An Example of Dotless Braille for Nemeth

Multiple meanings for one cell

Although many sighted persons learn to read either simulated braille or ASCII braille, others find this frustrating. Moreover, it is likely that even some who are comfortable reading literary braille transcriptions will find this tedious for Nemeth because of all the additional meanings for the cells.

The two main difficulties that persons accustomed to print find with braille are (1) the new characters and (2) the use of context to distinguish among numerous different meanings for the same cell. (This latter is, of course, an if not the essential feature of braille.) The simple algebra example on a previous page shows that the same braille cell is used for the period punctuation mark as for the Nemeth numeral four. (In fact, this is why the keystroke for the numeral four was chosen as the ASCII code for this cell.) In all, seven of the Nemeth numerals use cells that are also used as punctuation marks in the Nemeth code.

Actually (dots 2-5-6) is not only used for both the numeral four and the period, it still means dis and dd in literary contexts in Nemeth just as in literary braille. It is, of course, necessary in Nemeth for many cells other than those used for numerals to take on extra meanings.

Many of the Nemeth signs use the same cells as the various letter signs of the literary braille code. If you are familiar with literary braille, you can see in the next Figure that the same braille cell is used for the plus sign as for ing. (This example is fully explained on the page about Nemeth and HTML.)

Interpreted: EXAMPLE 6. Factor
Simulated:   ,,example #6_4 ,factor
"Dotless:"   ,,EXAMPLE #6_. ,Factor

Interpreted: 12x2 + 7xy - 10y2.
Simulated:   #12x^2"+7xy-10y^2_4
"Dotless:"   #12x^2"+7xy-10y^2_.

Figure. Simulated braille with interpreted braille above and a "dotless" braille equivalent below.

Interpreting or back-translation

A common way of displaying Nemeth braille is to back-translate or interpret the braille to reflect the same overall meaning as read by the braille reader. The previous Figure shows interpreted braille above the simulated braille.

When correct braille is correctly back-translated, the print should reflect what the braille reader reads. Unfortunately, correctly interpreting Nemeth in all situations is a difficult problem and not as yet a fully-implemented feature in current applications. One difficulty is what to do about syntax errors in directly-entered braille and another difficulty is detecting the different rules used in literary and math contexts. The latter problem can be gotten around to some extent by back-translating material clearly designated as mathematical expressions.

Nemeth back-translation is important for blind students who wanted to communicate with sighted math and science teachers and is a major goal of the MAVIS project. A "typographically-correct Nemeth display" is a new feature of Braille 2000 and is available for user testing.

Displaying the meanings for each cell

Back-translation does not solve the problem of displaying braille per se for the sighted reader whose goal is to read the braille. Our solution to this problem is to show the meaning of each braille cell as in the previous Figure which has the meaning of each cell directly beneath it. This display method has been called both indirect and "dotless" braille. Of course, a person who wants to teach braille or to claim they really "know" braille ultimately needs to be able to read the dots with no help. However, indirect braille eases the problem of learning the basic principles of Nemeth without having to deal with dots at the same time.

Dotless braille is a many-to-one print equivalent to braille that displays the intended meanings of the braille cells as determined during the forward transcription process. The computer simply keeps track of both the braille cell (as ASCII braille, for example) together with its current meaning; this is known as extended braille. (This process is much simpler than interpreting the Nemeth after the fact and is not a solution to the problem of back-translating.) The computer can thus automatically generate ordinary braille from its internal extended braille representation with no added effort.

The dotless braille display uses standard print characters as shown below the simulated braille cells in the Figure. Here, for example, (dots 2-5-6) meant as a period are shown as a period. (Since braille, unlike print, uses a different character for a period and for a decimal point, this distinction would need to be made by, say, using color in order for a print display using both cells to qualify as a braille equivalent.)

Another change made to improve the print readability is to actually apply the braille indicators to the affected print characters. This means that the indicators themselves are redundant. However, they still need to be displayed to make the braille clear to a proofreader and to function as placeholders. In this case the indicators are shown as simulated braille but in a less-distracting light-colored font. (Note that while it is difficult to get braille cells and print to line up exactly using simple HTML code as done here, this is not a problem with special-purpose applications. For example, the Braille 2000 transcribing program has an option to scale each print line to have the same length as the corresponding braille line.)

If you want to try this idea with pen or pencil, see here for a way to write braille by hand. It's also fairly easy to do simple math this way using Microsoft Word.

Some Advantages of Dotless Braille

There are a number of advantages to a dotless braille display as contrasted to either simulated or ASCII braille or to back-translated braille.

If you have questions about Dotless Braille, please contact me at

This page was first posted on February 21, 2002 and last modified February 24, 2002.

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