Via slashdot, I found this article on an Amazonian tribe that does not seem words to describe numbers and counting. Rather, they have relative quantifiers that indicate a quantity from 1 to 4, 5 or 6, or ‘many’. In effect, small, medium, or large.
Of course, it’s probably a bit of a stretch, but as counting forms much of the basis of math (though I wouldn’t mind hearing discussions on that), this relates, as I see it, to whether mathematics is something inherent to the universe itself, or rather something more akin to an evolutionarily advantageous artifact of our brains. Some of our brains, anyway.
Evolution almost certainly plays a role here, as the language in question is spoken by about 300 people, and they likely haven’t spent a lot of time doing commerce with other cultures.
There were some interesting thoughts raised in the comments. For instance, one person noted that most people can easily recall about five separate objects at a glance, and the perception of quantity is likely linked to how easy it is to remember the objects. Another noted that this may be a different kind of language artifact – the researchers were having them count foreign objects, but should’ve asked them to count how many children they had, or some other familiar kind of object, the idea being that perhaps different words were used for different types of things. This is interesting, because linking quantity and type descriptors would greatly diversify what could be expressed.
There are far more questions I’d like to ask. For example, the researches only went up to 10 objects. What if they went straight from 10 to 1000? While both are ‘many’, there’s a pretty significant visual difference from the sheer amounts.
Also, I do wonder whether or not, even with the limited range of quantifiers, if the speakers here make use of any kind of computational-esque rules. For example, two ‘medium’ groups combined would always produce a ‘large’ group. Very fuzzy sort of addition. Of course, two ’small’ groups combined don’t necessarily produce anything definite.
It’s all very interesting.
I might recommend this New Yorker article.
The one-two-many thing isn’t right though.
he had determined that the Pirahã have no fixed numbers. The word that he had long taken to mean “one” (hoi, on a falling tone) is used by the Pirahã to refer, more generally, to “a small size or amount,” and the word for “two” (hoi, on a rising tone) is often used to mean “a somewhat larger size or amount.” Everett says that his earlier confusion arose over what’s known as the translation fallacy: the conviction that a word in one language is identical to a word in another, simply because, in some instances, they overlap in meaning.
Comment by Jason Dyer — July 14, 2008 @ 8:08 pm
I showed you snippets of this earlier, but check out the second part of this article. I don’t like the argument it portrays because I think it misses the bigger picture, but the latter half (is mathematics innate? No!!) makes a lot of points that define how I think about mathematical ability. Much like language (perhaps even as a subset of language…?), maths seems to be largely a product of cultural pressure and then artificial selection as we groom the skill through education and our own curiosity.
As far as math being something universal, something larger than “us,” I do think that mathematics is greater than the individual. But is it greater than human understanding? Is it something we are continuously discovering, a secret of the universe we unlock with great delight? I don’t think so. Mathematics *is* human understanding, and only a fraction of it at that. A collective invention of our species, perhaps. A feat so great that the individual has lost track of the fact that math, however mysterious and obscure, is ours. It wouldn’t be the first time the human brain came up with something that transcended any predictable function of it’s humble hardware.
Comment by emifox — July 15, 2008 @ 12:33 am
[...] Mathematics and Probability Theory Over on FoxMath there has recently been posted an interesting discussion about an Amazonian tribe whose language [...]
Pingback by Language, Mathematics and Probability Theory « The Twenty Eighth Line — July 16, 2008 @ 4:54 pm
I greatly enjoyed “The Mathematical Traveler” which covers this and other evolutionary counting systems. http://is.gd/WIj
Comment by Marc Brooks — July 18, 2008 @ 3:51 am