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Numerical Cognition Without Words

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/ www.sciencexpress.org / 19 August 2004 / Page 1/ 10.1126/science.1094492 Members of the Pirahã tribe use a “one-two-many” system of counting. I ask whether speakers of this innumerate language can appreciate larger numerosities without the benefit of words to encode them. This addresses the classic Whorfian question about whether language can determine thought. Results of numerical tasks with varying cognitive demands show that numerical cognition is clearly affected by the lack of a counting system in the language. Performance with quantities greater than 3 was remarkably poor, but showed a constant coefficient of variation, which is suggestive of an analog estimation process. Is it possible that there are some concepts that we cannot entertain because of the language that we speak? At issue here is the strongest version of Benjamin Lee Whorf’s hypothesis that language can determine the nature and content of thought. The strong version of Whorf’s hypothesis goes beyond the weaker claim that linguistic structure simply influences the way that we think about things in our everyday encounters. For example, recent studies suggest that language might affect how people mentally encode spatial relations (1–3), and how they conceive of the nature of individual objects and their material substances (4). However, none of these studies suggest that linguistic structure prevents us from entertaining the concepts that are available to speakers of alternative linguistic systems. The question of whether linguistic determinism exists in the stronger sense has two parts. The first is whether languages can be incommensurate: Are there terms that exist in one language that cannot be translated into another? The second is whether the lack of such translation precludes the speakers of one language from entertaining concepts that are encoded by the words or grammar of the other language. For many years, the answer to both questions appeared to be negative. While languages might have different ways in which situations are habitually described, it has generally been accepted that there would always be some way in which one could capture the equivalent meaning in any other language (5). Of course, when speaking of translatable concepts, we do not mean terms like ‘molecule’ or ‘quark’, which would not exist in a culture without advanced scientific institutions. Failure to know what molecules or quarks are does not signal an inability to understand the English language – surely people were still speaking English before such terms were introduced. On the other hand, one would question someone’s command of English if they did not understand the basic vocabulary and grammar. Words that indicate numerical quantities are clearly among the basic vocabulary of a language like English. But not all languages contain fully elaborated counting systems. Although no language has been recorded that completely lacks number words, there is a considerable range of counting systems that exists across cultures. Some cultures use a finite number of body parts to count 20 or 30 body tags (6). Many cultures use particular body parts like fingers as a recursive base for the count system as in our 10-based system. Finally, there are cultures that base their counting systems on a small-number somewhere between 2 and 4. Sometimes, the use of a small-number base is recursive and potentially infinite. For example, it is claimed that the Gumulgal South Sea Islanders counted with a recursive binary system: 1, 2, 2’1, 2’2, 2’2’1 and so on (6). The counting system that differs perhaps most from our own is the “one-two-many” system, where quantities beyond two are not counted but are simply referred to as ‘many’. If a culture is limited to such a counting system, is it possible for them to perceive or conceptualize quantities beyond the limited sets picked out by the counting sequence, or to make what we consider to be quite trivial distinctions such as that between 4 versus 5 objects? The Pirahã are such a culture. They live along the banks of the Maici River in the Lowland Amazonia region of Brazil. They maintain very much of a hunter-gatherer existence and reject assimilation into mainstream Brazilian culture. Almost completely monolingual in their own language, they have a population of less than 200 living in small villages of 10 to 20 people. They have only limited exchanges with outsiders, using primitive pidgin systems for communicating in trading goods without monetary exchange and without the use of Portuguese count words. The Pirahã counting system consists of the words: ‘hói’ (falling tone = ‘one’) and ‘hoí’ (rising tone = ‘two’). Larger quantities are designated as ‘baagi’ or ‘aibai’ (= ‘many’). Numerical Cognition Without Words: Evidence from Amazonia Peter Gordon Department of Biobehavioral Sciences, Columbia University, 525 West 120th Street, New York, NY 10027, USA. E-mail: [email protected]/ www.sciencexpress.org / 19 August 2004 / Page 2/ 10.1126/science.1094492 I was able to take three field trips ranging from one week to two months living with the Pirahã along with Dr. Daniel Everett and Keren Everett, two linguists who have lived and worked with the tribe for over 20 years and are completely familiar with their language and cultural practices. Observations were informed by their background of continuous and extensive immersion in the Pirahã culture. During my visits, I became interested in the counting system of the Pirahã that I had heard about and wanted to examine whether they really did have only two numbers, and how this would affect their ability to perceive numerosities that extended beyond the limited count sequence. Year 1: Initial observations. On my first week-long trip to the two most up-river Maici villages, I began with informal observations of the Pirahã use of the number words for one and two. I was also interested in the possibility that the one-two-many system might actually be a recursive base-2 system, that their limited number words might be supplemented by more extensive finger counting, or that there might be taboos associated with counting certain kinds of objects as suggested by Zaslavsky in her studies of African counting systems (7, 8). Keren Everett developed some simple tasks to see if our two Pirahã informants could refer to numerosities of arrays of objects using Pirahã terms and any finger counting


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