Where and When Did the Symbols "+" and "–" Originate? • Hacker News Board

Re: Where and When Did the Symbols "+" and "–" Originate?

#61

Post by mseebach » Wed, Mar 13, 2013, 2:30 PM UTC

kps wrote: post #49

mseebach wrote: post #29

Earlier quoted context omitted.

> The only place I've ever seen × or ÷ being used in arithmetics was primary school. No idea why they use them. Perhaps because the other prominent use is on the buttons of every single calculator in the world.

I recall using × and ÷ in primary school, before the advent of portable calculators. I know that's mere anecdotal evidence, but I believe there do exist reliable documentary sources from that era.

Clearly, the idea to put those symbols on calculator buttons didn't come from nowhere. I think our collective point is that there exists a separate tradition for using × and ÷.

Re: Where and When Did the Symbols "+" and "–" Originate?

#62

Post by Uncompetative » Wed, Mar 13, 2013, 2:35 PM UTC

simonh wrote: post #54

rmccue wrote: post #43

Earlier quoted context omitted.

More likely, it's because we don't have them on our keyboards. Programming languages are usually about reducing friction for programmers, but using the proper multiplication/division symbols would increase that for most people.

My best guess would be that we use * for multiplication because x being alphanumeric is a valid variable name. regarding keyboard presence, this is one of the things that irks me about Mac keyboards is the absence of the # character. I write little programs and scripts on my mac infrequently enough that I have to look up how to type it every blasted time. That, and how to take screenshots. The "Print Scrn" key on PCs…

    X = Y x Z

    B = T ^ F v T

    P = Q n R u S

    C = U cross V

    D = U dot V

    Area = Width by Height

i.e. just capitalising names means that you can define macros that operate as infix operators:

    L . R -> L dot R

    L dot R -> Dot[L, R]

Re: Where and When Did the Symbols "+" and "–" Originate?

#63

Post by Uncompetative » Wed, Mar 13, 2013, 2:44 PM UTC

mich41 wrote: post #19

abrahamsen wrote: post #13

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

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.

What then happens when you have to split a long line of math?

What then happens when you need to multiply 2 by 2?

The answer to the first question is that the following line is begun with a multiplication sign.

The answer to the second question is that bold roman type is used for vectors and often for other forms of tensor like a matrix to overload the semantics of dot and cross to not be scalar products were either of their arguments in italic.

Re: Where and When Did the Symbols "+" and "–" Originate?

#64

Post by recuter » Wed, Mar 13, 2013, 2:52 PM UTC

sp332 wrote: post #42

rootbear wrote: post #35

Earlier quoted context omitted.

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.

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.

As opposed to the many different and less terse idioms you have to do with regular languages? :)

Everything is alien before it becomes familiar, I think a condensed guide to get people up to speed on the symbols is all that's necessary.

APL doesn't feel like a weird throwback, it feels like it is from the future.

Re: Where and When Did the Symbols "+" and "–" Originate?

#65

Post by Uncompetative » Wed, Mar 13, 2013, 3:06 PM UTC

yread wrote: post #30

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

      123 ÷ 4/5 + 6 | 7 x 8

    = 123 ÷ 0.8 + 6 | 56

    =    153.75 + 6 | 56

    =        159.75 | 56

    = 2.85267 857142 857142 857142 857142 857142 857142 857142 857142 857142...

i.e. here | acts as a low precedence division operator, ÷ as an ordinary precedence division operator like infix / and the 'closefix' rational notation 3/4 has the highest precedence in my programming language

n.b. in case you were wondering P v Q is used for Boolean Or.

Re: Where and When Did the Symbols "+" and "–" Originate?

#66

Post by contingencies » Wed, Mar 13, 2013, 3:11 PM UTC

contingencies wrote: post #28

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 additio…

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!

Re: Where and When Did the Symbols "+" and "–" Originate?

#67

Post by lclarkmichalek » Wed, Mar 13, 2013, 3:21 PM UTC

rmccue wrote: post #40

zapdrive wrote: post #38

Earlier quoted context omitted.

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

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

That's also very much the standard in Britain.

Re: Where and When Did the Symbols "+" and "–" Originate?

#68

Post by kzrdude » Wed, Mar 13, 2013, 3:43 PM UTC

simonh wrote: post #54

rmccue wrote: post #43

Earlier quoted context omitted.

More likely, it's because we don't have them on our keyboards. Programming languages are usually about reducing friction for programmers, but using the proper multiplication/division symbols would increase that for most people.

My best guess would be that we use * for multiplication because x being alphanumeric is a valid variable name. regarding keyboard presence, this is one of the things that irks me about Mac keyboards is the absence of the # character. I write little programs and scripts on my mac infrequently enough that I have to look up how to type it every blasted time. That, and how to take screenshots. The "Print Scrn" key on PCs…

Some apple keyboards have # printed, I'm surprised they don't all have it.

Re: Where and When Did the Symbols "+" and "–" Originate?

#69

Post by kzrdude » Wed, Mar 13, 2013, 3:44 PM UTC

rmccue wrote: post #43

rootbear wrote: post #35

Earlier quoted context omitted.

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.

More likely, it's because we don't have them on our keyboards. Programming languages are usually about reducing friction for programmers, but using the proper multiplication/division symbols would increase that for most people.

Editors should help the user to remap their keyboard keys.. We as users should move the symbols we need so that they are easier to type. For programming I've moved all of \{}[]() to the home row (with alt gr). Just one option of many but it demonstrates the concept..

Re: Where and When Did the Symbols "+" and "–" Originate?

#70

Post by contingencies » Wed, Mar 13, 2013, 3:45 PM UTC

potatolicious wrote: post #58

aneth4 wrote: post #53

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 elabor…

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.

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...