The need to convey mathematics linearly—without the use of special typesetting and, often, with a limited character set as well—is a common one. Linear mathematics is necessary for computer codes from FORTRAN to Java, for HTML, for braille, and for numerous other applications. The Nemeth code solves the problem of linear mathematics in a particularly elegant and compact manner as compared to other linear math entry methods. This can be seen by comparing the HTML and Nemeth forms for the same mathematical expression. (Although HTML is not a general math entry system, it illustrates the basic mark-up approach used in full-featured systems such as LaTEX.)
A simple algebraic problem is used here to show the similarities and differences between HTML and Nemeth. The problem is an example from the BANA Unified English Braille Code Sampler 2 published in June 2001. (This sampler, which shows Nemeth and UEBC on facing pages, makes pretty obvious the clumsiness of the proposed new code. Click here to read more about the UEBC.) The print form of this example is on p. 59 and the Nemeth transcription, shown in simulated braille, is on p. 82.
Example 6. Factor
12x2 + 7xy -
10y2.
Figure 1. Displayed algebra
problem.
Web pages like this one are written in a linear source code which a browser, such as Microsoft Internet Explorer or Netscape, uses to determine how the display will appear on the computer screen or other display device. (You can see the source code itself by selecting a "View Source" option.) The displayed form of the equation in Figure 1 was produced from the HTML shown in Figure 2. (Obviously I had to "trick" the browser to make it display what appears to be source.)
<strong>Example 6.</strong> Factor
12<var>x</var><sup>2</sup> +
7<var>xy</var> -
10<var>y</var><sup>2</sup>. HTML source is a mix of the items that are to be displayed and pairs of (possibly nested) matching tags that control the display. Each start tag is paired with an end tag with the same name but preceded by a forward slash. The tags themselves are enclosed in angle brackets so the browser knows not to display the tags but only the other items. (The browser has defaults for the display options that are to be used with a particular tag but these can be changed by the author of the HTML.) HTML is meant to be read by computers (as well as programmers) and the simple syntax and explicit use of end tags makes it easy to understand but quite verbose.
The tags used in Fig. 2 have the following meanings:
Figure 3 repeats Fig. 2 with color-coding and an added linebreak to facilitate comparison with the Nemeth transcription of the same example. Figure 4 shows the Nemeth in ASCII braille and Figure 5 repeats it in SimBraille (or again in ASCII braille if you don't have SimBraille installed on your computer). Figure 6 shows the transcription in indirect or dotless braille. (If your aren't very facile with either ASCII braille or simulated braille, click here for more about how the last display approach is used here with Nemeth.)
<strong>Example 6.</strong> Factor
12<var>x</var><sup>2</sup> +
7<var>xy</var> - 10<var>y</var><sup>2</sup>. ,,example #6_4 ,factor
#12x^2"+7xy-10y^2_4
,,example #6_4 ,factor
#12x^2"+7xy-10y^2_4
,,EXAMPLE #6_. ,Factor
#12x^2"+7xy-10y^2_.
The braille composition indicators corresponding to the HTML strong and sup tags of Fig. 3 and the capitalization indicator are shown in red in Figures 4 and 5. The Base Line Indicator, which is an example of a braille termination indicator and corresponds to an HTML end tag, is shown in green. The Nemeth Numeric and Punctuation Indicators, which are braille change-of-semantics indicators, are shown in blue.
Nemeth is meant to be read by humans and a comparison of the HTML code in Fig. 3 with the corresponding Nemeth braille transcription in Figs. 4-6 show the compactness possible in a linear markup language that is carefully designed to make use of natural defaults and of context.
The first braille indicator is the pair of dot 6 cells. This symbol indicates that the following word is capitalized. Although the label was in boldface in print, the change is an example of braille's following special formats for structural items in a document. (In fact, using proper formats is one of the more difficult aspects of braille transcribing.)
The label is indicated in braille in all upper-case letters as required by the Nemeth code. [Rule V, Sec. 33] The default for the word capitalization symbol is that it applies to the whole word so no termination indicator is needed as in HTML. This is one example of the human-oriented rules used in Nemeth. The default for the letter capitalization symbol before the capital F in the word Factor is one letter.
The two indicators shown in blue don't have print analogs. They are needed since Nemeth uses the same cells for some numerals as for punctuation marks. The uses of the Numeric Indicator and the Punctuation Indicator in this example are explained on the next page.
The single-cell raise or Superscript indicator in Nemeth plays
the role of the sup tag in HTML. Notice that the first
superscript requires an explicit termination indicator but the
second one is terminated by default because of the Punctuation
Indicator.
All of the Nemeth rules illustrated by this Example are explained in more detail on the next page.
This page was first posted on March 05, 2002 and last modified on February 27, 2002.