## Numbers and Amazonian Tribes

The Guardian has a great extract from Alex Bellos‘ new book Alex’s Adventures in Numberland. Besides sounding like the title to a mathematician’s experimentation with LSD, the book dedicates a section (the abstract in the Guardian) on the work of  a linguist, Pierre Pica, and his discovery that the Munduruku tribe only count up to five. Although even this claim is dubious:

When there was one dot on the screen, the Munduruku said “pug“. When there were two, they said “xep xep“. But beyond two, they were not precise. When three dots showed up, “ebapug” was said only about 80% of the time. The reaction to four dots was “ebadipdip” in only 70% of cases. When shown five dots, “pug pogbi” was managed only 28% per cent of the time, with “ebadipdip” given instead in 15% of answers. In other words, for three and above the Munduruku’s number words were really just estimates. They were counting “one”, “two”, “three-ish”, “four-ish”, “five-ish”. Pica started to wonder whether “pug pogbi“, which literally means “handful”, even really qualified as a number. Maybe they could not count up to five, but only to four-ish?

The whole article reminded me of another Amazonian tribe, the Pirahã, and how they don’t even have a numerical system. In fact, many of the Amazonian tribes and languages are throwing up some interesting findings, like a restricted numerical system and the absence of both quantifiers and grammatical tense. For those of you interested, I’d recommend reading Dan Everett’s book (Don’t Sleep There Are Snakes) on his experiences with the Pirahã.

1. Jason Malloy could perhaps give an estimate of the IQ of these Amazonian tribes? – such peoples usually come out around 50-60 – or roughly equivalent in general intelligence to an average 8-10 year old European.

IQ therefore should at least be considered as an explanation for much lower complexity of language in such peoples.

Does anyone know whether different average levels of average IQ actually has been considered as a potential factor influencing language complexity, by these authors?

2. Actually, the languages of these groups tend to be morphologically more complex. So it’s not really an issue of tribes lacking language complexity. Languages in larger groups, such as users of English, are instead much more likely to use lexical strategies to encode evidentiality, negation, aspect, and possession.

There are several good papers in explaining, and providing reasons for, the differences between small communities and large communities of language users: Wray & Grace (2007) and Lupyan & Dale (2010).

3. Amazingly, there is IQ data for the Munduruku. And yet I can’t locate IQ data for the entire nation of panama.

4. Their IQs are probably about average. Do not confuse information with IQ. If they made an IQ test based upon what was considered important in their world you would probably score in the 50s. Our current IQ tests are very language based. They rarely test hand-eye coordination etc. Can you walk on your hands, can you tell a minor chord from a major chord? Can you discriminate two different types of basil by smell or taste? There are people who can do these things. I would love to design a test that is based more on sensory data than language and reasoning.
Do you know what plants to eat in Amazon that any 8 year old would know? If you were left in the forest there how long would you survive compared to the normal tribesman? Self-care is a pretty good gauge of intelligence. Significantly mentally retarded people (IQ=50) cannot care for themselves in any settings. It seems impossible that a person with an IQ of 50 or 60 could obtain: food, shelter, and security in such an environment. In many ways it is a more difficult environment to survive than ours, which would suggest they may have higher IQs as the low IQ people would die off.
A good test would be the Prince and Pauper scenario. Put an untrained Westerner in the Amazon and a tribesman in NYC and see who learns fastest. There is an old saying that the answers to toughest physics questions lie in the mind of some ghetto kid due to the exposure of a different culture; compared to the engineers who have all been trained the same way.

A better test for someone who uses sensory or physical movement to survive might be how fast can they pickup on sports or reaction times. Reaction time has shown some correlations with IQ and age.

While the tribesman may take a really long time to become competent. It is likely the Westerner would die before he would learn. You really do not have to be really smart to survive in the Western world.

5. If you are asked to say how many similar items there are in a collection, the answer depends in part on the testing method. If the testee is required just to look at the collection and say immediately how many items there are, the limit of reliable replies is about seven – i.e. if there are more than seven items, most people are unable to count them ‘at a glance’. If the testee is allowed to take plenty of time to count them, the limit is of course higher, but if the items are arranged in an irregular pattern people still ‘lose count’ fairly soon. Without knowing the testing regime used for these Amazonian people, the result is practically meaningless.

6. drHoward:

Most of your observations are quite reasonable; but you’ve erred significantly with your “Prince and the Pauper scenario”: you’ve botched any meaningful or even partially reliable conclusion being taken by comparing “apples to oranges.”

You’d exchange environments: an untrained westerner to the Amazon for an Amazonian tribesman to NYC. But, in the book (the reading of which, for me, was about 65 years ago), the “experiment” involved “changelings,”–infants separated at or shortly following birth–thus satisfying an elementary requirement of any “scientific” conclusion (that of control over significant “variables”–in such case the socialization eliminated by the age at which the exchange took place).
to oranges”

7. “a test that is based more on sensory data than language and reasoning.”

One that would lose all that nasty predictive ability. One at which myopes would do poorly and coyotes excel.

Chimps know more about which African wild plants are safe to eat than I do. I guess they’re smarter than me. And they survive in the wild.
I guess _they_ must have an IQ above 50. And turtles survive in the wild, so… I am reminded of a discussion in which most of the class argued that pigs are just as smart as people, in their own way. Now that I think of it, those undergraduates were pretty good evidence for their position.

Sarcasm off, scores on western-designed IQ tests are what matter, because they do a fair job of predicting achievement in western-influenced technological societies – which are the only societies that matter. When hunter-gatherers figure out how to beat those technological societies – when they can trump fusion bombs, jets, Iphones and penicillin – then their other ways of knowing will be worth revisiting. I’m not holding my breath.

8. ‘roughly equivalent in general intelligence to an average 8-10 year old European’

You are using a definition of IQ that is a hundred years old and almost as out of date. The last place I remember seeing it in an academic context was my mother’s undergraduate psychology textbooks from the 1970s. The intelligence of adults and adolescents is pretty incommensurable and in any case you can’t get ‘mental age = IQ/100 * age of adulthood’ (even if the tests once claimed this, long ago).

‘If they made an IQ test based upon what was considered important in their world you would probably score in the 50s.. [blah, blah]‘.

People who design these tests are quite familiar with the issues you describe. Don’t teach your grandma to suck eggs.

9. Do the amazon natives have a hard time learning about counting when exposed to the idea? Or learning the number words when they pick up a different language? There are three different things subject to evolution here–the natives’ brains, their language, and their culture. Any combination of them might be responsible for lacking the ability to count.

I suspect drHoward is right that someone who couldn’t handle the level of mental abstraction necessary to count past five would find it impossible to survive as a human in a difficult environment. My unschooled impression is that hunter-gatherers in remote places usually use quite a bit of passed-on-to-kids knowledge about hunting, making tools, food/poison/medicine plants, dangerous animals, etc., and that they typically need to be able to remember and describe past events and plan out future ones. It seems a lot more plausible to me that you’d lose the specific language/culture pieces for counting through disuse and mutation/drift/whatever than that you’d lose the mental ability to count. (Though I’m assuming that counting makes use of a general-purpose set of mental tools, rather than some single module that might have been lost with little impact on other stuff.)

10. I remember reading in a book of Czech globetrotters Hanzelka and Zikmund written in 60′s about counting of Xivaros (those making tsantsa heads…).
They counted up to ten, but remembering the numbers over six needed a co-work of the whole great-family. And yes, 10 was “I ended both hands”.

11. I have spent a lot of years with Northern Bush speakers in the Kalahari. They have words for one, two, three, and four (sort of: two-two literally.)

On the other hand I have watched my Bushman employees in local stores hand over a five pula note to pay 2.30 for something, count the change, and verify that it was correct.

Beats me how they were doing it.

Henry

12. Henry: actually that seems extremely interesting. As in, dissociating “numeracy” from “number-words”. Or perhaps simply showing that our experimental methods for assessing numeracy in non-literate societies are wrong.

(Well, either that, or maybe your employees were actually performing base-3 / base-10 conversions in their heads ;) )

13. Henry,

Did you actually ever see them dispute the change they received?

I’ve experienced people doing the same – very low IQ farm laborers in Ireland – glancing at their change and poking a coin/note or two and then quickly pocketing it. When asked how they calculate and verify the change so quickly, they invariably answer, “It looks about right” – in other words they aren’t actually counting or verifying anything, just going through the motions to try and defray the other person from cheating them?!