kdejute
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Thank you for posting this question!
Most of us on the committee would go with your Example 2 (brailling each line continuously using a runover position when necessary.)
None of use would go with your Example 1, because it requires some pretty complex navigation on the part of the reader.
(One additional suggestion was to consider tweaking Example 2 by forcing a line break after each comma so that every expression from "column 2" starts its own braille line. This may help the reader to navigate the material, especially when trying to revisit parts of it.)
–Kyle
Third and last, even when dealing with chemical notation that requires grade one indication past the 3rd cell in an expression, a transcriber should use a grade one word indicator instead of a grade one symbol indicator.
That's what it says in #5 in BANA's "Provisional Guidance for Transcribing Mathematics in UEB."
Unless a math expression can be correctly represented with only a grade 1 symbol indicator in the first three cells or before a single letter standing alone anywhere in the expression, begin the expression with a grade 1 word indicator (or a passage indicator if the expression includes spaces).
[Will the final (i.e., not provisional) version of BANA guidance say the same thing? I believe it will say something different. But, for now, we should follow what is published.]
Second, I very much sympathize with your question about, "How should we format formal proofs (and other labeled statements) in UEB Math/Science transcriptions?"
In short, Braille Formats is our formatting guide for anything not covered in RUEB, GTM, or BANA's "Provisional Guidance for Transcribing Mathematics in UEB."
One covered issue that is related to formal proofs comes from the "Provisional Guidance for Transcribing Mathematics in UEB." The first paragraph in #3 of that document says the following.
For technical materials, use margins 3-1; do not use blocked paragraphs. If the entire textbook is in blocked paragraphs, note the change to indented paragraphs in a TN.
So, in a UEB Math/Science transcription, we would probably format the print of "Example 26-73: Theorem with Auxiliary Captions" of The Nemeth Code as follows.
⠀⠀⠘⠂⠠⠮⠕⠗⠑⠍⠀⠘⠂⠼⠙⠲⠀⠠⠊⠋⠀⠞⠺⠕⠀⠇⠔⠑⠎⠀⠜⠑⠀⠉⠥⠞⠀⠃⠽
⠁⠀⠞⠗⠁⠝⠎⠧⠻⠎⠁⠇⠀⠯⠀⠁⠀⠏⠁⠊⠗⠀⠷⠀⠁⠇⠞⠻⠝⠁⠞⠑⠀⠔⠞⠻⠊⠕⠗
⠁⠝⠛⠇⠑⠎⠀⠜⠑⠀⠑⠟⠥⠁⠇⠂⠀⠮⠀⠞⠺⠕⠀⠇⠔⠑⠎⠀⠜⠑⠀⠏⠜⠁⠇⠇⠑⠇⠲
⠀⠀⠨⠂⠠⠛⠊⠧⠢⠒⠀⠠⠇⠔⠑⠎⠀⠰⠠⠠⠁⠃⠀⠯⠀⠰⠠⠠⠉⠙⠀⠉⠥⠞⠀⠃⠽
⠞⠗⠁⠝⠎⠧⠻⠎⠁⠇⠀⠠⠠⠗⠎⠀⠁⠞⠀⠏⠕⠔⠞⠎⠀⠰⠠⠑⠀⠯⠀⠰⠠⠋
⠗⠑⠎⠏⠑⠉⠞⠊⠧⠑⠇⠽⠆⠀⠸⠪⠭⠀⠐⠶⠀⠸⠪⠽⠲
⠀⠀⠨⠂⠠⠞⠕⠀⠨⠂⠠⠏⠗⠕⠧⠑⠒⠀⠰⠰⠰⠠⠠⠁⠃⠀⠼⠇⠀⠠⠠⠉⠙⠲⠰⠄
First, let's tackle the Dot Locator for "Use" (RUEB2024 §3.14)
I agree, the fourth paragraph in GTM 4.1 Spatial calculations (quoted below) gives us guidance regarding blank lines in relation to the numeric passage indicator or terminator that we simply do not have regarding blank lines in relation to grade 1 indicators, capitalized passage indicators, or their respective terminators.
The line above and below spatial calculations should either be blank, or should only contain the numeric passage indicator or terminator.
I would advocate for your #2 example, where you have replaced the blank lines around displayed material with a line that contains only the grade 1 passage indicator and a line that contains only the grade 1 terminator. For our convenience, I have attempted to recreate that example below.
⠼⠊⠲⠀⠠⠔⠙⠊⠉⠁⠞⠑⠀⠞⠗⠥⠑⠀⠕⠗⠀⠋⠁⠇⠎⠑⠒
⠐⠐⠿⠰⠰⠰
⠀⠀⠀⠀⠀⠀⠠⠎⠐⠖⠠⠕⠢⠼⠃⠀⠳⠕⠀⠠⠎⠠⠕⠢⠼⠃⠀⠳⠬
⠀⠀⠀⠀⠀⠀⠠⠓⠠⠉⠇⠀⠳⠕⠻⠘⠳⠪⠀⠠⠓⠔⠐⠖⠐⠖⠠⠉⠇⠔⠐⠤
⠀⠀⠀⠀⠀⠀⠠⠅⠠⠊⠐⠖⠠⠊⠢⠼⠃⠀⠳⠬⠳⠩⠀⠠⠅⠠⠊⠢⠼⠉
⠐⠐⠿⠰⠄
⠀⠀⠠⠁⠲⠀⠠⠞⠗⠥⠑
⠀⠀⠰⠠⠃⠲⠀⠠⠋⠁⠇⠎⠑
Thank you for your question, Fred.
Though I do not doubt our braille-using friends, students, and neighbors would make sense of contracted comments within a numeric passage, I cannot recommend it.
A numeric passage indicator sets grade 1 mode until the numeric terminator ends that grade 1 mode (RUEB2024 §6.9.1). If we use contracted braille within a numeric passage, then we use symbols that have a grade 1 meaning in an environment that says their grade 1 meaning is what's important.
In responses to your questions:
Q: Yes, everything within a numeric passage is in grade 1.
1) A math comment like 300×32, would be brailled without the numeric indicators within a numeric passage.
2) No. For the sake of clarity, translatability, and consistency, we should not braille text comments contracted within a numeric passage.
Regarding your key for comments: I really like your placements of the key letters (i.e., each following the quotient piece to which it applies). However, remember what RUEB2024 § says: "... any lowercase letter a-j is preceded by a grade 1 indicator." Since you'll have to use a grade 1 symbol indicator for each of those letters, I think you should get rid of the periods. Also, in your key listing, please check the formation (and grade 1 indicating) of your letters (especially the b). One more note: you do not need a blank line before the braille line that contains only a numeric terminator (GTM §4.1, last paragraph before 4.1.1).
In other words, regarding your #3, it is a good choice to use a key for the comments, and it seems practical to use a TN to explain the printed down arrows showing numbers in the dividend moving.
Last, but not least, I agree, spatial division with operation signs is challenging; I think you've done a very good job of aligning by place value and placing the symbols of operation where they apply.
Braille on!
–KyleFor what it is worth, personally, I would be tempted to use UEB's composite symbol for horizontal juxtaposition (GTM §14.3.4) but would probably not use it, trusting the braille user to recognize the significance of two sequential equals symbols without my grubby little transcriber hands getting into the content.
14.3.4 Horizontal Juxtaposition ;=
"Horizontal juxtaposition" is to be invoked only when two symbols are written in close proximity and it is clear from the usage that a new single symbol, distinct from the elementary symbols considered in sequence, is intended. Otherwise, symbols written one after the other should simply be brailled accordingly.If you had an example to share, Shellee, I would love that because the committee could come to a decision for that specific circumstance.
–Kyle
P.S. I noticed you quoted a sentence from a course, and I think there is a different interpretation than you assigned to it. The sentence is, "Linked expressions are displayed expressions that are made up of an 'anchor' and one or more 'links'." I believe the sentence means "linked expressions can be displayed" rather than "if something is a linked expression, then it is necessarily displayed."
Thank you for sharing more of your thoughts.
The committee has been discussing this, and our conclusions are summarized below:
- The fact that these expressions are itemized removes the need to treat them as displayed. [see BF2016 §9.1.2, which says, "For formatting purposes, lists, boxed material, and tables are not considered displayed material. ..."]
- Only the comparison symbols require spacing.
So, we recommend using the indention pattern and lack of blank lines that make up your Example 1.
And, we would probably omit all the spaces we could. I think that means keeping only two kinds of spaces: 1) spaces around symbols of comparison and 2) spaces that make a word more likely to keep its usual form. This is illustrated in a snippet below and in slightly more context in the attached picture and brf.
"7 .- t5?s"/.- t5?s
The big takeaway is that an itemized list is not displayed material.
As for spacing, the best choice is likely what you can best do consistently.
Braille on!
–KyleJanice, Computer Braille Code is no longer an active code in the United States. Please see the document BANA Positions on Computer Braille Code and Braille ASCII.
Does that lead you to further questions, or is that all you need?
–Kyle
Last, but not least, you asked, "Wouldn't the enclosure symbol be easier to understand when preceded by the shape termination symbol?"
I cannot say whether that would be easier to understand. However, I can point out that section 14.3 is titled "Combined shapes," and its first paragraph says that physical enclosure takes two symbols and makes a new, previously undefined symbol. For example, the "circled plus" is a single entity with a meaning all its own that is distinct from the "plus" and the "circle." So, the enclosed shape is part of the overall shape, and it would be inappropriate to put a shape terminator between the circle and whatever is enclosed.
I think the next necessary question is, "Does physical enclosure accurately transcribe the meaning of 'circling' in print (like "circle the correct answer")? ... Or would a typeform perhaps do a better job of transcribing the meaning of 'circling' while physical enclosure should be reserved for situations where the enclosing and enclosed shapes become something different from either (like the circled plus described above)? I do not have an answer to that question, and I suspect no one else does for sure either, for now.
Thank you for sharing your astute questions!
Please let us know if you need anything more or different.
–Kyle
Third, if we need to indicate "circling" (that is, physical enclosure in a circle) of a symbols-sequence that consists of more than one item, then yes, using braille grouping indicators is a good solution.
The example you shared is a simple up pointing arrow and a dollar sign circled together:
;;$=[<\+@s>
That symbols-sequence is a grade 1 word indicator, the two-cell symbol for a circle (shape indicator and a full cell), the physical enclosure cell, opening braille grouping indicator, the two-cell symbol for a simple up pointing arrow, the two-cell dollar symbol, closing braille grouping indicator, and then space.
Second, if we have to show a transcriber-defined symbol enclosed in a circle, I agree that the following would be the best way to do so (using "physical enclosure" as illustrated in GTM §14.3.1).
;;$=[?
That symbols-sequence is a grade 1 word indicator, the two-cell symbol for a circle (shape indicator and a full cell), the physical enclosure cell, the first transcriber-defined symbol, and then space.
You have likely already considered all angles of:
- using the transcriber-defined symbol vs. the transcriber-defined shape
- with what words you will identify whatever transcriber-defined thing you use
- where you will identify whatever transcriber-defined thing you use (i.e., on the Special Symbols Page or in a list of special symbols within the text)
I do think this would be understood by a 10th grade student. 😊
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Finally, does the termination of a shape leave the rest of the symbols-sequence in grade 2 (unless it is affected by a grade 1 word or passage indicator)? ... Many agree with your assessment that according to RUEB2024 §2.5.3, it does. However, the first example in GTM §14.3.1 might indicate otherwise.
RUEB2024 §2.5.3 says, "Grade 1 mode exists only when introduced by a grade 1 indicator or by a numeric indicator."
The first example in GTM §14.3.1 is: ;$=["6 (circle enclosing a plus sign) where the cell dots 2-4-6 does not have any grade 1 indicator or numeric mode affect it, BUT it is treated as if it has its grade 1 meaning (physical enclosure). Maybe the argument is that what's physically enclosed is part of the shape and so affected by the shape indicator's limited grade 1 mode (though that would be quite a unique effect for an indicator to have).
This issue is on the list of things to be clarified by ICEB's technical material code maintenance committee. Right now, I would follow RUEB2024 §2.5.3, as you have suggested.
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