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12 Mind Blowing Number Systems From Other Languages

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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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10 Facts About Samuel Johnson’s Dictionary
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October 16 is World Dictionary Day, which each year celebrates the birthday of the American lexicographer Noah Webster, who was born in Connecticut in 1758. Last year, Mental Floss marked the occasion with a list of facts about Webster’s American Dictionary of the English Language—the enormous two-volume dictionary, published in 1828 when Webster was 70 years old, that established many of the differences that still divide American and British English to this day. But while Webster was America’s foremost lexicographer, on the other side of the Atlantic, Great Britain had Dr. Samuel Johnson.

Johnson—whose 308th birthday was marked with a Google Doodle in September—published the equally groundbreaking Dictionary of the English Language in 1755, three years before Webster was even born. Its influence was arguably just as great as that of Webster’s, and it remained the foremost dictionary of British English until the early 1900s when the very first installments of the Oxford English Dictionary began to appear.

So to mark this year’s Dictionary Day, here are 10 facts about Johnson’s monumental dictionary.

1. IT WASN’T THE FIRST DICTIONARY.

With more than 40,000 entries, Johnson’s Dictionary of the English Language was certainly the largest dictionary in the history of the English language at the time but, despite popular opinion, it wasn’t the first. Early vocabularies and glossaries were being compiled as far back as the Old English period, when lists of words and their equivalents in languages like Latin and French first began to be used by scribes and translators. These were followed by educational word lists and then early bilingual dictionaries that began to emerge in the 16th century, which all paved the way for what is now considered the very first English dictionary: Robert Cawdrey’s Table Alphabeticall—in 1604.

2. SAMUEL JOHNSON BORROWED FROM THE DICTIONARIES THAT CAME BEFORE HIS.

In compiling his dictionary, Johnson drew on Nathan Bailey’s Dictionarium Britanicum, which had been published in 1730. (Ironically, a sequel to Bailey’s dictionary, A New Universal Etymological English Dictionary, was published in the same year as Johnson’s, and borrowed heavily from his work; its author, Joseph Nicoll Scott, even gave Johnson some credit for its publication.)

But just as Johnson had borrowed from Bailey and Scott had borrowed from Johnson, Bailey, too had borrowed from an earlier work—namely John Kersey’s Dictionarium Anglo-Britannicum (1708)—which was based in part on a technical vocabulary, John Harris’s Universal English Dictionary of Arts and Sciences. Lexicographic plagiarism was nothing new.

3. THE DICTIONARY WASN’T THE ONLY THING JOHNSON WROTE.

Although he’s best remembered as a lexicographer today, Johnson was actually something of a literary multitasker. As a journalist, he wrote for an early periodical called The Gentlemen’s Magazine. As a biographer, he wrote the Life of Mr Richard Savage (1744), a memoir of a friend and fellow writer who had died the previous year. Johnson also wrote numerous poems (London, published anonymously in 1738, was his first major published work), a novel (Rasselas, 1759), a stage play (Irene, 1749), and countless essays and critiques. He also co-edited an edition of Shakespeare’s plays. And in between all of that, he even found time to investigate a supposed haunted house in central London.

4. IT WAS THE FIRST DICTIONARY TO USE QUOTATIONS.

Johnson’s dictionary defined some 42,773 words, each of which was given a uniquely scholarly definition, complete with a suggested etymology and an armory of literary quotations—no fewer than 114,000 of them, in fact.

Johnson lifted quotations from books dating back to the 16th century for the citations in his dictionary, and relied heavily on the works of authors he admired and who were popular at the time—Shakespeare, John Milton, Alexander Pope, and Edmund Spenser included. In doing so, he established a lexicographic trend that still survives in dictionaries to this day.

5. IT TOOK MORE THAN EIGHT YEARS TO WRITE.

Defining 42,000 words and finding 114,000 quotes to help you do so takes time: Working from his home off Fleet Street in central London, Johnson and six assistants worked solidly for over eight years to bring his dictionary to print. (Webster, on the other hand, worked all but single-handedly, and used the 22 years it took him to compile his American Dictionary to learn 26 different languages.)

6. JOHNSON WAS WELL PAID FOR HIS TROUBLES.

Johnson was commissioned to write his dictionary by a group of London publishers, who paid him a princely 1,500 guineas—equivalent to roughly $300,000 (£225,000) today.

7. HE LEFT OUT A LOT OF WORDS.

The dictionary’s 42,000-word vocabulary might sound impressive, but it’s believed that the English language probably had as many as five times that many words around the time the dictionary was published in 1755. A lot of that shortfall was simply due to oversight: Johnson included the word irritable in four of his definitions, for instance, but didn’t list it as a headword in his own dictionary. He also failed to include a great many words found in the works of the authors he so admired, and in several of the source dictionaries he utilized, and in some cases he even failed to include the root forms of words whose derivatives were listed elsewhere in the dictionary. Athlete, for instance, didn’t make the final cut, whereas athletic did.

Johnson’s imposition of his own tastes and interests on his dictionary didn't help matters either. His dislike of French, for example, led to familiar words like unique, champagne, and bourgeois being omitted, while those he did include were given a thorough dressing down: ruse is defined as “a French word neither elegant nor necessary,” while finesse is dismissed as “an unnecessary word that is creeping into the language."

8. HE LEFT OUT THE LETTER X.

    At the foot of page 2308 of Johnson’s Dictionary is a note merely reading, “X is a letter which, though found in Saxon words, begins no word in the English language."

    9. HIS DEFINITIONS WEREN’T ALWAYS SO SCHOLARLY.

      As well as imposing his own taste on his dictionary, Johnson also famously employed his own sense of humor on his work. Among the most memorable of all his definitions is his explanation of oats as “a grain, which in England is generally given to horses, but in Scotland supports the people.” But he also defined monsieur as “a term of reproach for a Frenchman,” excise as “a hateful tax levied upon commodities and adjudged not by the common judges of property but wretches hired by those to whom excise is paid,” and luggage as “anything of more weight than value.” As an example of how to use the word dull, he explained that “to make dictionaries is dull work.”

      10. HE POKED LOTS OF FUN AT HIS OWN OCCUPATION.

      Listed on page 1195 of his dictionary, Johnson’s definition of lexicographer was “a writer of dictionaries; a harmless drudge.”

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      Something Something Soup Something
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      This Game About Soup Highlights How Tricky Language Is
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      Something Something Soup Something

      Soup, defined by Merriam-Webster as "a liquid food especially with a meat, fish, or vegetable stock as a base and often containing pieces of solid food," is the ultimate simple comfort food. But if you look closer at the definition, you'll notice it's surprisingly vague. Is ramen soup? What about gumbo? Is a soy vanilla latte actually a type of three-bean soup? The subjectivity of language makes this simple food category a lot more complicated than it seems.

      That’s the inspiration behind Something Something Soup Something, a new video game that has players label dishes as either soup or not soup. According to Waypoint, Italian philosopher, architect, and game designer Stefano Gualeni created the game after traveling the world asking people what constitutes soup. After interviewing candidates of 23 different nationalities, he concluded that the definition of soup "depends on the region, historical period, and the person with whom you're speaking."

      Gualeni took this real-life confusion and applied it to a sci-fi setting. In Something Something Soup Something, you play as a low-wage extra-terrestrial worker in the year 2078 preparing meals for human clientele. Your job is to determine which dishes pass as "soup" and can be served to the hungry guests while avoiding any items that may end up poisoning them. Options might include "rocks with celery and batteries in a cup served with chopsticks" or a "foamy liquid with a candy cane and a cooked egg served in a bowl with a fork."

      The five-minute game is meant to be tongue-in-cheek, but Gualeni also hopes to get people thinking about real philosophical questions. According to its description page, the game is meant to reveal "that even a familiar, ordinary concept like 'soup' is vague, shifting, and impossible to define exhaustively."

      You can try out Something Something Soup Something for free on your browser.

      [h/t Waypoint]

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