A unified account of numerosity perception


  • 1.

    Jevons, W. S. The power of numerical discrimination. Nature 3, 281–282 (1871).


    Google Scholar
     

  • 2.

    Mandler, G. & Shebo, B. J. Subitizing: an analysis of its component processes. J. Exp. Psychol. Gen. 111, 1–22 (1982).

    CAS 
    PubMed 

    Google Scholar
     

  • 3.

    Revkin, S. K., Piazza, M., Izard, V., Cohen, L. & Dehaene, S. Does subitizing reflect numerical estimation? Psychol. Sci. 19, 607–614 (2008).

    PubMed 

    Google Scholar
     

  • 4.

    Feigenson, L., Dehaene, S. & Spelke, E. Core systems of number. Trends Cogn. Sci. 8, 307–314 (2004).

    PubMed 

    Google Scholar
     

  • 5.

    Dehaene, S. The Number Sense: How the Mind Creates Mathematics (Oxford Univ. Press, 2011).

  • 6.

    Kaufman, E. L., Lord, M. W., Reese, T. W. & Volkmann, J. The discrimination of visual number. Am. J. Psychol. 62, 498–525 (1949).

    CAS 
    PubMed 

    Google Scholar
     

  • 7.

    Pica, P., Lemer, C., Izard, V. & Dehaene, S. Exact and approximate arithmetic in an Amazonian indigene group. Science 306, 499–503 (2004).

    CAS 
    PubMed 

    Google Scholar
     

  • 8.

    Burr, D. C., Turi, M. & Anobile, G. Subitizing but not estimation of numerosity requires attentional resources. J. Vis. 10, 20 (2010).

    PubMed 

    Google Scholar
     

  • 9.

    Gallistel, C. R. & Gelman, R. Preverbal and verbal counting and computation. Cognition 44, 43–74 (1992).

    CAS 
    PubMed 

    Google Scholar
     

  • 10.

    Xu, F. & Spelke, E. S. Large number discrimination in 6-month-old infants. Cognition 74, B1–B11 (2000).

    CAS 
    PubMed 

    Google Scholar
     

  • 11.

    Platt, J. R. & Johnson, D. M. Localization of position within a homogeneous behavior chain: effects of error contingencies. Learn. Motiv. 2, 386–414 (1971).


    Google Scholar
     

  • 12.

    Meck, W. H. & Church, R. M. A mode control model of counting and timing processes. J. Exp. Psychol. Anim. Behav. Process. 9, 320–334 (1983).

    CAS 
    PubMed 

    Google Scholar
     

  • 13.

    Gallistel, C. R. The Organization of Learning (MIT Press, 1990).

  • 14.

    Cantlon, J. F. & Brannon, E. M. Basic math in monkeys and college students. PLoS Biol. 5, e328 (2007).

    PubMed 
    PubMed Central 

    Google Scholar
     

  • 15.

    Cantlon, J. F. Math, monkeys, and the developing brain. Proc. Natl Acad. Sci. USA 109, 10725–10732 (2012).

    CAS 
    PubMed 

    Google Scholar
     

  • 16.

    Yang, T.-I. & Chiao, C.-C. Number sense and state-dependent valuation in cuttlefish. Proc. R. Soc. B 283, 20161379 (2016).

    PubMed 

    Google Scholar
     

  • 17.

    Uller, C., Jaeger, R., Guidry, G. & Martin, C. Salamanders (Plethodon cinereus) go for more: rudiments of number in an amphibian. Anim. Cogn. 6, 105–112 (2003).

    PubMed 

    Google Scholar
     

  • 18.

    Piantadosi, S. T. & Cantlon, J. F. True numerical cognition in the wild. Psychol. Sci. 28, 462–469 (2017).

    PubMed 
    PubMed Central 

    Google Scholar
     

  • 19.

    McComb, K., Packer, C. & Pusey, A. Roaring and numerical assessment in contests between groups of female lions, Panthera leo. Anim. Behav. 47, 379–387 (1994).


    Google Scholar
     

  • 20.

    Sims, C. R. Rate–distortion theory and human perception. Cognition 152, 181–198 (2016).

    PubMed 

    Google Scholar
     

  • 21.

    Sims, C. R., Jacobs, R. A. & Knill, D. C. An ideal observer analysis of visual working memory. Psychol. Rev. 119, 807–830 (2012).

    PubMed 
    PubMed Central 

    Google Scholar
     

  • 22.

    Brady, T. F., Störmer, V. S. & Alvarez, G. A. Working memory is not fixed-capacity: more active storage capacity for real-world objects than for simple stimuli. Proc. Natl Acad. Sci. USA 113, 7459–7464 (2016).

    CAS 
    PubMed 

    Google Scholar
     

  • 23.

    Brady, T. F. & Tenenbaum, J. B. A probabilistic model of visual working memory: incorporating higher order regularities into working memory capacity estimates. Psychol. Rev. 120, 85–109 (2013).

    PubMed 

    Google Scholar
     

  • 24.

    Olshausen, B. A. & Field, D. J. Emergence of simple-cell receptive field properties by learning a sparse code for natural images. Nature 381, 607–609 (1996).

    CAS 
    PubMed 

    Google Scholar
     

  • 25.

    Simoncelli, E. P. & Olshausen, B. A. Natural image statistics and neural representation. Annu. Rev. Neurosci. 24, 1193–1216 (2001).

    CAS 
    PubMed 

    Google Scholar
     

  • 26.

    Olshausen, B. A. & Field, D. J. Sparse coding of sensory inputs. Curr. Opin. Neurobiol. 14, 481–487 (2004).

    CAS 
    PubMed 

    Google Scholar
     

  • 27.

    Geisler, W. S. Contributions of ideal observer theory to vision research. Vis. Res. 51, 771–781 (2011).

    PubMed 

    Google Scholar
     

  • 28.

    Choo, H. & Franconeri, S. Enumeration of small collections violates Weber’s law. Psychon. Bull. Rev. 21, 93–99 (2014).

    CAS 
    PubMed 

    Google Scholar
     

  • 29.

    Izard, V. & Dehaene, S. Calibrating the mental number line. Cognition 106, 1221–1247 (2008).

    PubMed 

    Google Scholar
     

  • 30.

    Cheyette, S. J. & Piantadosi, S. T. A primarily serial, foveal accumulator underlies approximate numerical estimation. Proc. Natl Acad. Sci. USA 116, 17729–17734 (2019).

    CAS 
    PubMed 

    Google Scholar
     

  • 31.

    Inglis, M. & Gilmore, C. Sampling from the mental number line: how are approximate number system representations formed? Cognition 129, 63–69 (2013).

    PubMed 

    Google Scholar
     

  • 32.

    Melcher, D. & Piazza, M. The role of attentional priority and saliency in determining capacity limits in enumeration and visual working memory. PLoS ONE 6, e29296 (2011).

    CAS 
    PubMed 
    PubMed Central 

    Google Scholar
     

  • 33.

    Nieder, A. & Dehaene, S. Representation of number in the brain. Annu. Rev. Neurosci. 32, 185–208 (2009).

    CAS 
    PubMed 

    Google Scholar
     

  • 34.

    Anderson, J. R. & Schooler, L. J. Reflections of the environment in memory. Psychol. Sci. 2, 396–408 (1991).


    Google Scholar
     

  • 35.

    Dehaene, S. & Mehler, J. Cross-linguistic regularities in the frequency of number words. Cognition 43, 1–29 (1992).

    CAS 
    PubMed 

    Google Scholar
     

  • 36.

    Piantadosi, S. T. A rational analysis of the approximate number system. Psychon. Bull. Rev. 23, 877–886 (2016).

    PubMed 
    PubMed Central 

    Google Scholar
     

  • 37.

    Stone, J. V. Principles of Neural Information Theory (Sebtel, 2018).

  • 38.

    Shannon, C. E. A mathematical theory of communication. Bell Syst. Tech. J. 27, 379–423 (1948).


    Google Scholar
     

  • 39.

    Gallistel, C. R. Finding numbers in the brain. Phil. Trans. R. Soc. B 373, 20170119 (2018).


    Google Scholar
     

  • 40.

    Cover, T. M. & Thomas, J. A. Elements of Information Theory (John Wiley & Sons, 2012).

  • 41.

    Gelman, A. & Hill, J. Data Analysis Using Regression and Multilevel/Hierarchical Models (Cambridge Univ. Press, 2006).

  • 42.

    Barnard, A. M. et al. Inherently analog quantity representations in olive baboons (Papio anubis). Front. Psychol. 4, 253 (2013).

    PubMed 
    PubMed Central 

    Google Scholar
     

  • 43.

    Gallistel, C. & Gelman, R. in Memories, Thoughts, and Emotions: Essays in Honor of George Mandler (eds Kessen, W., Ortony, A. & Kraik, F.) 65–81 (Psychology Press, 1991).

  • 44.

    Piazza, M., Fumarola, A., Chinello, A. & Melcher, D. Subitizing reflects visuo-spatial object individuation capacity. Cognition 121, 147–153 (2011).

    PubMed 

    Google Scholar
     

  • 45.

    Trick, L. M. & Pylyshyn, Z. W. Why are small and large numbers enumerated differently? A limited-capacity preattentive stage in vision. Psychol. Rev. 101, 80–102 (1994).

    CAS 
    PubMed 

    Google Scholar
     

  • 46.

    Anderson, D. & Burnham, K. Model Selection and Multi-model Inference 2nd edn (Springer, 2004).

  • 47.

    Atkinson, J., Campbell, F. W. & Francis, M. R. The magic number 4 ± 0: a new look at visual numerosity judgements. Perception 5, 327–334 (1976).

    CAS 
    PubMed 

    Google Scholar
     

  • 48.

    Ginsburg, N. Effect of item arrangement on perceived numerosity: randomness vs regularity. Percept. Mot. Skills 43, 663–668 (1976).


    Google Scholar
     

  • 49.

    DeWind, N. K., Bonner, M. F. & Brannon, E. M. Similarly oriented objects appear more numerous. J. Vis. 20, 4 (2020).

    PubMed 
    PubMed Central 

    Google Scholar
     

  • 50.

    Luck, S. J. & Vogel, E. K. The capacity of visual working memory for features and conjunctions. Nature 390, 279–281 (1997).

    CAS 

    Google Scholar
     

  • 51.

    Awh, E., Barton, B. & Vogel, E. K. Visual working memory represents a fixed number of items regardless of complexity. Psychol. Sci. 18, 622–628 (2007).

    PubMed 

    Google Scholar
     

  • 52.

    Ma, W. J., Husain, M. & Bays, P. M. Changing concepts of working memory. Nat. Neurosci. 17, 347–356 (2014).

    CAS 
    PubMed 
    PubMed Central 

    Google Scholar
     

  • 53.

    Keshvari, S., Van den Berg, R. & Ma, W. J. No evidence for an item limit in change detection. PLoS Comput. Biol. 9, e1002927 (2013).

    CAS 
    PubMed 
    PubMed Central 

    Google Scholar
     

  • 54.

    Van den Berg, R., Shin, H., Chou, W.-C., George, R. & Ma, W. J. Variability in encoding precision accounts for visual short-term memory limitations. Proc. Natl Acad. Sci. USA 109, 8780–8785 (2012).

    PubMed 

    Google Scholar
     

  • 55.

    Starr, A., Libertus, M. E. & Brannon, E. M. Infants show ratio-dependent number discrimination regardless of set size. Infancy 18, 927–941 (2013).


    Google Scholar
     

  • 56.

    Agrillo, C., Petrazzini, M. E. M. & Bisazza, A. Numerical acuity of fish is improved in the presence of moving targets, but only in the subitizing range. Anim. Cogn. 17, 307–316 (2014).

    PubMed 

    Google Scholar
     

  • 57.

    Petrazzini, M. E. M., Mantese, F. & Prato-Previde, E. Food quantity discrimination in puppies (Canis lupus familiaris). Anim. Cogn. 23, 703–710 (2020).


    Google Scholar
     

  • 58.

    Elmore, L. C. et al. Visual short-term memory compared in rhesus monkeys and humans. Curr. Biol. 21, 975–979 (2011).

    CAS 
    PubMed 
    PubMed Central 

    Google Scholar
     

  • 59.

    Tomonaga, M. & Matsuzawa, T. Enumeration of briefly presented items by the chimpanzee (Pan troglodytes) and humans (Homo sapiens). Anim. Learn. Behav. 30, 143–157 (2002).

    PubMed 

    Google Scholar
     

  • 60.

    Inoue, S. & Matsuzawa, T. Working memory of numerals in chimpanzees. Curr. Biol. 17, R1004–R1005 (2007).

    CAS 
    PubMed 

    Google Scholar
     

  • 61.

    Green, C. S. & Bavelier, D. Action video game modifies visual selective attention. Nature 423, 534–537 (2003).

    CAS 
    PubMed 

    Google Scholar
     

  • 62.

    Green, C. S. & Bavelier, D. Enumeration versus multiple object tracking: the case of action video game players. Cognition 101, 217–245 (2006).

    CAS 
    PubMed 

    Google Scholar
     

  • 63.

    Alexander, R. M. The gaits of bipedal and quadrupedal animals. Int. J. Rob. Res. 3, 49–59 (1984).


    Google Scholar
     

  • 64.

    Griffiths, T. L., Lieder, F. & Goodman, N. D. Rational use of cognitive resources: levels of analysis between the computational and the algorithmic. Top. Cogn. Sci. 7, 217–229 (2015).

    PubMed 

    Google Scholar
     



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