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The approximate number system represents magnitude and precision

Published online by Cambridge University Press:  15 December 2021

Charles R. Gallistel Open the ORCID record for Charles R. Gallistel [Opens in a new window]
Charles R. Gallistel*
Affiliation:
Rutgers Center for Cognitive Science and Department of Psychology, Piscataway, NJ08854-8020, USA. galliste@ruccs.rutgers.eduhttps://ruccs.rutgers.edu/gallistel-research-interests
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Abstract

Numbers are symbols manipulated in accord with the axioms of arithmetic. They sometimes represent discrete and continuous quantities (e.g., numerosities, durations, rates, distances, directions, and probabilities), but they are often simply names. Brains, including insect brains, represent the rational numbers with a fixed-point data type, consisting of a significand and an exponent, thereby conveying both magnitude and precision.

Type
Open Peer Commentary
Information
Behavioral and Brain Sciences , Volume 44 , 2021 , e187
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press

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References

Buehlmann, C., Graham, P., Hansson, B. S., & Knaden, M. (2014). Desert ants locate food by combining high sensitivity to food odors with extensive crosswind runs. Current Biology, 24(9), 960–964. doi: http://www.sciencedirect.com/science/article/pii/S0960982214002541CrossRefGoogle ScholarPubMed
Carey, S., & Barner, D. (2019). Ontogenetic origins of human integer representations. Trends in Cognitive Science, 23(10), 823–835. doi: 10.1016/j.tics.2019.07.004CrossRefGoogle ScholarPubMed
Chaitin, G. J. (2005). Meta math: The quest for omega. Random House.Google Scholar
Cheyette, S., & Piantadosi, S. (2020). A unified account of numerosity perception. Nature Human Behaviour, 4, 1265–1272. doi: 10.1038/s41562-020-00946-0CrossRefGoogle ScholarPubMed
Cordes, S., Gelman, R., Gallistel, C., & Whalen, J. (2001). Variability signatures distinguish verbal from nonverbal counting for both large and small numbers. Psychonomic Bulletin & Review, 8(4), 698–707. https://doi.org/10.3758/BF03196206CrossRefGoogle ScholarPubMed
Durgin, F. H., Akagi, M., Gallistel, C. R., & Haiken, W. (2009). The precision of locomotor odometery in humans. Experimental Brain Research, 193(3), 429–436. doi: 10.1007/s00221-008-1640-1CrossRefGoogle Scholar
Frege, G. (1884). Die grundlagen der arithmetik: Eine logisch-mathematische untersuchung über den begriff der zahl. Wilhelm Koebner.Google Scholar
Gallistel, C. R. (2017). Finding numbers in the brain. Philosophical Transactions of the Royal Society (London). Series B, 373(1740), 1–10. doi: 10.1098/rstb.2017.0119Google Scholar
Gallistel, C. R., & Gelman, R. (2000). Non-verbal numerical cognition: From reals to integers. Trends in Cognitive Sciences, 4(2), 59–65. doi: 10.1016/s1364-6613(99)01424-2CrossRefGoogle ScholarPubMed
Gelman, R. (1972). The nature and development of early number concepts. In Reese, H. W. (Ed.), Advances in child development, vol. 3 (pp. 115–167). Academic Press.Google Scholar
Gelman, R., & Gallistel, C. R. (1978). The child's understanding of number. Harvard University Press.Google Scholar
Gibbon, J., Malapani, C., Dale, C. L., & Gallistel, C. R. (1997). Toward a neurobiology of temporal cognition: Advances and challenges. Current Opinion in Neurobiology, 7(2), 170–184. doi: 10.1016/s0959-4388(97)80005-0CrossRefGoogle Scholar
Halberda, J. (2016). Epistemic limitations and precise estimates in analog magnitude representation. In Barner, D. & Baron, A. S. (Eds.), Oxford Series in cognitive development. Core knowledge and conceptual change (pp. 171–190). Oxford University Press.10.1093/acprof:oso/9780190467630.003.0010CrossRefGoogle Scholar
Knopp, K. (1952). Elements of the theory of functions. Dover.Google Scholar
Leslie, A. M., Gelman, R., & Gallistel, C. R. (2008). The generative basis of natural number concepts. Trends in Cognitive Sciences, 12(6), 213–218.10.1016/j.tics.2008.03.004CrossRefGoogle ScholarPubMed
Wittlinger, M., Wehner, R., & Wolf, H. (2006). The ant odometer: Stepping on stilts and stumps. Science (New York, N.Y.), 312, 1965–1967. doi: 10.1126/science.1126912CrossRefGoogle ScholarPubMed