Re: Commercial minus as italic variant of division sign in German and Scandinavian context

[Asmus Freytag]

On 1/16/2014 8:12 AM, Leif Halvard Silli wrote:

Asmus Freytag, Thu, 16 Jan 2014 07:24:45 -0800:

On 1/16/2014 5:34 AM, Leif Halvard Silli wrote:

when looking at my message in Firefox [1], the commercial minus
looks like a “handwritten” variant of the division sign.

the fact that the "slant" is reverse, rather than forward,
is contrary to the way oblique or italic fonts usually work.

So, again, I find your suggestion of "italic variant" not helpful.

Got it. ;-) Will stop using "italic" about it!

OK. I'll hold you to it.

Meanwhile, I think there
*is* something to say about the slant, the slant does seem to be
primarily linked to *style*.


Style in Unicode is used on two ways.

A) to indicate that a distinction is glyphic and can be ignored
B) to indicate that a glyph shape relates to a typographical style

A is wrong for 00F7 vs 2012 vs 2052. The distinctions are deliberate
and authors (and readers) would take exception if you substituted
another "style" of symbol. The fact is that these are not simply
accidental but correct disunifications.

In a sense, it's no different from "z" being used for the soft-s in
English (if not exclusively), "s" being used for both soft and hard
s in German and never being used for soft-s in Scandinavia.

When Unicode says it encodes the "semantics" of a character,
it doesn't mean that these semantics can't be context sensitive
or that different contexts can't call for different characters for
the same semantics. (In the minus case we are talking mathematical
semantics, while in the letter case we are talking phonetics, but
otherwise there's not a whole lot of distinction in the context
sensitive nature of character use).

The most useful concept (I have found) in these kinds of investigations
is "character identity". Here it is clear that something like 00F7
that can mean both division and minus (based on context) has
a different identity from 2012 or 2052 that (in math use) can only
mean minus. And 2052 is different from 2012 in that it is limited
to certain contexts, and 2012 cannot be used in marking papers.

So, just acknowledge that, and if you feel the need to add value,
do so by better descriptions of which context which character is
used in.

B is relevant for math alphabets, because the glyphs really are
constrained to match a typographical style. It's not relevant to
the case here, because 2052 is not a specific "style" of the
"same thing in another font".

Just now, at colourbox.de, I found some
vector icons which are simply labelled as minus icons, and which both
of them are shaped like the DIVISION SIGN, and which occurs side by
side with a plus sign. The labels for the icons are simply “Icon -
minus - schwarz weiß“ and ”Icon - minus - hellblau”.  See:


You find it in Google if you search for ”kaufmännische Minuszeichen”.
Take that as a hint.


This could be for two reasons.

A) there is some use where 00F7 has the semantics of minus.
B) the icon is misnamed in the source because of the visual similarity 
with a minus


Unfortunately, by itself, you can't use that source to distinguish A from B.





Anyway, when I spoke if 2052 as an italic version of 00F7, I meant in
the, kind of, “mathematical” sense: […]

Where the case for 00F7 and 2052 differs from the mathematical alphabets is
that in the latter case the shape variants are (to a very large
extent) accurately described by the typographical moniker. A bold is a bold.

The only exception that I can think of is in the realm of "script",
where some authors prefer a slightly different style that isn't tied
to 18th century copperplate.

And by script you mean "handwriting style". That makes sense. That is
how I perceive the German, commercial minus.
It may be derived from a handwritten mark - most accounting wasn't 
typeset - but
the exception that I was referring to are Knuth's "Euler" fonts which he 
uses instead
of "script" in his mathematical works. Their ductus retains just faint 
traces of handwriting,
and none of the elaborate styles of handwriting that typical "script" 
fonts are based
on, but they serve their purpose in mathematics (unless you are a 
purist) because they

are distinct from all the other styles and arguably a bit more readable.

Your applying my comment to 2052 is taking it wildly out of context.



Suggest better text for the book chapter that details the precise
places that have been established as using 00F7 in the capacity
of "minus sign". That would be more helpful than trying to somehow
treat 00F7 and 2052 as glyphic variants of each other. They are
separate characters, with distinct usage conventions that simply
happen to employ both a line and two dots. (The fallback of ./. for
2052 is  interesting in this context).

Ok. Will try. Though I think better text would tie them, rather than
separate them. But I think you are artificially separating them.

I am arguing that they have a distinct "identity

Re: Commercial minus as italic variant of division sign in German and Scandinavian context

[Leif Halvard Silli]

Asmus Freytag, Thu, 16 Jan 2014 07:24:45 -0800:
> On 1/16/2014 5:34 AM, Leif Halvard Silli wrote:

>> when looking at my message in Firefox [1], the commercial minus
>> looks like a “handwritten” variant of the division sign.

> the fact that the "slant" is reverse, rather than forward, 
> is contrary to the way oblique or italic fonts usually work.
> 
> So, again, I find your suggestion of "italic variant" not helpful.

Got it. ;-) Will stop using "italic" about it! Meanwhile, I think there 
*is* something to say about the slant, the slant does seem to be 
primarily linked to *style*. Just now, at colourbox.de, I found some 
vector icons which are simply labelled as minus icons, and which both 
of them are shaped like the DIVISION SIGN, and which occurs side by 
side with a plus sign. The labels for the icons are simply “Icon - 
minus - schwarz weiß“ and ”Icon - minus - hellblau”.  See: 


You find it in Google if you search for ”kaufmännische Minuszeichen”. 
Take that as a hint.

>> Also, I wonder about the claim in the General Punctuation section that
>> commercial minus is used in taxation forms in Scandinavia and Germany.
   […]
> I would not be surprised if the actual situation is a bit more 
> detailed than expressed in Unicode's namelist annotations (or
> even the descriptions in the chapter texts).
> 
> However, I can't assist you in tracking those down as I have access 
> to no taxation forms that use any of these characters. :)

:-)

>> Anyway, when I spoke if 2052 as an italic version of 00F7, I meant in
>> the, kind of, “mathematical” sense: […]

> Where the case for 00F7 and 2052 differs from the mathematical alphabets is
> that in the latter case the shape variants are (to a very large 
> extent) accurately described by the typographical moniker. A bold is a bold.
> 
> The only exception that I can think of is in the realm of "script", 
> where some authors prefer a slightly different style that isn't tied
> to 18th century copperplate.

And by script you mean "handwriting style". That makes sense. That is 
how I perceive the German, commercial minus. 

> Suggest better text for the book chapter that details the precise 
> places that have been established as using 00F7 in the capacity
> of "minus sign". That would be more helpful than trying to somehow 
> treat 00F7 and 2052 as glyphic variants of each other. They are
> separate characters, with distinct usage conventions that simply
> happen to employ both a line and two dots. (The fallback of ./. for
> 2052 is  interesting in this context).

Ok. Will try. Though I think better text would tie them, rather than 
separate them. But I think you are artificially separating them.

> I was focused only at the minority use of 00F7 as a minus sign, in 
> which case
> it and 2052 AND 002D and 2012 all function as variants of each other (but
> not as glyphic variants --- they are spelling variants).

Good point. It is like the V and U - they have a common history.

>> It is an argument for seeing 00F7 as (also) a hyphen-minus variant, no?
> Once you get into the dashes, there's tons of variant usage. What's 
> documented in Unicode tends to be from predominantly English-language 
> style manuals, but if you extend this to all publications in all 
> (Western) languages including recent historic times, I'm sure you'd 
> find surprising variations.

Does the Unicode spec say this - that is is predominantly English 
language based?

>> As it is today, no one seems to realize how commercial
>> minus relates to “division sign minus”.
> "additional" names are ruled out - except to fix something that's 
> badly broken.
> Neither of these characters has names that are misleading, mistyped or both.
> 
> There are many characters with deep relations that many users do no know
> about. And, in this case, there seem to be some issues with the precise
> relation you are trying to implement.

I saw it as if in a mist. Now it becomes clearer and clearer to me. :-)

This fun page indicates that the ./. “fallback” has a 35 year history. 
http://www.wertpapier-forum.de/topic/14587-kennzahlenanalyse/page__st__20 
Which could fit well together with a theory that the script variant 
grew in popularity when the ”international” ÷ division sign of 
computers entered German math. That ÷ as minus ”went back” due to 
computers and calculators, seems to be the general trend.
-- 
leif halvard silli

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Re: Commercial minus as italic variant of division sign in German and Scandinavian context

[Asmus Freytag]

On 1/16/2014 5:34 AM, Leif Halvard Silli wrote:

Asmus,

I am not certain that commercial minus isn’t sometimes used as italics
for the ”division sign minus”. For instance, when looking at my message
in Firefox [1], the commercial minus looks like a “handwritten” variant
of the division sign. I think it would be entirely possible to use a
that way looking commercial minus in a Norwegian taxation formulary,
for instance. (I attach a screenshot of it.) I suspect that it is a
monospace Courier font.
The screen shot indeed shows a glyph for 2052 that superficially looks 
like a
*reverse* (!) oblique variant of the glyph for 00F7. I say 
"superficially" because

the other distinction is the use of heavier dots.

However, the fact that the "slant" is reverse, rather than forward, is 
contrary to

the way oblique or italic fonts usually work.

So, again, I find your suggestion of "italic variant" not helpful.


Also, I wonder about the claim in the General Punctuation section that
commercial minus is used in taxation forms in Scandinavia and Germany.
I would dearly like to see the evidence for that claim. I must say that
I suspect that the use of the division sign in Norwegian taxation forms
for this purpose have been counted in a s evidence for that claim -
could it be that our ”straight commercial minus” was counted as, well,
a commercial minus? Could it be that the wish to see oneself - or us -
in the “German tradition”, made one draw the wrong conclusion about
which character we use?


I would not be surprised if the actual situation is a bit more detailed 
than expressed
in Unicode's namelist annotations (or even the descriptions in the 
chapter texts).


However, I can't assist you in tracking those down as I have access to 
no taxation

forms that use any of these characters. :)


Anyway, when I spoke if 2052 as an italic version of 00F7, I meant in
the, kind of, “mathematical” sense: Unicode for instance contains both
MATHEMATICAL BOLD ITALIC CAPITAL A, and MATHEMATICAL BOLD CAPITAL A,
and even if they are (I believe) used for different mathematical
purposes, everyone sees and knows that they are variants of one and the
same letter - the capital A. And also, in some contexts, one might be
able to use a normal capital A instead of the mathematical ones.


This is getting even less helpful.

The mathematical alphabets exist, because in mathematics, you cannot 
substitute
one shape for another without destroying the semantics (and there are 
general

conventions about what shape to use where).

The latter is similar to the uses of 00F7 and 2052 both. There are 
conventions

where each of them is appropriate and these conventions depend on rathere
selected user communities (school books, tax forms, accounting, math), just
like the use of certain mathematical alphabet styles in physics may not be
shared in all mathematical disciplines.

Where the case for 00F7 and 2052 differs from the mathematical alphabets is
that in the latter case the shape variants are (to a very large extent) 
accurately

described by the typographical moniker. A bold is a bold.

The only exception that I can think of is in the realm of "script", 
where some
authors prefer a slightly different style that isn't tied to 18th 
century copperplate.


The same knowledge is not present about 00F7 and 2052. The best would
have been if the two characters shared a similar name. For instance, if
00F7 got an additional, synonymous name, like STRAIGHT COMMERCIAL
MINUS, or perhaps, better, COMMERCIAL HYPHEN-MINUS. Then the
relationship would be clear - or at least clearer. Like MATHEMATICAL
BOLD ITALIC CAPITAL A, and MATHEMATICAL BOLD CAPITAL A show, two
characters do not need to be 100% synonymous just because their names
only differs in a stylistic way, so to speak.

Well, 00F7 is *most often* used as a division sign. Check calculator keys.


When reading Unicode, one is only left to guess about the relationship
between 00F7 and 2052. For instance, 2052 is described in the general
punctuation - and distinguished there from the ”normal” minus and
hyphen-minus, whereas 0057 is not described there. A sentence, there,
that said that, in some countries, it is actually the 00F7 and not the
2052, that is used, would be very helpful and enlightenting.  Likewise,
there is no description of 00F7 amongst the dashes/hyphens.


Suggest better text for the book chapter that details the precise places 
that have
been established as using 00F7 in the capacity of "minus sign". That 
would be
more helpful than trying to somehow treat 00F7 and 2052 as glyphic 
variants of each
other. They are separate characters, with distinct usage conventions 
that simply happen
to employ both a line and two dots. (The fallback of ./. for 2052 is 
interesting in this context).


You wrote:


Further, while italic (as well as oblique fonts) tend to slant the letter
forms, there's not a universal, established practice of turning horizontal
dashes into slashes to mark the alternation

Re: Aw: Commercial minus as italic variant of division sign in German and Scandinavian context

[Leif Halvard Silli]

"Jörg Knappen", Thu, 16 Jan 2014 09:26:10 +0100 (CET):
> The most important word in the comment on 00F7 ÷ DIVISION SIGN is 
> "occasionally".
>  
> In fact, the occasions are such rare that you can live a whole life 
> in germany without encountering one of them.
>  
> On the other hand, 00F7 ÷ DIVISION SIGN is used _frequently_ in 
> german schoolbooks to denote ...
> division (books aimed at professionals doing math prefer : (COLON) or 
> / (SLASH) for this purpose, but schoolbooks don't).

This sounds like Norway ...
  
> 2052 ⁒ commercial minus sign _always_ means subtraction and it has 
> this shape (or the alternate shape ./.)
> in all contexts, roman or italic. It is not the italic version of 
> some other symbol.

So, I can only once more emphasize that when I said ”italics” I meant 
it the way Unicode already have many characters (primarily mathematical 
ones) which are distinguished, in name, only by a reference to the 
style of the letter. Hope this helps.

As for the clarity of 2052 ⁒ commercial minus sign, no, you are wrong. 
While it is clear to you, in Germany, perhaps, at least in some 
Scandinavian school contexts, it has a different meaning, namely as a 
“well done” sign, from the teacher.

As for the Norwegian context, I guess we can say that the use of ÷ 
DIVISION SIGN as minus sing is more on the down than on the up. But it 
has its contexts (and just last week, I received an ad for glasses were 
it was used), and no one thinks about it. It is not an issue. When we 
get the taxation form on paper or in PDF form, the division minus is 
there, and everyone understands it correctly. (Knock on woods - *some* 
probably stumbles.) They don’t every realize what they see - it is 
knowledge that is unaccounted for. (For instance, until I took this up, 
Wikipedia made no mention of it.  Hah! Even Unicode 6.3 talks about the 
”commercial minus sign” in _Scandinavian_ taxation forms, without (is 
my claim) understanding that it talks about DIVISION SIGN. See my reply 
to Asmus.)

So what I don’t want is that the ”untraditional” uses of ÷ DIVISION 
SIGN are left in the dark as some strange traditions without any roots. 
Also, I don't want the commercial minus to live a life as if it is such 
a unique thing. Let us document things properly.

Leif Halvard Silli


> Gesendet: Donnerstag, 16. Januar 2014 um 04:43 Uhr
> Von: "Leif Halvard Silli" 
> An: unicode@unicode.org
> Betreff: Commercial minus as italic variant of division sign in 
> German and Scandinavian context
> Thanks to our discussion in July 2012,[1] the Unicode code charts now
> says, about 00F7 ÷ DIVISION SIGN, this:
> 
> “• occasionally used as an alternate, more visually
> distinct version of 2212 − {MINUS SIGN} or 2011 ‑
> {NON-BREAKING HYPHEN} in some contexts
> [… snip …]
> → 2052 ⁒ commercial minus sign”
> 
> However, I think it can also be added somewhere that commercial minus
> is just the italic variant of ”division minus”. I’ll hereby argue for
> this based on an old German book on ”commercial arithmetics” I have
> come accross, plus what the the July 2012 discussion and what Unicode
> already says about the commercial sign:
> 
> FIRST: IDENTICAL CONTEXTS.
> 
> German language is an important locale for the Commercial Minus. In
> German, the Commercial minus is both referred to as ”kaufmännische
> Minus(zeichen)” and as "buchhalterische Minus" (”Commercial Minus
> Character” and ”Bookkeeper Minus”). And, speaking of ”division minus”
> in the context I know best, Norway, we find it in advertising
> (commercial context) and in book keeping documentation and taxation
> forms. Simply put, what the Unicode 6.2 ”General Punctuation” section
> says about Commercial Minus, can also be said about DIVISION SIGN used
> as minus: «U+2052 % commercial minus sign is used in commercial or tax
> related forms or publications in several European countries, including
> Germany and Scandinavia.» So, basically and for the most part, the
> commercial minus and the ”division sign minus” occur in the very same
> contexts, with very much the same meaning. This is a strong hint that
> they are the same character.
> 
> SECOND: GERMAN USE OF DIVISION SIGN FOR MINUS IN COMMERCIAL CONTEXT.
> 
> Is there any proof that German used both an italics variant and a
> non-italics variant of the “division minus”? Seemingly yes. The book
> “Kaufmännische Arithmetik” (“Commercial arithmetics”) from 1825 by
> Johann Philipp Schellenberg. By reading section 118 «Anhang zur
> Addition und Subtraction der Brüche» [”Appendix about the addition and
> subtraction of fractions”]) at page 213 and onwards,[2] we can conclude
> that he describes as “commercial” use of the ÷ ”division minus”, where
> the ÷ signifies a _negative remainder_ of a divi

Re: Commercial minus as italic variant of division sign in German and Scandinavian context

[Leif Halvard Silli]

Asmus, 

I am not certain that commercial minus isn’t sometimes used as italics 
for the ”division sign minus”. For instance, when looking at my message 
in Firefox [1], the commercial minus looks like a “handwritten” variant 
of the division sign. I think it would be entirely possible to use a 
that way looking commercial minus in a Norwegian taxation formulary, 
for instance. (I attach a screenshot of it.) I suspect that it is a 
monospace Courier font. 

Also, I wonder about the claim in the General Punctuation section that 
commercial minus is used in taxation forms in Scandinavia and Germany. 
I would dearly like to see the evidence for that claim. I must say that 
I suspect that the use of the division sign in Norwegian taxation forms 
for this purpose have been counted in a s evidence for that claim - 
could it be that our ”straight commercial minus” was counted as, well, 
a commercial minus? Could it be that the wish to see oneself - or us - 
in the “German tradition”, made one draw the wrong conclusion about 
which character we use?

Anyway, when I spoke if 2052 as an italic version of 00F7, I meant in 
the, kind of, “mathematical” sense: Unicode for instance contains both 
MATHEMATICAL BOLD ITALIC CAPITAL A, and MATHEMATICAL BOLD CAPITAL A, 
and even if they are (I believe) used for different mathematical 
purposes, everyone sees and knows that they are variants of one and the 
same letter - the capital A. And also, in some contexts, one might be 
able to use a normal capital A instead of the mathematical ones.

The same knowledge is not present about 00F7 and 2052. The best would 
have been if the two characters shared a similar name. For instance, if 
00F7 got an additional, synonymous name, like STRAIGHT COMMERCIAL 
MINUS, or perhaps, better, COMMERCIAL HYPHEN-MINUS. Then the 
relationship would be clear - or at least clearer. Like MATHEMATICAL 
BOLD ITALIC CAPITAL A, and MATHEMATICAL BOLD CAPITAL A show, two 
characters do not need to be 100% synonymous just because their names 
only differs in a stylistic way, so to speak.

When reading Unicode, one is only left to guess about the relationship 
between 00F7 and 2052. For instance, 2052 is described in the general 
punctuation - and distinguished there from the ”normal” minus and 
hyphen-minus, whereas 0057 is not described there. A sentence, there, 
that said that, in some countries, it is actually the 00F7 and not the 
2052, that is used, would be very helpful and enlightenting.  Likewise, 
there is no description of 00F7 amongst the dashes/hyphens.

You wrote:

> Further, while italic (as well as oblique fonts) tend to slant the letter
> forms, there's not a universal, established practice of turning horizontal
> dashes into slashes to mark the alternation between roman and
> italic fonts. From that perspective, considering one the "italic"
> variant of the other also appears to be a non-starter.

Right. And I can only underline once more that I meant ”italic” as part 
of the name, see above.

You:

> However, it seems to be possible to establish that these two
> characters are indeed rather close variants: […]

Indeed.

> The choice of variant, though, is driven by context and tradition
> for a given type of document, not by choice of font style.
> And, the choice of using 2052 instead of hyphen-minus or minus
> is deliberate and conscious, making it an alternate spelling rather
> than an alternate "glyph".

Well, yes.

> If 00F7 can be used to stand in as a marked 2011, as claimed in
> the Unicode namelist annotation then that use is clearly NOT
> as a variant of 2052, because 2011 does not have
> any connotations of negation.

It is an argument for seeing 00F7 as (also) a hyphen-minus variant, no?

> That means the semantic
> relations between 00F7 and 2052 only partially overlap, which
> is yet another indication that thinking of one as a font-style
> variant of the other is not particularly helpful - even if the
> ultimate origin may have derived from the same sign.
> 
> At this stage of the game, they are properly disunified,
> just as i and j or u and v.

I am not really arguing for their unification - which anyhow is 
impossible, if I have understood the stability rules of Unicode. 
(Whereas an *additional* name is not ruled out, if I got it right.) I 
am ”only” arguing that Unicode takes information that clearly links the 
two together. As it is today, no one seems to realize how commercial 
minus relates to “division sign minus”.


[1] http://unicode.org/pipermail/unicode/2014-January/13.html
[2] attachment of the file “screenshot-of-minuses.png" <>

Leif Halvard Silli

Asmus Freytag, Wed, 15 Jan 2014 23:17:46 -0800:
> I find it unhelpful to consider 2052 as the italic variant of 00F7, and
> further find the "evidence" for that not all that germane.
> 
> Both are variants of the "-" sign, and so ipso facto are variants of
> each other.
> 
> However, to identify something as "italic" to me would require that
> one form is used

Aw: Commercial minus as italic variant of division sign in German and Scandinavian context

[Jörg Knappen]

The most important word in the comment on 00F7 ÷ DIVISION SIGN is "occasionally".

 

In fact, the occasions are such rare that you can live a whole life in germany

without encountering one of them.

 

On the other hand, 00F7 ÷ DIVISION SIGN is used _frequently_ in german schoolbooks to denote ...

division (books aimed at professionals doing math prefer : (COLON) or / (SLASH) for this

purpose, but schoolbooks don't).

 

2052 ⁒ commercial minus sign _always_ means subtraction and it has this shape (or the alternate shape ./.)

in all contexts, roman or italic. It is not the italic version of some other symbol.

 

Hope this helps,

 

Jörg Knappen

 

 

Gesendet: Donnerstag, 16. Januar 2014 um 04:43 Uhr
Von: "Leif Halvard Silli" 
An: unicode@unicode.org
Betreff: Commercial minus as italic variant of division sign in German and Scandinavian context

Thanks to our discussion in July 2012,[1] the Unicode code charts now
says, about 00F7 ÷ DIVISION SIGN, this:

“• occasionally used as an alternate, more visually
distinct version of 2212 − {MINUS SIGN} or 2011 ‑
{NON-BREAKING HYPHEN} in some contexts
[… snip …]
→ 2052 ⁒ commercial minus sign”

However, I think it can also be added somewhere that commercial minus
is just the italic variant of ”division minus”. I’ll hereby argue for
this based on an old German book on ”commercial arithmetics” I have
come accross, plus what the the July 2012 discussion and what Unicode
already says about the commercial sign:

FIRST: IDENTICAL CONTEXTS.

German language is an important locale for the Commercial Minus. In
German, the Commercial minus is both referred to as ”kaufmännische
Minus(zeichen)” and as "buchhalterische Minus" (”Commercial Minus
Character” and ”Bookkeeper Minus”). And, speaking of ”division minus”
in the context I know best, Norway, we find it in advertising
(commercial context) and in book keeping documentation and taxation
forms. Simply put, what the Unicode 6.2 ”General Punctuation” section
says about Commercial Minus, can also be said about DIVISION SIGN used
as minus: «U+2052 % commercial minus sign is used in commercial or tax
related forms or publications in several European countries, including
Germany and Scandinavia.» So, basically and for the most part, the
commercial minus and the ”division sign minus” occur in the very same
contexts, with very much the same meaning. This is a strong hint that
they are the same character.

SECOND: GERMAN USE OF DIVISION SIGN FOR MINUS IN COMMERCIAL CONTEXT.

Is there any proof that German used both an italics variant and a
non-italics variant of the “division minus”? Seemingly yes. The book
“Kaufmännische Arithmetik” (“Commercial arithmetics”) from 1825 by
Johann Philipp Schellenberg. By reading section 118 «Anhang zur
Addition und Subtraction der Brüche» [”Appendix about the addition and
subtraction of fractions”]) at page 213 and onwards,[2] we can conclude
that he describes as “commercial” use of the ÷ ”division minus”, where
the ÷ signifies a _negative remainder_ of a division (while the plus
sign is used to signify a positive remainder). Or to quote, from page
214: «so wird das Fehlende durch das [Zei]chen ÷ (minus) bemerkt, und
bei Berechn[nung der Preis der Waare abgezogen» [”then the lacking
remainder is marked with the ÷ (minus) and withdrawn when the price of
the commodity is calculated”]. {Note that some bits of the text are
lacking, I marked my guessed in square brackets.} I did not find (yet)
that he used the italic commercial minus, however, the context is
correct. (My guess is that the italics variant has been put to more
use, in the computer age, partly to separate it from the DIVISION SIGN
or may be simply because people started to see it often in handwriting
but seldom in print. And so would not have recognized it in the form of
the non-italic division sign.)

THIRD: IDENTICAL INTERPRETATION

The word “abgezogen” in the above quote is interesting since the Code
Charts for 2052 ⁒ COMMERCIAL MINUS cites the related German word
“abzüglich”. And from the Swedish context, the charts quotes the
_expression_ “med avdrag”. English translation might be ”to be withdrawn”
or ”with subtraction/rebate [for]”. Simply put, we here see the
commercial meaning.

WHAT ABOUT COMMERCIAL MINUS AS “CORRECT” SIGN IN SCANDINAVIAN SCHOOLS?

UNICODE 6.3 notes that in some European (e.g. Finnish, Swedish and
perhaps Norwegian) traditions, teachers use the Commercial Minus Sign
to signify that something is correct (whereas a red check mark is used
to signify error). If my theory is right, that commercial minus and
division sign minus are the same signs, how on earth is that possible?
How can a minus sign count as positive for the student?

The answer is, I think, to be found in the Code Chart’s Swedish
description ("med avdrag"/"with subtraction/rebate"). Because, I think
that the correct understanding is not that it means "correct" or "OK".
R

Re: Commercial minus as italic variant of division sign in German and Scandinavian context

[Asmus Freytag]

I find it unhelpful to consider 2052 as the italic variant of 00F7, and
further find the "evidence" for that not all that germane.

Both are variants of the "-" sign, and so ipso facto are variants of
each other.

However, to identify something as "italic" to me would require that
one form is used in the context of italic fonts, while the other is not.

I cannot see anything supporting that interpretation in the "evidence"
adduced below.

On the contrary, you would expect both forms available in sans-serif
and typewriter fonts (those being perhaps the most common for
accounting), and perhaps also roman.

Further, while italic (as well as oblique fonts) tend to slant the letter
forms, there's not a universal, established practice of turning horizontal
dashes into slashes to mark the alternation between roman and
italic fonts. From that perspective, considering one the "italic"
variant of the other also appears to be a non-starter.

However, it seems to be possible to establish that these two
characters are indeed rather close variants: both are used
to visually emphasize the minus sign by means of decorating
it with a pair of dots. And both are employed in situations that
are have a large semantic overlap. (Not surprisingly, because their
meaning is based on the minus sign).

The choice of variant, though, is driven by context and tradition
for a given type of document, not by choice of font style.
And, the choice of using 2052 instead of hyphen-minus or minus
is deliberate and conscious, making it an alternate spelling rather
than an alternate "glyph".

If 00F7 can be used to stand in as a marked 2011, as claimed in
the Unicode namelist annotation then that use is clearly NOT
as a variant of 2052, because 2011 does not have
any connotations of negation. That means the semantic
relations between 00F7 and 2052 only partially overlap, which
is yet another indication that thinking of one as a font-style
variant of the other is not particularly helpful - even if the
ultimate origin may have derived from the same sign.

At this stage of the game, they are properly disunified,
just as i and j or u and v.

A./




On 1/15/2014 7:43 PM, Leif Halvard Silli wrote:

Thanks to our discussion in July 2012,[1] the Unicode code charts now
says, about 00F7 ÷ DIVISION SIGN, this:

   “• occasionally used as an alternate, more visually
  distinct version of 2212 − {MINUS SIGN} or 2011 ‑
  {NON-BREAKING HYPHEN} in some contexts
 [… snip …]
→ 2052 ⁒ commercial minus sign”

However, I think it can also be added somewhere that commercial minus
is just the italic variant of ”division minus”. I’ll hereby argue for
this based on an old German book on ”commercial arithmetics” I have
come accross, plus what the the July 2012 discussion and what Unicode
already says about the commercial sign:

FIRST: IDENTICAL CONTEXTS.

German language is an important locale for the Commercial Minus. In
German, the Commercial minus is both referred to as ”kaufmännische
Minus(zeichen)” and as "buchhalterische Minus" (”Commercial Minus
Character” and ”Bookkeeper Minus”). And, speaking of ”division minus”
in the context I know best, Norway, we find it in advertising
(commercial context) and in book keeping documentation and taxation
forms. Simply put, what the Unicode 6.2 ”General Punctuation” section
says about Commercial Minus, can also be said about DIVISION SIGN used
as minus: «U+2052 % commercial minus sign is used in commercial or tax
related forms or publications in several European countries, including
Germany and Scandinavia.» So, basically and for the most part, the
commercial minus and the ”division sign minus” occur in the very same
contexts, with very much the same meaning. This is a strong hint that
they are the same character.

SECOND: GERMAN USE OF DIVISION SIGN FOR MINUS IN COMMERCIAL CONTEXT.

Is there any proof that German used both an italics variant and a
non-italics variant of the “division minus”? Seemingly yes. The book
“Kaufmännische Arithmetik” (“Commercial arithmetics”) from 1825 by
Johann Philipp Schellenberg. By reading section 118 «Anhang zur
Addition und Subtraction der Brüche» [”Appendix about the addition and
subtraction of fractions”]) at page 213 and onwards,[2] we can conclude
that he describes as “commercial” use of the ÷ ”division minus”, where
the ÷ signifies a _negative remainder_ of a division (while the plus
sign is used to signify a positive remainder). Or to quote, from page
214: «so wird das Fehlende durch das [Zei]chen ÷ (minus) bemerkt, und
bei Berechn[nung der Preis der Waare abgezogen» [”then the lacking
remainder is marked with the ÷ (minus) and withdrawn when the price of
the commodity is calculated”]. {Note that some bits of the text are
lacking, I marked my guessed in square brackets.} I did not find (yet)
that he used the italic commercial minus, however, the context is
correct. (My guess is that the italics variant has been put to more
use, in the computer age, partly to

Commercial minus as italic variant of division sign in German and Scandinavian context

[Leif Halvard Silli]

Thanks to our discussion in July 2012,[1] the Unicode code charts now 
says, about 00F7 ÷ DIVISION SIGN, this:

  “• occasionally used as an alternate, more visually
 distinct version of 2212 − {MINUS SIGN} or 2011 ‑ 
 {NON-BREAKING HYPHEN} in some contexts  
[… snip …]
   → 2052 ⁒ commercial minus sign”

However, I think it can also be added somewhere that commercial minus 
is just the italic variant of ”division minus”. I’ll hereby argue for 
this based on an old German book on ”commercial arithmetics” I have 
come accross, plus what the the July 2012 discussion and what Unicode 
already says about the commercial sign:

FIRST: IDENTICAL CONTEXTS. 

   German language is an important locale for the Commercial Minus. In 
German, the Commercial minus is both referred to as ”kaufmännische 
Minus(zeichen)” and as "buchhalterische Minus" (”Commercial Minus 
Character” and ”Bookkeeper Minus”). And, speaking of ”division minus” 
in the context I know best, Norway, we find it in advertising 
(commercial context) and in book keeping documentation and taxation 
forms. Simply put, what the Unicode 6.2 ”General Punctuation” section 
says about Commercial Minus, can also be said about DIVISION SIGN used 
as minus: «U+2052 % commercial minus sign is used in commercial or tax 
related forms or publications in several European countries, including 
Germany and Scandinavia.» So, basically and for the most part, the 
commercial minus and the ”division sign minus” occur in the very same 
contexts, with very much the same meaning. This is a strong hint that 
they are the same character.

SECOND: GERMAN USE OF DIVISION SIGN FOR MINUS IN COMMERCIAL CONTEXT.

   Is there any proof that German used both an italics variant and a 
non-italics variant of the “division minus”? Seemingly yes. The book 
“Kaufmännische Arithmetik” (“Commercial arithmetics”) from 1825 by 
Johann Philipp Schellenberg. By reading section 118 «Anhang zur 
Addition und Subtraction der Brüche» [”Appendix about the addition and 
subtraction of fractions”]) at page 213 and onwards,[2] we can conclude 
that he describes as “commercial” use of the ÷ ”division minus”, where 
the ÷ signifies a _negative remainder_ of a division (while the plus 
sign is used to signify a positive remainder). Or to quote, from page 
214: «so wird das Fehlende durch das [Zei]chen ÷ (minus) bemerkt, und 
bei Berechn[nung der Preis der Waare abgezogen» [”then the lacking 
remainder is marked with the ÷ (minus) and withdrawn when the price of 
the commodity is calculated”]. {Note that some bits of the text are 
lacking, I marked my guessed in square brackets.} I did not find (yet) 
that he used the italic commercial minus, however, the context is 
correct. (My guess is that the italics variant has been put to more 
use, in the computer age, partly to separate it from the DIVISION SIGN 
or may be simply because people started to see it often in handwriting 
but seldom in print. And so would not have recognized it in the form of 
the non-italic division sign.)

THIRD: IDENTICAL INTERPRETATION

The word “abgezogen” in the above quote is interesting since the Code 
Charts for 2052 ⁒ COMMERCIAL MINUS cites the related German word 
“abzüglich”. And from the Swedish context, the charts quotes the 
expression “med avdrag”. English translation might be ”to be withdrawn” 
or ”with subtraction/rebate [for]”. Simply put, we here see the 
commercial meaning.

WHAT ABOUT COMMERCIAL MINUS AS “CORRECT” SIGN  IN SCANDINAVIAN SCHOOLS?

UNICODE 6.3 notes that in some European (e.g. Finnish, Swedish and 
perhaps Norwegian) traditions, teachers use the Commercial Minus Sign 
to signify that something is correct (whereas a red check mark is used 
to signify error). If my theory is right, that commercial minus and 
division sign minus are the same signs, how on earth is that possible? 
How can a minus sign count as positive for the student?

The answer is, I think, to be found in the Code Chart’s Swedish 
description ("med avdrag"/"with subtraction/rebate"). Because, I think 
that the correct understanding is not that it means "correct" or "OK". 
Rather, it denotes something that is counted in the customer/student’s 
favor. So, you could say it it really means "slack", or "rebate".  So 
it really mans ”good answer“. It is a ”rebate” that the student 
rightfully deserves.

FOURTH: A DEEPER MEANING

If we look at it from a very high level, then we can say that the 
division minus is used to signify something that is the result of a 
calculation - such as a price, an entry in bookkeeping or, indeed, a 
character/mark/point/score in a (home)work evaluated by a teacher. 
Whereas the ”normal” minus sign is used to when we represent negative 
data. For example, in taxation, all the numbers one reports, is the 
result of some calculation. Likewise, when a teach ticks of an answer 
as “good answer”, then it is because the teacher has evaluated (a.k.a. 
”calculated”) the answer and found it to be good a