Piraha

[Baker, John]

        Gordon's original article, setting out his research and number claims in more detail, was originally published in Science 15 October 2004:  Vol. 306. no. 5695, pp. 496 - 499.  In the same issue, Pierre Pica and others published an article on the Mundurukú, an Amazonian tribe with number words up to 5.  They concluded:


        <<Together, our results shed some light on the issue of the relation between language and arithmetic. They suggest that a basic distinction must be introduced between approximate and exact mental representations of number, as also suggested by earlier behavioral and brain-imaging evidence and by recent research in another Amazon group, the Pirahã. With approximate quantities, the Mundurukú do not behave qualitatively differently from the French controls. They can mentally represent very large numbers of up to 80 dots, far beyond their naming range, and do not confuse number with other variables such as size and density. They also spontaneously apply concepts of addition, subtraction, and comparison to these approximate representations. This is true even for monolingual adults and young children who never learned any formal arithmetic. These data add to previous evidence that numerical approximation is a basic competence, independent of language, and available even to!
  preverbal infants and many animal species. We conclude that sophisticated numerical competence can be present in the absence of a well-developed lexicon of number words. This provides an important qualification of Gordon's version of Whorf's hypothesis according to which the lexicon of number words drastically limits the ability to entertain abstract number concepts.

        What the Mundurukú appear to lack, however, is a procedure for fast apprehension of exact numbers beyond 3 or 4. Our results thus support the hypothesis that language plays a special role in the emergence of exact arithmetic during child development (9-11). What is the mechanism for this developmental change? It is noteworthy that the Mundurukú have number names up to 5, and yet use them approximately in naming. Thus, the availability of number names, in itself, may not suffice to promote a mental representation of exact number. More crucial, perhaps, is that the Mundurukú do not have a counting routine. Although some have a rudimentary ability to count on their fingers, it is rarely used. By requiring an exact one-to-one pairing of objects with the sequence of numerals, counting may promote a conceptual integration of approximate number representations, discrete object representations, and the verbal code. Around the age of 3, Western children exhibit an abrupt chan!
 ge in number processing as they suddenly realize that each count word refers to a precise quantity. This "crystallization" of discrete numbers out of an initially approximate continuum of numerical magnitudes does not seem to occur in the Mundurukú.>>


Science 15 October 2004:  Vol. 306. no. 5695, pp. 499 - 503 (footnotes omitted).


John Baker


-----Original Message-----
From: American Dialect Society [mailto:ADS-L at LISTSERV.UGA.EDU] On Behalf Of Arnold M. Zwicky
Sent: Thursday, April 19, 2007 11:50 AM
To: ADS-L at LISTSERV.UGA.EDU
Subject: Re: Piraha

On Apr 18, 2007, at 10:05 AM, Wilson Gray wrote:

> Isn't "They can count only to two" an antiquated fallacy, based on a
> misunderstaning of the way that the culture uses number, that was
> first applied to the languages of Australia a century ago?

the claim is about counting in the sense of distinguishing groups of different size, not in the sense of having number words for counting.  here's the relevant piece of the New Yorker article, about Peter Gordon:

During a two-month stay with the Pirahã in 1992, Gordon ran several experiments with tribe members. In one, he sat across from a Pirahã subject and placed in front of himself an array of objects-nuts, AA batteries-and had the Pirahã match the array. The Pirahã could perform the task accurately when the array consisted of two or three items, but their performance with larger groupings was, Gordon later wrote, "remarkably poor." Gordon also showed subjects nuts, placed them in a can, and withdrew them one at a time. Each time he removed a nut, he asked the subject whether there were any left in the can.
The Pirahã answered correctly only with quantities of three or fewer.
Through these and other tests, Gordon concluded that Everett was
right: the people could not perform tasks involving quantities greater than three.
-----

in this sense of "counting", some animals can count, at least a bit.
crows, in particular, have been claimed to be able to count to three, four, or five, depending on who you read; as i recall, the experiments that have been done are versions of the subtraction task, though without the mediation of language.  and of course crows have no number words.

now, there are languages with, in a sense, only two number words.
(i'm away from my sources and am doing this from memory, so be
tolerant.)  however, speakers of these languages can count, in both
senses: they can distinguish groups of objects of various sizes, and they have a way of assigning names to these sizes.  let "x" be the word denoting 1 and "y" the word denoting 2.  then you count:

x
y
y x
y y
y y x
y y y
y y y x
y y y y
...

this is a purely additive system, and it gets tedious fast.  it's really only practical if you're not interested in counting very high, and of course there are cultures where there's no need to count very high.  (the need for counting no doubt comes with agriculture.)

the Pirahã just represent the limiting case.  knowing about systems like the one above, you could have predicted that eventually someone would find a group like the Pirahã.  dan everett seems to have been that lucky linguist.

arnold

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