Complexities of Melanesian measurement

BY PETER KRANZ

WESTERNERS SEEM TO THINK that our units of measurement (base 10 counting, the 24 hour clock etc) are some sort of immutable universal truths.  But shows gross ignorance of other cultures.

Not all languages have numeric systems. Specifically, there is not much need for numeric systems among hunter-gatherers who do not engage in commerce.

Many languages around the world have no numerals above two to four—or at least they did not before contact with colonisers—and speakers of these languages may have no tradition of using the numerals for counting.

Indeed, several languages from the Amazon have no numerals other than ‘one’.

Some Australian languages, such as Warlpiri, do not have words for quantities above two, as did many Khoisan languages at the time of European contact. Such languages do not have a word class of ‘numeral’.

Some Austronesian and Melanesian ethnic groups, including the Māori and some Papua New Guineans, count with the base number four.

But perhaps one of the most amazing counting systems was used by the Oksapmin in Papua New Guinea. 

In pre-contact times (prior to 1940) the Oksapmin used a 27-body part count system. That is they had a base 27 number system. Consider that only since the invention of computers has hexadecimal notation been widely use (that is base 16) - and this only due to a quirk of the first microprocessors.

Geoffrey Saxe of the University of California, Berkeley, has made a study of the Oksapmin counting system [http://gse.berkeley.edu/faculty/gsaxe/Research.html].

"To count as Oksapmin do,” he writes, “one begins with the thumb on one hand and enumerates 27 places around the upper periphery of the body, ending on the little finger of the opposite hand.

“To indicate a particular number, one points to the appropriate body part (for example, the ear) and says the body-part name out loud. Traditionally, each number is labelled by both a word and a gesture (pointing to the body part in question).

”To continue past the 27th body part (the ‘other little finger’), continue up to the wrist, forearm, and on up and around the body. There is no distinction between the name (including word and gesture) for the 21st body part (tan-besa, meaning ‘other forearm’) and the 29th body part (also tan-besa, or ‘other forearm’).

“Thus, context is crucial for an understanding of the numerical referent for any number in the Oksapmin counting system."

Papua New Guinea continues to amaze and delight.

Comments

[Peter Kranz]

More on a similar topic. PNG is teaching the world a lot of cool stuff!

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"Our study shows, for the first time, that the number-line concept is not a 'universal intuition' but a particular cultural tool that requires training and education to master," Nunez said. "Also, we document that precise number concepts can exist independently of linear or other metric-driven spatial representations."

Nunez and the research team, which includes UC San Diego cognitive science doctoral alumnus Kensy Cooperrider, now at Case Western Reserve University, and Jurg Wassmann, an anthropologist at the University of Heidelberg who has studied the indigenous group for 25 years, traveled to a remote area of the Finisterre Range of Papua New Guinea to conduct the study.

...

The indigenous Yupno in this area number some 5,000, spread over many small villages. They are subsistence farmers. Most have little formal schooling, if any at all. While there is no native writing system, there is a native counting system, with precise number concepts and specific words for numbers greater than 20. But there doesn't seem to be any evidence of measurement of any sort, Nunez said, "not with numbers, or feet or elbows."

"After confirming the Yupno participants' understanding of numbers with piles of oranges, the researchers gave the number-line task to 14 adults with no schooling and six adults with some degree of formal schooling. There was also a control group of participants in California.

The researchers found that unschooled Yupno adults placed numbers on the line (or mapped numbers onto space), but they did it in a categorical manner, using systematically only the endpoints: putting small numbers on the left endpoint and the mid-size and large numbers on the right, ignoring the extension of the line — an essential component of the number-line concept. Schooled Yupno adults used the line's extension but not quite as evenly as adults in California.

"Mathematics all over the world – from Europe to Asia to the Americas – is largely taught dogmatically, as objective fact, black and white, right/wrong," Nunez said. "But our work shows that there are meaningful human ideas in math, ingenious solutions and designs that have been mediated by writing and notational devices, like the number line. Perhaps we should think about bringing the human saga to the subject – instead of continuing to treat it romantically, as the 'universal language' it's not. Mathematics is neither hardwired, nor 'out there.'"
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And maybe they've stumbled across an explanation for PNG time?

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"The researchers ran several experiments while in Gua, Papua New Guinea, including those that examine another fundamental concept: time.

When talking about past, present and future, people all over the world show a tendency to conceive of these notions spatially, Nunez said. The most common spatial pattern is the one found in the English-speaking world, in which people talk about the future as being in front of them and the past behind, encapsulated, for example, in expressions such as the "week ahead" and "way back when."

In their time study with the Yupno, now in press at the journal Cognition, Nunez and colleagues find that the Yupno don't use their bodies as reference points for time – but rather their valley's slope and terrain.

Analysis of their gestures suggests they co-locate the present with themselves, as do all previously studied groups. (Picture for a moment how you probably point down at the ground when you talk about "now.") But, regardless of which way they are facing at the moment, the Yupno point uphill when talking about the future and downhill when talking about the past.

Interestingly and also very unusually, Nunez said, the Yupno seem to think of past and future not as being arranged on a line, such as the familiar "time line" we have in many Western cultures, but as having a three-dimensional bent shape that reflects the valley's terrain."

http://www.eurekalert.org/pub_releases/2012-04/uoc--sft042312.php

[Peter Kranz]

Watch for Geoffrey's new book "The Cultural Development of Mathematical Ideas" based on his studies with the Oksapmin.

http://www.amazon.com/Cultural-Development-Mathematical-Ideas-Computational/dp/0521761662

Hey Geoff - it's a bit expensive!

Geoffrey - on a theoretical level, do you accept the Sapir-Whorf hypothesis that our language helps determine our conceptual understanding of the world around us, and therefore our perceptions/conceptions are relative to our surroundings and culture?

I believe this idea has fallen into disfavour recently, but I always thought it rather enlightening - especially when applied to Anthropology.

It helps explain some of the misunderstandings western social scientists have exhibited when seeking to explore other cultures.

On the one hand we have Peter Winch - my old Uni teacher, sadly deceased - (The Idea of a Social Science...) who argues that social constucts are determined by language and are relative; on the other we have Chomsky and 'depth grammar' wherein all humans share a deep-seated universal way of interpreting the world based on the fundamental ways in which the brain works.

[Peter Kranz]

Wow, Geoffrey, thanks for your words.

I never realised that some of the people we talk about might be reading our comments! (S'pose I'd better be careful in future.)

All the best. And I thoroughly recommend that people visit your site and see the video of Oksapmin kids counting in base 27, which is pretty special.

[Geoffrey Saxe]

Hi Peter - You might find this site of interest... http://www.culturecognition.com/

The site provides video support for a forthcoming book on some of my work in Oksapmin communities (1978, 1980, 2001).

Enjoyed seeing the back and forth between Gapsy and you!

[Gapsy Selkambang]

Absolutely true, thanks Peter.

In our society, the counting system starts at an early age starting with the right hand..thumb and gets on easily.

I do recall our parents & our grandparents would hold our hands and teach on how to count...it has obviosly helped us Oksapmins to get along with world.

It's still taught in our elementary schools and students naturally become good in math.

[Peter Kranz]

Gapsy - Can you tell us more about Oksapmin counting?

And by the way, being civilised in my experience is nothing much to do with being in a remote area, or having been subjected to western ideas. In fact the reverse is often the case.

[Gapsy Han Guhyem]

As an Oksapmin folk, I am delighted and glad that we Oksapmins were civilised despite being labelled by many as one of the remotest places in PNG.

[Peter Kranz]

You can use any number as a base for counting.

When you get down to the 'basics' computers only use base 2 - or binary - ie. 0 and 1.

This works perfectly well, though its a bit tedious.

Eg. 1111101000 = 1,000

The higher your base is, the more compact your counting and arithmetic can be.

So the Oksapmin were way ahead of their time in inventing a base 27 system.

Like I said once before - the Garden of Eden where all God's truth originated - must have been in the Highlands of PNG.