Re: [EXTERNAL] Some braille references

This is not a braille issue, but here is an interesting
use of that notation which illustrates the need for intent
to allow correct pronunciation.  (But the braille is the
same in the two cases below.)

The expression  [A:B]  arises in abstract algebra in two
different ways:

1) When A is a group and B is a subgroup.
(Often the letters used are G and H)

2) When B is a field and A is an extension of B.
(Often the letter are E and F, or L and K)

In case 1) it is pronounced "The index of B in A".

In case 2) it is pronounced "The degree of A over B".

The arguments A and B occur in opposite order, and the
surrounding words are different.

These topics are part of a standard undergraduate math
degree (pure math, anyway), so this is not about some weird
and rare research notation.

I have seen vertical lines, or parentheses, in place of the
square brackets in case 1).  In case 2) it is usually square
brackets (but I will not claim it always is, because Deyan
will quickly find a counterexample!).


On Tue, 13 Jul 2021, Deyan Ginev wrote:

> Hi all,
>
> There is a certain futility in reinventing meaningful variants to the
> same visual glyph. Though the line where the futility starts is
> slightly blurry.
>
> In language, there are some safe distinctions that make perfect sense.
> A cyrillic "с" (our letter for "s"), may be best kept distinct from a
> Latin "c", as they're spoken differently when read as characters -
> even though they visually look the same. But when it comes to letters
> "k" vs "к", and especially "а" vs "а" there is no difference at all in
> the standalone character readout - you need a full word to get some
> variation. So already here the redundancy slowly starts begging the
> practical question of when these inventions begin to lose their value.
> Of course, having an alphabet fully fleshed out as its own block pays
> all kinds of worthwhile respects to the communities that use these
> alphabets, so it is very easy to make a call for inclusion there.
>
> But there are known harms that follow. See the "IDN homograph attack"
> article on how people well-versed in cyrillic have been dancing around
> unsuspecting readers using this expressivity of Unicode:
> https://en.wikipedia.org/wiki/IDN_homograph_attack
>
> I will admit to using a benign variant of this myself, when I once had
> the desire of leaving a form field blank, but a validator required me
> to add content. Despite them guarding for spaces, tabs and newline
> characters, when I entered a single "invisible times" character U+2062
> I successfully submitted. Because the application in question was not
> using proper Unicode sanitization, I danced around an otherwise
> intentional content guard.
>
> So, back to the colon character and its mathematical uses. I wanted to
> attach a list of notations that use it from our current Level lists:
>
> - ratio 1:2
> - such-that in set notation { x : x > 0 }
> - trilinear-coordinates x:y:z
> - covering-relation   <:
> - defined, e.g.   " L : system of equations " used in JEE exams, but
> also part of  := and ::=
> - separator in function/relation declarations,  f : A ↣ B  or  f : A ↠
> B  or f : A ⤖ B or ...
> - separator in index of subgroup, as mentioned by David Farmer, | $1 : $2 |
> - separator in Plücker coordinates ( a : b : c : ... )
> - separator in time, as mentioned by Neil, 1:30 pm
>
> There is no claim this list is complete - and anyone can publish a
> paper tomorrow that attempts to extend it when introducing a new
> mathematical construct.
> There are also other non-Math uses that would still be relevant to
> Braille, such as the namespace separators in some programming
> languages ::  or declaring symbols in Ruby via :name
> I think this illustrates the general challenge quite nicely.
>
> Greetings,
> Deyan
>
> On Tue, Jul 13, 2021 at 2:33 PM Susan Jolly <easjolly@ix.netcom.com> wrote:
>>
>> FWIW Unicode has long had a math symbol named ratio: U+2236.
>>
>> OTOH this article claims the symbol that looks like a colon in the notation
>> for the index of a subgroup is the colon found on a standard keyboard.
>> https://en.wikipedia.org/wiki/List_of_mathematical_symbols_by_subject
>>
>> Susan J.
>>
>