Counting higher than fingers and toes

Linguists speculate that the base-10 number system developed independently around the world because it was inspired by the most obvious tools we have to count with – our fingers.

In a Word

From English to Mandarin to Spanish, most languages with hundreds of millions of speakers use a base-10 number system, as we discussed in the column last week. Linguists speculate that this system developed independently around the world because it was inspired by the most obvious tools we have to count with – our fingers. If we look beyond the big, global languages, however, we’ll see that people have come up with different ways of numbering the world.

In some cultures, people have counted their fingers and toes, producing base-20 systems. French, as we saw last week, has the remnants of one of these between the numbers 70 and 99, making 82, for example, quatre-vingt-deux (four 20s + 2). 

It doesn’t seem natural to tally with digits in all cultures, though. Speakers of Yuki, a Native American language of northern California, counted the spaces between the fingers, making a base-8 system. The Northern Pame language, in Mexico, also has a base-8 system, because it counts the knuckles on closed fists. Kewa, in Papua New Guinea, counts the fingers, but not the thumb, of one hand, making a base-4 system. (The word for eight is kilapo, or “two hands”; 12 is ki repo, or “three hands.”)

Base-4 is fine for smaller numbers, but when the Kewa want to count higher, they use what might be considered a base-24 system, taking into account all kinds of body parts. The tallying begins with the fingers of the left hand and moves up the arm, to the radius (10), the ulna (11), and the winya ropa (13), the place where women wear armbands. When riga (24), between the eyes, is reached, the counting moves down the right side of the body to the fingers of the right hand. The Kewa don’t tend to count much past one cycle, being content to say that higher numbers are simply papu, or “very many.” Another Austronesian culture, the Kobon, do keep counting with their body-tally system, giving them numbers such as “hand turn around second time go back biceps other side,” or 61.

You may be feeling superior about good old base-10 at this point. It certainly seems easier to say “sixty-one” than to try to remember how many times you’ve gone past your right-side bicep, let alone adding that to “inside elbow other side.” But is base-10 really the best way to go? 

Some mathematicians argue that we would be even better off with a duodecimal, or base-12 system. Twelve can be divided by 2, 3, 4, and 6, producing “clean” fractions instead of .25 or the ever-repeating .3333333. Members of the Dozenal Society have been advocating such a switch for decades. If they had their way, we would all be counting like speakers of Iguta and Gure in Nigeria, or Chepang in the Himalayas.