Numerals 13-19 are based on 10. Why do 11 and 12 follow a different pattern?

Question

11 and 12 mean “one left” and “two left” respectively, referring to number 10. In other words, etymologically, they are NOT remnants of a base 12 number system. They are decimal, just like the -teen numerals.

So why do we have two distinct morphological implementations of the same way of counting?

Edit: I know that people used to count in 12’s a lot. But the unique pattern of “eleven” and “twelve” can’t be explained by that because etymologically, these names mean “[10]+1” and “[10]+2”. No connection to 12.

The fact that “twelve” is used more frequently than “thirteen” and “fourteen” could have resulted in more drastic sound changes, which could have given it its dissimilarity. But (1) that doesn’t explain 11, which has the same frequency as “thirteen” and “fourteen” yet doesn’t follow their pattern, (2) if that’s the result of a sound change only, it’s a pretty wild one. It would mean that -teen and that mixture of e’s and v’s in “eleven” and “twelve” both came from the same word that stood for 10. And this sound change would have affected other words, and it would have been described. But more importantly, “ten”, which is just as frequent as “twelve”, would have changed in the same way. But “ten” is way more similar to -teen than -lve.

I think it makes more sense to believe that these endings came from different words, and that there used to be more than one way of forming numerals, and that the -teen way eventually took over. But why didn’t it take over 11 and 12?

Answer 1

This pattern of numbering was present even in Old English:

tīen - ten

endleofan - eleven

tƿelf - twelve [note: the "p"-looking element is a wynn, pronounced /w/)

þrēotīne - thirteen

fēoƿertīne - fourteen

It is not clear why that break exists. A common presumption (as summarized in Mental Floss) is that eleven and twelve were used so frequently (e.g. in months of the year, hours in a day, inches in a foot, the twelve Apostles, the wergild price for a thane) that eleven and twelve could maintain nonstandard or colloquial forms. Indeed, ten and twelve appear more frequently than eleven or later numbers in corpus listings like NGram (for reference, eight and nine would be between ten and twelve in the same search):

Answer 2

Base-12, duodecimal systems are very ancient, and its manifest in language via culture. 20 is another one, as you see 4 and 20 in older English to express 80, and similar structures in French and other languages. It seems most likely that this is to do with the division of currency that dates back to Charlemagne, and lasted until 1971 when the UK switched to decimal. Numbers like 12 and 20 were waypoints in the currency system.

To digress for a moment:

The Sumerians may have something to do with it... they came up with the divisions of time and circles, and their sexagesimal system leading to duodecimal (base-12) systems for other application spaces. Even attempts at making symbols for it:

The Dozenal Society of Great Britain (DSGB) proposed symbols ⟨ rotated digit two, reversed or rotated digit three ⟩

12 is one of those features of ancient counting systems that predate even the European implementations in language, and in currency that date back to at least Charlemagne: the Carolingan currency system, a reform of the Roman system, where units like 20 and 12 became commonly-used in daily transactions.

https://www.britannica.com/topic/coin/Charlemagne-and-the-Carolingian-coinages

This might help explain why the pattern is seen across western European languages.

There is evidence of a bias towards duodecimal systems in ancient civilisations across the world independent of each other, in China, Egypt, Maya, and hints of it in African languages. https://www.math.drexel.edu/~jsteuber/Educ525/History/history.html

It may be ultimately due to an approximation of the number of lunar cycles in a year... which is nearer to 13, but not quite.

12 is just a very easy number to deal with mathematically for fractions. The Greeks consolidated the notion of 360 days in a year and degrees in a circle, and 12 fits into that nicely.

see also:

https://hsm.stackexchange.com/questions/2876/was-there-a-very-early-culture-thats-number-system-was-12-based-like-ours-is-1

Why do eleven and twelve get unique words and not end in "-teen"?

Answer 3

I apologise for the "copy and paste" job and the omission of the full route the words took.

The system that produced eleven and twelve does not appear to be duodecimal, which would have made our "24" significant, but purely decimal:

OED

Eleven:

Etymology: Cognate with Old Frisian andlova , allewa , elleva , […] Old Danish ællefue (Danish elleve ), Gothic ainlif < the Germanic base of one n. + an element of uncertain origin also found in twelve adj. and n. (see below).

Origin of the second element.

The original sense of the Germanic formation was apparently ‘one left (after counting to ten)’. The second element is either (a) < an ablaut variant of the same Germanic base as belive v.1 (see also leave v.1), or (b) < the same Germanic base as the Germanic forms cited at loan n.1 In the latter case, the development of the original labiovelar to labial fricative (compare -f- , -v- in the cognate forms cited above) would have taken place in the Germanic form of twelve adj. and n., and would subsequently have been extended by analogy to the Germanic form of eleven adj. and n.

A formation that is either similar or identical (depending on the origin of the second element in the Germanic word) is shown by Lithuanian vienuolika eleven < vienas one n. + a second element (used also in Lithuanian cardinal numerals from twelve to nineteen) < the same base as (with different ablaut grade) Lithuanian liekas spare, excessive, eleventh (itself < the same Indo-European base as the Germanic forms cited at loan n.1).

The entry for twelve has the additional

Analogous formations to eleven and twelve are the Lithuania vênů′lika 11, dvýlika 12, in which the second element, Lithuania -lika, has also the meaning of ‘left over’. All other Indo-European languages have or had forms composed of ‘two’ + ‘ten’, like the numbers 13 to 19; compare Latin duōdecim, Greek δώδεκα, Sanskrit dwādaçan.

From this one ten, and two ten are the first part of a sequence that then goes three ten (thirteen), etc.

Answer 4

Could the words for eleven and twelve be remnants of a base 20 numeric system? The words are similar in the norse languages: elva/elleve and tolv

The base 20 counting system is still visible in the Danish language. This is how the "uneven tens" are expressed:

50 = halvtreds = one half subtracted from three (times 20) = (3 - 0.5) * 20

51 = en og halvtreds = one plus one half subtracted from three (times 20) = 1 + ((3 - 0.5) * 20 )

70 = halvfjerds = one half subtracted from four (times 20) = (4 - 0.5) * 20

72 = to og halvfjerds = one half subtracted from four (times 20) = 2 + ((4 - 0.5) * 20 )

90 = halvfems = one half subtracted from five (times 20) = (4 - 0.5) * 20

92 = halvfems = one half subtracted from five (times 20) = (4 - 0.5) * 20

And I'm only guessing, but the "uneven tens" of 10 - 19 could be expressed similarly:

11 = one plus one half subtracted from one (times 20) = 1 + ((1 - 0.5) * 20 )

12 = two plus one half subtracted from one (times 20) = 2 + ((1 - 0.5) * 20 )

And the frequent use of 11 & 12 could explain why these numbers kept the non-standard form, while 13 - 19 submitted to the base 10 setup. It could also account for the sound changes mentioned. But the "elev" and "-lwe" parts remain and could be traced back to the word half/halv.

I am not in any way a scholar of this subject, so please feel free to criticize or elaborate on these ideas.