Amazonian tribe and maths

April 1, 2010 7:45 AM

Does a group of indigenous South Americans hold the key to our relationship with maths? Still, I thought it odd that numbers larger than five did not crop up at all in Amazonian daily life. What if you ask a Munduruku with six children how many kids they have? "He will say, 'I don't know,'" Pica said. "It is impossible to express."
posted by selton (63 comments total)

I don't totally buy that they aren't able to count children beyond five (that has the smell of a great joke to play on a visiting anthropologist, or of a mistranslation of a cultural norm, maybe), but the logarithmic thing made a lot of sense to me. I think all of us use numbers in both ways -- linearly for ages and measurements, but in ratios or log form for concepts and guesses. Neat stuff.
posted by Forktine at 7:55 AM on April 1, 2010

Half of the discussion in the Guardian's comments is whether the article is an April fools joke or not.
posted by selton at 7:55 AM on April 1, 2010

Sign me up as the first sucker then. If it is a joke, it has a tone that perfectly matches any number of articles about anthropology in the popular press. I like it either way, honestly.
posted by Forktine at 7:58 AM on April 1, 2010

Numbers are a burden to others, and integers a prison to oneself.

(not really, but it would be nice to take a vacation from numbers for awhile.)
posted by chambers at 7:59 AM on April 1, 2010

This was covered on Radiolab a while back. (I think that's the right ep.)
posted by kmz at 8:03 AM on April 1, 2010

This non-April article from 2004 is about the same researcher and tribe.
posted by burnmp3s at 8:03 AM on April 1, 2010

I thought the tribe With no tenses, plurals or numbers was the Piraha, who also don't have colors if my memory serves me right.
posted by dunkadunc at 8:04 AM on April 1, 2010

Previously on MeFi (although the tribe name is different): 1, 2
posted by rocket88 at 8:06 AM on April 1, 2010

Silly natives, only counting to 5.

Seriously though, 24 is the highest number.
posted by 2bucksplus at 8:06 AM on April 1, 2010 [5 favorites]

The date on the URL is March 31st not April 1st...
posted by zeoslap at 8:14 AM on April 1, 2010

I thought the tribe With no tenses, plurals or numbers was the Piraha, who also don't have colors if my memory serves me right.

Previously on MeFi (although the tribe name is different): 1, 2

Turns out it's two-ish different tribes.
posted by molybdenumblue at 8:20 AM on April 1, 2010 [5 favorites]

This reminds of a story I heard about a man who had always lived in a jungle. When he went with a researcher out of the jungle into a great open space for the first time he pointed to a person some distance away and said something like "look at that tiny little person!" In the jungle there are no distant views, so his understanding of perspective had not developed.
posted by mareli at 8:20 AM on April 1, 2010

(I'm a member of a North American tribe that has no concept of a plural form of "math")
posted by rocket88 at 8:21 AM on April 1, 2010 [23 favorites]

There was a RadioLab that covered the log thing before and it really intrigued me. I started wondering if you could recast arithmetic into "natural numbers" i.e. logs. Would that be easier to understand for kids? Would it confer some elegance (similar to using radians instead of degrees)? Unfortunately, logs frighten and confuse me so I didn't go much past wondering.

The basic problem is this:
Raising regular numbers to a power is the same as multiplying logs.
Multiplying regular numbers is the same as adding logs.
Adding regular numbers is the same as whating logs?
posted by DU at 8:33 AM on April 1, 2010

(And yes, I already know about slide rules. Basically: How can I add numbers on a slide rule.)
posted by DU at 8:34 AM on April 1, 2010

Back in linguistics undergrad this sort of thing came up a lot. One of the authorities on this is Eugene Chan, who has given us a catalog of the Numeral Systems of the World's Languages. (Kinda weird to navigate. Once you get down to purple language names, you can click to see the description of their number system.)

Here's the entry for Piraha, which dunkadunc metioned. Two words, distinguished only by tone, currently read as meaning "small quantity" and "larger quantity."

I remember this being mind-twisting when I first encountered it. So was my first encounter with the range of color term systems.
posted by mrettig at 8:39 AM on April 1, 2010 [2 favorites]

Does a group of indigenous South Americans hold the key to our relationship with maths?

NO.

When they try to teach math to the children of these people, the kids are able to learn it just fine. Adult's minds are inflexible. This isn't news.
posted by delmoi at 8:53 AM on April 1, 2010

DU

Adding the numbers together then dividing by the radix of the number system in use (i.e. 10).
posted by The Power Nap at 8:57 AM on April 1, 2010

Actually, in my opinion, this is cool precisely because it puts some of Dan Everett's claims about the Pirahã into perspective. Everett likes to throw around absolutes, and to talk about the Pirahã in terms of what they're missing: "The Pirahã have no numbers at all, and absolutely no concept of number, they cannot learn to count, they could never learn to think like we do because their culture includes a constraint against thinking abstractly, blah blah blah."

The claims being made here seem like a more nuanced version of Everett's. The Munduruku have numbers, although they don't always use them precisely; they have a concept of number, but it's not quite the same as ours; they estimate well, but calculate poorly, just like we do when we haven't had much practice; they could probably get better at calculating if they practiced a whole lot, but it isn't relevant to their lives, so they don't.
posted by nebulawindphone at 9:01 AM on April 1, 2010 [3 favorites]

Wait, that's not right at all.
posted by The Power Nap at 9:06 AM on April 1, 2010

The 'exact number sense' is a [uniquely] human property that probably stems from our ability to represent number very precisely with symbols," concluded Nieder. Which reinforces the point that numbers are a cultural artefact, a man-made construct, rather than something we acquire innately.

Am I just failing to understand something, or is this a false dichotomy? Just because we don't acquire something innately, does that automatically make it a "man-made construct"? If "numbers" here means our words and symbols for numbers, all right then; but if we mean the mathematical quantities or entities themselves and their properties, then this statement hugely oversteps reality. "Discovery" seems like a much more accurate description than "cultural artefact" or "man-made construct".
posted by newmoistness at 9:06 AM on April 1, 2010 [2 favorites]

Americans didn't use numbers much 250 years ago. This book is fascinating, or at least it was when I read it twenty years ago.
posted by mareli at 9:08 AM on April 1, 2010

Wait, that's not right at all.

I'm not sure there is any way to do it algebraically. Wolfram Alpha Won't give a general formula for log(x) + log(y)
posted by delmoi at 9:10 AM on April 1, 2010 [1 favorite]

Basically: How can I add numbers on a slide rule.

My father is an old school engineer and he says you cannot do it with the slide ruler.

Yup, I called him on the phone.

Great post !
posted by elmono at 9:37 AM on April 1, 2010

The number of users who like this cannot be expressed.
posted by zerobyproxy at 9:39 AM on April 1, 2010 [1 favorite]

I don't totally buy that they aren't able to count children beyond five

Isn't there some number of things which, if presented to you, you would just say "Dude, I'm not counting those up to figure out how many there are"?

Do you not believe that their words for numbers stop at some point, or do you not believe that 5 is the point beyond which they just don't care about counting?
posted by 23skidoo at 9:51 AM on April 1, 2010

delmoi: mine says
log(x)+log(y) = log(x y) for (x element R and x>0 and y element R and y>0)

Wolfram likes to allow complex numbers at all stages.
posted by a robot made out of meat at 9:54 AM on April 1, 2010

delmoi

I dug it up here.

log(a + b) = log(a) + log(1 + b/a)
posted by The Power Nap at 9:59 AM on April 1, 2010

Look at the number of comments here I cannot count!
posted by toastchee at 10:02 AM on April 1, 2010

they could never learn to think like we do because their culture includes a constraint against thinking abstractly

Dear linguistics: There are some things that you really shouldn't try to model with Optimality Theory. Thanks.
posted by sineala at 10:32 AM on April 1, 2010 [1 favorite]

[W]hile Pica stayed with the Munduruku, he easily slipped into a numberless existence. He slept in a hammock. He went hunting and ate tapir, armadillo and wild boar. He told the time from the position of the sun. If it rained, he stayed in; if it was sunny, he went out. There was never any need to count. [...] For the Munduruku, the whole idea of counting children is ludicrous. Why would a Munduruku adult want to count his children? They are looked after by all the adults in the community, Pika said, and no one is counting who belongs to whom.

*looks around at cubicle and glowing screen at which I will sit all day, makes note to pay bills online, thinks about arranging get together with friend that has to be done at least at week in advance because everybody is so busy, sighs*
posted by jokeefe at 10:36 AM on April 1, 2010 [2 favorites]

Do you not believe that their words for numbers stop at some point, or do you not believe that 5 is the point beyond which they just don't care about counting?

I am surprised by, and slightly suspicious of, the claim that they cannot count their own children beyond five. I'm not saying it's impossible -- people are adaptable and creative and do all kinds of amazing things. It just strikes me as something to which there might be a bit more than the anthropologist first saw, perhaps.

Or it could be totally true, what do I know? That's why this stuff is so interesting -- things one thinks of as universal turn out not to be, and things that we think make us unique often aren't.
posted by Forktine at 10:53 AM on April 1, 2010 [1 favorite]

Here is a previous mefi article about the Pirahã people. I just finished reading the book "Don't Sleep There are Snakes", which I found fascinating from both a linguistic and anthropological point of view.

For more on the debate of color and language, also consider reading "Talking Hands" by Margalit Fox which covers study of the unique sign language that is used by the Al-Sayyid tribe. It's a thoroughly fascinating and well-researched tome.
posted by plinth at 11:03 AM on April 1, 2010

log(a + b) = log(a) + log(1 + b/a)

Er... You're still adding two separate logarithms together.

log(x)+log(y) = log(x y) for (x element R and x>0 and y element R and y>0)

Ah, I missed that. I must not have been looking close enough, but there it is.
posted by delmoi at 11:32 AM on April 1, 2010

(Hmm, actually, reloading the page it doesn't come up with that answer at all. Weird. )
posted by delmoi at 11:40 AM on April 1, 2010

log(a + b) = log(a) + log(1 + b/a)

log(x)+log(y) = log(x y) for (x element R and x>0 and y element R and y>0)

If I may once again reference my complete bafflement of logs (mainly due to unfamiliarity), how does this work in practice.

Here I am, trying to figure out how many fingers and toes I have. I have 1 (that is, log 10) fingers and 1 (again, log 10) toes. I need to come up with 1.3something (that is, log 20).
posted by DU at 12:06 PM on April 1, 2010

among the munduruku pranks are sometimes played weeks before or after april fool's day.
posted by Hammond Rye at 12:24 PM on April 1, 2010 [1 favorite]

So if they can only count up to 5 is 3 still the magic number?
posted by spicynuts at 12:44 PM on April 1, 2010

chambers: ... it would be nice to take a vacation from numbers for awhile.

How many days?
posted by Greg_Ace at 12:53 PM on April 1, 2010 [1 favorite]

I recall reading that someone recently studied the tribe that B. Whorf studied and found all sorts of descriptions of times and durations.
posted by bdc34 at 1:47 PM on April 1, 2010

Here I am, trying to figure out how many fingers and toes I have.

Well, if a=b=10, then a+b = a(1 + b/a) = 10 * (1 + 1), and the log of that is log(10) + log(2) = 1.0 + 0.3, which is what you wanted.

But I don't think that answers your root question. It's correct and useful to say that logarithms transform multiplication into addition. But the converse is that exponentiation transforms addition into multiplication. I can't think of a way to transform that relationship into a statement about addition. In my mind, the natural numbers, succession, and addition occupy a very basic place.

The way you add with a slide rule is you throw away the logarithmic rule and hold two linearly-marked tape measures together.
posted by fantabulous timewaster at 2:57 PM on April 1, 2010 [2 favorites]

The Warlpiri Aboriginal community lives near Alice Springs and has words only for one, two and many.

Warlpiri people have always had words for numbers up to and including 4, and now have words for larger numbers, often based on English pronunciation and the shapes of Arabic numerals. For example, 7 is wirlki - the word for a hook-shaped boomerang that looks like a 7. 8 is milpa (eyes) or mapurlu, from the English marbles - two of each looks like the number 8. 10 is an interesting number - karlarla - mid-morning, 10 o'clock. All have the suffix 'pala' (fella) to distinguish from the root word (so wirlki, boomerang, but wirlkipala, 7).
posted by obiwanwasabi at 3:08 PM on April 1, 2010

Dear linguistics: There are some things that you really shouldn't try to model with Optimality Theory. Thanks.

Heh. Not that sort of constraint. A normal person probably would have said "rule" or "restriction" instead. But I have been writing semantics papers all week and am Not A Normal Person, at least as far as my lexicon is concerned.

It's kind of like how mathematicians can't count and ethicists steal books. You do enough linguistics and suddenly you can't talk good no more.
posted by nebulawindphone at 4:23 PM on April 1, 2010 [1 favorite]

Seriously though, 24 is the highest number .

One, two, many, lots. Don't need more dan dat.
posted by Evilspork at 4:26 PM on April 1, 2010

I recall reading that someone recently studied the tribe that B. Whorf studied and found all sorts of descriptions of times and durations.

That would be the Hopi. And yeah, they talk about time plenty.

But I think Whorf was making a more careful point than people give him credit for. The idea wasn't that the Hopi are unable to say "tomorrow" or "quickly" or "day" or whatever. Whorf knew full well that Hopi has a word for "day" — in fact, we can be sure that he knew it, because lots of his examples are based around the Hopi word for "day." Rather, as I understand it, he was claiming that the Hopi don't have an abstract noun that corresponds directly to our abstract noun "time."

This may be true and it may be false — I don't speak Hopi, so what do I know? — but it's less idiotic than the HURF DURF THOSE SAVAGES DON'T KNOW WHAT DAYS ARE caricature that Pinker (for instance) likes to draw of Whorf.
posted by nebulawindphone at 4:37 PM on April 1, 2010

bdc34, you're probably thinking about Ekkehart Malotki's Hopi Time.

I get a little annoyed at the Whorfian-anti-Whorfian argument. It's usually claimed that Whorf said the Hopi have no concept of time. Whorf said a lot of things about language that can be dismissed as silly or trivial. but he didn't actually say that. Whorf did claim that Hopi has different concept of time than English and other European languages. And he did claim that Hopi doesn't have word for time - which is true, but trivial. "Time" is an abstract noun in English, and Hopi doesn't have abstract nouns. It does, however, have words for "before," "after," "while," "during" and verbal constructions equivalent to tenses. Whorf also wrote a paper on the construction of complex sentences in Hopi, a lot of which have to be glossed with complex tense constructions in English, eg. 'I was going to do X, but then Y happened.'

(Whorf did insist on calling Hopi tenses "assertions" rather "tenses." but that's a different issue.)
posted by nangar at 4:39 PM on April 1, 2010

Er, like nebulawindphone said.
posted by nangar at 4:42 PM on April 1, 2010

High five!
posted by nebulawindphone at 6:15 PM on April 1, 2010

I can't think of a way to transform that relationship into a statement about addition. In my mind, the natural numbers, succession, and addition occupy a very basic place.

I guess this is the deal: If we are thinking of numbers logarithmically, then it might not even make sense to think about 10 + 10. The 1-2-3 in that world is 1-10-100. In that world, 10 + 10 is still 10. You didn't change the scale significantly, therefore you have the "same number".

It's like when we are talking about huge, rough numbers normally. "I might be off by a factor of 2, but the order of magnitude is right." Does it really matter what 1e16 + 1e16 is? No, because it's still basically 1e16.
posted by DU at 6:41 PM on April 1, 2010 [1 favorite]

These people, they're descended from rabbits?
posted by CheeseDigestsAll at 7:00 PM on April 1, 2010

Basically: How can I add numbers on a slide rule.

I started adding up all the numbers on my slide rule and it's lots. I recommend using a calculator to add them.
posted by Joe in Australia at 11:08 PM on April 1, 2010

The graphs for K through 2nd graders make me upset. The lines seem to have at most spurious relationships with the data.
posted by that girl at 11:27 PM on April 1, 2010

Well that explains the whole real estate bubble.
posted by fshgrl at 11:33 PM on April 1, 2010

DU, a nitpick: The 1-2-3 in that world is 1-10-100 10-100-1000.

Alternatively: The 1-2-3 0-1-2 in that world is 1-10-100.
posted by wobh at 11:42 PM on April 1, 2010

Does it really matter what 1e16 + 1e16 is? No, because it's still basically 1e16.

Huh? It's twice as mcuh.
posted by delmoi at 4:33 AM on April 2, 2010

Twice as much is nothing in the world of orders of magnitude.
posted by DU at 5:19 AM on April 2, 2010

DU, it depends on the magnitude doesn't it? Twice as much is an order of magnitude of 2 (maybe this is phrased differently by folks who know better "order of the second magnitude"?).
posted by wobh at 7:30 AM on April 2, 2010

Twice as much is one order of magnitude, in base 2. Logarithms aren't restricted to base 10 --- to me, that feels a little unnatural.

Twice 10¹⁶ is 10^16.3; if your mental arithmetic is fuzzy about the difference between sixteen and seventeen, this is a negligible difference.

I recently had occasion to compute the factorial of the factorial of eight, which is approximately 3.4 × 10^168,186 or 10^168,186.5. The three out front is the least interesting part of that number. That doesn't say much about the Piraha's logarithmic number sense, but it tells me a lot about mine.
posted by fantabulous timewaster at 7:30 AM on April 2, 2010

"Isn't there some number of things which, if presented to you, you would just say "Dude, I'm not counting those up to figure out how many there are"?

Do you not believe that their words for numbers stop at some point, or do you not believe that 5 is the point beyond which they just don't care about counting?"

That seems to be the idea. In their environment, the Munduruku simply don't need to count precise quantities beyond four or five, so they never developed concepts for numbers beyond that point. I find it amazing that anyone, anywhere on Earth wouldn't have a solid grasp of the numbers from one to ten, along with addition and subtraction, just because we all carry ten handy digits which can be used for reference. I mean, how can you look at six fingers and then look at your six kids, and not see that they are the same?

But I guess that's an insight that people don't have to make, since we come with this fuzzy, visual logarithmic sense built in. If a hunter gatherer can compare two quantities and know instantly that one looks smaller than the other, that's enough to get by in most situations. The important thing is that the amounts aren't equal, or that the ratios are off by an unacceptable amount. (Also, in the example with the children, the Munduruku would know at a glance which child is missing because he remembers each one as an individual.) It's only within the demands of modern human civilization, with our complex webs of synthetic and deduced concepts, that it becomes important to know the precise amounts of different quantities.
posted by Kevin Street at 2:55 PM on April 2, 2010

This reminds of a story I heard about a man who had always lived in a jungle. When he went with a researcher out of the jungle into a great open space for the first time he pointed to a person some distance away and said something like "look at that tiny little person!" In the jungle there are no distant views, so his understanding of perspective had not developed.

And THIS reminds me of some footage I saw of someone who had visited an Amazonian tribe, and one of the researchers/journalists had a small portable tape player. There was a shot of one of the Amazonians listening to a recording of Vivaldi's Four Seasons on the tape player, a faint smile on his face. One of the journalists asked him what he thought, and through a translator, he said it did sound interesting - then asked if what he was listening to was some kind of foreign language.

I wouldn't say that this person's understanding of music "hadn't developed," only that he had never before been exposed to something that resembled that kind of music. But I'm sure once he was told, "No, this is music," he thought, "oh, music can sound like this, too? Huh. Okay."

Same too with the guy who was thrown by perspective, or the people who were thrown by counting more than five kids. If you haven't ever had to use your sense of perspective before, you aren't going to get it first off -- but that doesn't mean you can't ever do it. If you are living somewhere where there's a high childhood mortality rate, the odds of your having more than five kids TO count are small, so why bother trying.

But take any of those people and introduce them to the idea that "oh, music can sound like this/tiny can sometimes mean far away/sometimes you can have more than five kids?" and now they know it IS a possibility. We are all capable of learning about new concepts, but those concepts do have to first be introduced to us.
posted by EmpressCallipygos at 4:55 PM on April 2, 2010

42.
posted by nathanlindstrom at 6:18 PM on April 2, 2010 [1 favorite]

It's kind of like how mathematicians can't count and ethicists steal books.

Or sometimes, philosophers will scale a wall, climb through a hatch in a roof and then fall through the tiles in a drop ceiling in a vain attempt to complete an essay for an ethics competition before the deadline.

Remember: "True philosophers don't need lawyers!".
posted by dunkadunc at 8:16 PM on April 4, 2010

Beautiful.

Sadly, the ethicists-steal-books thing turned out to be spurious too. Not a hoax, just yer usual lying with statistics. Oh well...
posted by nebulawindphone at 11:20 AM on April 5, 2010