How Languages Count: Number Systems from Base Ten to Twenties

Ten is common, twenty is not rare

Counting in tens is the default of most of the world’s languages, and the digits 0 to 9 have made it look universal. Yet several European languages still build part of their numbers on twenty, a vigesimal base. In the Maya number system twenty is the base throughout: kal is twenty and bak four hundred, and the counting runs in fives up to twenty.¹

In Basque the scores are visible in the words. Hogei is twenty, and berrogei, hirurogei and laurogei, forty, sixty and eighty, mean two-score, three-score and four-score; Basque counts this way up to a hundred.¹ Georgian does the same from thirty to ninety-nine, with otsi, twenty, inside the higher tens, so that ormotsi, forty, is two times twenty.¹

Belgian and Swiss French

Belgian and Swiss French use septante and nonante for seventy and ninety, so a Brussels speaker writes 1996 as mille neuf cent nonante-six. Eighty stays quatre-vingts in Belgium, while the Swiss cantons of Vaud, Valais and Fribourg say huitante.¹ Both words follow the pattern of trente, quarante, cinquante and soixante and continue it past sixty.

Why halv- means a half less

The Danish system rests on an old way of counting halves. Halvanden, one and a half, is literally half second: the second unit is only half there. In the same way halvtredje meant two and a half, halvfjerde three and a half, halvfemte four and a half, and these words stand inside halvtreds, halvfjerds and halvfems.² Halvtreds is short for halvtredje-sinds-tyve, two and a half times twenty, and tres for tre-sinds-tyve.² Only the names of these tens follow twenty, so Danish as a whole is not a vigesimal system.¹

A language without number words

Pirahã, a language of Brazil, is the best-known case of a language that may lack exact numbers. Daniel Everett first described hói and hoí, differing only in tone, as one and two, and later argued that they mean a small and a larger quantity.³

In experiments published in 2008, Michael Frank and colleagues placed spools of thread on a table one at a time and asked four speakers to name the amount. Hói was used for one spool and hoí for two, but when spools were taken away from a set of ten, one speaker already said hói when six remained. The authors concluded that the words are relative terms like few or fewer. The speakers could match exact quantities of visible objects; they had difficulty once a set was hidden before the match.³