8 ms·
Where and When Did the Symbols "+" and "–" Originate?
- aneth4 14y agoInteresting 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 14y agoBoth 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 14y agoFun 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-1911.jpg http://pratyeka.org/prokudin-gorskii/the-emir-of-bukhara-191...
- aneth4 14y agoI had not remembered the traditional version though, so thanks for pointing that out. Sell is 買 with a 士 radical on top. The simplified version standardized the 買 portion, but it doesn't affect the observation.
- adamnemecek 14y agoThis 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#Alternative_plus_sign http://en.wikipedia.org/wiki/Plus_and_minus_signs#Alternativ...
- ars 14y agoAnd the symbol for the 4 cardinal directions (like on a map) gets written as: ⊕ (A circled plus.)
- otibom 14y agoThat's XOR !
- delinka 14y agoWhich is addition. Without the carry.
- Kiro 14y agoCalm down.
- Daniel_Newby 14y agoThat wasn't excitement, just a factorial.
- recuter 14y agoI 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.
- arketyp 14y agoI 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.
- pavlov 14y agoWhat 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.
- znowi 14y agoOn the scale of the universe we're virtually non-existent :)
- xerula 14y agoOn the temporal / spatial scale of the universe we are virtually non-existent. On a scale that ranks everything in the universe according to physical / informational complexity & organization, we appear so far to be quite significant.
- chinpokomon 14y agoAfter reading the article, I got fixated on why you were dividing time by space... finishing the sentence, I realized that wasn't what you were trying to say at all. :-)
- henningb 14y agoSays the two week old baby with limited vision.
- znowi 14y agoOur yardstick is far too short to make any universe scale ranking on this subject. However, what we lack in knowledge, we thoroughly compensate in sense of ego and self-importance as species :)
- 14y ago
- meerita 14y agoI remember to read the answer of this in an Isaac Asimov's book: Asimov On Numbers.
- jnotarstefano 14y agoSeveral earliest known uses of other mathematical notations can be found at: http://jeff560.tripod.com/mathsym.html http://jeff560.tripod.com/mathsym.html
- kijin 14y ago> The asterisk was used by Johann Rahn (1622-1676) in 1659 in Teutsche Algebra Interesting. I've always thought that the use of an asterisk to denote multiplication was some sort of compromise owing to the lack of a "×" key on a typical computer keyboard. But it seems that there are much older precedents for it. Meanwhile, using a slash to denote division is explained in the Fractions page. > The diagonal fraction bar (also called a solidus or virgule) was introduced because the horizontal fraction bar was difficult typographically, requiring three terraces of type. An early handwritten document with forward slashes in lieu of fraction bars is Thomas Twining's Ledger of 1718 ...
- chinpokomon 14y agoInteresting. 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 14y agoAlso 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.
- lmm 14y agoI 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 14y agoIt'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
- Gormo 14y ago> bicause noe 2, thynges, can be moare equalle Which is not to say that a higher degree of equality can't be attained; it's just that then you'd have one thing instead of two.
- abrahamsen 14y agoKind of weird that no consensus have emerged for multiplication (·, ×, *, or horizontal juxtaposition) or division (÷, /, or vertical juxtaposition with horizontal line between) yet.
- jacquesm 14y agoThe / is actually the - from the other symbol and the .'s are placeholders for the numbers to the left and the right of the / so those are in fact pretty close.
- deleted 14y ago[deleted]
- mich41 14y agoEverybody 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 14y agoIn primary school in the Netherlands (and maybe elsewhere?), : is used for division.
- mich41 14y agoRight, I've seen this one too.
- pyrocrasty 14y agoIt's actually widely used for division, but only in some contexts. (It signifies a ratio, eg. "3:2 odds".)
- mseebach 14y ago
- gpvos 14y agoThere'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.
- contingencies 14y agoThe 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 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_manuscript.html http://www-history.mcs.st-and.ac.uk/PrintHT/Bakhshali_manusc... 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/9ROOTS.HTM http://www.hindunet.org/hindu_history/sarasvati/dictionary/9... http://vedabase.net/y/yuta http://vedabase.net/y/yuta http://dictionary.tamilcube.com/sanskrit-dictionary.aspx?term=yuta http://dictionary.tamilcube.com/sanskrit-dictionary.aspx?ter... http://www.hinduwebsite.com/sacredscripts/sanskrit_dictionary.asp http://www.hinduwebsite.com/sacredscripts/sanskrit_dictionar...) 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 http://dictionary.reference.com/browse/yoke https://en.wiktionary.org/wiki/Appendix:List_of_Proto-Indo-European_roots/y https://en.wiktionary.org/wiki/Appendix:List_of_Proto-Indo-E... Hrrm... there must be something published on this already. Anyone with academic library access? :) I'm up in the Himalayan foothills, hehehe.
- contingencies 14y agoHad 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 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!
- yread 14y agoWe 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 http://en.wikipedia.org/wiki/Long_division
- zapdrive 14y agoIn India its usually written: 500 ÷ 4 = 125. Its not a + sign, it a bar stuck between a :
- rmccue 14y agoThat'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 14y agoThat's also very much the standard in Britain.
- Uncompetative 14y ago123 ÷ 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.
- yaddayadda 14y agoThe 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 14y agoI 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 14y ago* 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 14y agoAlso to avoid ambiguity. Since x is alphanumeric it's a valid variable name in most programming languages.
- qompiler 14y agoChinese 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 14y agoAnd 卖买 are sell and buy respectively.
- yaix 14y ago> 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.
- kps 14y agoThey appeared just at the right time to be carried around the world by movable type. Same goes for non-mathematical punctuation. To put it another way, mass production of text froze the symbols that happened to be in use at the time.
- chiph 14y agoOne 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 14y agoMedieval 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/Central/editions/paleo.html#abbrev http://isites.harvard.edu/fs/docs/icb.topic453618.files/Cent... EDIT: In fact, the second symbol on that list, the abbreviation for "and," seems half-way to becoming a +.