | 0046 | capital letter F [3.4] | |
| G | 0047 | capital letter G [3.4] | |
| H | 0048 | capital letter H [3.4] | |
| I | 0049 | capital letter I [3.4] | |
| J | 004a | capital letter J [3.4] | |
| K | 004b | capital letter K [3.4] | |
| L | 004c | capital letter L [3.4] | |
| M | 004d | capital letter M [3.4] | |
| N | 004e | capital letter N [3.4] | |
| O | 004f | capital letter O [3.4] | |
| P | 0050 | capital letter P [3.4] | |
| Q | 0051 | capital letter Q [3.4] | |
| R | 0052 | capital letter R [3.4] | |
| S | 0053 | capital letter S [3.4] | |
| T | 0054 | capital letter T [3.4] | |
| U | 0055 | capital letter U [3.4] | |
| V | 0056 | capital letter V [3.4] | |
| X | 0058 | capital letter X [3.4] | |
| Y | 0059 | capital letter Y [3.4] | |
| Z | 005a | capital letter Z [3.4] | |
| ∴ | 2234 | "therefore" (three dots in upright pyramid) [3.13] | |
| n/a | n/a | when surrounded by spaces/other d'l segments, diagonal line segment [3.26] | |
| n/a | n/a | bar under previous item [3.11] | |
| W | 0057 | capital letter W [3.4] | |
| " | 0022 | nondirectional double quote [3.4] | |
| ‘ | 2018 | opening single quote [3.4] | |
| ’ | 2019 | closing single quote [3.4] | |
| n/a | n/a | when surrounded by spaces/other d'l segments, diagonal line segment [3.26] | |
| n/a | n/a | capitals mode terminator [3.3] | |
| — | 2014 | dash [3.4] or single line bond [3.18] | |
| Æ | 00c6 | AE diphthong (uppercase) [3.25] | |
| Π| 0152 | OE diphthong (uppercase) [3.25] | |
| n/a | n/a | cedilla under following capital letter symbol [3.21] | |
| n/a | n/a | grave over following capital letter symbol [3.21] | |
| n/a | n/a | circumflex over following capital letter symbol [3.21] | |
| n/a | n/a | simple right-pointing arrow under previous item [3.11] | |
| n/a | n/a | circle above following capital letter symbol [3.21] | |
| n/a | n/a | tilde as in nyay over following capital letter symbol [3.21] | |
| n/a | n/a | dieresis/umlaut over following capital letter symbol [3.21] | |
| n/a | n/a | dot under previous item [3.11] | |
| n/a | n/a | ligature-to-capital-letter indicator [3.21] | |
| n/a | n/a | acute over following capital letter symbol [3.21] | |
| n/a | n/a | when surrounded by spaces/other v'l segments, vertical line segment [3.26] | |
| n/a | n/a | capital reserved non-Roman letter [3.22] | |
| n/a | n/a | capital reserved non-Roman letter [3.22] | |
| n/a | n/a | capital reserved non-Roman letter [3.22] | |
| n/a | n/a | capital reserved non-Roman letter [3.22] | |
| n/a | n/a | capital reserved non-Roman letter [3.22] | |
| n/a | n/a | capital reserved non-Roman letter [3.22] | |
| n/a | n/a | capital reserved non-Roman letter [3.22] | |
| n/a | n/a | capital reserved non-Roman letter [3.22] | |
| n/a | n/a | capital reserved non-Roman letter [3.22] | |
| n/a | n/a | capital reserved non-Roman letter [3.22] | |
| n/a | n/a | capital reserved non-Roman letter [3.22] | |
| n/a | n/a | capital reserved non-Roman letter [3.22] | |
| n/a | n/a | capital reserved non-Roman letter [3.22] | |
| n/a | n/a | capital reserved non-Roman letter [3.22] | |
| n/a | n/a | capital reserved non-Roman letter [3.22] | |
| n/a | n/a | capital reserved non-Roman letter [3.22] | |
| n/a | n/a | capital reserved non-Roman letter [3.22] | |
| n/a | n/a | capital reserved non-Roman letter [3.22] | |
| n/a | n/a | capital reserved non-Roman letter [3.22] | |
| n/a | n/a | capital reserved non-Roman letter [3.22] | |
| n/a | n/a | capital reserved non-Roman letter [3.22] | |
| n/a | n/a | capital reserved non-Roman letter [3.22] | |
| n/a | n/a | capital reserved non-Roman letter [3.22] | |
| n/a | n/a | capital reserved non-Roman letter [3.22] | |
| n/a | n/a | capital reserved non-Roman letter [3.22] | |
| n/a | n/a | "big" (multi-line) opening curly brace [3.15] | |
| n/a | n/a | tilde under previous item [3.11] | |
| n/a | n/a | "big" (multi-line) vertical bar [3.15] | |
| n/a | n/a | capital reserved non-Roman letter [3.22] | |
| n/a | n/a | "big" (multi-line) closing curly brace [3.15] | |
| n/a | n/a | closing non-UEB passage indicator [3.23] | |
| n/a | n/a | "big" (multi-line) opening round parenthesis [3.15] | |
| n/a | n/a | hat under previous item [3.11] | |
| n/a | n/a | "big" (multi-line) closing round parenthesis [3.15] | |
| Α | 0391 | capital Greek alpha [3.22] | |
| Β | 0392 | capital Greek beta [3.22] | |
| Δ | 0394 | capital Greek delta [3.22] | |
| Ε | 0395 | capital Greek epsilon [3.22] | |
| Φ | 03a6 | capital Greek phi [3.22] | |
| Γ | 0393 | capital Greek gamma [3.22] | |
| Ι | 0399 | capital Greek iota [3.22] | |
| Κ | 039a | capital Greek kappa [3.22] | |
| Λ | 039b | capital Greek lambda [3.22] | |
| Μ | 039c | capital Greek mu [3.22] | |
| Ν | 039d | capital Greek nu [3.22] | |
| Ο | 039f | capital Greek omicron [3.22] | |
| Π | 03a0 | capital Greek pi [3.22] | |
| Ρ | 03a1 | capital Greek rho [3.22] | |
| Σ | 03a3 | capital Greek sigma [3.22] | |
| Τ | 03a4 | capital Greek tau [3.22] | |
| Υ | 03a5 | capital Greek upsilon [3.22] | |
| Ξ | 039e | capital Greek xi [3.22] | |
| Ψ | 03a8 | capital Greek psi [3.22] | |
| Ζ | 0396 | capital Greek zeta [3.22] | |
| Χ | 03a7 | capital Greek chi [3.22] | |
| n/a | n/a | "big" (multi-line) opening square bracket [3.15] | |
| Θ | 0398 | capital Greek theta [3.22] | |
| Η | 0397 | capital Greek eta [3.22] | |
| Ω | 03a9 | capital Greek omega [3.22] | |
| n/a | n/a | "big" (multi-line) closing square bracket [3.15] | |
| n/a | n/a | capitalized letters-word indicator [3.3] | |
| n/a | n/a | capitalized passage indicator [3.3] |
1. In the 1995 Committee 2 report, the broken vertical bar is identified as the ASCII
vertical bar code or "pipe" while the solid vertical bar is listed as a separate
character and specifically "not the ASCII code". However, it has subsequently become clear, both
in ASCII listings and in Unicode listings where codes 0000-007f correspond to ASCII,
and despite appearances on many if not most keyboards to this day,
that it is the solid vertical bar that is properly the ASCII symbol or "pipe" while the
broken vertical bar is distinct. See
http://www.cs.tut.fi/~jkorpela/latin1/ascii-hist.html
for information on the history of this character's inclusion in ASCII.
2. In the 1995 Committee 2 report, the common trademark symbol was described as a circled "TM"; however, in general current usage, it appears as in the Unicode list, i.e. in the superscript position but not encircled.
3. Filled and solid assigned shapes are formed in the same way as the regular shapes, substituting the appropriate indicator.
4. Alignment mode was described in the Committee II Supplementary Report of October 1999; it was removed from UEB by a later decision.
The following table lists symbols having a special interpretation within arrow mode (see section 3.12). These interpretations apply only within that mode.
| Braille | Description |
|---|---|
| right (east) arrow orientation indicator and terminator | |
| up and right (northeast) arrow orientation indicator and terminator | |
| curved, full, in line of direction arrow-tip | |
| regular barb, full, in line of direction arrow-tip | |
| curved, full, counter to line of direction arrow-tip | |
| down and right (southeast) arrow orientation indicator and terminator | |
| down (south) arrow orientation indicator and terminator | |
| up and left (northwest) arrow orientation indicator and terminator | |
| straight, full, (directionless) arrow-tip | |
| left (west) arrow orientation indicator and terminator | |
| regular barb, full, counter to line of direction arrow-tip | |
| dotted, long shaft | |
| short single straight line shaft | |
| medium single straight line shaft | |
| long single straight line shaft | |
| sharp turn the right (in line of direction) shaft | |
| curved or bent to the right (in line of direction) shaft | |
| double, short shaft | |
| curved or bent to the left (in line of direction) shaft | |
| sharp turn the left (in line of direction) shaft | |
| up (north) arrow orientation indicator and terminator | |
| down and left (southwest) arrow orientation indicator and terminator | |
| regular barb, upper half, in line of direction arrow-tip | |
| curved, upper half, in line of direction arrow-tip | |
| curved, upper half, counter to line of direction arrow-tip | |
| straight, upper half, (directionless) arrow-tip | |
| regular barb, upper half, counter to line of direction arrow-tip | |
| regular barb, lower half, in line of direction arrow-tip | |
| curved, lower half, in line of direction arrow-tip | |
| curved, lower half, counter to line of direction arrow-tip | |
| straight, lower half, (directionless) arrow-tip | |
| regular barb, lower half, counter to line of direction arrow-tip |
The following table lists symbols having a special interpretation within horizontal line mode (see section 3.26). (Note that the rules for horizontal line mode allow an arrow indicator [dots 1256] to commence an arrow within the line, and also allow for arbitrary symbols, beyond those listed here and other than the arrow indicator, to be used.) These interpretations apply only within horizontal line mode. Note that symbols used for vertical and diagonal line segments appear within the main symbol list (see G.1 above).
| Braille | Description |
|---|---|
| left corner with upward vertical (e.g. lower left of box) | |
| right corner with upward vertical (e.g. lower right of box) | |
| triple horizontal line segment | |
| crossing with left-leaning diagonal line | |
| crossing with vertical line | |
| dotted or dashed horizontal line segment | |
| simple (solid single) horizontal line segment | |
| right corner with downward vertical (e.g. upper right of box) | |
| left corner with downward vertical (e.g. upper left of box) | |
| double horizontal line segment | |
| crossing with right-leaning diagonal line | |
| terminates horizontal line-drawing mode |
72a. American Association of Workers for the Blind &c. (compiling authority). The Nemeth Braille Code for Mathematics and Science Notation, 1972 Revision. American Printing House for the Blind, P.O. Box 6085, Louisville, Kentucky 40206-0085, 1972. (An official BANA code.)
72b. C. E. Aucamp and J.P. Van Eeden (compilers). English Braille, South African Usage. The School for the Blind, 20 Adderley St., Worcester, R.S.A. 1972.
75a. All-Russia Association of the Blind (VOS). A System of Braille Notation on Mathematics, Physics, Astronomy and Chemistry (a manual Parts I and II). VOS, Moscow, 1975; translated from the Russian by Levit, M.A. and Etkina, L.I.
77a. American Association of Workers for the Blind &c. (compiling authority). Code of Braille Textbook Formats and Techniques, 1977. American Printing House for the Blind, Louisville, Kentucky, 1977. (An official BANA code.)
84a. Abraham Nemeth, Ph.D. Monograph on The Nemeth Unified Code for Mathematics, Science and Computer Notation. Unpublished, 1984.
87a. Braille Authority of North America (compiling authority). Code for Computer Braille Notation. American Printing House for the Blind, Louisville, Kentucky 40206-0085, 1987. (An official BANA code.)
87b. B. Smith, in collaboration with the Mathematics, Science, Computer Science of Committee of the Australian Braille Authority. Mathematics Braille Code Changes 1987. Royal Blind Society, Enfield, NSW 1987.
88a. Mathematics, Science, Computer Science of Committee of the Australian Braille Authority. Changes to the Literary Braille Code as a Result of the Mathematics Braille Code Changes 1987. Royal Blind Society, Enfield, NSW 1988.
89a. Braille Authority of the United Kingdom, Mathematics Committee. Braille Mathematics Notation, 1987. The Royal National Institute for the Blind, Bakewell Road, Orton Southgate, Peterborough, Cambridgeshire PE2 0XU, 1989. (An official BAUK code.)
89b. Braille Authority of the United Kingdom, Science Committee. Braille Science Notation, 1989. The Royal National Institute for the Blind, Bakewell Road, Orton Southgate, Peterborough, Cambridgeshire PE2 0XU, 1989. (An official BAUK code.)
89c. Association of American Publishers. Markup of Mathematical Formulas. Electronic Publishing Special Interest Group, c/o OCLC, 6565 Frantz Rd., Dublin Ohio 1989.
90a. United Nations Educational, Scientific and Cultural Organization (UNESCO) and National Library Service for the Blind and Physically Handicapped, Library of Congress (NLS). World Braille Usage. NLS, Washington, D.C. 1990.
90b. Henry M. Robert (revised edition by Sarah C. Robert). Robert's Rules of Order Newly Revised (9th Edition). Scott Foresman, 1990.
90c. Donald Knuth. The TEXbook. Addison-Wesley, Reading, Mass., 1990.
90d. Charles F. Goldfarb. The SGML Handbook. Clarendon Press, Oxford 1990.
90e. Mathematics, Science, Computer Science of Committee of the Australian Braille Authority. Rules for the Brailling of Chemistry Material. Royal Blind Society, Enfield, NSW 1990.
90f. The International Phonetic Alphabet Braille Code. Updated 1990. (Monograph from Royal National Institute for the Blind, London.)
91a. American Association of Workers for the Blind &c. (compiling authority). English Braille American Edition, 1959 (with revisions and addenda through October 1991). American Printing House for the Blind, P.O. Box 6085, Louisville, Kentucky 40206-0085, 1991. (An official BANA code; most recent version 2002.)
91b. The Unicode Consortium. The Unicode Standard, Worldwide Character Encoding, Version 1.0, Volume 1. Addison-Wesley Publishing, Reading, MA, 1991. (current version defined by: The Unicode Standard, Version 4.0. Boston, MA, Addison-Wesley, 2003. ISBN 0-321-18578-1.)
91c. Organización Nacional de Ciegos Españoles (ONCE). Codigo Matematico Unificado para la Lengua Castellano. Approved at Montevideo, 1987 (final acceptance circa 1991). ONCE, Madrid, circa 1991.
92a. Braille Authority of the United Kingdom (compiling authority). British Braille--A Restatement of Standard English Braille. The Royal National Institute for the Blind, Bakewell Road, Orton Southgate, Peterborough, Cambridgeshire PE2 0XU, 1992. (An official BAUK code.)
95a. Committee 2 of the ICEB UEBC Research Project. Report by the Objective II Committee. March 2, 1995 (corrections through June 22, 1995).
96a. Braille Authority of the United Kingdom, Computer Committee. Braille Computer Notation [Draft]. The Royal National Institute for the Blind, Bakewell Road, Orton Southgate, Peterborough, Cambridgeshire PE2 0XU, 1996. (An official BAUK code.)
97a. Braille Authority of North America (compiling authority). Braille Code for Chemical Notation. 1997. (An official BANA code.)
99a. Committee 2 of the ICEB UEBC Research Project. Supplementary Report by the Objective II Committee. October 15, 1999 (corrections through January 9, 2000).
2001a. Committees 2 and 4 of the ICEB UEBC Research Project. Report by the Joint Session of the Objective II Committee and the Objective IV Committee. February 27, 2001.
2004a. U.S. Library of Congress Web site on standard
ISO 639-2
http://www.loc.gov/standards/iso639-2/.