vb960314.htm

How Much Space Does Grade 2 Braille Really Save?

I.K. Durre

Abstract: This article reports on a study of a unique method for calculating the space-saving capacity of all Grade 2 braille contractions and the literary braille code as a whole. The study found that, contrary to the widespread belief that contracted braille saves 31 percent over print, the actual text reduction is about 20 percent.

Saving space was one of the major reasons for the introduction of contracted braille (Foulke, 1982; Irwin, 1970; Zickel & Hooper, 1957). However, how much space actually is saved with Grade 2 braille (Braille Authority of North America, 1994) has received little attention from researchers. This article reports on the author's investigation of the space-saving capacity of each contraction and of the literary Grade 2 braille code as a whole (Durre, 1992).

The space-saving capacity of braille is directly affected by the frequency with which contractions appear in written English, but little research has been done in this area either (Kederis, Siems, & Haynes, 1965), and none has been done in recent years (Durre, 1992). The frequency of letter strings, however, was of major concern when it was decided to include contractions in the braille code. Thus, there is no justification for including a contraction in the code if it does not save space. Contractions that do not save space only complicate the learnability and applicability of the code and may block the usage of dot combinations for frequent letter strings that would warrant their contracted representation but are not included in the code (Durre, 1992).

Because there are only 64 braille characters in the code, including the blank with no raised dots, most dot patterns have come to be used for multiple purposes. These multiple uses of braille symbols have created a virtual maze of rules and exceptions governing the correct usage of contractions. The braille symbol composed of dots 1, 2, 4, and 5 shall serve as a brief example. In its upper cell use, it can mean the letter g or the word go. When dropped to the lower cell, using dots 2, 3, 5, and 6, it can have four more meanings: were, gg, and opening or closing parentheses.

Multiple rules and regulations are necessary to ensure the correct interpretation and usage of the contractions. Thus, besides alphabet letters, punctuation marks, numbers, composition signs, and special symbols, the code was extended over time to include 189 contractions. In addition, it was necessary to devise special codes covering music, mathematics, computer symbols, and for textbook formats and techniques (Cranmer & Nemeth, 1991).

The study by Kederis et al. (1965) was only marginally concerned with how much space Grade 2 braille really saves, and it is outdated because multiple revisions of the code have occurred since it was conducted. On the basis of their contraction counts, Kederis et al. concluded that Grade 2 braille shortens a print text consisting only of alphabet letters by 31 percent-a figure that many incorrectly came to regard as the space-saving capacity of the braille code. Kederis et al. also stated that their counts revealed that "braille used 26.5% fewer characters" than print when "numbers, punctuation, and special signs" were considered (p. 44). However, it seems that they omitted blanks, which are an essential part of written language, from their calculations. Thus, the percentage they reported is not correct.

Method

To determine precisely how much space Grade 2 braille saves, one needs to take the following aspects into account: the frequency of letter strings in the English language; rules governing the use of contractions; overlapping and duplication of existing contractions; and occurrences of punctuation marks, composition signs, numbers, and blanks. The actual space-saving capacity of a contraction must be regarded as a function of the frequency with which a letter string appears and the number of characters saved by substituting the contraction for the string. Additional constraints apply:

> 1 . There are a number of instances in which the contraction cannot be used because of the correct application of the code rules. For example, ed cannot be used in reduced

> 2. One must determine the number of characters saved that the use of other contractions would produce. For instance, the contraction for although, which is five characters shorter than the spelled-out word, contributes only two actual characters because the use of the contractions th, ou, and gh would be three cells fewer than the spelled out word if the contraction for although did not exist.

For this study, computer-assisted counts, in combination with manual adjustments, were applied to a random sample of text passages containing 232,631 characters and 39,717 words of all reading levels and various topics.

The sample comprised 177,760 letters (76.41%), 45,663 blanks (19.63%), 7,929 punctuation marks (3.41%), and 1,279 digits (.55%). The total space-saving capacity of each contraction was normed to a text of 10,000 print characters, resulting in the average number of characters by which a text of that length is shortened by each contraction. This method allows for the convenient comparison and ranking of the actual space-saving capacities of all contractions. For a detailed description of the study, including the sampling text passages, data collection, method, and analysis, see Durre (1992).

Results

Table 1 presents the ranks of all 189 braille contractions according to their actual spacesaving capacity. The top space savers are those that either have their own unique dot pattern (such as th, the, in, and, and er) or are alphabet letter contractions (such as that, people, have, and will). The best space saver is th, with a normed space-saving capacity of 216.31, followed by the, in, and, and er, all of which have a normed space-saving capacity of more than 100. These five highest ranked contractions together contribute to 22.5 percent of the total reduction of text achievable by Grade 2 braille.

The top 25 contractions furnish two-thirds of the total amount of characters the Grade 2 braille can save. Furthermore, 95 percent of the total space-saving capacity of the code is achieved by the top-ranked 100 contractions, whereas the other 89 contractions together contribute only 5 percent to the possible reduction of a text. In other words, these 89 contractions together shorten a text of 10,000 characters by only 100 characters.

Compared to the print version, the total number of spaces saved by using Grade 2 braille amounted to 53,808 characters (23.13%). This number does not take number signs and capital signs into account. Adjusting for the extra spaces needed for braille capitalization reduced the number of characters saved by 5,820, and adjusting for extra spaces for number signs lowered the number of characters saved by another 478. The overall reduction of the text sample totaled 47,510. Thus, the braille code takes up 20.42 percent less space than does print.

Discussion

At first glance, the results of this study and those of Kederis et al. (1965) seem to differ. Calculations in the latter study were based on "approximately 291,000 words" (p. 40), with an approximate total of 1,315,400 letters (blanks not included). Since each word needs to be separated from the next word by a blank, the text used by Kederis et al. must have contained at least 291,000 blanks, leading to the overall text length of approximately 1,606,000 print characters. Using this adjusted total, one finds that Kederis et al.'s text was reduced by about 22 percent. The slight difference of 1.5 percent between this modified result of Kederis et al.'s study and the author's study may be attributed to the difference in the samples and to changes in the braille code that were introduced after the earlier investigation.

NOTE: Table 1 is included at the end of this document.

The number of contractions included in the braille code is customarily, but incorrectly, referred to as 189, when there are actually 187 contractions, since against and neither are concatenations of strings for which contractions exist. If these two were not included in the code as separate contractions, their braille forms would still be the same because against is made up of again and st, and neither consists of n plus either Therefore, both their actual and spacesaving value and their total space-saving capacity are always zero, regardless of the frequency with which they appear in a given text.

A considerable number of contractions demonstrated poor space-saving qualities, including 12 that did not appear in the sample text (which accounts for their space-saving value of zero in Table 1). Not only do these contractions contribute little to the reduction of text, but they add unnecessarily to the complexity of the code.

In general, the findings of this study concur with those reported by Kederis et al. (1965). Contractions that appeared with a high frequency in the counts done for this study also showed a high frequency in Kederis et al.'s study, and low occurrences also coincided. Because this study used a different approach in assessing the amount of space saved by contractions, the respective values obtained in the two studies cannot be compared directly. However, this study confirmed the general tendency reported by Kederis et al. More extensive research on a larger text sample should be undertaken to verify and fine-tune the results of this study.

Conclusion

On the basis of the findings reported here, many contractions in the braille code are poor space savers, and only a few are efficient. For example, eliminating the 89 worst space savers would lead to a minimal extension of a given braille text, but would greatly improve the learnability of the code, since it would reduce the number of contractions to be learned by almost half.

The widespread misconception that Grade 2 braille compacts the length of a text by one-third is based on Kederis et al.'s (1965) misleading report. In fact, this study found that the correct percentage of text reduction was only about one-fifth, which coincides with Kederis et al.'s findings.

The new method of calculating the space-saving capacity of Grade 2 braille developed for this study could be used to test the space-saving capacity of any code model. Research on a new unified braille code must consider the spacesaving capacity of contractions and Grade 2 braille as a whole.

References

Braille Authority of North America (Ed.). (1994). English braille, American edition-1994. Louisville, KY: American Printing House for the Blind.

Cranmer, T.V. & Nemeth, A. (1991, July-August). A uniform braille code. Braille Monitor pp. 377-383.

Durre, I.K. (1992). Analysis of the space-saving capacity of the braille code. Unpublished master's thesis, University of Northern Colorado, Greeley.

Foulke, E. (1982). Reading braille. In W. Schiff & E. Foulke (Eds.), Tactual perception: A sourcebook (pp. 168-208). New York: Cambridge University Press.

Irwin, R.B. (1970). The war of the dots. New York: American Foundation for the Blind.

Kederis, C.J., Siems, J.R., & Hayes, R.L. (1965). A frequency count of the symbology of English braille Grade 2, American usage. International Journal for the Education of the Blind, 15, 38-46.

Zickel, V.E. & Hooper, M.S. (1957). The program of braille research: A progress report. International Journal for the Education of the Blind, 6, 79-86.

Ingeborg K. Durre, M.A., director, Arizona Instructional Resource Center, Foundation for Blind Children, 1235 East Harmont Drive, Phoenix, AZ 85020; E-mail: durre@enuxsa.eas.asu.edu.

Table 1: Ranking of contractions according to their space-saving ability
Ranking | Contraction | NSC* |  | Ranking | Contraction | NSC* |  | Ranking | Contraction | NSC*
1 | th | 216.31 |  | 66 | because | 5.50 |  | 131 | together | 1.55
2 | the | 151.83 |  | 67 | sion | 5.24 |  | 132 | here | 1.46
3 | in | 139.36 |  | 68 | ong | 5.12 |  | 133 | letter | 1.42
4 | and | 114.47 |  | 69 | after | 4.90 |  |  | rather | 1.42
5 | er | 108.41 |  | 70 | into | 4.64 |  | 135 | according | 1.38
6 | to | 75.4 |  |  | ness | 4.64 |  |  | although | 1.38
7 | en | 71.62 |  | 72 | there | 4.60 |  |  | character | 1.38
8 | ou | 69.94 |  | 73 | under | 4.56 |  |  | either | 1.38
9 | of | 68.95 |  | 74 | day | 4.51 |  |  | great | 1.38
10 | ar | 68.69 |  |  | world | 4.51 |  |  | receive | 1.38
11 | ed | 65.77 |  | 76 | him | 4.43 |  | 141 | much | 1.33
12 | st | 59.19 |  | 77 | do | 4.38 |  | 142 | above | 1.29
13 | ing | 53.52 |  |  | very | 4.38 |  |  | blind | 1.29
14 | for | 48.19 |  | 79 | ence | 4.34 |  |  | necessary | 1.29
15 | tion | 43.24 |  | 80 | good | 4.30 |  |  | today | 1.29
16 | that | 35.59 |  |  | so | 4.30 |  | 146 | before | 1.25
17 | ch | 32.41 |  | 82 | their | 4.17 |  | 147 | afternoon | 1.16
18 | was | 28.46 |  | 83 | out | 4.13 |  | 148 | behind | 1.12
19 | ea | 27.34 |  | 84 | still | 4.00 |  |  | us | 1.12
20 | ow | 26.35 |  | 85 | your | 3.74 |  | 150 | beyond | 1.03
21 | wh | 25.88 |  | 86 | through | 3.70 |  |  | cannot | 1.03
22 | with | 25.23 |  | 87 | also | 3.61 |  | 152 | almost | 0.95
23 | sh | 24.85 |  |  | every | 3.61 |  | 153 | braille | 0.86
24 | people | 22.57 |  | 89 | mother | 3.54 |  |  | spirit | 0.86
25 | have | 20.63 |  | 90 | again | 3.35 |  | 155 | beside | 0.77
26 | his | 19.26 |  |  | first | 3.35 |  |  | upon | 0.77
27 | be | 19.13 |  |  | just | 3.35 |  |  | yourself | 0.77
28 | from | 18.57 |  | 93 | go | 3.31 |  | 158 | knowledge | 0.64
29 | gh | 17.50 |  | 94 | right | 3.27 |  |  | myself | 0.64
30 | will | 17.15 |  | 95 | less | 3.18 |  | 160 | tonight | 0.56
31 | it | 15.73 |  | 96 | question | 3.10 |  | 161 | ourselves | 0.52
32 | not | 15.39 |  | 97 | dd | 3.01 |  |  | whose | 0.52
33 | by | 15.30 |  | 98 | friend | 2.97 |  | 163 | enough | 0.34
34 | but | 14.96 |  | 99 | those | 2.92 |  |  | o'clock | 0.34
35 | con | 14.87 |  | 100 | if | 2.88 |  |  | paid | 0.34
| some | 14.87 |  | 101 | should | 2.84 |  | 166 | below | 0.30
37 | com | 14.53 |  | 102 | cc | 2.75 |  | 167 | herself | 0.26
38 | you | 14.49 |  | 103 | name | 2.67 |  | 168 | tomorrow | 0.21
39 | this | 14.01 |  |  | part | 2.67 |  | 169 | beneath | 0.17
40 | said | 12.55 |  | 105 | between | 2.58 |  | 170 | child | 0.13
41 | one | 12.42 |  |  | know | 2.58 |  |  | perceive | 0.13
42 | ation | 11.99 |  | 107 | word | 2.49 |  |  | receiving | 0.13
43 | ble | 11.95 |  | 108 | across | 2.32 |  | 173 | afterward | 0.09
44 | little | 11.86 |  |  | always | 2.32 |  |  | altogether | 0.09
45 | were | 11.09 |  | 110 | quite | 2.24 |  |  | lord | 0.09
46 | like | 10.57 |  | 111 | already | 2.19 |  | 176 | against | 0
47 | ally | 10.49 |  |  | ful | 2.19 |  |  | conceive | 0
48 | as | 9.80 |  |  | himself | 2.19 |  |  | conceiving | 0
49 | more | 9.29 |  |  | must | 2.19 |  |  | deceive | 0
50 | time | 8.68 |  | 115 | where | 2.11 |  |  | deceiving | 0
51 | dis | 8.17 |  | 116 | children | 2.06 |  |  | declare | 0
52 | which | 8.00 |  | 117 | ount | 2.02 |  |  | declaring | 0
53 | can | 7.57 |  | 118 | its | 1.98 |  |  | neither | 0
54 | ever | 7.44 |  |  | these | 1.98 |  |  | oneself | 0
55 | ance | 7.31 |  | 120 | immediate | 1.93 |  |  | perceiving | 0
56 | about | 7.05 |  |  | bb | 1.93 |  |  | rejoice | 0
57 | ound | 6.83 |  | 122 | itself | 1.89 |  |  | rejoicing | 0
58 | many | 6.79 |  | 123 | such | 1.85 |  |  | thyself | 0
59 | work | 6.71 |  | 124 | ought | 1.81 |  |  | yourselves | 0
60 | had | 6.62 |  |  | young | 1.81 |  |  |  |
61 | ity | 5.80 |  | 126 | gg | 1.76 |  |  |  |
| shall | 5.80 |  | 127 | perhaps | 1.68 |  |  |  |
63 | could | 5.76 |  |  | quick | 1.68 |  |  |  |
64 | ment | 5.72 |  | 129 | father | 1.55 |  |  |  |
65 | would | 5.67 |  |  | themselves | 1.55 |  |  |  |

*NSC=normed space-saving capacity: the average number of characters by which a text of 10,000 characters is shortened by a contraction.

Note: A rank can be shared by two or more contractions, if they have equal space-saving capacity; to emphasize such rank sharing, only the first contraction (in alphabetical order) shows the shared ranking number.