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numbers and the making of us
6 february 2018
Caleb Everett's Numbers and the Making of Us has an interesting central contention: mathematics is centrally related to language, in fact wouldn't exist without linguistic structures that enable us to do math. It's interesting, at least to a 21st-century American, because we tend to think of math and language as being opposites, even enemies. STEM and the humanities are eternal opponents; the world of education is divided into math and verbal skills, which in turn seem to mirror the natural division of the human brain.
Not so, says Everett. The human brain doesn't know much about math, intrinsically. Without words to form our mathematical understanding, we can't easily perceive quantities greater than three. The best we can do, innately, with larger numbers, is to make a rough guess: three dozen things are more than 13 things, 100 things are more than 50; but the nearer such totals get to one another – even at very low quantities indeed – the more they tend to blend together in our estimation.
The limit-of-three claim makes some sense, and is easy to test in a rough fashion. Let's say you come upon a group of people in some open area. How many people? Two or three, you can tell immediately. Maybe even four or five, particularly if you were expecting to find a given four or five people there. Seven or eight? You have to do a quick count, which generally involves saying a sequence of counting words to yourself or aloud. Maybe you hasten the task by counting by twos or threes, but count you must. Aside from certain stereotypical patterns, like pips on dice or dominoes, gatherings of many more than three items tend to need counting each time you find them.
Everett brings evidence that there are people who cannot do that – not just individually innumerate people, but entire linguistic groups who are anumerate, who lack the numbers that allow them to characterize quantities greater than three. Such peoples, who include the Munduruku and the Pirahã of South America, do perfectly well at estimation: they are not under the impression that a group of three dozen people is less than a family of four. But they cannot name precisely how many more, because they cannot make a verbal count: they lack the words for it.
If the Pirahã sound familiar, especially in conjunction with the name Everett, it's because they are something of a celebrity tribe. You could have read about them right here, though it is more likely you read of them in dozens of other places. A while back, Everett's father Daniel became well-known in the academic/intellectual world thanks to claims that the Pirahã, a group he'd lived with and studied intensively, were linguistically and thus intellectually different from the rest of humanity. Not cognitively different, Caleb Everett hastens to add. Pirahã are very good at solving problems from their own Umwelt, and if they leave the group as infants and are raised elsewhere, they grow up like the people they live among. But their language lacks some elements once supposed to be universal. Everett père focused on syntax, and Everett fils, here, tackles the problem of Pirahã numbers, or the lack of them.
Most of the evidence for innate limits on human calculation comes from the Pirahã, the more numerous but still quite isolated Munduruku, from "homesigners" who invent isolated takes on non-oral language, and from studies done on pre-linguistic infants. The trouble with trying to observe humans in "natural" settings is that virtually everyone on Earth grows up counting happily to ten, and potentially well beyond, in a native language already well-equipped for enumeration. Humans may lack an inborn concept of the number "four," but it does not take a Ramanujan to observe that sometimes things come in sets of one more than three. Once that predictably encountered set is named, "five" (conveniently the number of fingers in a fist) is a logical progression, and soon we reach the condition of almost every recorded language: unique, unanalysable terms for the numbers 1 through 10 (two fists), and then generative ways of combining those unique elements to yield numbers up to 100 and more, or for that matter up to infinity.
Everett (Caleb, now) is quite good at explicating the range of number terms in natural languages. It is plausible that a sense for mathematics is largely linguistically instilled, and that acquiring it as an adult would be as hard as acquiring a foreign language as an adult. (We would still have to account for the Ramanujans of the world, mathematical virtuosos to an extent far beyond the training that culture provides, but that phenomenon is perhaps separate.)
Everett's argument, though, becomes tendentious midway through the book, when he asserts that
Language is best considered by many scholars to be a collage of culturally variable but often similar strategies for communication and information management. (144)Everett presents that assertion as a growing refutation of the notion of a "language instinct," popularized by Steven Pinker. But the "language instinct" theory is based on the empirical fact that any developmentally normal child acquires any of the world's languages with perfect ease. Those languages must be similar enough, and the mechanism that unfolds in the developing brain must fit them well enough, that language is unlikely to be a "collage" of strategies, like different techniques for building houses or weaving cloth. Naturally, no child acquires language in a vacuum; we acquire language through listening and conversation, and (as I noted above) past a certain age we cannot acquire languages anymore, but must learn them laboriously and imperfectly. But language is not like learning to lay tile or write computer code; leave a kid among speakers and the kid will simply start speaking.
Come to find from the footnotes that the "collage of strategies" view of language is held primarily by Daniel Everett and by Vyvyan Evans, a polemic opponent of Steven Pinker. "Many scholars" thus reduces to Evans and two members of the Everett family. The debate may be interesting and earnest, but the "collage" side is a distinct minority, and one that must explain the overwhelming empirical facts against them.
The political charge of these competing theories is somewhat hard to disentangle. I sometimes get the sense that the "collage of strategies" view of language is meant to be a left-wing, culturally relativist rejoinder to oppressive theories of "instinct." But Steven Pinker is a functionalist-libertarian at his rightmost, and quite liberal on many issues; his hero, Noam Chomsky, is as left-wing as Americans get. On matters linguistic, both Pinker and Chomsky seem to me often quite neutral politically; they are up against a great wall of fact, and they do not try to wish their way around it.
The Pirahã give Everett some culturally-relative hope that language is not universal enough to include the number "four," though virtually all languages include that number. Everett's point seems reasonable. Most languages have words for things they find handy, and lack them for things they don't. The Eskimos may not have four hundred words for "snow," but the Pirahã surely don't have any, living in the rain forest and all. Maybe they don't need "four," either. A synergy between math and language is an intriguing hypothesis and deserving of far more study, both observational and theoretical.
The rest of Numbers and the Making of Us is less interesting, diverging into generalities. Everett's hypothesis about the origin of number terms is literally that someone saw that things came in more than threes and made up a word for it (192-201). He goes on to show that numbers are pretty useful cross-culturally. This is less than compelling stuff, but the initial exposition in the volume, where Everett is on firmer ground closer to his own speciality, is clear and thought-provoking. I recommend Numbers and the Making of Us to readers who will come to it with some healthy skepticism.
Everett, Caleb. Numbers and the Making of Us. Cambridge, MA: Harvard University Press, 2017. QA 141 .E94