no numbers

The Pirahã are an indigenous people, numbering around 700, living along the banks of the Maici River in the jungle of northwest Brazil. Their language, also called Pirahã, is so unusual in so many ways that it was profiled in 2007 in a 12,000-word piece in the New Yorker by John Colapinto, who wrote:

Unrelated to any other extant tongue, and based on just eight consonants and three vowels, Pirahã has one of the simplest sound systems known. Yet it possesses such a complex array of tones, stresses, and syllable lengths that its speakers can dispense with their vowels and consonants altogether and sing, hum, or whistle conversations.

Among Pirahã’s many peculiarities is an almost complete lack of numeracy, an extremely rare linguistic trait of which there are only a few documented cases. The language contains no words at all for discrete numbers and only three that approximate some notion of quantity—hói, a “small size or amount,” hoí, a “somewhat larger size or amount,” and baágiso, which can mean either to “cause to come together” or “a bunch.”

With no way to express exact integers, the obvious question is: How do the Pirahã count? More pragmatically, how do they ask for two of something instead of just one? The answer—according to some of the more recent research on anumeracy, published by anthropological linguist Caleb Everett in the journal Cognitive Science—suggests, almost inconceivably, that they don’t.

Everett, the son of Christian missionaries turned linguists, lived on and off with the Pirahã during his early childhood. His parents, he told me, speak Pirahã as fluently as any Westerners ever have, though for a non-native speaker to master the language is a near impossibility. A couple of years ago, Everett traveled back to the Pirahã villages to run a few very simple experiments.

For one test, he would lay down on a table a line of evenly spaced items, say batteries, and ask the Pirahã to make a second line just like the first. For another, he would show someone a line of items and then hide it from view. Again, he would ask for a second line just like the first. In both cases, no mistakes were made as long as the lines were just two or three items long. But, as Everett wrote in his paper, “The proportion of correct responses generally drops significantly for numbers exceeding 2 or 3.” This was true for all tasks, including a non-visual test that involved clapping. English speakers, on the other hand, make no errors at all, except when a relatively long line of items, say seven or more, is shown quickly and then hidden. We can only count so fast, after all, but the Pirahã appear not to be counting at all—because, well, how could they? Instead, they’re employing what Everett calls an “analog estimation strategy,” which works well for a few items but breaks down beyond that.

If necessity is the mother of invention, then perhaps the Pirahã never needed numbers, either because precise counting is not culturally valued or because that value has a sufficient, anumeric workaround. Nothing about the Pirahã’s self-contained way of life seems to require quantity recognition over three, says Everett, a fact that’s not lost on outsiders, who sometimes take advantage of them when trading goods. Attempts over the years to teach number words and basic arithmetic to the Pirahã have met with little success, in large part because they’re uninterested. In fact, the Pirahã have a term for all languages not their own; it translates as “crooked head,” which is intended as a “clear pejorative,” as Colapinto points out:

The Pirahã consider all forms of human discourse other than their own to be laughably inferior, and they are unique among Amazonian peoples in remaining monolingual.

In our increasingly data-driven culture, where we reincarnate ourselves more and more as spreadsheets, anumeracy is unthinkable. Many fear, amid the “advanced stats” revolution in all aspects of life, that what it means to be and feel human is forever changing, and not for the better. It’s perhaps comforting to know, then, that while we’re busy charting our heart rate and measuring our intake and poring over the wins above replacement values for our fantasy league, the Pirahã, immune to the relentless tyranny of numbers, will simply enjoy the game.

Thanks to Kebmodee for bringing this to the attention of the It’s Interesting community.

  1. Binary systems predating Leibniz also existed in the ancient world. The aforementioned I Ching that inspired Leibniz dates from the 9th century BC in China.[5] The binary system of the I Ching, a text for divination, is based on the duality of yin and yang.[6] Leibniz interpreted the hexagrams as evidence of binary calculus.[3] The text contains a set of eight trigrams (Bagua) and a set of 64 hexagrams (“sixty-four” gua), analogous to the three-bit and six-bit binary numerals, were in use at least as early as the Zhou Dynasty of ancient China. The Bushmen of Africa communicated using drums with binary tones which enabled them to encode messages.[6] The Indian scholar Pingala (around 5th–2nd centuries BC) developed a binary system for describing prosody.[7][8] He used binary numbers in the form of short and long syllables (the latter equal in length to two short syllables), making it similar to Morse code.[9][10] Pingala’s Hindu classic titled Chandaḥśāstra (8.23) describes the formation of a matrix in order to give a unique value to each meter. An example of such a matrix is as follows (note that these binary representations are “backwards” compared to modern, Western positional notation):[11][12]
    0 0 0 0 numerical value 1101 0 0 0 numerical value 2100 1 0 0 numerical value 3101 1 0 0 numerical value 410

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