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In short, why is it not oneteen and twoteen, and we start at thirteen in English?

In another thread, I supposed that despite that fact that people have ten fingers, amounts of items leading up to and including twelve were more common because twelve is more easily divisible evenly by two, three, four, and six. Both English and German (which are related) switch to a -teen (-zehn auf Deutsch) ending after twelve. Based on that thread, so does Norwegian. Could this be the explanation?

Looking at other languages (Arabic, Japanese, even a related romance language of French), this doesn't seem to apply, and you'd think that if something so fundamental as divisibility were the explanation, we'd see a more universal distribution across them.

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We had a related discussion @ math.SE ... –  user730 Dec 22 '10 at 6:53
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Perhaps lending credence to your idea about divisibility, 12 is a highly composite number; the next one is 24. –  Mitch Schwartz Dec 22 '10 at 6:58
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This applies to romance languages as well. Spanish has unique words for eleven, twelve, thirteen, fourteen and fifteen. After that, they switch to a 10 + pattern. –  Eric Dec 22 '10 at 8:52
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And traditional Welsh has an even more complicated pattern: "one-on-ten", "two-on-ten" up to "four-on-ten", then "fifteen" (i.e. the word is clearly made up of "five" and "ten", but is contracted into a single word), then "one-on-fifteen", "two-on-fifteen", "two-nine" (!), and "four-on-fifteen". –  Colin Fine Dec 22 '10 at 17:30
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I am a newcomer to this website. Stumbled upon this while browsing through the net, but this is a goldmine of information. Coming to the point of numbers, I could say in many Indian language numbers upto 20 are unique like say Bangla my mothertongue. Counting 16 using fingers and thumbs is what we are taught from childhood and it is only when I traveled to UK I realized that counting up to 12, not 16, is prevalent. –  user45219 May 31 '13 at 12:41

3 Answers 3

up vote 38 down vote accepted

Actually, eleven and twelve also seem to be derived from 10+1 and 10+2. Let me quote from the classic book Number: The Language of Science by Tobias Dantzig (1930, republished with nice foreword by Barry Mazur):

Indeed, there is no mistaking the influence of our ten fingers on the “selection” of the base of our number system. In all Indo-European languages, as well as Semitic, Mongolian, and most primitive languages, the base of numeration is ten, i.e., there are independent number words up to ten, beyond which some compounding principle is used until 100 is reached. All these languages have independent words for 100 and 1000, and some languages for even higher decimal units. There are apparent exceptions, such as the English eleven and twelve, or the German elf and zwölf, but these have been traced to ein-lif and zwo-lif; lif being old German for ten.

And presumably this was inherited in other Germanic languages. (English, German and Norwegian all belong to the Germanic subfamily of Indo-European; French belongs to Italic.) Note that we can still discern a trace of "two" in "twelve".

That answers your question, but note that there are traces of other bases in our number words:

It is true that in addition to the decimal system, two other bases are reasonably widespread, but their character confirms to a remarkable degree the anthropomorphic nature of our counting scheme. These two other systems are the quinary, base 5, and the vigesimal, base 20. […]

Many languages still bear the traces of a quinary system, and it is reasonable to believe that some decimal systems passed through the quinary stage. Some philologists claim that even the Indo-European number languages are of a quinary origin. They point to the Greek word pempazein, to count by fives, and also to the unquestionably quinary character of the Roman numerals. However, there is no other evidence of this sort, and it is much more probable that our group of languages passed through a preliminary vigesimal stage. […]

While pure vigesimal systems are rare, there are numerous languages where the decimal and the vigesimal systems have merged. We have the English score, two-score, and three-score; the French vingt (20) and quatre-vingt (4 × 20). The old French used this form still more frequently; a hospital in Paris originally built for 300 blind veterans bears the quaint name of Quinze-Vingt (Fifteen-score); the name Onze-Vingt (Eleven-score) was given to a corps of police-sergeants comprising 220 men.

Also, we do have words like "dozen" (12) and "gross" (144) (any others?) for a few numbers not divisible by 5 (because highly divisible numbers are useful), but these words are sporadic and do not form the basis for any number-naming system in English as far as I know.


Edit: On further research, even though it's undisputed that eleven and twelve come from 1+10 and 2+10, the actual meaning of the lif part seems uncertain. The Online Etymology Dictionary confidently says:

c.1200, elleovene, from O.E. endleofan, lit. "one left" (over ten), from P.Gmc. *ainlif- (cf. O.S. elleban, O.Fris. andlova, Du. elf, O.H.G. einlif, Ger. elf, O.N. ellifu, Goth. ainlif), a compound of *ain "one" (see one) + PIE *leikw- "leave, remain" (cf. Gk. leipein "to leave behind;" see relinquish). Viking survivors who escaped an Anglo-Saxon victory were daroþa laf "the leavings of spears," while hamora laf "the leavings of hammers" was an O.E. kenning for "swords" (both from "The Battle of Brunanburgh"). Twelve reflects the same formation; outside Germanic the only instance of this formation is in Lithuanian, which uses it all the way to 19 (vienio-lika "eleven," dvy-lika "twelve," try-lika "thirteen," keturio-lika "fourteen," etc.)

But the OED says that "left" is just one theory:

Etymology: Common Teutonic: Old English ęndleofon corresponds to Old Frisian andlova, elleva, Old Saxon elleban (Middle Dutch elleven, Dutch elf), Old High German einlif (Middle High German eilf, German elf), Old Norse ellifu (Swedish ellifva, elfva, Danish elleve), Gothic ainlif < Old Germanic *ainlif- < *ain- (shortened < *aino-) [one] + -lif- of uncertain origin. Outside Teutonic the only analogous form is the Lithuanian vënó-lika, where -lika (answering in function to English -teen) is the terminal element of all the numerals from 11 to 19.

The Old English, Old Frisian, Old Saxon, and Old Norse forms represent a type *ainlifun, apparently assimilated to *tehun [ten]. The theory that the ending is a variant of Old Germanic *tehun, Aryan *dekm [ten], is now abandoned; some would derive it from the Aryan root *leiq or < *leip (both meaning to leave, to remain) so that eleven would mean ‘one left’ (after counting ten.)

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I have never heard anyone seriously propose any other etymology for the *-lif- part than the PIE root *leikw-. The OED seems to ignore the fact that the Germanic and Lithuanian forms correspond exactly to each other, each indicating a thematicised zero grade (common in deriving adjectives). The ‘left’ theory is, if not the only one available, at least by far the most attractive one. –  Janus Bahs Jacquet Sep 14 '13 at 13:00

An entirely different theory to ShreevatsaR's, which (I think) I read from Charles Seife's Zero: The Biography of a Dangerous Idea:

This is evidence of English having roots in a base-12 counting system. This was almost certainly based off counting using the joints of your fingers (four fingers, three joints), and using your thumb as a pointer to keep track of where you were.

As a computer scientist, I've trained myself to use a similar system using the tops of my fingers as well, giving base-16 counting on one hand.

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That 12/16 counting system with the thumb place holder is brilliant! Not sure when I'll ever need it, but I'll keep that one in mind! –  Joost Schuur Dec 22 '10 at 13:36
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This is an appealing theory (and what I might have thought), but unfortunately it's in conflict with the etymological evidence. :-) BTW, Charles Seife's Zero actually says "In English, eleven and twelve seem to be derived from “one over [ten]” and “two over [ten],” while thirteen, fourteen, fifteen, and so on are contractions of “three and ten,” “four and ten,” and “five and ten.” From this, linguists conclude that ten was the basic unit in the Germanic protolanguages that English came from, and thus those people used a base-10 number system." –  ShreevatsaR Dec 22 '10 at 16:55
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And certainly in time the base-12 counting system holds well: 5x12 seconds, 5x12 minutes, 2x12 hours. Fractions have almost only been expressed in sexagesimal notations up to the 18th century. –  johanvdw Dec 22 '10 at 19:05
    
@Shreevatsa: Fair enough. It's been several years since I read the book, so I could well be misremembering. That said, I'd love to know where I got the idea for the thumb-placeholder counting; I'm pretty sure I read about it somewhere –  me_and Jan 4 '11 at 13:58

The thing of "Dubbing numbers unique names up till 12(twelve) and no further" may have also been influenced by the number of times you see a full moon during a year. You cannot precisely tell whether it has or hasn't been a full year just by observing seasons. But you can tell one year's time quite precisely if you keep measuring the maximum and minimum shadow lengths of stationary objects throughout a year. Then if you count how many moons have passed during that time then 12 is a number that you encounter in nature as well as 10 which is the number of your fingers.

(One other kinda weird hypothesis was that Sumerians perhaps had 6 fingers on each hand, but that one, of course, is quite unsupported.)

As for the situation in French language (where numbers are named uniquely from 1 to 16; and then from 17 on it becomes "seven and ten" "eight and ten" etc.) counting the number of joints on four fingers using your thumb while also counting the fingernails, seems to be the only sensible explanation of why it came to be so.

As for the Arabic and Asian languages (Chinese-Turkish-Japanese etc.) 11 and 12 don't have unique names but are stated in the sense of one-teen two-teen.

Yet somehow in Indian and in Korean there are even more counter-intuitive hybrid patterns of counting numbers. You can use google translate's latinization (Ä) feature to see for yourself.

Enlightening, isn't it!

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11-16 in French (and similarly 11-15 in Spanish etc.) are clearly derived from 1-6 plus an ending, and this why dozen in English starts with d. –  Henry Oct 22 '12 at 20:02
    
...Our counting patter is quite fine. Korean counting pattern goes like this: one two three... ten-one, ten-two, ten-three... twenty-one, twenty two, twenty three... –  Sȱɳɨȼ Ʈħe ǶḝÐɠḝħȱɠ Jun 1 '13 at 1:27

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