           UEBC and Numbers
             July 2002

Q. I understand that UEBC has adopted the
  traditional "upper" numbers, as found in
  English literary braille, for all purposes.
  Did you do this just because they are traditional?
A. Our decision-making involved balancing many
  issues, including tradition, but no one
  issue dominated all the others. In the case
  of numbers, we considered the matter from the
  beginning, weighing the merits of all three
  systems that have been used in various braille codes
  for different purposes. We kept in mind that
  UEBC is to be used for general reading,
  including math and science, but not only for those
  subject areas. In the end, we reached the same
  conclusion that Louis Braille himself reached in his
  original design, namely that upper numbers
  serve general reading purposes best.
Q. When you speak of decision-making, who made
  the decision on numbers?
A. All the members of the working committee that
  made the original recommendation were knowledgeable
  in technical subjects including math,
  psychology and computer notation. And at
  all times, a majority of those members were blind
  persons and users of braille. Following an open
  international evaluation, their recommendation was
  later ratified by unanimous vote of the
  countries participating in the General
  Assembly of the International Council on
  English Braille. In general, the entire
  UEBC development process has been open
  and democratic, in the spirit of blind persons
  controlling their own destiny--and it remains so.
Q. But don't lower numbers work best for math and
  science?
A. There are some limited contexts in which the letters
  a through j may immediately follow digits with
  higher frequency than in general literature,
  and in those circumstances lower numbers appear
  to have an advantage because they do not require an
  indicator to signal the switch to letters.
  Algebraic expressions in which those letters
  appear as variables or coefficients, and
  hexadecimal numbers where those letters are themselves
  used as digits, are commonly given as
  examples. However, after carefully evaluating
  the real frequency of such cases, even in works
  that are mathematical or scientific in
  nature, the committee found that it is far more
  common for punctuation marks such as the period,
  comma or colon to follow digits--by a margin
  of seven or more to one. Wherever that happens, an
  indicator--or dual representation--is
  required with lower numbers but not with upper
  numbers.
Q. Have others validated those findings? And what
  do they mean in concrete cases?
A. Any reader can easily verify those
  statistics by sampling random pages from books
  and magazines, including highly technical
  ones. Or, you can simply reflect how often
  you really encounter equations and hexadecimal
  numbers in real life (not counting examples
  prepared for a UEBC discussion) as compared with
  dates, times and other cases where punctuation
  marks touch numbers. Then imagine reading
  examples such as

  At 12:00 noon on July 4, 2002
  ...

  with an indicator or dual representation at
  the punctuation marks, again and again ...
Q. What do you mean by "dual representation"
  as an alternative to an indicator?
A. A group that advocates lower numbers for
  all purposes also advocates using dots
  16 for a comma and dots 12456 for period or
  decimal following digits. This saves the
  extra cell that would be required for an
  indicator in those cases, but at the cost of
  having two braille forms of those punctuation marks
  --an example of what can happen when "save
  cells" dominates all other design
  considerations.
Q. Is the problem with punctuation marks the only
  reason for not choosing lower numbers?
A. No, another very important reason
  derives from the fundamental design of braille.
  If you examine the familiar "seven line"
  table in which Louis Braille presented the 63 braille
  signs, and reflect upon the way in which those
  signs are used, it becomes obvious that the first
  four lines, all of which are upper signs, are
  the ones that are used for "primary" symbols that
  need to be able to stand by themselves, such as the letters.
  By contrast, the signs in lines five through seven
  are mainly used for "auxiliary"
  symbols, such as punctuation marks and
  indicators, that are normally found in close
  proximity to primary symbols. Following this
  principle, it is natural that the numbers,
  no less than the letters, deserve to be treated
  as primary and hence upper symbols.
Q. What does this design principle affect?
A. It greatly affects the "look and feel" of
  braille as we know it. For example, words are
  mostly in the upper dots while punctuation
  marks are "out of the way" in the lower dots. That
  in turn affects not only aesthetics but the
  way that braille is most naturally learned and
  understood. For example, two dots, one just
  above the other, are naturally understood to be
  dots 12 unless cells in close proximity
  force one of the other possibilities, such as
  dots 23. Interestingly, that effect also
  makes lower numbers on their own, without a
  supporting upper-cell indicator,
  unsuitable for use in hexadecimal numbers.
  For example, with lower numbers you couldn't
  tell the difference between fd and 64 unless some
  unambiguous sign happened to be close enough so
  that you could tell whether the dots were upper
  or lower.
Q. What about in algebra?
A. It is even more clear in algebra than in
  other subject areas that numbers and letters are
  parallel in our thinking. Letters stand for numbers,
  and consequently occupy the same places in
  equations in relationship to the signs of operation and
  comparison. Notice how, for example, "two
  plus two equals 4":

  2 .! 2 .) 4

  has the same rhythm as "x plus y
  equals z":

  x .! y .) z

Q. But I've heard that the indicators
  required by upper numbers lead to problems with
  alignment in spatial math, and in general
  make math expressions so long and cumbersome that
  it is difficult for people who use upper numbers
  to become proficient in math. Is this true?
A. No. Spatial math can be aligned with
  upper numbers, just as with other number
  forms. Some math expressions are expanded in
  UEBC, some are actually reduced in length,
  as compared with other codes. The speculative
  notion that learning and use of math is inherently
  hampered by the use of upper numbers is
  completely disproved by the long experience of braille
  users in the many other countries where upper
  numbers have always been used for most purposes
  in math and science. There is no evidence that blind
  people in those countries are less likely
  to achieve proficiency in technical areas just
  because they use upper numbers.
Q. Did Louis Braille himself consider lower
  numbers?
A. Yes, he did consider them--and in the end, as
  we have noted, chose the upper number system that
  is still used for most purposes in most codes
  throughout the world.
Q. Has any other kind of number system been
  considered?
A. Yes, there is a third type of system that
  is used for technical notation in some
  European codes. It uses the same upper
  dot patterns as the upper numbers, but with dot
  6 added--except for zero, which would clash
  with the letter w. These "dot-6" digits, using
  dots 346 for zero, look like this:

  child gh shall this which ed er out ow +

Q. What are the advantages of dot-6
  numbers?
A. First, they do not clash with letters nor with
  punctuation marks. While they do clash with some
  English contractions, that would not be a problem within
  a passage marked as in grade 1, which
  UEBC provides for. Consequently, in such
  passages, digits would have their own unique
  identity and there would be no need for any
  associated indicators. Second, they are
  upper forms and therefore suitable for use as
  primary symbols. In fact, they are
  "strong" symbols whose braille dot patterns cannot
  be confused no matter how isolated they might
  be from other symbols on the page.
Q. Why, then, did UEBC not adopt dot-6
  numbers?
A. While there was stronger support for them than
  for lower numbers, in the end the dot-6 numbers
  were judged to be too dense--that is, there
  would be too many dots per cell over longer
  numbers for optimum readability.
Q. Is readability, then, the main strength of
  UEBC?
A. You could say that, because "readability" pretty
  well sums up the point of most of the goals
  listed for UEBC, as well as being a goal in
  its own right.
Q. But what about writeability, and in particular
  the need for experts working in technical areas
  to write and manipulate notation quickly, even
  at the expense of some ambiguity?
A. We are aware of this need, and while we
  feel that unambiguous readability is more
  important for the basic code and the general
  reader and so needs to be developed first, we also
  believe that UEBC can eventually be extended
  to include a "rapid writing mode" that would
  meet the needs of experts. In fact, the
  ability to fall back to a "shorthand" of this
  kind has been considered in the UEBC design
  process right along.
Q. Would such a mode amount to a separate
  code, such as we now have?
A. No. Being based upon a well-
  established UEBC, the symbols in a
  rapid-writing mode would be closely similar
  --e.g. the same root, but with the prefix
  dropped.
Q. What would such a mode be like?
A. An obvious possibility would be to drop the
  dot 5 prefix from many 2-cell operators,
  so that for example the plus sign would be just
  dots 235. Now that would create an
  ambiguity with the exclamation mark, which does
  occur in math expressions as the factorial
  operator--though far less frequently than the
  plus sign. The user of the rapid-writing
  mode would have the option of using a grade 1
  symbol indicator so that factorials were
  clear, or simply assuming that, as the writer,
  he or she would be able to figure out which is which when
  reading back. That illustrates another
  feature of rapid-writing mode as it would
  likely be used in practice--the dropping of
  indicators that the user can safely assume
  to be implicit when reading back.
Q. Is this like anything we do in braille now?
A. Yes. Grade 3 braille is an extension of
  grade 2 that well serves those expert
  users who feel a need for very rapid reading and
  writing, while regular grade 2 is the
  formal code that serves for general reading and is
  used in publishing. It would be the same with this
  projected rapid-writing mode and regular
  UEBC.



















 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
