‘Anumeric’ people: when a language has no words for numbers
theconversation.com
theconversation.com
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.
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.
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?
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.
The strong version has been refuted, the 'soft' version is pretty well accepted among linguists.
-This is too good an opportunity to reference Tom Lehrer's "New Math":
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.
[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
Almost certainly. Of course, 8 would still be represented as 1-0.
Or base 15, since the (mathematical) concept of zero seems to evade primitive cultures.
Even Everett Sr doesn't agree that the piraha can't count - http://itre.cis.upenn.edu/~myl/languagelog/archives/001387.h...
"Number as a cognitive technology: Evidence from Pirahã language and cognition" http://www.sciencedirect.com/science/article/pii/S0010027708...
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.
http://www.chronicle.com/blogs/linguafranca/2012/03/28/poiso... http://languagelog.ldc.upenn.edu/nll/?p=3857
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
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 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.
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 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 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'm not sure if this is the article I originally saw - I seem to remember reading a longer one.
It makes for good quips in Hollywood movies I guess. Not so great for science.
ling.auf.net/lingbuzz/000427/current.pdf
It get that's a common thing, but would prefer an external party to agree with some of his outlandish claims.