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Numbers are a significant cognitive device, integral to the functioning of society, from the democratic apply of holding elections (counting votes) to spectacular feats of engineering that require advanced arithmetic to attain (Cantlon et al., 2009).
Numbers are extremely versatile, serving totally different functions relying on their context of use. For instance, think about the next sentence: “Participant quantity 23 took 2nd place by scoring 3 objectives”. This sentence options nominal, ordinal, and cardinal numbers, in that order. Nominals function distinctive identifiers (e.g., communications numbers), ordinals index positions in ordered sequences (e.g., years, pages), and cardinals quantify units (e.g., folks, objects) and parts of typical scales (e.g., {dollars}, miles).
The relative prevalence of those three quantity varieties in pure language had by no means been systematically examined till our latest analysis. Earlier research primarily centered on how usually totally different numbers are used, discovering that quantity frequency decreases with magnitude in a logarithmic trend (Coupland, 2011; Dehaene & Mehler, 1992; Dorogovtsev et al., 2005; Jansen & Pollmann, 2001; Woodin et al., 2024). This discovering helps the argument that numerical cognition itself is logarithmically scaled (Dehaene & Mehler, 1992). These research additionally confirmed that spherical numbers (i.e., multiples of 10 and typically 5), which are sometimes used imprecisely, are used extra continuously than unround numbers, particularly at increased magnitudes. This outcome has been linked to the concept the approximate quantity system is more and more imprecise for bigger numbers (Woodin et al., 2024; see additionally Rinaldi & Marelli, 2020)
Nonetheless, these claims have been primarily based on quantitative makes use of of numbers, and the info used to assist such claims are more likely to have included ordinal or nominal makes use of. Subsequently, the extent to which such claims relating to numerical cognition are warranted will depend on how a lot the quantity frequencies seize quantitative, cardinal makes use of.
In our examine, not too long ago revealed in Cognitive Science, we carried out the primary corpus evaluation investigating the relative prevalence of cardinal, ordinal, and nominal numbers in pure language. By manually annotating 3,600 concordances within the Corpus of Modern American English (COCA; Davies, 2008), we examined how these totally different quantity varieties are utilized in American English. Concordances, or concordance strains, are strains of textual content that present how phrases (in our case, numbers) are utilized in context.
Determine 1. Counts (bars) and percentages (textual content) of concordances containing cardinal, ordinal, and nominal numbers, with cardinal numbers subdivided into pure cardinals and measurements.
Our outcomes present that, in American English, cardinals are dominant, adopted by ordinals, then nominals (see Fig. 1). Amongst quantitative makes use of of numbers, measurements (scales) are extra widespread than pure cardinals (units). Just for cardinals do spherical numbers (operationalized right here as multiples of 5) dominate and improve with magnitude (see Fig. 2).
These outcomes display that cardinals are probably the most prototypical quantity kind, suggesting the validity of claims referring to the logarithmic nature of numerical cognition (Dehaene & Mehler, 1992), in addition to the approximate quantity system (Woodin et al., 2024). Nonetheless, nominals and particularly ordinals are nonetheless comparatively widespread, and so ought to be not less than acknowledged when aggregating quantity frequencies, even when cardinals are the focus of analyses.
Our findings are additionally related for developmental analysis: youngsters have a tendency to amass ordinals after cardinals, and it’s assumed that nominals are acquired later (e.g., Colomé & Noël, 2012; Fischer & Beckey, 1990; Miller et al., 2000). Our outcomes increase the likelihood that the order wherein youngsters purchase totally different quantity varieties is influenced by differential publicity to those varieties in grownup language use. In different phrases, later acquisition might not essentially entail elevated cognitive issue.
Basically, our paper uncovers an image of numerical communication extra advanced and nuanced than aggregated quantity frequencies reveal by themselves, with language serving as an essential channel by way of which numerical and mathematical cognition might be noticed and analyzed.
Determine 2. Percentages of concordances containing pure cardinals, measurements, ordinals, and nominals for every order of magnitude which can be spherical (i.e., multiples of 5).
Greg Woodin is a Put up-doctoral Analysis Fellow within the Division of Linguistics and Communication on the College of Birmingham. His analysis crosscuts linguistics, psychology, and cognitive science, utilising computational corpus strategies and experiments to discover metaphor, iconicity, and multimodal numerical communication.
Bodo Winter is a Professor of Linguistics within the Division of Linguistics and Communication on the College of Birmingham. His analysis makes use of information science-driven linguistics to check multimodal communication, together with iconicity, gesture and metaphor. In his Future Leaders Fellowship, he’s investigating how folks talk numerical data throughout totally different communication channels.
References
Cantlon, J. F., Libertus, M. E., Pinel, P., Dehaene, S., Brannon, E. M., & Pelphrey, Ok. A. (2009). The neural improvement of an summary idea of quantity. Journal of Cognitive Neuroscience, 21(11), 2217. https://doi.org/10.1162/jocn.2008.21159
Colomé, À., & Noël, M.-P. (2012). One first? Acquisition of the cardinal and ordinal makes use of of numbers in preschoolers. Journal of Experimental Baby Psychology, 113, 233–247. https://doi.org/10.1016/j.jecp.2012.03.005
Coupland, N. (2011). How frequent are numbers? Language and Communication, 31(1), Article 1. https://doi.org/10.1016/j.langcom.2010.09.001
Davies, M. (2008). The Corpus of Modern American English (COCA) [Computer software]. https://www.english-corpora.org/coca/
Dehaene, S., & Mehler, J. (1992). Cross-linguistic regularities within the frequency of quantity phrases. Cognition, 43(1), 1–29.
Dorogovtsev, S., Mendes, J. F., & Oliveira, J. (2005). Frequency of prevalence of numbers within the World Large Net. Physica A: Statistical Mechanics and Its Purposes, 360, 548–556. https://doi.org/10.1016/j.physa.2005.06.064
Fischer, F. E., & Beckey, R. D. (1990). Starting kindergartners’ notion of quantity. Perceptual and Motor Expertise, 70, 419–425. https://doi.org/10.2466/PMS.70.2.419-425
Jansen, C. J. M., & Pollmann, M. M. W. (2001). On spherical numbers: Pragmatic points of numerical expressions. Journal of Quantitative Linguistics, 8(3), 187–201. https://doi.org/10.1076/jqul.8.3.187.4095
Miller, Ok., Main, S. M., Shu, H., & Zhang, H. (2000). Ordinal data: Quantity names and quantity ideas in Chinese language and English. Canadian Journal of Experimental Psychology = Revue Canadienne De Psychologie Experimentale, 54(2), 129–140. https://doi.org/10.1037/h0087335
Rinaldi, L., & Marelli, M. (2020). The usage of quantity phrases in pure language obeys Weber’s legislation. Journal of Experimental Psychology: Common, 149(7), 1215–1230. https://doi.org/10.1037/xge0000715
Woodin, G., Winter, B., Littlemore, J., Perlman, M., & Grieve, J. (2024). Massive-scale patterns of quantity use in spoken and written English. Corpus Linguistics and Linguistic Concept, 20(1), 123–152. https://doi.org/10.1515/cllt-2022-0082
