The Last Speakers (19 page)

BODY COUNTING

Cleverness in the island nation is not limited to knowledge gained from water spirits. One of the most remarkable cultural innovations of Papua New Guinea is the wild profusion of body-counting systems. Nowhere in the world is such a wide variety of body math systems found, using points on the body like pegs on a cribbage board or beads on an abacus. These systems, far from being the primitive enumerations that scientists first labeled them, are highly sophisticated. Some permit addition and subtraction. counting ad infinitum, even multiplication. All ingeniously bootstrap and augment human memory by using the body as a short-term memory buffer. Using only bodies and body parts, some could count to infinity.
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We live in a world regulated by mathematics and numbers, and we are drilled in arithmetic from an early age. Skill in algebra is a gateway to high SAT scores and higher education, so we can be forgiven for thinking that math is a kind of anchoring rock that we depend on and that does not change. But viewed through the lens of other cultures, numbers look very different. Indeed, the whole premise of our counting system, based on units of ten, turns out to be a cultural whim, a mere preference.

Body counting is only the tip of the complexity iceberg, and New Guinea cultures hold many more mathematical surprises. We sat down in a small village on the Ambonwari River with the local schoolteacher, a man named Julius.
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He spoke excellent English and had worked over the years with a visiting anthropologist, so he had the patience needed to teach foreigners things that should be perfectly obvious. Greg Anderson and I set up our camera and recording equipment and sat in the village's main house, with about a hundred people observing us. Much to their amusement, we were flummoxed by something they regard as utterly simple—counting to one!

Here's how our session unfolded. We started with a simple question, and learned that the word for the number one is
mban
—or so we thought. After a long detour through the number system, we found out that “mban” is just one manifestation of the chameleon-like word for “one” in this language. Like that colorful lizard, it changes its appearance continually, but unlike the chameleon, its changes are governed not just by the surroundings (e.g., what word it is modifying) but also by a complex system that divides all nouns up into special categories (e.g., living male things are different from living female things, which are different from inanimate objects that end in the letter
n,
and so on. Here's how the dialogue unfolded:

Greg, with his astounding language aptitude and love of numbers, counted right back: “So, mban, kripai, kriyen mau, samunung, suwam, sambaimbiyam, samba kripai, samba kriyen mau, samba usanam, sumbri.”

I was still struggling with one, and I thought I had heard something ever so slightly different, so I asked, “One is
mbang?”

Julius replied, “
Mbang.”

So it seemed we had two words for one, “mbam” and “mbang.” Julius, patient as a schoolteacher, clarified: “All right, there is different ways in counting.
Mbang
we say for different things.
Mbam
also is the same as one. So, different items, we name them in different numbering systems.”

Intrigued, we began trying to figure out when to say which form by asking him to count objects. “One banana” was
mambaing mbang
and “one coconut” was
wurang mbang.
This seemed clear: “one” is “mbang.” But sometimes it is pronounced “mban”: “one pig” is
imbiyan mban
and “one dog” is
wiya mban.

Then we were confounded yet again: “one house” was translated as
yam mbo.

Now it seemed like a simple three-way split. Words than end in
-ng
take the word “mbang,” words that end in a vowel or
-n
take “mban,” and some other set of words, which we hoped to identify, take “mbo.”

We tested our hypothesis by finding another word that ended in -
ng—pambang,
“bow and arrow”—predicting that it would be modified by “mbang.” But we were wrong. Being wrong with your initial hypothesis is just where things start to get complex and interesting. So we kept asking for more examples.

How about one man? Julius said: “
Yermasanar mban.”

And one woman, we asked?
Yermasanma mbanma.

So it seemed the word for woman had a special suffix-
ma
, to make it “mbanma.” We confirmed this with other words denoting female persons: “One daughter” is
kiyawi mbanma,
and “one sister” is
mamiyang mbanma
.

I asked: “What else do you count with
mbo
? What about canoes?”

I exclaimed: “How to count to one in this language!” and Greg agreed, “Yes, we'll never get past one!”

Throughout this baffling dialogue, we had deduced several general principles of the counting system, without fully grasping its complexity. How do you choose which form of “one”? It depends partly on the sounds contained in the word; if a word ends in -
ng
or -
k,
you use “mbang,” which matches it. If a word ends in
-n,
you use “mban.” Some words that end in -
ai
take “mbai.” But we uncovered multiple exceptions, where some special consideration overrides the expected choice. One special consideration has to do with the type of word—for example, whether it is a male or female person or animal. If it comes in small quantities or numbers, a body part for example, then it takes “mbaiya.”

A system like this requires speakers to keep track of multiple different categories: what sounds make up a word, what does the word refer to? Is it male or female, numerous or scarce, and so on? Each piece of information might lead you to use a different form, but not all information is equal. Some facts are more important than others, so they override, and that is another factor that must be learned by speakers. They seem to do it all effortlessly, as attested by the villagers' delight and laughter in hearing us attempt to learn the system.

As we left the village, we marveled at all the many different ways to say “one.” And we wondered how much of that complexity appears in the higher numbers, which might not only classify objects into different groups but also require the speaker to do mental mathematics.

If you survey the world's languages, you find radically different ways of counting, different ways of apprehending and framing mathematical relationships. Some of these, as discussed above, are based on using the human body as a living abacus. Others are more abstract and work with a number other than ten (which is our number base) to build larger numbers.

One of our favorite eureka moments was captured in India for the documentary film
The Linguists
.
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A speaker of Sora, Oruncho Gamango, was teaching us the numbers:
A-boy
means one,
BA-goo
is two, and
YA-gee
is three. Each number had a unique name, all the way up past
GEL-jee,
ten.
GEL-moy
means 11, and 12 is
MEE-gel.

We dutifully wrote down the names, which were all unique labels up to 12. English also has unique names for numbers up to 12, and then it begins to build numbers 13 and above using ten as a base, so “eighteen” can be thought of as “eight” plus “ten,” and ten is a basic building block in English that builds the higher numbers.

By this point, we thought Sora would be a straightforward system, even a bit routine. But when Oruncho reached 13, he repeated the word for 12, followed by the word for 1: “Twelve is
MEE-gel,
and 13 is
MEE-gel BOY.”

Greg and I burst into smiles at the discovery. Sora uses a base-12 system. This is unusual though not unique in the world, but we felt happy because we had not personally documented such a system before in the course of our fieldwork. Then, as the numbers became higher, another pattern emerged. Sora also uses 20 as a base to build numbers. In the higher numbers, you can combine 20, 12, and other numbers, so that the way to say 93 in Sora is actually “four twenty twelve one”! (This may remind some readers of French numbers.)

Each language potentially has a unique way of counting, and mathematicians tell us that there is nothing sacred about using ten as a base—it is merely a convenience. We could have a sophisticated mathematics using 4 or 6 or 12 as a base. Yet these alternative ways of counting are rapidly vanishing, as the standard base-ten counting system continues to spread. Numbers and quantities are a deep property of the physical universe, and mankind has contemplated them for ages. But smaller languages, with their sometimes radically different ways of conceptualizing numbers, may hold some unique insights—if we can learn them before they vanish.