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".
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 and that the student
has calculated correctly/well.

CIRCUMSTANCIAL EVIDENCE

The commercial minus looks like a percentage sign. And also, in
programming, e.g. JavaScript, the percentage sign is often used for the
modulo operator - which is an operator that finds the dividend of a
division.

Hence, when we take all this together, I believe we have to conclude
that the COMMERCIAL MINUS is just the italic variant of the DIVISION
SIGN.

PS: For more German documentation of this custom, it would probably be
wise to research books about bookkeeping as well as ”commercial
arithmetics”. I also have a suspicion that it would be worth
investigation contexts where modulo/division remainders operations are
found - for instance, in calendar calculations.

[1] http://www.unicode.org/mail-arch/unicode-ml/y2012-m07/0053.html
[2]
https://archive.org/stream/kaufmnnischeari00schegoog#page/n229/mode/2up

-- 
leif halvard silli
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