The Language Without Numbers

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An interesting news story from the past few years is the Amazonian language Pirahã which lacks number words. That is, instead of counting quantities (1,2,3,4...), the Pirahã only estimate quantities (relatively small, relatively large). The latest study from MIT seems to confirm this. Interestingly, when objects are taken away from a pile, the estimates change so that "small" may become 5-6 instead of 1-2 as previously thought.

This has perplexed linguists since almost all languages have some sort of counting (even in remote locations). The only other examples of low-tech numbers had been systems of 1,2, many. We normally think of counting as a "basic" cognitive skill, but it appears to be primarily cultural.

I first about this in 2000 from a guest speaker Peter Gordon. His evidence was convincing, but there have been some points I have been pondering.

  • Pirahã children who learn Portuguese also learn to count - it's not a difference in cognition [Peter Gordon, personal communication]
  • Not surprisingly, male laborers in Brazil are stiffed a lot because they do not pay as much attention to "exact" quantities. However the Pirahã women are reported to gently mock their men folk for this [Gordon, p.c.] It reminds me of cultural gender stereotypes like men can't pick coordinating colors and women can't work with computers (and yes many of us buy into them whether they are 100% true).
  • Many animals can easily distinguish quantities of 1,2,3, (or a little more) on sight, but after that they guesstimate. In this study, monkeys can recognize quanities of 1-4, but estimate after that. This predicts that a basic counting would be something like 1,2,3, many, but the Pirahã system is even more basic.

It is startling to think that counting could be essentially "cultural" because almost every other culture has some form of counting, but when I read more, I did realize that there is some truth to this. For instance, most languages have unique words for one such as one, aon (Irish), bat (Basque), but once you get into the range of 1,000,000 (one million), the word starts to resemble million in many languages (e.g. 1 million = milioi in Basque). That's because the concept of such a large quantity is relatively new (few hunter-gatherers needed to count to 106). As modern technology spreads, so do numbers (Basque itself apparently borrowed 1,000 mila from the Romans (i.e. Latin millia).

Even in my lifetime, I can see the scale of numbers "escalating". When I was a teen, 80 KB (80 kilobytes or 80,000 bytes) was a lot of memory, then in college computer drives came in sizes of 1-2 MB (megabytes or 1-2 million bytes), but today you need a hard drive of about 80 GB (80 giga butes, or 80 billion bytes). Now I'm seeing references to terabyte drives (a trliion bytes). Believe me I could not tell you what giga- and tera- were in 8th grade. Now I see on the Wikipedia SI prefix page that you can get up to yotta- (1 septillion or 1024). But I'm pretty sure there's some room for more prefixes

Postscript (24 Jul)

Pirahã is considered to be a member of the Muran language familty, and I had been wondering if the related languages had any counting. Alas, all the other Muran languages are now extinct. I'm still not sure about Everett's claim that Pirahã culture does not deal with abstract topics - That is unbelievably rare considering almost all cultures have art, mythology, and pretty elaborate kinship systems.