UNUSUAL NUMBER SYSTEMS.

LH favorite Arika Okrent has a nice Mental Floss post about “weird things that languages can do with number words,” from Oksapmin, with its base-27 counting system based on body parts (there’s a convenient diagram), to Nimbia, a dialect of the Gwandara language of Nigeria, which uses base 12 (143 is gume kwada ni kwada ‘eleven dozen and eleven,’ 144 is wo). Fun!

Comments

  1. Bukiyip wins. Counting different things in different bases, while apparently using the same words for the numbers* in both systems? How does that come about and how did they not give up ages ago?
    *the one number word quoted, anauwip, is 20-base 3 (6 base 10) and 20-base 6 (24 base 10).

  2. @s/o Is 20(6) not 12(10)?

  3. sorry, you’re right, i’ve done my math wrong

  4. I don’t even know how I got that, I misread as well as miscaluclated. The second system is base 4, not 6, so “anauwip” is 120 base 4. I’m even more impressed by the Bukiyip-speakers.

  5. I’m surprised that the description of the base-20 Yoruba system with subtraction didn’t mention the Roman numerals, that also use subtraction, as, for example, XIX means 10 – 1 + 10 = 19. However, I agree that the Bukiyip system is the most impressive. I don’t often need to count betel nuts, but the next time I do I’ll need to make sure I using the proper system.

  6. Jeffry House says:

    Can anyone explain exactly how Danish came to have 20-based higher numbers, but Norwegian not? The Danish 60, 70, and so on look odd to me in a way that “tyve” for “tjue” does not, to say nothing of “bog” for “book”. The latter two could be found in Kjelland or Jonas Lie, but not the ones for 60, 70, and so on. (Or so my inner nordmann tells me.)

  7. Bill Walderman says:

    The origin of the Danish number system: Somewhere I have a book that explains this, but I can’t find it. I think it was this:
    http://www.amazon.com/Danish-Comprehensive-Grammar-Grammars/dp/0415491932/ref=dp_ob_title_bk
    The Danes are firmly convinced that it is part of their heritage from the ancient Viking past, and cling to it tenaciously–efforts to promote a shift to the English-like system used by the other North Germanic languages such as Norwegian have been unsuccessful. (They do make a concession to the system prevalent elsewhere in Scandinavia in writing checks, though.)
    My recollection is that, contrary to the Danes’ belief, the system actually originated in the 19th century — it was how shopkeepers counted out change. Of course, the Danes don’t perform mental arithmetic as they count–they don’t think of halvtreds as halvtredssyndtyve and mentally multiply 20 by 2 1/2 to arrive at 50. They just think “halvtreds = 50″, just as English speakers don’t need to multiply 5 by 10 when confronted by “fifty”. The ordinal numerals 50 and above are so unwieldy that the Danes avoid using them, especially with the Germanic pre-position of the single digits: femoghalvtredssyndtyvende = 55th (five and two and a half times twenty-eth).

  8. Elizabeth Kendall says:

    Dear Languagehat,
    What a terrific blog. I will follow it!
    Mainly, thank you for THE OTHER THING. I am infinitely grateful.

  9. You’re most welcome, and I’m glad you like the blog!
    (Note for bemused denizens of the Hattery: THE OTHER THING is an editing thing.)

  10. Skandinavians don’t write cheques. We use the giro.

  11. Trond Engen says:

    We do use giro, but those long identification numbers are killing me. I’ll urge my brother, the internet bank system programmer, to add support for septemvigesimals.
    It’s another touch of weirdness that both hands are counted from thumb to pinky. And that reminds me: Could ‘pinky’ derive from *penkWe by some mysterious way?

  12. My grandfather used to say he was brought up to count in base five:
    ain, tain, tethery, fethery, pip
    ainpip, tainpip, tetherypip, fetherypip, dick,
    aindick, taindick, tetherydick, fetherydick, bumpit,
    ainbumpit, tainbumpit, tetherybumpit, fetherybumpit, gigit etc.
    This is a variant of the “Anglo-Cymric Score” as mentioned in, for example, THE COUNTING-OUT RHYMES OF CHILDREN by HENRY CARRINGTON BOLTON.

  13. Ah yes, “yan tan tethera”; we discussed it here.

  14. Nobody has gotten pinky past Dutch pinkje, though it also existed in Middle English in the form pink. No cognates, no etymology.

  15. The Danish system is attested in an authorization clause added to the Bylaws of Flensborg with a date of 1295 (“thet aar fra wors hærræ aar thusind tv hundrith oc half fæmpt sin tiygh oc fæm”).
    1295 is after the Viking age, but this is one of the earliest manuscripts in Danish — it will be hard to disprove that Danish Vikings counted like that as well.

  16. Bill Walderman says:

    Thanks, Lars. I stand corrected. The Danish system doesn’t seem to have featured in Old Norse, at least not in the Western Norwegian/Old Icelandic variety, or in any other Germanic language. So when and how did this numeral system originate? Is there any evidence or even speculation on this point?

  17. Bill, the scholarly Dictionary of the Danish Language (Ordbog over det Danske Sprog) does not trace the 50-70-90 construction any further back than the citation I gave.
    It traces Danish ‘halvanden’ (one and a half) back to Old Norse ‘halfr annar’, so I assume they would have done so for 50-70-90 if they could.
    I did find ‘halfr þriði tugur’ in Landnamabok, but that is 2½ times ten = 25.
    (I don’t have access to Skautrup’s History of the Danish Language beyond the snippets of the index offered by Google, but it doesn’t seem to mention the words in the first volume, the one treating the oldest language stages).

  18. Trond Engen says:

    ‘halfr þriði tugur’
    Samlagets Norrøn Ordbok (ON dictionary) says under ‘half-’ that it’s used in compounds with numerical adjectives ending in ‘-tugr’ or ‘-ræðr’ to denote the lack of a half ten, especially as ‘halfþritugr’ “25″. Nothing about half twenties, so I think it’s safe to assume that it’s not in the corpus.

  19. William Walderman says:

    Thanks, Lars and Trond. I wonder whether the origin of the Danish vigesimal system and perhaps the French, can be traced to the division of the pound–the monetary unit in use in medieval and early modern Europe and in Britain right up through the first two or three decades of my life–into 20 soldi (sous) or shillings. According to Wikipedia, this monetary system (with the sou divisible into 12 pence) was established by Charlemagne: http://en.wikipedia.org/wiki/French_livre ,
    but I wonder whether it goes back even further to the Dark Ages and maybe even to late antiquity. Can anyone enlighten me on the pre-decimal Danish monetary system?
    Incidentally, I found my copy of the Danish Grammar I referred to earlier. It seems to say that the decimal numeral system, with multiples of ten ending in -ti, had actually been in use in Denmark before the 19th century, but the older vigesimal system came to predominate during that period.

  20. Bill, librae et solidi et denarii silver coin designs go back at least to the early Roman Empire.

  21. Bill Walderman says:

    John, yes, the libra was a Roman unit of weight, divided into 12 unciae (ounces), and you’re right that solidi and denarii were Roman monetary units. The question I was raising is whether the libra, divided into 20 units (solidi/soldi or shillings), was used as a monetary unit before Charlemagne instituted a standardized system.
    My thought is that the French or Danish vigesimal number systems might be traceable to the medieval vigesimal monetary system based on the division of the pound/libra into 20 units, which seems to have been first instituted by Charlemagne. I was wondering whether this system might go back even earlier to monetary systems in use in the Dark Ages or late antiquity, but I haven’t been able to find any evidence of that.
    Of course, it’s also possible that Charlemagne’s twenty soldi to the livre reflects a vigesimal way of thinking that is also reflected in the French and Danish languages. And the livre and even the solidus must have been very large amounts that wouldn’t be used in everyday transactions–they probably existed mostly as accounting units.
    Any information about the medieval Danish monetary system might shed some light on the subject, too.

  22. Bill, the oldest Danish monetary system went like this: 10 penning to the ørtug, 3 ørtug to the øre, 8 øre to the mark. As a metal weight, the mark was about 233g, or eight ounces, and indeed some people want to see the Latin “(uncia) aurea” in the word øre. This was soon (12-13th c) replaced by the Hanseatic (“lybske”) system of 12 pence to the shilling, 16 shilling to the mark. Not much there to inspire vigesimal counting.
    Later monetary history in Denmark (and Norway) didn’t see that system change much, but for long periods there were three parallel systems: Danish coinage, Lübeck coinage, generally at about twice the value for a given denomination, and the relatively stable Thaler/dollar/daler silver pieces, relative to which the others were always losing value.

  23. J.W. Brewer says:

    Bill, via google books you can peruse the “Coins and Mints” section of “Medieval Scandinavia: An Encyclopedia,” which asserts that circa 1100 there were 240 pennies to a mark, but the next unit up wasn’t at that point a dozen pennies. At various other points in medieval Denmark per that source a mark was 288 pennies or 192 pennies (in England and Scotland at around the same time per other sources a mark was 160 pennies, i.e. 13 shillings & fourpence). For more recent Danish currency, wikipedia alleges that “The Danish currency system established in 1625 consisted of 12 penning = 1 skilling, 16 skilling [i.e. 192 pennies] = 1 mark, 6 mark = 1 rigsdaler and 8 mark = 1 krone.”

  24. Trond Engen says:

    Isn’t it the English- and Swedish-style counting (twenty-two, tjugotvå) that is the recent accountancy innovation? It’s documented in Norwegian from the 17th century. I knew it had been in sporadic use, but not for how long, until I read the no.wiki article on the new counting system. It’s weak on sources, but I think it’s safe to assume that the 17th century usage is from the oldest known Norwegian arithmetics book, Tyge Hanssøn’s Arithmetica Danica from 1645.
    And still, as everybody knows, the switch to the new system in Norwegian was engineered by the telephone authorities, supported by a broad alliance of mathsteachers, and approved by parliamentary decision in 1950. It soon became hated by the conservative Riksmål movement, but it doesn’t really belong on a Nynorsk-Samnorsk-Bokmål axis at all. Anyway, it’s been a slow but steady success, and sociolinguistic surveys show that those who grow up now use only the new way of counting. I do maths in the new system but use the old one in free speech, which is typical of those a generation older than me.
    -
    As much as I like the idea that counting in twenties is connected to weight- and monetary units, it would work better if the twenties were the smallest sub-fraction, not the largest.

  25. Bill Walderman says:

    Thanks to everyone who set me straight. It occurs to me that we have a somewhat archaic vigesimal system in English — counting in scores — so perhaps the French and Danish systems aren’t as strange as they seem to language learners.

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