Last week, some of you may have seen this article about a study on Australian aboriginies. The study suggests that, even without having the language to describe numbers, the human mind has an innate ability to count and differentiate between numbers.

The study focused on two Aborigine tribes in Australia, and found that even though both tribes lack words for individual numbers (the languages only have words to describe ‘one,’ ‘two,’ ‘few,’ and ‘many’), members of the tribe nevertheless seem to have a sense for different numbers and counting. This conclusion was reached, for example, by banging two sticks together n times, and asking children to represent those n times with concrete objects.

I am no linguist, so I cannot speak to the linguistic ramifications of this study. From a mathematical viewpoint, however, it is certainly a good thing to hear, because it suggests that the ability to count is innate within all of us, independent (in a sense) of processes so natural that we take them for granted (e.g. language).

It is tempting to extrapolate broad claims from this, e.g. mathematics is so fundamental, we all have an ingrained understanding of it on a basic level. This may sound a bit insulting, however, to those who have struggled in their math career, and is also a bit unfair since we can’t really extrapolate much about mathematics in general on the basis of this one study. However, the suggestion that such a fundamental mathematics principal is somehow innately wired into our brain hopefully will help persuade skeptics that, at least on some level, mathematics is not a black box – in fact, the theory is often developed from natural and intuitive principles, and is motivated by the desire to solve real-world problems.

At the same time, one hopes this news does not spell the end for Count von Count. Even though we apparently can count without the language to describe what we are doing, having the language certainly can’t be a bad thing, can it? For his sake, let’s hope not.

Count von Count may need to diversify.

You had better get a comment from Gabe-o on this one!

i. love. that you have a math blog.

In a lot of ways, this is part of a larger linguistic question: the Sapir-Whorf hypothesis. The SWH (loosely) says that our language usage shapes our thoughts. Obviously that’s true to some extent, but how much? Does not having a word for a concept prevent you from understanding the concept? Almost certainly not, and I think that’s what this study shows in the special case of numbers.

The bigger question is whether lacking a word for a concept impedes understanding, and if so how much. I guess it would be interesting to compare counting abilities of ‘one-two-many’ speakers and ‘one-two-three’ speakers.

All that said, though, I would be very reluctant to say that this indicates that there is any innateness to counting. And even if counting is innate, counting could exist as a skill separate from any math. People could think of the number line as no more logically ordered than the alphabet. ’3′ follows ’2′ as surely as ‘C’ follows ‘B’, and if you hit a stick nine times, I could count up to ‘G’, but that doesn’t mean that I would associate ‘G’ with the abstract mathematical notion of nine.

But I may be saying all this in hopes that Count Von Count will stay gainfully employed. The aristocracy doesn’t pay as well as it used to.

Also, you may be interested in the recent research on the Piraha. They’re an Amazonian tribe that appears not to use linguistic recursion, which is totally irrelevant to your point. The more relevant point is that there has been some question, if I remember correctly, as to what their counting abilities are.