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Today I've heard a talk about division rules. The lecturer stated that base 12 has a lot of division rules and was therefore commonly used in trade.

English and German name their numbers like they count (with 11 and 12 as exception), but not French:

  # |   English |           German | French
-----------------------------------------------
  0 |      zero |            null  | zero
  1 |       one |            eins  | un
  2 |       two |            zwei  | deux
  3 |     three |            drei  | trois
  4 |      four |            vier  | quatre
  5 |      five |            fünf  | cinq
  6 |       six |           sechs  | six
  7 |     seven |          sieben  | sept
  8 |     eight |            acht  | huit
  9 |      nine |            neun  | neuf
 10 |       ten |            zehn  | dix
 11 |    eleven |             elf  | onze
 12 |    twelve |           zwölf  | douze
 13 | thir|teen |       drei|zehn  | treize
 14 | four|teen |       vier|zehn  | quatorze
 15 |  fif|teen |       fünf|zehn  | quinze
 16 |  six|teen |       sech|zehn  | seize
 17 |seven|teen |       sieb|zehn  | dix-sept
            18 and 19 are "regular"
 20 |    twenty |          zwanzig | vingt
 21 |twenty-one |  ein|und|zwanzig | vingt et un
 22 |twenty-two | zwei|und|zwanzig | vingt-deux
            23 - 69 are "regular"
 70 |  seven|ty |         sieb|zig | soixante-dix = 60 + 10
              ....
 80 |   eigh|ty |         acht|zig | quatre-vingts = 4*20 ?!?!
 81 |eighty-one |  ein|und|achtzig | quatre-vingt-un = 4*20 + 1
      ...

So my question is:

Why do French count so strangely after 79?

(Are there other languages that count similar? What's the historic / mathematical reason for this system?)

Related Questions

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    $\begingroup$ Note that there exist words ("huitante", "nonante") used in some variants of French for 80, 90 (source). $\endgroup$
    – Alfonso Fernandez
    May 14, 2013 at 10:14
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    $\begingroup$ I wouldn't say that from 23 to 79 they are regular: what about soixante-quinze for 75? Some varieties of French have septante, but soixante-dix is, I'd say, more common. $\endgroup$
    – egreg
    May 14, 2013 at 11:47
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    $\begingroup$ French.SE is probably a better fit for this question? $\endgroup$
    – Najib Idrissi
    May 14, 2013 at 11:54
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    $\begingroup$ For perspective, a Chinese person would wonder why we count so strange in English. There was an article once which hypothesized that Chinese kids progress faster in maths than English kids because English kids end up wasting a lot of time/mental power to internalize the *teens. $\endgroup$
    – Supr
    May 14, 2013 at 12:35
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    $\begingroup$ of the limited number of languages I know, Japanese seems to be the most straight-forward for counting, with the translations being essentially one, two, ..., nine, ten, ten one, ten two, ..., ten nine, two ten, two ten one, two ten two, ..., ..., nine ten nine, hundred, hundred one. It makes learning to count in japanese, as simple as learning 0-10, 100, 1,000, and 10,000. $\endgroup$
    – zzzzBov
    May 14, 2013 at 14:29

8 Answers 8

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Many languages have (at least relicts of) non-decimal counting, very often vigesimal (because we have 20 fingers plus toes), but also many other systems. I recommend an old Gutenberg project of mine, The Number Concept

Note for example that the Danish word for 55 is femoghalvtreds "five more than half the third twenty-block"

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    $\begingroup$ Another suggestion I've heard is that some cultures count both above and below the larger knuckle on each finger to end up with base 20. Others also use gaps between the fingers in conjunction with various parts of each finger to get some strange bases. $\endgroup$
    – mdp
    May 14, 2013 at 10:18
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    $\begingroup$ @Matt: Yes, but we would take you for a Swede. $\endgroup$
    – hmakholm left over Monica
    May 14, 2013 at 10:38
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    $\begingroup$ @HenningMakholm Even if I don't pronounce any of the consonants? ;-) $\endgroup$
    – mdp
    May 14, 2013 at 10:48
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    $\begingroup$ In bases vigesimal, binary and decimal, I am the very model of a modern Major General. $\endgroup$
    – Kaz
    May 14, 2013 at 18:17
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    $\begingroup$ I can even count the ordinals and numbers infinitesimal. $\endgroup$
    – Tim
    May 14, 2013 at 18:20
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Actually, if you go back in time a bit in English, you'll realise that English was 'strange' too:

Four score and seven years ago our fathers brought forth on this continent a new nation, conceived in liberty, and dedicated to the proposition that all men are created equal.

(The Gettysberg Address, 1863)

Now if you were to translate that into French in 1863, you'd get pretty much what you'd get today:

Il y a quatre-vingt sept ans, nos pères donnèrent naissance sur ce continent à une nouvelle nation conçue dans la liberté et vouée à la thèse selon laquelle tous les hommes sont créés égaux.

Why this has remained the case in French but has changed in English is probably more of a question for French.SE or English.SE.

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  • $\begingroup$ OT: the latest book by Douglas Hofstadter and Emmanuel Sander has a passage in which the authors explain that such a translation would be correct at a basic level but wrong at a higher one: but this really belongs to another SE. $\endgroup$
    – mau
    May 14, 2013 at 11:38
  • $\begingroup$ @mau With the answers/discussion spanning multiple languages; unless there's a generic linguistics SE I'm not sure where it would go. $\endgroup$
    – Dan Is Fiddling By Firelight
    May 14, 2013 at 12:41
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    $\begingroup$ Linguistics? $\endgroup$
    – TRiG
    May 14, 2013 at 13:07
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    $\begingroup$ I don't think "fourscore and seven" was actually common in English in 1863; Lincoln was using unusually ornate language for rhetorical effect. $\endgroup$
    – MJD
    May 14, 2013 at 18:17
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    $\begingroup$ According to Google Ngram viewer, "eighty" has been more common than "fourscore" since at least the 1600s. $\endgroup$
    – Dan
    May 15, 2013 at 1:52
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actually numbers from 11 to 16 are quite regular in French (and in Italian) too: they just are a derivation from Latin.

        | French    | Italian       | Latin 
un      | on·ze     | un·dici       | un·decim
deux    | dou·ze    | do·dici       | duo·decim
trois   | trei·ze   | tre·dici      | tre·decim
quatre  | quator·ze | quattor·dici  | quattuor·decim
cinq    | quin·ze   | quin·dici     | quin·decim
six     | sei·ze    | se·dici       | se·decim
sept    | dix-sept  | dici(as)sette | septem·decim
huit    | dix-huit  | dici-otto     | duo·de·viginti
neuf    | dix-neuf  | dici(an)nove  | un·de·viginti

(18 and 19 in Latin are computed as 20-2 and 20-1). Each language has its own way to cope with small numbers.

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    $\begingroup$ And in Spanish too: once, doce, trece, catorce, quince … $\endgroup$
    – fitojb
    May 14, 2013 at 17:12
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Ya, right, so strange, so how about to use Chinese count? Maybe a little convenient. :D

  # |   English |           Chinese
----------------------------------------------
  0 |      zero |            零
  1 |       one |            一
  2 |       two |            二
  3 |     three |            三
  4 |      four |            四
  5 |      five |            五
  6 |       six |            六
  7 |     seven |            七
  8 |     eight |            八
  9 |      nine |            九
 10 |       ten |            十
 11 |    eleven |            十|一
 12 |    twelve |            十|二
 13 | thir|teen |            十|三
 14 | four|teen |            十|四
 15 |  fif|teen |            十|五
 16 |  six|teen |            十|六
 17 |seven|teen |            十|七
                             十|八
                             十|九
 20 |    twenty |            二|十
 21 |twenty-one |            二|十|一
 22 |twenty-two |            二|十|二

100,000,000 | 1 hundred million  |  一|亿 （1 followed by eight zeros）
OK, let me show you the 999,999,999.   九亿九千九百九十九万九千九百九十九

Just imagine that what if we use this to do math. ;-P

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    $\begingroup$ Funny thing that the most crowded ideogram is that of "zero". $\endgroup$
    – Andrea Mori
    May 14, 2013 at 17:30
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    $\begingroup$ @AndreaMori It seems to leave zero whitespace ... $\endgroup$
    – Hagen von Eitzen
    May 14, 2013 at 17:45
  • $\begingroup$ @AndreaMori maybe because, as in most societies I guess, zero is quite an advanced concept, so it came later and all the "simple" ideograms were already used? $\endgroup$
    – Olivier Dulac
    May 14, 2013 at 17:51
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    $\begingroup$ For larger calculations Chinese historically used abacuses, and recorded the numbers using rod numerals, which are superbly uniform and simple. Your complaint is analogous to an Anglophone saying "let me show you 999,999,999: nine hundred ninety-nine million, nine hundred ninety-nine thousand, nine hundred and ninety nine. Just imagine if we used this to do math." The point is, we didn't and don't, and neither did the Chinese. $\endgroup$
    – MJD
    May 14, 2013 at 18:19
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    $\begingroup$ @Laurent ya, thanks for clarification, sometimes, we can use simplified "〇" to substitute "零" in Chinese, but not in all cases, and notice that it is not Arabic numeral 0, or letter 'o' or 'O', it only exists in Chinese numeric phrase. $\endgroup$
    – Hang Pan
    May 15, 2013 at 8:19
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Actually, the French system was designed regularly, i.e. with "septante" for 70, "octante" for 80 and "nonante" for 90. But this system was not accepted at the time (roughly the 16th century), because people were used to the old system ("quatre-vingt", etc.). But the old system remained in Belgium (for "septante" and "nonante") and Switzerland (for "septante, the slightly modified "huitante" in Vaud canton, and "nonante").

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This is a bit of a guess but I think this has a lot to do with whether the numbering system was rationalised at any point.

If you tell someone from England that you're having trouble sleeping he'll probably suggest you count sheep. I won't attempt a weak joke about having a bedroom full of farm animals. The phrase comes from an old numbering system 

 1  |  yan
 2  |  tan
 3  |  tether  
 4  |  mether
 5  |  pip  
 6  |  nether
 7  |  aether
 8  |  oevro
 9  |  cuevro
10  |  dick
11  |  yanadick
12  |  tanadick
13  |  tetherdick
14  |  methradick
15  |  bumfit
16  |  yanabum
17  |  tanabum
18  |  tetherbum
19  |  metherbum
20  |  jiggit

This died out a long time ago but shepherds kept it up for longer. So to count sheep is to If you look on Wikipedia there are loads of different ones people counted differently in different areas of the country. (It seems the one my great-granddad taught me isn't in there.)

At some point this was changed by introducing a new numbering system. Similarly The swedes and Norwegians use a base 10 numbering system today, but they used to use the Danish system. Similarly German (I think) has undergone several standardizations to keep it as one language. It wouldn't surprise me if there used to be less rational German counting systems that died out.

If the French tried to rationalise their numbering is would have been during the revolution. But as they tried to rationalise everything, including a ten hour day and a decimal calender (Today is Carp the 25th of Flower) A lot of things didn't take off. So I would guess the numbers were one of the things that failed.

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These numberphile videos explain the irregularity quite well:

Problem with french numbers

In english 1-12 have individual names and after that we have the -teens (4 and 10, 5 and 10, etc.) similar break point happens at the 17th number in the French number system. The major problem which occurs is at 70s. *The French have no word for 70, they call is 60 and 10 - soixante-dix.*So on, 71 is 60 and 11 till 79.

Similarly, 80 is also not invented, it is 4 20s, quatre-vingt. 81 is 4 20s 1, quatre-vingt-un. 90 is, 4 20s 10, quatre-vingt-dix. 91 is 4 20s 11, quatre-vignt-onze.

Finally, they have a word for 100, ceut.

It looks similar to roman numbers Roman number system, where you repeat the letters to combine the values. X is 10 XX is 20 and so on.

Another peculiar thing in french grading system, 19 out of 20

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    $\begingroup$ It is not true that there is no word for 70, really, not for either 80 and 90: there are there perfectly good words septante and so on. They are just local variations. In English you have the same thing, and a famous speech starts «four score and seven years ago...». $\endgroup$
    – Mariano Suárez-Álvarez
    May 14, 2013 at 17:52
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    $\begingroup$ About the 19/20 video, it is amazing how a deep tone of voice and a lot of self-confidence can help make believe pure nonsense: the summary of the video reads In French culture, it is traditional for all grades to be out of 20 - and many teachers will NEVER give full marks! and this is indeed what the video says. Well, while the first part is true, the second part is plain false. $\endgroup$
    – Did
    May 26, 2013 at 9:22
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As former Chinese then French colonists we Vietnamese dropped the Chinese script and took on the Roman alphabets and the Arabic numbers as our own, thank to France. But we didn't take on the French counting system. Ours is very straight forward, and like Chinese, is mostly a monosyllabic language.

một (one),
hai (two),
ba (three),
Bốn (four),
năm (five),
sáu (six),
bảy (seven),
tám (eight),
chín (nine),
mười (ten),
mười một (ten one = eleven),
mười hai (ten two = twelve),
hai mươi (two tens = 2(10) = 20),
hai mươi một (two tens one = 2(10) + 1 = 21),
ba mươi (three tens = 3(10) = 30),
ba mươi một (three tens one = 3(10) + 1 = 31),
một trăm (one hundred),
một trăm một (one hundred one = 1(100) + 1 = 101),
hai trăm (two hundreds).

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