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Speaking of Mathematics

Brian Hayes

This column originally appeared in the March-April 1996 issue of American Scientist.

Computers, and networks of computers, have opened up a new channel of communication for people who are blind or visually impaired. Much information stored and transmitted in electronic form—including vast streams of text that flow over the Internet—can be made accessible to the visually impaired reader through a computer equipped with a nonvisual output device. This device commonly takes the form of a text-to-speech transducer that reads aloud the content of a display screen. Compared with other media such as tape-recorded books and Braille publications, computerized sources of information offer the important advantages of immediacy and independence: Visually disabled readers get the information as soon as anyone else does, and they can get at it without assistance.

Text-to-speech systems work reasonably well with plain, linear prose, like that found in most newspaper articles and electronic-mail messages. But what about the visually impaired student of mathematics or computer science or engineering, whose reading matter may well include more-challenging constructs? Take a look at this equation:

Click to Enlarge Image

Now try to visualize it without seeing it. A text-to-speech system is likely to stumble badly when trying to read such an expression. For one thing, the usual left-to-right convention of English fails here; in some places within the equation the natural sequence is from top to bottom, and elsewhere from bottom to top. Furthermore, reading the symbols in any fixed sequence yields a phonetic string so long that you've forgotten the beginning by the time you reach the end.

The challenges of teaching a computer to read mathematics aloud are taken up in a thoughtful series of papers by T. V. Raman, and in a software system called AsTeR, which Raman developed while he was a doctoral candidate at Cornell University. AsTeR performs audio formatting and rendering of mathematical notation, and it allows the listener to browse actively through complex mathematical expressions and other forms of structured text. Systems like AsTeR are obviously important to the specific community that needs them most, but they have a wider significance as well. AsTeR illustrates some subtle principles about how best to encode and present information, principles of value to everyone.

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