Pi in the Sky

by Belle Waring on August 23, 2004

A note in todays Washington Post describes a very interesting experiment:

Peter Gordon, a behavioral scientist at Columbia University, conducted an unusual set of experiments with seven adults of the 200-member Piraha tribe of Amazonian Indians in Brazil.

The tribe’s counting system consists of three words—one that means “roughly one,” one that means “a small quantity” and one that means “many.”

Gordon asked the Piraha subjects to perform various tasks in which performance would be greatly enhanced by the ability to count. These included laying out the same number of nuts or sticks that he had laid out; distinguishing two boxes whose only difference was the number of fish drawn on their tops; and knowing when a tin can was empty after watching the researcher put nuts into the can and then withdraw them one by one.

Gordon found that the Piraha were essentially incapable of following or accounting for more than three objects. When a task involved larger numbers—even five or six—the subjects’ answers were little more than guesses, even though they clearly understood the tests and were working hard on them.

He attributed this surprising finding to the fact the Piraha “have no privileged name for the singular quantity”—in other words, no one, no notion of an integer.

“The present study represents a rare and perhaps unique case for strong linguistic determinism”—the idea that language determines thought—Gordon wrote.

John D. Barrow explores similar ideas in his lively book Pi in the Sky: Counting, Thinking and Being. The most surprising thing, to me, is not the poor performance of the Piraha on these tests, given their linguistic disadvantage. Rather, I am amazed that anyone could get through life, particularly a no-doubt difficult struggle for existence in the jungles of the Amazon, with such a piss-poor numbering system. Perhaps the category “roughly one” has some unique areas of application which I am unable to appreciate. And it is by no means inconsistent with my strongly Platonic beliefs about numbers that it might take humans a long time to discover the existence of these supernatural, world-ordering entities. But the advantages of being able to count properly, even up to ten or twenty, seem so overwhelming, and the principles involved so obvious, that I am astonished anyone can get by without them.



eszter 08.23.04 at 7:23 am

Good point.:)

There’s more on this research project over at the Language Log (with links to an academic abstract of the work, etc.) for those interested in more details.


Jacques Distler 08.23.04 at 7:24 am

Differential calculus seems pretty damned-intuitive to me. Where shall we draw the line?

Reminds me of the old joke:

You’re a Mathematician? Wow! Math was always my worst subject. I mean I did OK in grade school and high school and in college. But K-theory completely blew me away!


belle waring 08.23.04 at 7:35 am

200 people is a small group, but it surely has happened that a Piraha adult has had to keep track of more than three small children. Are they really unable to look and see whether all of them are there? perhaps they just memorize a list of the children’s names and then match a name to a child until they run out of names or children?


novalis 08.23.04 at 7:48 am

Belle, keeping track of children doesn’t require counting. Counting is used to map objects to numbers. So, if I have to keep track of four children, and I look around and child C is missing, it need not concern me that there are now three children.

Actually, this whole thing makes me think of the rabbits in watership down, who could count no higher than four. Five and above were “hrair”, which loosely translates to “one thousand.” To mix up literature a bit, Nyarlathotep would be “The Black Goat With Hrair Young.” Anyway, this got me to wondering: let’s say a rabbit goes into a room with five objects. She sees that there are hrair, but wants to know more precisely. So, she moves one out of the room. When she comes back, there are four. So, she knows it’s “four plus one” objects. So now she’s got a procedure for counting to five (which she has to call “four plus one”). Can we build a whole counting system out of this? Yes. The “plus one” thing turns out to be just the successor operator, about which I am too lazy to say more than that it’s sufficient.


Ralph 08.23.04 at 8:16 am

I have heard about such people “roughly one” time before this. George Gamow’s wonderful book, “One, Two, Three… Infinity” draws its title from the author’s description of a tribe which could count no higher than three. Beyond that, it was just “many.”

I always assumed Gamow’s tribe was mythical. Maybe they were, in fact, the Piraha. Or maybe there is “a small quantity” of tribes in the same situation.

I cannot recommend Gamow’s book too highly for anyone who loves math.


lightning 08.23.04 at 9:12 am

And a big “welcome back” to the Sapir- Whorf hypothesis!


Michael Kremer 08.23.04 at 9:50 am

There is considerably more on the strangeness of the Piraha in this Toronto Globe and Mail story:

It goes beyond numbers… (The s-w hypothesis is mentioned at the end of the story, also.)


Michael Kremer 08.23.04 at 9:54 am




Scott Martens 08.23.04 at 10:03 am

Well, as someone with a very anti-Platonic view of mathematics, I can’t say I’m surprised. It doesn’t strike me as qualitatively different from the lack of habitual use of the plural in Chinese, or how Russian gets by without definite articles. Toddlers do remarkable things without any genuine ability to count beyond 5. If grown-ups lead a simple enough life, I imagine they can get by without it either.


Omada 08.23.04 at 10:27 am

Shub Niggurath is the one with Hrair Young. Nyarlathotep is the one with hrair forms. Wait, is today out-the-geek day?

Anyway, the Globe and Mail story is mindboggling. What an alien people.


Hunt 08.23.04 at 11:39 am

The Sapir-Whorf hypothesis is a bit different, but linguistic relativism was never really gone. It just flew a bit under the radar after experiments, particularly on color, called it into question in the late 60s and early 70s. It’s came back with a vengance in the 90s, and is probably here to say (this book is a good collection of contemporary views and research).

Interestingly, our number system ain’t so great, either. Between 10 and 20, we have some really weird numbers. Not surprisingly then, children in cultures with numbering systems that make sense in that range, using something like ten-one, ten-two, ten-three, etc. (like in Chinese), instead of eleven, twelve, and thirteen, actually get a head start in learning numbers and math. It’s the Roman’s fault.


belle waring 08.23.04 at 11:50 am

in addition to the Watership Down ‘hrair’, there are also the funny aliens in Greg Bear’s Anvil of Stars. they are creatures composed of a number of smaller, simpler, snake-like creatures which, when alone are not fully intelligent (but are very good at chess). when they get together a higher-order consciosness emerges. these aliens are supposed to do math in which it’s all about irrational numbers, in some sense (like, those are the basic units.) yes, this is the geekiest thread ever. all praise el-ahrairah.


abb1 08.23.04 at 12:37 pm

In New Zealand aborigines’ language you say “three on the other foot” for “18”. Cool, huh?

I’ve read the Language Instinct by Pinker and he argues against the Whorf’s theory very convincingly. It’ll take more than a bunch of these Piraha guys to revive it.


Tim F 08.23.04 at 1:08 pm

There’s more on the Piraha at http://lings.ln.man.ac.uk/Info/staff/DE/cultgram.pdf . The author doesn’t argue for the Sapir-Whorf hypothesis, but rather takes issue with Chomsky etc., from the other side – it’s not that language determines culture, more like culture determines language.


Lynn Rutherford 08.23.04 at 5:30 pm

Where Mathematics Comes From by Lakoff and Nunez is an interesting study. The book is based on research in cognitive blending and its application to logic to mathematics.


Windhorse 08.23.04 at 5:41 pm

I had the good fortune to speak with a western-educated member of the Amazonian Uru-e-wau-wau tribe at a weekend workshop where other indigenous people from South American were present. He said of the Shuar tribe representative that his people only have four number concepts: one, two, three, and “many.” He said they also essentially only possess three “times” of day: dawn, midday, and sunset. One of his points: these people rarely get psychosomatic illnesses such as cancer, and maybe people in the West (and North) need to reflect on that.


smith the smithson 08.23.04 at 6:44 pm

“But the advantages of being able to count properly, even up to ten or twenty, seem so overwhelming, and the principles involved so obvious, that I am astonished anyone can get by without them.”

What need do you have to count to 10 when you are living off the land? What is relevant to them in terms of day to day life might fit VERY well with this numbering system. Consider that “a small quantity” means something that needs to be used wisely because it will soon be used up. “Many” means plentiful, so use all you want. If you are living off the land, that would seem to cover the important categories of resources.


Brey 08.23.04 at 7:29 pm

To approach this differently one might ask, “What is it about their existence that makes counting unnecessary?” Maybe precision in counting is a result of economic transactions of a certain type. For survival precise counting isn’t so necessary. I thin about building a fire here. I never count the pieces of wood. I just know when its about enough to produce hot coals for cooking.


Dan Simon 08.23.04 at 8:21 pm

I read somewhere about a primitive Amazonian tribe that had no understanding of the World Wide Web. They had email lists and FTP, of course, but even text browsing was beyond them, and e-commerce was an unknown concept. (They did all their home shopping using telephone orders from catalogs or television stations.) Apparently, their lives were so primitive that they simply had no need for HTTP.

(This may or may not be the same tribe that Woody Allen wrote about years ago, explaining that they have no word for “no” in their language, and instead answer questions and requests negatively by nodding and saying, “we’ll get back to you.”)


epist 08.23.04 at 8:24 pm

I’ve always had a hunch that mathematical thinking was subtended by two very different processes.

One process involved basic visualization of representations of small discreet quantities. This is how we handle manipulations of small sums.

The other process is a complex of concepts, heuristics and literary representations, combined with rote memory. This is how we handle all other mathematical thought, from the multiplication tables we commit to memory to the geometric deductions we learn to do in our heads in the 7th grade, to proofs.

The first is absolutely necessary, it seems to me, for human social life. But it doesn’t require much in the way of precise linguistic representation, since the judgements are usually so easy and obvious, and so universally shared by all participants, that context will almost always painlessly disambiguate.

If I have four guests in the next room, and I send my child to fetch water, but he brings only three glasses, I don’t need a word for ‘four’, ‘three’ or indeed any number to comminicate the problem to him. Nor does he need linguistic concepts like those embodied in the integers to see his mistake and how to remedy it.

The more abstract process(es) have their uses, god knows, but they aren’t necessary for societal existence. At least so it seems to me. . .


Doctor Memory 08.23.04 at 8:24 pm

Windhorse intones: …psychosomatic illnesses such as cancer…

You’ll just have to imagine my spit-take here. Care to elaborate on that? I promise not to be chewing anything this time.

(Something other than his word that his tribe has lower-than-average cancer incidences and some control for factors like lack of smoking, lack of localized air/water pollution, and higher rates of early death by predators, starvation and blunt trauma would be good to include while you’re at it.)


rab d 08.24.04 at 1:20 am

“In New Zealand aborigines language you say three on the other foot for 18 “

In the Maori language 18 is tekau ma waru
ten and eight


Windhorse 08.24.04 at 3:56 am

Doc Memory, about 1/8 of a second after I pressed “Post” I knew with an agonizing certainty that the cancer sentence would come back to haunt me.

Kind of a “Khaaaaaaaaaan!!!” moment.

Firstly, the cancer rate claim is his not mine, but it’s fairly easy to determine what diseases occur how often when you live in a tribe of fifty people. Secondly, there is a fair amount of literature noting psychosomatic components to certain cancers. And thirdly, your point about lack of environmetal toxins is well taken.

Blunt trauma is less of an issue for the Shuar now that they no longer fight neighboring tribes to collect heads for shrinking (they’re famous for it!). Skin rashes and fungi, however, have increased since missionaries came and told them they must wear clothing to be saved, and the combination of tremendous humidity and gym shorts is a sure recipe for fun, as we all know.


Spot 08.24.04 at 6:22 am

Mathematical Cognition, Vol. 1

The Handbook of Mathematical Cognition

A couple good resources. Things are a bit more complex than they appear.


Tony Marmo 08.24.04 at 6:54 am

I must protest and speak in behalf of the Pirahã:

I am really impressed by the reactions to the news mentioned. People easily accept any announced findings without much criticism.

Why doesn’t anyone at first place doubt the accuracy of the whole concept that Pirahã language does not allow People to count more than an x quantity? Or that by any reason a human would be unable to count.

On the linguistic side, I have already explained why the findings cannot correspond to the truth about Pirahã. There is no such a thing as a natural language L that cannot be used to convey certain ideas. Any language is enough developed to do it. And it does not require any large vocabulary to do so. A short list of lexical items will do it.

On the cognitive side, the idea is even more implausible. It would mean that, for instance, the Pirahã could not make a sensus of their own population by counting elements of sets and by counting sets of elements and subsets of sets, etc.

I beg your pardon, but this is hilarious, if it is not another sad way to sell some Indians short. I definitely cannot have any other reaction but to protest. It is not the first time science is used as a pretext to ethnocentic misconceptions about other cultures.


Ray Davis 08.24.04 at 3:02 pm

I recommend taking a look at the original research article that tim f. mentions, which, as always, make more interesting reading than the journalists’ versions. Everett doesn’t simply _claim_ that the Pirahã can’t count: he argues with ethnographic evidence. As to “how anyone could get through life” — well, that’s kind of tough anywhere, and it sounds like the Pirahã haven’t been spectacular successes by most measures, but Everett indicates that they deal with their cognitive blindspots the same way we deal with our own: culturally. With communal (and transient) ownership, valorization of hardships, and a very simple kin system, they can scrape by amongst themselves.


V. 08.24.04 at 3:14 pm

Tony, I think you’re being misled by some inaccuracies and infelicities in the reporting on this study. (You might still disagree with the conclusions, but the premises on which you’re doing so now are not the actual claims of the case.) Part of the problem is that the translation of these Pirahã words as “one-ish”, “two-ish” and “many” is misleading. Those words don’t serve as counting words in the way that ours do, which is why they don’t stack in sets the way you propose. Rather than counting, the norm in their culture seems to be to conceive of things strictly in terms of magnitude, and not enumeration.

Here‘s Daniel Everett, one of the linguistic anthropologists who’s been living with the Pirahã for decades and who speaks their language, who served as a consultant for the cognitive psychologist Peter Gordon, on the subject: ‘”The word he [Gordon] translates as ‘one’ means just a relatively small amount, the word for ‘two’ means a relatively bigger amount,” he said in an interview from Brazil… when the Piraha are talking and use the “oneish” word to talk about something such as fish, you can’t tell whether they are describing a single fish, a small fish, or one or two fish.’


Tony Marmo 08.24.04 at 4:36 pm

I agree that perhaps the original research has been misrepresented. I shall look into it as soon as I have some time.

But even in the way you try to explain what is going on, the idea that a certain group of humans can measure magnitude and not enumerate put in rough terms is an ethnocentric absurdity.

I give you one example of how the things could be conversed: Eskimo has many words for snow. This does not and cannot mean that English Canadians cannot grasp or distinguish the several kinds of snow accordingly to Eskimo classification. But, of course, an ethnocentric Eskimo could argue that if Eskimos decided to make anthropological studies of us Whites.

And mind you that in the example above we think of taxonomy, something that really depends on conventions. The capacity of enumerate is too radical of human cognition to be impaired in the manner described. It does not depend on language or culture. To think the contrary would be the same as to claim that another People could not memorise things because their language and their cultural conventions are different from others. That is not a possibility. Not at all.

There are precedents. Once years ago someone just stated that a certain language lacked temporal expressions, an error which later was fully exposed. But ok, I shall look into the research before expressing any final verdict. Perhaps I change my point of view.


james 08.24.04 at 5:23 pm

A Sci-Fi book series by David Brin deals with a similar concept. The basic concept was that language limited the formation of ideas. When new ideas needed to be created language had to expand. In the story, only non-standard languages where capable of double negative or contradictory statements. Such as “this statement is a lie”. Without this ability, the galactic civilizations lacked the concepts to question the order of the civilization.

On a more practical note. Languages tend to expand when new ideas are introduced. The more important a concept to a society, the more likely that society will have a word for it. That is why Eskimos have over 40 words for frozen water (snow) and English has closer to 8. A simpler explanation for the Piraha lacking distinct counting, is they do not need it. A subsistence life really only has enough / not enough.


Dan Simon 08.24.04 at 7:37 pm

The capacity of enumerate is too radical of human cognition to be impaired in the manner described.

Whoever said that the Piraha have no capacity to enumerate? Did the human race suddenly develop the cognitive capacity to browse the Web in the mid-90’s (to use my fanciful example from above)? Were North Americans incapable of conceiving of a single lineup at the bank until some time in the seventies? And are they somehow incapable of conceiving of a single lineup at the supermarket today?

Incredibly simple, retrospectively obvious, magnificently life-improving conceptual innovations are continually being introduced into all societies, though clearly at different rates. Sometimes, looking back on them, one wonders what on earth was wrong with the people who hadn’t thought of them yet. One is even tempted, for an instant, to imagine some kind of cognitive impairment that caused them not to see the foolishness of the old way of doing things–but of course there is no need for such a ludicrous explanation, when “they simply hadn’t thought of the alternative” suffices.

I find it perfectly plausible that just as nobody had thought of “zero” anywhere before about 1500 years ago, nobody among the Piraha has thought of “one” yet. (Or perhaps several have, but have been unable to persuade the others of its utility.) Many things that we think are obvious are actually wonderfully subtle ideas that familiarity has prevented us from appreciating. I see it as no criticism of the Piraha that they have given me the opportunity to appreciate another one.


Ray Davis 08.24.04 at 7:50 pm

Like Dan Simon, I don’t find anything intuitively untoward about Everett’s research. As I understand the development of tallying, it, like writing, seems to have been pushed by economic discrepencies and religious concerns. Flatten economy and empty cosmogony, and where’s the impetus for number? Everett writes that the one context in which the Pirahã seem to be disturbed by a sense of “something missing” is while trading with outsiders.


tom mcclive 08.24.04 at 10:44 pm

Do people *still* believe that Eskimos have many words for snow?


german 08.25.04 at 12:14 am

Where Mathematics Comes From by Lakoff and Nunez is an interesting study. The book is based on research in cognitive blending and its application to logic to mathematics


vernaculo 08.25.04 at 1:05 am

Do people still use insult-words like “Eskimo” to describe circumpolar people?
A diverse group of folk who, in a neat way, circle the earth.
There may not have been 300 different words for types of snow, but the ability to describe exactly the conditions of an unforgiving environment were crucial to them, and the means of that expression were there, obviously, regardless of the linguists documentation.
As Ray Davis points out, it’s contact and taking the “test” that are problematic for the Pirahã. These natives will make soft meat for the merchants they encounter but it needs emphasizing, they were living successfully, without numbers, for countless thousands of years.
The assumption is that “our” way of living is more adaptable – even through incipient, and catastrophic, ecological disruption – and likely to be still more successful in future.
That assumption is baseless and void of proof. A teenager driving his father’s car at 100mph knows he’s immortal just as certainly, and just as validly.

As far as people spitting up over someone else describing cancer as “psychosomatic”…
That the psyche impinges on somatic function is beyond debate, the question being only degree and mechanism.
Less than two hundred years ago the majority view of medical professionals as to the cause of disease was “miasma”.
In a more local context having seriously propounded that absurdity would be enough to delegitimize any further expression.


serial catowner 08.25.04 at 1:17 am

Fair amount of ethnocentrism here. Counting only matters if you have a quantity of something that’s the same or can be measured. If not, the ability to count is usually misleading. One reason we often buy fruit by the pound, to save arguments about whether one batch of 10 apples is better than an alternate batch of ten apples.

You experience this all day, every day. Theoretically identical in size, minutes vary widely in their value to us and their size as we experience it. Counting minutes is usually a good sign that you’ve lost control and are actually losing minutes faster than you think you can sustain. Which of course is insane; you don’t ‘lose’ minutes, they pass at exactly the same rate at all times. They were never yours to begin with. That’s what makes them minutes.


Tony Marmo 08.25.04 at 4:41 am

The use of machines, such as computers or airplanes, or of simple implements, such as pencils or knives, involve different kinds of knowledge, which are acquired through human experience. And of course, such examples, as the examples given by Dan Simon, depend on technological development and social-economic organisation.

But some cognitive capacities are radical or fundamental and have not been invented. There is no term of comparison between the capacity to enumerate and that to browse the internet. If there is no internet in the society where one lives, he or she will probably not know how to browse the internet. And, this is the same for other non-elementary instances of mathematical knowledge, such as the use of zero and negative and complex numbers, or the method of solving second degree equations.

But to count, to enumerate, or to use natural numbers is a natural capacity, something that does not depend on the cultural environment. The same applies to the cognitive capacities of memorising things or of commanding your legs to walk.

To belief the contrary is the same as to claim that culture or language can have a more devastating impact on the lives of people than a stroke or a any form of cerebral damage.


novalis 08.25.04 at 7:41 am

omada, I knew my merely second-hand knowledge of Lovecraft would come back and bite me someday. Oh, the humiliation of being outgeeked on CT! ;)

Belle, I don’t recall that from Anvil of Stars (but maybe I’ve blocked it out). In Sundiver (another book I’ve blocked out), some of the aliens don’t have irrational numbers. My friend Mark demolishes that view quite eloquently.


Dan Simon 08.25.04 at 7:55 am

to count, to enumerate, or to use natural numbers is a natural capacity, something that does not depend on the cultural environment.

Really? What about counting by twos? By fives? By seventeens? Addition? Multiplication?

My understanding is that even in our mathematically advanced society, dealing with numbers beyond five or six is a completely mechanical, non-intuitive process. For the untutored Piraha, the threshold seems to be three. That doesn’t sound to me like the kind of fundamental difference in cognitive capacities that couldn’t be put down to lack of familiarity and practice.

they were living successfully, without numbers, for countless thousands of years.
The assumption is that “our” way of living is more adaptable – even through incipient, and catastrophic, ecological disruption – and likely to be still more successful in future.
That assumption is baseless and void of proof.

Well, given that “our” way has resulted in billions of healthy, long-lived people dominating the habitable parts of the planet, while their way has resulted in a tiny tribe of low-lifespan, resource-poor tribespeople in a remote patch of South America, I’m inclined to place my bets with “our” way and take my chances.

In fact, I’d go further and surmise that the invention of the natural numbers would find some application–indeed, likely a whole bunch of applications–in the world of the Piraha, even in their state. Arithmetic is, after all, an extraordinarily versatile conceptual tool.


Tony Marmo 08.25.04 at 9:44 am

Of course, Dan. What you point is not an objection. Counting by twos, fives, tens, twelves, are systems that can be created and changed thanks to the very natural capacity of counting. Without such capacity, none of such systems would have been possible from the very start.

Next time there will someone claiming to have discovered a society where People do not walk, even considering that their legs, bones, nerves and brains in perfect state. They will not walk because in their culture there is no concept for motion. After that, another great mind will claim an even more curious discovery: a village of languageless humans. Those will be real hits.


bellatrys 08.25.04 at 10:35 am

Psychological stress exacerbates cancers. It also exacerbates heart disease, diabetes, MS, and every other ailment known to man. This does not mean that all diseases are “psychosomatic.” (I could go into detail about the fact that ‘cancer’ is a name for a class comprising hundreds of different diseases with different causes and symptoms, and that it seems to always have a genetic aspect *and* a triggering aspect, as well as a basic explanation of why emotional strain has objective physical consequences, but I’ll just join Doctor Memory in finishing wiping off my screen here…)


bellatrys 08.25.04 at 10:55 am

More geekdom – the Trolls in Discworld:

“One, two, many, lots.”


vernaculo 08.25.04 at 11:17 am

dan simon-
given that “our” way has resulted in billions of healthy, long-lived people dominating the habitable parts of the planet, while their way has resulted in a tiny tribe of low-lifespan, resource-poor tribespeople in a remote patch of South America, I’m inclined to place my bets with “our” way and take my chances.

Since the teenager in his dad’s car didn’t seem to have much effect, how about this:
Crack cocaine is probably about as good as pharmacological euphoria’s going to get. It’s pretty seductive, I’ve been near it, but never on it. I’ve seen it “work”, as a drug and as a lifestyle. The parallel with “our” way, as opposed to the primitive way of the indigenes in question, is pretty symmetrical.
The “way” you defend has been around for less than a century, or if you want to stretch it, less than two centuries. In that time it’s brought its own adherents to the brink of extinction, though most of them haven’t confronted that yet. It has spent the capital of its, and the world’s, natural resources beyond replenishing in “our” lifetimes. Children are kept indoors now, moving from one controlled environment to another; the fields that surround “our” cities are hostile landscapes of poison and industrial geometries, birdless monoculture deserts. The US alone burns 380 million gallons of gas every day.
The automobile is the single largest killer of people under 30, and yet it’s the first technology most of the chauvinists of “our” way would point to as indispensable.
Billions of healthy people for how much longer. Ten years? A century?
And how much of a factor is happiness in your definition of healthy? With enough medical technology a brain-dead body in a coma can be kept “healthy” for years. Happiness doesn’t mean anything in that context though, does it?
My main point is the timeline. The aborigines – thousands of years, tens of thousands. You, “us”, this – a few decades.
Decades in which the conditions have been set for massive climate and ecological disruption to be made ineluctable, and inadvertently, blindly.
But like the crack-head’s minutes of rushing bliss those few years have been so exhilarating, and so saturated in power, there’s no way you’ll go back. No way.


serial catowner 08.25.04 at 5:27 pm

Claiming that “to count, to enumerate” are natural abilities is a weak reed, in the absence of any proof.

For example, ducks can’t count above three, a fact I read in a book, but easily observed by looking at duck mothers with older ducklings. Count ’em, there are usually three.

The same book said people can usually count to about seven, which makes us about twice as smart as a duck, or a “whole lot smarter” than ducks- take your pick.

But choose wisely- your ability to ‘naturally enumerate’ will be reflected in your answer.


Tony Marmo 08.25.04 at 6:03 pm

Well, Serial Catowner, I was talking about what is natural for humans. I thought this was understood.

But, ok, if you read that Ducks can count up to three, so it means that even Ducks can count. One extra example of how absurd is to assume that the Pirahãs would lack a capability that, according to your post, even some birds possess.


Windhorse 08.25.04 at 9:00 pm

Bellatrys, I was actually thinking in terms of cancer having both a genetic and a triggering aspect when I wrote the post, but there’s no way I could offer enough qualifiers in the space allotted to prevent someone taking issue with a general claim. I don’t think anyone is claiming that all diseases are psychosomatic, but in the case of Amazonian tribes they have fewer triggers for cancer both in terms of stresses and toxins.

Your point about stress being involved in a number of pathologies is well taken, and seems to support the point I was trying to make. A less stressful existence will naturally equal less stress-related illnesses including heart disease, the triggering of some kinds of cancers, insulin-response conditions, low-immunity responses, and others.

Interestingly, the issues of counting ability and stress and health seem to be interwoven. If you don’t learn to count, you will never develop the necessary technology to introduce, say, dioxin into your environment, and you will not have that or other environmental toxins to cope with. You won’t have three things to sell by 4PM, or a $2000.00 mortgage due by the 1st, so your overall stress level will be lower. And this is part of what Vernaculo is trying to communicate, it seems to me. Indigenous people won’t experience all the benefits (including advanced medicine) that come with having to manage an industrial society, that’s for sure. But they have learned to live in harsh environments for thousands of years, and if it weren’t for the fact that bulldozers are at their doorstep, would likely continue for thousands more.

So is the hunter-gatherer way of life subjectively preferable or less preferable to our way of living? I guess the answer depends on what kind of life you want. I think there is an unspoken assumption behind many of these posts that because they have a relatively primitive lifestyle that it can only be harsh and unsatisfying, that these people can’t have rich lives. Probably the only way to test that perception is to live with them for a while. I know a few people who have, and they personally have come away humbled by the experience, for whatever that is worth.

Is their societal-technological level objectively preferable or less preferable, as some people here have asked? Well, that question may be easier to answer if we don’t find a way to reign in the deleterious effects of an industrial civilization on the world.


Joseph Hertzlinger 08.29.04 at 7:39 am

They haven’t been living successfully, without numbers, for countless thousands of years, they have been living successfully, without numbers, for countless manies of years.

Similarly, we have many years of oil left, etc.


Tony Marmo 08.30.04 at 7:48 pm

Well, probably next claim will be that, as do not count the days, they have no concept of year, so you cannot think that they have lived for years.

I have had the patience to browse some sections of Daniel’s work and so far none of the examples he himself presents supports his claims. It is that he expects to find data in a certain morphological format, but not all languages bear it.

I give you one example:

(1) Canadians went to the water.

A sentence like (1) in many languages is interpreted as having an implicit some operator, or a usually frequence, etc. In other languages the bare plural can be understood as a most phrase.

Well, what happens in one example of Daniel’s paper, number (15), is that they use the name of their People to convey the idea that all the persons went to swim. That is something very logical, because if you think that elements a1…an belong to a set S, and if you say something about S, you mean all elements of S and not only one or some of them.

In another example, the Pirahã speakers could not be more explicative to him. In (16) they say that they eat most of the fish and that by consequence a part of the fish was left.

And the funny thing is that he uses these examples to show that neither all nor most exist in Pirahã.

Daniel’s work is a 52 page essay and it is time-consuming, so I cannot promise I can finish it, since I have other readings to complete.

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