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The approximate number system represents rational numbers: The special case of an empty set

Published online by Cambridge University Press:  15 December 2021

Michal Pinhas Open the ORCID record for Michal Pinhas [Opens in a new window] ,
Rut Zaks-Ohayon  and
Joseph Tzelgov
Michal Pinhas
Affiliation:
Department of Behavioral Sciences, Ariel University, Ariel40700, Israel. michalpi@ariel.ac.ilhttps://pinhaslab.com
Rut Zaks-Ohayon
Affiliation:
Department of Psychology, Achva Academic College, Arugot, 79800, Israel Department of Cognitive and Brain Sciences, Ben-Gurion University of the Negev, Beer Sheva84105, Israel. zaksru@post.bgu.ac.il
Joseph Tzelgov
Affiliation:
Department of Psychology, Achva Academic College, Arugot, 79800, Israel Department of Cognitive and Brain Sciences, Ben-Gurion University of the Negev, Beer Sheva84105, Israel. zaksru@post.bgu.ac.il Department of Psychology, and Zlotowski Center for Neuroscience, Ben-Gurion University of the Negev, Beer Sheva84105, Israel. tzelgov@bgu.ac.ilhttps://in.bgu.ac.il/humsos/psych/eng/Pages/staff/Joseph_en.aspx
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Abstract

We agree with Clarke and Beck that the approximate number system represents rational numbers, and we demonstrate our support by highlighting the case of the empty set – the non-symbolic manifestation of zero. It is particularly interesting because of its perceptual and semantic uniqueness, and its exploration reveals fundamental new insights about how numerical information is represented.

Type
Open Peer Commentary
Information
Behavioral and Brain Sciences , Volume 44 , 2021 , e202
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press

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References

Banks, W. P. (1977). Encoding and processing of symbolic information in comparative judgments. In Bower, G. H. (Ed.), The psychology of learning and motivation (Vol. 11, pp. 101–159). Academic Press. https://doi.org/10.1016/S0079-7421(08)60476-4Google Scholar
Beran, M. J., Perdue, B. M., & Evans, T. A. (2015). Monkey mathematical abilities. In Cohen Kadosh, R. & Dowker, N. (Eds.), The Oxford handbook of numerical cognition (pp. 237–257). Oxford University Press. https://doi.org/10.1093/oxfordhb/9780199642342.001.0001Google Scholar
Biro, D., & Matsuzawa, T. (2001). Use of numerical symbols by the chimpanzee (Pan troglodytes): Cardinals, ordinals, and the introduction of zero. Animal Cognition, 4, 193–199. https://doi.org/10.1007/s100710100086CrossRefGoogle ScholarPubMed
Gebuis, T., Cohen Kadosh, R., & Gevers, W. (2016). Sensory-integration system rather than approximate number system underlies numerosity processing: A critical review. Acta Psychologica, 171, 17–35. https://doi.org/10.1016/j.actpsy.2016.09.003CrossRefGoogle ScholarPubMed
Howard, S. R., Avarguès-Weber, A., Garcia, J. E., Greentree, A. D., & Dyer, A. G. (2018). Numerical ordering of zero in honey bees. Science (New York, N.Y.), 360, 1124–1126. https://doi.org/10.1126/science.aar4975CrossRefGoogle ScholarPubMed
Kaufman, E. L., Lord, M. W., Reese, T. W., & Volkmann, J. (1949). The discrimination of visual number. The American Journal of Psychology, 62(4), 498–525. https://doi.org/10.2307/1418556CrossRefGoogle ScholarPubMed
Leibovich, T., Katzin, N., Harel, M., & Henik, A. (2017). From “sense of number” to “sense of magnitude”: The role of continuous magnitudes in numerical cognition. Behavioral and Brain Sciences, 40, e164. https://doi.org/10.1017/S0140525X16000960CrossRefGoogle Scholar
Leth-Steensen, C., & Marley, A. (2000). A model of response time effects in symbolic comparison. Psychological Review, 107(1), 62–100. https://doi.org/10.1037/0033-295X.107.1.162CrossRefGoogle Scholar
Merritt, D. J., & Brannon, E. M. (2013). Nothing to it: Precursors to a zero concept in preschoolers. Behavioural Processes, 93, 91–97. https://doi.org/10.1016/j.beproc.2012.11.001CrossRefGoogle ScholarPubMed
Merritt, D. J., Rugani, R., & Brannon, E. M. (2009). Empty sets as part of the numerical continuum: Conceptual precursors to the zero concept in rhesus monkeys. Journal of Experimental Psychology: General, 138(2), 258–269. https://doi.org/10.1037/a0015231CrossRefGoogle ScholarPubMed
Moyer, R. S., & Landauer, T. K. (1967). Time required for judgements of numerical inequality. Nature, 215, 1519–1520. https://doi.org/10.1038/2151519a0CrossRefGoogle ScholarPubMed
Nieder, A. (2013). Coding of abstract quantity by “number neurons” of the primate brain. Journal of Comparative Physiology A, 199(1), 1–16. https://doi.org/10.1007/s00359-012-0763-9CrossRefGoogle Scholar
Nieder, A. (2016). Representing something out of nothing: The dawning of zero. Trends in Cognitive Sciences, 20(11), 830–842. https://doi.org/10.1016/j.tics.2016.08.008CrossRefGoogle ScholarPubMed
Okuyama, S., Kuki, T., & Mushiake, H. (2015). Representation of the numerosity “zero” in the parietal cortex of the monkey. Scientific Reports, 5, 10059. https://doi.org/10.1038/srep10059CrossRefGoogle ScholarPubMed
Pepperberg, I. M., & Gordon, J. D. (2005). Number comprehension by a grey parrot (Psittacus erithacus), including a zero-like concept. Journal of Comparative Psychology, 119, 197–209. https://doi.org/10.1037/0735-7036.119.2.197CrossRefGoogle Scholar
Pinhas, M., & Tzelgov, J. (2012). Expanding on the mental number line: Zero is perceived as the “smallest.” Journal of Experimental Psychology: Learning, Memory, and Cognition, 38(5), 1187–1205. https://doi.org/10.1037/a0027390Google ScholarPubMed
Pinhas, M., Buchman, C., Lavro, D., Mesika, D., Tzelgov, J., & Berger, A. (2015). The neural signatures of processing semantic end values in automatic number comparisons. Frontiers in Human Neuroscience, 9, 645. https://doi.org/10.3389/fnhum.2015.00645CrossRefGoogle ScholarPubMed
Ramirez-Cardenas, A., Moskaleva, M., & Nieder, A. (2016). Neuronal representation of numerosity zero in the primate parieto-frontal number network. Current Biology, 26, 1285–1294. https://doi.org/10.1016/j.cub.2016.03.052CrossRefGoogle ScholarPubMed
Seife, C. (2000). Zero: The biography of a dangerous idea. Penguin. https://doi.org/10.1086/426210Google Scholar
Zaks-Ohayon, R., Pinhas, M., & Tzelgov, J. (2021a). On the indicators for perceiving empty sets as zero. Acta Psychologica, 213, 103237. https://doi.org/10.1016/j.actpsy.2020.103237CrossRefGoogle Scholar
Zaks-Ohayon, R., Pinhas, M., & Tzelgov, J. (2021b). Nonsymbolic and symbolic representations of null numerosity. Psychological Research. https://doi.org/10.1007/s00426-021-01515-4CrossRefGoogle Scholar