12 Mind Blowing Number Systems From Other Languages

Today is a big day for lovers of the number 12, and no one loves 12s more than the members of the Dozenal Society. The Dozenal Society advocates for ditching the base-10 system we use for counting in favor of a base-12 system. Because 12 is cleanly divisible by more factors than 10 is (1, 2, 3, 4, 6 and 12 vs. 1, 2, 5 and 10), such a system would neaten up our mathematical lives in various ways. But a dozenal system would require us to change our number words so that, for example, what we know as 20 would mean 24 (2x12), 30 would mean 36, and so on. Does that blow your mind a little too much? Well there are all sorts of weird things that languages can do with number words. Here are 12 of them.

1. Oksapmin, base-27 body part counting

Photo Courtesy of Austronesian Counting

The Oksapmin people of New Guinea have a base-27 counting system. The words for numbers are the words for the 27 body parts they use for counting, starting at the thumb of one hand, going up to the nose, then down the other side of the body to the pinky of the other hand, as shown in the drawing. 'One' is tip^na (thumb), 6 is dopa (wrist), 12 is nata (ear), 16 is tan-nata (ear on the other side), all the way to 27, or tan-h^th^ta (pinky on the other side).

2. Tzotzil, base-20 body part counting

Tzotzil, a Mayan language spoken in Mexico, has a vigesimal, or base-20, counting system. Why might a base-20 system come about? Fingers and toes! For numbers above 20, you refer to the digits of the next full man (vinik). Twenty-one is jun scha'vinik (first digit of the second man), 42 is chib yoxvinik (second digit of the third man), and 70 is lajuneb chanvinik (tenth digit of the fourth man).

3. Yoruba, base-20 with subtraction

Yoruba, a Niger-Congo language spoken in West Africa, also has a base-20 system, but it is complicated by the fact that for each 10 numbers you advance, you add for the digits 1-4 and subtract for the digits 5-9. Fourteen (??rinlá) is 10+4 while 17 (eétàdílógún) is 20-3. So, combining base-20 and subtraction means 77 is m?tadil?g?rin, or (20x4)-3.

4. Traditional Welsh, base-20 with a pivot at 15

Though modern Welsh uses base-10 numbers, the traditional system was base-20, with the added twist of using 15 as a reference point. Once you advance by 15 (pymtheg) you add units to that number. So 16 is un ar bymtheg (one on 15), 36 is un ar bymtheg ar hugain (one on 15 on 20), and so on.

5. Alamblak, numbers built from 1, 2, 5, and 20

In Alamblak, a language of Papua New Guinea, there are only words for 1, 2, 5, and 20, and all other numbers are built out of those. So 14 is (5x2)+2+2, or tir hosfi hosfihosf, and 59 is (20x2)+(5x(2+1))+(2+2) or yima hosfi tir hosfirpati hosfihosf.

6. Ndom, base-6

Ndom, another language of Papua New Guinea, has a base-6, or senary number system. It has basic words for 6, 18, and 36 (mer, tondor, nif) and other numbers are built with reference to those. The number 25 is tondor abo mer abo sas (18+6+1), and 90 is nif thef abo tondor ((36x2)+18).

7. Huli, base-15

The Papua New Guinea language Huli uses a base-15, or pentadecimal system. Numbers which are multiples of 15 are simple words. Where the English word for 225 is quite long, the Huli word is ngui ngui, or 15 15. However 80 in Huli is ngui dau, ngui waragane-gonaga duria ((15x5)+the 5th member of the 6th 15).

8. Bukiyip, base-3 and base-4 together

In Bukiyip, another Papua New Guinea language also known as Mountain Arapesh, there are two counting systems, and which one you use depends on what you are counting. Coconuts, days, and fish are counted in base-3. Betel nuts, bananas, and shields are counted in base-4. The word anauwip means 6 in the base-3 system and 24 in the base-4 system!

9. Supyire, numbers built from 1, 5, 10, 20, 80, and 400

Supyire, a Niger-Congo language spoken in Mali has basic number words for 1, 5, 10, 20, 80 and 400, and builds the rest of the numbers from those. The word for 600 is kàmpwòò ná ?kwuu shuuní ná bééshùùnnì, or 400+(80x2)+(20x2)

10. Danish, forms some multiples of ten with fractions

Danish counting looks pretty familiar until you get to 50, and then things get weird with fractions. The number 50 is halvtreds, a shortening of halv tred sinds tyve ("half third times 20" or 2½x20). The number 70 is 3½x20, and 90 is 4½x20.

11. French, mix of base-10 and base-20

French uses base-10 counting until 70, at which point it transitions to a mixture with base-20. The number 70 is soixante-dix (60+10), 80 is quatre-vingts (4x20), and 90 is quatre-vingts-dix ((4x20)+10).

12. Nimbia, base-12

Even though, as the dozenalists claim, 12 is the best base mathematically, there are relatively few base-12 systems found in the world's languages. In Nimbia, a dialect of the Gwandara language of Nigeria, multiples of 12 are the basic number words around which everything else is built. The number 29 is gume bi ni biyar ((12x2)+5), and 95 is gume bo'o ni kwada ((12x7)+11).

You can see more number systems here. Many of the more exotic ones are dying out. David K. Harrison's book When Languages Die explains how we lose "an important window into human cognition, problem-solving, and adaptation" when these number systems disappear.

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Why Do Americans Call It ‘Soccer’ Instead of ‘Football’?
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iStock

While more Americans than ever are embracing soccer, they can't even get the sport's name right, according to some purists. For most of the world, including the vast majority of Europe and South America, it’s football, fútbol, or some other variation. In the United States, Canada, Japan, and a few other stragglers, it’s firmly known as soccer, much to the annoyance of those who can't understand how a sport played with feet and a ball can be called anything else. So why the conflict?

According to a paper [PDF] by University of Michigan professor Stefan Szymanski, it all began in England in the early 1800s, when a version of the sport of football—based on a game played by “common people” in the Middle Ages—found its way into the recreational scene of some of the country’s most privileged schools. To give uniformity to the competitions between these schools and clubs, a set of standard rules was drafted by students in Cambridge in 1848. These rules would become further solidified when they were adopted by the more organized Football Association in 1863.

It wasn't long before variations of the sport began to splinter off—in 1871, the Rugby Football Union was founded, using Rugby School rules from the 1830s that allowed a player to run with the ball in their hands. This new take on the sport would be known as rugby football, or rugger, to separate itself from association football, the traditional feet-only version of the sport. From there, association football would get the nickname assoccer, leading eventually to just soccer. The addition of an "er" at the end of a word was something of a trend at the time, which is why we get the awkward transformation of association into assoccer and soccer.

The first recorded American football game was between the colleges of Rutgers and Princeton in 1869 and used unique rules derived from those in both association and rugby football. Though this new, evolving game would just be called football in the U.S., elsewhere it would become known as gridiron football or American football, much in the way Gaelic football and Australian football have their own distinctions. Eventually in England, rugby football was shortened to just rugby, while association football simply became known as football. Which meant that now there were two footballs, on opposite sides of the Atlantic, and neither side would budge. And Americans would begin referring to England's football by the previous nickname, soccer.

Despite the confusion nowadays, soccer was still a colloquial term used in England well into the 20th century—it rose in popularity following World War II before falling out of favor in the 1970s and ‘80s, according to Szymanski. In more recent years, it’s mostly been used in England in a strictly American context, like when publications and the media refer to U.S. leagues like Major League Soccer (MLS). Currently, soccer is mostly used in countries that have their own competing version of football—including the United States, Canada, and Australia.

While it boils the blood of certain traditionalists, soccer is by no means an Americanism—like the sport itself, this is purely an English export.

Have you got a Big Question you'd like us to answer? If so, let us know by emailing us at bigquestions@mentalfloss.com.

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YouTube, Hélio Surdos
How a Deaf-Blind Person Watches the World Cup
YouTube, Hélio Surdos
YouTube, Hélio Surdos

Brazilian Sign Language interpreter Hélio Fonseca de Araújo woke up on the day before the opening of the World Cup in 2014 thinking about how he could help his friend Carlos, who is deaf and blind, get access to all the excitement. So he hit the hardware store, rigged up a tabletop model of the field, and enlisted his friend Regiane to provide extra interpretation for all the complex information that needs to come through in a game. He recently brought the setup out again for this World Cup.

Here you can see Carlos watching the Brazil vs. Croatia match live, while Hélio provides Brazilian Sign Language interpretation (which Carlos follows by feeling it with his own hands—this is called tactile signing), and Regiane relays information about fouls, cards, times, and player jersey numbers with social-haptic communication on Carlos’s back.

This is the moment in the second half when it appeared that Brazil had scored a goal, but a foul was called. Hélio later makes sure Carlos can see how Neymar covered his face with his shirt.

And here is Coutinho’s game-turning goal for Brazil.

If you're wondering why Carlos occasionally looks at the screen, many deaf blind people have some residual sight (or hearing). Many deaf-blind people become fluent in sign language as deaf people, before they begin to lose their sight.

See the entire video at Hélio’s YouTube channel here.

A version of this story ran in 2014.

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