International Council on English Braille (ICEB)
Unified English Braille (UEB) Project
From the Committee 2 Archives: The Second Debate on Numbers

Prefatory Notes

This document contains the entire text of every message posted to the listserv for UEB Committee 2 ("Extending the Base Code") between November 10, 1993, when the chair put the subject of numbers up for debate for the second time, and January 20, 1994, when the last motion relevant to the representation of numbers in UEB was decided. Editorial intervention has been limited to correcting obvious typos and such mechanical matters as removing routine headers and email addresses. This series of messages is extracted from a stream within which other subjects, from contracted function names in British maths to routine administrative matters, were also being discussed, so there is much discussion here that is not closely related to numbers, especially in the earlier messages. However, it has been deemed best to include everything, so as not to lose the context and sometimes subtle interrelationships between subjects.

Also, as mentioned in the first message, there was a first debate on numbers that is summarized in the first (November 1992) Committee 2 report (see especially Appendix B, "Major Alternatives Considered"). Of course there were also remarks concerning numbers at various other times during the work of Committee 2, which continued up to the time that UEB was accepted by the ICEB in 2004. If you need to access more of this detail, including the full original text of any of the messages quoted here, it's all available in the UEBC Working Committee Archives section within UEBC Research Project Information.

Although that first debate had resulted in a decision reaffirming the traditional "upper" representation for numbers, that decision was set aside and the whole matter of numbers, including possibilities that were rejected during the earlier debate, was put up for reconsideration. The reasons for this reopening of the issue are given in the opening message, and so will not be repeated here, but the important thing to keep in mind when reading this second debate is that it covers all the same ground as the first as well as some additional ground, and so is more comprehensive as well as the one that matters to the eventual definition of UEB.

During this period, Committee 2 comprised the following members, often referred to by their initials:

Messages are identified for reference purposes by the author's initials and a date code (which corresponds to a file name within a monthly zip file if you have occasion to visit the abovementioned archives). The messages are listed by actual time received, which for various reasons (including the different time zones involved) doesn't always perfectly correspond to the reference date, so that some may seem to be out of order.

Observers were also invited to comment, and all such messages posted during the subject period are included, with the observer's full name given with the first such message.

Procedurally, the committee followed Robert's Rules of Order with adaptations as necessary for deliberations through an email list. This implied some formality with respect to the placement and and treatment of motions. The chair issued "status of the meeting" messages (identified as zs...) as necessary to clarify where motions stood.

When discussing braille characters, the committee members sometimes used dot numbers but more often used "ASCII-braille" equivalents, the latter being explained in message by JS on November 16 (js3b16), which happens to occur in this series. In many cases where the latter was used, a simulated braille font has been applied in this document for convenience.

The remaining sections of this document present the messages received during the subject period in time order, headed by the date, author, and subject, with the aforementioned reference ID in parentheses.

-- J. Sullivan, editor (and chair of Committee 2 during its existence)
June 25, 2012

1993-11-10 JS: More on numbers (js3b10)

I am just returning to Committee II work, having had a week in which I had to attend to other matters, including a short trip. Nevertheless, the subject of numbers has never been far from my mind. Perhaps all of us have been similarly preoccupied, and that accounts for the rather general silence since announcing the subject of numbers, or perhaps it is a (quite reasonable!) reluctance to jump into these murky waters. In any case it does seem to be time to put our toes in, at least.

First, especially for the sake of the four new members, I think a brief summary of where we are, and how we got there, is in order.

As is obvious from reading the November 1992 report, the original four committee members wished to have only one system of numbers -- that was the one point, in fact, on which we were unanimous. Moreover, we gave full consideration to only two basic possibilities for that system: (1) traditional, that is "upper" numbers as are used in the current SEB, and (2) "lower" numbers as are used in current Nemeth code, in the American computer code, and for some purposes in British maths. The reason was that those are the only two systems that have been used in the BANA countries, which at that time was the projected domain for the UBC. In fact, even lower numbers seemed to be a questionable departure, in the light of the charge to stay as close to SEB as possible. Thus, we gave only cursory consideration to French numbers, as are used in British computer code and some other European codes (including French "Informatique"); they seemed like just too large a change in terms of our perception of the Project as it was then. (Of course, it may well be that we will come back to that same conclusion.)

We spent a great deal of time on those two possibilities, hoping to reach a unanimous position on such a fundamental issue. Though we were unable to do better than a 3-1 majority position, the matter was quite thoroughly discussed. Our early papers, now in the BBS archive, can be consulted for further details. The majority position, for reasons that are summarized in Appendix B of the report and are briefly summarized again below, was that Louis Braille's original upper-number system was the better of the two for the projected purposes of the UBC.

Since that November 1992 report, several things have happened that now causes us to look again at the issue of numbers--not necessarily to change anything, but at least to approach the matter with a broadened set of underlying assumptions. First and most obviously, the Project having been internationalized, the scope of UBC has been widened to encompass a larger constituency, at least some of whom have used British Computer Notation and consequently French numbers. Secondly, the feedback from technical braille users seems often to focus on the inefficiency of upper numbers in technical contexts. Thirdly, as we have heard, notably from John Gardner in Sacramento, there is more interest in French numbers than we might have expected, even in North America, and so the assumption that they would be unacceptable needs to be reexamined. Fourthly, having applied for a direct ruling on the matter from our parent committee, we know that French numbers need not be summarily considered outside the scope of our charge.

To begin, let us consider those cases most often mentioned in the second item above, that is where our current upper-number system leads to a representation that is inefficient, perhaps too much so for certain technical purposes.

To state the obvious, upper numbers have problems when the letters a-j immediately follow digits; the necessary added indicator in such cases lengthens the expression and thus presumably affects adversely the ability to read it and to work with it in computation. There are many examples where such juxtapositions occur, which we may categorize as follows: (1) Alphanumeric designations, such as postal codes, automobile license numbers, catalog and part numbers, and the like. Even our own message numbers, e.g. this one (js3b10), fall into this category. (2) Ordinal endings, e.g. "3d" meaning "third". (3) Implied multiplication in classical mathematics, e.g. in a term such as "32a27bx" in a polynomial. (4) Numbers in bases higher than 10, where a is commonly used for a digit standing for 10, b for 11, etc. Hexadecimal (base 16) numbers are particularly common examples of these in current computer work, e.g. "3f0a" might represent a value in a 16-bit computer memory location. Probably the worst example of this kind would be a page full of hexadecimal numbers, all arranged for computation.

These cases are of course not new to us, having been considered at great length while pondering upper vs. lower numbers. And before going on, I hasten to point out that it would distort our perception greatly if we were to dwell exclusively on such cases, even though they no doubt exist, and can even occur densely at times, and are clearly important to some people in some circumstances--for they are not really representative of the general case. In particular, as mentioned in the report, the overall statistics show that numbers abut punctuation marks much more frequently than they do letters, even in literature with a scientific bias. This is clearly even more noticeable in general literature, and particularly so in literature for young readers. If we are to work toward providing a good solution for the abovementioned special cases, then, we surely want to do so in a way that does not encumber the general case.

With the addition of French numbers to the list, we now have three possible systems. While I am sure I cannot do full justice to all that has been and may yet be said, let me venture to summarize their strengths and weaknesses as follows:

1. Upper numbers, i.e. the system currently recommended in our report: Strengths: This is the original, traditional and internationally accepted system. Ordinary quantitative numbers in ordinary contexts, i.e. in sentences with punctuation, never need special indicators. Numbers, like most words, stand in an upper position and thus generally contrast with punctuation, which traditionally is put slightly "out of the way" in a lower position. Weaknesses: Since the upper numbers clash with the letters a-j, there is inefficiency in certain alphanumeric cases, as cited above.

2. Lower numbers. Strengths: The problem of juxtaposition with letters is solved. Also, the digits retain their "shape" despite the displacement, and so are easily read by persons already familiar with upper numbers. Weaknesses: Since lower numbers clash with common punctuation marks, then when numbers and punctuation are juxtaposed, indicators are required to signal each switch in meaning, and as noted these occur more frequently and more pervasively than digit-letter juxtapositions. The traditional notion of numbers and words being in the primary upper position, with punctuation down and out of the way, is disturbed. Also, the number sign would continue to be needed in most cases, because otherwise isolated lower numbers could be easily misread as letters. Finally, they are not traditional, even though they have been used in some technical codes and so can't be dismissed as untried.

3. French numbers. Strengths: Juxtapositions of digits with both letters and punctuation marks are handled without excessive indicators. In fact, in an extended grade 1 context, which I presume would characterize most intensive technical notation, numbers may be arbitrarily intermixed with letters and punctuation marks without any indicators at all, not even a numeric indicator. Thus, where efficiency is said to be critically needed, French numbers are clearly the most efficient of the three systems. Also, whether in grade 1 or grade 2 context, and no matter how isolated, digits are always readable unambiguously. Weaknesses: Many people report that they find them somewhat slower to read, at least at first. The reason usually given is that the dot 6 causes something of a "shape" change. Bruce has suggested that "dot density" might be the culprit. Whatever it is, it seems clear that an initial slowdown is widely experienced. Also, they take up ten "strong" symbols that we might want to use for other purposes, such as the British mathematical bracket or the Nemeth fraction line. Finally, they are not traditional, even though they have been used in some technical codes and so can't be dismissed as untried.

Underlying some of the above points, there are certain implicit assumptions about other possibilities that are being ruled out. For example, we know instinctively that we cannot consider resolving the upper-number digit-letter clash problem by changing the configuration of the letters. With the lower numbers, we feel the same way about the traditional punctuation marks, although here the matter has been somewhat less hard and fast; we have, after all, ventured to suggest changing the question mark and parentheses. And, underlying the debate about which one of these representation systems we choose, there is an assumption that we would not, in a unified code, want to use more than one of them.

I think that, when the options are weighed, we will want to stay, in the main, with traditional numbers for most purposes. For even though I can't imagine why the initial slowdown with French numbers would not vanish after a period of acclimation, I can easily imagine that many people would find that initial experience reason enough to dislike them, and consequently to reject UBC as a whole if it were based entirely on French numbers. Even so, I think we can do a needed service for technical readers, and a lot for the future, if we leave "room" for selective use of French numbers in our system. Yes, it does mean introducing a kind of dual system, and that is not as good as a single system, but I think that the overall benefits are worth the price. What I have in mind goes something like this:

1. The assigned grade 1 meanings of the "French" numbers, that is the ten single-character symbols *<%?:$]\[+ would be 1 through 0, respectively. (Note that various European codes use different characters for the 0; the French actually use #.) Those assignments would of course not affect their established grade 2 contraction meanings, nor would they affect the possibilities for assignments of multi-cell symbols incorporating those characters and formed according to our symbol construction rules.

2. In grade 2, traditional numbers as in current SEB and in the November 1992 report, would remain defined as such.

3. In grade 1, the traditional numbers would also remain defined, which means that one could use either traditional numbers or the French numbers. In other words, in the braille-to-print direction (which is the one we are now concentrated on), either form would be understood without any ambiguity.

4. Since grade 1 can be used throughout a document, or anywhere selectively by use of the grade 1 indicator, French numbers could actually be used for all numbers in exceptional cases.

5. Since either traditional or French numbers would be readable in the braille-to-print direction, it would eventually be necessary to give guidelines as to which to use when going in the print-to-braille direction. I envision that the normal rule would be to use traditional numbers in all cases except when transcribing for particular reader(s) whose express preference is for French numbers, and possibly also when reasonably well-defined situations arise, such as hexadecimal numbers arranged for computation.

One of the main benefits of a system like this is that it would leave the future of the French numbers "open" to find its own level. Those who like French numbers will choose to use them, and as their technical merits become obvious and people become acclimated, it is even conceivable that they would supplant traditional numbers in general use. But the same is also true for traditional numbers. And if both forms continue to coexist, which in my opinion is the most likely scenario, there is still no ambiguity and a lot of good accomplished as the needs of both groups are met in a code that, despite the duality, is still a single common code.

If there is interest in a system like this, I could easily frame a motion along these lines. There are, of course, a number of other issues, some of them touched on here, that need to be discussed, whether before or after such a motion: what other symbols we might want to assign to single characters, and whether there are enough left over after assigning those ten; whether French numbers eventually are just as readable as upper or lower numbers, or remain slower to read permanently; whether we should ask for a study to sort out that question; how we might handle certain common numeric forms, such as fractions, subscripts and superscripts, in a reasonably efficient fashion; and so on. I look forward to hearing your views.

1993-11-14 TC: Saving space with contracted math (tc3b14)

After reading and rereading Stephens piece dated November 3, 1993 I found it necessary to make hard copy braille notes to follow his examples. I'm not very good at visualizing braille characters using only dot numbers, but I don't know a better way to discuss matters on this forum. With only minor effort, I think I have a good understanding of the points made.

I have some difficulty with the purpose of the proposal: That is, using compact braille math notation to save space. It's my feeling that efforts to save space should be left to the literary contractions committee. The Grade II contractions have served us well as a space saving mechanism, and that the committee (to be appointed for the purpose) should pursue the matter further. Adding space-saving techniques of the kind proposed for math would be a completely new concept outside of the UK and would place an additional burden on new students of braille, not to mention the teachers of braille.

The use of dropped numbers also bothers me, because they interfere with punctuation marks. Differentiating between dropped numbers and punctuation would require redefining some punctuation symbols, frequent use of punctuation indicators or both.

On first thought, it seems to me that a punctuation indicator would be different from a grade one indicator (and quite different from a number indicator,) and so I would expect we would find ourselves in a situation where some notation would be burdened by Mr. Poole's "buckles and braces." I hope I am correctly crediting Bill with coining that expression. In any case I like it!

After considering the pluses and minuses, I believe the benefits of Stephen's compact math notation is outweighed by the complexity added to the code.

I see that Joe has some further comments on "Numbers Again" in his Js3b10 memo. I am going to read it now, and try to give him my two-cents-worth later today.

1993-11-16 AN: Reaction to Steve's explanation of contractions in British math code (an3b16)

First, a matter of social protocol. The North American members of our committee have been addressing and referring to each other by the names by which we are known in social circles. Thus, I address my North American colleagues as Tim, Joe, and Emerson, and they address and refer to me as Abe. In the same spirit, I would like to address and refer to Mr. Phippen as Steve and have him address and refer to me as Abe. I am not sure that "Steve" is the proper name to use, however, and would appreciate enlightenment on this subject in his next communication. Dale Carnegie, in his "How to Win Friends and Influence People," offers as his first lesson the importance of getting a fellow's name right.

Next I want to thank Steve for his very clear explanation of what is meant by "contraction" as that term relates to the British math code. I am happy that we now have a basis for meaningful communication on this subject. I would probably call Steve's "contractions" "notational abbreviations," since "contractions" in a Grade-1 context conjures up conflicting and incompatible concepts, whereas a "notational abbreviation" in a Grade-1 context is a perfectly rational concept. This again points up the need for careful terminology so as to avoid misunderstandings of this kind.

I am not at all certain that our committee has agreed upon a protocol by which to represent braille characters in our written submissions, so I also will use dot numbers when showing braille examples.

For purposes of comparison, I will use Steve's example in his sp3b04 submission. His example was: x, with a subscript of 2 and a superscript of 3, to which y was then added. Using the contracted forms of the British math code, this example would be written as:

According to the principles in my proposal, this example would be written:

In the above example, both codes require six cells. I am somewhat perplexed that British braille readers who are usually much more sensitive to space-saving than we are in North America tolerate the extravagance of three cells for the plus sign as well as four or five other common arithmetic operators. The space before such operators gives the braille reader who is unfamiliar with print a distorted impression of common print practice. While it is true that a sighted person can often not determine whether such operators are surrounded by spaces or not, at least such operators are, for the most part, centered between their two adjacent graphics.

In the Nemeth Code, the subscript indicator, the superscript indicator and the base-level indicator form a family with an easily discernible relationship between its individual members. The indicators are:

All three indicators contain dot 5. When dot 4 is added, the reader's attention is directed "upward" to the superscript position. When dot 6 is added, the reader's attention is directed "downward" to the subscript position. When no dot is added, the reader's attention stays at the base level. It is interesting to note that, at one time, in the Marburg code and in the Russian code, dots 34 served as the superscript indicator and dots 16 as the subscript indicator. These "oblique" lines directed the reader's attention as desired. Dots 156 was used to terminate the effect of either the subscript indicator or the superscript indicator. In the course of time, the function of dots 34 was preempted by the need for a fraction line and another superscript indicator was substituted. As a result, the British math code retains only the original subscript indicator. In the British math code, the three indicators are represented by arbitrary symbols not related to one another in any apparent way.

In my proposal, the effect of a level indicator is terminated by another level indicator. Thus, in the example we are considering, dots 45 terminates the effect of the preceding level indicator and initiates the superscript level.

In his submission, Steve then proceeds to show how the above example would be written in the uncontracted form. The one-cell "subscript-2" would now expand to four cells as follows:

In this example, both level indicators are of the first order and so they both are relative to x. If the 3 were superscript to the 2 rather than to the x, we would be dealing with a second-order superscript. How to deal with that would take us too far afield at this time.

In the British math code, the superscript-3 in its uncontracted form would expand from one to three cells:

In the Nemeth Code version of the same example, there would be no expansion, since the expression is not contracted in the first place. The base-level indicator would terminate the effect of the preceding superscript indicator. Altogether, the example in the British math code would require 13 cells; in the Nemeth Code, it would require 8 cells.

At this point, I cannot resist digressing for a moment to tell a story which makes my point succinctly. Johnny arrived at school well after his class was already in session. "Why did you come to school so late today?" asked his teacher. "Well," Johnny replied, "I took a shortcut."

Just as in the contracted and the uncontracted forms in the British math code, the Nemeth Code transcription would also be intelligible and unambiguous.

By far the most common punctuation marks in mathematics, and particularly at the superscript or the subscript level, are the period and the comma. For these, my proposal has created a dual period and a dual comma, although the Nemeth Code contains only a dual comma. For all other punctuation marks that require a punctuation indicator, the Nemeth Code like the British code would require one.

Having made this detailed analysis, it is amazing that the two codes employ almost the same principles to effect the braille representation of the example under discussion. The only differences lie in the assignment of the braille symbols which represent the level indicators and the plus sign, which I regard to be a minor problem. Changing a principle underlying the construction of a code is a much more serious problem than the reassignment of braille symbols. My proposal uses the principle by which a level indicator both terminates the effect of the preceding level indicator and initiates a new level. In this respect, the two codes differ in principle. In the British code, the level indicator and its terminator behave like enclosure symbols for the expression at the indicated level.

Now that I understand Steve's concept of "contractions" in Grade 1, which I have thought of and renamed "notational abbreviations," allow me to make an assessment of the situation with which we are dealing from my point of view. Steve is quite right when he observes that the intent of our Committee is not to use notational abbreviations in a Grade-1 context. The use of notational abbreviations is alien to all braille codes except to the British math code and to the family of math codes to which it belongs. Steve tells us that the uncontracted forms are never used, even at the most elementary level. I must therefore conclude that the concept of "contracted" and "uncontracted" in the sense that Steve has described were educed for the purpose of justifying a dual system when an uncontracted system proved to be too clumsy, while at the same time maintaining that the system is based on the use of upper numbers. On the other hand, the uncontracted forms are, indeed, clumsy and would be difficult to sell not only to UK braille readers but to others as well. This is a problem which our committee will have to resolve and will doubtless be the subject of submissions from all of us.

1993-11-16 JS: ASCII Braille (js3b16)

While dot numbers are a perfectly fine way of describing braille, the method we have most often used, especially for longer examples, is the simple and widely understood code that I, for want of a better term, tend to call "ASCII Braille". It's the code that is built-in to the hardware on many braille devices of North American origin, and not coincidentally it forms the basis for the Computer Braille Code used in BANA countries (although it is not actually the same as CBC, which is why I try to avoid the often-heard term "computer braille"). We at Duxbury sometimes call it "computer grade 0" on that account, which is why our dollar code to indicate extended direct braille is "cz". Anyway, I know that you all know the code -- including Stephen Phippen who raised the question, because he submitted an entire example (sp3812.brf) in that code! So, to avoid belaboring the issue, the following is the traditional 7-line braille character table, first using dot numbers, then generated directly using ASCII Braille:

On many popular braille note-taking devices, it is more convenient to generate alternatives for certain characters, namely: curly braces for both square brackets, accent grave for the at-sign, vertical bar for the backslash, and tilde for the caret. That variant is of course just as easily understood, though I tend to stay with the code as presented above because a vertical bar in an unformatted braille (BRU) file is usually the equivalent of a dollar sign in a print text file -- that is, it has a special control meaning.

1993-11-16 BM: Miscellaneous (bm3b16)

My silence during the last few weeks is due to a combination of factors, including vacation, a week-long conference, and numerous other hectic pursuits. Hopefully, I can now focus more consistently on UBC.

First, a few administrative-type matters:

1. I will be sending all of you a copy of the Australian braille Maths Code and the Australian braille Chemistry Code. The files are in ASCII braille form suitable for embossing. If this format is not convenient, let me know and I'll try and obtain a different format.

2. In JS3A19, Joe wrote, in connection with the Braille Research Centre: "I generally won't relay these items as broadcast messages, since many if not most of you already receive automatically, or can otherwise easily access, BRC materials." As I don't at this stage receive or know how to access the BRC materials, I would appreciate any information on how to do this.

3. On a somewhat tangential note, we here in Australia are starting to look at the question of "braille bills". I would like to study some of the US ones, such as the Texas Braille Bill. Are any of these available electronically, either via FTP on Internet or elsewhere? For that matter, is the ADA available in electronic form?

4. If there is to be a face-to-face meeting of our Committee in the first half of next year, we will probably have to start planning fairly soon. I, for one, feel that such a meeting would be useful, if only because it would give us all an opportunity to meet and learn about each other's personalities. While E-mail has many advantages, it can be a bit impersonal, particularly if, like me, you can't put a voice to the majority of the names with whom one is communicating (or at least corresponding). In any case, if things continue to progress as they have been, we may well have some substantive matters that we could discuss by March or April 1994.

5. Are the Minutes of the BANA meeting available yet, and (what is more to the point) is it possible for a non-BANA participant such as me to obtain a copy?

Turning now to the question of numbers, as summarised by Joe in JS3b10. Since my previous submission in which I discussed French Numbers in relation to the idea of cell density, I have been doing quite a lot of thinking about French, upper and lower numbers, and I have just about come to the conclusion that both for political and structural reasons, we should stick with the "traditional" upper numbers that are currently used in SEB. I recognise the cases that Joe cited in JS3b10, such as hex (and other non-decimal) numbers arranged for computation, and the designations of postal districts, but I don't believe that these case are numerous enough to warrant the general use of French numbers.

Joe's proposal of a dual system has advantages and disadvantages. On the positive side, it would give us a way of dealing with exceptional cases within the framework of UBC; it would also allow UBC to be used more completely on braille displays attached to computers. On the negative side, I see real problems with a dual system from a transcribing point of view. While a particular student may request that a book be transcribed using French numbers, a subsequent student may wish to read the same book but be unfamiliar with or bothered by French numbers, necessitating a re-translation and re- format (assuming, of course, that the braille version of the book had been produced on computer). Secondly, my experience has been that no matter how carefully one tries to define the situations in which a particular choice has to be made, there will always be transcribers who will find it difficult to make the choice, and there will always be situations that are not covered by the original prescription. Furthermore, I am not convinced that the cases requiring attention are particularly common. How often are hex numbers arranged for computation encountered, and by whom? Tying up 10 symbols that could otherwise be used as single-cell symbols seems to me to be unjustified. I already have misgivings about the extra reading space required for Mathematics in UBC, and the prospect of 10 fewer one-cell symbols adds to my misgivings.

As you can see, I think that the disadvantages of the dual system outweigh the advantages. I look forward to your comments, particularly any that refute my preceding arguments.

As Joe noted, we have been assuming that if we were to use lower numbers, we would continue to use the traditional punctuation signs. In a soon-to-follow offering, I will be suggesting that we change the sign for the full-stop (period). If we were to adopt this suggestion, added to those to change the question-mark and parentheses, we would have succeeded in changing quite a few punctuation signs, so perhaps we should not dismiss the idea completely yet. Of course, whether such a wholesale change would be accepted by the braille-using community is quite another matter.

1993-11-16 TC: Motion to adopt upper numbers (tc3b16)

I move the we adopt the Standard English Braille numbers as the primary numbers of the Unified Braille Code. This motion applies only to ordinary numbers written in ordinary literary and technical materials and does not rule out the use of other symbols to represent numbers in special circumstances such as subscripts, superscripts.

Discussion: We now have on the floor papers from several members dealing with numbers.

I have been using French numbers here for several months and feel that there may yet be a situation where they would be very useful. I hope that we won't dismiss this possibility at this time.

I note that numbers written in the lower position of the braille cell are used for subscripts in the UK and for some other special purposes. I am not proposing to dismiss lower numbers in all circumstances.

We are using traditional numbers in all of our countries. I do not see any possibility that we could change this practice, even if we thought other systems may be technically superior. I believe that it would be constructive to reaffirm our commitment to continuing this practice. We would then be free to consider special cases.

This motion is offered to facilitate the work of the Committee by promoting expression of consensus on an important decision where I believe there is general agreement so that we can continue our progress toward our goal of developing the Unified Braille Code.

I urge you to vote yes on this motion.

1993-11-17 BM: Second to TC's motion (bm3b17)

I would like to second Tim's motion in TC3B16. I agree with Tim that we should use upper numbers in the majority of cases. As I expressed in BM3B16, I'm not convinced that we need any other system at all, but, like Tim, I don't want to dismiss other possibilities at this stage.

I also agree that it would be constructive to reaffirm our commitment to continuing with upper numbers. While in theory we may not need to move for the retention of the status quo, there are psychological and political advantages in doing so that we should not overlook.

1993-11-17 JS: Miscellaneous administrative (response to bm3b16) (js3b17)

To join the Braille Research Center's forum, one needs only send a two-word message, viz.:


to the Internet address:

{email address removed}

An automatically-generated response will confirm that the sender is now on the BRCTR "list server" and will give further instructions as to obtaining other services, such as index browsing, by the same mechanism of sending one or more commands as a message to the list server. As with our UBC2 list, anything sent to the BRCTR forum will be automatically copied to all participants in the forum.

In a phone conversation earlier today, Tim said he should be able to access electronic archives that contain copies of the various braille bills; I too would be interested in electronic copies of these even though I probably have paper copies buried in some of my pile-files.

I agree that a regular meeting seems like a good idea, and so conferred with Darleen Bogart on that subject earlier today. I would like to be sure that we get a good chance to meet as a group unto ourselves, not just in the context of a large convention or series of other meetings with all the distractions and other commitments that usually involves, so I was skeptical at first of the obvious idea of meeting in late April in connection with the CTEVH convention, ICEB meeting, and BANA meeting. However, it does seem--not only for expense reasons but also as a matter of general convenience for all the members--that that would make a lot of sense. The concern about becoming "buried" in other matters would also be alleviated if we had our meeting concurrently with the BANA meeting (since there are no people who need to be at both), which occurs after CTEVH and ICEB. I project that a 3-day meeting would be useful, with (approximate) dates April 26th through 28th. Before we firm that up, I'd like to hear your thoughts on the matter.

I forgot to ask Darleen about the BANA minutes, but I would be surprised if they are ready yet, since the meeting occurred only about two weeks ago. I feel sure that they'll be freely available when ready. I was there for the part of the meeting that was on UBC-related subjects, the primary one being Emerson's report on the reader evaluation that he conducted. (The tables that Emerson developed are, I believe, obtainable through the BRCTR forum; they are also are in the BRCSL93.ZIP archive on our BBS.) I also gave a brief, informal summary of our state of progress.

1993-11-17 JS: Chairman's Report on Status of the Meeting (zs3b17)




By TC in file tc3b16: to retain the traditional (upper) number system, while not ruling out the possibility of French or lower numbers for special uses. Seconded: BM. Voting deadline: Dec. 1st. Votes recorded to date: for: BM, TC; against: none.






I would like to welcome the following persons, who have been added to our UBC2 list as observers:

1993-11-18 AN: The number problem (an3b18)

The time has arrived to come to serious grips with the problem of numbers. I want to thank Joe for giving us a very accurate and full history of our deliberations concerning the various number systems. He has also given us a very fair evaluation of the pros and cons of each of the three number systems under consideration -- traditional numbers, dropped numbers, and "French" numbers. I have carefully read and reread his recommendations and I must say at the outset that I am in total disagreement with his recommended solution.

His recommended solution amounts to a de facto commitment to the upper-number system as the basis for a uniform code -- the worst possible choice. In the past sixty or seventy years, this system has failed to meet the needs of technical requirements whenever it was tried. Mr. H. M. Taylor was, as far as I know, the first to attempt to devise a technical code for mathematics and chemistry based on upper numbers. It failed to achieve its purpose. Far from being a robust code, it was ineffective at all but the lowest levels of mathematics and chemistry.

The British claim that their math code is based on the upper-number system. However, to achieve anything like a viable code, they resorted to the use of dropped numbers in fractions, superscripts and subscripts to avoid the clumsiness and burdensome notation which would be imposed by the use of pure upper numbers. In effect, their code is based on a dual number system in which both upper and lower numbers are used. There are other codes which are related to the British math code. Some of these may have preceded the British math code, and some may have followed it. But they form a well-identified family because they use almost identical operation signs and other constructs. All of these codes employ a dual number system. Any code based on a dual number system is not a uniform code. I do not claim that we can avoid duality under every circumstance. However, we should explore every possibility to avoid it. We certainly should not embrace duality without so much as a sideways look, as we are doing. To embellish an insightful remark that Bruce made in his bm3b16 submission: "... no matter how carefully one tries to define the situations in which a particular choice has to be made between upper numbers, lower numbers, or French numbers, there will always be transcribers who will find it difficult to make the choice, and there will always be situations that are not coverthe by the original prescription."

BANA convened this committee for the purpose of creating a uniform code. Adopting the motion to use all three number systems as circumstances dictate, albeit with a preference to upper numbers, is a mindless violation of that charge. In the paper that Tim and I wrote which was the catalyst for this project, we said: "The dollar sign, for example, has one representation in the literary code, another in the Nemeth Code, and still another in the Computer Braille Code. The same is true for the percent sign, the square brackets, and others. ''' It is time to modernize the braille system." If the motion that has now been made and seconded carries, as in all likelihood it will, I can envision a document similar to ours in some future generation, provided that braille is still viable at that time, that says: "The upper numbers, for example, are used in situation A, the lower numbers are used in situation B, and the French numbers are used in situation C. It is time to modernize the braille system."

We should not choose a number system because it offers a better solution to some particular problem or other, like the alignment of hexadecimal numbers; we should choose that number system that solves all or most of the foreseeable problems in the best possible way. The number system that does that job is the dropped number system. If the British math code and those codes related to it would drop all their numbers, there would be no loss of ambiguity, and a giant step toward uniformity would be achieved. In the following example, I will use upper numbers and the plus sign contained in our current committee report, namely: dots 346:


In spite of the fact that the Grade-1 indicator at the beginning of this word asserts its mode as Grade 1, the Grade-1 indicator must be used three more times in the interior of this word because of the conflict between upper numbers and the letters from a to j. There is also the additional complication of the three numeric indicators. Using lower numbers in this same word, we would have:


This expression is not particularly advanced algebra. I hope that Tim finds enough "buckles and braces" in the upper-numbers version of the above example required to keep it afloat to convince him that that system needs some rehabilitation therapy before it can be used as a viable number system in a uniform braille code.

One of the most convoluted rules in the SEB codebook is the rule that deals with the letter sign. The principal culprit is the upper numbers which conflict with the letters from a to j. In the course of several years, BANA has promulgated several rules concerning the use of the letter sign and has subsequently reversed itself.

I have been presented with the argument that some choices must be made on the basis of political expediency. My perception is that this political expediency is more perceived than real, and that its proponents are engaged in a form of visceral reasoning designed to retain the status quo in that part of the braille universe in which they happen to reside. In the American Declaration of Independence, Thomas Jefferson said: "Prudence, indeed, ... hath shewn, that mankind are more disposed to suffer, while evils are sufferable, than to right themselves by abolishing the forms to which they are accustomed." Adapting this observation to the matter at hand, "mankind" is the braille-using community, and the "forms" are the upper numbers. But Surely, the braille-using community would respond positively to a well-reasoned and well-presented case for a change which could be shown to have significant long-term benefits based on the merits of the proposed change. The change to dropped numbers that I propose is not such a radical change. And, as Tim and I pointed out in our paper, many other much more radical changes, such as from New York Point to American Braille, from American Braille to English Braille, from Grade 1-1/2 to Grade 2, and from the Taylor Code to the Nemeth Code (in this country), have been made in the past without untoward consequences.

The day that this motion carries will be a sad day in the history of braille. The detractors of braille will have been vindicated in their claim that braille is too hard to teach and to learn and that it should be replaced by other access-to-print techniques such as tape recording, computers, and closed-circuit TV (where this is applicable) -- that in fact, braille is obsolete. We should be able to do better than that. As you probably have surmised by now, my vote is against Tim's motion and Bruce's second of that motion.

1993-11-18 TC: Let's go to London (tc3b18)

We can do better than meet in California concurrently with BANA.

We should choose a meeting place that would enhance expectation of progress in gaining international involvement and commitment to our project in addition to technical discussions within the Committee.

After sitting here for an hour, thinking of the pros and cons of meeting in various cities in North America and the various other countries represented in ICEB, I think London, England would be our best choice.

I have no doubt that we can come up with a good foundation for the Unified Braille Code. I'm confident we can get it accepted here and in Canada. I am equally confident that we need to keep the interest and strengthen the commitment of the UK to assure acceptance of a single braille code in all English speaking countries.

Don't kid yourselves, guys, we need strong support from Stephen Phippen and Bill Poole, and they in turn, need support of their constituents if they are to establish UBC in the UK.

So, I say let's go to London, invite observers at our meeting, hope they out number us two-to-one, and see if we can't win support by dint of hart work and honest effort.

I, for one, would be willing to stay on for a few days (at my own expense,) just to act humble and dispel the ugly American image.

1993-11-26 AN: Additional thoughts about numbers (an3b26)

One of the theoretical benefits to be gained by using upper numbers is freedom from the punctuation indicator. This is an illusory advantage. I can think of two situations in which the punctuation indicator will be required regardless of the number system we use. The first situation is that in which a punctuation mark occurs in a word position which can legally be occupied by a Grade-2 contraction. Thus, a colon in the middle of a word will need a punctuation indicator to distinguish it from the cc contraction, a period in the interior of a word will need the punctuation indicator to distinguish it from the dd contraction, etc. The second situation is that in which an isolated punctuation occurs. Thus a question mark between two spaces will require a punctuation indicator as will any other punctuation mark.

The sheer clumsiness and inefficiency entailed in the use of upper numbers with its recurring Grade-1 and numeric indicators have resulted in the British math code and its cognates resorting to a dual number system in which lower numbers are used in frequently occurring specified situations. If we use the upper number system, we will be faced with the same necessity. As soon as lower numbers are admitted into the system, a punctuation indicator will be required in situations in addition to those cited above, thus losing the theoretical advantage of being free from that necessity. In the British math code and its cognates there is a Grade-2 period and two Grade-1 periods. Thus, if the number 3.5 is followed by a period, the decimal point has one representation and the final period another. Furthermore, there is a Grade-2 comma and two Grade-1 commas. Thus if the number 1,000,000 is followed by a comma, the interior commas are represented by dot 3 and the final comma by dot 2. Furthermore, one of the Grade-1 commas cannot be distinguished from the apostrophe at the perceptual level, although context makes the distinction clear to a human being. It would be difficult to explain to a computer how to make this distinction. As soon as there are two of anything in a braille code, a set of rules will have to be promulgated for determining which choice to make, these rules will inevitably be incapable of covering all the situations that can arise, situations will inevitably arise in which the choice is doubtful in the mind of the transcriber, and a set of exceptions will inevitably be needed as experience points up the need.

To claim that upper numbers are customary and traditional neither imparts nor detracts from the intrinsic merit of that system. At best, such a claim can decide in favor of the customary system when a competing system shows no clear-cut advantages. This, however, is not the case we are considering. Between the upper-number and the dropped-number systems, the advantages of the dropped-number system outweigh those of the upper-number system by a wide margin.

I exhort my colleagues to listen to reason of the logical rather than of the visceral variety. Let us propose a code that is uniform, simple, straightforward, and free of the obstacles and impediments in the code we have been called upon to fix and free of the obfuscation of the kind I have described above.

1993-11-26 JS: Vote &c. on numbers (js3b26)

This is a "yes" vote on Tim's motion tc3b16, to retain the upper (traditional) numbers for use in literary context, without ruling out the use of one of the other number systems in technical context. My reasons were summarized in js3b10, with which this motion is quite consistent even though I am specifically in favor of French numbers rather than lower numbers as the secondary system for technical contexts. I have been preparing a motion that would accomplish the task of reserving the French digits, i.e. provisionally assigning those meanings in grade 1, which requires a slight rearrangement of our current provisional assignments, and had hoped to submit that motion with this vote. Alas, as usual there have been too many distractions this past week, and it will be at least later today, more likely another day or two, before I can get it ready.

Tim's motion, if it passes, would not actually change anything from the November 1992 report, which was based entirely on upper numbers, but would narrow the scope of our current deliberations to exclude systems based entirely on lower numbers or entirely on French numbers. It would reconfirm upper numbers as the primary system, and thus leave us, in my opinion, with three possibilities: (1) upper numbers only, (2) upper numbers with lower numbers secondarily, or (3) upper numbers with French numbers secondarily. (I do not recall that any member has actually proposed that upper, lower and French numbers all be used; I am going to assume, therefore, that we need not consider that possibility.)

Just as I would dislike a singular system based on lower numbers, and for many of the same reasons, I would dislike a dual system in which lower numbers were the secondary form. The case against lower numbers is summarized in the November 1992 report, and again in js3b10; some details are given in various memos now in our archives; for still further amplification one would have to recall our oral discussions over some 18 months, which of course were not attended by every current committee member. As the subject of lower numbers keeps coming up, some additional points and variations on points have crystallized in my mind even in the last few weeks--none of them in favor of lower numbers. The question I would like to ask is this: Is there a reason for me (or anyone) to write a paper going over all this again? Would that be beating a dead horse, or would it be helpful to our own decision-making to bring it all together? Beyond us, might such a paper serve as a basis to amplify the summary position now in our report? Do we believe that such an amplification would actually help people to make up their minds? I await your views with interest. In the meantime, I'll go on working on French numbers for secondary (grade 1) use, which I am ever more convinced can give us the best of both worlds: a system nearly as good as an all-French-number system for technical readers, yet one that does not burden general readers with any change at all.

1993-11-27 JS: Motion to reserve French digits (js3b27)

This memo is to fill in the details on the secondary level of a unified yet dual numbering system, where the current "upper" numbers are the primary system and are used exclusively in grade 2, but French numbers are used optionally in grade 1. This is consistent with Tim's motion tc3b16, and is pretty much in accord with my own recent writings on the subject. It bears mention, though, that I have been influenced by Bruce's observation on the burden to transcribers to make choices when options are presented, and for that reason among others have concluded that we should use French numbers more or less always in grade 1, with only one easily identified exception, as will be developed further below. This memo also presents a possibility for returning to the SEB question mark, and finally presents some general ideas about using "notational abbreviations" for commonly-occurring forms.

As things stand in our report, there are seventeen "strong" roots--that is, roots that are neither alphabetic nor lower signs. As roots, these are also single-character symbols, and they include all ten characters that we have come to call French digits. The list, with our current grade 1 assignments and with the associated French digits in brackets, is as follows (in traditional braille order):

Obviously, five of our provisional grade 1 assignments clash with the French digits. Coincidentally, one of those clashes is with our proposed new question mark, and so now may be the best time to consider changing that symbol back to its SEB form, even though the issues are not otherwise strongly related.

In the motion below, the reasons for symbol choices are given in brackets, as those must also appear in the report. Further arguments, examples &c. will be deferred to the discussion following the motion, to keep the motion itself as succinct as possible.

I move that we change the assignments in our report, and the supporting text appropriately, as follows:

1. (Part A.) Change the single-character symbol =8 (dots 236) from "opening quote" in grade 1 to a dual interpretation, depending on the surrounding symbols, as follows: (1) When that symbol in grade 1 is followed by a non-space and preceded by either a space, opening round parenthesis, opening square bracket, a hyphen, or a dash, then it is to be interpreted as an opening quote. (2) In all other circumstances in grade 1, it is to be interpreted as a question mark. (3) In grade 2, the contraction meaning "his" has priority wherever it applies; in all other circumstances the reading rules are the same as for grade 1. (Part B.) Assign the new symbols ^8 (45, 236) and .8 (46, 236) to mean opening quote and question mark, respectively, in both grades. [The prefixes suggest the position of the "dots" in the corresponding print sign, and also provide upper dots so that the composite symbol is physically unambiguous even if isolated.] (Part C.) The transcribing rule would be: use the one-cell symbol in preference to the two-cell symbol wherever it is unambiguous; otherwise use the two-cell symbol. (Part D.) Reassign the grade 1 meaning of : (156) to the digit 5.

2. Assign the grade 1 meaning of the symbol ! (2346) to the plus sign. [This is the integral sign in both British maths and Nemeth codes; thus an association with "summation" would be familiar to readers of those codes.] Reassign the grade 1 meaning of the symbol + to the digit 0.

3. Assign the meaning (in both grades) of @& (4, 12346) to ampersand. [That is the "emphasized" symbol in current SEB.] Reassign the grade 1 meaning of & (12346) to the fraction open. [The notion of "and" is naturally associated with fractions, as in "one and one-half".] Reassign the grade 1 meaning of < (126) to the digit 2.

4. Deassign, for now, the "keycap, termination of radical &c." grade 1 meaning associated with [ (246). Reassign the grade 1 meaning of [ to the digit 9.

5. Deassign, for now, all the sans serif indicators, among them "7 (5, 2356). Assign the meaning of "7 (in both grades) to the equals sign. [This is based on the British maths symbol, with dot 5 instead of 56 because the latter would clash with our single-symbol grade 1 indicator.] Reassign the grade 1 meaning of the symbol = to vertical line. [The rationale for such an assignment is obvious]. Reassign the grade 1 meaning of the symbol \ to the digit 8.

6. Assign the grade 1 meanings for the remaining five French digits whose symbols are currently unassigned.

7. Adopt the following transcription rule for digits: When in grade 2, the customary (upper) digits are to be used; when in grade 1, the French digits are to be used, except in the case where the reason for using grade 1 is for teaching grade 2.


When the foregoing reassignments have been made, the table of seventeen "strong" single-character symbols would be as follows:

There would be a new assignment for one of the lower roots, viz.: and finally there would be several new or changed 2-cell symbols:

I will organize the remaining discussion on this motion into four main parts: A. An outline of the main positive reasons for French numbers in general. B. Replies to some of the objections that are sure to come up. C. The elements of the motion. D. Some examples and a look ahead. In this I will be going over again some (but not all!) of the ground covered in my own earlier memos, mainly jsm19 (in archive xx36), js3815, js3818, and js3b10, as well as expressions by others on the subject, in an effort to make this memo reasonably self-contained.

A. An outline of the main positive reasons for French numbers in general: (1) They contain upper dots, as is consistent with their level of importance as text elements. That is: in general, digits are clearly as important as letters, and in braille tradition letters and thus most words are put in the upper position while punctuation marks, as secondary elements, are in the "down out of the way" lower position. We can understand why Louis Braille, who had to deal with accented letters and thus an effectively larger alphabet, did not arrive at the "French" digits, as we call them. However, even after deciding to use the indicator approach that we still use, he could have used either lower or upper digits. He chose upper digits. Now I do not presume to know for sure why he made that choice (and I would be very interested to hear from anyone who might know more about that early history), but I certainly agree with it both on the grounds of style, that is because numbers are more like letters than punctuation marks, and on the grounds that overall it is more efficient to indicate following letters than the more frequent punctuation marks. (2) French digits are strong, unambiguous characters that are easily and accurately identifiable no matter how isolated. This again is consistent with the importance of numbers. That property is also present with the other number forms if the number sign is always required, but as we all know there will be at least some cases where space considerations will drive the code towards omission of that indicator. Then, if you ask your boss how big your monthly raise is and he hands back a slip with the answer in unindicated upper or lower numbers, you might not know whether he said "218" or "bah". More seriously, that issue could easily affect either transcribing choices, readability, or both when faced with arrays that contain numbers, letters, punctuation marks and mixtures of the three. (3) On the subject of transcribing choices, any system that calls for an indicator to be used some times and not others is inherently dual, with all that implies for transcribers. With French numbers, once you have made the decision to use grade 1 (which decision we have yet to discuss; see below), and if you are not using grade 1 for the purpose of instructing in grade 2 (which the transcriber, or user of a translating program, would certainly know), then you would use French numbers, and there would never be any question of an indicator. (4) In fact, using French numbers, an indicator is never needed, neither before nor after a number; digits are written simply as the symbols that they are, without regard to context, which is certainly the ultimate in simplicity. (5) French digits are used in British Computer Notation and a number of other European computer codes (although the choices for the digit 0 vary), and so are consistent with established international usage (though admittedly less so than the upper numbers, which is one reason why the upper numbers should remain primary). (6) Because of the absence of indicators, French numbers are clearly the most efficient system in grade 1, in terms of the linear distance (number of cells) required to express numbers generally. Grade 1 is, presumably, the grade that will most likely be used for exceptionally dense and lengthy technical expressions, and that is precisely where technical readers have expressed greatest concerns about efficiency. Yet this efficiency is achieved with zero impact on the reader of general literature, which is generally in grade 2. (7) Finally, to reserve the French digits is to leave the best options open for the future generation of braille readers, who may choose for themselves to stay with traditional numbers or to switch, partially or fully, to French numbers in the course of time.

B. Replies to some of the objections that are sure to come up: There are three main objections that I have heard: that any duality in number system is inconsistent with a unified code; that French numbers are "hard to read"; and that the ten single-character symbols taken up are, or may be, more needed for other purposes.

B1. On duality: A single representation is better than a dual one, granted. But before we get too intent on the duality of an upper/French number system, we should reflect on the fact that we already have a great many dualities in SEB and in braille generally--even in numbers, where now there are three competing forms so at least reducing that to two would be a step in the right direction. Examples of SEB dualities certainly abound in the area of applying the contraction rules: Should we use "be" or "er" in "Bering"? Should the "ed" be used in "reduce"? And so on, and on. Perhaps a more critical duality arises when there are two grades, as in current English Braille and as we have been directed to continue. For then there is inevitably the question: When should the transcriber use one grade vs. the other? We have been aware of these kinds of issues, and discussed them in section 1.3 of our report. To following paragraph is directly extracted from that section:

Reading Rules: The committee felt that a braille code should be considered primarily from the point of view of translating braille to print rather than that of translating print to braille. That is because we want to be sure that the braille reader, or equivalently the person who writes originally in braille, can determine unambiguously how the corresponding print is spelled and punctuated. Going the other way, it is less critical that there be only one braille representation of a given print text, even though it is of course desirable that there be only one. For example, the print text "ABC" can be represented in braille either as ,,abc or as ,a,b,c. It may be desirable to prefer one of these representations over the other in a given case, which is a matter for the transcribing rules; it is more important, however, that the reading rules assure that only one print text is precisely defined by either braille representation.

In short, there are definitely transcribing, i.e. print-to-braille, dualities in our current systems, and some of those will inevitably remain in UBC. Thus some duality does not in itself mean that a code is not a single unified system. What is most important is that the duality does not create ambiguity in the braille-to-print direction (and an upper/French number system would not). That ensures that, even if a transcriber (or a program) makes a poor choice as to which representation to use, the text remains clearly readable even if not optimally so. Of course it is also important to devise transcribing rules that are practical, effective, and as clear as possible, so that good choices are made in the vast majority of cases. We are not yet at the stage of fully nailing down such rules for grade 1 vs. grade 2, for example, though we must eventually do so--and I'll bet it won't be easy. But, following the principle of divide-and-conquer, I think we are absolutely right to postpone deep consideration of that subject until we have more fully decided, based on the more primary needs of braille users, just what is in grade 1 and grade 2.

Finally, we must consider whether the reasons for a duality are strong enough to justify the inevitable extra complexity thereby introduced into the system. Here we have a situation where, if we were to insist on a single representation, we would be sure to leave one or another large population deeply dissatisfied. For if on the one hand we chose on technical grounds alone--that is, if we ignored current readers and braille tradition and acted as if we were rediscovering braille from the beginning--we would surely choose a system where each digit had its own single-character representation not dependent on an indicator. In other words, we would choose French numbers, or some equivalent. We would then find many general readers, who seldom read technical material and who like the numbers as they are, resenting the time required to reacclimate to a new set of numbers, all for benefits that would accrue mostly to other people. If on the other hand we choose on the basis of braille tradition and current reader preferences alone, we would obviously choose just upper numbers. We would then find many technical readers upset that their expressed needs had not been met, and future generations stuck with a system less than ideally suited for technical purposes. With a dual system, both those dual needs are met, with negligible inconvenience to either group and within a system that is still uniform overall. That benefit easily outweighs any added complexity, which itself is actually very slight. For the set of symbols involved is the digits, an easily identified group in itself, and the duality involved is simply the addition of a dot (except for the zero, which is equally simple). Thus no one will take any significant time to learn how the duality works.

B2. On the difficulty of reading French numbers: A number of persons have reported an initial slowdown when first encountering numbers with dot 6 added. That phenomenon in itself is not surprising, nor is it important in the long run if it gradually disappears with acclimation. One way to determine whether it disappears or persists would be to conduct experiments. I would encourage any such experiments, whether of the informal introspective variety or the more formal kind on significant populations, and if anyone has any data on the question I would be glad to hear it. (Tim, for example, reports rapid acclimation to French numbers.) But, even if we don't have enough such data, I do think that we can usefully apply some collective sense and simple reasoning.

It seems to be a matter of general agreement that, in experienced readers, braille cells are read by the "fingerful", that is that cell patterns are experienced in gestalt fashion, as whole shapes rather than as a series of dots. That fact in itself would explain why there is an initial slowdown when a dot 6 is added, because the "shape" changes. In other words, while the simplicity of adding a single dot is obviously a mnemonic aid while first reading French numbers, it does not completely overcome the fact that it is an unfamiliar shape; one is, at first, constantly resolving the shape mentally in two steps, such as "the e-shape plus dot 6 must be 5".

That explanation for the initial slowdown is the one that seems to come up most often and that coincides with the way that the senses work generally (and I trust Emerson will correct me if I have misstated the psychological principle). If that is indeed the explanation, then the same principle clearly predicts that with experience the "e-shape plus dot 6" will gradually become recognized simply as "5", that is as a unit just as all other braille shapes already have, and so the slowdown will disappear. In fact, since there is one less shape involved, because there is no number sign needed, the eventual reading speed should be higher than with upper or dropped numbers.

The only other explanation for the slowdown that I have heard is that cells of higher dot density are inherently harder to read. That is an interesting hypothesis, and if it is correct we would have to be more concerned because of course there would be no extinguishing effect. However, I cannot for the life of me see how it can be correct and square with what people, both teachers and readers, tell me of their experiences. Braille readers are taught to read at a steady speed, and by all accounts that effect is achieved after the practice necessary to any learning experience. That is what one would expect from the "fingerful" concept of the preceding paragraph. But if more dots means permanently slower reading, it would regularly take longer to read a "y" than an "n" because of the extra dot 6, and a lot longer to read an "n" than a "c", and so on. If such a thing is true, it does not seem to be common experience, and so I think a lot more data would be needed to build a convincing case. And, to make one final point on this theme: if the number of dots determines the reading speed, rather than the number of cells, French numbers still come out ahead as long as the number of nonzero digits is fewer than four.

B3. On the possible other uses for the ten single-character symbols used for the French digits: That would certainly be an issue, if there were enough other print symbols and indicators that we felt were important enough to need single-cell symbols. It would be awkward, for example, to have 2-cell subscript or superscript indicators, or fraction indicators. But we have already provided for those. In any case, when judging importance, which is mostly a matter of frequency, what is more important than numbers, especially in technical material? Certainly integral signs and square root signs occur often in classical mathematics, as do slashes in computer programs, but do they occur more often than numbers overall? We must keep in mind that, because of its universal scope, UBC cannot hope to be as efficient in each sub-area a code designed specifically for that area. (Since I expanded that idea rather fully only a month ago, in js3a26, I'll give it a rest here.)

C. The elements of the motion: This is to go over some specific issues and will parallel the numbered paragraphs of the motion.

C1. The net effect of the changes related to the opening quote and the question mark would be to virtually restore current SEB usage, except that now we would have something definitive to do in unusual cases where question marks or opening quote marks were strangely placed, e.g. isolated, placed amidst unspaced letters, or what not. The transcribing rule would be quite easy to apply, both for humans and for programs. Also, as a potentially useful side-effect, the symbol : (156) would be freed for potential use as an end-word contraction in grade 2. (The "wh" is not particularly useful at the end of a word, which is why we chose it for the question mark.) There are a number of good arguments for the "es", for example--but that is off our subject, and up to the contraction committee anyway.

C2. A one-cell symbol for plus sign, as provided here, is in my opinion necessary for parallelism with the minus sign, if the minus sign remains single-cell. (In our current report, the minus sign and hyphen are not differentiated.) This need not prejudice us in a later discussion on the minus sign, and if we do decide to make the minus a two-cell symbol, such as "- (5, 36), then I would be in favor of changing the plus sign to a two-cell symbol, such as "6 (5, 235), also.

C3. While ampersand occurs commonly enough in some technical contexts, e.g. the double ampersand used for logical conjunction in the C programming language and the ampersand commonly used to introduce entity references in SGML, I can't think of any situation where their usage is so dense that a two-cell symbol would constitute a legitimate burden. It seems more important to optimize for the treatment of fractions, partly because three indicators are involved in all, and partly because they occur so routinely in everday situations, such as in recipes.

C4. Naturally we eventually have to provide for keycap and radical termination indicators, but at the moment it will do no harm to set them aside. When we come to them, two-cell symbols seem to me to be adequate in terms of overall frequency; perhaps also we could consider using the fraction terminator to terminate radicals.

C5. Again, while sans serif certainly occurs as a meaningful distinguishing typeform now and again, that is uncommon enough that we can safely set the issue aside for purposes of this motion. Our general structure provides for a rich set of typeform indicators. We can always swap the "sans serif" indicator group with the group associated with an even less common typeform if we feel so inclined, and we also have transcriber-defined typeform indicators to relieve any worry that something might come up that we haven't covered in that area. The assignment of a two-cell symbol to the equals sign might raise questions, but we should remember that both current math codes use two-cell symbols that are further expanded by required spaces, yet no one seems worried that they are too long. The assignment of "7 (5, 2356) to "equals" would obviously be consistent with assignment of "8 (5, 236) to the "multiplied by" (times or cross-multiplication symbol) and "4 (5, 256) to the "divided by" symbol. I would favor such assignments, though that is a subject for later in our work.

C6. This is self-explanatory.

C7. As already mentioned, transcribers would normally be aware when a grade transcription is for purposes of teaching grade 2 and might already be doing other special things, such as using just a few introductory contractions, so implementation of the exception should not be a problem. Likewise, it will be easy enough to provide an option in transcribing programs, so that upper numbers can be used in grade 1 if desired, though French numbers would be the default.

D. Some examples and a look ahead: Until further mention, the assumed context is grade 1. That is, we assume that an entire work is being transcribed in grade 1, or that a grade 1 passage has been introduced by a grade 1 passage indicator (56, 56, 56). Alternatively, of course, grade 1 word (56, 56) indicators or single symbol indicators (56) could be used appropriately.

The first example would be the one introduced by Stephen Phippen in sp3b04, i.e. in words: x subscript 2 all cubed plus y. Now in our current report we have explicitly left open the question of whether the grade 1 symbol 7 (2356) is to act as a "closer", which goes with a British maths treatment of indices, or as a "base line indicator", which goes with a Nemeth treatment. In order not to prejudice that question, which also must come up later but we need not decide here, the example using French numbers can be presented both ways, and in the order just mentioned:
(Note: while the second treatment is slightly shorter in this example, the opposite is true in others, so no general conclusions should be drawn; anyway that is a subject for another time.)

If we expand the preceding example so that x has the subscript "2,5" (as when x is from the second row, fifth column of a matrix), then we would have:

If we further expand even on that, so the exponent is not just 3 but itself a subscripted expression, say k sub 18 all plus 7, we would have:

Looking at these examples, I can't help but think of John Gardner's DotsPlus system. Many of you know about DotsPlus, but in case you don't, one of its most notable characteristics is that it avoids spatial relationship indicators, such as our subscript and exponent indicators, by simply following the same spatial conventions in braille as in print. Thus exponents are slightly up and subscripts slightly down, for instance. (DotsPlus also permits a raised-line image of a print sign and its braille equivalent to be used interchangeably. That characteristic makes it very interesting, right now, as a possible tool for persons already familiar with print signs to learn braille by a process of gradual substitution. It does not mean, though, that DotsPlus documents cannot be entirely braille.) Now it is obvious that most current braille writing mechanisms, starting with the slate and right up through braille press plate embossers, are not practical for slightly up and down placements. Thus, for UBC to be practical in current terms, we need to provide for spatial relationship indicators, as indeed we are. But, will it always be true that free spatial placement of braille cells will be impractical with inexpensive, portable writing mechanisms? "Always" is a long time; I sure would not want to stake my reputation, much less the future of braille, on such an assumption. (I'm already able to carry, in my briefcase, a computer that is considerably more powerful than one that, back when I started working with computers just over 30 years ago, entirely occupied a very large room.) Then, if it may one day be possible to write subscripts and such spatially, and if even now some specially produced materials are beginning to appear in that form, it becomes more obvious how important it will be to have strong, physically unambiguous digits such as provided by the French numbers. Neither upper nor lower numbers, without the cumbersome indicator, provides that characteristic.

Turning now to a case considerably more familiar to most people, consider "three and one-half" written as a mixed number, with the one-half arranged vertically and right next to the 3. In French numbers, it could be written:
(See below for commentary on grade 2 treatment of this example.)

If that same example were written in print linearly, i.e. with a hyphen between the whole number and the fraction and a slash between the numerator and denominator, we would write:

To include an example from a computer program, the following is a line from "hook.c", a sample program distributed with the widely used PROCOMM PLUS communications program (the full text of which you therefore probably already have). I presume that it is readable without further explanation:
unsigned char textmode2 _/@* input mode +3,aspect *3word @*_/

But what about grade 2? If we are in grade 2 and encounter the first mixed number case given above, we could get away with writing:
because of the rule (remember?) that "grade 1 word" is implied by numeric mode. However, that rule has proved controversial, and we may or may not choose to keep it, and anyway we may not like to use both upper and French numbers in the very same expression. Of course we could always excurse into grade 1:
But, maybe we don't like that either, because we really want to stay with upper numbers and an essentially grade 2 treatment. Well, we could write something like:
or, if we stay with the "numbers imply grade 1" rule, perhaps:

(As you can see, we do have a number of important decisions yet to make, even after numbers.) Let us say, to keep with this example, that we aren't really happy with any of the grade 2 treatments presented above. Are we stuck? No. This is where the ability of our system to introduce useful "notational abbreviations" (I like that term) comes into play. Let us say, for example, that we later defined the symbol #& (3456, 12346) to be an indicator meaning "simple numeric fraction", and defined its scope to be similar to regular numbers but also to span the fraction line indicator. (To be clear, this is not part of this motion; I'm just musing.) Then, we could write:
or maybe even adopt the old "implied numerator 1" concept:
and now our recipes would look a lot better. We could do similar things with simple numeric subscripts and superscripts, so that the familiar formula for water would come out in grade 2 as
with no concern that the O would be interpreted at the subscript level.

In summary, French numbers give us unsurpassed efficiency and clarity in the grade 1 treatment of technical expressions, no matter how complicated. And in grade 2 with upper numbers, simple things do remain simple, slightly more complex things can be made as simple as we feel necessary, and for really complex cases, to which grade 2 was never meant to apply, we can always use grade 1.

1993-11-30 RS: Vote on tc3b16 (rs3b30)

This is to vote in favour of the motion TC3B16.

In response to your query, Joe, in JS3B26, A summary of points made regarding the advantages and disadvantages of both lower and French numbers would help to clarify a stance on this topic.


1993-11-30 EF: Motions (ef3b30)

I cast an affirmative vote for Joe's motion to continue the use of the number sign and upper cell numbers while in the Grade II Mode, and French numbers while in the Grade I Mode. Any scheme for writing numbers will be attended by some problems, but of the schemes currently under consideration, the scheme set forth in Joe's motion leaves fewer problems to be solved than the others.

This scheme has another practical advantage. Most of the objections to the Committee's first draft of the Unified Braille Code were raised by a vociferous minority whose members read only text for which the current literary code is adequate. I think I could summarize their position by saying "you can do any damned thing you want to as long as you don't change the braille I'm used to reading." There will have to be a few changes in the braille they are used to reading, but if we do not change the way numbers are written, the magnitude of the change will be considerably smaller.

In regard to this vociferous minority, there is another fact we need to keep in mind. Although the minority in question has been very vociferous, it is also very small. The opinions of the majority, who use braille for purposes beyond the reading of novels, have ranged from neutral to quite supportive. We should not neglect the opinions of the majority.

Joe's statement that contained the motion concerning numbers also contained a number of recommendations concerning the meanings to be assigned to various dot configurations. These recommendations appear to be included in the motion, but I am not sure they should be. They all seem reasonable to me, but I should think we would want to discuss them for a while before we make a motion concerning them. Joe, if you will accept a friendly amendment, I propose that we vote on the motion concerning numbers now, and save the specific assignment of meanings for a later motion.

In regard to the place where our next face-to-face meeting should be, I agree with Tim that holding it in London would be a convincing statement that the project is, in fact, an international effort. I am at the Braille Research Center, and the file containing Tim's comment concerning where to meet is on my computer at home. As I remember, he expressed his preference as a motion, although the authenticity of what I remember does not amount to much. In any case, if there is simply not enough money to pay for a meeting in London, I am reluctant to vote for an impossibility.

1993-12-01 JS: Motions on French digits (js3c01)

I appreciate the support expressed by Emerson in ef3b30; I am also sympathetic with the point that perhaps it is a bit too much to deal with all those dot assignments at the same time as the general concept of using French numbers to supplement upper numbers. (My intent was to be sure that any such motion present at least one plan for dealing with all the detailed ramifications, in accord with our general rule that motions must be sufficiently specific. Most of the particular assignments discussed are not, to my mind, essential to the main point.) In a telephone discussion with Emerson a short while ago, we have agreed that probably the best way to construct this would be as two separate motions:

1. A motion implied by Emerson in ef3b30, identified and seconded herein by me: that in principle French numbers be adopted for use in grade 1 while the upper numbers continue to be used in grade 2.

2. The original motion js3b27, seconded by Emerson, which will obviously remain in suspense while motion ef3b30 is discussed.

With the vote received from Emerson on motion tc3b16, that motion has technically been decided a day early, but I'll give it until tomorrow before issuing the required status report, on which the two above motions will also appear.

I did not take Tim's exhortation to meet in London (in tc3b18) as an actual motion, by the way, in accord with our general rule that motions be introduced by words that clearly identify that fact, preferably "I move ...". Still, I'm sympathetic with his general thought, echoed by Emerson, that London may be a more central location--logically, if perhaps not physically. Obviously, we (and more to the point our parent committee) would have to address the sticky question of how the overall funding for such a location would compare with California, and likewise how the local arrangements would get put in place. I'll try to talk with Darleen about all this in the next few days.

Also in the next few days, I hope to put together a summary paper on lower numbers, as requested by Raeleen Smith in response to my offer to do that. Most of it will undoubtedly be restatement of ideas already expressed, but I do have a few new thoughts or variations that may be of use. Anyway, I agree that we will probably need new words to put into our report, expanding upon those already in the appendix on alternatives.

An observer has expressed concern that motion tc3b16 seemed to have been introduced prematurely, and possibly had the effect of cutting off useful debate on the subject of numbers. I don't actually agree, but I can understand how that impression might arise if one had joined us fairly recently and was not aware of the great amount of deliberation that had already taken place even before the grade 1 indicator issue was settled and numbers came again into the foreground of our attention. Much of that deliberation can be found in our archives, starting with the work of the original committee from archive xx26 onwards, and the expanded committee from xx35 onwards. If an observer has access to our BBS, any of these archives can be downloaded, although anyone with a slower modem may find the whole group a bit much. (Even though these archives are compressed, the xx series is now just under a megabyte, and everything on the BBS is just over 1.5 megabytes.) So, if any observer feels that it is impractical to download the history, please let me know your address and I'll mail you disks (1.44M DOS format unless you request something else) with the archives to date.

1993-12-04 JS: Chairman's Report on Status of the Meeting (zs3c04)


By TC in file tc3b16: to retain the traditional (upper) number system, while not ruling out the possibility of French or lower numbers for special uses. Seconded: BM. Voting deadline: Dec. 1st. Votes for: BM, TC, JS, RS, EF, SP; against: AN. The motion is adopted.


By EF in file ef3b30 (see also js3c01): to establish in principle French numbers for use as a secondary system, in grade 1. Seconded: JS. Voting deadline: Jan. 4, 1994. Votes recorded to date: for: EF, JS; against: none.


By JS in file js3b27 (see also js3c01): to fix the details implied by French numbers used as a secondary system, in grade 1. Seconded: EF.




The motion just passed, tc3b16, has no immediate effect on our report, which is already based on upper numbers. However, it does leave open the possibility of a secondary numbering system. One such system is proposed by the motion now before us.

I have allotted an unusually long deliberation period to the motion on French numbers, first to allay any fears that we may be moving too fast, and secondly to accommodate both the holiday period and an opportunity for observers to introduce themselves and put forth their own thoughts on all relevant matters (not just pending motions). For that purpose, the week of Sunday, December 12th through Saturday, December 18th, will be "observer week". During that week, any and all submissions from observers through our list server, that is the Internet address
{email address removed}
will be welcome. By contrast, I would ask the regular members to remain "off the air" during that week, and just listen. That timing should, I think, give everyone time to prepare what they want to say and say it, and still give us time to act thoughtfully on the pending motion.

I realize I am overdue to edit the November 1992 report to reflect the motions that have already passed. There still isn't much that has actually changed, but for your information the adopted motions, prior to this, were reported in status reports zs3906, zs3922, and zs3a29. Their net effect is to cause the term "literal mode" to be replaced by "grade 1", and to delete the recommendation to remove the final-letter contractions beginning with dots 56.

Raeleen Smith's preferred E-mail address has changed. I would like to welcome Priscilla Harris and Clive Lansink as observers (the latter by indirect means and so not included on the server list). Also, I will be adding Phyllis Campana as soon as I get the address right, probably by Monday or Tuesday next. Our server list now reads as follows:

The projected meeting site for early next year remains California, primarily on logistics grounds, with the London site favored for another meeting late that year or early the following year. Details to follow.

1993-12-09 AN: Response to Joe's motion concerning "French" numbers (an3c09)

I have carefully read Joe's motion and attendant memo concerning "French" numbers in js3b27. My reaction is almost completely negative. His presentation contains so much controvertial material at all levels, that it is not possible to give a response which addressess all the points contained therein. Therefore, I will content myself by addressing what I consider to be the major points.

Uniformity and Duality: In his very first sentence, Joe uses the phrase: "a unified yet dual numbering system." My response: No code can be uniform that features a dual number system just as no object can be black when it is white. I have yet to learn from any colleague on this committee what his or her conception is of a uniform braille code, even though I have presented my view on this matter and have invited the rest of us to do so as well in an3a04. In the paper that Tim and I wrote and which was the catalyst for this project, we pointed to a number of dualities and even threefold multiplicities which were causing confusion among school children and adults alike, and calling attention to these dualities played a decisive role in BANA's decision to launch this project. Now it is proposed to ignore the lessons of the past and deliberately to build duality into the braille code we are developing. School children will be back to where they are now with one set of numbers for history, English, and social studies and another set of numbers for math and science. But now it will be worse; where there used to be just one set of (dropped) numbers in a math book, now there will be two sets. Our committee was convened by BANA to put an end to that situation. A proclamation that a code can be uniform and at the same time feature a dual number system does not make that statement true no matter how often, how loudly, how fervently, or by how many people it is intoned. That uniformity and duality are consistent is fiction.

In order to support the duality of the two number systems, Joe found it necessary to introduce additional dualities among the punctuation marks. We have hardly begun to construct a braille code. How many more dualities will be needed? Joe proposes the criterion of ambiguity to be applied in deciding which of two representations should be used. Who decides what is ambiguous, and how do you get a computer to make that decision? If there is one representation that resolves ambiguity, why not use that representation uniformly and avoid another duality?

Grade 1 vs. Grade 2: Joe continues by proposing: "the current 'upper' numbers are the primary system and are used exclusively in Grade 2, but French numbers are used optionally in Grade 1." What does this mean? I thought I finally understood the distinction between Grade 1 and Grade 2, from the point of view of our committee. Upon reading this statement, I find that I do not. I herewith submit my understanding of what is Grade 1 and what is Grade 2 taking into account the committee's motion on that subject:

A Grade-1 document contains no SEB contractions. Hard-copy Grade-1 documents are rare. There may be some at the kindergarten or first-grade level as an auxiliary in the process of teaching braille to young children. For personal use, a document may be generated on an embosser from a file captured from a database, bulletin board or similar remote source, or it may be generated from a file on an E-text disk. A file may also be generated by a back-translator operating on a Grade 2 file to produce a file that can be read on a screen or printed out at a remote location for used by a sighted person. Such files are variously designated as Grade-0, computer code, or machine braille code. They have the common characteristic of containing no contractions so that, in this respect, they behave like traditional Grade-1 documents. Grade-1 punctuations and composition signs are those of SEB, except as they may have been reassigned or augmented by our committee. Any notational symbols or indicators that our committee may have devised are symbols or indicators belonging to Grade 1. For example, dots 345, the end-fraction indicator that our committee has devised is an indicator belonging to Grade 1. Digits are always symbols belonging to Grade 1 whether they are represented as upper numbers, dropped numbers, or "French" numbers. If digits are represented as upper numbers, the numeric indicator is required to distinguish the digits from letters or letter strings. Additionally, even in a Grade-1 document, the Grade-1 indicator, dots 56, will be required to mark places in the interior of a word where digits end and letters from a to j begin. Similarly, the numeric indicator, dots 3456, will be required in the interior of a word to mark the transition from letters to digits. If digits are represented as dropped numbers, the numeric indicator is not required but may be desirable for purposes of orientation. If digits are represented as "French" numbers, the numeric indicator is not required. In a Grade-1 document, the Grade-1 indicator, dots 56, is required only with upper numbers as explained above.

A Grade-2 document contains all the standard contractions of SEB except as our committee may have altered them or the rules for their use. Almost all hardcopy braille documents are in Grade 2. In a Grade-2 document, there are "islands" of Grade-1 text. These may be words or phrases, either embedded within the host text or displayed, in which the braille symbols are not to be interpreted as SEB contractions. In documents of a technical nature, such words and phrases may be more numerous than in non-technical documents, but for the most part, Grade-2 text with its contractions predominates. Such Grade-1 "islands" require the Grade-1 indicator, dots 56, or the numeric indicator, dots 3456, in accordance with the rules that our committee has devised. If digits are represented as upper numbers, the numeric indicator is required to distinguish them from letters, letter strings, alphabetic whole-word contractions, or short-form words. Grade-1 indicators or numeric indicators may be required in the interior of a word for the reasons I have mentioned in the case of a Grade-1 document. If digits are represented as dropped numbers, the numeric indicator is required when they could otherwise be taken as lower-sign whole words like "be," "enough," "were," "his," "in," or "was." The numeric indicator may also be desirable for purposes of orientation. Neither the Grade-1 indicator nor the numeric indicator would ever be required in the interior of a word. If digits are represented as "French" numbers, the numeric indicator is not required; however, the Grade-1 indicator, dots 56, is required to prevent interpreting the "French" digits as SEB contractions.

I repeat: What does Joe's motion mean? Since Grade-1 documents are rare, I presume that he is talking about Grade-2 documents. An upper number is a Grade-1 word -- one of the Grade-1 "islands" in an otherwise Grade-2 document -- requiring a numeric indicator that tells us so. A "French" number is also a Grade-1 word -- another such "island" -- and must be introduced by the Grade-1 indicator to tell us so. If my analysis is incorrect, I need enlightenment.

Furthermore, at whose option do we use "French" numbers? Early in his or her career, a transcriber is imbued with the cardinal principle that uniform transcription is required, so that text transcribed by one group or at one location will contain the same braille rendition as a text transcribed by another group at another location. I can, with confidence, order any book from the Braille Book Bank maintained by the National Braille Association (NBA), knowing that I will encounter the same braille forms no matter where or by whom the book was transcribed. If transcribers are given options as to which of the two number systems to use, this would no longer be possible.

Notational Abbreviations: As if duality were not sufficiently confusing to the braille reader and to the transcriber, Joe now proposes to implement notational abbreviations. Some forms of notational abbreviations are sanctioned in SEB. For example, in Section 23 of "English Braille, American Edition," it is allowed to condense references by placing p (for page), v (for volume, and ch (for chapter) before the number sign, and it is allowed to replace Roman numerals by Arabic numerals. This causes confusion and trouble. As a professor who had to publish papers from time to time and to include correct citations of other works, I had to keep a card on file showing the correct method for submitting such citations in print; following the braille version would have branded me as semiliterate. How would the braille reader know that he is encountering a notational abbreviation that the transcriber has supplied? Only by concluding that no other interpretation of the braille characters makes any sense. While notational abbreviations are suitable for personal use, and everyone uses some form of them for that purpose, there is, in my opinion, no place for notational abbreviations in a standard braille code.

Numbers -- Individual Representation vs. an Indicator: Joe maintains that if we were rediscovering braille from the beginning, we would surely choose a system where each digit had its own single-character representation. Now if anyone had the opportunity of discovering braille from the beginning, it would be Louis Braille himself. But he did not do what Joe proposes that we would surely do; he employed the mechanism of an indicator instead. To set aside ten "strong" characters for use as "French" numbers when such numbers are to be used as a secondary and optional set is a resource extravagance we simply cannot afford. Nevertheless, Joe undertakes to rearrange the "braille furniture" so as to clear the ten "strong" symbols that are needed for the "French" numbers. In so doing, it was necessary to make some strange reassignments to basic symbols. For example, the new plus sign would now be dots 2346, an association unknown in any current code. Joe says that this sign can be associated with the integral sign, which represents the limit of a summation process, which is the same both in the British and in the Nemeth Code. This is just hype. Try telling that to a seven-year-old about to learn addition and being introduced to the plus sign.

Need for Care in Symbol Assignment: Making symbol assignments is not a trivial matter. Among other important principles in making symbol assignments, the preservation of symmetry is an important goal. In reassigning Braille symbols, Joe has destroyed the symmetry that we had for the begin-fraction and end-fraction indicators. In the Committee II report of last fall, the begin-fraction indicator was dots 126 and the end-fraction indicator was dots 345. Dots 345 has been retained, but dots 126 has not, thereby destroying a symetric combination of indicators. Symmetry is an important feature of a code. It helps people learn and remember the large number of symbols that are required in a technical presentation. All codes have attempted to preserve symmetry where possible. The British have even adopted the pair { and o for "less than" and "greater than" in spite of the fact that one of the members of the pair is the letter o -- a daring step. Another important assignment principle is to keep together related symbols in families. It is not prudent to make assignments quickly, grabbing the first likely symbol still available, and assigning to it the meaning of the graphic or indicator currently clamoring for attention. Assigning meanings to braille symbols is akin to playing a chess game. We must look ahead to future requirements and attempt to make assignments in such a way as to preserve symmetry and family relationships among graphic symbols and indicators. If we do not do this, we will generate a fragmented set of assignments in which the symbols bear no discernible relationship among themselves.

Need for Indicators: Joe suggests that with "French" numbers, we can get by without indicators. In a lighter vein, he supposes that you have asked your boss for a raise and your boss hands you back a slip of paper with an unindicated upper-number or dropped-number message. You read 218 or bah but you don't know which. My response to this fantasy is as follows: If the same boss hands back a slip with the answer in unindicated "French" numbers, you might not know whether he said "81" or 8|*40 So, to Joe's "bah" I will, particularly at this season of the year, add my own "humbug," which, both in Grade 1 and in Grade 2 is my characterization of the soundness of his reasoning on this point. Furthermore, Joe claims that an indicator is never needed neither before or after a number. No indicator? Anyone attempting to write "397" in "French" numbers without an indicator is likely to be "all wet." Additionally, I ask: "If 'French' numbers are so useful in the British computer code, why did they not import them into their math code?"

About Readability and Density of "French" Numbers: At this point, I interrupt myself to share with my colleagues a portion of a letter I sent to John Gardner. As we all know, John has submitted a proposal for our consideration which advocates "French" numbers. Here is what I said to John about "French" numbers:

"The short answer is that French numbers will not work. Imagine walking into a store where the proprietor is an immigrant, that is, English is not his native language. Business is slow and you find him deeply involved in adding a column of figures in one of his ledgers. As you approach, you notice that he is keeping track of his mental process by speaking the numbers softly under his breath. What language do you suppose you are hearing? The invariable answer is that he will be enunciating or thinking the digits with which he is dealing in his native language. It doesn't matter whether he has been in this country for twenty years or more and has otherwise acquired fluency in English. He will still be using his native language either mentally or verbally to perform his calculations. And the same is true for braille users whose first exposure to braille included the numbers as they are currently written in this country. They will always revert to those numbers whenever they can. For more than two months, now, I have tried to become comfortable with French numbers. I have written addresses and phone numbers on cards, put those cards aside for several days, and then tried to read them back. I have sat at my braillewriter for an hour at a time writing dates, model numbers, Canadian postal zones, and similar items in French numbers in an attempt to become comfortable with them and acquire some proficiency in their use. All to no avail. Yes, I can read French numbers, but never without a conscious mental effort to decode them by stripping off all the dots 6 so as to reveal their "true" identity. And yes, I can write French numbers, but not without the mental effort of encoding them by adding dot 6 to the digits whose forms are familiar to me. Despite high motivation and concentrated effort, I have so far failed in making the use of French numbers either comfortable, rapid, or automatic. I believe that this would also be the case for long-term braille users if they were required to use French numbers. You are in an advantageous position. You are, relatively speaking, a new braille user. Like a child who can learn any language, you can readily become accustomed to French numbers just as you could to any other system of numbers. But for long-time braille users, matters are as I have described them above. To gain acceptance, French numbers would have to demonstrate a logical superiority several orders of magnitude greater than they do at present. Braille users would gladly forego the advantages of French numbers, some real and some perceived, and would gladly welcome any alternative in order to avoid their use. French numbers have another annoying disadvantage; they create "dense" braille. I have made this observation in my proposal and Mr. Maguire of Australia has made the same observation, going so far as to calculate the average number of dots required to represent a French digit. When I read your examples which contain these dense numbers, together with your four-dot times sign and five-dot plus sign, I find that I am trying to read the holes instead of the dots. Imagine trying to take notes on a braille slate in a math class using your code. The four-dot number sign and your five-dot enclosure symbols do not help the situation either. So much for French numbers now, ...."

Advantages of Dropped Numbers: Dropped numbers are intuitive. The learning curve required to use them has a slope of zero. I recently tutored a young girl age 11. I presented her with a column of figures brailled in dropped numbers to add. Without a single question and without any hesitation, she added them. How many people make a transition every day from their hard-copy books and magazines with upper numbers to their computers with dropped numbers and back again without even a slight shifting of mental gears? Dropped numbers, in addition to the above advantages, have all the advantages of "French" numbers. No Grade-1 word in which dropped numbers occur will ever require an interior numeric indicator or an interior Grade-1 indicator, as is also the case for a Grade-1 word containing "French" numbers. While a Grade-1 word that begins with a dropped digit will require a numeric indicator, the same Grade-1 word that begins with a "French" digit will require the Grade-1 indicator. "French" numbers have no demonstrated superiority. I will present below a simple but typical math expression written first in upper numbers, then in "French" numbers, and then in dropped numbers. I will use the traditional plus sign in the upper-number and in the dropped-number version, but I will use Joe's proposed new plus sign in the "French" number version.

Upper: #a+#b;a+#c;b+#d;c
"French": ;*!<a!%b!?c
Dropped: #1+2a+3b+4c

The upper-number version requires four numeric indicators and three Grade-1 indicators to communicate its message. The "French" version requires only the introductory Grade-1 indicator, but it cannot be read quickly, comfortably, or intuitively. The dropped-number version has only the introductory numeric indicator (replacing the Grade-1 indicator in the "French"-number version) and otherwise occupies the same space as the "French" version. With which version are you most comfortable? Can you conjure up an example in which the "French"-number version is clearly superior to the dropped-number version? If so, is such an example sufficiently frequent or so markedly superior using "French" numbers as to warrant turning the braille code on its head to accommodate "French" numbers?

Joe's Examples: Please read the last section in js3b27 in which Joe analyzes several examples, particularly the example for writing 3-1/2. He muses about how to write this mixed number in four or five different ways, using upper and "French" numbers in the same expression, using notational abbreviations, and variations of both. Despite his commentary, he makes a better case against "French" numbers in that small section than I could ever do.

Conclusion: BANA has given us a mandate to be as conservative as possible in our work. The code that results from this committee should look familiar and friendly to long-term braille readers. Things should be changed as little as possible and only when our work indicates that there is a clear need to change something. For example, we spent a long time debating what the Grade-1 indicator (alias letter sign) should be. It was dots 56 to begin with and, fortunately, the matter was resolved by retaining dots 56 for this purpose. Meanwhile, no issue arose to make anyone think that the original dots 56 was an obstacle to our future work.

We should not go on a quest for thrills, adventure, and excitement for their own sake. Our present preoccupation with "French" numbers is just such a quest. There is no need to go so far afield to develop the code entrusted to us by BANA.

The motion to undertake this project was made in Albuquerque in October of 1991. More than two years have elapsed since that time. It has become more than abundantly clear in our work that upper numbers cannot serve as the basis for a uniform code. The principal reason is the intolerable rapid alternation between number signs and letter signs required whenever letters and numbers occur in close proximity as they do in model numbers, serial numbers, catalog numbers, foreign postal zones, and even more frequently in math and science texts. An example of this phenomenon was presented earlier in this paper. Nevertheless, refusing to be persuaded by the facts, this committee insists in using upper numbers as the primary set of numbers in the uniform code. Dropped numbers do not have this problem. They are universally known throughout the world. As I have pointed out in earlier parts of this paper, the transition to lower numbers has an attendant learning curve with zero slope. There is not a single substantial advantage that "French" numbers have over dropped numbers. Yet this committee behaves as if dropped numbers did not exist. Their adoption would cause the least dislocation in the reading habits of the braille-using community. All we need do is look at some of the examples offered using "French" numbers to get a feel as to how readable they are.

This committee is proposing a code with an unworkable set of upper numbers, an unreadable set of "French" numbers, and an impossible set of guidelines for deciding which number system to use. Will the Ad Hoc Committee and BANA stand idly by and witness the certain failure of this project if this motion is adopted?

1993-12-19 JS: Clarifications on French digits (js3c10)

I have been working on the promised paper on lower numbers. As usual the required time has proven longer, and the available time shorter, than hoped. Today or tomorrow, with luck! In the meantime, I have naturally read Abe's message of yesterday, and find that some of his difficulty with the motions on French numbers (ef3b30 and js3b27) apparently arise from misconceptions which, lest confusion reign, I should correct immediately:

1. Motion js3b27 does not call for "optional" use of French numbers in grade 1, in the sense that Abe was concerned about. Although that term is (probably unfortunately) used in the prefatory remarks, subsequent sentences make it clear that I was persuaded by Bruce's earlier observations about transcriber choices, and so motion js3b27 would establish that French numbers are always to be used in grade 1, with the one clear exception mentioned. The only "option" involved is whether to use grade 1 or grade 2 in the first place; we have not yet developed guidelines covering that decision, although clearly we must do so, a point that I develop in paragraph B1 of the discussion attached to the motion. Finally, the term "option" is also used in discussion paragraph C7, in which context I hope it is clear that it refers to a program option, not to an option that would really be open to a person using a program to produce braille according to code.

2. Abe says "In order to support the duality of the two number systems, Joe found it necessary to introduce additional dualities among the punctuation marks." I assume here he speaking of the treatment of opening quote and question mark that is detailed in the motion. The linkage is incorrect, however: that treatment does not derive from French numbers as such, but from the fact that current customary braille uses the same symbol for both those punctuation marks. That is, we could have French numbers with or without that particular treatment of opening quote and question mark; likewise we could have that or a similar treatment of those punctuation marks with or without French numbers. French numbers do not in themselves induce any dualities in the punctuation marks; nor do the upper numbers, for that matter; only the lower numbers, for obvious reasons, induce dualities in the punctuation marks. To address a further concern expressed in the same paragraph: in grade 1, French numbers do not induce any dualities at all, with punctuation marks or any other kind of symbol, and there need not be any worry that any will arise. Similarly, there is nothing in the motion that would present an ambiguity in interpreting the braille, whether by readers or computers.

3. I did say that indicators, either before or after, are never required with French numbers, but there was an important antecedent: you must be in grade 1. I thought that was stated often enough to be clear in context, but if not, my apologies and now I hope that it is. Of course, if you are in grade 2, you must establish grade 1 in order to use French numbers, which are to be used only in that grade, and that takes one of the indicators that we have established for that purpose. For the most part, my assumption is that an "extended" grade 1 mode, in particular the grade 1 passage introduced by the triple letter indicator, will be in effect throughout really intense technical notation. For that reason, I tend to present the more complex examples with a stated assumption that grade 1 is in effect, rather than use the more local indicator that might be appropriate if the example occurred as a more isolated "island".

4. My use of the term "notational abbreviations" in the musings towards the end of motion js3b27 (which are not part of the motion), was intended to be consistent with the way Abe used the term when he coined the phrase in an3b16: to refer to a kind of shortening used in grade 2, like contractions but not contractions because we prefer to reserve that term for specifically those shortenings that apply to words and letter groups. If I have misconstrued the way Abe intended the term to be used, then perhaps I should choose another, and would be glad to do so. In any case, the kinds of things I mused about would never involve any ambiguity in interpretation of the braille, whether by computer or a human reader; they thus have nothing in common with the kinds of things that Abe put in the same category, which from the fault that he found with them, evidently did involve ambiguity.

I hope that these clarifications assist in a clear understanding of what is being moved. On a procedural point, I hope also that it is clear that the currently active motion is not mine with all its details on a possible implementation, but Emerson's motion on the general principle of adopting French numbers in grade 1. Of course it is fair to debate either one, or even to present on other matters, but the current voting is actually on the latter.

1993-12-10 TC: YES for French Numbers (tc3c10)

I vote YES on Joe's motion to use French numbers in Grade I Braille.

The use of French numbers in technical writing goes a long way toward overcoming barriers to a sensible extension of SEB into a single unified code. The motion (in JS3c04) will result in a code that is compact, unambiguous, easy to read and easy to learn. It eliminates the irksome thicket of braille indicators that tell the reader how to interpret symbols in expressions formed by juxtaposing digits, letters and punctuation marks. We could even write in braille such unlikely combinations as a1,b2;c3: et cetera. I've always wanted to be able to write unlikely stuff.

And best of all, we can leave braille in the popular press pretty much alone. Those who read only Shakespeare and Steven King novels will be undisturbed.

Need I mention the ultimate benefit? We can stop calling them "French numbers" in favor of G1 numbers.

1993-12-11 JS: On lower numbers (js3c11)

To follow up Raeleen Smith's request, this memo is to try to bring together some of the points made about lower numbers since the deliberations of the original committee began. The discussion associated with motion js3b27 did much the same for French numbers, so I presume that I need not get into aspects of that subject that do not involve comparisons with lower numbers. I will try to include positive aspects of lower numbers as well as negative ones, but I will not claim that this is a neutral view. It would be impossible to have considered this matter through all that debate without having formed an opinion, and as is evident from motion js3b27, I prefer either of the upper-cell systems over the lower numbers.

For what it's worth, that preference was not built-in, but has been formed, clarified and strengthened over time. When I served on the original committee that designed the BANA Computer Braille Code, I concurred with the decision establishing the basic character set, which includes lower numbers. But CBC was a code with a purpose very different from that of UBC, and by the time we began work on UBC, I had my doubts about the wisdom of using lower numbers in a more general code where it was not really feasible to change all of the conflicting punctuation marks, as CBC had done. My current preference became more clearly established when I did a short survey to determine whether, even in literature with a decided scientific bias, numbers more frequently abut letters or punctuation marks. (See the related point below.) Subsequent, more detailed analyses of other issues have only led me in the same direction.

Still, it's just a preference. And when I think about what I can do most constructively in this piece of writing, it would be to start off with a decidely positive statement about all three numbering systems: upper, lower and French. The fact is: they all can "work," if we want them to. That is, any one of them, or any combination, can form the basis for a complete and consistent system, free of any ambiguity in interpreting the braille. Each system has been in existence for some time, and used by significant populations, which implies that each must have something going for it. Each no doubt has been the vehicle for the writing and reading of much good, useful braille. Consequently, each system is advocated, sometimes with understandable passion, by perfectly sane, well-intentioned people. The differences are real enough, but a lot of it comes down to taste--how many indicators are too many, or in what specific circumstances we don't like to see them, for instance. And as Cicero said, there's little point in arguing over taste. But in this case we have no choice but to make a choice, and when we get all through I hope that all interested parties can rally around the decision of this committee, whatever that is. For my part, I'll say this: if, after a full and fair debate, a group of this collective wisdom decides it wants to use lower numbers, then on that grounds alone I'll be convinced they must be the best thing since sliced bread.

A word about examples, which I will use to help explain some of the points: Everyone seems to like examples, probably because of the well-known principle that people really think inductively. They are useful, but I do hope that the inevitable limitations of examples do not divert attention from the more important underlying issues. No example, being by definition a particular instance, can truly represent all cases. And when exemplifying a generic system that can be realized in various actual or potential forms, such as lower numbers, there is a particular difficulty: as soon as one gives an example in one of those forms, the example can be criticized for not having followed one of the other forms. The three major official English codes that use lower numbers, viz.: Nemeth code, British maths, and CBC, all use them quite differently. Added to these, variants have been proposed that still use lower numbers but change certain details of the implementation. The upper and French number systems can also vary in certain details. With no slight intended towards the other possibilities, I will tend in my examples to utilize our current Committee II report as the basis for exemplifying upper numbers, the French number system proposed in motion js3b27 for French numbers, and Abe Nemeth's most recent proposals for lower numbers--the latter primarily because it uses lower numbers for all purposes, not just certain ones. In making that choice, there may be unintended but unavoidable unfairness to other systems, which may not have all of the problems illustrated (though they may, of course, have others). There may even be unintended unfairness to Abe's proposal, if I have misunderstood some detail of his proposal, or if some further "tweak" in the rules would fix a problem that arises in an example. That is why I hope that people reading this will look deeper than the tangential details that sometimes become the focus when examples are presented.

Characteristics of a lower number system: The main characteristics of the lower number system we will be using, then, can be summarized as follows. In common with our current UBC system, there two grades of braille, grade 1 and grade 2. However, these grades apply only to whole works; the grade context, i.e. "mode", does not change within a work as it might with the current UBC system. Instead, there is an additional mode called "literal context" that can be turned on and off, within an otherwise grade 2 or grade 1 context. (Note: the "literal mode" of the November 1992 Committee report is not the same as the literal mode being described here. We have since changed our report terminology to simply "grade 1".) This literal context disallows contractions, as does grade 1, and goes further in that the ten lower signs associated with digits are now assumed to have that meaning rather than being understood as punctuation marks, as they might be in grade 2 or grade 1. Thus, once in literal mode, the digits themselves usually need no introducing number sign (although they might in cases of physical ambiguity, as will be discussed). The punctuation marks that conflict with the digits, however, such as the colon, either need a preceding "punctuation indicator" to distinguish them from digits, or need to be represented by a dual symbol, i.e. one that is different from that used in grade 1 or grade 2 mode. In this system, the comma and period are handled by such dual symbols, * (dots 16) and ] (dots 12456) respectively; the others are prefaced by a punctuation indicator _ (dots 456). Like the UBC grade 1, the literal mode can be entered for an entire passage or for a single word, but unlike the UBC grade 1, it cannot be entered for just one symbol. Between the two systems, the indicators are somewhat similar and, though this is just a superficial difference, it can be a bit confusing to someone just getting into this subject. In UBC, a single letter sign signals grade 1 for a single symbol, a double letter sign for a word, and a triple letter sign for a passage. In the lower sign system, a single letter sign within a word is used for subscripting, at the beginning of the word it signals literal mode for the duration of the word, and a double letter sign signals a literal passage. The number sign also can introduce literal mode for the duration of a word, just as it can introduce a grade 1 word in UBC.

Various writings by Abe Nemeth, notably ANCODE (in archive xx36), should be consulted for further details of the lower number system outlined above.

In a nutshell, this lower number system takes a particular approach to enhancing efficiency when numbers are present, at the expense of efficiency when certain common punctuation marks are present. It should not surprise us that its strengths are most evident when we avoid punctuation marks, and its weaknesses are most prominent when punctuation marks occur frequently.

Another important preliminary note on examples: In the general literary examples, unless otherwise mentioned, an overall grade 2 context is assumed, and so appropriate indicators are used to establish any specialized mode that is necessary. In the examples dealing with exclusively technical notation, a grade 1 passage mode is assumed to have been established for the upper (UBC with French numbers) case, and a literal phrase for the lower case, by some prior indicator that is not shown.

With that, let us consider some issues, one by one. I'll begin with a matter that is at the level of general philosophy, but that I think underlies a matter of taste that I have heard expressed by a number of readers. I'll continue with issues and examples based mostly on "ordinary" literary material, with more complex technical cases coming later in the sequence.

1. Lower numbers and the general scheme of braille: In general, braille represents primary information in the upper cells. The logic behind this is evident in the familiar chart of seven "lines" that is used to present and explain the 63 possible characters of braille. The upper group of four such lines, each containing ten characters for a total of forty, has a notable characteristic: every character has at least one dot on its top row and also at least one left-hand dot on its top or middle row. In other words: first, either dot 1 or dot 4 is raised, or both; and second, either dot 1 or dot 2 is raised, or both. Only on the fifth line of the chart, and below, do we find characters that have dots only in the second or third row, or dots only in the right column, or whose only left-hand dot is in the third row. This arrangement is obviously no accident, but is related to the issue of recognizing the characters easily while concentrating primarily on the upper part of the cell. That inference is confirmed by the fact that the letters, which of course are the primary information-bearing symbols in ordinary literary text, were assigned within those top four lines in the customary chart. In the original French, that naturally enough included the frequently-occurring accented letters, and one dipthong, with the result that all forty characters were taken up with letters. The bottom three lines were assigned to punctuation marks and indicators. Punctuation marks were mostly assigned to lower cells that have left-hand dots, thus achieving two goals: they gain some measure of recognizability from the letters that they (usually) follow, and, being "down and out of the way", they are perceived as having the same kind of ancillary role that their print counterparts play. Indicators were the remaining characters, mostly biased towards those with right-hand dots, which obviously gain readability from the letters that (usually) follow them.

Despite the fact that some grade 2 contractions disturb these patterns somewhat, they are still clearly noticeable in braille to this day: primary information is mostly upper, ancillary markings are mostly lower. Now in terms of the information borne, digits are clearly in the same class as letters. In ordinary text, in fact, a case can be made that they are even more critical, because there is not enough redunancy in a typical number to help you fill in a missing or garbled digit, whereas you can usually deduce what a missing or garbled letter must be. In any case, digits are not less important than letters. Yet, to relegate them to the lower cell is to give them the look and feel of punctuation marks, and in the process to introduce other complications that we will take up in turn. If there is any doubt that doing that would run counter to the original design of braille, we need only reflect that, once the decision had been taken to use a numeric indicator, the option to use either lower or upper characters after the indicator was just as open then as it is now--except that, in terms of the basic design, the upper choice was clearly the more natural.

Example from Boston Globe of Dec. 7, page 3, with upper numbers:
,nelson 0 #ah ye>s old & sett+ up *airs on ! %ip =a ,sun"d s]vice :5 ! vessel 0 hit )a #a1gfj-p.d bomb on ! morn+ ( ,dec4 #g1 #aida4
and with lower numbers:
,nelson 0 #18 ye>s old & sett+ up *airs on ! %ip =a ,sun"d s]vice :5 ! vessel 0 hit )a #1*760-p.d bomb on ! morn+ ( ,dec4 #7* #1941]

2. Modes and their effects, and the number of modes: As the foregoing example illustrates, once literal mode is established it can and often will envelop what, from a natural point of view, is ordinary sentence punctuation. True, a change of rules would have allowed us to write something like:
,dec4 #7_1 #1941_4
instead, and that might or might not be preferable, but that does not change the basic point that one must be quite clear about how far a mode extends. This can surprisingly affect even cases that do not involve numbers at all. Consider the following example, starting with the UBC treatment which in this case coincides with SEB:
8,he m>k$ ! map ) ;x40
and then in the lower-number system:
7,he m>k$ ! map ) ;x]7
With UBC, there are just two extended modes, grade 1 and grade 2. Numeric mode has a distinct existence within each of these, but is always quite local, applying just for the duration of a number. In this lower system, there are three extended modes, the most important being grade 2 and literal mode. Grade 1 is a kind of intermediary; it is like grade 2 without contractions, but shares with literal mode the characteristic of not needing a punctuation indicator on parentheses. Thus, if we show the above example first in grade 1 and then in grade 2 for each system, we would have, for UBC:
8,he marked the map with x40
8,he m>k$ ! map ) ;x40
and for the lower-number system:
7,he marked the map with x47
7,he m>k$ ! map ) ;x]7
In the lower-number system, if the extended literal mode were in effect (as might happen, for example, in a computer file containing heavy markup intermixed with ordinary-looking text), we would have a third possible treatment:
_7,he marked the map with x]_7
Clearly, it is already enough of a complication to have two extended modes, although that much is a given of our assignment. But to add a third extended mode would tax all of our abilities to keep track of what is in effect at any given time. Computers wouldn't mind, but I think that people would.

3. Physical ambiguity: With the lower number system, once an extended literal mode (literal phrase) is established, it is no longer necessary to use the numeric indicator on the digits, since those particular lower signs are already understood as digits. That would be one of the perceived efficiencies in extended technical material, obviously. However, if we use the literal phrase concept for such efficient treatment of, say, a whole series of aligned hexadecimal numbers, a particular danger arises. If some portion of the text contains numbers that do not happen to contain any of the hexadecimal digits beyond 9, and if we persist in omitting the number sign, and if no other abutting symbols come to the rescue, then in that portion the numbers become indistinguishable from upper-cell counterparts. (Please don't say "bah"! Sooner or later, it would happen!) Of course, we could go ahead and use the number sign in that case, relinquishing efficiency. That, however, would involve more rules and their attendant complications. By contrast, a system with regular upper numbers in grade 2 and French numbers in grade 1 never has this kind of problem.

4. The question of duality: Both the systems we are considering involve duality. If in UBC we use upper numbers in grade 2 context and French numbers in grade 1, then the necessary duality involves those ten symbols, and only those. In the lower number system we are considering, there is a directly defined duality in two of the punctuation marks, comma and period (decimal point), as used inside and outside literal mode. Beyond those, there are also less obvious additional dualities that are necessarily induced by this system. Certain other punctuation marks, as we have seen, require a punctuation indicator within literal mode, and do not outside; that is two ways of writing the same symbol, whatever it is called. Moreover, even the digits within literal mode, as discussed in the foregoing paragraph, may sometimes need number signs and sometimes may not. That too is a kind of duality.

5. The overall statistical frequency of number-letter juxtapositions vs. number-punctuation cases: Considering general and general technical literature, it is an interesting question whether letters or (certain) punctuation marks tend to follow digits more commonly. That is because, obviously, the regular upper numbers and the lower numbers are just opposites when it comes to which case requires a following indicator, i.e. a letter sign or punctuation indicator. As it happens, even in literature biased toward inclusion of scientific technical notation at a fairly high level, letters follow numbers much less frequently than do punctuation marks. Remarkably, that fact holds up even if we disregard commas, periods (decimal points), and parentheses, on the grounds that those are to be handled in some way other than indicators. This was the conclusion of a short survey of material from "Scientific American" (see JSSCIAM1, in archive xx26). The implication is that, if we move from upper numbers to lower numbers, and thus from a clash with alphabetics to a clash with punctuation marks, there would be an overall increase in the indicators required.

6. The frequency of such juxtapositions in elementary literature: Not surprisingly, the preponderance of digit-punctuation cases over digit-letter cases is even more striking in literature for very young readers. The National Braille Press kindly let me scan eight of their children's books, not a selective sample but their whole children's production for a period of time, to test that fact. In those eight books, totalling roughly 60,000 characters of text, there was not a single instance of a letter following a digit. By contrast, there were 18 cases of punctuation marks following digits: eight commas, eight periods, and two colons. To be fair, in this sample all the comma and period cases occurred in the front matter legalisms that, perhaps, not all the young readers would actually read--but of course some would. Turning to the two digit-colon cases that occurred in the main text, I can't resist quoting their full context, from one of Dr. Seuss' delightful classics:
The Happy Way Bus leaves at 4:42
and will take you directly to Solla Sollew
So, until further notice, the 4:42
Cannot possibly take you to Solla Sollew. ...
With an upper number system, the bus would leave at:
whereas with lower numbers it would depart at:

7. The fundamental nature of such juxtapositions in general literary material: The preceding two statistical arguments are compelling enough, but are perhaps even less important than an underlying difference in the very nature of digit-letter cases as opposed to most digit-punctuation cases in general English. To illustrate, consider the case of this sentence:
5 is Johnny's age.
In an elementary classroom, the teacher might point out that the meaning is the same if one rearranges the words:
Johnny's age is 5.
With upper numbers, a blind child in that class can rearrange the words right along with his or her sighted schoolmates, with the same result and the same learning experience. But with lower numbers, there is suddenly a problem that arises when the 5 comes up against the period. Either a "punctuation indicator" must be supplied, or the dual period used, or poor Johnny will age rapidly!

At first glance, it might appear that this is not so different from a sentence in which, say, Johnny reads paragraph 4g. That is, it might appear that using punctuation indicators would be essentially similar to using letter signs. The point here is not that punctuation indicator rules are impossible to learn, but that they come up when two otherwise commonplace and independent elements in the sentence, a number and a punctuation mark, happen to come in contact. That kind of rule is tough on human beings--though easy enough for computers, by the way--and especially so on people who are just getting a grip on those elements in the first place. By contrast, "4g" is a thing unto itself, and probably looks rather special, one might even say "technical", to any young reader. Consequently, there is no particular surprise or difficulty in learning that a special treatment for this kind of thing is required.

It is not only young children who are likely to find punctuation indicators distasteful on these grounds. Adult professionals whose work does not commonly involve advanced math or scientific notation are likely to wonder why we would lower the numbers, yielding no increase in efficiency for them at all (because the number sign would still be required), yet creating the burden that one must think twice about these chance juxtapositions every time a number or punctuation mark is inserted in a sentence.

8. Intense technical notation where punctuation marks are scarce: At last we come to cases involving extended technical notation, where, given the reason they were devised, we would expect that lower numbers might do somewhat better. And sometimes they do, if we steer clear of punctuation marks. For instance in algebra, especially at the elementary level, one tends to see few of the affected punctuation marks within typical expressions and equations. It is also easy to imagine such things as hexadecimal numbers, or catalog numbers, absent punctuation marks, concentrated in an array. We can illustrate such a case below, borrowed from an3c09. The first illustration is with French numbers, the second with lower numbers (and recall that extended modes grade 1 or literal modes are assumed in effect in these kinds of examples):
They are the same length, but depending on one's background one would probably find one or the other easier to read. For sure, anyone used to the BANA technical codes would like the second better, but that is a point we will come to later.

9. Intense technical material where punctuation marks occur frequently: While the lower-number system looks good enough when punctuation marks are scarce, unfortunately that condition does not characterize all the technical material that we must provide for.

Even in some branches of classical mathematics, punctuation marks can become common enough. For example, I've just cracked open my old college text on integral equations (and have breathed a sigh of relief that my last test in that subject was over 30 years ago). There are quite a few commas, semicolons, and exclamation marks [factorials] within the set-off technical notation, as well as elsewhere. And, as it happens, there are not many numbers, so the use of lower numbers would cost more than it would gain here.

But we need not get that esoteric. Computer programs, which many people deal with all the time and in many forms and degrees of technicality, commonly contain a great many punctuation marks, and easily illustrate the difficulty one gets into with lower numbers. Take for example a program statement such as the following (shown first in BANA CBC):
i = (j?3:k);
Again assuming an extended literal or grade 1 mode, we have the following treatment in a lower number system:
i = (j_83_3k)_2
and in French numbers:
i "7 (j8%3k)2
which is more compact, despite the 2-cell equal sign, and more easily followed (once one gets used to the digits) because of the lack of indicators.

Even where the dual comma and period of the lower-number system avoid the need for punctuation indicators, routine notation within computer programs can easily come out harder to read with lower numbers than with French numbers. For example (in BANA CBC):
(in lower numbers):
(in French numbers):

From these examples, the nature of the trade-off inherent in lower numbers becomes clear. Lower numbers do fine in those notations, including much of classical mathematics, that seldom involve punctuation marks. But that comes at a distinct sacrifice to punctuation marks that are common both in general literature and in certain other technical fields, such as computer programming. By contrast, the upper/French number system is always at least as compact in mathematics as the lower-numbers system, yet it has no affect at all on punctuation, either in general literature or in punctuation-intensive technical contexts.

10. A count of punctuation marks in an actual program: If there is any doubt that punctuation marks are common in computer programs, you might wish to examine one that, if you use the popular PROCOMM PLUS communication program, is probably already on your disk. It is HOOK.C, and is a typical example (if there is such a thing) of code in the language C. In that program, with just under 600 nonblank lines, there are 180 instances of periods or commas that would be dual, and 400 instances of semicolons, colons, double-quotes, question marks and exclamation points that would each require a punctuation indicator in the literal mode of a lower-number system. Interestingly, there are only 371 leading digits, and just six cases of letters following digits, so even a straightforward grade 1 upper-number treatment would yield fewer indicators than the lower-number treatment. There would not, of course, be any such indicators with a French number treatment.

11. Readability: We come now to a subject that is bound to occupy much of our attention, and that is whether lowered digits are quicker to read than French digits. I have already written on this subject in js3b27; see paragraph B2 in particular. Personally, I accept that experienced English Braille readers, who obviously already know the upper numbers, find themselves initially slowed down by French numbers. I also think it stands to reason that the very same "whole-shape recognition" principle that give rise to this phenomenon also guarantees that it is temporary and will disappear in time, with learning. Anyone who has mastered 189 equivalences between letter-groups and their contractions can certainly learn the 10 equivalences for the digits, especially since the shapes are closely related. On the other hand, I can't say I know how long that would take. A good guess is that it would vary from case to case. Age would surely play a role. I am aware that I learn more slowly now than when I was 18. (It's a shame, too, because then I already knew everything and didn't need to learn quickly; since then I've declined amazingly and could use the assist.) Perhaps it would make sense to do some experiments that would reassure people that it is possible to learn to read French digits easily, and about how long that takes, and whether there may be some people for whom acclimation will take a long time or never occur. In any case, it seems clear enough that this slowdown phenomenon is not a concern for beginning braille readers. That being the case, I would ask how much we are willing to do for the future. As the Amish say, "We have not inherited the land from our fathers; we have borrowed it from our children." Is not the same true for braille?

1993-12-10 AN: Questions (an3c10)

First, I agree with Joe's observation about the duality of the two punctuation marks he discussed in js3b27. I refer to the alternative quotation mark and the alternative question mark. It is true that this duality is unrelated to "French" numbers. Nevertheless, I still ask: If one form is ambiguous and the other form is not, why not use the unambiguous form uniformly thereby avoiding the need to formulate a rule?

I have some questions about Joe's motion. Perhaps, since Joe made the motion, he is the best one to answer these questions. Do we envision that many more books, particularly those of a technical nature, will now be brailled entirely in Grade 1? For example, will an elementary-grade arithmetic book be brailled entirely in Grade 1? What about a high school algebra book or a college calculus or physics book? Or do we mean that all such books will use Grade 2 as the host text and that only the "islands" of which I spoke in my last submission containing technical material will be in Grade 1 and be indicated as such by the indicators we have devised? What kind of numbers will be used in those "islands" which are surrounded by Grade-2 text? Since such "islands" are indicated as Grade 1, and since Joe's motion proposes to use "French" numbers in Grade 1, the interpretation can be made that "French" numbers will be used in such "islands." On the other hand, since these "islands" are surrounded by the host text which is Grade 2, it is also possible to make the interpretation that upper numbers should be used in those "islands" since Joe's motion calls for upper numbers to be used in Grade 2. Even one or two examples would be helpful.

Although I have written against "French" numbers, I never formally voted on Emerson's motion. So I take this occasion to vote "no" on that motion.

1993-12-11 EF: (ef3c11)

In Abe's contribution to the Forum on December 10, he expressed uncertainty concerning the way numbers would be written when they occur in intense technical passages, written in the Grade 1 mode, and surrounded by English text written in the Grade 2 mode. The Grade 1 passage would be initiated by the Grade 1 Passage Indicator, and terminated by the End of Grade 1 Passage Indicator. While the Grade 1 Passage Indicator was in effect, French numbers would be used. After termination of the Grade 1 passage, upper numbers would be used. This seems so simple and obvious that I don't understand Abe's uncertainty, and I wonder if there is a subtlety that I have missed.

1993-12-11 TC: Braille Mentoring / KEEPING UP (tc3c11)

Come! Come! Abe. Your clever rhetoric conceals more than it reveals. In your harangue of December 9, 1993, badgering Joe and beating the dead horse of dropped numbers you maligned the truly elegant system of French numbers by shamelessly stating in public:

"When I read your examples which contain these dense numbers, together with your four-dot times sign and five-dot plus sign, I find that I am trying to read the holes instead of the dots."

And now I find myself in the embarrassing position of having to explain to a learned colleague that recognition of all braille characters is as dependent upon perceiving the absence of dots in a braille cell as it is in detecting those that are present. You see, Abe, the way we recognize the letter Q is by noticing that dot 6 is absent, the way we recognize the letter z depends on noting the absence of dots 2 and 4.

I have a lot of confidence in you, Doctor. You can learn to read French numbers with ease. All you need do is stop reading the cell holes and start reading the whole cells.

(Oh, I do hope that I have not too cleverly concealed the humor in this contribution to the weighty deliberations of our forum.)

1993-12-11 JS: Chairman's Report on Status of the Meeting (zs3c11)




By EF in file ef3b30 (see also js3c01): to establish in principle French numbers for use as a secondary system, in grade 1. Seconded: JS. Voting deadline: Jan. 4, 1994. Votes recorded to date: for: EF, JS, TC; against: AN.


By JS in file js3b27 (see also js3c01): to fix the details implied by French numbers used as a secondary system, in grade 1. Seconded: EF.




This is to remind us all that next week, from tomorrow, Sunday, December 12th through Saturday, December 18th, will be an "observer week". During that week, any and all submissions from observers through our list server, that is the Internet address
{email address removed}
will be welcome. By contrast, I would ask the regular members to remain "off the air" during that week, and just listen.

To answer a few likely questions about the messages to be sent by observers: (1) You may have noticed format coding in our messages. However, no particular "coding" style, or in fact any coding at all, is required. The information is paramount, and informality is just fine. (2) It is OK to forward messages from other parties, if you think the information is relevant. We're all looking forward to hearing from you!

Aside to John Gardner: Thanks for your message. I presume the above answers your question about the observer period.

Regarding the questions from Abe Nemeth in an3c10: I think the paper I sent up an hour or so ago, js3c11, contains examples and other material that will help answer those questions. If not, let's keep talking after "observer week".

I would like to welcome Phyllis Campana and Caryn Navy as observers, adding the following addresses to the server list:

1993-12-11 AN: The dots and the holes (an3c11)

It took my friend Tim about six weeks to determine exactly how much my (admittedly) clever rhetoric reveals and conceals. The quote which Tim includes in tc3c11 should technically be enclosed in single rather than in double quotes. What he quoted was a portion of a letter from me to John Gardner. In my an3c09 submission, I quoted a portion of my letter to John, and then Tim quoted my quote back to me. He thought I was maligning Joe when, in fact, I was maligning John. My letter to John was written on October 26, 1993. In that letter, I requested permission from John to share it with Tim. (I share almost all of my "inner secrets" with Tim.) I received a reply from John almost immediately in which he granted permission to share the contents of that letter. Accordingly, I E-mailed a copy of that letter to Tim containing that recycled quote a day later. It took Tim until today to react. It is Tim, I fear, who is in need of mentoring in reading comprehension which deficit he should remedy before attempting to cope with the more difficult challenge of "French" numbers.

And now let me give my would-be mentor-turned-disciple a lesson in Advanced Braille Reading 401. When the text contains a q or a z or, for that matter, any other letter, the chances are that I do not read that letter at all, whether it has holes or not. As soon as context tells me what word or phrase is in the text, I skip over many letters or even words and proceed quickly and immediately to the next part of the text for continuing my comprehension. This is why braille proofreaders frequently fail to detect missing or extra dots. With numbers, however, it is different. You can't guess what digit is under your finger from context. You actually have to READ it. Have you ever read about an 8organiz,n (&=! bl80 Could you do it without stumbling a little? It is the density of all those dots that causes the stumbling. In the above phrase, you have a little context to guide you. When reading "French" numbers, however, you have none, so you stumble a lot. By the way, I use quotes when writing "French" to remind myself (and us) that these are not really "French" numbers, but still let Joe enjoy the excitement he feels in that phrase. Now along comes Tim to deprive him of that pleasure by renaming them "G1 numbers."

Tim is absolutely correct when he says that I can easily learn to read, and even to write, "French" numbers. I have even done so without changing my braille reading and writing habits, as Tim has advised me to do. The rub is, Tim, that I can not do it rapidly, comfortably, or intuitively, as I can with either upper numbers or dropped numbers. And Face it, Tim, neither can you, nor can anyone in the braille-reading community. I can read lickety-split through a braille document without breaking stride upon encountering either an upper number or a dropped number. I can read through telephone numbers, street addresses, model numbers, etc. in either upper numbers or dropped numbers. But when it comes to "French" numbers, I must shift my mental gears into "low" so that I can climb that steep hill by painstakingly decoding every digit, stripping off its dot 6 in order to reveal its "true identity." And I can write braille lickety-split either on a braille writer or on the Braille 'n Speak, almost as fast as normal conversation until I have to write a "French" number. I must encode each digit carefully; the process is neither comfortable, rapid, nor intuitive.

Every day, Tim switches from his hard-copy braille books and magazines with its upper numbers to his computer with its dropped numbers and back again with the alacrity and ease of Superman leaping over a tall building. But in the other direction, that is, if his hard-copy braille should contain dropped numbers or his computer should contain upper numbers, he shows a tendency to become violent. Tim, you are clearly being charmed by the siren of philosophical garbledegook and motivated by the lure of political expediency. But extricate yourself from those external and irrelevant influences; think hard and, most of all, honestly about this important issue. If you do, you will find that "French" numbers have no clear advantage over dropped numbers. And even if they did, the fact of their unreadability and of being alien to everything else we know in the braille system would disqualify them from being a viable candidate.

It is now 9:30 p.m. on Saturday night, December 11. I still have to proofread this document and put it on the Internet. Perhaps I will have the honor of having the last word before we all push the "talk" button to the "off" position and the "listen" button to the "on" position.

1993-12-12 CG {Chris Gray, observer}: Bystander Commentary on Numbers (cg3c12)

I have been observing the discussion regarding numbers with growing concern and a great sense of discouragement for a meaningful unified braille code. In the paragraphs below, I intend to make a number of points that take issue with the direction of current discussion and raise various points that have not yet been adequately addressed--to my mind at any rate. To the new members of Committee II, I apologize in advance for the length and potentially harsh tone to some of my remarks. I recognize and wish to acknowledge that you are placed in the middle of a work in progress. I encourage you to participate fully in this discussion and not to be too readily swayed by by premature votes and decisions that have already been made on this issue.

Before proceeding, I think that I should say a few words about my own biases regarding numbers. We all have them, and I hope that by openly acknowledging mine, I can at least approach this discussion fairly and with all my cards on the table. On balance, I am biased toward a numbering system that uses lower-cell numbers. For reasons I intend to enumerate below, this seems to me the most reasonable course of action. Secondly, I am biased toward the reader whether the reader is using material today or tomorrow. Both readers and their materials must be protected from change that is too great or that markedly decreases the availability of essential material for study and information.

These biases, and my study of braille and the current discussion lead me to make the following points regarding numbers and the work of Committee II.

1. Committee II is in serious risk of failure by suggesting in its most recently passed motion that a dual system of numbering may be considered and proposed to the entire UBC committee;

2. The consideration of a dual system of numbering is not within the purview of Committee II authority and clearly violates requirements placed on the committee in its original charge.

3. The 'European' system of numbering has not been shown by Committee II (to date) to be valid or acceptable under any circumstances except for some possible experimentation.

4. Committee II has not given due consideration to the effect of either an upper-number or French numbering system to the U.S. Chemistry code.

5. The characteristics of learning and using upper and lower numbers, as opposed to European numbers, are markedly similar and advantageous to readers. French numbers are similar to readers, educators, producers, or volunteer transcribers.

6. There are various reasons to question the wide use or acceptance of 'European' numbers even in France/Europe.

7. The net affect of a dual system of numbers, and particularly a system that uses European numbers, is to place the vast majority of the burden of a unified braille code on the shoulders of those of us who use technical materials for work and pleasure.


1. Committee II is in serious risk of failure by suggesting in its most recently passed motion that a dual system of numbering may be considered and proposed to the entire UBC committee.

At its last meeting, and before this project was internationalized, Committee II requested permission to consider the European system of numbering. Presumably, this was done because problems were being discovered, showing Committee II members that the upper-cell numbers might be unacceptable. Space problems, high use of the letter-sign, and decreased readibility were suggested as some of the more significant concerns leading to a desire to consider the European numbers.

After this consideration, it has been decided that upper-cell numbers will still be accepted. However, none of the perceived problems has gone away. Thus, another numbering system would be nice to use for certain circumstances--as yet undefined. To put this less charitably or diplomatically, Committee II has not found a way out of its dilemma with the European numbers. And yet, the dilemma remains. This may mean that the problem is intellectually insoluble. In my view, it definitely means that this committee has found no solution to the upper number problem identified by them. This could therefore seriously jeopardize the committee's chances for success. The proof that upper-cell numbers provide no real solution lies in the suggestion that French numbers are also needed.

Suggestions: I'd like to suggest that two very successful systems for transcribing mathematics currently exist: the British system with roots in the Taylor code; and the Nemeth Code system currently adopted by BANA. Secondly, Committee II's task is to find a way to either unify the concepts and ideas of these two codes into one, or adopt one as a primary model and fold it into a unified code.

As proof of the robustness of his overall code ideas, Abe has produced a paper for Committee II consideration, ANCODE, and perhaps a similar paper can be devised by Stephen for the BAUK code. I have seen no refutation of or even discussion of Abe's proposal during the present discussion of numbers which perplexes me. Is it possible that the newer members of Committee II have not had time to absorb all the material needed to make a coherent decision?

2. The consideration of a dual system of numbering is not within the realm of Committee II authority and clearly violates requirements placed on the committee in its original charge.

Committee II has violated two fundamental charges that were given to it when the unification project was originally adopted. The first charge which is violated is to create a 'unified' code. A dual system of numbering provides no marked improvement over our present system; it merely provides a superficial reorientation to the fundamental problems we face today. It is fascinating and sometimes amusing to read the examples Joe and Abe bring to bear on each side of the French vs. lower number debate. What is shown by the aggregate set of examples is the fundamental truth that neither system solves all problems. Each falls prey to an inherent weakness in braille which is unavoidalbe due to our limited number of dots. It is most unfortunate that in Tim's "yes" vote, he claims a superiority for the French numbering system but clarifies none of the points that each numbering system raises about the other. In any event, a dual numbering system solves nothing and basically brings us back to the situation that created the desire for code unification in the first place. Trading one dual system for another solves nothing and provides only disruption and virtual chaos for readers.

The second charge that has been violated is to create a code that requires as few changes as possible to the present literary code. When BANA agreed to allow Committee II to consider French numbers, this basic requirement did not disappear. It was at most suspended in order to allow the greatest possible intellectual freedom for the committee. The only possibility for acceptance of such a fundamental change in braille as a total system would be if this change significantly and undeniably improved usability, readibility, transcribability, and availability of braille to readers. A dual system of numbering cannot be supposed to do this whatever the secondary numbering system might be.

Regarding Tim's assertion that this proposal would allow people to continue reading without disruption, I suggest that a very basic point is missed in such thinking. While I don't personally read much Steven King, I do read lots of popular literature. I read Shakespeare and dabble in some linguistics and languages. In additon to that, I read and use technical materials related to mathematics and computers on a daily basis. I know that I am by no means unique in this regard. So, I'm wondering just who is being protected?

By following the path currently under discussion, Committee II makes mathematics and technical materials the dumping ground for a problem you cannot seem to solve. This imposes fundamental change on readers in these disciplines. In no way have you justified such a far-reaching change to this set of readers. I say this as one of the most ardent supporters of a unified braille code; as one of the only early supporters of the ideas within BANA that ultimately lead to the formation of the Ad Hoc Committee. I have seriously risked my standing with those who I represent to BANA because of my strong support of Committee II and the concept of a unified code. I hope you can see from this that I'm not opposed to change. I can even accept more radical change for those of us who rely for our livelihood on technical materials in braille. But, it had better be for an overwhelmingly good reason. To make obsolete 99% of all technical materials on both sides of the Atlantic and around the globe for English-speaking people is fairly serious in my opinion.

A final point on this topic is that I define 'literary braille' to include material produced in Grade 1 braille. Grade 1 braille could not remain identical if upper-cell numbers were replaced with French numbers. So, one would probably have to have two Grade 1's; one for islands of technical material; the other more widely known Grade 1 for literary transcriptions done solely in Grade 1.

Thus, the implication of the motion just passed by Committee II that there might be a dual numbering system would be an invalid part of the Committee II report. In addition, the current motion on the floor is out of order and should be withdrawn. I do not raise this issue as a point of parliamentary procedure, but on the grounds that the motion violates the two charges mentioned above that have been given to this committee.

3. The 'European' system of numbering has not been shown by Committee 2 (to date) to be valid or acceptable under any circumstances except for some possible experimentation.

Let's start this point with a bit of perspective building and level setting. The following points are factually true regarding French numbers:

1. They have no constituency or user base in BANA countries;

2. They have a small constituency in BAUK countries for materials produced in BAUK computer braille;

3. No valid research on their usability exists for English-speaking users;

4. They have been shown by the deliberations of Committee II to have conflicts when used in Grade 2 braille as well as other usability issues that make them unsuitable for use in Grade 2 text;

5. Then have been shown in Committee 2 deliberations to have similar characteristics to lower-cell numbers when used in a Grade 1 context.

It is my assumption that anybody would agree with these five statements whether or not they favor using the French numbers. Given these facts, I request a list of equally valid facts that persuade members of Committee II to disregard the five points I have made above. You must have a considerable catalog of such facts in order to be persuaded that using a virtually untried and unused numbering system with no BANA constituency and absolutely no usability documentation will improve an already shaky situation for the braille-using community.

Dealing more directly with the European numbering system itself, the best reason for considering it is that it is being used in a limited way in the BAUK computer braille code. Including this numbering system was done for various reasons, some of which relate to the manner in which languages were created for VersaBraille users in the early 1980s. An important starting point for a discussion of these numbers would be for input from BAUK/Stephen Phippen regarding the number of books or other materials that have been prdocued in this code and their acceptance by BAUK code readers.

In BANA countries, we had a provisional computer code from 1972 until 1986. Its existence could lead one to believe that this was the way to handle computer braille for BANA readers. However, it was not the best way as shown by the more recently adopted and far more popular CBC.

I have two specific reasons for directing the question of usability to Stephen. First, he is the only committee member with any valid experience with European numbers and the only member with a possible constituency of users. Secondly, I have anecdotal evidence from the UK that would suggest the BAUK computer braille code has met with very limited acceptance. In fact, several years ago Tom Maley suggested to me in a casual conversation about technology that the French numbers had been somewhat of a disaster in his early experience. In addition, I know from my own observation in the field that many UK users of VersaBraille equipment use and prefer U.S. computer braille for their code selection on VersaBrailles. This tell me something very important i.e. even in the one place where a noncontroversial, true test of European numbers has taken place, it has met with limited acceptance, perhaps even negligible acceptance.

It may be that the BAUK computer braille code is in a transitional state as was the BANA computer braille code of 1972. I certainly don't mean this as any sort of criticism of BAUK codes. To a degree, any new code is a kind of trial, and success or failure can only be judged over time with serious use. Committee II needs to know BAUK's experience in detail though before making any recommendations to the Ad Hoc committee. So, I sincerely hope that Stephen will share his knowledge and opinions regarding this matter with Committee II and its onlookers. My apologies to any Committee II member who has had experience I have overlooked in this analysis. I might also point out in concluding this thought that personal experience doesn't count regarding this particular point. I'm interested in experience and acceptance by a group of users.

Regarding suitability, I could have added one final point to the five that began this section. It would be: Committee II has found French numbers to be unsuitable for general use in English braille. I did not do this because it seemed unnecessarily pointed and could be viewed as somewhat judgmental on my part. However, it does have much truth in it.

More to the point, since French numbers are deemed unsuitable for general reading, what is it about these numbers that makes them more suitable for technical readers? While similar to the question of duality raised previously, this is a somewhat different issue inasmuch as there could be arguments (other than political ones) that prove certain materials to be best suited for French numbers. A caveat that must be added to this however is that it must be better ONLY for French numbers i.e. there is a certain order of hierarchy that Committee II should use. If we accept the original report as a starting point, the first test that must be failed is for upper numbers. The second test is lower numbers. The last test--or resort in my judgmental view--would be French numbers.

I categorically reject the assumption that French numbers could or should be viewed as equal in theoretical consideration with lower numbers. Such an assumption is politically ridiculous, unreasonably disruptive to a materials delivery system that has been at work for over twenty-five years, and which braille as a reading medium simply could not withstand. Only the most overriding proof of French number superiority could change my view in this regard. So far, I've only seen that it could be seen to be as good as lower-cell numbers but that they each have similar problems.

4. Committee 2 has not given due consideration to the effect of either an upper-number or French numbering system to the U.S. Chemistry code.

This point is relatively self-explanatory. I would only like to add the following amplification. First, this was discussed in detail during the BANA meeting of November 1-3, 1993. This work is ongoing and as a member of the technical committee, I'd like to say that I feel our proposed chemistry code is the single most significant contribution to blind chemists that has been made to date. It is spatial in nature, broadly extensible for brailling varying types of chemistry, and has been used successfully by a significant number of blind children and college students. I will attempt no comparison between this work and the system provided by Bruce which I haven't yet had time to properly review.

Use of the French numbers would be devastating to this work as would use of upper-cell numbers. In chemistry as in mathematics, a great many number-letter combinations occur together. Use of French numbers virtually destroys any chance for symmetry between related symbols (dots 346 matched with dots 146 for example). We use shape symmetry extensively to try and graphically show bonds and other relationships.

I believe that any reasonable person must conclude that French numbers and this chemistry code could not be made to work together to the reader's advantage. Thus, you have clear evidence of a technical discipline for which French numbers is not an answer. To claim that this chemistry code is not an adopted code would not be entirely accurate inasmuch as it has been widely used in the U.S. and Canada and is a logical extension of Nemeth code. In addition, it has been a part of NBA and CTEVH workshops for several years. I venture to say that there is more text available using this code in the English-speaking world than there is using French numbers and would be happy to undertake a bibliographic comparison if that would assist Committee II with its deliberations.

I question the wisdom of voting on any motions regarding numbers before the chemistry code issues was raised and discussed by the Committee. This represents a certain lack of good faith on the part of the original members of the BANA-appointed Committee II. This is the second occasion on which you have chosen to completely disregard a code subset that is widely used in BANA countries. Is the linguistics code used by BANA transcribers receiving a similar neglect and what are the implications of that? Are the new members of Committee II well informed regarding these codes? If not, then I feel the committee may be acting in some haste by passing motions that seem at first take to be insignificant but that inexorably create a frameowrk that hampers real progress.

5. The characteristics of learning and using upper and lower numbers, as opposed to European numbers, are markedly similar and advantageous to readers.

Committee II needs to carefully consider the fact that there is very little difference from a reading point of view between upper and lower numbers. The fact that both BANA and BAUK employ both types of numbers is probably for this very reason. From a learning perspective, there is an analogy between upper/lower numbers and many upper case/lower case letters in the print alphabet. A change of position with a retained shape is easy to teach and to read. Both sets of numbers have a low incidence of dots so their reading and writing can be accomplished with more speed regardless of the individual pace of each user.

Though they do follow an explainable pattern, the French numbers all have different shapes from present numbers--upper or lower. All but one of their shapes are larger than the corresponding upper or lower number.

By now, I expected to see some professional commentary on these potential problems enter into Committee II's deliberations. Specifically, I wish to request from Emerson some professional study regarding these matters. This professional study should come before we embark on what may prove to be an unwise course of action in attempting to use these numbers with all their attendant unknown complications. I don't know and would not want to prescribe a meaning to 'professional study'. I would go so far as to suggest that enough other problems can be raised to call any lengthy study into serious question. However, Emerson serves on this committee in part as a professional analyst. Some analysis is essential before we take seriously the adoption of or significant testing of a wholly new system of numbering.

Here is what I believe: First, if we were to be forced to use a dual numbering system, it would be more advantageous for the secondary system to be as similar as possible to the primary system i.e. lower numbers. Secondly, nobody will accept two separate sets of numbers that are shaped differently if they have used lower-cell numbers.

While it is not the work of Committee 2 to do field testing, it is your responsibility to give due consideration to the effectiveness of your recommendations. I think Emerson's input is essential in developing this thinking.

6. There are various reasons to question the wide use or acceptance of 'European' numbers even in France/Europe.

What do we factually know about the use in Europe of the French numbering system? Is it used universally in Europe or Western Europe? Do countries have dual codes with upper-cell numbers and French numbers coexisting that are used by their braille presses and transcribing agencies? It is not clear to me that Committee II is in command of such information and you simply must be in order to consider a recommendation of this dual code to the Ad Hoc committee.

Secondly, I have some anecdotal information from France which suggests that the French numbers have acceptance problems even in the country for which they are named. While in Paris on November 17-20 of this year, I evaluated a braille box. While reading some braille, I encountered French numbers and was surprised at how quickly and easily I could read them. Thinking I was either losing my mind, suffering more than I thought from jet lag, or that my practicing of these numbers was finally paying off, I stopped and took a long look at the string of numbers I had read with relative ease. Upon more careful examination, I realized these particular numbers were formed with dot 8 as the lower cell addition rather than dot 6. This has the effect of more readily allowing the reader to ignore or not touch the lower dot once you become aware that a string of numbers has been encountered.

I questioned the creator of the box who had also coded the computer braille portion of the driving software. He told me that this symbology was in use with other equipment and that it was gaining popularity because of the problems of reading the numbers with dot 6 added to them. He has responded to his user groups difficulties with these numbers by using dot 8 instead of dot 6.

I mention this story in order to inject a cautionary note into Committee II's deliberations. Don't be too hasty to push onto English-speaking users a system that may be called into question in the very country which is being promoted as its champion. On the other hand, perhaps acceptance is very widespread and what I saw was just a tiny experiment or aberration. In any event, I'd like to know, and I'd like to be reassured that you have considered these points in a rigorous manner.

Finally, I would like to know somewhat more about the ways that countries use braille who also use French numbers. For example, we know that France has a system of contractions that is far more complex and comprehensive than SEB. Does that increase user tolerance for a system of large and different-style numbers for technical codes?

7. ... Conclusion

Finally, the net effect of a dual system of numbers, and particularly a system that uses European numbers, is to place the vast majority of the burden of change on the shoulders of those of us who use technical materials for work and pleasure. For a unified code, and speaking for a moment solely for myself, I would accept a heavy burden of change and work! For just another dual system of braille, I do not, and I believe my constituency will not, accept any such burden. Committee II now founders in a morass that is in part created due to a stubborn resistance to consider seriously lower-cell numbers. To a large extent, you are attempting to make decisions in a factual vacuum fuelled only by assumptions about the acceptance of the French numbering system--even by the French people. You place at considerable risk the entire UBC project by flirting with a system with no proponent outside the committee save one.

These are somewhat harsh and and uncompromising statements. But, they are no more so than I feel your adoption of a French-number system would be to the braille-using public of the English-speaking world.

I'm not a "codesmith". I'm a reader. My technical development was greatly hindered by the changes from Taylor, to early Nemeth, to 1972 Nemeth code and by the accompanying lack of ability to read and properly understand any of those codes for years. For my high school and many of my college years, I turned completely away from all but the required technical courses. Only over time did I come back to computers---almost by accident--and begin again to do technical work. Much of this was due to lacks and changes in our codes. A unified code, while it would create similar disruption, could help others avoid such a situation. But, it must be unified, and it must make sense, and it must not place all existing material on the scrap heap!

I firmly believe that a unified code can be accomplished. Further, I believe that Committee II is our best hope in achieving that end through your creation of a framework for the surrounding tasks that have been defined. But, you must find a real solution to the problem of numbers. You've got to avoid the temptation to flirt with clever, interesting (but functionally irrelevant) ideas because they're intellectually interesting. We've got to have a unified code we can get people to support and use.

The U.S. public has never adopted the metric system, despite its technical superiority. What do you think would happen to a system that redefined the shapes of 0 through 9? Do you think blind users will be any more open-minded? I do not!

1993-12-15 EF: Questionnaire (ef3c15)

When I prepared the first questionnaire that was sent to those who evaluated the first proposal for a unified braille code, I did not have enough time to ask for advice concerning questions that should be included. I was worried about the willingness of evaluators to submit to a long questionnaire, and in retrospect, I believe that I reacted by making it too short. Following is a longer version, It includes a question about the way in which numbers should be written. Depending on the Committee's recommendation concerning numbers, this question may have to be changed. I have just included it in its present form as a place holder for a question about numbers. Please feel free to suggest any question you think should be added, and feel free to chalenge the inclusion of any question now on the list. You can send your criticisms and suggestions to me at

Better still, you can use my e-mail address, which is <{email address removed}>.

Unified Braille Code Questionnaire

Please supply the information requested below. If you write your answers in braille, write them on a separate sheet of paper, and begin each answer on a new line that starts with the number of the question you are answering. If you need more than one sheet of paper, please place your name on the first line of each new sheet.

Rate the importance of item 9 on a scale that extends from 1 (very unimportant) to 5 (very important).

Rate items 10 and 11 on a scale that extends from 1 to 5. 1 = completely unacceptable; 2 = would probably not be tolerated; 3 = neutral; 4 = acceptable; 5 = well worth the price.

Rate items 12, 13, and 14 on a scale that extends from 1 to 5 (1 = should not be done; 2 = not necessary; 3 = neutral; 4 = desirable; 5 = very desirable).

Rate item 15 on a scale that extends from 1 to 5 (1 = should not be attempted; 2= unimportant; 3 = neutral; 4 = worth trying; 5 = essential).

1993-12-15 JG {John Gardner, observer}: Comments on numbers (jg3c15)

I have been following the deliberations and commentaries on unified braille with interest and increasingly with concern. The community seems to be falling apart at a time it needs to be coming together. Since I originally proposed the European Computer numbers, it is my duty to explain why, and I do that below. I also have three specific suggestions that may help bring us closer together and settle our differences rationally. With luck we will end up with a code that we all like and that is good enough that we will all be happy to defend it against the inevitable critics who will oppose any change whatsoever. I wish us all the wisdom of Solomon and lots of luck.

For observers who do not know, all major countries in Europe use single cell numbers in their braille computer codes - the digits 1-9 are defined as a-k with an extra dot-6. Definitions for digit 0 vary, with the full cell, the number sign, and the dot-3-4-6 symbol being used respectively in the UK, France, and Germany. Most other European countries adopt the German (technically the DIN) standard, and it is this set, not the French set that has been proposed for ubc. I will just call them EC, for European computer, numbers.

To my knowledge there are only four general scenarios for numbers that are presently used somewhere or other in BANA or BAUK. These are:

There are certainly a wide range of other possible number definitions, some with major advantages. For example, one could redefine half the EC numbers to obtain a character set having no major conflict among letters, numbers, or punctuation marks and having average dot density lower than upper or lower numbers. However this set has little relation to present numbers. I think a proposal like that would be utterly harebrained and that most people will agree that the only realistic possibilities are the four I list. In fact, there are only three that are really realistic. Redefinition of all punctuation marks for a general braille code is almost as unthinkable as redefining letters, so I drop 2(b) from any further discussion. Each of the remaining three possibilities has advantages and disadvantages.

The problem with both upper and lower numbers is that many types of important technical materials are so loaded with indicators that they become almost impossibly clumsy to read and write. There are three problems with EC numbers. One is that they are unfamiliar to most English-speaking braille users; the second is that the dot density is significantly larger than with the other choices; finally the lack of overlap with letters or punctuation is a two-edged sword. It removes all ambiguities but takes up more symbol space.

As a recently blind person whose braille ability is poor, I can read EC numbers just as easily, or more honestly, with just as much difficulty, as I can other braille cells. When I proposed the EC numbers for the ubc, they seemed almost a panacea. Their larger symbol space requirement is more than offset by the lack of ambiguity. Although unfamiliar to most English- speaking braille users, I thought that their obvious advantages would win over reluctant readers. However I did not appreciate fully the possible problems caused by their larger dot density. I do not need to be convinced that less is more when it comes to reading rapidly. However it remains unclear to me whether the EC dot density is a minor or major problem.

My reason for championing EC numbers was based, I hope, on sound scientific ground and a strong bias for a ubc technical code that is easy enough for the average child to use and good enough to serve the needs of professional users. Designing that kind of technical code is not trivial. If one starts off with a character set in which numbers require indicators, the code has two strikes against it at the start. I am convinced that one can design a far better code than anything used presently if unambiguous single-cell numbers are part of the basic character set.

Since I am on sabbatical in Germany this year and know that the Germans are possibly the most braille-dedicated people on earth, I have turned to my German friends for advice on the usability of EC numbers. They cannot understand what the big fuss is all about. EC numbers are part of their computer code, and they just learn and use them. No big deal. I have asked both users and teachers, and all seem happy with the EC numbers. This anecdotal evidence suggests that people are pretty adaptable and that EC numbers would not be the disaster that some people think. However, a decision as important as this one should be based on more than a few tidbits of anecdotal evidence.

To my knowledge there has never been a controlled test comparing the different number codes. Frankly I don't think a controlled statistically- valid ! test would be possible within bounds of human decency towards the test subjects. However, it should be possible to use American and European computer users as test subjects to answer a more limited set of questions that can provide enough insight to guide us. I strongly suggest that we conduct such a test before making any irrevocable decision about what the number code should be. I have three specific suggestions.

Suggestion 1 is to the ubc committee. Please regard the motion now under discussion as tentative pending the outcome of the tests. Of course all motions are tentative and can be revoked by future motions. However, if this motion is understood as tentative by all, the committee can conduct its business so the time loss would be minimized if the committee has to retract the motion later.

My advice is that the committee should approve the present motion and then spend a few weeks delving more deeply into advantages and disadvantages of EC numbers other than readability. You already know the disadvantages of upper and lower numbers relative to coding. I claim that EC numbers make a markedly superior code possible provided you adopt a minimal-symbol philosophy. That makes the loss of symbol space less important and results in a code that is far simpler to learn and remember. However I don't know whether it will be actually easier to read. I can read it fine, but can others? If this philosophy turns out to be unacceptable, the loss of symbol space may become a killer for EC numbers. In the end EC numbers may have to be rejected for reasons other than readability. I hope you will be willing to spend a bit of time on that subject before diving in too deeply into the nitty gritty.

My second two suggestions are actually invitations to certain people involving a lot of work. I hope they can find the time to respond positively. Emerson Foulke is the person who should set up and supervise any acceptable number test. I will be delighted to assist and take the role of proponent for EC numbers. I challenge Chris Gray to join us as the proponent of lower numbers.

I suggest that we write up a page or two of number-heavy braille text, including typical computer programs, algebraic expressions, a few wierd number combinations, and numbers of the kind commonly encountered in nontechnical literature. Chris and I would try to assure it is a fair test by spotting biases against our favorite numbers and by inserting a line or two in which we expect our choice to be particularly effective.

For Americans and Canadians we would make up a version in grade 2 braille and a version in BANA computer braille. For British we would make the computer version in the present BAUK code. For Germans I can arrange a translation into German contracted braille and the DIN code respectively. The German literary code uses the same upper numbers as English literary braille.

Next we would ask for volunteers among people who consider themselves good computer braille users, send them the pages, and ask them to tape record themselves while reading it back. We would ask them to tape record themselves during their first reading and if they think that the first reading was not representative of their best abilities, to read it a second time. We can then analyze the tapes for speed of reading, comprehensibility, and number constructions that are obviously hard to read. By comparing the reading of the literary and computer versions, we should be able at least crudely to normalize for differeng skill levels. I also suggest including a short questionairre about such things as when the person learned literary and computer braille and how long it took to learn the latter.

We can each hope that our point of view is confirmed, but we can mostly hope that the results are unambiguous. If any of us are not convinced of the validity of this test or think that too many people cheated, we could repeat the tests under better control at national meetings such as the ACB and NFB meetings in July or the German national meeting that will be held this year in May.

Although I will be surprised if I am right on all counts, I will boldly predict what we will find.

We can hope that this test will definitively determine whether there is a clear-cut best choice for numbers. Even if the results are not unambiguous, it should narrow the options and give us some quantitative measures of "readability". For example, if the results are exactly as I predict, lower numbers should be eliminated and considerations narrowed to upper and EC numbers. Furthermore, if upper numbers are found to be clearly superior for literary use and EC numbers clearly superior for technical use, then the present motion would be right on target.

My third suggestion is a request of Abe Nemeth and Steven Phippen. You are the leading proponents of two well-developed math codes that you find comfortable. You are both capable champions of the good things about your two codes. As you both know, I have recently made a proposal that has a significantly different philosophy from both of yours. I claim that the technical part of my code is a great deal simpler to learn, read, and write than either Nemeth or the BAUK code. My present proposal includes use of EC numbers in grade 2 braille, but it can easily be reformulated so that it does not and such that its impact on grade 2 braille is small, in fact smaller than either the original or present Committee 2 code. My code is also extremely computer-friendly, so both standard literature and scientific texts can be translated very easily to and from braille. It is not a complete panacea. It has some inherent disadvantages, ones I believe are insignificant, but others may disagree.

I would like to provide the ubc committee (and anybody they want to share it with) a quick and easy way to compare the advantages and disadvantages of my code relative to yours. I believe that such a comparison could help greatly in guiding future directions. Even if the committee hates my code philosophy there may be enough good ideas there to warrent your time and attention. If the committee wants more detail on my code, I will be glad to supply it, but I don't feel that an observer has the right to request more than a quick and easy look by the committee at his/her suggestions.

I propose that the three of us prepare a few examples of coded math equations. Suppose that each of us prepares, say four equations each, ranging from simple arithmetic to calculus (or beyond) that illustrate good features of our codes. Then we will each code all 12 equations and make the whole thing available to the ubc committee. I will provide an explanation of the meaning of symbols in my examples so nobody has to learn the whole code to understand the examples. I suspect that nobody on the committee will need that kind of explanation from either of you, but if anybody does, I am sure you will be willing to supply it.

If you agree to do this and either of you cannot print up his part of this packet, I will be glad to do so provided you send me the materials by e mail coded in the usual format of the ubc committee. I will then supply the package to the committee in braille and electronic form.

Aside from illustrating the virtues of three technical codes, this little exercise will put together a packet explicitly illustrating the advantages and disadvantages of all three number system possibilities. I hope you think this is worth your effort.

I wish to thank the committee for providing this forum for observers. !

1993-12-17 JS: Procedural notes (js3c17)

Please pardon this intrusion into the observers' time on the floor for just a few procedural points:

1. I have set up a new standing file series on the BBS, called ICESL??.ZIP, to hold selected items from ICEB and our parent (UBC Project) committee for a given year. For example, ICESL93.ZIP holds the items for the current year, including the minutes from the Sydney meeting in June.

2. The message that Darleen sent in the last few days, relating to future meetings (including ours in April) is in the new archive ICESL93.ZIP, with file name FUTRMTG.TXT. Incidentally, if any of the recipients are unfamiliar with the methods for handling binary files (i.e. the UUENCODE/UUDECODE utilities), please let me know and I will be glad to send the file as a plain text message.

3. (This is in reply to a question from John Gardner, but really for everybody.) Yes, observers are encouraged to forward material from all persons who have something to say about subjects of interest to the Committee. Thoughtful presentations on all sides are welcome, and while careful scientific studies are obviously of great value, testimony of the "I like ..." or "I dislike ..." or "I didn't like but have come to like ..." or "I liked at first but now dislike ..." variety is also useful--lest we operate in a vacuum, separated from the direct voice of individual readers.

1993-12-17 CG: Gardner Challenge (cg3c17)

What John Gardner suggests by way of research is interesting. Of course, I would be willing to be involved in such a project and have no problem being a proponent of lower-cell numbers. I cannot resist pointing out though that the very need for such research is just one more reason to question the validity of a Committee II recommendation to use this EC numbering system.

There is one impression that John makes which I feel some need to mention. It is that in part the UBC work recognizes--and I believe there was an implication that it seeks to resolve--serious deficits in lower-cell numbers. In fact, deficits of any numbering system per se had nothing to do with the inception of this project. The overriding reason for the UBC work is to unify differing number/braille systems that are in use in the English-speaking world. The only reason for even considering numbers is in order to find a way around symbol ambiguity.

For a computer code, EC numbers are an excellent alternative. For a code in a vacuum, EC numbers are certainly as good as lower-cell numbers in terms of code construction; probably not for readability. But, what about a math code? Is there any math or technical code other than computer codes that employ these constructs? In Germany, these numbers were introduced as part of the computer code. What do Germans do for mathematics or other sciences?

Perhaps most important of all, this work is not being done in a vacuum. BAUK and BANA countries have math codes and technical codes already. Whatever is decided will create change in one or more of these codes. I do not subscribe to the idea that the best solution, given that change is required, is to find a third, entirely new alternative that forces drastic change on all parties in order to avoid deciding who is hurt more and less in the process of change. What must be decided is how to help the reader most. I cannot bring myself to believe that redevising all our technical codes from scratch in order to accommodate a new numbering system--no matter how interesting--is in readers' best interests. Braille is already in serious jeopardy as a communications system. The addition of dot 6 to numbers may as well be analogized to the pounding of the final nail into braille's coffin.

Thanks to all for listening and for the chance to speak up on this issue. You are in a very unenviable position and I certainly appreciate and respect that. Best wishes for the Holiday season.

Chris Gray

1993-12-20 JS: Season's greetings (js3c20)

First, I would like to thank those observers who took the time to submit their views during the "observer week" just past. Also, please remember that it is always possible, via messages to me or the other Committee members, to be heard. I should have more to say about that later, and should also address some of the issues raised during the observer dialog.

But not now. I received an E-mail message from a friend in Australia a few days ago, and in it he concludes by noting that he and I should both get away from our computers and spend some time with our families. He is right, of course. I had to smile, thinking that not the least blessing of the Internet is the swiftness with which it can bring kind counsel from halfway around the world.

As I take his advice for the next week or so, I encourage all of you to do the same, if you are so inclined. If not, please go right ahead, as I will be keeping up with the mail and maintenance of the BBS in the interim.

This is the season of Light, of Peace, and of Renewal. So may we all be touched by these things: our minds enlightened, our hearts filled with peace, and our spirits renewed to guide us--not only in our little project, but in our larger lives as well.

2012-12-19 AB: Response to Joe's paper on dropped numbers contained in js3c11 (an3c19)

I would like to begin by saying that Joe's paper was one of the most interesting and well-organized submissions of recent memory. The purpose of the paper was allegedly to respond to Raeleen's request for more information about dropped numbers. Instead of developing the subject of dropped numbers, however, Joe uses them as a sparring partner for an opportunity to promote his preference for the "French" number system. Of course, you know that I will respond to the points he raises so that Raeleen might have a more balanced view of the situation. At the end of this submission, I will raise some points of my own.

Joe, of course, is right when he claims that any one of the three competing number systems will work, and even work without ambiguity. Being unambiguous is a necessary attribute of a uniform code, but it is by no means sufficient. A uniform code must also interface well with the braille user. To this end, there are several other requirements.

(a) Braille symbols must be readily recognized when reading and readily recalled when writing. In a robust code, there will be several hundred symbols. Of course, no one user is expected to know them all. Nevertheless, the braille symbols that he does use must be organized to facilitate their recognition and recall. There are several mechanisms available to us to achieve this goal. One such mechanism is the preservation of symmetry of symbols in braille when they are symmetric in print. a second mechanism is to group symbols together which constitute recognizable families. A third mechanism is to devise dot patterns that imitate or at least suggest the shape of the corresponding print graphic. This committee has paid scant attention to these mechanisms. Instead, we have been operating on an ad hoc basis, assigning available braille symbols to print graphics that are in the forefront of our immediate attention. If we do not take the assignment process more seriously, there will be a fragmented set of assignments with no discernible relationships among themselves. In rearranging the "braille furniture" to make room for the "French"-number symbols, Joe has destroyed the symmetry that existed between the begin-fraction and end-fraction indicators without a single pang or regret. I have had a very long time to think about how to make assignments, and I invite you to look at ANCODE to see how they were made.

(b) Indicators must interfere as little as possible with the symbols which convey the content of the text. This committee has had repeated experience with how upper numbers offend in this respect. In a recent submission, I demonstrated with a simple example using upper numbers that seven indicators were required to support an expression in which there were only ten content symbols. Yet this committee continues to ignore this problem as if I had never called attention to it and to advocate for upper numbers as the primary choice. Realizing that neither the upper number system nor the "French" number system is by itself an adequate basis for a uniform code, there is now a motion on the floor that the proposed code should be based on both systems.

I have proposed a two-level set of Grade-1 indicators instead of the three-level set which this committee currently supports. The need for a Grade-1 indicator in the middle of an otherwise Grade-2 word for indicating a single Grade-1 character is so rare, that it is not sensible to maintain the three-level structure of Grade-1 indicators just to support such rare occurrences. I have proposed the simplest of rules: A word is either entirely Grade 1 or entirely Grade 2. I know from experience that failure to apply this rule leads to all sorts of dilemmas. When is a word predominantly Grade 1 and when is it predominantly Grade 2? The problem is like deciding whether a zebra is black with white stripes or white with black stripes. >From the braille reader's point of view, a three-level Grade-1 indicator system is unnecessarily burdensome, particularly when the implementation of my suggestion would do much to relieve this situation.

(c) A uniform code cannot have a dual number system (more about this toward the end of this paper.) I take sharp issue with Joe with regard to his claim that any combination of number systems can work. I continue to maintain that only one number system can work; otherwise we do not have a uniform code. I, and many other blind people as well, have had the experience of being guided by a well-intentioned but uninformed would-be helper. Getting behind me and placing his hands on my two shoulders he propels me in some random manner in this direction and that by first applying pressure to one shoulder or another in some random pattern. Reading a text in which there are two number systems has much the same effect on the braille reader. First we must read using the numbers from one set and then using the numbers from the other in some random order depending on the content of the text. And which number system should be used is definitely NOT a matter of taste. How a number system affects the first two factors I have mentioned above -- patern recognition and the use of indicators -- determines the superiority of one system over the other, not personal preference.

I will dismiss the case in which an entire document is in classic Grade 1 as moot. No document with the kind of material we are discussing is ever brailled in classic Grade 1. On the other hand, there are many documents in what I will call quasi-Grade 1. These include computer programs and documents that have been back-translated for the purpose of using speech to access them. Such documents are variously described as being in Grade 0, in computer braille, or in machine braille. Such documents, of course, are fair game for discussion purposes. Joe has given quite an accurate description of how my proposal, based on the system of dropped numbers, works. I will claim here that the absence of an indicator for a single symbol is an advantage, not a disadvantage. I have already discussed this above.

At this point, I would like to clarify A point in my proposal that I probably did not make clear. Even within a phrase that has been previously introduced by the double Grade-1 indicator, a word that begins with a digit still requires the numeric indicator. This familiar character serves for physical orientation, even though, from a logical point of view, it may not be necessary. Another point: the numeric indicator is used to introduce only a digit, it does not take the period (decimal point) or the comma into account, as does the UBC report. Still another point: If the first word of a phrase begins with a digit, the phrase is introduced by ;# (dots 56 3456). I also did not make this clear in my proposal. With these conventions, a numeric indicator, if it occurs at all, occurs only at the beginning of a word; there is never a time when it would be used in the interior of a word. Similarly, the Grade-1 indicator (dots 56), if it occurs at all, occurs only at the beginning of a word, never in its interior. The code based on the UBC proposal does not share these properties.

Joe points to the inefficiency of a code based on dropped numbers when punctuation is present. As we know, Joe has made a tabulation of number-letter and number-punctuation juxtapositions using a 50-page sample from "Scientific American." This tabulation is contained in jssciam1 submitted in June of 1992. Before submitting this tabulation, Joe made all the appropriate disclaimers concerning the statistical validity of that sample. I have looked at this tabulation again. Joe counted 676 juxtapositions. One of the categories that Joe identified was the category of punctuations which occupy the lower part of the cell. He reports that there were 96 such juxtapositions either before a number, between two numbers, or after a number. Unfortunately, he included among such punctuation the hyphen, the dash, the apostrophe, the left single quote and the right single quote, none of which require the punctuation indicator in my proposal based on the use of dropped numbers. I have no way of knowing by how much to reduce the 96 count because of the inclusion of the above-mentioned punctuations. So I will make no reduction at all. Juxtaposition with lower punctuation, requiring the punctuation indicator then, occurs about 14 percent of the time in this sample. If the 50 print pages of Joe's sample were transcribed into braille, they would occupy about 125 braille pages. An incidence of 96 punctuation indicators in a 125-page braille text, which is less than one occurrence per braille page, can hardly be described as inefficient, particularly when weighed against the benefits of a code based on dropped numbers. This is the first of three attempts to discredit a dropped-number system on the basis of the need for a punctuation indicator. I will point out the other two as we proceed. Joe now advances several numbered arguments to which I will respond using corresponding numbers.

1. The Esthetics of the Braille Character Set: To associate the relative importance of a graphic with the dot pattern that represents that graphic is a subjective flight of fancy. I do not believe that braille readers have any awareness of that kind of association. It is a kind of Rorschach test in which one uses braille dot patterns rather than ink blots to read esthetic values into the dot patterns. Only four punctuations in print can be thought of as "down and out of the way." They are the period, the comma, the colon, and the semicolon. The hyphen and the dash are neither "up" nor "down," and are certainly not "out of the way." The apostrophe, the left and right single quotes, and the left and right double quotes are "up and out of the way." All the other punctuations, like the left and right parentheses, the left and right brackets, the left and right braces, the left and right angle brackets, as well as the slash, the question mark and the exclamation mark are fat cats that sit astride "all four lanes of the print highway." If ever there was a killer ink blob in print, it is the gg sequence of letters. Yet this letter sequence is represented by a lower sign in braille without the slightest sense of artistic violation. Of course, the biggest lower sign available was chosen to represent this letter combination. Digits, which are supposed to have primary importance, are sometimes printed so small when they are in the superscript or subscript position, that people with normal eyesight sometimes use a magnifier to identify them. For me, the example that Joe shows us is just as easy to read in one form as in the other. If one is used to reading only upper numbers, then the second example looks strange. If one is used to reading only dropped numbers, then the first example looks strange. And if one is used to reading both upper and dropped numbers, then both forms are equally readable. In my case, the second version came as an old familiar friend. Habit, not esthetics, is what determines preference. Are we supposed to use this esthetic factor as a weight in choosing between dropped numbers and "French" numbers? I would say to Joe what Queen Gertrude said to Lord Polonius: "More matter with less art!" [Hamlet: Act II, Scene II, Line 95.]

2. Simultaneous Modes: As Joe surely knows from the early work of our committee, literal mode (as we called it then) for a word extends through the entire word; and if that word includes punctuation, then it extends to the punctuation as well. In the "dropped-number" example, the right quote needs the punctuation indicator, thus:

7,he m>k$ ! map ) ;x}_7

Without the punctuation indicator we would have a 7, so that ;x}7 might be one of the committees in the ANSI organization.

Joe has misinterpreted my intention and, naturally, reacts to his conception of my intent. In my "dropped-numbers" proposed code, there is only a Grade-2 mode and a Grade-1 mode. A Grade-1 word is introduced by the numeric indicator (dots 3456) if that word begins with a digit or with the Grade-1 indicator (dots 56) if that word begins with a non-digit. A Grade-1 phrase begins with a ;# (dots 56 3456) indicator if its first word begins with a digit and with ;; (dots 56 56) if its first word begins with a non-digit. My proposed code does not have a "number" mode, local or otherwise. Thus, the mode structure in my proposed "dropped-number" code is simplicity itself. In the next set of "dropped-number" examples shown both in classic Grade 1 and Grade 2, the final quote requires the punctuation indicator in both examples. The third possible treatment of which Joe speaks is the only treatment and would apply to the previous examples, as I have already indicated.

3. Physical Ambiguity: Again Joe misinterprets me. As I have indicated earlier in this submission, a word that begins with a digit requires the numeric indicator even in the interior of a literal phrase to avoid the kind of ambiguity that Joe points to, even though such a numeric indicator would not be required on logical grounds.

4. Duality: I have repeatedly called attention to the duality of the period and the comma and have deplored that duality as a necessary evil, given the braille system as it is today. However, as I have also repeatedly pointed out, these are the only two dual symbols in my proposed "dropped-number" code.

To read hidden duality into punctuation marks because of the punctuation indicator is an act of desperation. In SEB, we could also claim hidden duality for each of the digits on the grounds that if the digit is the first in a sequence of numeric symbols it must be represented by using the numeric indicator, but if it is in the interior of a sequence of numeric digits, then it can be represented without the numeric indicator. Come on, Joe, if you will withdraw your charges of hidden duality in my code on account of the punctuation indicator, then I will withdraw my charge of hidden duality in yours because of the numeric indicator. See Section 3.4, "Simple Numeric Indicators," in the "Report by the Objective II Committee" for "enlightenment?"

5. Statistical Considerations: In an earlier part of this submission, I indicated that in Joe's "Scientific American" study, the incidence of punctuation indicators in a braille transcription of that document would be less than one punctuation indicator per braille page. My proposed "dropped-numbers" code can hardly be indicted as inefficient on these grounds.

6. Statistics in Elementary Literature: Joe reports that in his study of literature for elementary students, there were two instances in which the punctuation indicator would be required in a sample containing 60,000 characters. It doesn't even pay to turn on a calculator to compute what percentage that is. This is the second attempt to discredit the "dropped-numbers" proposal based on the need for a punctuation indicator. I enjoyed the quote from Dr. Seuss, but I can't see any problem. I would transcribe 4:42 as:


in my proposed "dropped-numbers" code, just as Joe has correctly done. The punctuation indicator is effective for just one punctuation at a time.

7. Juxtaposition: The distinction that Joe makes here is nothing more than grasping for straws in the wind. It is a difference without a distinction. There's nothing technical about 4g if Johnny happens to live in apartment 4g or if he happens to be in Grade 2b. Surely, Johnny has a qualified teacher who is able to guide him through the treacherous Terrain of the braille system, where there are obstacles much more numerous and formidable than the ineffectual ones to which Joe calls attention.

8. Intense Technical Material with Scarce Punctuation: To get both versions of the example to have the same length, it is necessary that both are embedded in a longer technical text. If these were single words surrounded by Grade 2 text, the "French"-number version would require two Grade-1 indicators, but the "lower-number" version would require only one.

9. Intense Technical Material with Frequent Punctuation: Integral equations -- I once taught such a course. I agree with Joe that it's a good thing that we went to college when we did. Commas do not require the punctuation indicator. Exclamation points used as factorial signs are not punctuations. Two-cell symbols are common in advanced math, and the factorial sign happens to be one of them. That leaves the semicolons. How many of those there are Joe does not say. This is the third attempt to discredit the "dropped-number" proposal based on its need for a punctuation indicator. This time we are not provided with any statistics. As Joe pointed out early in his paper, selected examples don't prove much. What we need is a large number of typical and problem examples from various fields. They should be selected to point up the strengths and the weaknesses of the competing number systems. John Gardner's proposal to submit examples for evaluation and examination is a good one.

10. Punctuation Frequency in Computer Programs: Some more side-by-side examples for comparison, please.

11. Readability: Of course one can learn to read and write "French" numbers. How steep is the learning curve? Can one ever achieve the comfort, speed and intuitiveness of either upper numbers or dropped numbers, or is improvement only incremental? How well does retention of the acquired skill persist after a lapse of time? And, finally, do "French" numbers have such a clear advantage that the learning task and the adjustment are worth the trouble? These are questions that only a good, well-conceived experiment can answer.

And now, I will continue the numbering scheme and present some thoughts of my own which have more to do with the work of this committee than with the relative merits of the two competing number systems.

12. Is it possible that some of us are looking for excitement and adventure? In the early work of this committee, the possibility of using "French" numbers never came up for discussion. Of course, we all knew about them; at least I have known about them for more than 30 years. Not until John Gardner made his proposal and our committee was expanded did the possibility of using "French" numbers catch fire. In jsm19.txt Joe says: "Somehow I like '"French numbers"' as a working nickname, even though the committee may for good reason want to settle officially on some other name such as DIN, British Computer Code, European or Continental or whatever. (And really, do any of those other names sound as attractive, fun, or sophisticated?)" And ever since then, the subject of "French" numbers has taken up an inordinate amount of our committee's time and attention. While this number system is part of the computer code for several countries, it has never been incorporated into the math or science codes of those countries, even though it has been available for so many years. Whatever its merits or deficiencies, "French" numbers Are not in the mainstream of the braille system of any country. Computer codes have limited purposes and limited use, and "French" numbers may adequately serve those purposes and uses. On the other hand, dropped numbers are centrally used both in the Nemeth Code and in the British math Code, although they play radically different roles in their respective codes. Of course, they are also part of the American Computer Braille Code.

Then the suggestion appeared that we should use dot 4 or dot 5 to replace dots 56 as the Grade-1 indicator. These possibilities are nothing more than the musings of a single individual and have no status in any known braille system. No situation arose that caused us to question the rightness of our original decission to use dots 56 as the Grade-1 indicator, Yet we devoted an inordinate amount of time considering this issue, to the point of making a motion and submitting the question to a vote. Fortunately, the committee's original decision was vindicated.

Then came the issue of notational abbreviations as used in the British math code. Fortunately, we did not spend a lot of time with this issue, but it was yet another distraction. We are not a philosophical debating society and we should not go off on excursions that impede and delay our main task, regardless of how interesting and exciting they may be. Meanwhile, six months have passed since our expanded committee has been at work and we have very little progress of substance to report.

13. I continue to press the issue of duality. I know that for now mine is a voice "crying in the wilderness." Nevertheless, my conscience does not allow me to back away from this issue, and I know that the rightness of this position must eventually prevail. We have duality right now by way of a Standard English Braille code in which upper numbers are used and a math and science code in which dropped numbers are used. It is this duality that Tim and I brought to BANA's attention in the paper that precipitated this project, and it is this duality which played an important role in BANA's decision to undertake this project. Should children continue to deal with two number systems with all the unpleasant implications inherent in such a course? The duality envisioned by the motion now on the floor is worse than the duality that now exists. At present, a child experiences the consequences of duality only when he migrates from a math or science book to a history or social studies book and back again. In each of these two generic categories the number system is constant. If the motion on the floor is adopted and a code based on it becomes official, a child will have to switch from one number system to the other in a random manner within any book he reads, no matter what the subject matter. What would be so terrible if ALL books were based on a braille code featuring dropped numbers only? Books with upper numbers would not become obsolete because the transition between reading upper numbers and reading dropped numbers is so intuitive. The training of vision teachers would become much simpler because no special courses in Nemeth Code would be required. Transcribers would need no intensive special courses and no additional special certification. A braille user could learn as few or as many of the technical symbols of the code as he requires without unlearning what he already uses. And most of all, a child would never have to face the awful prospect of having to learn another number system. The resulting code would be simple, robust and UNIFORM. My wife's mother had a pithy saying: "Dare to tell the truth and be prepared to have your head knocked in." So be it.

14. And meanwhile, the silence on the part of most of our observers and all of our overseas colleagues tells me that they are sitting back and watching this display of squabbling and infighting with great amusement, bewilderment, and disbelief. As long as there is blindness among us in the human race, I have a vision of what braille ought to be, unencumbered by political alliances, intense loyalties, or the inertia of the status quo. Let's not put obstacles in the way of blind children more than they already have. Who has the courage to advocate for BRAILLE rather than for some parochial issue that relies on braille to lend it credibility? This is not our finest hour.

1993-12-20 CL {Clive Lansink, observer}: Numbering systems (cl3c20)

During this time when the floor is available to observers, I feel it is time for me to pass on my comments on numbering systems. I regret I have not followed the initial arguments in detail, and have been more attracted to the issue by recent comments. So I hope my comments do not display too much ignorance of previous discussions.

First and foremost, I believe we should aim at a single numbering system rather than a dual one. Furthermore, if we can agree on that as a matter of principle, then the best single numbering system in my view would be the lower numbers, because they resemble the existing upper numbers in shape. However if we do not agree on the need for a single numbering system, then that leaves us presumably with retaining the existing upper numbers for literary braille (whatever that is these days), and we then need to decide on what other numbering system should be used for scientific or other special purposes (and again the problem is that these days there is a real blurring of when something is specialized or not).

To expand my comments:

We must get away from continuing the distinction between literary braille and other codes that are used in specialized situations such as science and maths. Nowadays, even in texts that might be handled directly through literary braille, you can come across constructions in the print which are simply not handled by what we know now as literary braille. Codes such as Nemeth have always been able to handle complicated print constructions, but we've always had to treat these as specialized. I would like to see a single code that can cope with virtually all specialized situations, perhaps by the use of symbols that most readers would not have to learn. In other words, a base code with various incremental levels of complexity that can be brought in as the need arises. But I would see the handling of numbers as being fundamental to the base code, and therefore I feel we need to come back to the principle of a single numbering system.

The problem that occurs with multiple codes, particularly if they are diverse, is that the whole work being transcribed must be judged as to which code is best to handle it. The current situation is that if literary braille is judged to be appropriate for a given book, then the book will be transcribed according to that code, and any instances in which the code does not cope with the particulars of the print will most likely be ignored or incorrectly transcribed. By "incorrectly", I mean that there will probably be a failure to deliver a true and impartial interpretation of the exact print to the braille reader in those instances. The transcriber will avoid switching to an alternative code for fear of making that whole passage unreadable to anyone who does not know the other code.

If we accept the argument to support the use of just one numbering system, the next question is what system should it be?

It seems reasonable that any numbering system will include a numeric indicator to inform the reader that we're now reading something that contains numbers. It also seems reasonable that any numeric indicator would need a corresponding punctuation or similar indicator to indicate the end of the number. No matter what numbering system is used, I can't see any way of realy avoiding that, especially if most contractions are to be retained and if we want to construct a code that can cope with today's print complexities. That is the very reason for this whole unified code issue.

The question then is what numbering system to use. I can accept there are some advantages in the use of French numbers. But it appears to me from the reading that this system is only being proposed as a secondary numbering system. My aim is to push for a single only numbering system, and in that context, the lower numbering system is in my view a clear leader.

The main advantage is its similarity to the existing numbering system, except that the digits are in the lower half of the cell. The added dot six in French numbers clearly changes the overall shape of the characters, and I agree with the sentiment that you have to switch more gears mentally to cope with that. I would also accept though that in the long term we would get used to that. But I wonder how many people who are in favour of French numbers would support it as the "single" numbering system.

In summary, I believe we need to start from the foundation of a single base code to cope with today's print, and that this really demands one numbering system. My personal view is that in that context, the lower number system is the best.

Thank you for the opportunity to contribute directly to these most fascinating discussions, and I feel sure that after a while we will reach consensus on the best braille system that will meet the needs of blind people in tomorrow's fast changing world. Once again I apologize if my comments indicate some ignorance of the full detail of the discussions thus far.


1993-12-18 SP: For the attention of Committee 2 (sp3c18)

In response to Joe's request, I have asked a few people who are used to reading "French numbers" from their use of the UK computer code, and the general opinion seems to be that this style of numbers does not impede reading in any way. Braille computer displays are reprogrammable and some UK users change the braille character set to the UK code out of preference ("French numbers" and normal punctuation), some do not bother or do not want to and leave it with the US computer code (lower numbers, different punctuation). There does, however, understandably seem to be a real, if temporary, difficulty when making the transition from one system to the other.

However, it was also said by an experienced computer user (who uses the UK code both on his terminal, and of course in braille computer books), and who is also a UK maths code user, that if a choice had to be made he would regard it preferable to drop computer code "French numbers" used in transcription rather than disturb the use of ordinary numbers and the rest of the system in maths code. This view coincides with that of the Chairman of our Computer Committee which I reported in an earlier file on the bulletin board. In fact all of the people I have asked (without any prompting from me) have said that they are against disturbing the number system used in maths code, and indeed are against disturbing the general structure of the maths code - and these are people who are computer code users. When I informally sounded out a maths teacher of the visually- impaired about possible changes to the maths code he said (again without any prompting) that if there were any changes "there would be uproar amongst the teachers". Now I don't pretend that this is necessarily a balanced viewpoint, but I do think these comments are worth relating so that there is no illusion in the committee about the realities of the situation as it appears to me.

It is one thing to devise a braille code, but it is a completely different matter to devise a code which is politically implementable. The revision of the UK maths code in 1987 was, I believe, approaching the limit at that time of what was politically implementable. If you read the introduction to the code book you will find a summary of what was done - i.e. not much by this committee's standards. This revision was written after the key points were raised, discussed and agreed by a committee with representatives from interested groups - users, teachers, producers, etc. I am much less comfortable with the procedure adopted in this committee and project generally where we are doing this in reverse. One idea which I have mentioned before and actually think may turn out to be a genuine possibility (but so far has not been welcomed by anyone else!) is that a code proposed by this project could exist in parallel with the current codes. This would allow people to make up their own minds and would leave the situation capable of developing over whatever time was needed, rather than alienating the braille reading and using public.

So, it is very difficult for me to decide how to vote on the current issue of numbers: if I vote on the basis of what is closest to being politically implementable in the UK as a replacement for the existing codes then it must be against "French numbers" as the standard system to be used for technical braille (i.e. grade one). If I am to vote about just a hypothetical braille system or a braille system which may for a time run in parallel with the existing codes then I am not really sure what I think. I am still very concerned about the hideously long way the proposed code would braille simple technical expressions as compared to the existing UK codes, with or without "French numbers". Just imagine doing a chemistry textbook in it - all letter signs, dot 6's and subscript indicators and terminators - Ugh! Who would want to read it? In any case I think one would have a very hard time trying to sell the proposed code with "French numbers" to the British on the basis of it being a "unified code" because the British already use the same numbers, including the technique I have described in an earlier file for superscripts and subscripts, in literary, maths and chemistry text, not to mention the same arithmetical signs, and without any special mode indicators, etc., so the "unified code" would be less unified than what they already use!

As I have said in an earlier file I do think we ought to try to substantiate or refute the casual opinions such as those I have reported before we get carried away into cloud-cuckoo-land with this project. The January 4th deadline is much too soon to do this.

Anyway, I will not place my vote till after Christmas and I have had more time to worry about this. I have given a copy of Joe's proposal to Bill Poole and hope he can advise me.

1993-12-27 AN: Letter to John Gardner (an3c27)

December 27, 1993

Dear John,

Thanks for your warm and friendly letter. Although I have you in mind as I reply, I am taking the liberty of sharing this letter with my colleagues on Committee II because it contains material which may be of interest to them and because there is nothing of a personal nature in this letter. I must explain to my colleagues that I somehow lost the file you submitted during the week for observers (jg3c15) and, when I asked you to replace it, not only did you do so graciously but you also included a few inquiries to which this letter responds. Therefore, I will e-mail this letter as I always do to the committee, and a copy will come to you as a qualified observer..

You have some questions about how my proposal works. I will send you my proposal of June 16, 1993 as a separate file. It is an 85K document, so don't start it too close to lunch time. Nevertheless, I will answer the more specific questions you pose in your current communication right now.

As you know, I am proposing to use dropped numbers everywhere without exception. This would include page numbers at the corners of pages, dates on title pages, etc. As you also know, I have created dual representations for the comma and the period. I deplore the need to do this, but it was necessary to preserve the braille system as we know it today. Not all punctuations require the punctuation indicator. Those that do are: the semicolon, the colon, the question mark, the exclamation mark, and the neutral (as opposed to oriented) double quote. The punctuation indicator would be used only in Grade-1 words, that is, words in which Grade-2 contractions would not be permitted. the punctuation marks themselves would not be changed from what they currently are in Standard English Braille. Then there are parentheses. In agreement with you and with almost everyone else, I use ( (dots 12356) and ) (dots 23456) for the parentheses. In Standard English Braille, however, these are the contractions for "of" and "with". Therefore, the punctuation indicator would be required before these symbols, but only in Grade-2 words, that is, in words where contractions are permitted. Thus, parentheses are treated differently than the other punctuation marks. Parentheses require the punctuation indicator in Grade-2 words, but not in Grade-1 words, whereas the other punctuation marks listed above require the punctuation indicator only in Grade-1 words but not in Grade-2 words.

In June of 1992, Joe chose a sample of 50 pages from "Scientific American" on which to do a statistical analysis for getting a handle on just how frequently the punctuation indicator would be required. Without going into detail, he found that in these 50 pages, the punctuation indicator would be required 96 times. If these 50 pages were transcribed into braille, they would produce a braille document of about 125 pages. So, the punctuation indicator would be required about 96 times in a 125-page braille document. This is an occurrence of about once in every page and a third of braille. Joe made all the proper disclaimers about the validity of this statistical analysis. In another study using children's books, he found that the punctuation indicator would be required twice in a 60,000-character document. He also examined a textbook on integral equations, but did not report how often these punctuation indicators would be required.

Next, you inquire about the handling of fractions. There are several principles involved here. The first is the "just-in-time" principle. Just as a sighted person knows that he has encountered a fraction, the braille reader should have the same information at the same time. This is why I devised fraction indicators. With their use I know immediately that I have encountered a fraction and I know exactly what belongs to the numerator and what belongs to the denominator. If I used your enclosure method in the quadratic equation, I would not know that I was dealing with a fraction until I reached nearly to the end of the whole formula. The British code handles fractions like you do thereby incurring the same problems for the braille reader, except that their enclosure symbols are printable. The second principle demands that no enclosures be used in braille when there are none in print. The print form of the quadratic equation contains no enclosures whatever, yet your transcription requires three sets of enclosures, one for the numerator of the fraction, one for the argument of the radical sign, and one for the denominator. It would be a non-trivial task for a computer to reconstruct the formula in its original printed form from your braille version. There is also a psychological dimension involved. As a new enclosure opens, the braille reader must review in his mind which enclosures are already open and push this new one onto his mental stack. And when an enclosure ends, he must pop the matching opening enclosure from the stack and review in his mind which enclosures are still open. There is a limit to the human span of attention and, in advanced math, this limit would be reached fairly soon.

And then you ask about radicals. In particular, you ask how I would write "the square root of the cube root of x equals the sixth root of x." My proposed radical sign is > (dots 345). You will notice that the dot pattern bears an unmistakable resemblance to the radical sign in print. In our current Committee II discussions, Joe is proposing that this braille symbol serve as the end-fraction indicator, so that the mnemonic association in my proposal would be lost. Without any attached superscript, the radical symbol indicates the square root. For other radical indices, just attach an appropriate superscript to the radical sign. My proposal implements a "nesting" principle which would have to be used in the example you propose. On the left side of your equation there is a two-level nested structure. I will transcribe your proposed equation and then I will give you a blow-by-blow analysis of what is going on. Your equation would be written thus:

;;,>>~3"x{,{ = >~6"x{;

Before going further, you should braille out the example so as better to follow my remarks. Now for the analysis.

1. ;; (dots 56 56) tells you that you are entering a Grade-1 phrase in which braille characters must not be interpreted as Grade-2 contractions. Had we been dealing with a Grade-1 word rather than with a Grade-1 phrase, only one occurrence of ; (dots 56) would have been required.

2. ,> (dots 6, 345) tells you that this is a nested radical structure with one level lower than the one you are currently at. Had there been still deeper levels, there would be additional dots 6 to tell you exactly how many deeper levels there are. This is another instance of the "just-in-time" principle. You wouldn't want to trip over an inner radical deep inside an equation without having been warned to expect it.

3. > (dots 345) is the lower-level radical.

4. ^3 (dots 45 25) is the superscript 3, so that this lower-level radical is the cube root. In general, the superscript could have been more complicated than just a 3; it could have been n+1 for example, and still no enclosures would have been required.

5. " (dot 5) is the base-level indicator. It tells you that the superscript is finished and that you have returned to the base level.

6. x is the argument of the lower-level radical. Again, in general, the argument of the inner radical could have been much more complicated than just x, and still no enclosures would be required because the radical itself acts as the opening enclosure and the terminating indicator acts to end the enclosure.

7. { (dots 246) terminates the lower-level radical.

8. ,{ (dots 6 246) terminates the outer radical. It has the same number of dots 6 as the radical which it terminates.

9. = (dots 123456) is the equals sign.

10. > (dots 345) is the next radical. Since no nesting is involved here, no dot 6 is required.

11. ^6 (dots 45 235) is superscript 6; it indicates the sixth root. Again, the superscript can be as hairy as you like; it is enclosed on the left by the superscript indicator and on the right by the base-level indicator so that no extra enclosure symbols are required.

12. " (dot 5) is the base-level indicator again. It tells you that the superscript has ended and that you have returned to the base level.

13. x is the argument of the radical.

14. { (dots 246) terminates this radical.

15. ; (dots 56) tells you that the Grade-1 phrase (containing three words) has ended. The construction may at first seem complicated in braille; but it is also complicated in print. That is why mathematicians frequently abandon radicals altogether in favor of fractional exponents. Just the same, if you need to use radicals, here is a way to do it.

When it comes to complex fractions, which are really nested fractions, I use exactly the same mechanism. By putting the proper number of dots 6 before the begin-fraction indicator, the corresponding end-fraction indicator and the corresponding fraction bar for that fraction, the braille reader knows, "just-in time," exactly how deeply nested the fraction structure is. I have gone into this much detail here because none of it is in my proposal. My proposal only extends Standard English Braille to the same degree as does the Committee II report of last November. But I have been using these mechanisms for years; they are part of the authorized Nemeth Code. But read my proposal; then we can discuss it in as much or as little detail as you like.

I am now into your file of December 15 which you shared with our committee as an observer. You attempt to make a case for European numbers by pointing out that all the major European countries use them in their computer codes. I would like to point out, in turn, that none of these countries nor, for that matter, any country in the world, use them for their math and science codes. A math and science code must be much more robust than a computer code. Whereas European numbers can meet the restricted requirements of a computer code, they have been found to be inadequate for the much more demanding requirements of a math and science code. A math and science code must be capable of representing many more symbols than a computer code, which is mostly restricted to the ASCII character set. A math and science code must be capable of representing the two-dimensional structure of technical notation, such as superscripts, subscripts, and fractions, whereas a computer code is not concerned with such matters. And a math and science code must be able to interface much more intimately with the surrounding host text, which is almost always in Grade 2, than is required of a computer code. European numbers have been around for thirty years or more. If it were possible to build a coherent, robust math and science code based on European numbers, someone would have done it before now.

You apparently believe that a large number of indicators are required in a code based on dropped numbers. This is a misperception on your part as well as on the part of many other people. What is true is that a punctuation indicator is required in a code based on dropped numbers, whereas it is not required in a code based on European numbers. Earlier in this submission I pointed out the frequency with which a punctuation indicator might be required, based on the admittedly nonrepresentative samples that Joe examined. A punctuation indicator that occurs less than once per braille page cannot be a deciding factor when choosing the number system on which a code should be based. You may be surprised when I point out to you that in a code based on a dropped-number system, a numeric indicator is theoretically not necessary, just as it is theoretically not necessary in a code based on European numbers. What is necessary is a mechanism for distinguishing between Grade 1 and Grade 2 text, and this necessity remains no matter which of the three number systems underlies the code which our committee is considering. Thus, either in a dropped-number code or in a European-number code, ; (dots 56) could serve as the basis for a system of Grade-1 indicators at all times without ambiguity. It could not do so in an upper-number code. Then why do I not advocate the use of ; (dots 56) as the Grade-1 indicators at all times in my proposed dropped-number code? Theoretically, it would work perfectly well. The answer is rooted in history. I use the numeric indicator instead as a Grade-1 indicator when a word begins with a dropped digit because of its close association with numbers among braille readers and because it serves as an orienting character to show the position in the cell in which a dropped number occurs. Note that the numeric indicator used in this way has no remote effect as it does with upper numbers. Therefore, no rules are required for determining when and when not the effect of the numeric indicator terminates. As long as I know that I am in Grade 1, a letter from a to j when dropped can only be interpreted as a digit whether or not there is any nearby numeric indicator or any numeric indicator at all. Only the punctuation indicator can override this interpretation, and then only for one character in a restricted set of five punctuation marks. Consider the expression:


in which there is no numeric indicator at all but in which the dropped numbers have an unambiguous identity as digits and are easily recognized by long-term braille readers. To represent the same expression using European numbers requires that the plus sign be changed because the one in the above example is reserved for the European 0. This is a manifestation of the crowding effect which European numbers exert on the rest of the code by reserving ten of the most valuable braille characters available to us. Joe has proposed that the plus sign be represented as ! (dots 2346). Using this new plus sign, the same expression in European numbers would come out like this:


and, although the representation is just as unambiguous as the one which uses dropped numbers, the latter expression is more difficult to recognize by long-term braille readers.

And now, let me summarize the four principal disadvantages of European numbers, as I see them:

1. European numbers are more difficult to recognize when reading and more difficult to recall when writing than are either upper numbers or dropped numbers. They involve a mental decoding process when reading and a mental encoding process when writing. European numbers are to long-term braille readers what a foreign language is to a person whose native language is English. One can certainly learn to use European numbers in reading and writing just as one can learn to read or write in a foreign language, but never with the speed, comfort, and intuitiveness of the numbers to which the braille reader is accustomed. Greater skill can be acquired with practice, but some of this skill will be lost if too much time passes without using this skill. On the other hand, dropped numbers are just as intuitive as upper numbers; they have the "look and feel" of upper numbers. In a recent tutoring session with an eleven-year-old blind girl, I asked her to add up a column of figures brailled as dropped numbers. With no prompting from me and with no questions from her, she proceeded to add them up. The learning curve for dropped numbers has a slope of zero.

2. European numbers consume ten of the most valuable braille characters. With only 64 dot patterns available, of which 26 are claimed by the letters of the alphabet, this is an extravagant depletion of braille resources. It means that future assignments will require two-cell or three-cell constructs because most of the one-cell characters have been reserved for the use of European numbers. In the example above involving the radicals, { (dots 246) could no longer be the termination indicator because it is reserved for the European 9. Since no other one-cell characters are available, the termination indicator would have to be a two-cell symbol.

3. European numbers produce dense braille. Dense braille is more difficult to read than braille characters in which the dots are more sparse. Have you ever come across the phrase: "An organization (&=! blind." Almost everyone stumbles over this one because of the high dot density. One can guess at words, but for numbers, you must palpate all the dots to achieve identification with certainty. Furthermore, it would be almost impossible to take notes with a slate and stylus if one had to use European numbers. Even recording someone's address and phone number would become a chore, and the same is true about writing amounts of money.

4. European numbers deprive the code user of symmetric pairs of characters. In the Nemeth Code, the begin-fraction indicator is represented as ? (dots 1456), and the end-fraction indicator is represented as # (dots 3456). This pair of characters has an "up-down" kind of symmetry appropriate for fractions. With European numbers, this symmetry would be lost because the symbol which now represents the begin-fraction indicator is reserved for a European 4. In the Committee II report, the recommended fraction indicators are < (dots 126) and > (dots 345). This is a "left-right" symmetry and not as appropriate for fractions as the one in the Nemeth Code. Nevertheless, this symmetry would also be lost because the symbol which represents the begin-fraction indicator is reserved for the European 2. The result is a code in which print symmetries are not reflected in braille symmetries, and in which there are no discernible relationships among braille symbols which represent a family of print symbols. Such a code becomes difficult to learn and to use.

I do not agree that we need to undertake a research project to test the relative merits of the dropped numbers vs. the European numbers. Your thinking is based on the misperception that far more indicators would be required when using dropped numbers than when using European numbers. As I have attempted to show above, apart from the punctuation indicator whose occurrence is sufficiently sparse as not to be a deciding factor, no more indicators are required with dropped numbers than are required with European numbers. Recall the example with your radicals in which there was no need for the numeric indicator even though the example contained dropped numbers. Also recall the example further along in which I compared how the same expression would be written first with dropped numbers and then with European numbers. In that example, too, there were no numeric indicators even though there are several dropped numbers. If one then takes into account the four major disadvantages of European numbers that I have listed and described above, which dropped numbers do not share, dropped numbers are so clearly superior as a number system that a test would be only of academic interest.

Next, you ask our committee to suspend the motion now on the floor until your proposed test can be conducted and conclusions reached. The motion on the floor does not deal with which number system is superior; it proposes a dual number system which your test would do nothing to resolve, regardless of its outcome. Furthermore, we could not carry out our work because what we do next depends on what we do now. Are you suggesting that we endow our code with minimal capabilities so that the loss of symbol space due to the use of European numbers will then be less noticeable? Our aim is to create a uniform code that does not restrict people from doing serious work. A code based on my proposal can handle anything of a scientific technical nature from first-grade arithmetic to quantum physics. And such a code could be used in a history book, a social studies book, or a murder mystery with no difficulty.

Chris has already responded positively to your second suggestion. However, I do not see any benefit in pursuing the project you propose. To my mind, a code is not uniform if it requires two number systems to make it work. That is what we have right now, and that is what our committee is called on to remedy. If a code is adopted based on the motion now on the floor, children who already know two number systems will have to learn a third number system. We know that an amphibious vehicle that is designed to travel both on land and on water is not as efficient as a Mercedes that travels only on land nor as efficient as a yacht that travels only on water. But the amphibious vehicle can travel on both, and that is something neither of the other vehicles can do. We must settle on a single number system for which the amphibious vehicle is the metaphor. That number system may not be as efficient in every area in which it must operate, but it will perform adequately in all of those areas.

With regard to your third suggestion, I would be happy to accede to your request. There should be enough representative examples from all the areas the code is intended to cope with. Each example should be written in my version, your version, and Steve's version. each one of us should then critique all three versions of the same example, pointing out the strong points and the weak points of each version. Someone will have to initiate and manage the project, someone will have to formulate the ground rules, and someone will have to judge the results.

This is a longer response to your inquiries than I intended to give or that you expected to receive. Writing it has helped me to clarify some of my thinking, and I hope that reading it will give you a sharper perspective.

Sincerely and cordially,

Abe {email address removed}

1993-12-28 JS: A checkpoint (js3c28)

Well, although it was too short, the holiday interlude was still enjoyable, and I hope the same was true for all of you as well.

I thought sure I must have had too much eggnog when I found myself reading, in Abe's rejoinder an3c19, that my motivation for bringing forward French numbers could be "excitement and adventure." This, based on quoting a bit of lighthearted banter about the working nickname! I think I'll give Abe the benefit of the doubt on this, and assume that he too is joking.

While on the subject of that working nickname, a less weighty subject being hard to imagine, I should perhaps enter a reminder here that "working nickname" was all that I intended in the matter. When it comes to our formal report, I would think it best to use a name that is free of any reference to geography or any specific use, such as for computers. That would obviously eliminate "French" along with some others. If there is no great objection, I expect to call them "dot-6" numbers, a neutral designation based on their common physical characteristic, in direct parallel to the "upper" and "lower" we use for the other numbers. But for now, in this company, do we always need to be that dry and formal? Put it this way: for breakfast, I could order "bread dipped in egg batter and fried". But somehow, I'd rather have "French toast"; it's not only fewer syllables, it even sounds more appetizing (to me, at least). And if others like other nicknames, as long as we understand them, that too should be just fine. I do hope that we can look beyond these kinds of issues to the things that really matter.

Coming back to Abe's memo, there are of course many points that I could debate, and would be willing to do so if there really seems to be a need. But before I expend my time writing, and your time reading, I think it best to do a little reality check on where we are and what our options are, given the course that we are on.

We have started with the committee report of November 1992 and have altered it--not greatly as yet, but by a deliberate process whereby proposed changes are moved, seconded, debated and voted upon. More changes, large and small, may well take place, by the same process. This is in accord with our charter, and also with common sense and the traditional ways in which "deliberative assemblies" operate. The details of our procedures are spelled out mostly in js3725, with minor amendments in js3901 and js3903. They are based on the well-known Robert's Rules of Order (RRO), adapted for the practical circumstances of our "electronic meeting". We try to remain as informal as possible (maybe we'll start calling them "Bob's Rules"), but we must nevertheless remain orderly or we will get nowhere. If there is any question about this, I urge members to re-read those memoranda.

At the beginning of this month, we passed motion tc3b16, to retain the traditional (upper) number system for principal uses, while not ruling out the possibility of French or lower numbers for special uses. At 6-1, the vote was not close, being even more lopsided than the 3-1 margin by which the original committee reached a similar conclusion.

Unless we go back and reconsider that action, we cannot now consider a numbering system that incorporates all lower numbers, nor can we consider one that incorporates all French numbers. The only possibilities are: (1) all upper numbers, (2) upper numbers primary with lower numbers secondary, and (3) upper numbers primary with French numbers secondary. If we take no further action, we have option (1) as the system described in our current report. But by reason of the companion motions ef3b30 and js3b27, we are actually considering option (3) at the moment.

There are of course procedures by which a motion to reconsider can be brought forward. If my memory serves (I make no claim to be a parliamentarian), such a motion must be brought by someone who was on the prevailing side of the original vote. I can look all that up if there is interest. But in the face of a 6-1 majority, it is obvious that at least 3 people will have to change their minds in order to reconsider our earlier decision to reaffirm the traditional upper numbers for primary use. Based upon what people have been saying, or not saying, I do not sense any such shift in basic positions. I conclude therefore that we have progressed beyond the point where we need expend our energies considering alternate systems that do not use upper numbers for principal purposes.

I will close with a reminder that voting deadlines are not cast in stone but may be routinely extended by a week or so, or even longer for good reason or by action of the committee itself; see paragraph 15 of js3725. In a recent memo (sp3c18), Stephen Phippen mentioned that the January 4th deadline for the current motion was much too soon to substantiate or refute some opinions that he had heard. I did not, however get a clear sense of whether that was actually a request to extend, and if so by how much time, or an expression of despair that any reasonable amount of time would be adequate. If he (and others) could make their wishes known in that respect, then I see no reason that they cannot be accommodated.

1993-12-28 TC: Speed VS Accuracy (tc3c28)

I never thought much about readability of numbers till the subject received so much attention by our committee. It never occurred to me that reading reams of numbers was dependent more on speed than accuracy.

The suggestion made by John Gardner, that we design controlled experiments to scientifically determine which number system can be read the fastest, begs the question. "Do we need to know that?" Is rapid reading of numbers something that is important to me as a Braille reader?

So, now I am paying a lot more attention to how I deal with numbers on a moment-to-moment basis. I am a little surprised by what I observe in my own reading habits.

I read a lot of Braille every day. In addition to the submissions to this forum, I emboss a lot of articles from CompuServe, the Internet and bulletin boards so that I may thoroughly read and understand the materials. I presently use the Duxbury Translation system with a translation table based on French numbers that I asked Joe to prepare. The rest of the Braille that makes up my daily diet consists of books, periodicals obtained through the library plus catalogs and other literature from vendors in the blindness industry. All of these use the traditional Braille numbers, with one exception, a computer magazine that uses the American Computer Braille Code. (This is the one that gives me the most problems, but it is not very important to this discussion.)

I don't read most numbers. Looking at a table of contents, I stop reading as soon as I discover that I am not interested in an item without bothering to see what page it begins on. On the other hand, if I see an article I want to read, then I look at the number at the end of the line and dwell on it for a brief moment in order to fix it in my memory while I continue reading the rest of the table. (I often forget and have to look again for the page number when I decide to turn to the article.)

I continue reading the table and memorizing page numbers for each article of interest, up to a maximum of about three, at which point I decide to go to the first article. With so much to read, I usually do not find a lot of interest in any one magazine.

It's much the same when I read the computer magazine. I skip most articles, skim some and read a few in their entirety. If I come upon some computer code, I either skip it altogether or I slow down (slow way down) to read and comprehend the significance of every symbol. I switch to "study mode." I struggle to extract the meaning of the code; what the programmer is doing in each line. Unambiguous clarity of each symbol is my only concern for the duration of this study. At these moments, speed is the furthest thing from my mind.

Catalogs contain a lot of numbers that are best skipped. I usually don't bother to check the price, and never bother reading the catalog numbers of items that I do not intend to buy.

Submissions by Group II members and observers to this forum receive special attention. I Braille them all. I read each one with care. I punch the Braille pages and place them in labeled and indexed binders. Most of these papers were translated using American SEB. A few used a translation table based on the proposed dot five indicator for grade one. The more recent translations use French numbers, with the exception of ANCODE from Abe. I have no difficulty in reading any of these papers, now contained in three 4-inch thick binders. I read the prose as rapidly as I can and skip numbers of no importance to the discussion. When numbers of interest and importance are encountered, I SLOW DOWN.

It's my conclusion that Dr. Gardner's readability tests would not yield convincing results. Nevertheless, his comments include ideas that are much appreciated and deserve careful study. As a late comer to blindness, he brings to our discussion a fresh perspective with little bias and no vested interest.

1993-12-30 JS: Reports by users of dot-6 numbers (js3c30)

John Gardner has kindly taken the trouble to seek opinions from users of dot-6 numbers in Germany, where he is now on Sabbatical. They're called DIN numbers there; I presume that everyone knows by now that those are the same as what I call French numbers, some may call EC numbers, etc.

I got a bit mixed up and thought that John was going to send these up during observer week, but now that I re-read his message I see that he already gave me permission to share them with you, and so I'm doing that now, with apologies for the delay.

John describes Mario Eiland <{email address removed}> as a blind computer science student from Oregon State who is spending this year at the University of Karlsruhe as an exchange student, and Peter Brass as the head of the German computer club, a part of the Union of blind and visually-impaired of Germany, and "several other things". After a telephone conversation with him, John says "Sounds like the Germans went through a period of complaining when the DIN numbers were introduced but have accepted it."

The text of the two quotes follow. (I've corrected a few minor editing glitches in Mario's message.)


Hello, I am not sure exactly what DIN code is. If it's the computer code they use here, well, yah, at first it was hard to get use to it. Now, I am doing fine. I am still learning a few things here and there. But no, I can read the numbers pretty well. I will get back to you about the other students later. This weekend I can't, I am going to Dortmund for a conference. An International conference. Basically it's a conference where students from every part of the world that are blind get together and discuss problems that they've had as blind international students. It should be interesting.

I will let you know more when I get back I am leaving tomorrow at 12:00 Noon. Schoene Wocheende.



Dear Mr. Gardner,

Thanks very much for your phone call of last Saturday. It was very good to hear from you again, and I am looking forward to meeting you either here in Berlin at at some place else in the not too distant future.

Here a few lines concerning the acceptance of dot 6 as an indicator for digits in computer braille.

For any e-mail contacts you can not only use my CompuServe id, but also another internet adress on Geonet, it reads: {email address removed}. I check both Geonet and CompuServe regularly, about three or four times a week.

I have not yet been successful getting an internet account at the FU here, because the department I have connections with just got a new department head, and thus things are being changed around somewhat. So I will have to wait and see.

For now best regards to you

Peter B.

P.s. My observations on the acceptance of computer braille are not merely of a personal nature, I have noticed this as an information technology consultant over the past 7 or 8 years, I can see this today as both a teacher at a business school for the blind where we train people for clerical professions and as a resource teacher for visually impaired kids that are being mainstreamed. I am also actively involved with several groups and organizations who deal - among other things - with curricular questions of computer training for visually impaired people.

Now here is the text as promised:

In order to achieve a 1-1 representation of characters on a computer screen and on a braille output device, European computer braille systems employ some form or other of representing a digit by only one character, thus omitting the number sign. Most widely used is the German method of adding the braille dot 6 to the first nine letters of the alphabet. The figure 0 does not strictly adhere to this convention since it could be mistaken for a w. Instead 0 is represented by the braille dots 3,4,6.

In the early years of braille displays and embossers a number of blind people as well as their educators were concerned about the additional braille system to be mastered, but when computers began to move into the work place and into education at a rapid pace in the mid eighties, this concern soon vanished.

After some initial hesitation, most blind people quickly took to this new system and not only accepted it but also welcomed it because it provided extra reading speed when reading uncontracted braille from the computer.

I have been teaching the use of computers, peripherals and various software packages to many blind people (high school and university students as well as working adults) over the last 7-8 years, and I never noticed more than some initial bewilderment over the new braille symbols to be acquired.

When talking to colleagues in the field, I found that they all share this opinion. We have actually observed that some blind people carry over the use of computer braille conventions to their braille writing when using a brailler or slate and stylus.

Peter Brass!

1994-01-04 RS: (untitled) (rs4102)

I feel it is time to break the extended silence from "down under" and move towards greater participation in current discussions. The silence has by no means indicated a withdrawal of interest in or commitment to the work of Committee II. More truly it is confirmation of this commitment and the need to have a good grasp of the obviously difficult task. It also reflects a time delay in coming to grips with past discussions and deliberations.

While I do not wish to delay the committee's progress unnecessarily, I believe that a matter as significant as the current motion requires clear understanding by all committee members who also have a responsibility to their constituent countries. Based on the information and data that I have absorbed to date It is not possible for me to reach a firm position on which to vote by the deadline of 4 January. At the same time failing to vote may hinder the international involvement and co-operation of this project. To test whether I am alone in my present dilemma or whether other newcomers to Committee II have similar difficulties, I move that the deadline for voting on EF3B30 be extended to 22 January 1994. For me, this extension would enable a thorough perusal of Archive files, consultation with other interested persons in New Zealand and hopefully additional input from representatives from countries who, to date, have remained relatively silent. Greater input from those countries experienced in the use of BAUK codes would be particularly valuable in developing a global perspective of this project.

To date much of the discussions indicate observations according to individual experiences and situations. These observations are useful particularly when viewed collectively. Specific research data to support our observations would indeed be helpful. For example, I firmly endorse the dots and holes concept, the problems that new (and not so new) braille readers experience with dot density such as the proposed French numbers, the preference of upper dots over lower dots for ease of recognition, particularly by less experienced readers. Is research data available that confirms or refutes my firmly held observations? Similarly, is research data available related to the problems associated with retaining a single numbering system as proposed in the original Committee II report?

Raeleen Smith

1994-01-03 JS: Some issues raised by observers (js4103)

During the "observer week" that we had in mid-December, there were a number of issues raised, probably more than I will have the time and energy to address. However, there were two in particular that I would like to comment upon, as they relate to the direction and methodology we are taking, and I think I may be able to provide a bit of clarification on those matters.

The first such issue is whether UBC would seek to preserve subject-based distinctions, e.g. "math" vs. "general literature" vs. "computer programs", in its formulation. That goes to the very heart of what UBC is all about, and--believe it or not--there seems to be broad agreement among the Committee II participants that the answer to that should be "No". For example, when I use terms such as "in dense mathematics" or "in C language programs" or "in text with SGML markup", I am using descriptive language so that we can consider how well this or that approach will work in real subject areas that our code is supposed to handle. I am not referring to categorizations that a transcriber (or program) would need to make as part of a transcription. Therefore, rather than saying "this is math, so I must use this approach, whereas if it were literature I would use another approach ...", the transcriber would simply react to the symbols that are present, without it being necessary to discern the underlying "meaning" or "subject area". This kind of concept seems to underlie all our writings, my colleagues' as well as my own, and that is why I say that there is broad agreement on that point--which may be why it does not come up, in direct form, very often. (Of course it is possible that I have mistaken a colleague's meaning in some case, but if so I assume that we will hear a correction in due course.)

For that reason, questions of completeness (being "able to transcribe anything") and nonambiguity of representation in the braille (being able to read anything and know for sure exactly what symbols are represented) are, strictly speaking, independent of the matters that we have so earnestly been debating of late, e.g. which kind of numbers to use. That is not to minimize the practical differences that accompany the various approaches, but simply to state that all of them are intended to yield a complete and nonambiguous code, and so agree in goal.

As usual, a balancing cautionary note is in order. Despite the general philosophy described above, there are some kinds of materials that remain outside our intended domain, and even some distinctions within that domain that we may need to keep making. Music, for example, is excluded by definition. We have suggested that extensive foreign language text, even in English-based instruction material, might be better treated outside our system. And we have acknowledged that, practically speaking, only "meaningful" font changes and not merely stylistic ones should ordinarily be brought to the reader's attention. In summary, it seems to be unavoidable that sometimes a human transcriber (or a human user of a computer program) would need to make some distinctions that, if this were a perfect world, we would all surely want to eliminate.

This issue is closely related to our initial emphasis on "reader rules" as opposed to "transcriber rules", as discussed in the November 1992 report; js3a26 also discusses some aspects of this subject.

The second issue I would like to comment on relates to our methodology, whereby we are extending a system based on SEB (Standard English Braille, i.e. the American and British literary codes considered as a single code) to encompass technical notation, rather than using one of the existing technical codes as a working starting point. It was pointed out that the latter approach could save the existing literature and the transcriber and reader experience in the adopted code. There is therefore a reasonable basis for thinking that we should start with some specific technical code. In fact, I suspect that many people assumed that we would follow such an approach, especially in the beginning when we were just a BANA committee and included among our number the chief architects of the existing BANA technical codes.

The first point that needs to be made, though I think not the most important one, is that the adoption of a particular technical code does not seem to be implied in the charge given to us by our parent committee. As I see it, there are actually five existing relevant English codes: SEB, British Maths, Nemeth Code, CBC and British Computer Notation. (I realize I am not counting some significant variants and extensions of these.) Of these, only SEB was put to us as having what I will call "presumptive" status: that is, we were to presume we should stick to SEB as it is, including contractions, etc., unless we had good reason to change something. We were not told to consider any other code in that category. Moreover, certain aspects of the charge given to us seem to imply that we would work outward from SEB rather than adopt one of the technical codes alongside SEB. Even the name of our subcommittee, which incorporated the phrase "extending the base code", has that connotation. Of course it has always been obvious we would consider, and draw heavily from, existing technical codes; that is just common sense. But, even when we were a BANA committee, we were pointedly directed to "consider the BAUK codes", lest we lean too hastily in the obvious direction. Finally, when we presented our report in November 1992, no one to my recollection mentioned failure to adopt a technical code as a point of divergence from the charge given to us.

A second point is that, even if we had decided on our own to adopt one of the math or computer codes as a presumptive standard, how would we have decided which one? The adherents of the two maths codes have had decades to convince each other that theirs is "best", but neither has prevailed, as we know. Choosing between them would send us off on an impossible (and unnecessary) tangent; I think the recent debate over numbers would look, by comparison, like a minor tiff over pizza topping. And, even if we somehow ever reached such a choice, we would be little progressed from where we are now: we would still need to extend a base code to encompass the "winner". And further, as we proceeded to do that, even the "winning" technical code would most likely need changes that ardent devotees would consider too large, leading to the question of who "won" after all.

The third point, which I think is the central one, is that the method we are using does respect the existing technical codes, and where possible borrows from them and builds toward them, in an orderly and neutral fashion. In that sense it can be viewed as one way to try for a synthesis--though I must hasten to point out that no synthesis can be expected to be "close" to all of these codes, for they are just too different. In the process, it is entirely possible that UBC will borrow more from one tradition than another, though if it does so it will be for a reason, case by case. In other words, there is no inherent reason that we must reach a conclusion much different from one that we might reach by starting with some particular technical code. In any event, we do not expect nor want to build a code that is different just for the sake of being different.

It may be useful to reflect that no code is entirely characterized by any one of its elements. Nemeth code, for example, is not just lower numbers, but incorporates many other symbols and, importantly, structural aspects such as ways of showing fractions, subscripts, superscripts, radicals and so forth. A code that followed many of these structural aspects while using, say, upper numbers would surely not present an impossible hurdle for Nemeth code users to get over. For the same reasons, it is overly pessimistic to assume that the work done on supplementary codes would necessarily be lost; in all probability many of the same "ways of doing things"--which are always among the hardest things to work out in a code--could be adapted even if some different symbology were needed here and there. The same general comments could be applied to British maths, or either of the other codes.

More could be said about related matters, such as the expected useful life of existing technical transcriptions, and no doubt other subjects further afield. But I hope that the above offers some clarification on the main points, at least.

A final note for observers: As I have mentioned before, observers are by no means "cut off" from making their views known, even outside the periods of time designated for observer comments. I and the other committee members are generally open to receiving messages, and, if you so request, would most likely bring them to the full committee's attention, at least in summary form, no matter whose views they support. (Of course we do have to worry about relevancy, redundancy and such, but thus far I would say that seems to be more of a theoretical than a practical worry.)

1994-01-03 JS: Voting deadline on motion ef3b30 (js4103a)

I am pleased to hear from Raeleen and I think that the proposed date of 22 January is entirely reasonable. I'll wait until I've had a chance to check the fax at the office tomorrow morning (it being now late Sunday evening, my local time), just in case Stephen Phippen has requested an even later date by that means. Then, I'll issue a "Chairman's status report" with the new date.

I still hope that we will have progressed at least a little beyond numbers by the time it is necessary to "close" our report for the April meetings. (We must keep in mind the need to pre-circulate at least a month in advance.) But we need not fault ourselves too much for having taken a long time with numbers. The original committee did the same, and we were not considering as many options; it is a truly difficult subject.

In fact, at a church service a few days ago, I had a reminder just how long we've been at it. I suppose I might have been in a half-daydreaming state--unaccustomed, of course--when the lector announced "A Reading from the Book of Numbers." When the actual reading started a few seconds later, and I came out of my reverie, I realized that my subconscious had already anticipated something like "3, 632, 127.45 ..." --and was preparing to count letter signs and punctuation indicators!

1994-01-03 BM: Miscellaneous (bm4103)

Firstly, greetings and best wishes to all of you for the new year. Here in Sydney it is very hot - over the century mark in the Fahrenheit scale - in marked contrast to the weather on the east coast of the US. Australia is currently playing South Africa in the cricket test, and this reminds me that unfortunately we have not, as yet, had any input from South Africa on the question of number systems. While my present submission is ostensibly about numbers, there are some issues that I will discuss first, because they are important in their own right, but also because they do have a bearing, in a general way, on the subject of numbers.

1. Political Expediency: In An3218, Abe made the following provocative assertion: "I have been presented with the argument that some choices must be made on the basis of political expediency. My perception is that this political expediency is more perceived than real, and that its proponents are engaged in a form of visceral reasoning designed to retain the status quo in that part of the braille universe in which they happen to reside." As I made mention of "political" considerations in BM3b16, and as I believe that the notion of "political expediency" is one that we cannot and must not overlook, it seems timely to consider it further.

Maybe the term "political expediency" is the wrong one. What I at any rate mean by the term is probably better conveyed by "political sensitivity". To illustrate, I offer the following: Over the last fifty or so years, the Australian Government has tried a number of approaches in its dealings with the Australian Aborigines. Segregation and "conversion" on mission stations was widely practised, even until fairly recently, but then the idea of assimilation became the flavour of the month: let's encourage the Aborigines to become like white Australians, and everybody will be happy. So the Government built nice bungalow-style houses for Aborigines, just like the white people had. So, what did many Aborigines do? Did they humbly thank the Government for its philanthropy, get married and settle down to have 2.5 children like everybody else? in fact, They dismantled the houses, and used the materials for firewood or to build temporary structures that were more in keeping with their traditional nomadic lifestyle. Had the Government been more politically sensitive, they would have used the money for other things, like improving the quality of health care available to Aborigines.

The analogy with the development of the UBC is probably clear by now. I believe that we must be sensitive to the needs and wishes of the braille-using community. If it is clear that a particular proposal will be rejected or accepted so grudgingly that teachers will not teach it, nor transcribers and others use it, then we must either mount a very skilful advertising campaign, or not waste further time on it.

I am disturbed when I hear or read comments to the effect that those who oppose change are a pesky minority, the implication being that they don't know what is good for them, and that they are spoiling things for the rest of us. My experience in conducting or being involved in workshops on the UBC in Australia is that many braille users have a real fear that braille is going to be made more inaccessible to them, or that it is going to be destroyed altogether. Many braille users - particularly those for whom braille has been a difficult medium to acquire - see their independence and sense of identity as being under threat. For people who are blind, braille is more than a literacy medium, important though that is. It is a symbol of identity - of belonging to a group - just as the Sabbath was to the Jews in the Diaspora, or African music and culture is to many black Americans today.

When we are discussing proposals for changes to the braille system, we must, imho, be attuned to the sensitivities and fears of those who use it, recognising that for many blind people, braille is a symbol of their independence - an independence that has only come after a hard-fought struggle. If we regard the opponents of change as mere grumblers or obstacles, we will be unlikely either to succeed or be judged kindly by history. This is what I mean by "political expediency", although I will be inclined to refer to it as "political sensitivity" or just "sensitivity" in the future, unless someone can provide me with a more accurate term.

2. Time Frame: some concerns have been expressed that Committee II is taking too long to resolve issues, and that it is spending too much time discussing tangential or individually-motivated proposals. That has not been my perception: those of us who are members of Committee II are here because, in the opinion of our respective National Braille Authorities, we have something to contribute. Part of that contribution is to provide the interface between our braille-using consituencies and the Committee, but an equally- important facet of our contribution is as individuals who have experience with and commitment to braille. So far, I have not seen a proposal that has struck me as being frivolous or irrelevant, or unworthy of full discussion.

If the UBC project had remained a BANA affair, things might have been simpler for Committee II participants. But it was internationalised, and as such we now have the task of trying to unify codes that are very different, if not in symbology and structure then certainly in philosophy. In striving to achieve this task, there are bound to be new ideas that will cause us to re-examine issues that we thought we had settled. I cannot emphasise too strongly that for countries such as Australia and South Africa that purchase considerable quantities of braille from both Britain and the US, it is vital that the UBC project results in a single code. If the end result is that Britain and the US have incompatible or even substantially different literary codes, then I see it as a real possibility that braille will no longer be used in Australia, except by an elite few. I heard not so long ago that an Itinerant Teacher expressed the belief that there was no point teaching braille to blind children because they will not have the opportunity to use it once they leave school. A visiting Special Education "expert" from the US was asked at a recent Special Education Conference in Australia whether she thought that braille was important for blind students. Her answer was that braille isn't important, because Stevie Wonder doesn't use it. Because she was seen as an "expert" the educational administrators present at the conference took note, and they are the ones who make decisions as to what resources are made available to blind students in schools. We don't have Braille Bills in Australia yet: I know of one family that had to take their vision-impaired daughter from a State school and enrol her (at considerably more expense) in a private school because the State education authority would not teach her braille. I mention these examples to show just how much is really at stake. What we do now is really going to have a lasting impact on braille, and I don't want to be known in later life as one of the infamous Gang of Eight who gave the educational bureaucrats the opportunity to kill braille. If it means that we have to spend another six, or even twelve, months discussing individuals' proposals, I think it is time well-spent.

3. Research: some suggestions have been made for research into the relative efficiency of the three number systems. I also made a suggestion along these lines. I still think this would be a useful exercise, but I believe that it is the function of the Braille Research Centre to conduct such research, not individuals, whether members of this Committee or not.

4. Terms of Reference: some concern has also been expressed that Committee II is going beyond its terms of reference in considering a change to the number system. Such is not my understanding. If we believe that we cannot develop a Unified Braille Code without changing the number system, I think we have the mandate to do so. What we do have to do is to make as few changes as possible to existing braille - it really comes down to what is possible. The internationalisation of the project may mean that we will have to consider changes that would not have been necessary had the project remained as a US endeavour.

And now back to numbers. I have been keenly observing the flow of opinions on this subject, though not with amusement or disbelief. Far from it: the issue is a complex one, and there are many subjective factors that cannot be resolved by "logic", be it of the Aristotelian or the fuzzy kind. I also wanted to consult with some of my colleagues before I expressed further views on the matter.

When I supported the motion that allowed for the use of French numbers, I envisaged that they would only be used in a limited, definable number of cases that would be of a sufficiently specialised nature as to be of little interest to the average braille reader. The current proposal, to use French numbers in Grade 1, and upper numbers in Grade 2, is one that I cannot support, for the following reasons:

1. Duality: I do not see some duality as being incompatible with the concept of a unified code, but such duality must be adequately justifiable on grounds such as ease of reading or preserving the usefulness of existing braille books. We might, on such grounds, allow the present symbol for both opening and closing parentheses to remain (note that I am not saying that we should do so, only that we might, and that such a decision would not be incompatible with the concept of a unified code). However, numbers are another matter. I do not believe we can have a dual system of numbers of the kind that is envisaged in the current motion while remaining true to the concept of a unified code. It would perpetuate the exact kind of duality that the UBC project was designed to remove.

2. Political Sensitivity: Stephen, in Sp3c18, mentioned the difficulties of selling the 1988 revision of the British Maths Code to teachers. Reading between the lines of his message, it seems reasonable to assume that teachers in the UK would simply not accept French numbers even if they were called EC numbers. Although the British and Australian situations are somewhat different, I suspect that it would be a major challenge for us to convince teachers (let alone readers and transcribers) to teach two systems of numbers. And it's not just the teachers: it's also the educational administrators who determine policy and who provide resources. Braille is under enough threat now in some educational circles for something as far-reaching as a totally new system of numbers (new, that is, for the majority of readers and teachers) to act as a negative factor. Now I am not saying that we should be subject to the will of bureaucrats or the misinformed, but, as I discussed earlier, we would have to be very sure of the undeniable benefits of French numbers to all readers before we were to introduce them. At this stage, I'm not at all sure that all braille users would benefit.

3. Learning: it seems that there are significant numbers of people, both children and adult, for whom braille is a difficult medium to acquire and use. To introduce a dual number system that just about everybody would have to learn would only add to this learning burden. There are also many braille users now whose use of braille is infrequent (for example, some library borrowers may read one volume a month), or limited to specific areas (such as recipe books or knitting patterns) who would find it prohibitively burdensome to learn a new set of numbers. The result may well be that at least some of these readers would reduce or stop their use of braille in favour of talking books or in situ readers.

In addition, there are, from my experience, quite a few braille readers who study Mathematics, Chemistry or Computing not so much because they have skills in those areas but because these subjects are part of the school curriculum. These students are often not fluent braille readers, and they generally find the technical codes difficult to read. One student that we supported with braille material never wrote anything in braille, preferring to use a computer with speech synthesiser. I doubt whether this particular student, or others in similar situations, would have used technical braille at all if it were written using French numbers.

4. Imprecision: there are apparently quite a few braille users who only learn Grade 1. What system of numbers would they learn? If they only learnt the French system, they would be unable to read page-numbers, volume numbers and so on. On the other hand, if they only learnt the upper numbers, then they would have trouble if they wanted to read some Maths written in Grade 1, or perhaps even a recipe that talked about fractional quantities and oven temperatures. I think it would be difficult to establish guidelines as to what such users of braille should learn, just as it would be difficult to establish clear and unequivocal guidelines for transcribers as to when they should use Grade 1 (and hence French numbers). There would, inevitably, be differences of interpretation between transcribers.

5. Difficulties for Existing Braille Readers: I have left this point for last because, although French numbers are (at least in my view) more difficult for existing braille readers to use, existing braille readers will not be here forever, and we do need to project our unified code into the future. Good braille readers, or those who are sufficiently motivated, will adjust to any code change. There are some aspects of French numbers, such as their relatively higher average dot density, that might make them difficult for anyone to use, but it is very difficult to establish this when all we have to use as subjects are existing braille readers. I personally find it more difficult to read French numbers than either upper or lower numbers, and it seems that the other finger-readers of braille on Committee II do as well. But what we really need to ask is whether readers learning braille for the first time would find it more difficult to deal with French numbers.

The two conclusions that I have reached are:

1. We must have a single system of numbers that is used as the default in all material, with the possible provision of a second system (French numbers) that could be used in a small number of cases in which they had demonstrable benefits.

2. French numbers are not a viable candidate for use as the primary number system.

I still believe that the traditional, upper numbers are the best ones to be used, because they are so widespread now as to be almost universal, even beyond the English-braille-using world. For general literature, they present no difficulties, and are easy to learn and use. On the other hand, no Mathematics or Science code uses them exclusively, probably for reasons of compactness. The British Mathematics and Chemistry Codes are more compact than the Australian ones, and both are more compact than the Nemeth Code. The use of lower numbers in the codes of both countries is a principal instrument for achieving this compactness. When we were revising the Australian Maths and Chemistry codes in 1987-90, we removed some of the elements that, while adding to the compactness of the codes, resulted in ambiguity. So, for example, we now require that the subscript and superscript signs always be shown explicitly, and we show all capital letters explicitly. Our guiding principle is that the braille reader should not have to understand the requirements of the subject matter in order to decode the braille. In this respect, the Australian codes have more in common with the Nemeth code, and it would probably be a fairly painless exercise for us to adopt dropped numbers.

My real problem with dropped numbers is that they would require excessive use of the punctuation indicator. I know about the Scientific American sample, but I just don't think that such a sample is in any way representative of what the average braille reader reads. From my experience, the average braille reader reads novels, recipe books, maybe knitting patterns, and (in the case of students) textbooks. The average braille reader doesn't read Mathematics, Chemistry or Computing books to any significant extent (a consequence of this view is that none of us on Committee II is an average braille reader). There are many situations in which the punctuation indicator would be required in such "average" material: before periods following numbered instructions or exercises, before periods and commas following chapter, page and volume numbers, and before punctuation following dates. I think you would find that in such material the punctuation indicator would be required much more frequently than once per page. If we assume that the literary code is the primary code, it is unreasonable to expect the ordinary braille reader to bear the burden of all these extra punctuation indicators so that it _might_ be easier for people studying Maths, Chemistry or Computing. Moreover, such sequences as:


would cause as much confusion for many readers as


I can hear people reading "four three four two - what does that mean?"

Which brings me back to the conclusion that upper numbers, despite the expansion that their use will cause in technical material, should nevertheless be used. It seems that we either have a code that is free from excessive use of indicators when dealing with general literary material, or one that offers compactness in technical contexts. Unless either we adopt French numbers, or change some of the punctuation marks so as to reduce the need for indicators. I have already ruled out in my own mind the general use of French numbers, but the thought of changing some punctuation marks remains to be explored, and to me it is a rather tempting one.

This submission is already long enough, so I will not develop further the idea of changing punctuation marks, except by saying that if we changed the full-stop to dot 3, and the apostrophe to dots 4-5, there would be significant benefits in my view.

1994-01-03 BM: Vote on Motion re French Numbers (bm4103a)

I wish to vote against the motion in EF3B30 and JS3C01 that would establish, in principle, the use of French numbers in Grade 1.

My reasons for so voting are developed in BM4103.

Noting RS4102, I have no difficulty with an extension to the voting deadline, because this is an important matter. I would also suggest that Joe, in his capacity as Committee Chair, try to get some input from South Africa and Canada. South Africa in particular is in a unique situation with respect to the use of braille codes, and it would be useful to get their thoughts.

1994-01-03 JS: Chairman's Report on Status of the Meeting (zs4103)




By EF in file ef3b30 (see also js3c01): to establish in principle French numbers for use as a secondary system, in grade 1. Seconded: JS. Voting deadline: Jan. 22, 1994 (extended from original date of Jan. 4). Votes recorded to date: for: EF, JS, TC; against: AN, BM.


By JS in file js3b27 (see also js3c01): to fix the details implied by French numbers used as a secondary system, in grade 1. Seconded: EF.




I agree with Bruce Maguire's observation, in bm4103a, on the importance of South Africa's participation in this critical debate. Mostly behind the scenes, I have been doing my best to encourage and enable that participation, and will continue to do so. Along those lines, to make sure that Christo de Klerk and Connie Aucamp have timely notice of the extension of voting date on motion ef3b30, I will fax them a copy of this particular status report. Similarly, I'll fax a copy to Stephen Phippen.

1994-01-05 AN: Miscellaneous topics (an4105)

This submission addresses three topics: dot-6 numbers, the punctuation indicator, and parentheses.

1. Dot-6 Numbers: I voted against dot-6 numbers as a secondary number system solely on the grounds that it would produce a code with a dual number system. Apart from that aspect, I must confess that I still do not completely understand how the system would work. I will submit two examples and ask my colleagues to transcribe those examples for me assuming that the motion now being considered should carry.

(a) My wife drives a Buick Century and mostly she lets me ride along with her. The vehicle identification, stamped right on the engine, is:


in which all the letters are uppercase. How should this ID be transcribed? Please include Grade-1 indicators where appropriate, and please supply the rationale for the transcription. Would the transcription be different if the leading digit were not present so that the ID number began with a letter? According to the second paragraph in the discussion of Section 3.4 of our committee report, when the numeric indicator ceases to be effective, we are in literal mode. This is what we now call Grade-1 mode. The dropped-number version is straightforward. It contains one numeric indicator at the beginning of the word, and according to my proposal, serves as a Grade-1 indicator. This example is typical of a whole class of similar constructs that we have been calling model numbers, serial numbers, catalog, numbers, etc. Also included in this category are hexadecimal numbers consisting of strings of alphanumeric characters (letters and digits). Unlike model and serial numbers, hexadecimal numbers frequently participate in calculations. Thus, hexadecimal numbers sometimes appear in an equation or in a computational scheme as for addition or multiplication, and at other times they are simply mentioned in the host expository text. Will the reader see the same hexadecimal number in two versions: as dot-6 numbers in an equation or in a computational scheme and as upper numbers when embedded in an expository sentence?

(b) I now turn my attention to another situation. One of the braille magazines to which I subscribe deals with business applications of computers. Frequently, the size and weight of a piece of hardware are specified. Although I am making up the following numbers, they are typical of what one might find. For example, a PC notebook might be specified as:

Weight: 4 1/2 lbs.
Dimensions: 9 1/2 by 4 1/2 by 2 in.

In this example, the mixed numbers are printed with a space between the integral part and the fractional part. Also, the fraction line is a slash. Please transcribe these two lines and supply the rationale for the transcription. Here, the problem is the need to use fraction indicators. In order that these indicators not be interpreted as Grade-2 contractions, the Grade-1 indicator is required. Joe's proposed fraction indicators should be used, namely, & (dots 12346) for the begin-fraction indicator and > (dots 345) for the end-fraction indicator.

2. The Punctuation Indicator: The most common punctuation marks, by far, are the comma and the period. In my proposal, I have regretfully created dual representations for these two punctuation marks. Therefore, the only punctuation marks which would require the punctuation indicator in a Grade-1 word are the following five: semicolon, colon, exclamation mark, question mark, and the neutral (as opposed to an oriented) double quote. The punctuation marks themselves would be the same as in Standard English Braille.

The only serious objection that I have heard concerning the viability of dropped numbers is the requirement for a punctuation indicator. Different people have different concepts as to how sparse or how dense they might be. Here, then, is a valid research project for the Braille Research Center. By examining a representative set of materials, such as arithmetic textbooks, algebra textbooks, advance math textbooks, computer programs, computer manuals and reference guides, chemistry textbooks, popular periodicals, novels, how-to publications, etc., the result of the research should give us some idea of the distribution of events requiring the punctuation indicator. Such a result would be much better than widely ranging guesses on the part of different people. We will then have a good idea of how serious this problem is.

I must call attention to the fact that even though the BAUK math code uses the upper-number system, that code also requires a punctuation indicator, and that code also uses a dual comma and a dual period. In addition, the upper-number system requires a frequent restatement of the number sign and the letter sign, which the dropped-number system avoids. In fact, the restatement of these indicators is so annoying that BAUK was driven to devise what Steven calls contractions and what I have called notational abbreviations. Without these, the BAUK code would become so cumbersome as to be unusable for practical purposes. Steven has called attention to this in sp3c18. These notational abbreviations make use of -- gasp! -- dropped numbers so that the BAUK code is a de facto dual-number code. These dropped numbers are so intuitive, that the notational abbreviations are not identified in the official codebook. The codebook simply states that in such-and-such circumstances, the numbers are dropped. In my proposal, there are no notational abbreviations. Despite this fact, I do not believe that my proposal produces a code which is significantly less compact than the BAUK code, as Bruce maintains. If compactness is a real issue, then here is another research project for the Braille Research Center to conduct.

3. Parentheses: I make the following suggestion concerning parentheses -- 7 (dots 2356) should be used for both the opening and the closing parentheses, but only under the following circumstances:

(a) The parenthesis (either left or right) is part of a Grade-2 word.

(b) There is no parentheses enclosed within the current farenthesis pair.

(c) The current parenthesis is itself not enclosed by an outer parenthesis pair.

(d) The current parenthesis has a mate.

This would take care of most of the commonly occurring situations involving parentheses. In ordinary prose, the reader would detect no change in the parentheses to which he is accustomed. Item (d) is included here so that if a parenthesis has no mate, the reader will know which component of the parenthesis pair he is dealing with. The down side of this suggestion is that it creates another duality; parentheses would be represented in one way under certain situations and in another way under different situations.

This completes my agenda as announced at the beginning of this submission. I am serious about requesting the transcription of my two examples. I do not intend any entrapment. I simply do not completely understand how these would be transcribed if the motion now on the floor is implemented.

1994-01-06 EF: Reactions (ef4105)

Following are a few responses to observations made by, opinions expressed by, and positions taken by Observers and Committee II members.

Chris maintains that the need to conduct research concerning the readability of dot-6 numbers, upper numbers, and lower numbers places in doubt the validity of Committee II's adoption of the motion to use dot-6 numbers. The reasoning is that Committee II should not adopt a motion concerning the code until research can provide evidence in support of the recommendation embodied in the motion. As I understand it, the motion to use dot-6 numbers in the Grade I mode is, in fact, a motion to investigate their feasibility. Suppose that, as a result of this investigation, it should turn out that they are more economical, produce fewer situations that require disambiguation by the use of indicators than the other numbering systems under consideration, and that they make possible coding rules that allow the code to be extended to new areas with the assurance that there will be no conflicts. In other words, suppose it turned out that a code with dot-6 numbers was technically superior to a code with either upper numbers or a code with lower numbers. Would that not be the time to conduct research concerning their readability? I do not, for a moment, dispute the value of research. I am in favor of evidence. However, I also know that too much research at the wrong time can be more of a hindrance than a help. If every step in the process of developing a code must be submitted to research before a motion can be voted on, it is likely that none of us will live long enough to see the completion of this project. Both Chris and Abe question the readability of dot-6 numbers. I agree that they will probably be read more slowly at first by many readers, but I believe that this difficulty will be overcome with a little practice. However, in spite of the strength of subjective convictions for or against dot-6 numbers, questions concerning their readability do not, at present, have answers. We can certainly conduct an experiment, but we should do so at the appropriate time. Designing an experiment that permits conclusions will require some ingenuity. We must be careful not to compare measures of the readability of unfamiliar dot-6 numbers with measures of the readability of familiar upper numbers or lower numbers. The experiment must also be protected against biases that may predetermine the experimental outcome. Whether we conduct a readability experiment now or after we have determined the technical feasibility of dot-6 numbers, I will, of course, accept responsibility for conducting it, but let us not be too hasty.

What Is Unification?
If I am right about the position taken by Chris, he understands our task to be the achievement of a unified code that incorporates the ways of writing numbers and other symbols in all of the codes now in use. This seems to me to be an impossible demand. The different codes now in use are not compatible. I suppose it would be possible, at a cost of considerable increase in complexity, to devise a set of coding rules that would leave intact all of the ways in which numbers are now written, but the result would hardly be a unified code. The hope of finding one way to write numbers, regardless of context, is a major reason for attempting a unified code. If the code is to be unified, we would be foolish not to try to avail ourselves of the insights inherent in the different codes now in use, but some numbering systems will have to be sacrificed.

Between the Horns of the Dilemma
Chris observes that more than one math code and more than one technical code are in use in English-speaking countries, and that some changes will have to be made in at least one of them in order to achieve unity, but he suspects that Committee II is opting for a completely new code, the dot-6 code, in order to avoid choosing between existing codes. Naturally, he regards this as an unacceptable reason. If it were the reason for considering a completely different code, I would agree with him, but it is not the reason. If one of the existing codes would make possible an unambiguous unified, economical, and readable code, I would be happy to go with it. The fact is that both upper numbers and lower numbers cause problems. If upper numbers are used, then indicator symbols must be used so that they can be distinguished from some letters. If lower numbers are used, indicator symbols must be used so that numbers can be distinguished from punctuation marks. Frequently occurring indicators add clutter that increases the difficulty of reading. Those among us who read computer notation written in the Interim Computer Braille Code have undoubtedly experienced the irritation caused by having to wade through a string of eight or nine characters in order to find the single character of interest. Dot-6 numbers avoid some of these problems. They are not confused either with letters or with punctuation marks.

Symbol shortage
It is true that if dot-6 numbers were adopted, some of the symbols now in use in mathematics and computer notation would be in conflict with the symbols used for dot-6 numbers, and new ways would have to be worked out for writing those symbols. Abe believes that this would be an impossible task. If he were right, we would, of course, have to abandon dot-6 numbers, but I am not convinced. I think we should try before we conclude that it is impossible.

Personal Investment and Flexibility
If a unified code is what we really want, some or all of us will have to be willing to give ground. Chris hopes for a unified code that leaves intact, or nearly so, a chemistry code the development of which has cost him and those who have worked with him a few years of hard work. Abe has devoted many years to the development of a mathematics code, and he hopes for a unified code that leaves it intact, or nearly so. I understand the disappointment of people who have made such investments. There may be some consolation in the recognition that substantial parts of their codes, such as concepts of code construction, are likely to survive. There are others who, though their reasons for being apprehensive about change are not as compelling, are reluctant to accept changes in a code that meets their needs quite well as it stands. It is obvious that we cannot satisfy everyone, and the decision has already been made that we should try to disturb the reading of advocates of the literary code less than the reading of users of other codes. Chris believes that we must be very careful to hold at a minimum the difficulties offered by a new unified code to readers of all of the codes now in use - the literary code, the mathematics code, the computer code, the chemistry code, etc. We are obligated by our charge to make no more changes in the literary code than are absolutely necessary in order to achieve an internally consistent unified code, but I don't see how we can possibly accept the same obligation in regard to the other codes. Furthermore, in my experience, the readers of these other codes are, for the most part, the readers who are more flexible and more willing to explore new ways of representing meanings.

A Dual Numbering System
In view of the objective of achieving a unified code, how can we justify two ways of writing numbers? Chris believes that the charge given to Committee II forbids proposing a dual numbering system, and since he is a strong advocate of lower numbers, he is apparently willing to ask those readers who are advocates for the literary code to accept lower numbers. They may, in the end, have to do so, but I can assure you that they will be at least as upset by the prospect of lower numbers as he is by the prospect of dot-6 numbers. Abe is also strongly opposed to a system that allows two ways of writing numbers because it violates the concept of a unified code. I agree that a dual numbering system that uses upper numbers in literary code and dot-6 numbers elsewhere is inconsistent with the concept of a completely unified code, and I would personally be content with a code that discards upper numbers and uses only dot-6 numbers. However, it may sometimes be necessary to make a concession here and there. After wrestling with the incompatible demands of different groups of readers, I think a majority of Committee II members concluded that total consistency is not always immediately possible, and that we would not be straying too far from purity by allowing the use of upper numbers in literary code. This may be an opinion not shared by other committee members, but I believe that if a unified code were adopted that allowed upper numbers in Grade II and dot-6 numbers in Grade I (or lower numbers, for that matter), those readers who are staunch advocates of the literary code would, as time passed and reading experience increased, become familiar with dot-6 numbers, and a time would come when they would not be greatly disturbed by a proposal to drop upper numbers. Were this to come to pass, our unified code would be purified.

Primary or Secondary, or What?
Although, by our votes, we have agreed to call the upper numbers used in the Base Code primary numbers, and to call dot-6 numbers used in the math and other extensions of the Base Code secondary numbers, on reflection, I find this terminology a little puzzling. In technical fields, numbers are of primary importance. Do we really intend to suggest that the numbers used in these fields are of secondary importance? I think we send the wrong message when we make the primary/secondary distinction. It would be better to say literary numbers and mathematical numbers, or Grade II numbers and Grade I numbers.

The Transfer Problem
Abe points out that the transition from upper numbers to lower numbers would be easier because although the numbers occupy different cell positions, their shapes do not change. This is undoubtedly true, and the transfer to dot-6 numbers would probably require more time. My own experience and the experience of a few others with whom I have spoken suggests that the additional time would not be as formidable as Abe fears. I predict that, with practice, readers would be as comfortable with dot-6 numbers as they are with the numbers to which they are now accustomed, and the price in learning time might very well be outweighed by the advantages offered by dot-6 numbers. The chance is good enough to warrant exploring dot-6 numbers more thoroughly.

The Symbol Shortage
Abe contends that dot-6 numbers, though adequate for computer notation, are not adequate for mathematics because, in math, there is simply too much to be represented. He supports this belief with two reasons: (a) the symbols stolen from the Nemeth code by a dot-6 code, would make it impossible to create a mathematics code without resorting to very clumsy constructions; (b) were it possible to use dot-6 numbers and still construct a mathematics code, someone would have done it. Well, maybe or maybe not. I do not find his second reason very convincing. However, the first reason deserves more consideration. I doubt that the use of dot-6 numbers would make the construction of a practical mathematics code impossible, and I do not think that Abe has demonstrated that it would. He maintains that usurping 10 strong symbols for use as dot-6 numbers forces Joe to replace them with strange symbols. For instance, because the old plus sign is now the zero, Joe proposes dots 2346 for the plus sign, and Abe objects that this is a strange association for all braille readers. However, when Abe's code was introduced, many of the associations between dot patterns and meanings were also unfamiliar, but readers were not overwhelmed by the difficulty of learning them. He maintains (and correctly so in my opinion) that symmetry is important in choosing symbols that are used in pairs.

In our first attempt at a unified code, we proposed dots 126 for the beginning of fraction indicator, and dots 345 for the end of fraction indicator. However, if dot-6 numbers are used, dots 126 cannot be used, because that dot pattern is the number 2. Consequently, another beginning of fraction indicator must be found, and in so doing, we destroy symmetry. Of course, this is true, but Joe's suggestion was only a suggestion, not an accomplished fact, and we are still completely free to search for symmetrical symbols.

Meeting Changing Needs
Bruce contends that many braille readers read novels, recipes, knitting instructions, etc., and that they constitute a majority. I do not doubt that this is true, but I am also sure that the majority is shrinking. As the years pass, braille readers are setting and realizing higher and higher educational objectives for themselves. One result is that braille readers are reading more technical literature and more general literature in which technical symbols are generously distributed. We should think of the needs of future readers at least as much as we think of the needs of readers whose preferences were formed many years ago, under circumstances that were different than the circumstances that presently prevail and that will prevail even more assertively as time passes.

For Bruce, dot-6 numbers are out, and the choice comes down to one of whether we should inconvenience general readers by requiring them to get used to lower numbers and indicator symbols needed to distinguish between numbers and letters, or inconvenience technical readers by requiring them to use number signs and letter signs in order to distinguish between numbers and letters. We are supposed to take the inconvenience of those who need only literary code more seriously than the inconvenience of those who also need other codes. However, the needs of those who read only general literature and the needs of those who also read technical literature will converge, and the fact remains that by using dot-6 numbers, ambiguity would be reduced for both groups of readers.

A General Concern
In our first draft of a unified code, we wrote rules for the formulation of new symbols which, if rigorously applied, guarantee that, as the code is extended into new areas, improper symbols will not inadvertently be created. It seems to me that we need this kind of assurance. I am not aware of the existence of such rules in the codes proposed by Abe and by John Gardner. I know nothing about the chemistry code on which Chris has worked. Do these three codes include rules of this type? Should they? I think that assurance rules, to coin a term, should be required, but I would not be at all surprised to discover that some committee members will disagree with me vehemently.

It is possible to write rules that will allow us to use any one of the three ways of writing numbers that we have considered. Each way has costs and benefits. If lower numbers are used, they can be mixed with letters, but indicators must also be used, so that they will not be confused with punctuation marks. If upper numbers are used, they can be mixed with punctuation marks, but indicators must also be used so that they will not be confused with letters. This would not be a serious problem for general reading matter written in the Grade II mode, but text having a high density of numbers, which would probably require frequent recourse to the Grade I mode, would necessitate the frequent use of Grade I indicators and Grade I termination indicators. The noise introduced by their use might make text more difficult to read. If dot-6 numbers are used, neither punctuation indicators nor letter indicators are needed, and all else being equal, a code that did not need these indicators would be preferable. However, if dot-6 numbers are used, the supply of strong symbols will be reduced, and it may be that not enough strong symbols will remain to meet other essential needs. All things considered, it seems to me that the advantages of dot-6 numbers are persuasive enough so that their use deserves to be investigated, and since we have already voted to do so, I believe that we should proceed with the investigation.

1994-01-06 TC: Rationale for compromise (tc4106)

I think that this committee clearly understands its responsibility to recommend a Braille code based on Standard English Braille. We are instructed to accomplish our task without making changes to SEB beyond the absolute minimum necessary to the addition of symbols required in technical writing. When we have finished with our work, readers of literary works should notice virtually no difference with the UBC and the Grade II Standard English Braille. There is no room for compromise on this mandate.

The role of Braille in the education of blind people has been diminished in recent years. Its importance to every-day lives of blind men and women is questioned. It is because of this precarious situation of Braille that we are constrained from recommending ANY change to the familiar SEB.

If we cannot make disturbing changes to the code used by the majority of Braille readers, then the only recourse is to offer the best compromise to the advanced users of Braille--namely, computer scientists, mathematicians and other specialists. It seems reasonable to believe that these advanced scholars are better suited to adapting their reading habits than are the rest of us. Whether that is true or not, it appears that we have no other choice than to change technical notation.

There are options that should be considered to ease the pain (though I doubt the complaining) of the comfortable minority who are quite satisfied with their special codes. I expect to be told that the specialists shouldn't be asked to make any sacrifices and that the changes they want to make to SEB are really minor. Abe tells me that it would be real easy for the average Braille reader to adjust to the little insignificant changes to their numbers, punctuation marks and mode indicators. Easy for him!

To my mind, the path is clear. We have accepted the mandate to leave SEB essentially unchanged. From here, we can establish the indicators required and add the additional symbols necessary for technical writing. Much of this work has ben recommended in the first report of Group II. That report should be reviewed and adjusted wherever necessary to ease the burden-of-change on the technicians and scientists. Abe could help us do that, if only he would forsake his mission to get the world to accept the Nemeth code as the basis of the Unified Braille Code..

It is at this point that I ask myself what changes to the code would be most useful to me? I am not a mathematician or trained scientist; I nevertheless spend most of my time reading technical papers. Although I could adjust to the use of indicators to clarify expressions that include juxtaposed numbers, letters and punctuation marks, I prefer unambiguous expressions in a more compact notation. To achieve this beauty, I favor adding dot six to indicate numbers instead of preceding each with a number sign. My experience of the last few months confirms that this simple technique results in truly unambiguous and uncluttered scientific notation.

If the dot density of the dot-six numbers is troublesome to the majority of our committee, then we should seriously consider using dropped numbers in Grade I Braille. But, right away it becomes obvious that we wouldn't be able to confine changes to numbers alone because the dropped numbers clash with the punctuation marks. There may be other advantages and disadvantages to dropped numbers in Grade I that I haven't considered. These could be explored if a motion is made and seconded to place the matter on the floor.

Some have suggested that using different numbers in Grade I would place a heavy burden on children learning Braille for the first time. Is this true? It certainly would have been true when I went to school back in the 1930's. But is it true now? Back then I learned only Grade I Braille in the first grade. Grade 1 1/2 was introduced in the second grade. It seems to me that it was either the 4th or 5th grade before I was given a book in Grade II. Come to think of it, I was never taught Grade II. I was left to learn to read it without any help from my sighted teacher. I'm told that it isn't done that way nowadays. Kids start right out learning Grade II--if they are lucky enough to be taught Braille at all. Is this peculiar to the US? How is Braille taught in other countries? If Grade II is taught first, then learning Grade I would not be required until the student was somewhat advanced.

Some members of our committee see using different numbers in Grade I as a dual system instead of a single "unified" code. This is a legitimate point of view. Furthermore, if this degree of duality is an unacceptable compromise, then it is reasonable to vote against using different numbers in Grade I. The loss of this one motion is not a disaster. We will simply move ahead with the already approved single number system for both Grade I and Grade II. The only losers will be the elitists.


Well, I finished saying (as best I can) what I wanted to say, except for a grumble about the way we have to meet. I don't like what the medium does to spontaneity, good humor, bad temper, and all the subtleties that go with live meetings. Submitting everything to a spelling checker is a chore and submitting to a grammar checker is humiliating, even though I usually overrule it. The worst part of all is the loss of all the brilliant and clever rejoinders that I thought of when I read some of your ideas but promptly forgot before I started writing this.

This last stuff may not have helped you, but I feel better. Love and Happy New Year.

1994-01-10 JS: Thoughts on research, and three questions (js4110)

From the point of view of a native, our New England winters have seemed uncommonly mild for the last several years, to the point where I am easily persuaded that systematic global warming is real, and the adverb "uncommonly" may be called into question. But for about two weeks now, a series of snowstorms--about two feet from the current one, and it's still snowing--have reminded me of what it can be like, and of what I recall to be more or less normal, until recently.

All that reminds me how tricky statistics can be. Averages and trends, no matter how carefully observed, are subject to sampling errors; contrary sub-trends and exceptions can either be missed or be overrepresented in our attempt to understand the main truth. And of course everything depends on the right data being observed--that is, the right question being asked--in the first place. No wonder that it is hard to come to a consensus. From what I have read, there is no general agreement on the extent nor even on the fact of global warming; the debate still rages despite the gathering of data in overwhelming quantities over many years' time.

The same kinds of problems plague us in our work. On a few recent occasions, we have heard questions and proposals for research that, if taken too absolutely--that is, if taken as requests for the kind of research that would convince anyone anytime no matter what--cannot realistically be addressed. For, even if we could define to everyone's satisfaction what such research would be like, I have a feeling that it would occupy not only us and BRC but also half the Gallup organization for a great deal of time. The problem is that we are concerned with all possible literature, past, present and future, excluding only music and material substantially in languages other than English. As if that were not enough, we are also concerned about patterns of readership: in other words, what kinds of literature are actually read (or ideally would be read), and how often, and by whom, and under what circumstances. The work that goes into developing standard samples, such as the Brown Corpus, should disabuse us of any idea that it is easy to come up with samples that everyone would agree are truly and proportionately representative of all literature and all actual or desirable reading patterns. And then, even if that hurdle were cleared, we would still have to cope with the question of how different actual and potential braille readers, with their different reading patterns and preferences, different levels of experience, and different reactions to different kinds of change, would fare under various proposed methods of encoding the numbers (and other things, of course). Whew!

Others, notably Emerson in ef4105, have expressed similar sentiments, and so I assume that I need not go on about the subject. I bring it up not to be discouraging, but in a way to be reassuring: that we are being sensible in debating these matters even if we do not, and practically speaking cannot, have absolutely every conceivable fact in hand. We still have common sense, judgment based on considerable experience, logic, individual testimony, and of course some small targeted studies, to guide us.

With that, I'd like to take up three recent questions that seem concrete enough to try out a few answers.

1. In rs4102, Raeleen Smith asks "... is research data available related to the problems associated with retaining a single numbering system as proposed in the original Committee II report?"

If the data requested is of the statistical variety, I don't know of any other than the little "Scientific American" survey that I recently referred to. And that study concluded, in effect, that there is NOT sufficient evidence, on statistical grounds, that the letter signs induced by upper numbers are all that onerous--even in material with an obvious bias towards scientific content. Bruce was correct in noting that the material was not representative. It was not intended to be, for if it were, there would have been even less chance that scientific notation would have played a role. As it was, since the results were not close and they agreed with what one would expect in more general literature, the reader is left to infer that the much more difficult task of identifying a provably representative sample was unnecessary, since the results would surely be the same, only stronger. In other words, even though the material was surely rather unlike that available to Louis Braille over 150 years ago, it nevertheless led to the same conclusion that he had arrived at.

So why on earth are we even considering any other numbers? Good question. We are trying to do something for cases that are decidely low-incidence but that, for those who are affected by them, can occur in "bursts". If I may quote from a message I wrote at the beginning of our consideration of this subject, js3b10:

"To state the obvious, upper numbers have problems when the letters a-j immediately follow digits; the necessary added indicator in such cases lengthens the expression and thus presumably affects adversely the ability to read it and to work with it in computation. There are many examples where such juxtapositions occur, which we may categorize as follows: (1) Alphanumeric designations, such as postal codes, automobile license numbers, catalog and part numbers, and the like. Even our own message numbers, e.g. this one (js3b10), fall into this category. (2) Ordinal endings, e.g. "3d" meaning "third". (3) Implied multiplication in classical mathematics, e.g. in a term such as "32a27bx" in a polynomial. (4) Numbers in bases higher than 10, where a is commonly used for a digit standing for 10, b for 11, etc. Hexadecimal (base 16) numbers are particularly common examples of these in current computer work, e.g. "3f0a" might represent a value in a 16-bit computer memory location. Probably the worst example of this kind would be a page full of hexadecimal numbers, all arranged for computation.

"These cases are of course not new to us, having been considered at great length while pondering upper vs. lower numbers. And before going on, I hasten to point out that it would distort our perception greatly if we were to dwell exclusively on such cases, even though they no doubt exist, and can even occur densely at times, and are clearly important to some people in some circumstances--for they are not really representative of the general case. ..."

In other words: we know that some people spend chunks of time dealing with notation systems where digits, and even digit-letter combinations, occur more commonly than in general, representative literature. I can confirm that myself: sometimes I spend short periods working with computer programs, or juggling algebraic equations, or even subtracting in hexadecimal (though the latter is pretty darned rare, these days). Those who do these things in braille tell us that the letter signs and number signs that accompany digits get in the way of working with them. So, we are dealing with anecdotal evidence, but still it is believable anecdotal evidence, and we would like to consider ways that we can alleviate that difficulty--though, if we keep our heads really clear about it, I think we will choose to do so in a way that does not burden the general reader or actually increase the overall incidence of indicators.

If you can stand one more plug for limited use of French numbers here, that is the point of them: when you really have an intense collection of numbers, they do the job best. For, once you get past whatever indicator says you're in grade 1, digits become, mirabile dictu, just plain ordinary symbols that can be written without any thought of indicators, whether for letters, punctuation marks, or even for the numbers themselves, and you can read them no matter how they are arranged. The proposal that they be used in grade 1 (except where grade 1 is being used for purposes of teaching grade 2), could, perhaps, lead to their overuse, if I correctly understand Bruce's point. However, I am not too sure just how else one could define the conditions of use; if anyone has any ideas on that point, and would like to propose an appropriate amendment, I am all ears.

2. In an4105, Abe asks how those of us who favor French numbers would braille a moter vehicle identification number ("VIN" number), specifically:


and also some mixed numbers written linearly, viz.:

Weight: 4 1/2 lbs. Dimensions: 9 1/2 by 4 1/2 by 2 in.

Taking up the first example, I will start by transcribing according to our current (upper number) rules, both for purposes of contrast and also to make a particular point.

If we jump right in and take the capitals as they come, we would of course have:
However, since we have an extended capitals mode, we might choose to use it, yielding:
In this case, the second expression is one cell longer, so perhaps our transcriber rules, which are yet to be completely defined for this purpose, might favor the first kind of treatment except where the surrounding text would change the balance--e.g., if this were only one of several VIN numbers in a list. The important point, though, is that either of these transcriptions, when read according to the reading rules, yields a completely unambiguous understanding of the abstract symbols being represented. (Usually, we loosely refer to those symbols as "the print", but I would maintain that it is more correct to say that both the print and the braille are, on an equal and parallel footing, representing symbols.)

It is quite important that we keep in mind the distinction between reading rules and transcriber rules, and the reasons why we are deferring complete resolution of all transcriber issues until the reading rules are more clearly settled--matters that are amplified in the report itself, and in other writings, so I will not go over all that again.

Turning to the question of how this number would be represented if the current motion were adopted, the first point that needs to be made is that, if the transcribing rules did not call for treatment of this number in grade 1, then one of the already given transcriptions could still be valid. (Technically, we would have to change our minds about grade 1 being automatically assumed after any digit, but that is a rather fine point at this stage.) However, in the spirit of the question, let us hypothesize that the transcribing rules did call for numbers of this kind always to be done in grade 1, even if there is only one of them inside an otherwise ordinary sentence. Then, assuming we would want the most economical treatment of capitals, we would have:
which is five cells shorter than the upper-number treatment. I will not, however, blame people who are not impressed that those five cells, in this one case, prove the case for French numbers. We must, as I have urged before, think most carefully about the underlying principles.

In the second case, where mixed numbers are written in linear fashion, it is my understanding of our earlier decisions (as stated in the current report) that we would write such an expression linearly in braille also, using the "slash" character just as in print. (By contrast, the the fraction indicators would be used only for those expressions actually written as fractions, with a numerator over a denominator separated by a fraction line.) So, in the case presented, we would be unlikely to use French numbers but instead would write:
,wei<t3 #d #a_/#b lbs4
,dim5.ns3 #i #a_/#b by #d #a_/#b by #b in4
(The use or non-use of an "in" contraction in the last word would of course depend on ultimate resolution of lower-sign rules, which is obviously beside the point here.)

3. As I was writing the above, a message arrived from Clive Lansink, directed to several of us, with a question about how French numbers would be distinguished from contractions in grade 2. (The full text of Clive's message is being relayed separately, to the full ubc2 forum.) Abe Nemeth also sent an answer to that question, explaining how our grade 1 indicators would always make the distinction plain.

I would like to add some further clarification, however, because there are a couple of respects in which Abe's answer does not reflect what is actually envisioned by the current motion.

The first point, a minor one, is that none of the French number proposals would have led to transcribing "36" as:
In jsm19 (see archive xx36), where a system based on French numbers was discussed, the number sign (dots 3456) was suggested to replace the double-letter sign as the grade-1-word indicator, and so we would have written:
If we were to use French numbers for all purposes, we surely would want to do that (or one of several other things) to avoid a double indicator on simple numbers. As for the current proposal, see the next point.

The second and more important point is, by reason of a decision already taken by the committee, we are no longer considering a numbering system that uses anything other than regular upper numbers for principal purposes, i.e. in regular grade 2 transcriptions such as the following (from js3c11):
,nelson 0 #ah ye>s old & sett+ up *airs on ! %ip =a ,sun"d s]vice :5 ! vessel 0 hit )a #a1gfj-p.d bomb on ! morn+ ( ,dec4 #g1 #aida4

This means that, if we are to use any other kind of number for secondary purposes, we must state the conditions of use. The current motion states that whenever grade 1 is used, other than for purposes of teaching grade 2, French numbers would be used. The intention here is to capture just those cases where grade 1 is being used because the density of unusual and/or unusually positioned symbols has caused us to use a "grade 1 passage". Remember that we have not yet fully defined those conditions from a transcribing point of view, but rather are still concentrating on the reading rules (which ARE well defined), such situations may well be exemplified by the following. In both cases, the grade 1 passage indicators have been shown, on the hypothesis that the surrounding text is ordinary grade 2:

The first case is from the book "Programming perl", published by O'Reilly, in the description of "sprintf" in Chapter 4 (page 187 in the March 1992 printing). First, in BANA CBC code, we would have:
$width = 20; $value = sin(1.0);
foreach $precision (0..($width-2)) {
printf "%${width}.${precision}f\n", $value;

Transcribed according to our current report as it would be modified by ef3b30/js3b27, it would look like:
;;;@swidth "7 <+2 @svalue "7 sin(*4+)2
foreach @sprecision (+44(@swidth-<)) .(
printf 8.0@s.(width.)4@s.(precision.)f_*n01 @svalue2

Those familiar with CBC should not, of course, expect the second treatment to look as familiar as the first--but it does illustrate the principle. There aren't too many numbers in this example, by the way, so the benefits may not be as apparent as in other cases where numbers are plentiful and arbitrarily positioned next to letters and punctuation marks. That is the thing about computer programs; there's no telling what kinds of patterns will be encountered in that respect--although, if I have not yet sufficiently stressed the point, we can definitely expect that punctuation marks will more commonly follow digits than letters will.

This second case has more numbers, although there is still no way to capture all the variations. This is a two-line fragment from the source tables that we use for our British translation. Again, in CBC:
P 1 2 'ong~'o~ {-ong: Ts'ong 931201}
15 2 's~'s~ {e.11: avoid dbl ': 100's; rmv'd v10;22, restored 10;23}
And in UBC modified by ef3b30/js3b27:
;;;,p * < 'ong"/'o"/ .(-ong3 ,ts'ong [%*<+*.)
*: < 's"/'s"/ .(e4**3 avoid dbl '3 *++'s2 rmv'd v*+2<<1 restored *+2<%.);

I realize that both examples are likely to look like "garbage" to most readers, no matter what the braille code used, because the underlying language is (probably) unfamiliar. That, however, is the way it is with a lot of computerese. The point is: with UBC in grade 1, as with CBC, arbitrary semi-messes such as these can be expressed by simple transcription of the symbols as they come, and French numbers extend that simplicity to digits by removing any need for context-sensitive indicators, or indeed any indicators.


I feel the need to make another personal observation on the question of number systems. Because I am an observer, I have elected to send my thoughts to specific people only. If one of you chooses to share them with the Committee that is fine with me.

I was moved to writing this message after reading Tim's comments on numbering systems. just now. There is a point he made which raises for me an important question that perhaps needs clarifying.

Is the prime objective to preserve as much as possible the existing literary braille code? In Tim's message, he said "We are instructed to accomplish our task without making changes to SEB beyond the absolute minimum necessary to the addition of symbols required in technical writing. When we have finished with our work, readers of literary works should notice virtually no difference with the UBC and the Grade II Standard English Braille. There is no room for compromise on this mandate."

If this is the case, then my earlier point, made to the UBC Group during observers' time, seems clear. I may be missing something, and if so, will someone please enlighten me.

It seems that no matter what additional numbering system is used, there is a need for an indicator to tell us when we are switching into a "numbers" mode and when we are switching out of it. It is said that the advantage of the dot 6 numbering scheme is that it avoids clashes with the existing punctuation marks. Thus there is no need for a punctuation indicator to upset readability.

But they do destroy some of the most frequently used contractions in today's grade II braille. If these contractions are to remain, in order to preserve Standard English Braille as much as possible, then we still need an indicator to tell us that the following symbols are not contractions but are actually dot 6 numbers.

If I said I was going out to the garden shed, this would be a "36", unless it was understood that the number 36, even when written using dot 6 numbers, will be written with a number indicator.

A sentence like "a child will go out." will be read as "a 1 will go 8." unless we indicate that these are numbers, not whole-word contractions. This last example illustrates the "W" problem. The reader will have to remember that a J with a dot 6 is not a 0.

If I burn my finger, "ouch", well is this "81"?

We can adopt dot 6 or lower numbers, and I've no doubt that braille readers will get used to either system. But with regard to dot 6 numbers and not clashing with punctuation symbols, unless we agree to drop the current meanings of these dot 6 symbols, both as in-word and whole-word contractions, then we must accept the need for a numeric indicator to switch us into numbers mode, and a symbol to take us out again.

But if we agree on that, then the "advantage" of dot 6 numbers, specifically that they do not clash with punctuation marks, seems irrelevant.

I then come back to the question of what is most readable to today's braille reader. Is the number "81" best written as 81 in dot 6 numbers, or in lower numbers. Given that each situation will in my view require a numeric indicator, and (depending on context) a punctuation or similar indicator to mark the end of the number, I believe the advantage should go to the lower number form, because of its similar shape to existing upper numbers, and again this assumes that the objective is to come up with a code that retains the properties of Standard English Braille as much as possible.

Perhaps it is difficult to make a decision between two numbering systems in isolation. The real point of interest is what will the final unified code look like with either numbering system. So I would like to see the debate move away from the numbering systems themselves, and focus more on the consequences of adopting either one. Once everyone has a clear idea of what the code would look like in a more complete form with either numbering system, it will be easier I think for people to agree on which numbering system is the best.


1994-01-09 AN: Reply to Clive Lansink (an4109)

All of us on the committee except Bruce received a posting from Clive Lansink of New Zealand. Below is my reply to him. I am posting my reply to Clive to the committee because it is of general interest. As our Chairman, it is Joe's prerogative to include Clive's communication as part of our committee records if he chooses to do so.

January 9, 1994

Dear Clive,

Thank you for your interest in the work of our Objective II Committee. I will attempt to respond to your concerns, and I will share my response to you with the others whom you have addressed. However, I have not communicated with any of them concerning your submission and so I do not know whether any of them will respond to you.

First, let me address the issue of the mandate by BANA to our committee. I have before me the first draft of BANA's guidelines as well as the official Action Plan. I will quote the relevant wording from the official Action Plan which is contained in Objective II: "... their [the new symbols] inclusion in the code must not make it necessary to alter any of the symbols in the Basic Code except those that are changed to bring about parallel forms in braille and print." In addition to the Plan of Action, there is also a letter from Darleen, who was then president of BANA, appointing Joe to be the chairman of Committee II. BANA routinely "charges" each committee that it appoints. This "charge" is for the purpose of prescribing the parameters under which the appointed committee must operate. The relevant item in the "charge" to our committee is Item 5, which I now quote: "Symbols in the Basic Code must not be altered except to bring about parallel forms in braille and print." Further along in the letter of appointment, we find the following: "The real challenge will be to devise a code with only minor changes to the present literary code that will allow present readers to read it without difficulty and to devise a code that will allow readers of the future to read material in our libraries with only minor inconveniences. While dwelling on allowable 'minor changes' I realize the term has not been defined in advance. We are all looking to the wisdom of your committee to make only those changes, be they elimination of a symbol, further restrictions on its use, or the introduction of a new symbol which will meet our criteria." I believe that when Raeleen was appointed to our committee, she was supplied with the full documentation of the Plan of Action and the letter of Joe's appointment, together with other documents. From the wording and tone of these quotes, it seems to me that BANA's mandate is more permissive than is implied in Tim's phrases such as "the absolute minimum necessary," "readers of literary works should notice virtually no difference with the UBC," and "there is no room for compromise on this mandate," which he apparently employed to punctuate the sincerity of his convictions.

If you have been following our committee discussions, you know that three numbering systems are implicitly on the table at all times. These are: the upper-number system, the dropped-number system, and the dot-6 system. The dot-6 system is the system we used to call "French" numbers. Since every braille character (except dot 4) is either a Grade-2 contraction, part of such a contraction, or part of a short-form word, a method must be devised for the reader so that he will know whether to interpret a braille character as playing a role as in the contraction system of Grade-2 or whether he should interpret it as having the meaning assigned to it by our committee. Such a method is required regardless of the number system or systems we implement in the code that we recommend to BANA. The method that our committee has adopted for this purpose is a system of indicators that we used to call "notational indicators" or "literal indicators," but which we have now agreed to call "Grade-1 indicators." This system of Grade-1 indicators is based on the letter sign familiar to readers of Standard English Braille, and is a significant enhancement and extension of that concept. The basic component of the Grade-1 system of indicators is ; (dots 56), which is the same character that is used in Standard English Braille for the letter sign. According to current committee thinking, a single occurrence of this component affects only the next symbol. A double occurrence of this component affests the word that follows and its effect is terminated when the word has ended. (We currently define a word as a string of braille characters between spaces and which contains no interior spaces of its own.) A triple occurrence of this component affects an entire phrase; its effect must be terminated by a single component at the end of the phrase. (We define a phrase as a string of two or more consecutive words including the spaces between the words.)

With this background, then, I believe I can resolve your questions. If you read or write %$ (dots 146 1246) without a Grade-1 indicator, then it is the word "shed" as it always was in Standard English Braille. But if you read or write ;;%$ (dots 56 56 146 1246), then you are dealing with the dot-6 number "36." Similarly, if you read or write * (dots 16) or \ (dots 1256), you are reading or writing the contractions for the words "child" and "out" respectively. But if you read or write these characters preceded by the Grade-1 indicator ; (dots 56), then you are reading or writing the dot-6 numbers for "1" and "8" respectively. Also, without any indicators, \* (dots 1256 16) is an appropriate response if you burn your finger, but if this word includes the Grade-1 indicater ;; (dots 56 56) at its beginning, then you are dealing with the dot-6 number "81." As you can see, it is the system of Grade-1 indicators and not the numeric indicator that allows contractions and dot-6 numbers to exist side by side without conflict. Note, however, that, according to current committee thinking, a single-digit dot-6 number requires only one component for the Grade-1 indicator, whereas a multidigit dot-6 number requires two such components. The Grade-1 indicator serves not only as the numeric indicator in the case of dot-6 numbers, but it also affects other braille symbols that are not dot-6 numbers. For example, ( (dots 12356) is the contraction for "of" without any indicator, but it is the left parenthesis when affected by a Grade-1 indicator.

Since you raise the issue of the numeric indicator, I will attempt to analyze the role which the numeric indicator plays in each of the three number systems. As I have demonstrated above, the Grade-1 indicator acts like the numeric indicator in the case of dot-6 numbers. In the case of dropped numbers, the Grade-1 system of indicators could be used in exactly the same way as it is used with dot-6 numbers so that, theoretically, a numeric indicator would not be required with dropped numbers. I must emphasize at this point that our committee has not yet considered dropped numbers except as a possible number system, nor, for that matter, is that number system even on our agenda for detailed consideration. Nevertheless, since the dropped-number system has been part of the Nemeth Code for more than 40 years in this country, and since it is part of the computer code used in this country, and since that system is known all over the world even where the Nemeth Code nor the American computer code are not used, that system is so familiar to the braille-reading community that I believe it is valid to discuss it. But please be mindful that what I say here is my own point of view and does not represent the official position of our committee. Even though the Grade-1 system of indicators is theoretically adequate for distinguishing dropped numbers from lower part-word and whole-word contractions of Standard English Braille, I advocate the use of the numeric indicator to introduce a word whose first symbol is a digit. I do so for three reasons: (1) It is a character associated with numbers in the minds of braille readers. (2) It acts as a cell locator so that the braille reader can identify the position of the character in the next cell. (3) It avoids the problem of having a one-cell Grade-1 indicator before a single-digit number and a 2-cell Grade-1 indicator before a multidigit number. Converting your examples to dropped numbers would yield #36 instead of ;;%$, #1 instead of ;*, #8 instead of ;\, and #81 instead of ;;\*. In the upper-number system, the numeric indicator is essential to distinguish between the digits and the corresponding letters. Furthermore, the numeric indicator with upper numbers has a remote effect on braille characters to its right, and rules (which always bring exceptions) are required to specify the extent to which the numeric indicator is effective. Even when the numeric indicator is used with dropped numbers, it has no such remote effect. In that system, the numeric indicator is merely a substitute for the double-component Grade-1 indicator for a word. In fact, the numeric indicator is not needed at all in an expression like ;;x+2a in which the first symbol of the word is not a digit.

Since you also raise the issue of deciding between two number systems, I will offer you my point of view as succinctly as I can. As I see it, there are two distinct, although related, problems. The first problem is that of deciding whether the code that our committee formulates should be based on two number systems or just one. The second problem is that of determining which two systems should be used if the decision is to use two number systems, or of determining which of the three number systems should be used if the decision is to use just one number system.

With respect to the first problem, I am firmly convinced that our project must fail if it proposes a code based on two number systems. There aren't enough rules in the world to determine with certainty which situation requires the first number system and which situation requires the second. As you probably know, my code has gone through four revisions. In the first two revisions, the code attempted to maintain a dual number system using upper numbers and dropped numbers. Transcriber A could adduce a valid reason why upper numbers should be used in a certain situation, and transcriber B could adduce an equally valid reason why dropped numbers should be used in the same situation. The result was a non-uniform code which resulted in non-uniform transcriptions. And the same will be true of the code which our committee develops if it is based on two number systems.

With respect to the second problem of choosing which of the three number systems should be the basis of the code we formulate, there are faults to be found in all three systems. Nevertheless, I am convinced that the dropped-number system offers the best hope for success. It is already familiar to hundreds, if not thousands, of braille readers for reasons I have already mentioned. Dropped numbers have the "look and feel" of upper numbers to which braille readers are accustomed, and there is no learning involved in adjusting to them. I would regard the adjustment to dropped numbers as a "minor change" in the spirit of our BANA mandate. The need for a punctuation indicator with dropped numbers is the only substantial argument against the use of that system. Compared with the problems inherent in the other two number systems, the need for a punctuation indicator with dropped numbers is minor and tolerable.

With respect to dot-6 numbers, it is difficult to imagine a number system that deviates further from the number system to which braille readers are accustomed. Although this system is used in many European countries for their computer codes, no full-blown math or science code employs that system. So many valuable braille characters must be reserved to represent dot-6 digits, that one-cell assignments to frequently occurring symbols are no longer possible. For example, if dot-6 numbers are implemented, both the square root symbol and its terminator will require two-cell representations. The repeated use of so many two-cell symbols will, in my opinion, more than nullify whatever advantage may be gained by not having a punctuation indicator.

The upper-number system is incapable of representing anything more than the most rudimentary notational forms. Without going into detail here, I will simply assert that no robust, usable, uniform code can be formulated based on the upper-number system. The Taylor Code attempted to do so and failed. The British attempted to do it and were driven to use dropped numbers as a second number system. Despite the fact that the British math code requires two number systems, it also requires the use of a punctuation indicator.

Since you are evidently following the debate in our committee with interest, I thought that I should bring to your attention the principal issues concerning the three number systems we are considering and the complex interrelation between them. I hope that by so doing, I have answered the questions you raised in your submission. Thank you for the opportunity to express myself on this important issue.


Abraham Nemeth, Ph.D.
{email address removed}

1994-01-12 JS: NOT about numbers (js4112)

This is for a few brief announcements that, believe it or not, have almost nothing to do with braille numbers.

First, Stephen Phippen can now be reached via the Internet address of Keith Gladstone of RNIB, namely:
{email address removed}
The ubc2 server list has been updated accordingly.

Secondly, I am pleased to welcome Jo Churcher as an observer; her E-mail address is:
Jo Churcher <{email address removed}>

Thirdly, our congratulations and best wishes to observer Bill Jolley, who has announced that he is leaving his job at Telecom to assume the position of Executive Officer of the National Federation of Blind Citizens of Australia. Because of the move, Bill's current E-mail address will no longer really be valid after this week (although there will be a period of occasional monitoring) and consequently I'll be removing that address from the list server later today. To reach Bill while he is out of E-mail contact, you can use the NFBCA fax number: {tel. no. removed} or voice number: {tel. no. removed}.

1994-01-12 SP: Vote on French numbers (sp4112)

I am voting against the motion proposing to use French numbers in grade 1 mode for the following reasons:

1. French numbers use up too many useful braille signs.

2. French numbers are at the same time unnecessarily obscure in ordinary contexts, and insufficiently compact in technical contexts.

3. I am in favour of retaining ordinary SEB style numbers and adopting a scheme of compactly indicating superscript and subscript numbers in technical contexts along the lines I stated in an earlier file (I have repeated the rules below). Such rules can be framed in a way that allow the compact method to be optional, but without any ambiguity. Thus in ordinary contexts the compact notation would probably not normally be used so most people will not need to concern themselves with the method, whereas in technical contexts such as mathematics or chemistry it would be used, with great advantage to readabilty and conciseness.

This compact notation for superscript and subscript numbers is a tried and tested system in BAUK's and allied authorities' mathematics and chemistry codes, and it is used successfully at all levels and is well liked. The system (or similar) is also used in the technical codes of many other countries, including Germany, Spain, Russia and Japan, and our adoption would be a positive move in terms of wider international compatability. We could also retain the existing superscript, subscript and index termination signs.

Adoption of this system would partially remove one of the main potential complaints about the unified code, i.e. that of clumsy treatment of mathematics and chemistry text, but if adopted in the way suggested would not impose itself on readers of ordinary text. Although logically possible, I do not think that a system such as this would coexist so naturally with French numbers if the latter were adopted as the basic system for grade one.

4. The issue of one-to-one representation is an important one, but mainly in the context of the use of braille displays. However, in this case the trend is towards using 8-dot displays, and 8-dot braille is a separate system from that which we are discussing. Users in this country often use dot 7 to indicate capitals. They could use dot 8 in a similar way to indicate numerals, which would enable them to use as much of the single cell 6-dot character set in the unified code as they wished to. However, this is a matter for them to decide, and there are no doubt many possibilities. One- for-one representation is not thoroughly possible in any six dot code, and the feedback from UK computer users seems to be that using ordinary SEB style numbers in computer text transcriptions would be acceptable.

Suggested Rules For Compactly Representing Numerical Indices in Technical Text (From SP3b04.txt)

Reading Rule:
(a) Strings of lower a-j signs immediately following the subscript or superscript sign indicate digits until the sequence is terminated by another sign (i.e. not lower a-j), and then the subscript or superscript is itself automatically terminated.

Transcribing Rules (i.e. in order for it to work, the above rule requires of the transcriber):

(a) Do not combine (i.e. concatenate) lower digits with any other symbol in the same subscript or superscript position: If other symbols are present, then the number should be written out in full and the subscript or superscript must have a termination sign.

(b) Punctuation marks following lower a-j signs representing subscript or superscript digits must be preceded by dot 6 [perhaps this should be dots 56?].

(c) Punctuation marks immediately following subscript or superscript signs must be preceded by dot 6 [or dots 56?], and the subscript or superscript must have a termination sign.

A more compressed scheme (like the UK code) would be to add to reading rule (a):

(b) A string of lower a-j signs following a grade 1 indicated letter represents subscript digits until the sequence is terminated by another sign, and then the subscript is itself terminated.

1994-01-12 JS: another brief note (js4112a)

Sorry about the double-send of js4112. In this (overly?) automated world, it seems mistakes are also sometimes too easy.

I have just noted that some unknown problem has developed with Priscilla Harris' E-mail address, inciting the "mailer-daemons" to send back our messages. I have been unable to reach Priscilla by phone, and so until the problem is cleared I have removed the address from the server.

1994-01-12 JS: A letter from M. Jacquin (js4112b)

Back in December, I decided it might be worthwhile to ask someone in (where else?) France about their experience with French numbers. So I wrote to my friend and colleague Mr. Michel Jacquin, Vice President of the well-known Association Valentin Haüy in Paris. Mr. Jacquin worked for many years in nuclear physics, became blind later in life, and for nearly a decade now it has been my privilege to work with him on French braille translation. I value the judgment and good humor (as will be obvious), as well as technical background, that he brings to bear on a subject. And so I asked him if organized studies had been conducted into readability of the dot-6 numbers, and if he could tell me anything else about them from the French perspective.

Mr. Jacquin kindly wrote quite a long and informative reply, which I received yesterday. It was, as will be obvious, rather negative as concerns usage of these kinds of numbers generally--but more positive for usage in very limited circumstances.

There a few points about French braille that I should probably point out, with apologies to those who are already aware of these things: (1) The capital sign is dots 4-6, not dot 6. (2) The dot 6 is used for grade 1 indication, somewhat like our projected use for dots 56, though as Mr. Jacquin says the scope and meaning of the symbol is not thoroughly defined. (3) In technical material where upper numbers are not used, the French use the number sign itself (dots 3456) for zero, not the 346 used in the DIN standard and proposed in our current motions.

The following, between the divider lines, is the part of Mr. Jacquin's letter that deals with French numbers; I have numbered his paragraphs for reference:


1. About the French mathematical notation, I will begin with a little piece of history: it was invented and defined by a war blind, Mr. Antoine, in 1920, at first for this own needs (he was a high level professor in mathematics). As a mathematical notation, it is relatively clever and useful (it is still valid nowadays, with some small additions). It deals not only with numbers but also with many other topics (percentage, square root, subscripts etc.). As for the representation of numbers, the idea was to avoid an excess of number prefixes (since numbers are very frequent in mathematics and accented letters are not used in formulae).

2. All would have continued to be well if, in 1964, a Committee of teachers, without any organized study and without consulting blind people and their associations, decided, probably for their own commodity, to "unify" the representation of numbers and only a small part of the other elements of the mathematical notation. Since that time, there are strong "churches" for or against this usage. I am myself in the "against" party, not for the defense of my own habits, I hope, but for logical reasons, most of them valid only for French:

3. --If the Antoine numbers avoid the use of number prefixes in mathematics, it is not the case for general literary material, where accented letters are present practically in every word. There it was necessary to define a new number prefix, dot 6 (having as you know, an other meaning: Grade 1 prefix). The only profit was the "unification" for teachers (but not for pupils, since magazines and books continued to use "old" numbers). In my opinion, the price paid is relatively high.

4. --More confusion between accented letters and numbers and in the comprehension of dot 6, now extensively used for many different purposes (change of color, attribute etc., and each time without any precision about what change).

5. --confusion about the 0 (the previous number prefix, dots 3-4-5-6).

6. --a greater difficulty to read numbers. There are no "organized" studies about the numbers (you know, blind people are only a small part of the citizens, and no great money and intellectual effort were spent on them, before that media wrote about "blind people skying, driving a plane, or climbing the Anapurna"). However, I read somewhere (but I would not be able easily to put my hand on the relevant paper in my library) a study about the much greater ease for reading "upper characters" (greater speed and less errors) than others (if I remember well it was an English or American study). And I easily believe it, since I experience it myself (I became blind at the age of 47) and I have difficulty in reading, not only "Antoine numbers", but also words when they begin with a capital prefix and so on.

7. --another fact is that, as you well know, blind people are mostly aged people, more than two thirds of them are older than 65 years, and are not adept at mathematics. In fact, most people, even sighted ones, are not really using mathematics formulae, except in schools. On the other hand, children and mathematics users are supposed to have a more supple brain, and be able to change codes more easily.

8. All in all, for French braille, the balance seems to me rather negative, and it seems to me that it was not worth bothering so many people with so small a result. But it is naturally not the same for American, since there are no accented letters, and 15 more braille combinations are available (no real need to make "acrobatic feats" with braille cells). Only the last two factors are to be taken into account, and a "unified code" naturally has its price. In my opinion, every factor has to be seriously "weighted".

9. The difficulty is probably to distinguish between natural opposition against any new usage (particularly among blind people) and an "instinctive feeling" of a real problem that people are unable to explain.

10. To summarize: apart from an American or English study about "upper" cells compared with others, I know no other "organized" procedure in France. There seems to be no difficulty with young people, chiefly born blind ones, only with aged persons, or rather with persons who became blind after 40 years or more.


(I will add only a few notes, since I think Mr. Jacquin speaks pretty well for himself.)

Many of Mr. Jacquin's points, positive and negative, are of course quite familiar in the context of our debate.

The account in paragraph 1 reminded me that I had previously heard the dot-6 numbers referred to as "Antoine numbers" as well as "French numbers" but had forgotten, if I ever knew, that they were used as far back as 1920. So they have been used by the French for a long time, and for technical purposes other than computers, which were of course not even invented in 1920.

It is mainly on paragraph 2, where Mr. Jacquin says "all would have continued to be well if, in 1964 ..." that I base my conclusion that French numbers for limited purposes, such as no doubt originally envisioned by Mr. Antoine, work just fine, even though the French have not had good experience with usage for all purposes. Such limited use is consistent with our current motions.

1994-01-12 EF: (untitled, to the BRCTR and UBC2 forums) (ef4112)

Following is a possible design for an experiment to investigate the effect on reading braille of having or not having spaces between contractions such as "for" "the" "and" etc. I welcome any suggestions you may have for improving it. It is only a first draft, so don't hesitate to criticize it.

Braille Reading Rate as a Function of the presence or Absence of Spaces Between Certain Contracted Words

The experiment to be described employs a repeated measures design. Each Subject is tested twice, once on uncompressed braille and once on compressed braille. In compressed braille the spaces between the contractions for words such as "for", "and", and "the" are omitted. In uncompressed braille, the spaces between such contracted words are included. Repeated measures designs are often criticized by purists because there may be no logical grounds for excluding the possibility of a practice effect. However, because of the counterbalancing in the design of the experiment described here, and the use of experienced braille readers as subjects, I do not think there is much reason to worry about a practice effect.

What Should Subjects Read?

Two reading passages will be needed because, if a Subject read the same passage in uncompressed and compressed form, there would certainly be a practice effect. The passages should be approximately equal in length. A length in the neighborhood of 2000 words should be adequate. The passages should be matched for level of difficulty, and the level of difficulty should be appropriate for the subjects who will be tested. The passages should be closely matched in regard to the number of contracted words that are or are not separated by spaces. If comprehension is to be measured, passages should be found for which reliable and valid tests of comprehension already exist, because obtaining evidence for reliability and validity is a major undertaking.

What Should Be Measured?

At a minimum, reading rate should be determined. This is easily done by measuring the time required to complete a passage, and by dividing that time by the number of words (or possibly the number of syllables) in the passage. It would also be interesting to know whether the insertion of spaces has a larger effect in some cases than in others. However, in order to do so, it would be necessary to measure reading rate continuously in order to detect moment-to-moment variations in reading rate, but the instrumentation we would need to do this would probably make it impractical.

It is not obvious to me that the difference between compressed and uncompressed braille should have much bearing on comprehension. However, it is certainly possible to estimate comprehension, and perhaps we should do so, if for no other reason, because we will get questions about comprehension.

Finally, we should count the additional spaces required for the uncompressed braille. This would give us an idea of the additional distance to be covered by the reading fingers of a subject who is reading uncompressed braille. Because distance means time, the additional distance might account for any reduction in reading rate that is found. We should also determine the number of additional pages required for the uncompressed passages. We will probably find that a fairly large number of additional spaces will not increase the number of pages very much. This is because, in many cases, lines of text will be short enough to accommodate additional spaces without exceeding the maximum permissible line length.

Who Will The Subjects Be?

The subjects should have enough braille reading experience so that their reading rates are stable; that is, no longer a function of practice. However, they need not be experienced readers of mathematics or scientific and technical literature, because the passages they will be reading are nontechnical, and handled quite adequately by the current literary code.

High School students should meet the requirements so far mentioned, and it would be more economical to test High School students than adults who are no longer in school. This is true because it is usually possible to test several High School students at each testing site.

It would be possible to conduct a developmental study by testing subjects over a wide age range, in order to investigate the possibility of an interaction between the compression/noncompression variable and the age or reading experience variable. However, a developmental study would be much larger and more expensive, and I think we can answer the question that is the reason for the experiment with a smaller experiment in which age is not an independent variable.

The Design of the Experiment

In the design shown below, S stands for Subject, uncomp stands for uncompressed, comp stands for compressed, and pas stands for passage. First indicates that the passage recorded in its row and immediately preceding it is to be read first. Second indicates that the passage to which it refers is to be read second. Thus, the entries in the first row of the table indicate that the first Subject will read passage 1 in its uncompressed form first, and passage 2 in its compressed form second.

S1 pas1 uncomp first pas2 comp second
S2 pas2 uncomp first pas1 comp second
S3 pas1 comp first pas2 uncomp second
S4 pas2 comp first pas2 uncomp second

With this design, each passage will be read in both compressed and uncompressed form, each passage will be read both first and second, and each Subject will read both an uncompressed and a compressed passage.

Ten replications of this design would be required in order to have measures of the reading of both uncompressed and compressed braille for forty subjects. Twenty five replications would be required in order to test 100 subjects. I think that, for an experiment of this sort, 40 subjects should be enough. However, in order to give braille readers everywhere a sense of participation, a broad geographic distribution of subjects will probably be demanded, and achieving this distribution will increase considerably the number of subjects to be tested.

1994-01-12 TC: Response to Clive Lansink (tc4112)

The examples shown in your January 9, 1994 message which you felt could be misread are all literary constructions that would be written in literary code with normal Grade II contractions. The present motion provides that dot six numbers would be used only in Grade I braille, thus there could be no confusion of how the sentences in your examples would be read. There would be no reason to write those sentences in Grade I, unless you were teaching a student how to read Grade II. In that event, contractions would not be allowed (because you are writing in Grade I) and so the words "child, ouch, out" and so on would be spelled out.

The rules for deciding when to spell out text in Grade I or use literary code are yet to be discussed. These rules are not likely to be as complicated as the present decisions concerning whether a passage is best rendered in Grade II, Grade I, Computer Braille Code or maths code.

Clive, I do indeed believe that we are constrained to making only those changes to the literary code that are necessary to the success of our project. The operative word here is "necessary." Another committee will deal with the subject of contractions, and perhaps other "improvements" to the literary code--but not this committee which I believe should deal with the rules and mechanisms required to make the literary code extendable.

It is also my personal observation that most Braille users do not want changes made to the literary code.

The first time I mentioned a uniform braille code to my wife, she said "You just want to make it so I can't read it." She did not say that she would not be able to "learn" to read it, rather she was giving me notice that she did not want to learn anything new in order to continue her usual reading schedule.

The first time I mentioned a uniform braille code to Dr. Kenneth Jernigan, he said "Tim, leave it alone; you will kill it." He knew that change would exact a terrible price.

More recently, Dr. Foulke commented in a memo to this forum dated September 1, 1993 "I can summarize the comments of many of these braille readers by saying that they have no objection to a unified braille code as long as you don't change anything."

I believe that the experience in the UK bears out the belief that people will reject change, even if it is superior to the familiar.

Over the last few years I have often entertained the thought, how wonderful it would be if we could start over and design a new braille code based on scientific principles. Alas, that will never happen. I now know that my desire for the perfect code must yield to the superior pressure of human nature. I now hold the view that our project stirs powerful psychological and political forces that simply cannot be ignored.

Readers of technical materials are just as devoted to their computer codes and maths codes. They too might well echo the refrain that resists change. Herein lies the conflict.

To my mind, the choice is clear. Changes should be made that leave grade two braille essentially unchanged while providing a useful, unambiguous and uncluttered code for technical writing.

It seems to me that Grade I is the best solution available to us. I use the term Grade I to mean the absence of Grade II symbols. When these contractions are not allowed, these braille characters may be assigned Grade I meanings. The present motion to assign ten of these Braille characters the meanings of dot six numbers would not in any way affect reading Grade II. At the same time, these assignments would enable technical writing without any indicators beyond the initial indication that Grade I is invoked.

I admit that this is not the way I would prefer to design a system of notation if we were starting over. Since we are not starting anew, it seems to me to be the best compromise yet proposed. It isn't pure. But then, what is, in a political world?

1994-01-14 JS: Announcement on upcoming 18-equation comparison (js4114)

In a message I received from John Gardner yesterday, he describes an exercise in which he, Abe Nemeth and Stephen Phippen are participating. As I understand it, each has submitted six equations in math and science notation to the others, each will code all 18 in his proposed method for UBC, and finally the results will be submitted to us along with comments (as separate messages) from each of the participants. My response, in part, was:

"Thanks for yesterday's message about the comparison work that you, Stephen Phippen and Abe Nemeth are doing. I'm sure that the committee will find the material interesting, and you are right that I have no problem with you sending your comments about the results directly to the ubc forum--that would save me the trouble of relaying them, as I certainly would in any case.

"You did not say when to expect that the results and comments would be ready, but as you have already gone a certain ways with it, I assume that it could be available fairly soon. Consequently, I will at least announce that this is coming, so the committee members will be looking for it."

To that, let me add that I will naturally want to give equal consideration to any participant, whether committee member or observer, to comment on their study; please let me know your wishes in that respect.

1994-01-18 JS: Typeface distinctions: an example (js4118)

Our current UBC provides for a rich array of typeface distinctions, to the point where I've heard some worrying that we have gone too far. However, just yesterday I received a message from Greg Lowney of Microsoft, describing a forthcoming document (on CD, though that's not material for us) that apparently will require four different colors and four different type styles--to make significant, not just aesthetic, distinctions. If that real-life example is any indication, perhaps we should worry that we haven't gone far enough! I wrote him a message back, by the way, so that he would be aware how interesting this example is for braille. His original message is attached for your information.


For the next MSDN CD we're including a Fortran extensions set of files that uses blue text to differentiate the Fortran extensions from the basic Fortran info. This blue text is formatted in underline, bold, italic and regular, depending on the context. The length of blue text varies from one word in a paragraph to 3 to 4 pages. We need to maintain this convention and cannot reformat the whole book to separate the blue text out and use black. The keywords and jumps in the CD are all coded in green. This cannot change. We need to use a color for the Fortran extensions text. The color should be readable onscreen and not dither too badly when printed. Any advice on color selection? Unfortunately it cannot be configured by the user due to the tools being used.

Also, while it is quite regrettable, I reviewed these documents a long time ago and had to agree that it is not feasible to restructure them so as to remove the dependence on color. Luckily this drawback is limited to this one product because of the special nature of the information. I also understand this convention is pretty standard among Fortran products.


Greg Lowney
Senior Program Manager
Accessibility and Disabilities Group
Microsoft Corporation

One Microsoft Way
Redmond, WA 98052-6399
voice: {tel. no. removed}
tt/tdd: {tel. no. removed}
fax: {tel. no. removed}
internet: {email address removed} (preferred)
compuserve: {email address removed} (binary files only please)

1994-01-20 RS: (untitled) (rs4120)

This is to vote against the current motion related to French numbers. I apologise for the delay in recording this vote and appreciate the committee's agreeing to a time extension. The following summarises the reasons for the negative vote.

1. Dot density: The dot clusters make recognition more difficult than for either upper or lower numbers. Numbers can not be recognised from context and accuracy is essential. Hence ease of recognition is an important factor.

2. Choice of symbols: The use of French numbers would in turn necessitate further changes to existing codes.

3. Unified system: The present motion indicates a move towards a dual system. If a move towards a dual system is necessary, all feasible options should be investigated and compared.

Some further comments re numbers:

1. Problems associated with lower numbers include both the need for punctuation indicators and the loss of the upper dots of the cell which predominate, particularly for less experienced readers.

2. A unified system that incorporated the representation of complex materials could be accepted by "the average reader" in a similar way that any "average reader" of print will tend to ignore unfamiliar symbols. Of course, a note of caution is introduced here when comparing the ease of scanning print with the more difficult process of scanning braille.

3. The terms of primary and secondary are understood as primary being a starting and formative stage and secondary being a continuation which is no less important though extended from primary. This, in fact, is the terminology used in our educational system which is referred to as primary, secondary and tertiary education from commencing school through to and including University level.

4. There would be a conflict of terminology between Grade One braille as represented in Dot 6 numbers, and the standard Grade One numbers. An ICEB study group has been working on a Grade One code.

5. Children in New Zealand are introduced to contracted braille when learning to read. Adults are introduced to the alphabet with a controlled vocabulary. This encourages recognition of words rather than of individual letters. Some persons may use uncontracted braille particularly for labelling or notetaking. There is flexibility in teaching/learning according to individual needs.

1994-01-20 CD: Relay of fax message from Christo de Klerk (cd4119)


8 Collett Street

Dear Joe

Unfortunately the fax regarding the proposal about the primary number system arrived while I was away on leave, which explains why we did not vote on the issue. We would, however like to cast our vote regarding the secondary number system.

Our local committee discussed the matter and I was instructed to vote against the French system. The committee members do not like the numbers with dot 6 and are concerned about the readability. The view was expressed that it could endanger the system if basic symbols like alphabetic characters and numeric digits are changed. As we are still busy digesting all the information, we still have a fairly open mind on the matter.

Please pass our vote through to the appropriate destination. It seems that we will soon be able to make use of Internet, which will enable us to participate more actively.

Everything of the best.


Christo de Klerk

1994-01-20 JS: Chairman's Report on Status of the Meeting (zs4120)


By EF in file ef3b30 (see also js3c01): to establish in principle French numbers for use as a secondary system, in grade 1. Seconded: JS. Voting deadline: Jan. 22, 1994 (extended from original date of Jan. 4). Votes: for: EF, JS, TC; against: AN, BM, SP, RS, CD. The motion is lost.

By JS in file js3b27 (see also js3c01): to fix the details implied by French numbers used as a secondary system, in grade 1. Seconded: EF. The motion is rendered inadmissable by the decision on ef3b30.








Thanks and congratulations to the whole committee, which has clearly put a lot of hard work into considering French numbers for use in grade 1. With the failure of that proposal, our current UBC number system remains "all upper", and the possibilities still open are as follows:

1. To stay with upper numbers for all purposes. This could be accomplished by a direct motion to that effect, or would be the default if no secondary number proposal carries.

2. To use dot-6 numbers in some secondary way other than "always in grade 1". No proposals have been made along these lines, and I do not actually expect any, but they remain technically open.

3. To use lower numbers in some secondary way. The only proposal made of this kind was Stephen Phippen's in sp4112, in which he described a system using lower numbers in subscripts and superscripts. That was not actually a motion, though in my opinion that formality could be easily satisfied.

If no motions on numbers are forthcoming within the next week or so, nor intent to make such motions declared, I will assume we are finished with the subject and proceed on to the next, which will be common punctuation marks. The general idea of restoring the familiar question mark and parentheses, when they are not ambiguous, has been expressed now by several committee members, and in a very general sense the ideas seem to be fairly consistent--and so I am hoping that this would be one subject that would not produce so much controversy.

Changes to the ubc2 server address list were announced in js4112 and js4112a.

ICEB contact information
ICEB home page
Page content last updated: June 25, 2012