‘Anumeric’ people: when a language has no words for numbers(theconversation.com)
theconversation.com
‘Anumeric’ people: when a language has no words for numbers
https://theconversation.com/anumeric-people-what-happens-when-a-language-has-no-words-for-numbers-75828
43 comments
Referring to your baby ability remark, it is in fact true of most mammals and most birds. You can check out the works of Stanislas Dehaene on the subject.
That's interesting. I wonder how far back in evolution this goes and where is the common ancestor that first came with basic math abilities programmed in. And what sort of advantage it creates in the natural environment.
I'll be honest, I'm not going to look up the work.
Do those experiments show definitively that babies and animals understand that 1 + 1 = exactly 2 and nothing else? Or do they understand that 1-ish + 1-ish is more than 1 -- because this isn't that much different from what anumeric groups understand. Less and more are different from discrete arithmetic, strictly speaking.
For instance, 1 fish + 1 fish might be > 3 fish, if the first two fish we're talking about are 20 and 40 lbs respectively, and then the second set of three fish are ten pounders each. In the "real world", hunter-gatherers deal with continuous mass problems at least as often as they deal with standardized, discrete units.
Did these babies and animals understand that 1 + 1 = 2 and only 2, and not 2.5? Or 3?
The abstract idea of arithmetic is something on the scale of reasoning about an idealized circle, say, which doesn't exist in nature on a day-to-day basis.
Do those experiments show definitively that babies and animals understand that 1 + 1 = exactly 2 and nothing else? Or do they understand that 1-ish + 1-ish is more than 1 -- because this isn't that much different from what anumeric groups understand. Less and more are different from discrete arithmetic, strictly speaking.
For instance, 1 fish + 1 fish might be > 3 fish, if the first two fish we're talking about are 20 and 40 lbs respectively, and then the second set of three fish are ten pounders each. In the "real world", hunter-gatherers deal with continuous mass problems at least as often as they deal with standardized, discrete units.
Did these babies and animals understand that 1 + 1 = 2 and only 2, and not 2.5? Or 3?
The abstract idea of arithmetic is something on the scale of reasoning about an idealized circle, say, which doesn't exist in nature on a day-to-day basis.
The experiment involved putting teddy bears behind a blue screen. Two bears enter the screen and when the screen is lifted with one bear or three bears, the baby will express a lot more anxiety than seeing two bears
That just shows that they understand different or more than/less than.
This conclusion is refuted by the existence of Australian Aboriginal groups with no number words who count perfectly well - http://www.ucl.ac.uk/news/news-articles/news-releases-archiv....
Even Everett Sr doesn't agree that the piraha can't count - http://itre.cis.upenn.edu/~myl/languagelog/archives/001387.h...
Even Everett Sr doesn't agree that the piraha can't count - http://itre.cis.upenn.edu/~myl/languagelog/archives/001387.h...
It's worth reading some of the papers where they discuss performance at counting tasks among the Pirahã. IIRC there were some people who seemed understood there was a difference in the quantity but struggled to quantify or articulate it; and there were other people who didn't struggle to articulate it at all, they just didn't bother with it or think it important.
"Number as a cognitive technology: Evidence from Pirahã language and cognition" http://www.sciencedirect.com/science/article/pii/S0010027708...
"Number as a cognitive technology: Evidence from Pirahã language and cognition" http://www.sciencedirect.com/science/article/pii/S0010027708...
The interesting (to me) part of all this is cognitive impacts. To what extent does thinking in numbers impact how you think about stuff.
There are northeastern Australian languages without words for relative directions (behind you, left, right). They use absolute/cardinal directions instead. Reportedly, this fosters an unbelievable sense of direction and an instinctive internal compass.
I wonder if what other basics we could add to language and what that would give us.
There are northeastern Australian languages without words for relative directions (behind you, left, right). They use absolute/cardinal directions instead. Reportedly, this fosters an unbelievable sense of direction and an instinctive internal compass.
I wonder if what other basics we could add to language and what that would give us.
I wonder how that reflects on considerations of self and environment. Using your locality as prime rather than yourself.
Interesting, it seems the Everett family is still obsessed with the Pirahã. This is both a nice thing (indigenous languages and societies are poorly studied) as a bad one (it doesn't help them with more linguistic authority at all, others should study the Pirahã instead). As a linguist I used to feel a bit of shame for liking the Everett's research, oh well...
I'm curious, why is it shameful for liking their research?
Among many linguists the whole study of the Pirahã language is sort of bogus because it goes against a few core ideas of Chomsky that they love so much, almost like a dogma. I've never heard a linguist describing Everett's work as anything other than "cute, but wrong". Personally, I think that's all sad scientifically speaking.
You must hear from relatively a lot of generativist linguists and syntacticians. The linguists at Language Log and elsewhere regularly praise Everett's scholarship in descriptive linguistics. And there is literally no important dispute left, except non-Pirahã specialists claiming Pirahã has subordinate clauses. Getting Everett banned from working with the Pirahã is just sad and pathetic.
http://www.chronicle.com/blogs/linguafranca/2012/03/28/poiso... http://languagelog.ldc.upenn.edu/nll/?p=3857
http://www.chronicle.com/blogs/linguafranca/2012/03/28/poiso... http://languagelog.ldc.upenn.edu/nll/?p=3857
The Everett Sr.'s paper that I linked elsewhere in this thread mentions a bunch of other researchers that have studied Piraha.
That article ended too early. I was looking forward to reading about how anumeric people see the world, and what happens when they encounter situations where seeing exact quantities would be helpful.
Also some example of this: "I was continually impressed by their superior understanding of the riverine ecology we shared."
I was interested to see a comparison of cultures with varying degrees of numerology in their language. I've heard that certain languages make math much easier to understand, as factors and products are self evident in the way words for numbers are constructed.
Any examples of languages like this? Are you speaking about the number base that the language works in? I have heard that a base-12 system would be much more useful than base 10 due to its greater factoring potential (2x6, 3x4). This is why there are 12 inches in a foot, and 12 hours in a day, it makes working with thirds and quarter units much easier. Wouldn't it be even greater if we worked in base 12 and 12 was represented as 1-0?
I've wondered if Chinese and other Asian languages make math a little bit more straightforward with their more consistent logic in the naming of numbers. 11 = 10+1, 21 = 2x10+1, etc. European languages are logical to a decent extent but we absolutely have more exceptions.
My favorite numbers language quirk has always been French with its preserving the 'four-score' in its numerology. i.e. 95 = 4x20+15
I've wondered if Chinese and other Asian languages make math a little bit more straightforward with their more consistent logic in the naming of numbers. 11 = 10+1, 21 = 2x10+1, etc. European languages are logical to a decent extent but we absolutely have more exceptions.
My favorite numbers language quirk has always been French with its preserving the 'four-score' in its numerology. i.e. 95 = 4x20+15
Look for the book by his father (Daniel), Don't Sleep There Are Snakes.
I'm a bit sceptical about the explanation for base10, especially in Europe.
The UK changed from a base 12 money system in my lifetime, and the history of the metric system doesn't go back all that far: https://en.wikipedia.org/wiki/History_of_the_metric_system
More info here:
https://en.wikipedia.org/wiki/Duodecimal#Origin
I'm assuming the author is the son of Daniel Everett?
The depressing end to the documentary about the nativist argument with Chomisky - https://www.youtube.com/watch?v=fcOuBggle4Y - suggests that the Pirahã - one of the peoples mentioned in the article - have been thought numeracy through a government program.
The depressing end to the documentary about the nativist argument with Chomisky - https://www.youtube.com/watch?v=fcOuBggle4Y - suggests that the Pirahã - one of the peoples mentioned in the article - have been thought numeracy through a government program.
I didn't quite get the numeracy thing, Derriz.
At about 44 minutes, it states that they are being taught to count? Or do you mean something else?
I found it sad because their previous life/existence was fascinating; it seemed to be an example of a successful (as measured by happiness) human society that was amaterialistic.
I found it sad because their previous life/existence was fascinating; it seemed to be an example of a successful (as measured by happiness) human society that was amaterialistic.
So your fascination with their way of life is more important than kids getting basic education?
FIY, mandatory schooling doesn't apply to indigenous people. But they're still Brazilian citizens, and our government is obligated by law to offer education to all citizens. Indigenous people (including the Piraha) may also be entitled to e.g. retirement benefits, so it makes sense to learn arithmetic.
FIY, mandatory schooling doesn't apply to indigenous people. But they're still Brazilian citizens, and our government is obligated by law to offer education to all citizens. Indigenous people (including the Piraha) may also be entitled to e.g. retirement benefits, so it makes sense to learn arithmetic.
I'm sad because the opportunity to study and learn from a unique human culture and society is being lost and that officials representing the Brazilian government seemed to actively block attempts at further study - which was the point of the documentary.
I also somewhat fear, from what was shown in the documentary, for their future as in many cases, suddenly introducing a more modern/western way of life to an isolated people often seems to result in social breakdown.
I believe it's best to err on the side of caution in cases like this when you are interacting with a complex delicate system.
While I would consider myself a western liberal, fully appreciative of the benefits of a western scientific education and the use of modern technology to improve human existence, I would still expect great sensitivity when introducing such benefits to a people like this.
I'm not a relativist generally but in this case, the absolutist belief that these peoples' lives will be improved by exposing them to a modern education and technology reminds me that missionaries also had an absolute belief that introducing such people to the Bible (for example) would "improve" them and we know that the results were mixed in the latter case.
I also somewhat fear, from what was shown in the documentary, for their future as in many cases, suddenly introducing a more modern/western way of life to an isolated people often seems to result in social breakdown.
I believe it's best to err on the side of caution in cases like this when you are interacting with a complex delicate system.
While I would consider myself a western liberal, fully appreciative of the benefits of a western scientific education and the use of modern technology to improve human existence, I would still expect great sensitivity when introducing such benefits to a people like this.
I'm not a relativist generally but in this case, the absolutist belief that these peoples' lives will be improved by exposing them to a modern education and technology reminds me that missionaries also had an absolute belief that introducing such people to the Bible (for example) would "improve" them and we know that the results were mixed in the latter case.
> the absolutist belief that these peoples' lives will be improved by exposing them to a modern education
I haven't seen the documentary, did anyone say that? My point is if you get monetary benefits, then you need to be able to read, write, and do arithmetic. This isn't a controversial idea. We aren't talking about uncontacted tribes. And it's voluntary. Some people want to get education, and they should be able to. The idea the that the government should somehow deny them that is untenable.
And if you think the government should not offer them social security at all then you have a bigger problem.
I haven't seen the documentary, did anyone say that? My point is if you get monetary benefits, then you need to be able to read, write, and do arithmetic. This isn't a controversial idea. We aren't talking about uncontacted tribes. And it's voluntary. Some people want to get education, and they should be able to. The idea the that the government should somehow deny them that is untenable.
And if you think the government should not offer them social security at all then you have a bigger problem.
Related: Humans Naturally Think In Logarithms https://www.scientificamerican.com/article/a-natural-log/
I'm not sure if this is the article I originally saw - I seem to remember reading a longer one.
I'm not sure if this is the article I originally saw - I seem to remember reading a longer one.
Theories as amazing as this based on one researcher I'll always default to bullshit.
It makes for good quips in Hollywood movies I guess. Not so great for science.
http://muse.jhu.edu/article/270906
It makes for good quips in Hollywood movies I guess. Not so great for science.
http://muse.jhu.edu/article/270906
> This and many other experiments have converged upon a simple conclusion: When people do not have number words, they struggle to make quantitative distinctions that probably seem natural to someone like you or me.
This kind of thing has always fascinated me. It's not just about numbers, it's about how language shapes thought.
If a language lacked the ability to express the concept of sadness, would its people be sad? Or would they just be angry because they can't explain how they feel to anyone?
If we had four digits on each hand, as some cartoon characters have, would we think in octal?
This kind of thing has always fascinated me. It's not just about numbers, it's about how language shapes thought.
If a language lacked the ability to express the concept of sadness, would its people be sad? Or would they just be angry because they can't explain how they feel to anyone?
If we had four digits on each hand, as some cartoon characters have, would we think in octal?
It's not clear cut. It appears to be the case for things like counting, as detailed by the article.
For emotions, children obviously can express a range of them before acquiring language, so it does not seem it would be the case; but that is not really a settled matter (see eg https://en.wikipedia.org/wiki/Emotion_classification)
Regarding counting, some cultures have adopted different bases: for instance, some native american cultures do use octal as they count the space between fingers rather than fingers themselves. The Mayas used base 20, presumably due to using fingers + toes.
For emotions, children obviously can express a range of them before acquiring language, so it does not seem it would be the case; but that is not really a settled matter (see eg https://en.wikipedia.org/wiki/Emotion_classification)
Regarding counting, some cultures have adopted different bases: for instance, some native american cultures do use octal as they count the space between fingers rather than fingers themselves. The Mayas used base 20, presumably due to using fingers + toes.
Sounds like it supports the Safir-Whorf hypothesis (mentioned here by booleandilemma), which has generally been refuted by linguists in recent years: https://en.m.wikipedia.org/wiki/Linguistic_relativity
>which has generally been refuted by linguists in recent years
The strong version has been refuted, the 'soft' version is pretty well accepted among linguists.
The strong version has been refuted, the 'soft' version is pretty well accepted among linguists.
> If we had four digits on each hand, as some cartoon characters have, would we think in octal?
-This is too good an opportunity to reference Tom Lehrer's "New Math":
https://www.youtube.com/watch?v=W6OaYPVueW4
-This is too good an opportunity to reference Tom Lehrer's "New Math":
https://www.youtube.com/watch?v=W6OaYPVueW4
My take is that it's not the language that shapes thought, but something else that shapes both language and thought.
Case in point: There are a few particular feelings which I experience sometimes that I recognize every time - I just find it impossible to describe them using any language I know.
Example: A sudden feeling of not recognizing the people next to you. I mean, I am consciously aware that these are my e.g. relatives, but for a split second this feeling of familiarity fades. It is clearly different than the one I get when I look at people I don't know.
I can't even tell if I'm the only one I know who experiences this, because there are no words that could describe it accurately.
Case in point: There are a few particular feelings which I experience sometimes that I recognize every time - I just find it impossible to describe them using any language I know.
Example: A sudden feeling of not recognizing the people next to you. I mean, I am consciously aware that these are my e.g. relatives, but for a split second this feeling of familiarity fades. It is clearly different than the one I get when I look at people I don't know.
I can't even tell if I'm the only one I know who experiences this, because there are no words that could describe it accurately.
I think your example describes a type of jamais vu[1]. It happens to me (and presumably everyone else) too.
[1]"A sense of unfamiliarity with, or of never having experienced or seen before, something that should be familiar." https://en.wiktionary.org/wiki/jamais_vu
[1]"A sense of unfamiliarity with, or of never having experienced or seen before, something that should be familiar." https://en.wiktionary.org/wiki/jamais_vu
I think of it as a pie that can be sliced up in different ways. All humans have a full pie. But how we choose to categorize our emotions and thoughts into words absolutely has a huge impact on our cultural and internal priorities, mores etc.
> If we had four digits on each hand, as some cartoon characters have, would we think in octal
Almost certainly. Of course, 8 would still be represented as 1-0.
Almost certainly. Of course, 8 would still be represented as 1-0.
You should check this out if you're not familiar with it already:
https://en.m.wikipedia.org/wiki/Linguistic_relativity
https://en.m.wikipedia.org/wiki/Linguistic_relativity
Non-mobile link:
https://en.wikipedia.org/wiki/Linguistic_relativity
https://en.wikipedia.org/wiki/Linguistic_relativity
I think hexadecimal would be more natural.
Or base 15, since the (mathematical) concept of zero seems to evade primitive cultures.
Or base 15, since the (mathematical) concept of zero seems to evade primitive cultures.
I remember there was a research claiming babies have innate ability to perform simply addition and subtraction (1+1=2 for example), and here is a reference to babies innate ability predicts their math skills
https://today.duke.edu/2013/10/babymath
P.S. I was also told the hardest part of researching babies is to get clearance and approval from their parents
So it seems like we as human have the basic building block for math built-in, and it takes practices and further development to create complex concepts based on those simple blocks.