Four-Twenty and Nineteen Problems… But French Numbers Ain’t One!
Counting systems indifferent languages
Question for all theFrench speakers out there.
What’s the deal withnumbers?
Even if you only studieda little French in high school, you’ll know exactly what we’re talking about.
Numbers in French are, for English Speakers, a Bit of a Nightmare
Things are prettystraightforward when counting. Quarante (40), cinquante (50), soixante(60)… it all follows a logical pattern. That is, until you reach 69.
Then, suddenly everythingchanges. 71 – which you’d expect to be septante-et-un based on how precedingnumbers are formed – suddenly becomes soixante-et-onze, or ‘sixty-and-eleven’.
75, or soixante-quinze,is ‘sixty-fifteen’. 80 is not much simpler: quatre-vingts (four twenties).
And 98? Well. Let’sjust say that once you’ve learned quatre-vingt-dix-huit “four-twenty-ten-eight”you don’t easily forget it!
It’s not just French,either. Learners of Welsh, Irish, Danish, and Basque will also notice thatnumbers in these languages don’t follow the conventional tens + unitspattern that English does.
History of Counting and Numbering Systems in the World’s Languages
Like anything inlinguistics, there’s a reason for this.
Peoples throughouthistory developed different systems for counting things. The Maya, for example,devised a robust system to count and calculate large numbers using only threecharacters: a line, a dot, and a shell, which represents zero.
Because different civilizationsapproached counting things in different ways, the principles that they used toname numbers also differ. In many cases, the modern-day language continues to reflectthe former systems, even if the current counting system has adapted to fitmodern conventions.
Base 10 Numbers
The basic principle behinda numbering system is a base: units are counted individually until theyreach the ‘base’ number. Numbers larger than the base numeral are thenexpressed using multiples of the base.
The most prevalentsystem in use today, which English numbers are derived from, is the base 10 ordecimal system. In base 10, large numbers are expressed inmultiples of 10, with remainder units added on.
This is exactly what‘-ty’ describes in the words ‘sixty’, ‘seventy’, and ‘eighty’. It’s alinguistic marker to express the multiples of 10: ‘six tens’ and ‘seven tens’,etc. The word ‘eighty-two’ is the shortened way of saying ‘eight tens and two’.
That’s all there is toit, right?
Well, not so much.
Not all languages workon the base-10 (or decimal) system.
Although today’s worldis well acquainted with base 10 through widespread use in currency and themetric system, many languages spoken today pre-date the almost universal use ofbase-10 in maths.
These languages, suchas French, still feature the remnants of ancient counting systems in modern wordsfor numbers.
The most commonalternative numbering framework is the vigesimal, or base 20 system.
Base 20 (Vigesimal) Numbers
The word ‘vigesimal’ comes from the Latin word viginiti, meaning ‘twenty’, which is also the origin of the French number vingt (20).
Base 20 numbering worksin a similar way to base 10, except numbers are based in multiples of twenty.Then, the groups of 20 themselves are counted to express numbers 21 and over.
So, rather than express numbers using 1, 10, 100, 1,000, 10,000, and so on, with each category representing 10 x the previous category, vigesimal systems use 1, 20, 400, 8,000, and 160,000, etc.
In vigesimalnumbering, each number from 1-20 has its own name. Numbers over 20 are communicatedin a compound form using this structure:
[multiples of 20] + [remainder]
Expressed in vigesimalterms, the number for 72 would be described as “three twenties and twelve”. Here’s an example of it in use.
The Basque number for 44is berrogeita lau.
Let’s break it downand translate it:
berr-ogei-ta-lau
[two-twenties-and-four]
Very few languages nowuse a fully vigesimal system. Yup’ik, a language spoken in western andsouthwestern Alaska, is one of the surviving vigesimal numbering systems.
Hybrid Decimal-Vigesimal Systems or ‘Systems Within Systems’
Because the decimalsystem is so entrenched in the world via currency and the metric system, many base-20languages borrow elements of base-10 numbering systems to create a hybrid decimal-vigesimalsystem.
Basque is a perfectexample of this.
Let’s take the number256. A traditional base 20 system would express this number in terms of 20s.For a real-world example, a Yoruba speaker would say ‘thirteen-twenties minus four’.
Unlike Yoruba, Basque has‘borrowed’ the unit of 100 from the decimal system for easily expressinghundreds, and then uses base 20 to represent numbers under 100.
So, in Basque, 256would be:
berr-euneta berr-ogei-ta-hama-sei
[two-hundred] and [two-twenty-and-ten-six]
[decimal] + [vigesimal] + [decimal]
French is anotherexample of a hybrid system. Nowadays, only remnants of the French vigesimalsystem remain between numbers 70-99, found in constructions like quatre-vingt-quinze.
In Belgium and Switzerland,French speakers no longer use these traces of base 20, instead adopting a fullydecimal system. In Liège or Geneva, it’s most common to hear nonante-sept (ninety-seven)instead of quatre-vingt-dix-sept (four-twenty-ten-seven).
At least twentylanguages use hybrid decimal-vigesimal systems today, including Irish, Welsh, andDanish.
While the influence ofbase-20 systems is not exclusive to any one language family or geographicalregion, they tend to be found in clusters, due to the ancient vigesimalcounting systems of ancient civilizations. Many central American languagescontinue to use base 20 elements today thanks to the Mayan influence.
Other Numbering Systems
Outside of base 10 and20, there are a few other numbering systems used in languages spoken today, butthese are not common.
Quinary systems (base5) are common in modern Pacific languages, such as Drehu, a language fromFrench Polynesia.
The Ekari language,spoken on the island of New Guinea, uses a sexagesimal (base 60) system, withbase 20 and 10 also used to identify numbers below 60.
Base 60 was also usedby the ancient Sumerians in the 3rd millennium BC. In fact, theirsexagesimal counting system is the reason there are 60 minutes in an hour.
Spotting Numbering Systems in Action
For a fun challenge, whynot investigate the numbering system used in the language you are learning?
Write out the numbers1-20 in your target language, and also the tens 30-100. Look at therelationships between the numbers. Can you see any patterns or repetition inhow the numbers are constructed?
Even if, like inFrench, the pattern is not universal, you may still be able to identify cluesthat a non-decimal system influenced the numbering at some point in history.
