August 20, 2004

One, two, many -- or 'small size', 'large size', 'cause to come together'?

According to this 8/20/2004 Reuters story, Peter Gordon from Columbia University spent a few months in the Amazon with Dan and Keren Everett, testing the counting skills of the Pirahã, whose "words for numbers appear limited to 'one,' 'two' and 'many,' and the word for 'one' sometimes means a small quantity".

The article quotes Gordon as saying that "In all of these matching experiments, participants responded with relatively good accuracy with up to 2 or 3 items, but performance deteriorated considerably beyond that up to 8 to 10 items", despite the fact that "Piraha participants were actually trying very hard to get the answers correct, and they clearly understood the tasks."

Although I haven't asked Peter or Dan what they think, this story (though I suspect not its headline) seems to be a fairly accurate representation of their point of view. If so, it may be because the 400 word article contains about 250 words of direct quotations from Peter. From what I can tell, the article does manage to misspell the name of the tribe and its language, which doesn't matter much, and to state the central linguistic facts incorrectly, which does matter a bit, because it makes the situation seem less interesting that it really is. But in comparison to what one often sees, this is not too bad.

Dan's website links to an "abstract for paper in progress" called "On the absence of number and numerals in Pirahã". In the Documents and Papers section of Peter's website, there's a movie "[showing] a Pirahã participant using fingers and Piraha count words to enumerate quantities". There is also a wikipedia article on Pirahã.

The first small problem with the Reuters article is that the usual spelling for the language is "Pirahã", with a tilde over the final /a/, indicating that the vowel is nasalized. I suppose that Reuters has a policy against using diacritics in English-language articles, so this transduction is expected, and not relevant to the main point in any case.

The other problem with the article is a bit more interesting. As Dan's abstract explains, the relevant Pirahã noun qualifiers are actually /hóì/ (i.e. "hoi" with falling tone) meaning "small size or amount"; hòí (i.e. "hoi" with rising tone) meaning "large size or amount"; and then phrases like /bá à gì sò/ meaning "cause to come together". Dan chooses to call these "qualifiers" rather than "quantifiers" because he feels that they are not really "words naming numbers" at all. For example, someone who asks for "hóì fish" (if you'll forgive the mixture of Pirahã and English here -- see Dan's abstract for the real Pirahã phrase) is really asking for a small amount of fish, which could be one or two fish, or perhaps a small fish. It could not, crucially, be used to ask for one large fish. Someone who asks for "hòí fish" is really asking for "a {big/big pile of/many} fish".

Dan's point is that Pirahã is "lacking number and numerals entirely", and that "the very concept of counting is foreign to the Pirahãs". At the same time, their language does have a distinction between count and mass nouns, so that there is the equivalent of the English difference between "{many/*much foreigners}" and "{*many/much manioc meal". Again, see Dan's abstract for the details.

This is quite different from -- and more interesting than -- the Reuters statement that "their words for numbers appear limited to 'one,' 'two' and 'many,' and the word for 'one' sometimes means a small quantity".

As for the article's headline -- "Tribe has best excuse for poor math skills" -- I guess the kindest thing to say would that it attempts to relate the topic to the life experience of the audience.

But compared to some previous language-related stories, this one seems pretty good.

[Update: this article in the Toronto Globe and Mail is much better than the Reuters story, and also (unlike the Reuters story) mentions the new article in Science that is the reason for the item in the first place. The article in the Telegraph features explicitly Whorfian reactions from a variety of researchers, quoted from the news piece by Constance Holden in Science -- but the Telegraph mistakenly says that the article was published in Nature.

If you have a subscription to Science, you can read Holden's discussion (COGNITION: Life Without Numbers in the Amazon Science 2004; 305 (5687) : 1093a, in News of the Week), and the Gordon article itself.]

In fairness to Reuters, the "one-two-many" mistake is strongly encouraged by Gordon's Science article, whose abstract reads:

Members of the Pirahã tribe use a "one-two-many" system of counting. I ask whether speakers of this innumerate language can appreciate larger numerosities without the benefit of words to encode them. This addresses the classic Whorfian question about whether language can determine thought. Results of numerical tasks with varying cognitive demands show that numerical cognition is clearly affected by the lack of a counting system in the language. Performance with quantities greater than 3 was remarkably poor, but showed a constant coefficient of variation, which is suggestive of an analog estimation process.


[Update #2: The author of the entangledbank weblog emails with more flavorful Pirahã lore:

You don't reference this article in your latest Language Log: Everett discusses not just numerosity but other astonishing claims about Piraha language/culture: no embedding, no quantification, no creation legends, no fiction, no deep memory, no colour terms, pronouns borrowed, simplest kinship system, no relativization, no perfect. If even part of this is true it's a huge challenge to conventional wisdom. None of it reads as obviously loony, but I have to wonder whether he's some Borgesian fantasist, or some Margaret Mead being stitched up by the locals, because this is weird beyond most parameters. His glosses are highly suspect, with a deliberate Bloomfieldian strangeness. And the business about nominalized clauses is really shonky: by that standard any non-finite clause (I like to-go, I like ski-ing) is nominalized, depending on how alienly you translate the morpheme.

I have suggested that the one/two versus small/big distinction is not completely unlike English 'a'/'a couple of'. It's culturally conditioned by what artefacts are available and expected: 'a' basically means 'one', but if you're hammering and ask someone for a nail there's no strong pragmatic violation in being given several. Likewise 'a couple of' for many people means 'several', 'two or so'. So we have a precedent for numerals also having a less definite quantificational aura.

I agree that the lack of a number system seems to be the least of the interesting claims here. But I should add that Dan Everett is a skilled and reliable observer, and a number of other excellent linguists have spent time with the Pirahã in his company. So the Borgesian fantasy theory can be dismissed out of hand, I think. And it's hard to see why the Pirahã would have any motivation to play an elaborate linguistic and cultural joke on Dan (and everyone else) over so many years; and even harder to imagine how they could carry it off.

One point worth stressing, though, is that Dan Everett's account of what is going on is opposite to the way that Gordon and other are stating things: they're talking about the influence of language on thought, but Dan's discussion is mainly about the influence of culture on language. Specifically, he argues that

... these apparently disjointed facts about the Pirahã language -- gaps that are very surprising from just about any grammarian's perspective -- ultimately derive from a single cultural constraint in Pirahã, namely, to restrict communication to the immediate experience of the interlocutors, as stated in (1):

a. Grammar and other ways of living are restricted to concrete, immediate experience (where an experience is immediate in Pirahã if it has been seen or recounted as seen by a person alive at the time of telling).
b. Immediacy of experience is expressed by immediacy of information encoding -- one event per utterance.


[Update 8/26/2004: a fascinating set of comments by Dan Everett, introduced by Geoff Pullum, is here. ]

[Update 8/27/2004: and comments by Peter Gordon, author of the Science article, are here]


Posted by Mark Liberman at August 20, 2004 10:16 AM