Tutorial on Standard English
Braille
Logical
basis for cell assignments in English Braille.
The
assignment of Braille cells to the letters of the alphabet is an important
concept. Knowledge of this concept helps a sighted volunteer learn Braille
with greater ease. The concept is also useful when teaching others the
principles of Braille.
Braille has been around
for nearly two centuries and today, in the twenty first century, one is
amazed at the foresight of those who developed the scheme of Braille codes.
In essence, they had in mind the fact that Braille should not just be a
means for the Blind to read but must give them the means to read just as
normal persons would read a book. In other words, Braille must incorporate
all the important aspects of print, in a manner that a blind person can
understand the contents, exactly as a normal person reading printed text
does.
The requirement given
above implies that Braille codes should also convey the structure or organization
of printed text as close to what can be accomplished with a limited set
of sixty three cells. We will see how logically this has been done nearly
a hundred and fifty years before the advent of Information Technology.
Explaining the conceptual basis can be viewed as an academic exercise as
well, if we decide to bring in the computer to work with text in Braille!
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The
basis for cell assignment
Since we have
accepted in principle that Braille should match the presentation of information
in print form, The letters of the alphabet alone would not be adequate
in the assignment of codes. We also need to look at punctuation symbols
and other forms of presentation of text such as emphasized text, italicized
text etc., besides handling issues such as hyphenation, numerals and mathematical
symbols or even text in other scripts. Today, computers use nearly 96 different
symbols in standard English and even this is considered inadequate compared
to the rich set of characters seen in books printed more than a hundred
years ago. Is it at all possible for us to accomplish this with just 63?
Considering the fact
that the purpose of text is to convey information, it is entirely acceptable
that a symbol or a special letter sequence can be used in place of certain
words. This idea is not new to the present generation of epopulation where
email messages abound in contracted words, smileys and such, all done to
minimize the amount of text to be typed in to convey some information.
In developing Braille codes, the idea was to assign cells such that the
context in which a cell is read provides a new meaning to the cell. Thus
in essence, one can dispense with many symbols if their absence would not
lead to ambiguity in reading text. This way we can do away with capital
letters or even numerals. Hence the starting point for the assignment of
codes will be the set of 26 letters of the alphabet together with some
important punctuation symbols which are deemed essential.
We now observe that
about 30 to 35 cells will be the bare minimum that can convey basic information
in English. Punctuation symbols such as the period (full stop), comma,
semicolon, quotation marks, parentheses, question and exclamation marks
are quite important. These add upto eight symbols. The ten numerals can
also be handled without extra symbols if the context in which the numeral
is seen can be readily discerned. Braille uses a special cell to identify
the presence of a numeral. So we have thirty five cells to be assigned.
Which cells in the set of sixty three will these be?
Logical decision making
is called for at this point. If it is possible for
us to do the assignment in such a way that we can easily relate the letter
or symbol to the cell, learning Braille will be easier. So we now
look at how the sixty three cells can be arranged geometrically into groups
where cells in a group share a common property. The main idea is here is
that hopefully, we will be able to associate groups of cells with groups
of letters or special characters based on some criteria where groups share
some common properties.
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Grouping
of cells
The first approach
is to arrange the 64 possible cells into four groups of sixteen cells.
This arrangement is shown below.
We
quickly see that the sixteen patterns in the first row are repeated in
the other three with one perceivable difference for each row. The first
row consists of only the upper dots. The last cell in the first row does
not have any dots but it is a cell by its own right, signifying a space.
The second, third and fourth differ only in the lower dot positions and
here too, the logical structure is evident. The second row has only dot
3, the third, dots 3,6 and the fourth dot 6.
We will now be able
to identify the row a cell belongs to, by looking at the dots at the bottom
of the cell. However, our main concern is the assignment of cells to the
letters and symbols seen in text. So how do we reckon a letter with the
cell? For this we need to go a bit further and see if the letters and symbols
can be grouped logically and these groups matched with the rows. This will
be a bit tricky but surprisingly easy once we see the principle.
We have the following
sets to be assigned.
26 letters of the alphabet
8 punctuation symbols
Symbols to identify the print
form in which a word appears such as Italicized, Bold, Accented etc. Roughly
five of these to begin with.
A symbol to indicate the presence
of numerals. Also extending this idea to distinguish prose from poetry.
We have come up with
four groups and it seems logical to assign the letters, punctuaion etc.,
to the four groups following some rule. But such a direct assignment runs
into trouble as we see that there are twenty six letters of the alphabet
which do not nicely fit into the rows. A bit of home work in discerning
additional groups within the four rows will give us the desired results.
This is shown in the illustration below.
Seven
categories of cells
There are seven identifiable
groups each sharing a common property among its cells. Five of these have
10 cells each and the remaining two have six and seven cells respectively.
That is easy to remember.
The first five groups,
here after called lines, have ten cells each.
The sixth has six cells.
The seventh has seven cells.
The sixty fourth cell does
not have any dots and is counted out.
We
map the letters of the alphabet into the first three lines, in the
same order of the letters with one small difference which will be explained
shortly.
We
map the punctuation to a separate line.
We
map the context identifying symbols in to the sixth and seventh lines.
The fourth line is yet to
be accounted for.
We talked about the foresight
of the people who devised the Braille codes. Braille cells are large in
size compared to the letters or symbols in print and so the physical area
occupied by the Braille cells is several times greater than the corresponding
printed text. By assigning cells to very frequently occurring letter combinations
or short words, we can compress the text into fewer cells. This is precisely
what has been done. But there are so many frequently occurring letter combinations.
Which ones do we accommodate?
From a linguistic
analysis of text, the following have been identified as the important ones
which also will not cause ambiguity when used within words.
ch, gh, sh, th,
wh, ed, er, ou, ow (two letter sequences  9 )
and, for, of, the, with (words,
also letter sequences  5)
ea, be bb, con cc, dis dd,
en, ff, gg, in : also occur frequently in text. We see 8 of them here.
We now have seven groups
of letters, letter sequences, punctuation and context identifying symbols
which add upto 62! The small change mentioned above in assigning the letters
of the alphabet will now be explained. We pull 'w' out of the alphabet
and add it to the set of 9 above to make it 10. The reason for this is
based on the observation that 'w' is pronounced quite differently with
a sound not having any link to its name. The 63 cells are now accounted
for.
Here is the tally
of 63 items which will be coded.
25 letters of the alphabet (w
excluded)
5 short words which are frequently
used in sentences.
10 letter sequences of two letters
containing 'h', 'e', 'o' and 'w'.
10 letter sequences with repeating
letters, also accommodating many punctuation symbols to be identified from
the context.
6 context identifying symbols
and punctuation.
7 context identifying symbols
including contracted representations for text strings .
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The
actual assignment of codes
Before we discuss
the actual assignment, we need to understand how we can identify a cell
and thus the group of letters or symbols associated with it. We have seen
that five groups of 10 cells have already been identified as sharing a
common feature.
The following observations
are in order.
Group 7 is identified
easily as the set of cells which do not have any dots on the left, i.e.,
dots 123 are absent in these cells.
Group 6 is identified
next as the set of six cells which do not have dots 1 and 2. In this group,
if dot 5 is present, dot 4 will also be present.
Group 5 is identified
as 10 cells without the dots in the top row, i.e., dots 14. We must remember
that cells satisfying this property will also be seen in groups 6 or 7.
So a cell without dots 14 is in group 5 if it is not in group 6 or 7.
We
will now see that by committing to memory, just five basic patterns, we
will be able to identify all the 63 cells as belonging to one group or
other and thus decode the cell. The image below illustrates what
is required to be remembered to be able to identify the 10 patterns in
each of the first five groups.
The information
presented in the image is repeated below as ten combinations arranged vertically
one below the other using numerals.
1
12
14
145
15
124
1245
125
24
25
These ten patterns are repeated
in the second, third, fourth and fifth lines. Since we already know how
each line is specified, we should be in a position to associate any given
cell with one of the seven lines.
Let is put this idea
to test. Where does this cell fit in? 146
The presence of dot
1 excludes it from lines 5 , 6 and 7. Which one of the first four applies
is now decided by the dots at the bottom. Dot 6 is present but not 3 and
hence the cell is the third cell in the fourth line!
Summary
(The final assignments)
line 1  a through
j
line 2  k through t
line 3  uvxyz and for of
the with
line 4  nine two character
strings and 'w'
line 5  different two character
repetitions or punctuation symbols (In line 5 a cell may represent either
of the above depending on the context)
line 6  mixture of context
identifying symbols and letter sequences
line 7  Basically context
identifying symbols and those used in generating contracted forms of words.
These
assignments are shown below in tabular form.

Knowledge
of basic principles of Braille will help you
understand this tutorial better.
Contents
The basis
for cell assignments
Grouping
of cells
Seven groups
Assignment
of codes
Summary
Braille
codes for Mathematics
Over the years, Visually
handicapped persons have also benefited from the use of Braille for learning
mathematics. Devised by a Visually handicapped person himself, Nemeth codes
permit mathematical symbols to be specified through specific sequences
Braille cells which can be remembered without difficulty.
We have a separate page describing
the Nemeth coding scheme used for symbols
in Mathematics. It must be stated, that Nemeth codes are based on a simple
principle of the use of escape characters to specify how the cells which
follow should be interpreted.
