How to understand numeral systems in different languages
Numbers – you either love them or hate them, at least that’s the impression I get. I have never been very good with numbers; counting on my fingers and a reliable calculator were what got me through most of the Maths tests in school. For some reason I could cope fine during class but when it came to a test I would be like a deer caught in headlights. Imagine how I felt then when it came to Maths in another language! To make matters worse, the first foreign language I learnt was French. Now, I love the French language and the culture but French numbers took me so long to get used to because there is a different system to learn. OF course, once you know the logic it is quite straightforward but it has still always puzzled me how a language that in some ways is so similar to English can be so very different in other respects.
Up to 69 in French is reasonably straightforward but then you reach seventy and suddenly requires a little more concentration.
10 is dix
11 is onze
60 is soixante
but then 70 is soixante-dix (60 + 10)
71 is soixant-onze (60 + 11) and so forth.
Next we come to eighty and above, which goes like this:
20 is vingt
4 is quatre
then 80 is quatre-vingt (4 X 20)
and 90 is quatre-vingt-dix (4 X 20 + 10)
So, does anyone know about the history of this system and how it has resulted in this way of counting?
According to Michael Morgan this is “a remnant of Gaulish influence on French –
the system of counting in units of 20 is a feature of the Celtic languages. In Welsh, for example, 30 is ten-on-twenty, 31 is eleven-on-twenty, 40 is two-twenties, 60 is three-twenties, 80 is four twenties (pedwar ugain, cf. French quatre-vingts).”
When researching this further I discovered, or rather rediscovered, information about the ‘vigesimal’ or ‘base 20′ numeral system, which seems to be maintained here in the French numeral system, along with other European languages. It came to me then that my Granddad used to say four score and twenty years – often referencing the bible – and on researching this, I realised the connection. I am still a little unsure on why from 70 to 79 in French it works on the basis of 60 + 11, can anyone shed some light on this? However, the logic of 80 and above seems sensible.
What about other languages and their numeral systems? We have seen that in Welsh they work with a similar concept and this Celtic influence is perhaps the origin of the French systems. For example, in Welsh 11 is one-on-ten, 12 is two-ten, 13 is three-on-ten, 14 is four-on-ten, 15 is five-ten, 16 is one-on-five-ten, 17 is two-on-five-ten, 18 is two-nines, 19 is four-on-five-ten. These numbers are then combined with units of twenties, so 97 for example, is: dau ar bymtheg ar bedwar ugain (two-on-five-ten-on-four-twenties).
It seems that the Vigesimal system is actually commonly used as the base of many countries’ numeral systems and there are of course many variations stemming from this base. Take Yoruba for example, like many African languages, as explained by Claudia Zaslavsky in her book Africa Counts, the Yoruba numeral system works using complex system based on 20 and that uses subtraction to express numbers. For example:
35 = (2 x 20) – 5; 47 = (3 x 20) – 10 – 3; 51 = (3 x 20) – 10 + 1;
55 = (3 x 20) – 5; 67 = (4 x 20) – 10 – 3; 73 = (4 x 20) – 10 + 3;
86 = (5 x 20) – 10 – 4; 117 = (6 x 20) – 3
The numbers from 1 to 10 have unique names. The numbers 11, 12, 13, and 14 are written additively (i.e., 11 = 10 + 1, 12 = 10 + 2, 13 = 10 + 3, 14 = 10 + 4). But the numbers from 15 through 19 are written using subtraction from 20. The numbers 21, 22, 23, and 24 are also written additively. The numbers 25 -29 are written as subtractions from 30. Each number after 30 is written as a multiple of 20 plus or minus tens and units. This pattern is repeated for numbers up to 200. After 200, the system becomes irregular. The number 20 and its multiples are considered special to the Yoruba. Here are some of their Yoruba names: 20 = ogun; 40 = ogun meji; 200 = igba; 400 = irinwo.
Complicated, isn’t it? However, when you grow up with a numeral system it is most likely easier to get to grips with, though I’m sure it must still cause problems. What other numeral systems do you know? What interesting points can you share about their history?
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