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Unicode and Math, a Combination Whose Time Has Come — Finally!

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Unicode and Math, a Combination Whose Time Has Come — Finally! Unicode and math, a combination whose time has come — Finally! Barbara Beeton American Mathematical Society [email protected] Abstract To technical publishers looking at ways to provide mathematical content in elec- tronic form (Web pages, e-books, etc.), fonts are seen as an “f-word”. Without an adequate complement of symbols and alphabetic type styles available for di- rect presentation of mathematical expressions, the possibilities are limited to such workarounds as .gif and .pdf files, either of which limits the flexibility of presentation. The STIX project (Scientific and Technical Information eXchange), repre- senting a consortium of scientific and technical publishers and scientific societies, has been trying to do something about filling this gap. Starting with a com- prehensive list of symbols used in technical publishing, drawn from the fonts of consortium members and from other sources like the public entity sets for SGML as listed in the ISO Technical Report 9573-13, a proposal was made to the Unicode Technical Committee to add more math symbols and variant alphabets to Uni- code. Negotiations have been underway since mid-1997 (the wheels of standards organizations grind exceedingly slowly), but things are beginning to happen. This paper will share the latest information on the progress of additional math symbols in Unicode, and the plans for making fonts of these symbols freely available to anyone who needs them. Introduction tions — the things operated on. The number of dif- ferent alphabets used in some documents appears The composition of mathematics has never been to be limited only by what is available or by the straightforward; it has always required special fonts capacity of the typesetting system (manual, mecha- above and beyond the alphabetic complement re- nized or electronic). Only numerals seem to denote quired for text. Even if an author makes an effort more or less the same kinds of concepts in both ordi- to describe mathematical concepts and relationships nary prose and mathematical notation. Needless to in words, there comes a point where symbols become say, font foundries have never been overly eager to necessary for both clarity and conciseness. In some provide an unlimited supply of new symbol shapes fields (for example, symbolic logic), the use of nota- of arcane design and often intricate production re- tion has expanded to such a degree that it is nearly quirements. impossible to express concepts clearly in ordinary Complicating this situation is the fact that the words; symbols convey the desired meaning much audience for typeset mathematics is relatively small. more directly. The situation might be compared If the number of mathematicians clamoring for com- to that of two literate Chinese from different areas petently printed material in their subject were any- meeting, and communicating by writing rather than where near the number of readers of novels or sports in their different spoken dialects. There is some- magazines, or if these mathematicians had budgets times just no reasonable substitute for a common matching those of major advertising agencies, font writing system. foundries could muster much greater interest in do- Although symbols form a large and important ing this sort of work. part of written mathematics, mainly indicating op- erations, relations, and other similar concepts, al- phabets are also co-opted from their role of rep- Terminology resenting ordinary language to provide the nota- tion for mathematical constants, variables and func- When one looks at a printed page, one sees that it is constructed from many small elements. There are letters, digits, punctuation, symbols, dingbats, . 176 TUGboat, Volume 21 (2000), No. 3 — Proceedings of the 2000 Annual Meeting Unicode and math, a combination whose time has come — Finally! One might think to refer to all of these as characters. be one-to-many, or many-to-one. While this is not The dictionary [9] definition of character is, in part, only adequate, but even admirable, when dealing character ... 1. A sign or token placed with text, for mathematics it can introduce serious upon an object as an indication of some spe- ambiguity. cial fact, as ownership or origin; a mark, brand, or stamp. 2. Hence: a a graphic Codes symbol of any sort; esp., a graphic symbol The alphanumeric soup of standardized codes has employed in recording language, as a letter. already been mentioned. Consider the history of b Writing; printing. c ... codes used for computer input. Clear enough? Well, not quite. Although quite a few different models of digital In standardese, a term can have only one mean- computer architecture have been devised, very few ing. The basic ISO1 definition [5] is have been based on a wider range of possibilities for character A member of a set of elements the smallest element other than zero and one — on used for the organisation, control, or repre- and off. (This provides the rationale for naming the sentation of data. bit, “binary digit”.) Different combinations of bits, in strings of predefined length, designate characters. Thus the term character cannot be used in an ISO The number of bits in such a string is the limiting standard with any other meaning. factor in how many characters can comprise a code. Another relevant term is code; from the same Very early codes contained six bits — 64 char- dictionary [9]: acters, just enough for a single-case (latin) alphabet, code ... 3. A system of signals for commu- ten digits, five arithmetical operators (+, -, *, / and nication by telegraph, flags, etc. (. ); also, a =), the punctuation required to format real num- system of words or other symbols arbitrarily bers and accounting data, and a number of control used to represent words; as, a secret code. codes to support interaction with a Teletype ma- This is the term adopted to identify the system by chine. The following symbol complement, a variant which data is stored in a computer memory, and the of the BCD code, was available on a punched paper individual elements are known as coded characters, tape device used in the 1970s at AMS; symbols in or characters for short. Different computer coding the second row had to be preceded by an upshift and systems use different bit patterns to represent the followed by a downshift, as they were piggy-backed same character; for example, the letter A would have onto other characters. a different code in ASCII, BCD, EBCDIC, ISO 646, . , - / * # & $ ISO 8859-1, etc., but in each of these systems, A :;+=@()<>’" is still considered the same character. If it is in a context that might (in print) be represented in italic This was sufficient to support Fortran, Cobol, and or boldface, that makes no difference; the same code other antique programming languages, but not a di- is used for all. rect visual representation of mathematical expres- But an A in a font or on a printed page is not sions. (by this system) a character, and an italic A is differ- ASCII, in its original form, had seven bits and ent from a boldface A, and so on. The term adopted 128 characters, which could accommodate a lower- in standardese [3] for such an element is glyph: case alphabet and more symbols. (This is the code under which T X was first implemented.) ISO 646 is glyph A recognizable abstract graphic sym- E the “international” version of ASCII. A key princi- bol which is independent of any specific de- ple was — and is — that once a character gets into a sign. code, it is never removed, so the current 8-bit ASCII Thus it is clear that one code may represent many is backward compatible with the 7-bit version, at different glyphs. The reverse is also true: while the least insofar as what can be encoded. word “file” is spelled with four letters, and coded as Other codes have been promulgated by manu- four characters, when printed with a font that has facturers, national standards bodies, and the ISO. ligatures, only three glyphs are used. Until the mid-1980s, these codes were used almost The association between characters and glyphs exclusively to support processing of programming is referred to as mapping. What is important here languages and natural languages. Whatever sym- is that in neither direction is the mapping between bols were included were necessary to specify pro- a coded character and a glyph one-to-one; it may gramming operations, not the symbolic representa- 1 International Organization for Standardization tion of scientific disciplines, and typically, except for TUGboat, Volume 21 (2000), No. 3 — Proceedings of the 2000 Annual Meeting 177 Barbara Beeton the few symbols and punctuation characters that In the Unicode 3.0 manual [8], only one refer- were already present in six-bit codes, symbolic char- ence can be unambiguously associated with math acters were typically segregated in programming symbols: ISO 6862, Information and documenta- language–specific codes such as the one for APL. tion — Mathematics character set for bibliographic Some language codes already exceeded the typ- information interchange (no explicit references are ical eight-bit capacity of 256 elements. It is impossi- shown in the Unicode 2.0 manual). Many of the ble, for example, to fit in all the accented and vari- symbols listed in the annex to the SGML standard ant letters of the alphabet needed to represent all don’t appear in Unicode. More about this later. the languages based on the latin alphabet. And There are several design principles especially codes for Japanese and Chinese had to accommo- relevant to the designation of math symbols as char- date the nearly 10,000 characters used to publish acters [8]: newspapers, or, preferably, the 50,000 characters or • The Unicode Standard encodes characters, not more found in literary works.
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