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More on arithmetic in the Amazon
October 31, 2004 3:37 AM   Subscribe

More on arithmetic in the Amazon The 10/15 issue of Science has the official publication of Peter Gordon's work on numerical cognition among the Pirahã, and a companion article by Pierre Pica et al. on similar research among another Amazonian tribe, the Mundurukú. What with the U.S. election and the discovery of H. Floresiensis, this is not getting nearly as a much play as the pre-publication back in August of Peter Gordon's work. Brian Butterworth has an piece in the Guardian about both articles, and I've put some links, quotes and diagrams here. Compared to the reports on the Pirahã, the Mundurukú people, language, and experiments are all somewhat different, although the conclusions are broadly similar.
posted by myl (19 comments total) 1 user marked this as a favorite

 
why is this a big deal? it seems to me that the sappir-whorf is one of those things that is either interesting when interpreted in an extreme way that's not consistent with what we see, or states the uninteresting obvious when it is consistent with what we see.

here, people don't need to count, have no tradition of counting, and no cultural support for it. they cannot count and don't have the language for it. seems fair enough. what else do you expect? a bunch of intuitive mathematical wunderkinds that build piles of stones grouped in prime numbers without knowing why? of course not.
posted by andrew cooke at 4:27 AM on October 31, 2004


"here, people don't need to count, have no tradition of counting, and no cultural support for it. they cannot count and don't have the language for it. seems fair enough. what else do you expect?"

This is broadly speaking what I'd expect, FWIW, as I wrote here. But it's not what Sapir and Whorf thought -- they believed in the "formal completeness" of language as well as in the "tyranny" of language in predisposing habits of thought. And it's not what many present-day psychologists would have expected: some are still reluctant to believe that determining equivalence of small (<10) set cardinalities is not part of the general human cognitive toolkit.
posted by myl at 5:17 AM on October 31, 2004


ok, i don't have a clue about this, but as far as i see this doesn't mean that the language isn't formally complete. you wouldn't ned to teach these people english before they could do maths - you'd just need to give them good reason to need to learn to count. they already have sufficient language to count in binary. that's all you need.
posted by andrew cooke at 5:36 AM on October 31, 2004


having just read couple more links, i think my problem is that i don't see how you can separate cause and effect. why is it the language that is restricting how people think? why isn't it that people simply don't have words for things they don't think? is there something that explains this clearly?
posted by andrew cooke at 5:59 AM on October 31, 2004


It's frustrating reading high level popular articles like this. So many details! The one thing I really want to know; the article makes a curious assumption that subtraction is an innate skill that all people should have. Ie: "because they can't subtract, it must be because they have no words for big numbers". Isn't it simpler to assume they can't subtract just because, well, they've never needed to? No linguistic argument required.
posted by Nelson at 7:17 AM on October 31, 2004


I think I guessed the point of that research:

Starting from having absolutely no concept of quantities, numbers , counting ...

1. At some point in time, me and some other aborigen see apples ..out of experience we know "how much apple" are enough to satisfy our hunger..so I get apple, apple, apple (3). The other aborigen needs one less, so he gets apple, apple(2). Then I go home and tell my aborigen family about the meeting with another man, who wanted apple.

2.As I probably already ate some apples on the way home I need to show the apples I had got, or the apples the man had got..but I don't "know how to count" so i get some objects resembling apples in quantity and shape and show them to family..somewhere along the timeline the word "gnagna"=1 is invented and used long enough to become part of vocabulary.

3.Given the lack of the concept of "number" (and corresponding word) and given the lack of the process of "counting" (and corresponding word) what we have is that the word "gnagna"=1 is a visual representation of a quantity (one apple), but no more no less then that.

4. Let's imagine I aborigen have a powerful intuition about a counting method, proceed to explain to my fellow aboringes which in turn are amazed ; after doing that I need a word to describe the process I've just shown them..otherwise, in a culture in which knowledge is transfered orally, my method will probably be lost. I could call the counting method "zfutsu" or "bahwah" and it wouldn't matter..but to have this label stick long enough on the process I have to make a new word for a method never seen before.

5. But first I have to invent a "word" that has no physical representation in tangible world..I need a language flexible enough to allow word to exist without physical representation or manifestation (see tiger, feel fear -> word fear)

6. What the researcher are trying to look after (guess) is some relation between vocabulary and number processing in "primitive" human beings.

Running out of time, cya
posted by elpapacito at 7:39 AM on October 31, 2004


Perhaps they should take advantage of the Bush No Native South American Tribe Left Behind" program
posted by Postroad at 7:46 AM on October 31, 2004


here is a summary of the work i know on innate counting skill - seems that's controversial too.
posted by andrew cooke at 7:54 AM on October 31, 2004


excellent thread! The fpp was a great read, and the follow-up links by myl and andrew cooke helped me to grapple with what is at stake in this argument. This is a case study in why I love metafilter! thanks!
posted by limitedpie at 8:46 AM on October 31, 2004


I find it interesting simply because I guess I've always been lead to believe that math was a part of reason, and that reason was innate, and outside of what I learn from my culture. For instance, if I grew up alone on an island, I might not have a language, but I would still probably know that if I eat three fish a day for two days, I will have eaten six fish. But that's apparently not necessarily true. The words these tribes use for the concept of four can also be the same word they use for the concept of three.

This has a lot of ramifications; for one thing, doesn't it mean you could mount an argument that our mathematics is not justified because of its internal consistency, but because of group consensus? Which is just totally fucked up.
posted by Hildago at 12:08 PM on October 31, 2004


maths isn't going to collapse because people say "some fish" instead of "four fish".
posted by andrew cooke at 3:42 PM on October 31, 2004


Ughh. Linguistics? Epistemology? Neuropsychology? Why don't we just recapitulate, badly and in ignorance, at least a couple thousand years of speculation on the nature of the human mind and reality and cloak it in the "authority" of a narrow, contemporary discipline?

That'll be fun. It's always is, isn't it?
posted by Ethereal Bligh at 6:34 PM on October 31, 2004


The intuitive internal consistency of math collapses as early on as x²+1=0. You have to jury-rig a scaffolding around the problem just to continue to have a working system. Despite the name, you can't really imagine imaginary numbers--at least I can't--and therefore they don't derive from intuition.

I'm not trying to collapse mathematics, nobody is, but, like in any other field, you could probably mount an argument against our assumptions about mathematics that would cause us a certain amount of dread. The fact that these tribes don't have the concept of a discrete number is very unsettling, no matter what you say.

And ethereal, I have no idea what the content of that message was supposed to be.
posted by Hildago at 8:25 PM on October 31, 2004


Some comments by Pierre Pica, the lead author of the paper on the Mundurukú, can be found here, along with links to a copy of the paper and some other relevant research.
posted by myl at 4:22 AM on November 1, 2004


myl: Excellent post!

EB: I too am completely baffled.
posted by languagehat at 6:59 AM on November 1, 2004


For the many of us that are semi-numerate, i think this is great--No dread here at all. The tyranny of numbers will be toppled, my comrades! ; >

(And this is reminding me--i'm reading Quicksilver, and some just got watches with a seconds hand for the first time, so are timing everything now, and dictating things to people speaking, like "50 seconds!" "20 seconds!" etc)

And in the Guardian article, they talk of using a computer screen to give a counting test to a remote tribe--?!? Why use technology they don't know? How could that be the right way to ascertain what they can do/recognize/conceive?

I think EB's saying that we shouldn't try to fit the whole universe into any one theory, especially a new theory, not fully confirmed.
posted by amberglow at 8:11 AM on November 1, 2004


Amberglow's very close to correctly interpreting my cryptic and sarcastic comment.

My frustration is that the discussion of this particular study (and those like it) invites laypeople to make sweeping assertions (or speculations) about some fundamental issues in complete or nearly complete ignorance of the work done previously in the fields that are directly related to these fundamental issues. Furthermore, my experience is that the situation is hardly improved with regard to those who have expertise in one of these fields—because they rarely have expertise in the others and consequently make sweeping assertions or speculation in a similar ignorance (of the other fields) as the folks who don't know anything at all.

S-W, for example, is extremely naive (not necessarily right or wrong—just "naive" as in "elementary") epistemology.

In each and every contemporary speciality that concerns itself with the human mind and its comprehension of the universe (and this implicitly includes linguistics), I see a core ideology with related hidden assumptions. In some cases the ideologies and assumptions are similar from one speciality to another. In other cases they are very antagonistic. But they're almost always unquestioned. Philosophy itself is more self-critical of its ideologies and assumptions, but to compensate for this maturity it has the defect of being largely ignorant of most everything that happens in the practical world, including much of everything discovered by science.

My expertise varies widely from one discipline to another, and rarely does it approach anything that could fairly be called "expertise". Even so, my experience is wide and deep enough to at least be aware of, for example, the implicit mathematical debate between formalism and platonism in some of the above discussion in comments, the well-established linguistic work regarding number words in languages, [insert philosophy example here—there's too many to choose from, so I couldn't], etc. etc. And so I just boggle when someone argues whether or not subtraction is rationally necessary because I'm immediately siezed by a cascade of recollections of lines of argument from what I know of how various disciplines have long grapped with this essential question. From my pespective, it's like people keep confidently imagining that they've discovered perpetual motion as if no one has really considered the idea before. A linguist suddenly has a theory of Mind. No, wait, here's a neurologist with the theory of Mind. Over there, the AI researcher. Oops, no, the epistemologist has it all figured it out. Or just a group of laypeople who've learned of this or that study or one of these specialist's brilliant, ambitous theories. I certainly don't have the answers. But this is almost always an example of the blind men and the elephant debacle. It seems to me. But I'm really grouchy today.
posted by Ethereal Bligh at 8:57 AM on November 1, 2004


it really is like the blind men and the elephant, which, of course, proves that ancient parables are the true universal theories. ; >

I'm an Aesopian, and i approve this message
posted by amberglow at 9:28 AM on November 1, 2004


Oh, ok. I've now discussed this article with various people on and off line, and nobody is sharing or even really agreeing with my reaction to it, so probably I'm just grinding an axe I didn't know I had.
posted by Hildago at 9:35 AM on November 1, 2004


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