What exactly is a vigesimal counting system? Simply put, it's a base-20 numeral system, where counting proceeds in intervals of twenty, rather than the more prevalent decimal system. Base-10 is often argued to be the most natural counting system because of the amount of fingers on our hands, but the same argument could be made for vigesimal systems if toes are included!

This method of counting, mostly archaic nowadays, was once widespread among various ancient cultures, including the Maya, Aztecs, and Sumerians. Though largely supplanted by the decimal system, vigesimal counting lives on today, either in full force (Yoruba, Georgian, Iñupiat, Basque) or as scattered linguistic remnants (French, Danish, English) in select regions that otherwise adopted decimal.

Let’s take a look at how European languages incorporate this unusual metric into their numbers.

French

French follows a simple decimal pattern up until 70, which is “soixante-dix”, literally “sixty-ten”. This odd construction is often attributed by historians to the base-20 counting system used by Gauls, the modern “soixante-dix” being a hybrid of the classical “soixante” (sixty) and the obsolete “trois-vingts-dix” (three-twenties-ten). That line of thinking got entirely preserved for 80 and 90 though, respectively “quatre-vingts” (four-twenties) and “quatre-vingt-dix” (four-twenties-ten).

Interestingly, other French-speaking regions of the world stick closer to the decimal system, like Wallonia reverting 70 (septante) and 90 (nonante) to a simple base-10 structure, and Romandy going further by fixing 80 (huitante) as well.

If you’re in Paris, you might come across the

*Hôpital des Quinze-Vingts*, founded in 1260 with 300 beds and named accordingly “Hospital of the Fifteen Twenties” to follow the conventions of the time. Danish

In Danish, traces of the vigesimal system persist in everyday counting from 50 upwards. Like French, Danish employs a combination of base-10 and base-20 elements, even throwing some algebra into the mix! For instance, the number 50, "halvtreds," is a contraction of “

*halvtredje-sinds-tyve*" meaning "half-third times twenty", so two twenties plus a third twenty cut in half ( [2+½]x20 ). From 50, the tens alternate between the two systems: halvtreds, tres, halvfjerds, firs, halvfems, hundrede.An alternative, fully base-10 system is contextually preferred, for example for administrative tasks, literally counting the tens (ti): ti, toti, treti, firti, femti, seksti, syvti, otti, niti.

The base-10 is progressively being phased out though, as shown by the switch on bank notes to the vigesimal system. A 50-krone bank note used to show “femti”, but since the 2009 batch of notes, it now displays “halvtreds”.

Basque

In the Basque language, spoken primarily in the Basque region spanning across Spain and France, the vigesimal system is still alive and well. The construction of numbers above 20 (hogei) revolves around that magic number: 30 is hogeita hamar (contraction of hogei-ta-hamar, twenty-and-ten), 40 is berrogei (ber-hogei, two-twenties), 70 is hirurogeita hamar (hirur-hogei-ta-hamar, three-twenties-and-ten), etc.

Interestingly, Basque millers had their own numbers, varying from area to area but definitely distinct from the Arabic numbers we know and love. These systems have since fallen out of use, but remain an important vestige of the history of Basque, one of the very few isolates still in use today.

English

Not much to see in traditional numbers, but there is a little throwback to vigesimalism to be found: the score. Not talking sports here, but rather the somewhat old-timey way to bundle units of twenty. Sometimes adorned with a multiplicator (

*fourscore*meaning eighty), often used as an indeterminate unit of measurement (*scores of people on the beach*). Heavily hints at shepherds scoring their sticks to count livestock, twenty at a time. Try counting sheep by the score at nighttime, maybe you’ll fall asleep twenty times faster! Conclusion

It’s easy to overlook how many counting systems surround us. Those of us used to the metric system might believe decimal counting to be natural and self-evident, but many cultures and civilizations are around to warrant humility: Kharosthi script (India) is base-4, multiple Australian Aboriginal languages like Wubuy are base-5, Ndom (Indonesia) is base-6, and so on…

In an increasingly interconnected and standardized world, no one is to say how long these unique bits of linguistic history will last among living languages. No matter what, however, they will forever remain as markers of humanity’s fascinating variety in its approaches to the world, and historians still have many more stories to unearth about numeral systems and their origins.