One of Terry Pratchett’s neatest jokes in the Discworld novels concerns the troll (big creatures made of rock) system of counting, which entails only the words “one,” “two,” “many” and “lots”—a fact often cited by troll-haters as evidence of their stupidity. What the mockers don’t know is that troll numbers in fact follow a perfectly sensible quaternary system which begins “one, two, many-one, many-two, many-many, many-many-one…”
It’s a gag with a real world parallel: the Amazonian tribe known as the Pirahã, who lack the ability to quantify precisely any group of objects greater than two. And their language, as we’ve discussed in both the magazine and this blog, lies at the heart of a huge debate in modern linguistics, in which nothing less than Chomsky’s theory of Universal Grammar and the fundamental question of how language and thought relate are at stake.
In his latest book, The Stuff of Thought, the noted language and cognition researcher Steven Pinker has now weighed into the debate; and he offers—in my opinion—a brilliantly lucid exposition of just what it means when a remote hunter-gathering tribe cannot subtract three from six.
To conclude that the lack of precise number thoughts among the Pirahã is caused by their lack of precise number words is, Pinker argues, to make “a dubious leap from correlation to causation.” Instead, he points out, we need to realise that the idea of counting is very different to the idea of number:
It’s tempting to equate a use of the number five with the ability to count five things, but they are very different accomplishment. Counting is an algorithm, like long division or the use of logarithmic tables—in this case an algorithm for assessing the exact numerosity of a set of objects.
Thus, Pinker concludes, the fact that these hunter-gatherers have not developed a counting technique is no more a proof that language dictates thought than the fact that they have not developed a technique for building self-supporting stone arches. Indeed, the existence or non-existence of particular words in a particular language is not itself the crucial factor in whether a technique can be used by its speakers:
…the counting algorithm we teach preschoolers, like the more complex mental arithmetic we teach school-age children, co-opts words in the language. But it is not part of the language, like subject-verb agreement, nor does it come for free with the language… The prerequisite for exact number concepts beyond “two” is a counting algorithm, not a language with number words.
Responses will no doubt be pouring in already from those in the language-determines-thought camp. In the politest possible terms, I’m sure.