Re: [EXTERNAL] Some braille references

Indeed it appears that Nemeth code distinguishes "ratio" as a bit of a
special case.

I had some further correspondence with Susan Ousterhaus and she explained
that a colon is either considered a ratio or a punctuation mark. As a
ratio, the braille for ":" has spaces around it. As a punctuation mark,  it
has a punctuation marker that precedes it and there are no spaces added.
There is a revision to Nemeth that tries to clarify this a little bit. I
found the clarification wanting as it omits many uses of colon. MathWorld
has a page that lists 7 uses for ":".  MathWorld doesn't include its use in
time (e.g., 3:30pm), so really 8 uses.

#5 on MathWorld's list is a trilinear form (a:b:c) used in geometry for
triangles. They are another form of ratio, but the Nemeth spec (and the
pending update) is currently silent on them.

I tried to get some rationale as to when ":" is punctuation in Nemeth code
and when it isn't from Susan but she doesn't know. In math typesetting, ":"
is either a binary operator with symmetrical spacing or punctuation with
asymmetrical spacing (in TeX, it is ":" or "\colon"). I suspect Dr. Nememth
was trying to capture this with his rule for "ratio", but that is just my
speculation. If he really was doing that, then "ratio" is not really
semantic in Nemeth code as there is a difference in the typesetting. If
not, then it is semantic. Given the overall design philosophy of Nemeth
code, I suspect he really was trying to capture that typographical
difference but BANA doesn't seem to see it that way (although it is not
clear they actually know the difference as there are no mathematicians on
the committee AFAIK).

As it currently stands, we now have two exceptions to the "not semantic"
rules for braille:
1. binomials (and related notations) vs 2x1 column matrices (and related
notations)
2. ratio vs other uses of ":'' although the Nemeth spec doesn't cover many
uses of ":" in its text (so there may be other cases such as trilinear
forms and extension fields)

Anyone know anything else?

    Neil




On Fri, Jul 9, 2021 at 9:41 PM Neil Soiffer <soiffer@alum.mit.edu> wrote:

> Once more, Susan Jolly sent email with an interesting point. She pointed
> out something that may look like a semantic difference, but I don't think
> really is one, at least as far as we have been considering them. Rather
> than paraphrase what Susan said, I'm taking the liberty of quoting her:
>
> The factorial sign, ratio, decimal point, and  the comma separator in
>> numbers (or European decimal point) use different Nemeth symbols than do
>> the
>> exclamation, colon, period, and comma punctuation marks.  There may be
>> others I've forgotten.
>>
>> I guess this could be considered as a semantic distincton but the reason
>> is
>> not necessarily semantic.  The problem is of course that  many of the
>> dropped numbers used in Nemeth are also used as punctuation marks in
>> English
>> literary braille. My guess is that Dr Nemeth's use of separate symbols was
>> primarily to avoid adding clutter to the math.
>>
>
> To maybe add a little more clarification: Nemeth code has different
> meanings for some of the standard literary braille symbols including
> punctuation symbols, so if you really mean an exclamation mark (as at the
> end of sentence) instead of a factorial symbol, you need to encode the two
> differently. Basically you need to step out of math mode in these cases.
> That will occur in MathML inside of an mtext or embedded HTML.
>
>    Neil
>
>