O.-S.H. and N.-S.Y. conceived the study. O.-S.H., Y.-C.C., and N.-S.Y. designed the study. O.-S. H. and Y.-C.C. developed stimuli and Y.-C. C. collected and analyzed the data. O.-S.H. Y.-C. C. and N.-S.Y. interpreted the data. Y.-C.C. and O.-S.H. wrote the paper.
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Year 3
Quantity processing of Chinese numeral classifiers: Distance and congruity effects
Her, One-Soon; Chen, Ying-Chun; Yen, Nai-Shing
Introduction
In a classifier language such as Chinese, an additional element, known as
‘numeral classifier’ or simply ‘classifier’, is required when a noun (N) is quantified by a numeral (Num). Numeral classifiers that can appear in a classifier construction come in two subcategories, sortal classifiers (C) and mensural classifiers (M), which are also often referred to as ‘classifiers’ and ‘measure words’, respectively, among various other terms. In this paper, the overall syntactic category is referred to as
‘numeral classifiers’ or simply ‘classifiers’, abbreviated as ‘C/M’. Table 1 offers examples from Chinese, where ben and ke are Cs; xiang (box) and da (dozen) are Ms.
(Insert Table 1 roughly here)
Table 1. Examples of Chinese numeral classifiers Sortal Classifier (C) Mensural Classifier (M)
五 本 雜誌 五 箱 雜誌
wu ben zazhi wu xiang zazhi
5 C magazine 5 M-box magazine
‘5 magazines’ ‘5 boxes of magazines’
十 顆 蘋果 十 打 蘋果
shi ke pingguo shi da pingguo 10 C apple 10 M-dozen apple
’10 apples’ ’10 dozens of apples’
Grammarians had in fact been arguing for a long time whether C and M constitute one or two grammatical categories, until some recent studies that
demonstrated convincingly that C and M converge syntactically as one single category, in that they appear in the same structural position and are mutually exclusive (1-3);
yet, C and M diverge semantically, as Cs qualify the noun and contribute no
additional semantic information to the noun phrase, while Ms quantify the noun and provide additional information to the noun phrase (4, 5). This convergence and
divergence were further reconciled in Her’s (6) mathematical account, which suggests that the relation between Num and C/M is multiplication. Under this view, C and M converge as the multiplicand, with Num as the multiplier, while they diverge in terms of their respective values: all Cs are equally and necessarily of the numerical value 1, while an M’s value can be anything that is not necessarily 1. The precise formulation for the C/M distinction is: [Num X N] = [[Num × X] N], where X = C if and only if
X = 1, otherwise X = M (6). To be more specific, X, being the single category required between Num and N, is a C if its mathematical value is necessarily 1;
otherwise, X is an M. For example, in shi ke pingguo (ten C apple), shi (ten) and ke (C) form a multiplicative unit, i.e., (10×1). Similarly, in shi da pingguo (ten M-dozen apple), shi (ten) and da (M-dozen) also form a multiplicative unit, i.e., (10×12). In brief, C and M both play the role of multiplicand but differ in the sense that C = 1, M
≠ 1.
Her, Chen, & Yen (7) presented a taxonomy of the mathematical values that C/Ms denote based on two dimensions: numerical vs. non-numerical and fixed vs.
variable (Table 2). This taxonomy thus also serves to classify C/Ms into five subtypes accordingly. C stands on its own, whose value is numerical and fixed at 1. While M1
and M2 also both encode numerical values, the former denotes fixed values besides 1 and the latter does not. Likewise, M3 and M4 both encode non-numerical values, but the former has fixed values and the latter does not. Thus, C, M1, and M3 encode fixed values, while M2 and M4 do not.
(Insert Table 2 roughly here)
Table 2. Types of mathematical values denoted by C/Ms
Numerical Fixed n = 1 e.g., ben (本), ke (顆), tiao (條), zhi (隻) C
Her’s (6) theory implies that C/Ms play an important role in denoting
mathematical values. However, empirical studies examining quantity processing of C/Ms are scarce and have shown inconsistent results. While the findings by Cui et al.
(8) do not support this mathematical view of C/Ms, two more recent studies by Her et al. (7) and Her, Chen, & Yen (9) do support this view.
The study by Cui et al. (8) adopted a semantic distance comparison task using functional magnetic resonance imaging (fMRI) to investigate the neural correlates of quantity processing of Chinese numeral classifiers. Participants were asked to choose between two items the one that was semantically closer to the target item. The study compared the brain activations of processing numeral classifiers with those of processing tool nouns, numbers, and dot arrays and found that processing numeral classifiers and tool nouns induced higher activations in the left inferior frontal gyrus (IFG) and the left middle temporal gyrus (MTG) than numbers and dot arrays. Also, numeral classifiers, tool nouns, numbers, and dot arrays all activated the right IFG, right angular gyrus, right supplementary motor area, right precentral gyrus, left insula,
left cerebellum, and bilateral lenticular nucleus. However, the study did not find greater activations for processing numeral classifiers than tool nouns in the right intraparietal sulcus (IPS), which has been shown to represent abstract numerical magnitude (10, 11). These findings were inconsistent with Her’s (6) mathematical theory of C/M, which predicts that processing numeral classifiers would elicit greater brain activities in the right IPS compared with tool nouns, since C/Ms denote
mathematical values but tool nouns do not.
Her et al. (7) replicated the semantic distance comparison paradigm in Cui et al.
(8) but added the same noun to create minimal pairs of C/M phrases as experimental stimuli. By doing so, they managed to control the semantic attributes of C/Ms, which might have been a confounding factor in Cui et al. (8). Furthermore, they
distinguished the subcategories of C/Ms along the two dimensions in Table 2:
numerical type (numerical vs. non-numerical) and mathematical value type (fixed vs.
variable) to thoroughly examine whether participants processed different types of C/Ms based on their mathematical values. They found that participants responded more accurately and faster for C/Ms with fixed values than those with variable values regardless of the numerical type. These results suggested that at least some of the Chinese C/Ms denote mathematical values and preliminarily supported Her’s (6) view that C/Ms denote mathematical values.
Her et al. (9) further examined the neural correlates of C/Ms with fixed values by conducting the same task using fMRI. They found that the numeral classifiers induced greater neural activities than tool nouns in the bilateral inferior parietal lobule (IPL), middle frontal gyrus (MFG), right superior frontal gyrus (SFG), and left lingual gyrus.
Moreover, they showed that processing numeral classifiers, numbers, dot arrays, and number words elicited conjunct activations in the IPS. These findings again
corroborated Her’s (6) mathematical theory of C/M by offering neuroimaging
evidence implying that mathematical values play a role in Chinese numeral classifiers.
Given the contrasting findings regarding the quantity processing of C/Ms by previous studies, the aim of the current study was to re-examine the function of mathematical values of C/Ms by investigating whether participants represent them as numbers using another paradigm. Representation of numerical magnitude has shown two robust phenomena: the distance effect and congruity effect (12, 13). Dehaene, Dehaene-Lambertz, and Cohen (14) proposed that numbers are represented in order like a mental number line in the brain. As the mental representation of adjacent numerals (e.g. 2 and 3) may overlap to some extent, it is harder to discriminate them than distant numerals (e.g. 2 and 7) (15). Moreover, studies reported that the distance effect held not only for Arabic numerals, number words (16-18) but also dot arrays (20), angles, and lines (21). This could be interpreted in terms of Walsh’s (22) view
that numbers and physical stimuli may overlap and share common cognitive
mechanisms in the parietal lobe. Thus, the shared representation of magnitude could cause interference between numerical value and physical size. Besner and Colheart (13) first reported that reaction times (RT) changed in accordance with the congruity between the numerical value and physical size. They found that it took shorter to compare the digits when the numerical difference between the two digits corresponds to font size difference than when they are incongruent. This demonstrated that
although the physical size was irrelevant in the number comparison task, it was hard to ignore and interfered with numerical value. Henik and Tzelgov (23) further showed that numerical value also interfered with physical size. Moreover, congruent pairs facilitated RT compared with neutral trials in which the information of the irrelevant dimension was identical, whereas incongruent pairs took longer than neutral trials.
Given the two aforementioned features of number processing, in the present study we aimed to inspect how mathematical values of C/Ms function by using the number-size comparison task. Such a task is able to test whether C/Ms denote mathematical values and form a multiplication relation with the numerals ahead as Her (6) proposed. We expected to observe that C/Ms would reflect both the distance effect and the congruity effect. Firstly, smaller mathematical value difference of C/Ms would be harder to differentiate than a larger one, yielding lower accuracy and longer RT. Second, the mathematical value of C/Ms and their physical size may interfere with each other, that is, the performance of congruent trials would be facilitated and thus be more accurate and faster than neutral trials whereas it would be worsened for incongruent trials, with lower accuracy and longer RT. Third, the mathematical value of C/Ms may interact with the physical size. For example, it would be more difficult to make a comparison between the C/M phrases with close mathematical value distance plus incongruent physical size than other pairs under the mathematical value task.
Method
Participants
Twenty individuals (13 females, 7 males, ages 20-37, mean age = 22.6 ± 3.89 SD) were recruited from National Chengchi University. Participants were right-handed and had normal or corrected-to-normal vision. Their first language is Mandarin. Prior to the experiment, all participants gave written informed consent to the study. All methods were performed in accordance with the ethical principles of the Declaration of Helsinki and were approved by the Research Ethics Committee of National Taiwan University. Participants received NT$100 after finishing the experiment.
Task
Participants had to make two types of magnitude judgements on a pair of C/M phrases. In the mathematical value task, they had to choose the phrase that
represented a larger quantity. On the other hand, in the physical size task, they had to select the phrase that was shown in a larger font size.