You can't do the math without the words

Feb 21, 2012

Most people learn to count when they are children. Yet surprisingly, not all languages have words for numbers. A recent study published in the journal of Cognitive Science shows that a few tongues lack number words and as a result, people in these cultures have a difficult time performing common quantitative tasks. The findings add new insight to the way people acquire knowledge, perception and reasoning.

The Piraha of the are a group of about 700 semi-nomadic people living in small villages of about 10-15 , along the Maici River, a tributary of the Amazon. According to University of Miami (UM) anthropological linguist Caleb Everett, the Piraha are surprisingly unable to represent exact amounts. Their language contains just three imprecise words for quantities: Hòi means "small size or amount," hoì, means "somewhat larger amount," and baàgiso indicates to "cause to come together, or many." Linguists refer to languages that do not have number specific words as anumeric.

"The Piraha is a really fascinating group because they are really only one or two groups in the world that are totally anumeric," says Everett, assistant professor in the Department of Anthropology at the UM College of Arts and Sciences. "This is maybe one of the most extreme cases of language actually restricting how people think."

His study "Quantity Recognition Among speakers of an Anumeric Language" demonstrates that number words are essential tools of thought required to solve even the simplest quantitative problems, such as one-to-one correspondence.

"I'm interested in how the language you speak affects the way that you think," says Everett. "The question here is what tools like number words really allows us to do and how they change the way we think about the world."

The work was motivated by contradictory results on the numerical performance of the Piraha. An earlier article reported the people incapable of performing simple numeric tasks with quantities greater than three, while another showed they were capable of accomplishing such tasks.

Everett repeated all the field experiments of the two previous studies. The results indicated that the Piraha could not consistently perform simple mathematical tasks. For example, one test involved 14 adults in one village that were presented with lines of spools of thread and were asked to create a matching line of empty rubber balloons. The people were not able to do the one-to-one correspondence, when the numbers were greater than two or three.

The study provides a simple explanation for the controversy. Unbeknown to other researchers, the villagers that participated in one of the previous studies had received basic numerical training by Keren Madora, an American missionary that has worked with the indigenous people of the Amazon for 33 years, and co-author of this study. "Her knowledge of what had happened in that village was crucial. I understood then why they got the results that they did," Everett says.

Madora used the Piraha language to create number words. For instance she used the words "all the sons of the hand," to indicate the number four. The introduction of number words into the village provides a reasonable explanation for the disagreement in the previous studies.

The findings support the idea that is a key component in processes of the mind. "When they've been introduced to those words, their performance improved, so it's clearly a linguistic effect, rather than a generally cultural factor," Everett says. The study highlights the unique insight we gain about people and society by studying mother languages.

"Preservation of mother tongues is important because languages can tell us about aspects of human history, human cognition, and human culture that we would not have access to if the languages are gone," he says. "From a scientific perspective I think it's important, but it's most important from the perspective of the people, because they lose a lot of their cultural heritage when their languages die."

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User comments : 37

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Lurker2358
1.2 / 5 (9) Feb 21, 2012
How is that even physically possible for humans to have no concept of numbers?

I mean no offense, but I once saw an episode of Ripley's Believe it or Not in which a Dog had been trained to add, subtract, and multiply by reading a card and counting(by barking) the number one at a time.

Is it possible that these people are so in-bred that they've destroyed a gene effecting their brains?

If you can't count to 4 then you wouldn't be able to tell how closely related you are to someone, and would be marrying your close cousin every generation, which would be disastrous, because it would further reinforce any negative genes.
Mike_Massen
1.8 / 5 (4) Feb 21, 2012
Lurker2358 offered this odd question:-
How is that even physically possible for humans to have no concept of numbers?

Surely its not a physical issue, its one of need. Their culture has no need for that sort of precision - they have food and shelter in abundance and probably sex too and have lived in equilibrium (doubtless of several types) with their environment for a long time.

Lurker2358 continued with this logic which could be so easily mis-applied
Is it possible that these people are so in-bred that they've destroyed a gene effecting their brains?

Could use that reasoning for any number of sociopolitical paradigms ;-).

There could be a limited gene pool & less overall mutations, that is possible & also incest, that doesnt necessarily lead to comparatively reduced brain capacity. I can speculate however, that there is much in their culture regarding the patterns of interactions they have with environment which is likely to be very rich indeed...
tadchem
not rated yet Feb 21, 2012
Anecdotal evidence support the idea that crows can 'count' quite high, recognizing numbers of people as high as 12 or more, but they have no words.
I am told by a Filipina friend that the Ilokano language can only count to 10, but the Spanish taught them numbers and now they can count as high as they want - in Spanish.
ODesign
not rated yet Feb 21, 2012
by extension if we re-purpose language deliberately for political or economic gain we can decrease the ability of people to conceive of the concepts the words used to mean. Ever wonder how often people would recognize Malfeasance in practice if the news and media used the word when appropriate.
Deathclock
1 / 5 (1) Feb 21, 2012
by extension if we re-purpose language deliberately for political or economic gain we can decrease the ability of people to conceive of the concepts the words used to mean. Ever wonder how often people would recognize Malfeasance in practice if the news and media used the word when appropriate.


Corruption... it's basically a synonym, and it's used all the time.
Deathclock
2.8 / 5 (5) Feb 21, 2012
How is that even physically possible for humans to have no concept of numbers?


You think humans are born with numbers in their brain?

I mean no offense, but I once saw an episode of Ripley's Believe it or Not in which a Dog had been trained to add, subtract, and multiply by reading a card and counting(by barking) the number one at a time.


This has nothing at all to do with intelligence.

Is it possible that these people are so in-bred that they've destroyed a gene effecting their brains?


This is just stupid.
Deathclock
3 / 5 (2) Feb 21, 2012
You can't do math without counts (quantities, numbers, etc), and you can't have counts without classification.
kaasinees
1 / 5 (1) Feb 21, 2012
Math is nothing more than an abstract language based on algorithmic logic operations. The whole idea of Math is developed on abstraction. In other words classification as Deathclock says.
RitchieGuy
2 / 5 (3) Feb 21, 2012
heck. . .I can count to 20, but having to take my shoes off in a store is a little inconvenient and you should see the looks I get.

;))
Lurker2358
1 / 5 (6) Feb 21, 2012
You think humans are born with numbers in their brain?


My nephew definitely knew the difference between 1 and 2 by the time he could walk. "two mamma's" he'd say, when looking at two pictures of her on the frig.

This has nothing at all to do with intelligence.


Sure it does. Collective intelligence of a civilization is limited by it's language skills: spoken, written, or mechanical computation and communication.

Imagine if you can't count to 20...

speaker1, "Who missing? everyone here?"

speaker2, "Me not know. Um...1,2,3, um...3...um...me forget!"

speaker1, "What difference make? Let move!"

This is just stupid.


No, it's not.

There is precedent for similar inherited genetic problems. Some families have a genetic defect in the parts of their tongue and larynx which controls speech, and causes them to have a speech deficit even though they are otherwise intelligent and normal.
Jotaf
5 / 5 (5) Feb 21, 2012
Lurker, you are mistaken :) See the wikipedia article for Clever Hans. (The Amazing Horse That Can Do Math!)
shaffer_da
5 / 5 (5) Feb 21, 2012
Lurker, I can't even begin to say how misguided and ethnocentric your opinions are. I'll steal wikipedia's definition for brevity: "Ethnocentrism is making value judgments about another culture from perspectives of one's own cultural system. The ethnocentric individual will judge other groups relative to his or her own particular ethnic group or culture, especially with concern to language...."

Me not read the article!

Your nephew could count to two because someone TAUGHT HIM THOSE WORDS, genius. By your logic, we should all instinctively know how to speak Chinese, too. The article was very clear in stating that those villagers who worked with Madora were later able to understand numbers.

Cultures develop different traits out of NEED. Are you aware that prior to the modern era, different cultures had wildly varying numerical systems? Meaning they developed independently. These people never had a need, probably because of the fact that THEY LIVE IN THE JUNGLE.
Deathclock
1 / 5 (1) Feb 21, 2012
Exactly Shaffer, nothing more needs to be said to lurker about this.
vega12
not rated yet Feb 21, 2012
Imagine if you can't count to 20...

speaker1, "Who missing? everyone here?"

speaker2, "Me not know. Um...1,2,3, um...3...um...me forget!"

speaker1, "What difference make? Let move!"


What if living in such small groups means that they know everyone they are with very well, so they don't need to count a group they are in as a faceless number; they can just remember who they are with.
shaffer_da
4.8 / 5 (6) Feb 21, 2012
You assume that a lack of numbers must indicate some sort of cognitive problem, because your culture revolves around numbers. Classic ethnocentrism.

As for genetics, speech deficits are a totally unrelated issue. It's not an inherited problem, trust me. And I'm not being a bleeding-heart-sympathizer here either. You are just absolutely wrong here.

As for your "everyone here" situation -- your most logical solution to the situation depends on numbers. Since they don't have number words, they WOULDN'T RELY ON NUMBERS TO SOLVE THAT PROBLEM. The answer to "who missing" is "John and Cindy," because they would just look around to see who indeed was missing rather than count.

Your idea of "collective intelligence" is also flawed, because it assumes that one can somehow quantify the intelligence of an entire society over another, with your society of course being the smartest one. And don't mention IQ, because it's been shown to be a culturally biased measure time and time again.

shaffer_da
not rated yet Feb 21, 2012
I looked through some of your other comments Lurker, and you're obviously intelligent. You seem pretty well versed in Physics. But it doesn't look like you've ever taken an interest in anthropology. You don't see it, but precisely these kinds of assumptions are what allowed the Eugenics movement to take hold in America, and then develop into a much more dangerous and genocidal ideology in Germany. I'm not calling you a Nazi. I'm saying that kind of thinking lets you extrapolate and get way out of hand too quickly.
Deesky
4.5 / 5 (8) Feb 21, 2012
I looked through some of your other comments Lurker, and you're obviously intelligent. You seem pretty well versed in Physics.

You're quite mistaken. Lurker, aka QC aka QuantumConundrum aka... whatever, is well known here for his general ignorance in a diversity of fields, with honorable mention in physics and cosmology.
Deathclock
1 / 5 (1) Feb 21, 2012
Yeah I'd like to see the posts that made you think he was well versed in physics...
Tausch
3 / 5 (2) Feb 22, 2012
All sound is math.
All human ears perform Fourier Analysis.

In fact, humans with greater vocabularies than the Piraha have come to believe in descriptions using a 'sound' that humans with a greater repertoire of sounds have come to label with the sound called 'number'!



The Piraha have had other priorities - food, water, shelter - besides giving exact (sound) descriptions to Nature with a vocabulary that does support survival priorities.

They can identified literally all sounds of their environment.
They mimic literally all sounds of their environment.
Those sounds have as much meaning as the 'sound' of the word 'number' to a mathematician.

The assertion that the Piriha are "totally anumeric" can not be sustained with research, data or observation.

To save face, retraction is the only recourse for Cognitive Science and you.

And the only way you will acquire knowledge, perception and reasoning is when you understand the sounds of this comment when I read it out loud to you.
alfie_null
5 / 5 (2) Feb 22, 2012
Makes me wonder what concepts I'm missing because my culture doesn't have the right words.
antialias_physorg
5 / 5 (3) Feb 22, 2012
How is that even physically possible for humans to have no concept of numbers?

The more intersting question would be: what kind of society can an anumeric people form? Obviously barter wouldn't work very well. Wouldn't this have to lead to some form of communism?

Ever wonder how often people would recognize Malfeasance in practice if the news and media used the word when appropriate

1984. good book. Double-speak has plenty of real world examples today ('Misremember' vs. 'lie', 'rebel' vs. 'terrorist', 'job creator' vs. 'rich', 'super-PAC' vs. 'money laundering organisation' ... the list is endless)

You can't do math without counts (quantities, numbers, etc), and you can't have counts without classification.

Not quite. Math itself requires no numbers (if you study math then you will hardly ever be confronted with numbers at all). Applied math (physics) is another matter.
antialias_physorg
5 / 5 (2) Feb 22, 2012
heck. . .I can count to 20, but having to take my shoes off in a store is a little inconvenient

Use binary. Then fingers will last you to 1023.

Collective intelligence of a civilization is limited by it's language skills

collective intelligence? Pardon me for laughing. The feats of intelligence performed by a society are not performed by all in concert. It is performed by individuals with particularly high intelligence for the benefit and later use of all the others. There is no such thing as 'collective intelligence' - only the sumtotal of individual intelligence contributions that somehow share another common -but entirely unrelated- attribute (e.g. living in a particular geographical area).

All human ears perform Fourier Analysis

There's a difference between USING a signal that was decomposed into its fourier coefficients via a some material object (ears/brain) and performing the math.
Lurker2358
not rated yet Feb 22, 2012
There is no such thing as 'collective intelligence' - only the sumtotal of individual intelligence contributions that somehow share another common -but entirely unrelated- attribute (e.g. living in a particular geographical area).


Would have to disagree.

We build machines that are so complex that no one person or even group of people knows how to make all of the components.

Space Shuttle
Space Station
Computers
Particle Accelerators
Weather Models
Video Games - the big ones, not the little stuff
Operating Systems
Deesky
5 / 5 (1) Feb 22, 2012
We build machines that are so complex that no one person or even group of people knows how to make all of the components.

Space Shuttle
Space Station
Computers
Particle Accelerators
Weather Models
Video Games - the big ones, not the little stuff
Operating Systems


Apart from software, which is more of an ad-hock process, all the other items have blueprints and are specified down to the last nut and bolt, which means any group of individuals could built it in principle.

And with software, a single individual can code a highly complex piece of software, perhaps over many years, and he, himself, may not remember or know how it all works at a time down the track!
Tausch
1 / 5 (1) Feb 22, 2012
There's a difference between USING a signal that was decomposed into its fourier coefficients via a some material object (ears/brain) and performing the math. - AP


True. The subtle point is - is cognitive 'awareness' the all- decisive criteria to assert performances of math?

To label any human life form as anumeric simply because such life forms have not yet formalize the physical of their existence according to the conventions of a specific language (math) is detrimental bias on the part of the researchers.

You can do 'math' without words.

You are -

according to another society 'language' the quintessence of what those other societies languages have come to label by convention

- math.

All human languages are numeric.
Tausch
1 / 5 (1) Feb 22, 2012
Shaffer da has earned and deserves the highest rating. The comment above is equivalent to shaffer da's highest rated comment.
birdie_can_fly
not rated yet Feb 24, 2012
Makes me wonder what concepts I'm missing because my culture doesn't have the right words.


I think alfie_null is spot on. While the Piraha may not have words to specify exact quantities (as they have no need for such), they may have words that define other concepts more succinctly than our own. Such words may have been created by need, as is the case for Eskimos whose language has many words for 'ice' (based on description and application); or to aid philosophical discussion, a good example being the Greek language which has at least three different words for 'love'.

Am I saying we should adopt words from other languages when English falls short? If the use of such words will enlighten us and be of use, then yes. More importantly, we should recognise the innate value of other cultures and languages to understand concepts for which we have no words.
antialias_physorg
not rated yet Feb 24, 2012
hush1:
is cognitive 'awareness' the all- decisive criteria to assert performances of math

Yes it is, because math is an artificial (human created) model - not a fundamental property of the universe. The universe doesn't operate on math. Math is used to DESCRIBE it.

Don't confuse a model with the cause.

All human languages are numeric.

This is either a meaningless statement or totally wrong (if you read the article at all)
Tausch
1 / 5 (1) Feb 24, 2012
The language of math asserts the consensus of math's description to describe the models of the universe sufficiently, necessarily and, of course, incompletely.

Math is the language of choice and description to support and underscore all of science's models

Don't confuse a model with the cause. - AP


The ultimate 'cause' for science is unattainable.
Models/descriptions are sufficient, necessary and never complete.

The universe doesn't operate on math. - AP

Agreed. Of course not.

Humans 'operate' on descriptions. We assert our descriptions to function without cognitive awareness. You don't.

The researchers assert the Piraha people of the Amazon are a group in possession and use of a language and understanding that has no numeric concept.

We do not have an ultimate 'cause' for human languages.
We will always have a description for human languages.
By consent we agree math is the best descriptive, supportive tool for all of science, research, observation and data.
birdie_can_fly
not rated yet Feb 24, 2012
My apologies, Eskimos have multiple words for snow. I'm not sure if they have multiple words for ice. I suppose it's possible.
braindead
not rated yet Feb 25, 2012
We have a system of numbers - we have a system of words - suppose the aliens came and they had a system of something else we had never thought of? I am reminded of "Flatlanders" here.
braindead
not rated yet Feb 25, 2012
My apologies, Eskimos have multiple words for snow. I'm not sure if they have multiple words for ice. I suppose it's possible.


Skiers also have multiple words for snow too. I expect the Inuit have more though;) Glaciologists and oceanographers have multiple words for ice too. Ice and snow lie on a continuum anyway. Even Scott, in this hundredth anniversary year, knew the word "sastrugi" which I bet he didn't learn as a boy - language just fills to fit the need or doesn't if there is no need.

Lurker2358
not rated yet Feb 25, 2012
We have a system of numbers - we have a system of words - suppose the aliens came and they had a system of something else we had never thought of? I am reminded of "Flatlanders" here.


Humans have used pictures for communication. Hieroglyphs, diagrams, cave drawings, etc.

Western, modern civilization combines all forms of communication of which I am aware, either actively or as a novelty.

We still use hieroglyphs and similar pictures in traffic signs, as well as brand logos, hazardous material markings and other safety signs in the work place, etc.

We don't have universal translators yet, but some of the tools online using xml, scripts, and tables are nearly as good for translating.

Traffic lights could theoretically communicate 8 different states without using flashing, via binary. Right now, the non-flashing states are "go," "caution/transition," and "stop". Thing is, there's no need for the extra states, although some are set to flash during a malfunction or a disaster.
Isaacsname
not rated yet Feb 26, 2012
Wow,...I'm humbled by all the smart people here.

*yawn*

Has anybody here read Everett's book : Don't Sleep, There Are Snakes: Life and Language in the Amazonian Jungle

?

It's one of the most eye-opening books I have read in the past 10 years, aside from Rimbaud's " Illuminations ".

http://www.amazon...07386120

Well worth the read, it was a life-changing experience for a " man of the cloth " to lose all those silly sacrosanct precepts he'd been clinging to, humbling himself to learn some things.

Mike_Massen
1 / 5 (1) Feb 26, 2012
@Isaacsname
Re: "Don't Sleep..."
You mean it offers incontrovertible logic proving the fallacy of the rationale behind Moses' ideas in the bible, such as Genesis ?

I thought I was the only one who worked that out but haven't got around to writing a book on it yet :-(

I'm still working on the problems of religious memes ingrained by familial authority and linguistic constructs in respect of the self referential emotional hypnosis that makes many simplistic religious zealots and like minded automatons so fervently against anti-theists or anyone that doesn't automatically believe in "Voices in the Head" from 'oh so long ago' ;-)
determinist
not rated yet Feb 26, 2012
Is Lerker just stirring the pot to ellict predictable responses? We already know that he is a person of science and has a propensity for debate. You go Lerker!
Deathclock
1 / 5 (2) Feb 26, 2012
And with software, a single individual can code a highly complex piece of software, perhaps over many years, and he, himself, may not remember or know how it all works at a time down the track!


You've just described 75% of the sources of stress in my life...

"Oh by the way deathcloc, remember those 100,000 lines of code you wrote 3 years ago for this project? Did you use a CPU timer for the pulse width modulation or did you use the external real time clock? This is super important and I need the answer in the next 5 seconds!"

"I have no idea"

"WHAT DO YOU MEAN YOU DONT KNOW, YOU WROTE IT DIDNT YOU? HOW CAN YOU BE SO IRRESPONSIBLE NOW THE REVISED SCHEMATICS I JUST SUBMITTED MIGHT BE WRONG AND THE NEW BOARDS ARE BEING ETCHED AS WE SPEAK. What? No I didn't think of asking you earlier I thought you would just know!"

/facepalm.