I have been asked today to present to you the history of the development and adoption of the NEMETH CODE OF BRAILLE MATHEMATICS for the embossing of mathematics works in Braille, and to discuss some of the problems in the application of the Code. Before I do this, however, I think I should point out the inherent difficulty of any code of Braille mathematics, which difficulty is shared with the regular literary code and other scientific Braille codes, such as music and science. I refer to the fact that the six-dot Braille system, because of the limitation in the number of symbols to only 63 characters, is impossible of making exact reproductions of ink-print material in Braille. The best we can do is to assign a number of different meanings to each Braille symbol, thereby necessitating adherence to strict rules of usage and the employment of devices peculiar to Braille, such as the capital and number signs, which, for want of a better name I shall call "Braillisms," in order to make clear the meaning of any particular Braille character under any given situation. We must face the fact that Braille is a shorthand system, and a very arbitrary one at that. It is this problem of "Braillisms" which accounts for much of our troubles, in the writing of both literary (or regular) Braille, as well as the scientific Braille codes, although the use of "Braillisms" becomes much more pronounced when writing mathematical Braille symbols. If we keep this fact in mind, I think you will understand better the reasons for adopting the NEMETH CODE OF BRAILLE MATHEMATICS.
I first became involved in the problems of Braille mathematics in about 1940, when it had become all too clear to me, as Braille Editor of the American Printing House for the Blind, that the sketchy American Revision of the English Taylor Code then in use, and available only in Braille, was completely inadequate to guide a stereotypist or transcriber in the embossing of even simple mathematics texts. About that time, Mr. Frank C. Bryan, Manager of the Howe Press, and Mr. Edward J. Waterhouse, teacher at Perkins Institution, sent to the Printing House a manuscript of a proposed revision and expansion of the Taylor Code for use in this country, with the request that it be published in both Braille and ink-print form, for the use of the teachers and children in the schools and classes for the blind. Upon looking it over, I suggested additional changes and improvements, and also sought the aid of Mr. John B. Curtis, Founder and Former Supervisor of the Chicago Public School Classes for the Blind. This material was finally published in 1942 as BRAILLE MATHEMATICAL NOTATION: SECOND AMERICAN REVISION. Please understand that this revision was compounded by Mr. Bryan, Mr. Curtis, Mr. Waterhouse, and myself without any of us being endowed with authority to do so by the AAIB, the AAWB, or any other agency. It was adopted by the Printing House simply because there was nothing better in the field, and it was a help to some extent. However, when all four of us working with the code, and we at the Printing House in particular, tried to apply it to the writing of even freshman high school algebra, we were keenly aware of its deficiencies. Not only was it full of Braillisms, but it made absolutely no provision for many of the symbols employed in modern mathematics texts at even the primary school level, and absolutely none for books in higher mathematics. This necessitated the improvising of symbols and usages every time we tried to emboss a new mathematics text, and it was clear to all of us that, as time went on, the situation would get worse, not better.
In June, 1947, under the aegis of the American Foundation for the Blind, Dr. Robert B. Irwin called a meeting in Chicago of a committee comprising the following five peoples
At this meeting of the informal committee, the following materials were presented for the consideration of the American conferees:
The American Committee spent two days going over these materials most carefully, and submitted a detailed report to the English Committee, covering both agreements and disagreements and suggested changes. Additionally, it should be pointed out that this informal American Committee was not of the opinion that the British "SIMPLIFIED PRESENTATION OF THE INTERNATIONAL CODE FOR BRAILLE MATHEMATICS" should be recommended for adoption by the United States, even though there was some feeling towards the advisability of adopting an international Braille mathematics code. At that time, on the international side, the situation was as follows: "At the International Blind Congress held in Vienna in 1929, 21 committees were appointed to deal with various matters connected with the welfare of the blind. To No. VII Committee was entrusted the task of recommending, if possible, an International Braille Code of ’Mathematics and Chemistry.'
"Ten systems of transcribing mathematics into Braille and several for transcribing chemistry were submitted to the Committee. All were different, and several were incomplete, and though each system had proved sufficient for the needs of each country, there was no common basis among them - except that the signs of operation adopted in the INTERNATIONAL BRAILLE CODE OF MATHEMATICS were those in general use on the continent of Europe (but not in Great Britain).
"In view of this chaos, the Committee (international) had to decide whether (1) To construct an entirely new code; or (2) To base the new code on one of the existing national ones. The Committee decided to adopt the latter alternative. The German (Marburg) Code was selected, for two reasons: Firstly, that it was desirable to retain, at any rate, one existing system instead of scrapping all; and secondly, because the Marburg Code was responsible for the publication (at that time) of a larger number of mathematical works than any other. At the same time, the principle was accepted that the International Code must be the same for both elementary and advanced mathematics.
"In 1934, when it was made known that the French educational authorities were not prepared to adopt an international code in place of their own (that of the Association Valentin Haiiy), M. Henri felt compelled to resign his position as President of the Committee. In his place Dr. Juringius was appointed President. He was responsible for guiding the discussions of the Committee for a further three years - until agreement, by a majority, was reached in 1937 ... in the hope that this International Code would in time take the place of all those then in use." [Letter from John B. Curtis to Dr. Robert B. Irwin, July 20, 1949]
The hope that the International Code would in time take the place of all those then in use did not materialize. The French abandoned the mathematical project in 1934 and World War II put off cooperative efforts among the nations for several years. Finally, with the establishment of the World Braille Council in 1951, after due consideration, it became apparent that there was no real need for an international mathematics code, since the majority of blind people had little use for any but simple mathematics, -which any national code seemed to cover adequately, and any individual student of higher mathematics had the intelligence and ability to absorb any special code needed if he wished to employ books published in other countries. Hence, at the present time, there is no recommendation for further pursuit of an international code of Braille mathematics.
Going back to the work in this country; Following submission to the British of the report of the informal committee meeting in 1947, nothing more was heard from them until the spring of 1950, at which time another meeting of the informal American Committee was held on May 22-23. At this time the British revision of the material reported on previously by our Committee was again reviewed - again only the material on arithmetic. The advanced part of their code was never submitted for consideration by this Committee.
In the summer of 1950, both the AAIB and the AAWB adopted identical resolutions creating the American Joint Uniform Braille Committee, appointing three representatives from each Association to the Committee. At the organizational meeting of the Joint Uniform Braille Committee, held in Louisville, Kentucky, April 27-28, 1951, an official Sub-Committee on Mathematics was appointed, comprised of the following:
At this time, Mr. M. Robert Barnett, Executive Director of the Foundation, offered financial aid to the Sub-Committee with the understanding that it would complete its work within a period of one year. The first meeting of the Sub-Committee was held in New York on June 8, 1951. At this meeting I was able to report that the British had advised that a like official Sub-Committee on Mathematics of the newly reactivated British National Uniform type Committee had been appointed in England.
During the two-day meeting, the Sub-Committee on mathematics gave serious study to the possibilities before it:
Of the three, it was the unanimous feeling of the Sub-Committee that the Nemeth Code held the greatest promise of usefulness and effectiveness, and it was accordingly adopted for study and improvement, and recommendation to the British Sub-Committee for their adoption and endorsement.
Following this meeting, a year of intensive work by the Sub-Committee brought the NEMETH CODE to the point where it was approved for publication, which costs were paid for by the American Printing House for the Blind and the Foundation. In December, 1953j the Sub-Committee held a meeting to draw up an outline of procedure for testing the Code in the schools for the blind, the Printing House having previously, at its own expense, embossed an algebra in the Nemeth Code. At the 1954 Convention of the AAIB, the Committee met again at Batavia to review the findings of the participating schools which had used the algebra embossed in the Nemeth Code, and unanimously voted to recommend its official adoption for use in the United States and by the American Printing House for the Blind in the embossing of the mathematics texts for the schools and classes for the blind. At the Annual Meeting of the Board of Trustees on November 9, 1954, the NEMETH CODE OF BRAILLE MATHEMATICS was formally adopted by the Printing House for the writing of all works in mathematics. So much for history.
Since that time, the Printing House has embossed one complete set of arithmetics from the third through the eighth grades, a two-year course in algebra, plus another set of arithmetics for Grades III, IV, V, and VII, in this code. Like you transcribers of mathematics texts, we have had our troubles, and Mr. Nemeth has had to reinterpret the code many times for us. One of the results of our troubles was the revision of THE NEMETH CODE which was published in 1956, to include the additional needed explanations for the use of the code, particularly in the embossing of books for the lower grades.
Our problem and yours is to provide "the proof in the pudding." Fundamentally, it is the promise of the Sub-Committee on Mathematics that the Nemeth Code does make provision for all contingencies, particularly in the case of higher mathematics, which none of the other codes we examined did. Further, it includes fewer "Braillisms." However, because the Code was devised by a blind mathematician who is a professor of mathematics at the university level, probably not enough explanatory material has been provided for the embossing of books at the primary arithmetic level. Basically, however, the Code seems to be sound, and I think the pooling of experience will obviate much of our difficulties. I know that a transcriber working on a tight schedule is pretty much up against it at times trying to work out the correct usage for a particular situation, and I feel that there is a real need for some central authority, easy to get to and get a reply from, to settle such transcribing problems. Additionally, I am very much opposed personally to each transcriber simply devising his or her own interpretation to fit a given situation, without regard to what might be done by someone else, so that we wind up with a hodgepodge of usages which bear no relation one to another. I do not know the complete answer to this problem, but I would like to suggest that your group make a formal recommendation to the Joint Uniform Braille Committee that some way be found to set up an authority to provide necessary guidance to transcribers of mathematics texts — an authority which has the knowledge and the time and the finances to give the answers promptly, when needed. At present, we at the Printing House are trying to answer all questions which come our way for which we do have the answer. Additionally, we write to Mr. Nemeth for further help. Many people also write direct to Mr. Nemeth, and he has been most cooperative in sending me duplicates of his answers with a view to the Printing House compiling a compendium of information on the subject, so that the next time the problem comes up we can give a consistent answer.
The problem really boils down to one of finance, —as usual. Mr. Nemeth is a very busy man, making his living as a university professor, with all the additional work that such a position entails for a blind person. He does not have the time or the personal finances to keep up with the problem on a catch-as-catch-can basis. On the other hand, the Printing House is tied by the fact that our finances are all earmarked, and we cannot pay Mr. Nemeth to answer your questions, the answers to which we already know. As a temporary measure, I would like to suggest that all of you wishing and needing information write direct to me at the Printing House for information. If we know the answer, we can give it to you immediately. If we don't know it, we can then confer with Mr. Nemeth, and relay the information to you, keeping a copy for ourselves for future need. In this way, some orderly growth in all of our knowledge can be achieved, which can be used as a basis for a scientific revision or logical interpretation of the code for everyone. I ask your help on this basis.
Additionally, I should like to suggest that the group at this meeting interested in mathematics transcribing use the time for our workshop this afternoon to compile a list of points in the Nemeth Code which need further clarification for the benefit of transcribers and teachers of blind students. Frankly, I do not believe even Mr. Nemeth himself could offhand, in the time allotted, begin to answer your questions on how to write a particular problem or mathematical sequence, and I know that I, personally, feel uninclined to be a "lamb led to the slaughter." I believe, therefore, that the group here could do a much more constructive job if we would settle down to making some pertinent comments on individual points which need greater explanation and clarification. As a member of the Sub-Committee on Mathematics of the Joint Uniform Braille Committee, I would then be in a position to take these suggestions to our Sub-Committee and Mr. Nemeth for further consideration and possible publication as an addition to the present Nemeth Code. Please understand, however, that I shall be glad to take down the list of your questions for answer just as soon as I can return to the Printing House next week and refer them to our technical Braillists and/or Mr. Nemeth, as may be necessary.
Before closing, I should like to say that I took a good deal of your time to give you the historical background of the adoption of the Nemeth Code, so that you might know that it was not imposed on you and the blind users without a very great deal of thoughtful consideration. I firmly believe that we have the best code available, and I base this belief on the years of study of other codes so far devised. I can assure you that your problems are not nearly so great as they might be -- if that be any comfort.