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[Warning: Extreme Political Incorrectness Ahead!]

Here's an interesting article that says that human tribes without words for numbers larger than very small numbers (e.g., one) have trouble counting:

Some argue that--at least until recently--the Pirahã haven't needed a counting system. Because they don't trade with the outside world, they can simply indicate by gesture that they would like to exchange, for example, this basket of nuts for that chicken. Cultures with more elaborate trade systems--especially those that use currency--require the ability to label specific quantities, notes Gordon.

As a result, the tasks Gordon gave the Pirahã people in his Science study may have seemed alien to them. In one typical test, the researcher set out a group of one to 10 nuts and asked each participant to place an equal number of batteries--used because of their availability and size--on the table. The participants performed perfectly when matching sets of up to three batteries, but at four batteries the accuracy rate dropped to about 75 percent, and by nine none of the Pirahã got the right answer...

...the example of the Pirahã tribe shows that language may have more sway over numerical concepts than many previously imagined.

..."The lack of number-words seems to preclude the ability to entertain concepts of exact number," Gordon says. "There may be other ways to learn and represent exact numbers, but in the normal course of human learning, language is the route we take."


First, let's deal with the (politically hyperincorrect) notion that this is a tribe that's genetically incapable of dealing not only with higher math, but basic arithmetic.

It's possible, and to determine that, one would have to take a few offspring of the tribe, and raise them in a culture in which they were taught mathematics, and see if it took.

I think it unlikely--they're probably fully sapient--but that gets us on to my more serious politically incorrect take on this.

We've been told for years by the politically correct that "ebonics" or "black English" is as legitimate a form of the language as standard English, and that black children shouldn't be penalized for using it (even though such usage could cripple them in the potential range of employment and social opportunities in which they might otherwise engage). That it had its own grammar, but was just as useful a language, with the ability to express just as complex concepts, as the norm.

Well, maybe. But consider this thesis, based on the article cited.

If the grammar (and vocabulary) of a language can restrict the ability to deal with mathematical concepts, isn't it possible that an inner-city patois is similarly unable to allow the mind to grasp concepts that are necessary for life in a highly technological society?

What I have in mind is specifically the construction, "I ain't got no [fill in the blank]" or "I ain't got none."

Any rational breakdown of these phrases would indicate that they are a double negative (the word "ain't" presumably being "I have not"). There's nothing wrong with the word "ain't" in this analysis, though it's somewhat crude, but its meaning in this construction is important. If one were to interpret the phrase literally, accepting the meaning stated of the contraction "ain't," it would mean "I have not got no whatever," which is a double negative. Having none of nothing means that one has something. In the specific case, saying that "I have not got no bananas," would literally mean that I do in fact have a non-zero quantity of oblong, pointy-ended tropical fruit with a yellow skin and sweet starchy interior. That in fact, his statement meant the exact opposite of what he was attempting to convey. If one wanted to express the opposite--to wit, that one had none of said tropical fruit--one would say that "I have no bananas," with the singular negative descriptor.

Now, I know that everyone knows that when one says it the ebonics way that the meaning is intended to be that yes, he has no bananas, he has no bananas today.

But still.

This may sound pedantic, but the concept of a double negative is a vital one in the instruction of algebra (a pre-cursor for calculus, the gateway to higher mathematics). If you said to a fluent ebonics speaker (who was unfamiliar with standard English) "What is the product of negative two and negative two"? would it be:

a) easier
b) harder

to convey the notion that the answer was a positive four?

Just askin'

[/Extreme Political Correctness]

Posted by Rand Simberg at February 09, 2005 05:24 PM
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Here in Washington State, _today_, the chair of the King County Council (Seattle's county) said "The facts are clear. We had an election that was 99.98% accurate." When asked what numbers he'd used, it was "nearly 900,000 votes" and "an 1800 vote discrepancy" (Note that 'nearly' makes the discrepancy smallest if you assume the full 900,000 votes.)

In a contested election, the pivotal county's official 'Report on the November 2004 vote' is only off by _one_ order of magnitude. Sheesh.

I can't say if he's a proponent of ebonics, but he is adamantly opposed to our statewide assessment test.

Posted by Al at February 9, 2005 06:21 PM

Hang on a second here before you go off on ebonics like that. There are other languages, like russian, for instances, where double negatives are not positive. According to my source, my sister who learned russian and lived in southern Russia for a year and a half, the more negatives you put in, the more negative the whole sentence is. You have to put in at least two before anyone will believe that you are saying no.

Now I think you would agree that a culture which can support a space program with a language "handicapped" like that is not affected by language innumeracy in any significant way.

There are certainly other valid arguments against ebonics, but this is not one of them.

Posted by Anonymous Coward at February 9, 2005 06:52 PM

AC, how are Russian double negatives constructed? Language structure can be parallelled to the structure of an equation, so that elements such as negatives can relate in an additive rather than multiplicative manner.

That may be how it works in Russian syntax, or it may not. More information is required.

Posted by McGehee at February 9, 2005 08:13 PM

AC is exaggerating. Double negatives in Russian follow very strict rules, usually a negated verb with a nu1l subject, such as:

Ya nichevo ne znayu.

Literal translation: "I nothing not know".


Ya nigdye ne byl.

Meaning "I nowhere not was".

Those structures are so tight, normally people are not even aware they are double negatives. Indeed, if you drop one negation in either example, people will understand you (and will belive you :), but will also know you are not a native speaker. The phrase "I was nowhere" (Ya byl nigdye) is not grammatically correct in Russian.

But that does not mean you can throw double negations a la Ebonics. Aside from these special cases, a double negative in Russian is just that -- a positive. "Ne bez oshibok" (Not without mistakes) means just what it does in CORRECT English -- with mistakes.

Rand -- did you know that this form will not accept thw word N-U-L-L?

Posted by Ilya at February 9, 2005 08:52 PM

I very sceptical about Gordon's article. Why is language responsible for the difficulty with counting? Why isn't it something simpler like they haven't learned or they think it's unnecessary?

After all, I know some habitually late people. I know that they can tell time and still they're always late.

A better example: In oral story telling culture an exact retelling of a story is not a word for word retelling but a retelling that captures the essence (plot, etc.) of the story. In the same way, perhaps the "equal" of the Piraha is what we would consider approximately equal. Consider, Are six small chickens twice three large chickens?

Posted by Lars at February 9, 2005 09:36 PM

Professor (lecturing): There are some languages in which a double negative is a positive, and some in which it is a negative. However, there are no languages in which is a double positive is a negative.

Student (dismissively): yeah, yeah.

Posted by Paul Dietz at February 10, 2005 03:41 AM

I wasn't listening to true ebonics, but I recall years ago overhearing a conversation where the speaker (a woman) described some gossip and who said what. What struck me as odd was how she described all communication using some variant of "say". So-and-so said this, so-and-so was saying that. I still wonder in a 1984 sort of way what concepts of deception and misdeeds could be hidden if everyone had a vocabulary that limited.

Posted by Karl Hallowell at February 10, 2005 04:49 AM

Well, if you really want to get into the question of number words in preliterate peoples, you should read Karl Menninger's classic on the subject. Generally, preliterate people have very rudimentary number vocabularies, and when the need to handle larger numbers starts to arise, they develop techniques to allow them to discuss and record larger numbers in advance of developing the vocabulary -- like tally sticks, for example.

As for double negatives, AC is right -- there are plenty of languages that use them. They think of it as "agreement in negativity", sort of parallel to our concept of "agreement in number".

Posted by Jim Bennett at February 10, 2005 06:18 AM

Very true re Russian -- wow, there are highly experienced people reading this thread, for sure!

Re: "how she described all communication using some variant of "say". "

Interesting observation. There are some languages (such as Serbian) that have a special verb tense for things that a person has only been TOLD but hasn't actually witnessed directly. Sort of a pseudo-subjunctive ('subjective'?) tense. And others -- such as Japanese -- where there is a verb form restricted to actions DESIRED but not yet real.

And there are many tales from preliterate cultures involving counting in which people were quite capable of accurately conveying a large number without being able to verbally express it - one case that came to mind was a khoisan scout describing a herd of, I recall, 47 elephants by holding up all fingers four times, a fist once, and then two fingers, as if he had laborously matched, finger by finger, his hands to the herd, and remembered the result. Presumably if the tribe in the original story had been allowed to manually manipulate the two populations of objects, pairing them sequentially, they would have gotten the correct answer.

As to ability to manipulate numbers, years ago I worked for the DoD in Washington DC and for the sake of urban tranquility our office was required to hire several local kids as summer aides, and they were assigned to answer phones and write down telephone numbers. I recall the general exasperation that they rarely, if ever, got the verbally communicated number accurate on the note -- some digits would up transposed. But I presumed this was just a matter of practice because this is a mistake that anybody can make occasionally, and practice improves the skill.

Posted by Jim O at February 10, 2005 06:24 AM

"In a contested election, the pivotal county's official 'Report on the November 2004 vote' is only off by _one_ order of magnitude."

One of our Houston urban representatives in Congress has a habit, when describing somebody reversing a policy or view, as proclaiming that 'they have changed course an full 360 degrees on this issue', and nobody on her staff seems to have had the nerve (or knowledge) to tell her how big a fool it made her look.

Posted by Jim O at February 10, 2005 06:27 AM

Languages of Pao by Jack Vance covered a similar concept, that language effects culture. The story is about changing the language of the planet to help them be more militaristic and thus willing to defend themselves.

I wonder if such a theme could be written now. Anyway 2-points for science fiction for dealing with the topic.

Posted by rjschwarz at February 10, 2005 07:22 AM

In Spanish they say "No tengo nada," which is about as concise a double negative as you can get. But somehow the Spanish-speaking world does their sums. I agree with your idea, but you need a better example.

Posted by slimedog at February 10, 2005 08:46 AM

I'm not claiming that ebonics speakers are intrinsically incapable of learning algebra, Slimedog--just that this might be one more (of many) barrier to inner-city education.

Posted by Rand Simberg at February 10, 2005 08:49 AM

Some languages require in some cases that the verb distinguish how you know what you are stating. When I was studying Chippewa I remember that sentences that would use the verb "to be" in English had different forms depending on whether the knowledge was via direct and immediate observation, knowledge of habitual behavior, hearsay, or other indirect evidence.

Posted by Jim Bennett at February 10, 2005 08:55 AM

The whole Piraña flap has been viewed with considerable bemusement by linguists -- as Jim Bennett says, if people have a need to express complex numerical concepts they'll invent ways. (See also Language Log's extensive discussion:

The issue with Ebonics is that for any other diglossic situation (where two languages are in use in close proximity) the data clearly show that primary education in one's first language (with later transitions to prestige dialects if necessary) is far better than starting with a language with which the student is unfamiliar.

Posted by Gordon at February 10, 2005 08:58 AM

"I'm not claiming that ebonics speakers are intrinsically incapable of learning algebra, Slimedog--just that this might be one more (of many) barrier to inner-city education."

Let's look to the reverse examples. Pick German and French. (French uses two negating words in a sentence that ends up in the negative as well, but that's not what I wanted to focus on.

Although there are clear counter examples, I'd propose that French might be a better language for poetry and song than German. Conversely German appears more useful in the hard sciences. (Yes, Wagner, yes there's French scientific journals.)

But you can see _why_. The German approach of 'add more modifiers' gets you some seriously long words. Long words aren't necessarily going to fit your cadence. But you can arrive at precision when you can tack more modifiers into your word....

The main premise of this entire post is "All languages are not created equally useful for all tasks." It seems pretty irrefutable, and if it doesn't seem so then think about discussing the trajectories of quarks in the made up language of Klingon. Or Shakespeare in syntactically correct C.

Posted by Al at February 10, 2005 10:19 AM

As others have noted, that example is a bit off, there are other languages where a double negative is still negative, and those speakers do not seem to have issues with algebra.

Mind you, what interests me is how patterns of thought can affect language. For a good example, listen to the english spoken by a group of computer programmers or engineers. Even ignoring the technical jargon, people who are used to very precise thought use language in noticeably different grammatical patterns from common use. I myself have internalized boolean algebra to such a degree from programming that I have mistakenly answered "Do you want x or y" (where x and y are nominally opposite things) questions with "Yes", and then had to take a moment to figure out the reason for the other person's confusion. :P

Thusly I think that it is more likely to be that the tribes count poorly AND have few words for large, exact numbers, *because* they don't use large numbers often, rather than them counting poorly because they lack words for the numbers.

Posted by Monsyne Dragon at February 10, 2005 10:28 AM

I wouldn't worry too much about "ain't got no" as negatives are troublesome to all kinds of people and are frequently miscounted or ignored.

In logical arenas, like my computer programming world, that's a problem. One of the tasks I often find myself doing in program maintenance is to convert negative expressions to positives, like "not less than" to "greater than or equal to". Such changes usually make the logic easier to follow.

But linguistically, most people who say they "could care less" when they mean they couldn't are unaware that their meaning is based on irony, not logic.

Another phrase I used to tease my wife about until I realized many well educated friends have the same problem is the construction "I'm going to miss not going" when they can't make a trip.

But my favorite was about a year ago, when Newsday quoted an attorney who started a statement, "We have no doubt the Supreme Court will not disagree with this decision..."

In short, I ain't going to pick on nobody about this sort of thing no more.

Posted by Doug Murray at February 10, 2005 10:30 AM

Quoting Monsyne Dragon:
I myself have internalized boolean algebra to such a degree from programming that I have mistakenly answered "Do you want x or y" (where x and y are nominally opposite things) questions with "Yes", and then had to take a moment to figure out the reason for the other person's confusion. :P

That's odd. I program for a living and I didn't understand your point at first. I think of "Do you want x or y" as
if ( $desire eq x ){
answer (x);
} else $desire eq y ) {
answer (y);

not as:
if ( x or y ) { answer yes }
else { answer no }

I do see your point if the statement is taken literally.


Posted by Fred K at February 10, 2005 10:50 AM

Re: "ebonics" and math

I seem to recall seeing a book on this subject some years ago entitled 'Twice as Less.' Might be worth a look.

Posted by Dick Eagleson at February 10, 2005 10:55 AM

A fascinating post. The funny thing is, I have always taken mathematical thinking to be the prime example of non-verbal reasoning. At least, when I am doing serious mathematics -- not just calculation -- I seem to be using kinesthetic and visual structures in my head. The translation into words and symbols comes afterwards and is often quite laborious. Based on conversations with other mathematicians and physicists, I'd say that this sort of experience of math is widely shared.

But the present post suggests that those non-verbal structures may have some basis in the language that I learned as a child. Curious.

Posted by Ben at February 11, 2005 07:03 AM

I'm not sure which is more interesting, the ideas that the post suggests, or the reactions of the people that read it and completely ignored the first line and last two lines of the post...

Posted by John Breen III at February 11, 2005 08:34 AM

I have a small rebuttal over at:

Posted by tobias s buckell at February 11, 2005 08:54 AM

And I'm sorry I somehow gave you two trackbacks. I'm not sure how that happened.

Posted by tobias s buckell at February 11, 2005 08:55 AM

I too think mostly in the "kinesthetic and visual structures" that Ben described, and it has made helping my wife learn algebra challenging. All of the 'tricks' I learned from math teachers over the years mostly involve this kinesthetic/visual sense: they are all spacial, such as 'flip this side of the equation over there to the bottom' to describe division, for instance.

Turns out that it seems spacial reasoning ability corresponds to testosterone production, and that women with (naturally or artificially) elevated testosterone levels in the same range as men have comparable spacial reasoning ability. Cites are somewhere in my bloglines feeds in the past year :-)

Not surprising when you think about it from an evo-bio point of view: that kind of spacial and single focused mindset sounds an aweful lot like hunting, does it not?

One is literally hunting for a (hopefully!) singular solution in a maze that is the equations. Often you hit a blind dead end and have to back track. Done any nasty integrals by hand lately? :-)

Being so focused that you literally lose track of all of the outside world that isn't directly related to your singular goal is great for hunting, and lousy for raising kids. Which also neatly explains the female nack for multitasking.

Its a shame that the president of Harvard didn't have the right cites with him recently, isn't it?

And veering back to the more direct topic at hand, I certainly think differently in yet a different way when my mind is in 'French mode'. It's more emotionally precise, and yet a bit colder at the same time. BTW I think French is great for mathematics (I prefer the French version of 'The Fractal Geometry of Nature', for instance) but lousy for computer science.

And I have no clue which languages are best for other disciplines: my personal repertoire is English, French, and dozens of computer languages.

Posted by David Mercer at February 11, 2005 09:56 AM

I think it was Frederick the Great who said,

I speak French with my diplomats,
I speak Italian with my lover,
I speak English with my business man,
I speak German to my horse.

Posted by Bob Mitze at February 19, 2005 10:44 AM

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