Aren’t numbers a human universal? Sure, it’s hard to talk about curves without defining “curve” first, but if I can just draw in the sand and say “that’s a curve,” we’re back to the option of communicating the gist of things without handing the person a textbook. Could I communicate any sort of higher math I know in this way? This is tricky because I can’t think of anything, but that’s hardly a general proof. Maybe quaternions would be hard to communicate to a hunter-gatherer, but again “hard” is a far cry from impossible.
The last time I looked this up, all results on the Piraha language are due to a single anthropologist, Daniel Everett. There’s been some debate in the literature about whether or not he was actually correct about their innumeracy; see the “Further Reading” section on the wikipedia page for some examples.
On the object level, your belief-as-stated is not conclusively known. Everett sub 1986 believed that there were words for “one”, “two” and “many”; this belief was updated in 2008 when one speaker in an n=4 study used the word for “one” when there were six things presented to them.
On the meta-level, none of Everett’s results (as far as I know) have been replicated by an independent anthropologist, which means that your belief-as-stated has one point of failure. Given the surprising nature of his results, we should demand strong evidence that his results are true and not due to, e.g., cultural/linguistic misunderstandings. In fact, the linguistics community has indeed questioned the data closely.
Aren’t numbers a human universal? Sure, it’s hard to talk about curves without defining “curve” first, but if I can just draw in the sand and say “that’s a curve,” we’re back to the option of communicating the gist of things without handing the person a textbook. Could I communicate any sort of higher math I know in this way? This is tricky because I can’t think of anything, but that’s hardly a general proof. Maybe quaternions would be hard to communicate to a hunter-gatherer, but again “hard” is a far cry from impossible.
No. The Pirahã, for example, have no concept of exact numbers, only of smaller and larger amounts.
The last time I looked this up, all results on the Piraha language are due to a single anthropologist, Daniel Everett. There’s been some debate in the literature about whether or not he was actually correct about their innumeracy; see the “Further Reading” section on the wikipedia page for some examples.
I see nothing there that contradicts what I said, but it does seem most of the links are dead.
On the object level, your belief-as-stated is not conclusively known. Everett sub 1986 believed that there were words for “one”, “two” and “many”; this belief was updated in 2008 when one speaker in an n=4 study used the word for “one” when there were six things presented to them.
On the meta-level, none of Everett’s results (as far as I know) have been replicated by an independent anthropologist, which means that your belief-as-stated has one point of failure. Given the surprising nature of his results, we should demand strong evidence that his results are true and not due to, e.g., cultural/linguistic misunderstandings. In fact, the linguistics community has indeed questioned the data closely.