Outside of academia, the Piraha are most famous for the fact that their language has no numbers of any kind. There is a word for "one", but it can also mean "few", and there is a word that can mean either "two" or many. But if you want to say "three" or "four", you're simply out of luck.
The bizarre features of the language don’t stop there. Piraha uses only eleven phonemes, or basic sounds their words are built out of, which is tied for the fewest of any language. For comparison English has 40-something, depending on the dialect. Piraha has no discernible words for colors. They use the same word for mother and father, and there are no words for kinship relations more distant than siblings. But the most baffling thing that Piraha lacks - at least for linguists and cognitive psychologists - is something called “recursion”. Recursion is a property of grammatical structure that lets us embed one idea in another. It is the key that gives a language like English - or any natural language besides Piraha - its infinite expressive power.
All other languages in the world are basically on equal footing. Anything that you can say in English can be said equally well in Mandarin, Navaho, Swahili or Kivunjo, and vice versa. The only real trouble that comes up is if one language has a word that doesn’t have a translation in the other language, but in that case you can explain the meaning on the fly. Vocabulary and syntax may vary from language to language, but their expressive powers are all fundamentally equivalent. The only exception is Piraha; could this help explain why the language, and the people who speak it, are so unique in other ways?
The study of the Piraha was pioneered by Daniel Everett, and any discussion of the Piraha comes with the caveat that Everett’s ideas are controversial in the linguistics and anthropology communities. Everett began his career as a Christian missionary, sent to evangelize the Piraha because of his gifts with language. In twenty years of trying, no missionary had so far managed to even figure out their tongue, and it was hoped that Everett could finally bring them the Gospel. While Everett did manage to learn Piraha, the mission itself backfired. Not only did Everett fail to make converts (Piraha culture is focused on the here-and-now, and they couldn't understand Everett's fascination with a man he'd never met), but he lost his faith himself and became an academic linguist. It was Everett who first discovered the fascinating properties that Piraha has, but since then many of them have been verified by other researchers.
Let me give a little better explanation of what, exactly, recursion means in a language like English. In grammar, a “clause” is the smallest unit that makes a complete statement. For example, “I ate the cereal enthusiastically” conveys a single, complete thought. Structurally, a clause has one subject (“I”) and one verb (“ate”). It might also have things like an adverb (“enthusiastically”) or an object (“the cereal”), but the subject and the verb are the two essentials. A sentence that has only one clause is called a “simple sentence”, like the one above, but it is also possible to embed one clause into another and create a “complex sentence”. If you say “I ate the cereal, which had gone stale, enthusiastically” there are two separate pieces of information: “I ate the cereal enthusiastically” and “the cereal had gone stale”. The latter clause has been embedded into the former, adding an extra layer of meaning to it. Embeddings like this are what constitutes recursion.
There are many, many ways to embed one clause into another. A more complex example is “I think that the suitcase is heavy”. In this case the notion that "the suitcase is heavy" is treated as a subject of discussion in its own right; the sentence as a whole says that I think this proposition is true. So far we’ve only discussed sentences with one layer of recursion, but you can make it as deep as you want. “I think that the suitcase is heavier than the backpack that I still have from when I was in college.”
According to Everett, the Piraha language never embeds one clause within another. If you want to say “my friend, who grew up in Maine, now lives in Washington”, it must be broken into “my friend grew up in Maine” and “my friend lives in Washington”. And if you want to do more complicated embeddings you will have to be even more round-about. Piraha partially compensates for this by modifying the verb to convey additional information. For example, you can add a suffix to the verb to say whether you know your statement is true firsthand, or whether you heard that it was true, or inferred it. This is the equivalent of using recursion to say “I know for sure that...”, “I heard that...” or “It sure seems like...”. With a few work-arounds like this, the Piraha language is sufficient for the relatively simple life of its speakers, but it still lacks the expressive power of fully recursive language. You simply can’t say “I hope that the fish that jack caught tastes like the one that I ate at Sandy’s house when I was there for dinner”.
Though it may look a lot different at first, counting is essentially a recursive process. You start with the number one. What is two? Well, it’s the number that comes after one; the number one is embedded in two by the “+1” operation. What is three? In the same way it’s just two nested into the “+1” operation, and so on ad infinitim. The difference between counting and language is that counting only has one, very simple type of embedding; language is tremendously more complicated.
The Piraha’s lack of recursion is far-reaching. They don’t use it in their language. They don’t even do the recursive process of counting. Now, there are actually many hunter-gatherer tribes that don’t have specific words for numbers. But generally they will at least do things like counting on their fingers, and when they are taught a Western language they learn the numbers along with it. But what makes the Piraha stand out is that nobody has managed to teach them counting. Everett spent 8 months teaching math classes to them (which they had requested, so people couldn't take advantage of them while trading), and by the end not a single person could count to ten. In the same way, no adult Piraha have managed to master Portuguese, the language of mainstream Brazil; they can pick up enough vocabulary to do a little bit of trade, but they can never fluidly put sentences together. Everett explained both of these phenomena by saying that the Piraha are extremely conservative; they feel no need to absorb anything from other cultures, and indeed they actively resist foregin influence on their way of life. On the other hand Everett’s colleague Peter Gordon, a professor at Columbia University, studied them independently and concluded that it’s not by choice. According to Gordon, adult Piraha are cognitively incapable of learning to count. They simply can’t wrap their heads around the idea of repeatedly adding 1 to construct an infinite sequence of numbers.
If this is true, and the Piraha are truly incapable of counting, what could be the reason? There’s nothing deficient about their food or water that would cause a disability. It’s also not genetics; there is plenty of interbreeding between Piraha and other peoples. And furthermore, according to Everett the children *can* be taught to count. The one conspicuous thing that makes them unique is the lack of recursion in their language. This dovetails with the fact that they seem unable to master languages beyond Piraha; could this be the key?