Counting in twenties

As I mentioned the other day, they count in twenties in Manx Gaelic. Today I discovered that this system can be used for counting up to 199. For example, 100 is quig feed (five twenties) or keead (hundred), 120 = shey feed (six twenties) or keead as feed (hundred and twenty), and 199 = nuy feed as nuy-jeig (nine twenties and nineteen) or keead as kiare feed as nuy-jeig (hundred and four twenties and ninety).

This system is known as the vigesimal or base-20 counting system. The word vigesimal comes from the Latin vīgēsimus, which is a variant of vīcēsimus (twentieth) and influenced by viginti (twenty). The vigesimal system is also used in the other Celtic languages and in a number of other languages, at least to some extent.

There are vigesimal and decimal systems in Scottish Gaelic, though the decimal system in not widely used. The vigesimal system is rarely used in Irish, with the except of daichead (forty), a version of dhá fhichid (two twenties).

In Welsh both vigesimal and decimal systems are used, though the vigesimal system is more popular in north Wales. The number from 16-19 in the Welsh vigesimal system are unusual: 16 = un ar bymtheg (one on fifteen), 17 = dau ar bymtheg (two on fifteen), 18 = deunaw (two nines), and 19 = pedwar ar bymtheg (four on fifteen).

The Celtic languages that were once spoken in many parts of Britain used the vigesimal system. The so-called sheep-scoring numbers are remnants of these languages. They were related to Welsh and the numbers from 15-19 have more or less the same structure as those in Welsh. There are many versions of these numbers – here’s one from Keswick in Cumbria: yan (1), tyan (2), tethera (3), pethera (4), pimp (5), sethera (6), lethera (7), hovera (8), dovera (9), dick (10), yanadick (11), tanadick (12), tetheradick (13), petheradick (14), bumfit (15), yanabumfit (16), tanabumfit (17), tetherabumfit (18), petherabumfit (19), jiggit (20).

For more details see my sheep-scoring numbers page on Omniglot.

Other languages that used the vigesimal system include Cornish, Breton, Basque, Albanian, Georgian, Ainu, Mayan, Nahuatl, and to a limited extent in Danish and French.

Phrases such as ‘three score years and ten’ and ‘four score and seven’ demonstrate that the vigesimal system was once used in English. The word score comes from the Old English word scora and is related to the Old Norse word skor, which means notch, tally or twenty.

For more information on the vigesimal system, see: Wikipedia.

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8 Responses to Counting in twenties

  1. TJ says:

    thanks!
    now I know why they didn’t have great mathematicians!!

  2. Benjamin says:

    I don’t think that this is the reason for them not having great mathematicians. Further I think it absolutely doesn’t matter which numeral system you have. You can calculate everything with every system, but the rules would change respectively. It’s just hard for us base-10 humans to think in another system, because we just think in base-10 all the time. I think that’s a similar problem to the one about thinking without words. Once your brain is focused on words or a certain numeral system it’s (nearly) impossible to think in another way.

    The proof that mathematics are possible in other systems are computers. The calculate in binary and everyone trusts in the results, so they should be correct.

  3. Simon says:

    Perhaps I you use both the base-10 and base-20 systems, as they do in Wales, your mental arithmatic will be good as a result of switching between the two systems regularly.

  4. Zachary Read says:

    Well, in a language like french, where 80 is ‘four-twenty’ and 90 is ‘four-twenty and ten’, it doesn’t make math much different from the 10-base, since it isn’t very noticeable. It basically is base 10, just the names are used differently, such as 70 is ‘sixty and ten’.
    Any different base doesn’t change math, it just changes what we consider a big value. For example, the Mayans used a vigesimal system and had very acurate results.

  5. john says:

    Are you saying that these sheep-scoring numbers are currently used by English speakers in Great Britain?

  6. Simon says:

    John – I don’t think they’re still used. Though as far as I know, they were used until the beginning of the 20th century.

  7. Polly says:

    We all use base 60 in counting time in minutes and seconds and base 12 for counting hours in a day and months in a year. Also, 7 days make one week. These different bases don’t really represent a clear, practical benefit over regular base-10. I’ve even seen a metric clock, but so far it hasn’t caught on.

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