Future Reflections Special Issue: A Celebration of Braille
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by Caryn Navy
Reprinted with permission of the author from issue 93 of the Raised Dot Computing Newsletter, <http://personalpages.tds.net/~ti51/new93.htm>.
Editor’s Note: At the age of 90, Dr. Nemeth is still active physically and mentally; he works on Braille codes, travels, speaks (and tells terrible--and terribly funny--jokes), and is truly an inspiration and role model for blind youth everywhere. Here is the 1991 interview in which he explains to Caryn Navy (who is currently with Duxbury Systems) how he came to invent his math code:
Nemeth Code is the code for mathematics and scientific notation in North America. During my years of studying and teaching mathematics, I developed a great respect for Dr. Abraham Nemeth, who had developed this Braille code. He has had a very active academic career in mathematics and computer science, and he remains very active in his retirement. I was delighted that he agreed to talk with us about the background of the Nemeth Code and about himself.
Q. How did you get involved with developing the Nemeth Code?
A. I began working on my Braille math code in 1946 or 1947. At that time I had a day job at the American Foundation for the Blind (AFB), and I was taking night classes in math at Brooklyn College. Boys were returning home from World War II and going back to school. Many of them had passed Calculus I before the war and were now taking Calculus II. After that long interruption they needed some extra help. There was a room with a large blackboard where volunteers helped them with their math problems. Each student stationed himself at one panel of the blackboard and wrote out the problem he wanted help with. I was one of the volunteers. I asked the student to read me the problem, and then I worked out the solution on the blackboard. I didn’t find it difficult to write on the blackboard. Apparently the chairman of the math department happened to observe me and was impressed. One day I received a telegram from him asking if I could replace a member of the math faculty who was ill. The telegram asked if I could start next Monday. I said yes.
When I wanted to take notes, I needed a way to write things down. At the time people used the Taylor Code from England for writing mathematics in Braille. I thought that the Taylor Code used too many grouping symbols. I had already come up with rules to tell my readers how to read mathematics aloud to me. I began working on a Braille code which simulated my rules for speech. For example, when you say “x to the n power,” the phrase “to the” means “begin a superscript,” and the word “power” means “return to the baseline.” So in my Braille code I created symbols that mean “begin superscript” and “return to the baseline.” My personal code for Braille mathematics began to evolve. I used it for my work in calculus and statistics.
Q. Before you tell us how you came to share your private Braille math code with the rest of us, I’d like to know how you started taking evening math classes at Brooklyn College.
A. I was always interested in math. I went to the New York City public schools, and I spent a lot of after-school time at the Jewish Guild for the Blind. I had a good buddy there who was younger, and I showed him a lot of math. When he got to high school, he took a math placement test. The result was no surprise to me. It showed he knew a lot of algebra and could skip the first algebra class. That was the first case of advanced placement I ever heard of.
Anyway, I always liked math. But various counselors told me that I couldn’t have a career in math because I was blind. I heard this from so many counselors that I believed it. After all, there’s a saying, “If three people tell you that you’re drunk, you’d better lay down.” So I majored in psychology. I got a B.A. in psychology from Brooklyn College and an M.A. in psychology from Columbia University. But it wasn’t so easy to get a job as a psychologist either. I got a job at the AFB but not as a psychologist. My first wife, Florence, who died in 1970, knew how much I loved math. She asked, “Wouldn’t you rather be an unemployed mathematician than an unemployed psychologist?” So I started taking math classes at night at Brooklyn College and then got the teaching position there. I worked toward a Ph.D. in mathematics at Columbia University. I got a mathematics teaching job at the University of Detroit and finished my Ph.D. at Wayne State University in Detroit.
Q. How did your Braille math code become an official code?
A. Another blind employee at AFB was Dr. Clifford Witcher, a physicist from Columbia University. One day he asked me if I had a table of integrals in Braille. I said that I had one, but it was in my own private Braille code. So he asked me to teach him my code. When I showed him the code, he really liked it. Dr. Witcher happened to be a member of the Mathematics Subcommittee of the Joint Uniform Type Committee. This committee, an ancestor of BANA, was responsible for Braille codes in the U.S. and England (the word “Joint” referred to the U.S.A. and England).
[Editor’s Note: A table of integrals is a long list of formulas for performing a calculus operation called integration. A table of integrals is part of the holy liturgy for calculus students, engineers, physicists, and many others.]
Q. This really brings back memories for me. When I was a freshman in college, my new friend, David Holladay, asked me if I had a table of integrals in Braille. I told him that my Braille calculus textbook had a table of integrals at the end. He said that he had a much better one in print and wanted to Braille it for me over Christmas vacation. He asked me how the Braille math code worked and spent half an hour taking one page of notes on Nemeth Code. He took my Perkins Braille writer home over the vacation and did a really good job of Brailling his favorite table of integrals.
Anyway, what happened after Dr. Witcher became a fan of your private Braille math code?
A. Dr. Witcher asked me for a document proposing my Braille math code to the Joint Uniform Type Committee. Various members of the Mathematics Subcommittee were supposed to write different parts of the official code. But they ended up using my proposal, with minor editorial changes, as the official code book. That was the Nemeth Code, 1952 edition. It was published by the American Printing House for the Blind (APH). In 1956 they reorganized the code book. They made a separate section at the back of the book with all the rules not needed until after tenth grade. They soon realized what a mistake that was. The whole math curriculum changed when the U.S. wanted to catch up with the Russians after the Sputnik launch in 1957. Set theory was moved into the elementary school curriculum, but the set theory symbols were at the back of the Nemeth Code rule book.
Q. If Nemeth Code was proposed to the Joint Uniform Type Committee for the U.S. and England, why don’t they use Nemeth Code in England?
A. I don’t know. At some point the Braille Authority, with only three members, became responsible for Braille codes in just the U.S. Later they added Canada, and it became BANA (the Braille Authority of North America). I think they should add New Zealand and Australia to make it BANANA.
Q. What were the other revisions to the Nemeth Code?
A. APH published two newer editions of the official code book in 1965 and 1972.
Q. Were there any major changes in these revisions of the code book?
A. In 1965 we got rid of a rule about using two spaces to switch between text and mathematics. We also made parentheses more consistent. In 1972 the changes were noticed by transcribers but probably not by anybody else. Since 1972 there have been two addendums, for key caps (symbols for keys on a keyboard) and for ancient numeration systems.
Q. When will the Nemeth Code be finished?A. When will mathematical notation be finished? The purpose of changes is improvement, not changes. Mathematicians are intrinsically lazy creatures. They spend years trying to find an easier way to do things.
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