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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A New App Interprets Sign Language for the Amazon Echo
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The convenience of the Amazon Echo smart speaker only goes so far. Without any sort of visual interface, the voice-activated home assistant isn't very useful for deaf people—Alexa only understands three languages, none of which are American Sign Language. But Fast Company reports that one programmer has invented an ingenious system that allows the Echo to communicate visually.

Abhishek Singh's new artificial intelligence app acts as an interpreter between deaf people and Alexa. For it to work, users must sign at a web cam that's connected to a computer. The app translates the ASL signs from the webcam into text and reads it aloud for Alexa to hear. When Alexa talks back, the app generates a text version of the response for the user to read.

Singh had to teach his system ASL himself by signing various words at his web cam repeatedly. Working within the machine-learning platform Tensorflow, the AI program eventually collected enough data to recognize the meaning of certain gestures automatically.

While Amazon does have two smart home devices with screens—the Echo Show and Echo Spot—for now, Singh's app is one of the best options out there for signers using voice assistants that don't have visual components. He plans to make the code open-source and share his full methodology in order to make it accessible to as many people as possible.

Watch his demo in the video below.

[h/t Fast Company]

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How to Craft the Perfect Comeback, According to Experts
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In a 1997 episode of Seinfeld called “The Comeback,” George Costanza is merrily stuffing himself with free shrimp at a meeting. His coworker mocks him: “Hey, George, the ocean called. They’re running out of shrimp.” George stands humiliated as laughter fills the room, his mind searching frantically for the perfect riposte.

It’s only later, on the drive home, that he thinks of the comeback. But the moment has passed.

The common human experience of thinking of the perfect response too late—l’esprit de l’escalier, or "the wit of the staircase"—was identified by French philosopher Denis Diderot when he was so overwhelmed by an argument at a party that he could only think clearly again once he’d gotten to the bottom of the stairs.

We've all been there. Freestyle rappers, improv comedians, and others who rely on witty rejoinders for a living say their jobs make them better equipped to seize the opportunity for clever retorts in everyday life. They use a combination of timing, listening, and gagging their inner critics. Here are their insights for crafting the perfect comeback.

LISTEN TO YOUR OPPONENT’S ARGUMENT.

The next time you’re in a heated conversation, be less focused on what you're about to say and more attentive to what you're actually responding to. When you spend more time considering what your sparring partner is saying, “you’re deferring your response until you’ve fully heard the other person," Jim Tosone, a technology executive-turned-improv coach who developed the Improv Means Business program, tells Mental Floss. Your retorts may be more accurate, and therefore more successful, when you’re fully engaged with the other person’s thoughts.

DON’T THINK TOO MUCH.

According to Belina Raffy, the CEO of the Berlin-based company Maffick—which also uses improv skills in business—not overthinking the situation is key. “You’re taking yourself out of unfolding reality if you think too much,” she tells Mental Floss. It’s important to be in the moment, and to deliver your response to reflect that moment.

TRAIN THAT SPONTANEOUS MENTAL MUSCLE.

History’s most skilled comeback artists stored witticisms away for later use, and were able to pull them out of their memory at the critical time.

Winston Churchill was known for his comebacks, but Tim Riley, director and chief curator at the National Churchill Museum in Fulton, Missouri, tells Mental Floss that many of his burns were borrowed. One of his most famous lines was in response to politician Bessie Braddock’s jab, “Sir, you are drunk.” The prime minister replied, “And you, Bessie, are ugly. But I shall be sober in the morning, and you will still be ugly.”

Riley says this line was copied from comic W.C. Fields. Nevertheless, it took quick thinking to remember and reshape the quote in the moment, which is why Churchill was thought of as a master of timing. “It was an off-the-cuff recall of something he had synthesized, composed earlier, and that he was waiting to perform,” Riley says.

But in some situations, the retort must be created entirely in the moment. Training for spontaneity on stage also helps with being quicker-witted in social situations, New York City battle rap emcee iLLspokinn tells Mental Floss. It’s like working a spontaneous muscle that builds with each flex, so, you’re incrementally better each time at seizing that witty opportunity.

MUZZLE YOUR INNER CRITIC.

Anyone who has been in the audience for an improv show has seen how rapidly performers respond to every situation. Improv teaches you to release your inhibitions and say what drops into your mind: “It’s about letting go of the need to judge ourselves,” Raffy explains.

One way to break free of your internal editor might be to imagine yourself on stage. In improv theater, the funniest responses occur in the spur of the moment, says Douglas Widick, an improv performer who trained with Chicago’s Upright Citizens Brigade. By not letting one’s conscience be one’s guide, actors can give into their “deepest fantasies” and say the things they wouldn’t say in real life.

IF YOU HAVE AN EXTRA SECOND, HONE YOUR ZINGER.

The German version of Diderot’s term is Treppenwitz, also meaning the wit of the stairs. But the German phrase has evolved to mean the opposite: Something said that, in retrospect, was a bad joke. When squaring up to your rival, the high you get from spearing your opponent with a deadly verbal thrust can be shadowed by its opposite, the low that comes from blurting out a lame response that lands like a lead balloon.

That's a feeling that freestyle rapper Lex Rush hopes to avoid. “In the heat of the battle, you just go for it,” she tells Mental Floss. She likens the fight to a “stream of consciousness” that unfolds into the mic, which leaves her with little control over what she’s projecting into the crowd.

It may help to mull over your retort if you have a few extra seconds—especially if you’re the extroverted type. “Introverts may walk out of a meeting thinking, ‘Why didn’t I say that?’ while extroverts think, ‘Why did I say that?’” Tosone, the improv coach, says. Thinking before you speak, even just briefly, will help you deploy a successful comeback.

And if it doesn’t go your way, iLLspokinn advises brushing off your missed opportunity rather than dwelling on your error: “It can be toxic to hold onto it."

THROW DIGITAL SHADE ACCORDING TO THE SAME RULES—BUT BE QUICK ABOUT IT.

Texting and social media, as opposed to face-to-face contact, give you a few extra minutes to think through your responses. That could improve the quality of your zinger. “We’re still human beings, even on screens. And we prefer something that is well-stated and has a fun energy and wit about it," Scott Talan, a social media expert at American University, tells Mental Floss.

But don't wait too long: Replies lose their punch after a day or so. “Speed is integral to wit, whether in real life or screen life,” Talan says. “If you’re trying to be witty and have that reputation, then speed will help you."

Some companies have excelled in deploying savage social media burns as marketing strategies, winning viral retweets and recognition. The Wendy’s Twitter account has become so well known for its sassy replies that users often provoke it. “Bet you won’t follow me @Wendys,” a user challenged. “You won that bet,” Wendy’s immediately shot back.

George Costanza learns that lesson when he uses his rehearsed comeback at the next meeting. After his colleague repeats his shrimp insult, George stands and proudly announces, “Oh yeah? Well, the jerk store called, and they’re running out of you!”

There’s silence—until his nemesis comes back with a lethal move: “What’s the difference? You’re their all-time best-seller.”

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