Native language effect on number cognition

The present study tends to test the relationship between native language and its speakers‘ mathematical processing, specifically, the relationship between linguistic numeral expression and the numeral processing among Chinese, English and Thai speakers. The study discovers that the speakers from different native language backgrounds have different performance on numeral processing with accordance to the linguistic numeral term their native language provided. Therefore, numeral language characteristics have a significant effect on cognitive representation of numbers. Introduction Human languages differ from one another in considerable and innumerable ways in how they describe the world. There is evidence that cross-linguistic difference in lexicon and grammar results in nonlinguistic consequences. In recent years, research on linguistic relativity has enjoyed a considerable resurgence, and much new evidence regarding the effects of language on thought has become available using new fine-tuned methods. Various behavioral studies have shown that even the little quirks of language influence speakers‘ perception of objects (Boroditsky et al., 2003), substances (Imai & Gentner, 1997; Lucy et al. 2001), space (Levinson, 1996; Pederson et al., 1998) and time (Boroditsky, 2001; Casasanto & Boroditsky, 2008). This is known as linguistic relativity, also commonly referred to as the Sapir-Whorf hypothesis 1 , the notion that linguistic structure affects non-linguistic cognition, such that speakers talk differently ends up think differently. The current study tests a relatively understudied aspect, that is, whether languages affect the conceptulization of numbers and mathematical processing? Numbers and mathematics seems to be the most objective subject we deal with in daily life. However, although the vast majority of contries adopt the same convention by employing the Arabic notation when writing down a number, in detail the diversity of numeration syntax is stricking across languages. For example, it has been reported that some aborigines in the Queensland district of Australia are still using base 2 system—Number 1 is ―ganar‖, 2 is ―burla‖, 3 ―burla-ganar‖, and 4 ―burla-burla‖. Base 20 also has its adepts in Eskimo and Yoruba. And the traces of it can still be found in French, in which 80 is ―quatre-vingt‖ (four twenties). These languages form 1 The current Sapir-Whorf Hypothesis is the weak version. The strong version which claims that language determines minds (a.k.a. determinism) has long been abandoned. contrasts with languages express numbers with base 10 place value. For example, East Asian langauge such as Chinese perfectly aligns with the decimal structure. In such a language, the name of a number is just the decomposition in base ten, thus 17 is ―ten-seven‖ and 35 is ―three-ten-five‖, while in English the numbers 11 through 20 are denoted by special words (eleven, twelve, thirteen, twenty, etc.) Does this exuberant diversity of numerical languags lead to practical consequences? Along with the stemming of cognitive linguistics, many an empirical work has been done in the last two decades to answer this question. There have been a number of studies on numerical cognition, showing that differences in number naming systems can affect cognitive development and non-linguistic performance. For example, acquisition studies (Miura, Okamoto, Kim, Steere, & Fayol, 1993; Miura et al., 1994; Miller, Smith, Zhu, & Zhang,1995; Paik & Mix, 2003) have found that preschool-aged children whose native languages employ more systematic naming systems for their numbers outperform their counterparts who speak languages that use less transparent number naming systems on both number matching and number identification tasks. When asked to demonstrate numbers with combinations of individual unit cube block representing one and long blocks representing ten, Asian-language-speaking children who learned numerical names congruent with base 10 numeration systems (Fuson, 1990) were much more likely to use the blocks of 10 in constructing multi-digit numbers than their non-Asian-language-speaking counterparts, who lacked the access to such transparent numerical naming systems. For instance, when asked to represent number 12, Asian-language-speaking children were more likely to pick one long block and two individual blocks, while their non-Asian-language-speaking counterparts tended to choose twelve individual blocks. The authors of that study argued that ―numerical language characteristics may have a significant effect on cognitive representation of numbers‖ (Miura et al., 1994, p. 410), which in turn may enhance the performance of Asian-language-speaking children on tasks involving the concept of place value. The types of names given to various symbolic systems, such as numbers, have also been shown to affect the problem-solving abilities of competent symbol users. Seron and Fayol (1994) noticed that the verbal number system in French-speaking Belgium is simpler than the one used in France (in Belgium, 98 is roughly "ninety-eight" but in France, it is "four-twenty-eighteen"). They reported that second-grade children in France made more errors in Arabic number production than their Belgian counterparts. The effects of number naming systems also extend into adulthood and mathematical performance. For instance, one study showed that adult English speakers have difficulty reversing two-digit numbers ending in 1 (e.g., saying ―14‖ when shown ―41‖), while Chinese speakers showed no such difficulty, presumably a result of English‘s idiosyncratic rules for naming numbers between 11 and 19 (Miller & Zhu, 1991). However, some other scholars (Saxon & Towse, 1997; Brysbaert et al., 1998) argued that the influence of numerical language upon cognitive development is minimal and criticized the methodologies that were previously used, claiming that the significance of differences between different speakers‘ performances in the experiments done by Miura et al. may result from other factors rather than languages. In sum, the debate is ongoing about whether differences in number naming systems affect the acquisition and use of number concepts. Thus, it is meaningful to carry out further studies on the relationship between numeral language characteristics and cognitive representation of number. The cognition of numbers To purse the line of language and numeral cognition research, the current study focuses on the processing of large numbers. More specifically, I‘d like to test whether different linguistic expression of multi-digit numbers affects people‘s processing of these numbers. Human being‘s understanding of large numbers is very different from that of the low numbers such as 1, 2 and 3. It has been known to psychologists for more than a century that there is a strict limit on the number of objects that we are able to enumerate at once (James McKeen Cattel, 1886). When the object number is beyond three, errors accumulates. Also, the first three numbers are usually the ones that have particular ordinal forms (E.g., ―first‖, ―second‖, ―third‖ vs most ordinals end with ―-th‖ in English). Moreover, the numbers 1, 2, and 3 are also the only ones that can be expressed by grammatical inflections instead of words (singular, dual, and trial in some languages). The etymology of the first three numbers also tells us about the limit of our numeral cognition to some degree. The Indo-European root of the word ―three‖ suggests that it might once be the largest number meaning ―a lot‖ and ―beyond all others‖. Examples can be found in French très (very), the Italian troppo (too much), the English word through, and the Latin prefix trans(Dehaene, 2011). On the other hemisphere of the world, the word sān ―three‖ in Chinese is used as synonym of ―many‖ or ―all‖ in lots of idioms. Most interestingly, the structure of ideographic Chinese characters representing the first three numbers in Chinese is similar, consisting of one to three horizontal stocks respectively (一, 二, 三), while such predictable rules cannot be found in expressing numbers bigger than three (for example, 四 for ―four‖ and 五 for ―five‖). In a word, it seems that our ancestors‘ number sense might be confined to three. In fact, up to this very date, some Australian aboriginal tribes were reported to have linguistic terms only for the quantities 1, 2, some and a lot (Ifran, 1998; Gordon, 2004; Butterworth, Reeve, Reynolds & Lloyd, 2008). Pirahã, the Amazonian indigenous language, was arguably found to have no words for precise numbers, but rather concepts for a small amount and a larger amount (Everett, 1986; Frank et al., 2008). And this lack of number terms affects Pirahã people‘s performance in a few matching experiments conducted by researchers. Human languages move beyond three and linguistic terms assigned to greater numbers are useful as they allow the speakers to remember and compare information about quantity accurately across space and time. David Hume (year, page) once noted that ―I observe that when we mention any great number, such as a thousand, the mind has generally no adequate idea of it, but only a power of producing such an idea by its adequate idea of the decimals, under which the number is comprehended.‖ Therefore, humans generally have difficulty with large numbers and number terms are linguistic inventions that enable us to mentally represent large numbers to conquer the difficulty of making approximation. In the era of the Information Revolution, we are facing the trend of using larger and larger numbers more frequently in the areas of astronomy to unit as small as CPU. And it‘s interesting that world languages diverge again in expressing large numbers. In general, world languages employ two main systems in clustering multi-digit numerals—the tri-radical magnitude system and the tetra-radical one. The former one divides the number by a block of three digits at one time and the latter one divides multi-digit numbers by a block of four. Based on these two systems, Languages differentiate themselves in terms of the way to express different powers of ten 2 . For example, English employs the tri-radical magnitude system as most Indo-European languages does—thousand for 10 3 , million for 10 6 and billion for 10 9 In the naming of number terms, it is common that when no separate lexical items are available, the concepts are expressed by means of additive, deductive and multiplicative of other available number terms. For instance, in French, ninety is ―four twenties plus ten‖ (quatre-vingt-dix), using the multiplicative and additive methods. So in the situation that no separate lexical terms are assigned to expressing 10 4 or 10 5 , the language uses combined form of existing terms: the concept of ―thousand‖ with the help of ―ten‖ and ―hundred‖ to form compound words, i.e. ten-thousand and a hundred thousand. In the contrast, East Asian languages such as Chinese, Japanese and Korean use the tetra-radical system. In Chinese, for example, 10 4 and 10 8 are expressed by terms wàn 万 and yì亿, whereas 10 is expressed as ―hundred wàn‖ using multiplicative method by combining bǎi ―hundred‖ and wàn ―ten thousand‖. It is not surprising to find a term of 10 3 (qiān 千) in Chinese although it is generally a tetra-radical-system language, because a modern language would be inefficient without designing a term for the quantity of a thousand considering its frequent use. So the existence of qiān 千 does not contradict with the multi-digit clustering option that Chinese uses, as no separate lexical term for 10 6 is found in Chinese. A comparison of the linguistic terms of large number is presented in Table 1 below, showing those Chinese and English provide linguistic terms for large numbers in a systematically different way. 2 In this paper, scientific notations are used to record large numbers. English terms Chinese terms Million 10 6 Wàn 万 10 Billion 10 9 Yì 亿 10 Trillion 10 12 zhào 兆 10 Quadrillion 10 15 Jīng 京 10 Quintillion 10 18 Gāi 垓 10 Sextillion 10 21 Zǐ 秭 10 Septillion 10 24 Rang 穰 10 Octillion 10 27 Gōu 沟 10 Nonillion 10 30 Jiàn 涧 10 Decillion 10 33 Zhèng 正 10 Undecillion 10 36 Zài 载 10