A pair of stories (reproduced from The Globe and Mail and BBC News) about researchers’ discovery in 2004 that members of the Amazonian Piraha tribe apparently lack capacity for any kind of math whatsoever — not even simple counting. A few relativistic number words – “one-ish” and “two-ish” describe many and few, but that’s it. They are, apparently, alone in the world in their lack of any kind of numerical system.
… the hunter-gatherers seem to be the only group of humans known to have no concept of numbering and counting. Not only that, but adult Piraha apparently can’t learn to count or understand the concept of numbers or numerals, even when they asked anthropologists to teach them and have been given basic math lessons for months at a time.
So can they not do numbers because their language doesn’t contain the concept, or do they not have number words because their brains don’t contain the concept?
“The question is, is there any case where not having words for something doesn’t allow you to think about it?” Prof. Gordon asked about the Piraha and the Whorfian thesis. “I think this is a case for just that.”
This story brings to mind some questions I have thought of about the education system in the US.
With our narrow focus on teaching reading and math, to the detriment of science, history, and other substantive curriculum how are we affecting our children’s ability, interest, and acumen to learn new things? This is, of course, to say nothing of our insistence that these subjects must be measured by the rigid indices of the standardized test…
What I’m getting at is the human need for context and utility in the learning environment. What is the use of math and reading if such things are not given context and utility? In my subjective observations reading and math are easier to learn when applied as tools for another goal, such as in history and science. When applied in this manner the tools of basic learning become more obvious in their utility and more interesting because of the context – by learning how to read we can follow the reasoning of others, such as Alfred Nobel, learn about chemistry, and make things explode with dynamite. What competent eight-year-old boy would not desire to learn this, and by the osmosis of desires to make things explode, begin to acquire the skills of reading, writing, and mathematics!
It is my hypothesis, having not read the articles, possibly setting me on the road of error, that the Piraha have trouble with the concept of numbers because they have not, as of yet, found utility or context for their use. Simply learning to count for the sake of counting is not useful for adults who have grown up within a culture that also does not have any utility or context for such ideas.
This brings me to the question of, how might numbers relate to Piraha culture? Do the Piraha conceptualize the idea of ownership – of mine and yours? Do they have ideas on life and death? Existence and non-existence? Of distance or dimension; space? These may be points to start teaching adult Piraha the concept of numerals… and, perhaps provide some significant insights into our own motivations for learning and retention of ideas.
One of the things that trips me out here is the fact that we have a well-documented corpus of “idiot savantes” — people who can barely learn language or get by socially, but who can rattle off prime numbers faster than computers. In other words, we have lots of examples of math being somehow innate and prior to language or socialization. But this example shows just the opposite.
I’m curious whether there’s something more genetic than social/linguistic going on with the Piraha.
>I’m curious whether there’s something more genetic than social/linguistic going on with the Piraha.
Certainly this could also be the case, and would be fascinating to learn more about.
In turn, what processes of natural selection and evolution or transmutation brings about the innate ability to understand numbers? To answer such questions might begin us on the path to understanding the road from primordial soap to physics…
Mind blowing.
Soap, or soup?
Mind-blowing either way :)
The earth was cleaner in the olden days… :)
I lived with some hunter-gatherers in Centrafrique who didn’t do math. Sometimes we had little math classes while we were sitting in the forest – usually with Sharpies on leaves. The concept of addition and subtraction was totally foreign to the older guys. And when it was time to pay salaries, they had to just go on faith that we were calculating it right. But you know what? If I had some mushrooms, but Mangombe only had one mushroom, he’d damn sure point it out. You have to have a reason for numbers to matter to pay attention to them. But our notions of abstract numbers — three by itself, without counting anything in particular — don’t make any sense to those guys. Just as it wouldn’t to you if you grew up in their circumstances.
k
Goldenkate has it exactly right. All human societies develop numbers and mathematical structures sufficient to meet their needs…and no more. The ‘primitive’ people with the concept of ‘1’ and ‘2’ (sometimes ‘3’) don’t have much to count. Herding societies have something to count, so they develop a number system to count their animals, but not a system to manipulate those numbers. The meet their needs, and no more. The Romans met their needs with Roman numerals (but no place value), and we meet our needs with Hindu Arabic numerals (and place value).
The Australians at one time had a policy of taking and raising Aboriginal children within their ‘civilized’ society. Those kids, surrounded by things to count, did as well at math, on average, as the other kids.
Where else but in mathematics can all societies meet their needs? Huh?