
Where and When Did the Symbols "+" and "–" Originate? - paulgerhardt
https://blogs.stsci.edu/livio/2013/03/12/where-and-when-did-the-symbols-%E2%80%9C%E2%80%9D-and-%E2%80%9C%E2%80%93%E2%80%9D-originate/
======
adamnemecek
This always amazed me: "A Jewish tradition that dates from at least the 19th
century is to write plus using a symbol like an inverted T. This practice was
adopted into Israeli schools (this practice goes back to at least the
1940s)[11] and is still commonplace today in elementary schools (including
secular schools) but in fewer secondary schools.[12] It is also used
occasionally in books by religious authors, but most books for adults use the
international symbol "+". The usual explanation for this practice is that it
avoids the writing of a symbol "+" that looks like a Christian cross.[12]" [1]

[1]
[http://en.wikipedia.org/wiki/Plus_and_minus_signs#Alternativ...](http://en.wikipedia.org/wiki/Plus_and_minus_signs#Alternative_plus_sign)

~~~
recuter
I have an uncomfortable memory of my 1st grade teacher showing this to us and
me refusing to go along with what I insisted was an irrational superstition. I
didn't understand the context or what her old age meant.

Similarly, I was shocked as a kid when I visited the US and saw apartment
buildings skip the 13th floor numbering.

People are weird.

~~~
ghc
Similarly, in Japan one pronunciation of 4 is also the word for death, so it's
frequently omitted.

~~~
rucker
This is also true in China (at least in Mandarin-speaking regions, I don't
know about Cantonese or other dialects).

~~~
hcolomb
Also in Korea because of the Sino-Korean word for 4.

------
pavlov
What fascinates me most about this story is how it illustrates what a young
race we humans are intellectually.

If we ever want to be anything more than warring tribes, we must learn to
accumulate knowledge together. Universal symbols for addition and substraction
are the first small step on that very long road, yet it's only been a few
hundred years since we took that step.

On the scale of the universe, we are like a baby who just minutes ago learned
to grab onto objects and already is hell-bent on pouring a hot pot of tea on
herself using this new capability.

~~~
rootbear
And we're still using '*' for multiplication in our programming languages
instead of '×' because using anything other than ASCII for programming is just
too hard, or too weird, or whatever.

~~~
sp332
We already tried going full-APL but it only proved that it wasn't a good idea.
I mean this is impressive <https://www.youtube.com/watch?v=a9xAKttWgP4> but I
still think the notation is too obscure.

~~~
tel
Full APL isn't just unicode, though, it's also a total commitment to single-
character operators as the primary language construct. Take a look at some
Agda or Unicode-enabled Haskell code to see it really improving readability...
though hampering type-ability.

~~~
Peaker
Agda's use of Unicode makes it far less readable to me. Readability is a
subjective thing, of course.

~~~
tel
Fair. It's definitely in the eye of the beholder.

------
lmm
I always felt the origin of the equals sign was wonderful: "I will sette as I
doe often in woorke use, a paire of parralles, or Gemowe lines of one lengthe,
thus : ==, bicause noe 2, thynges, can be moare equalle."

~~~
panacea
It's what permits those two lines to be essentially irreducibly perfect in
describing "the same" that fascinates me. Any 'samer' and they would converge
and simply be -.

The opposite of something. It's only when we can separate nothing, that we can
begin to describe something.

(And is the universe the mathematical manifestation of everything that isn't
nothing?) /stoner

------
contingencies
_The Hindus, like the Greeks, usually had no mark for addition, except that
“yu” was used in the Bakhshali manuscript Arithmetic (which probably dates to
the third or fourth century)._

That's interesting. The Silk Road (<http://en.wikipedia.org/wiki/Silk_Road>)
was in full swing at that time. This is pure guesswork, but multiple classical
Chinese characters now pronounced _yu_ (予,与,餘,逾,與) meant something close to
addition. I wonder if there's a link?

There were a great many languages in operation there, and the Chinese were
primarily interested in trade. It wouldn't surprise me at all if there were a
regional patois language of business utilizing Chinese idiom that the
subcontinent and others were able to borrow from.

Likewise, the borrowing may have gone in the other direction.

Note that some of the above symbols are not so dissimilar from the + symbol,
allowing some minor scope for simplification.

On further investigation, [http://www-history.mcs.st-
and.ac.uk/PrintHT/Bakhshali_manusc...](http://www-history.mcs.st-
and.ac.uk/PrintHT/Bakhshali_manuscript.html) claims the Bakshali manuscript
_yu_ was "for yuta" (apparently Sanskrit/Devanagari: युत). Apparently _yu_ is
a well recognized word root meaning "to mix" or "(equipped) with" within
Sanskrit, _yuta_ being some kind of derived or more expanded/standalone form.
(Sources:
[http://www.hindunet.org/hindu_history/sarasvati/dictionary/9...](http://www.hindunet.org/hindu_history/sarasvati/dictionary/9ROOTS.HTM)
<http://vedabase.net/y/yuta> [http://dictionary.tamilcube.com/sanskrit-
dictionary.aspx?ter...](http://dictionary.tamilcube.com/sanskrit-
dictionary.aspx?term=yuta)
[http://www.hinduwebsite.com/sacredscripts/sanskrit_dictionar...](http://www.hinduwebsite.com/sacredscripts/sanskrit_dictionary.asp))

That _yu_ is apparently the same Sanskrit / proto Indo-European root as _yoga_
, or even the far-western-Barbarian modern derivation in English, _yoke_.
<http://dictionary.reference.com/browse/yoke>
[https://en.wiktionary.org/wiki/Appendix:List_of_Proto-
Indo-E...](https://en.wiktionary.org/wiki/Appendix:List_of_Proto-Indo-
European_roots/y)

Hrrm... there must be something published on this already. Anyone with
academic library access? :) I'm up in the Himalayan foothills, hehehe.

~~~
contingencies
Had a quick check for Basque/Estonian/Finnish online dictionaries as the major
outlying European languages out of further interest. Basque alone seems to use
the recognizable root _ek..._ (one would suppose from common root with the
Sanskrit for one: _eka_ ). Estonian and Finnish seem way closer to Latin
languages in most cases .. I checked words like _and, plus, sum, total_. Lots
of readily distinguishable slight variations, but no _yu_ to be found. What
about English _union_ , _unit_ and _unity_? Same root I suppose.
Dictionary.com claims union is from Latin _ūn(us)_ (one) via middle French but
that unit is only attested to 1642. It seems the Romans had some of that _yu_
going, too.

I guess that's as far as exploration will go with western sources: apparently
the Romans weren't big on composing etymologies. Perhaps Indian sources are
useful though: _Nirukta_ (Sanskrit: निरुक्त, IPA: _[n̪irukt̪ə]_ , explanation,
etymological interpretation) is supposed to be one of the six _Vedānga_
disciplines of Hinduism. One of the primary texts there is available at the
Internet Archive: <http://archive.org/details/nighantuniruktao00yaskuoft>

Potentially related tidbits I found there: " _Yosa_ (a woman) is derived from
(the root) _yu_ (to join).", " _Yutham_ (herd is derived from (the root) _yu_
(to connect).", " _Dasyu_ (demon) is derived from (the root) _das_ , meaning
to lay waste: in him the juices are wasted, or he causes works to be laid
waste." Also had some good discussions of _soma_ (a psychadelic draft).

OK, curiosity sated. Obviously there was some _yu_ going on circa Central Asia
at the dawn of history. Anything more specific seems like guesswork only. My
take is it was to _soma_ takers what _PLUR_ is to early ravers. Party on man!

~~~
sesqu
For Finnish, you may have missed the now deprecated word for summation,
"ynnä", meaning "as one". It's not from Latin or Chinese, though - at least
not recognizably so.

~~~
contingencies
Interesting. It would probably be seen as a Proto Indo-European root rather
than anything else. They were the folks tottering about Central Asia at the
dawn of history. There's an amusing bit of video about them at the start of
the BBC's _History of India_ series, featuring a crazed Russian archaeologist
who has been career-excavating early sites in Uzbekistan, and the neverending
human quest for intoxication!

------
jnotarstefano
Several earliest known uses of other mathematical notations can be found at:
<http://jeff560.tripod.com/mathsym.html>

~~~
chinpokomon
Interesting. The close parentheses form of division from 1540 looks like the
basis of the long division form of division, i.e. 2)6 with a bar or vinculum,
extending from the top of the parentheses over the 6. The long division form
finally takes its modern form in 1888. The transformation of that symbol seems
somewhat obvious and natural. I wonder if we are likely to see further
changes, as modern typesetting should resist the variations that handwriting
would introduce. I believe any change in the future will have to demonstrate
improved readability before it will be accepted.

~~~
gpvos
Also interesting: the form for long division that is used in the 19th century
in the US: divisor ) dividend ( quotient, is very similar to the long division
form that is still used in the Netherlands today: divisor / dividend \
quotient. Looking at Wikipedia, it seems all other countries have gone on to
different notations, though.

------
yread
We discussed this article in the office and among other things we found that
even today the notation for division (when calculating it by hand) varies
wildly:

In Czech Republic we would write

453: 12 = 37.75

In Netherlands:

12/453\37.75

In Russia:

    
    
           453 | 12
               | 37.75
    

all of them are listed on Wikipedia

<http://en.wikipedia.org/wiki/Long_division>

~~~
zapdrive
In India its usually written: 500 ÷ 4 = 125. Its not a + sign, it a bar stuck
between a :

~~~
rmccue
That's normal division, which is a notation. The GP is talking about long
division, which is a technique used to divide large numbers.

The symbol in Australia (and I'd say most of the English speaking world) looks
like a long square root sign with a curved vertical part:

    
    
      _______

12)12345

~~~
lclarkmichalek
That's also very much the standard in Britain.

------
abrahamsen
Kind of weird that no consensus have emerged for multiplication (·, ×, *, or
horizontal juxtaposition) or division (÷, /, or vertical juxtaposition with
horizontal line between) yet.

~~~
mich41
_Everybody_ uses juxtaposition for multiplication (or dot when some separation
is required) and horizontal line for division.

* and / are poor man's substitutes when all you have is ASCII.

× is used for vector products, Cartesian products and products of algebraic
structures in general.

The only place I've ever seen × or ÷ being used in arithmetics was primary
school. No idea why they use them.

~~~
gpvos
In primary school in the Netherlands (and maybe elsewhere?), : is used for
division.

~~~
pyrocrasty
It's actually widely used for division, but only in some contexts. (It
signifies a ratio, eg. "3:2 odds".)

------
arketyp
I always thought the plus sign had to do with two entities meeting or being
placed on top each other, like a road crossing or a pair of sticks, and that
the minus sign was just a spinn-off of that sign and also made sense in the
same way that Descartes used "..." according to the article.

------
yaddayadda
The next logical question is, "Where did × and ÷ originate?" From there, I've
always wondered how multiplication migrated from "×" to "∗"? And recently,
I've wondered if we will migrate "-" to something else? (This last derives
from having to annotate a range of numbers including positive and negative.
When "-" is used for both range and negative, it causes confusion.)

p.s. I tried to post this to the original poster's blog, but was told "...your
comment seems a bit spammy." Really? I'd say their blogger spam settings a
more than a bit off.

~~~
manish_gill
I always thought the * was used for multiplication to avoid confusing × with
the English alphabet X. We can usually distinguish them while writing
equations on paper(I write x in a cursive, for example).

~~~
kps
* was used for multiplication because there weren't enough bits to fit every symbol everyone would have liked into ASCII, so compromises were made, including preference for symbols that could be 'overloaded' with multiple meanings in different contexts.

~~~
simonh
Also to avoid ambiguity. Since x is alphanumeric it's a valid variable name in
most programming languages.

------
yaix
> Overall, what is perhaps most impressive in this story is the fact that
> symbols which first appeared in print only about five hundred years ago have
> become part of what is perhaps the most universal “language.”

They appeared just at the right time to be carried around the world by
conquista and colonialism. Same goes for time notation, etc.

~~~
chiph
One of the interesting things is why are there 24 hours in a day, 60 minutes
per hour, etc?

Mathematically, those values are useful because they can be factored in many
ways. But who picked them?

I was at the British Museum one time, and they had an horological exhibit
(clocks throughout the ages), so I asked one of the curators. He said it was
the Babylonians that chose those values.

But since this thread is about notation, I should be asking who picked the
colon (:) as the time separator that is generally used. And are there other
conventions for this?

------
pjungwir
Medieval manuscripts are full of strange squiggles used to abbreviate words or
word endings. It's almost like reading shorthand. Here is a short list for
Middle English [1] but for Latin there were dozens if not hundreds. So I'm not
surprised that + and - originate from that time.

[1]
[http://isites.harvard.edu/fs/docs/icb.topic453618.files/Cent...](http://isites.harvard.edu/fs/docs/icb.topic453618.files/Central/editions/paleo.html#abbrev)

EDIT: In fact, the second symbol on that list, the abbreviation for "and,"
seems half-way to becoming a +.

------
gpvos
There's an interesting note near the bottom about the ÷ symbol. Even today in
the Netherlands, a symbol like -/- (like a percent sign, but with minus signs
on both sides of the slash) is used as a kind of emphasized minus sign,
especially in money calculations in a vertical layout where otherwise addition
would be assumed. I don't know if this is used elsewhere, but it seems
probable to me that it derives from the ÷ symbol mentioned in the text.

------
aneth4
Interesting that there is no mention of ancient China, where money and
accounting were invented.

The Chinese for buy and sell are 买 and 卖 respectively, the first indicating
spending money and the second indicating receiving money.

Granted I don't know what I'm talking about, however I do know Chinese, and I
believe these characters far predate the 15th century as do most Chinese
characters.

Perhaps someone can elaborate on whether this is a sound theory.

~~~
potatolicious
Both those characters are simplified, which is to say largely different from
how they would have appeared throughout Chinese history.

Buy in traditional is: 買 Sell is: 賣

Both of these would be closer to the ancient form of expressing these
characters. I don't see "+" nor "-" in either of these characters.

~~~
contingencies
Fun fact: the one on the left, everything but the top part is a pictograph of
a shell, which was used for a kind of status symbol or possibly something
roughly equating our modern money in many early societies. When Marco Polo
arrived here in southwest China in the Yuan Dynasty (ie. just post Mongol-
invasion), shells were still in widespread use. In fact, Chinese literary
records document special requests to the emperor to except the region from the
national law requiring use of imperial money by the provincial governor they
placed in the region, who was an Uzbek and son of the then-king of Bokhara who
had ridden with the Mongol horde to take China. One of his father's later
successors was one of the Prokudin-Gorskii images (first colour images in the
region), over here: [http://pratyeka.org/prokudin-gorskii/the-emir-of-
bukhara-191...](http://pratyeka.org/prokudin-gorskii/the-emir-of-
bukhara-1911.jpg)

------
qompiler
Chinese write it as 加, if you start making the strokes you get a + in the
upper left. Consider this is over 6000 years old, probably the origin. My
theory.

Edit (more evidence): "The plus symbol as an abbreviation for the Latin et,
though appearing with the downward stroke not quite vertical, was found in a
manuscript dated 1417 (Cajori)."

There is an assumption here that it's an abbreviation for the Latin et. But
the downward stroke can be seen in the Chinese word.

~~~
aneth4
And 卖买 are sell and buy respectively.

------
meerita
I remember to read the answer of this in an Isaac Asimov's book: Asimov On
Numbers.

