The Counting Function and Its Representation in the Parietal Cortex in Humans and Animals

Article

Current data provide evidence that the ability to assess numbers is present not only in adult humans, but also in animals and children of preverbal age. Studies of behavior in infants and animals have demonstrated that the perception of number, the discrimination of quantities, and elementary addition and subtraction appear during onto- and phylogenesis before the appearance of speech. Number perception in humans and animals has common features: the greater the difference between numbers, the easier they are to discriminate; for a given difference between numbers, increases in size lead to increased difficulty in discrimination. Clinical data on counting impairments in patients and functional tomography studies of number operations in healthy subjects have shown that the key structures involved in number perception in humans are located in the parietal cortex. As demonstrated by experiments on monkeys and dogs, recognition of number in these species is also associated with the parietal area of the cortex. The similarity of the morphofunctional bases of “counting behavior” in humans and animals suggests that counting can be regarded as a functional mechanism of adaptive behavior which formed during evolution.

Key words

perception of stimulus number humans animals parietal area of the cortex 

References

  1. 1.
    A. N. Bregadze, “Individual responses of dogs to sequential ‘counting,’” Byull. Éksperim. Biol. Med., 2, 113–114 (1936).Google Scholar
  2. 2.
    A. N. Bregadze, “Acquisition of individual responses to complex sequential ‘counting’ in dogs,” Tr. Inst. Fiziol. im. I. S. Beritashvili (Tbilisi), 3, 415–430 (1937).Google Scholar
  3. 3.
    M. E. Varga, “Changes in evoked potentials on systematic use of series of uniform signals,” Zh. Vyssh. Nerv. Deyat., 22, No. 2, 403–407 (1972).Google Scholar
  4. 4.
    M. E. Varga, “Characteristics of the discrimination of the numbers of sequential signals by dogs,” Zh. Vyssh. Nerv. Deyat., 46, No. 4, 732–739 (1996).Google Scholar
  5. 5.
    M. E. Varga and G. V. Nikolaev, “Formation of conditioned reflexes to the number of sequential stimuli in dogs,” Zh. Vyssh. Nerv. Deyat., 33, No. 2, 267–276 (1983).Google Scholar
  6. 6.
    M. E. Varga, O. G. Pavlova, and V. N. Mats, “The importance of the parietal associative area of the cortex for ‘counting’ behavior in dogs,” Zh. Vyssh. Nerv. Deyat., 56, No. 6, 767–774 (2006).Google Scholar
  7. 7.
    M. E. Varga and Ya. M. Pressman, “Reflection in cortical evoked potentials of the quantitative parameters of series of unreinforced signals of different modality,” Zh. Vyssh. Nerv. Deyat., 30, No. 6, 1248–1255 (1980).Google Scholar
  8. 8.
    M. E. Varga and I. N. Tveritskaya, “The place conditioned reflex as the functional basis of an elementary model of counting in dogs,” Zh. Vyssh. Nerv. Deyat., 23, No. 3, 477–383.Google Scholar
  9. 9.
    M. E. Varga and I. N. Tveritskaya, “Changes in evoked potentials on systematic use of series of uniform signals with variable interstimulus intervals,” Zh. Vyssh. Nerv. Deyat., 26, No. 2, 375–380 (1976).Google Scholar
  10. 10.
    Z. A. Zorina, A. A. Smirnova, and O. F. Lazareva, “Do crows ‘count’?” Priroda, 2, 72–79 (2001).Google Scholar
  11. 11.
    N. N. Ladygina-Kots, Development of Mental Functions during the Evolution of Organisms [in Russian], Sovetskaya Nauka, Moscow (1958).Google Scholar
  12. 12.
    A. R. Luriya, Higher Cortical Functions in Humans and Their Impairments in Local Brain Lesions [in Russian], Akademicheskii Proekt, Moscow (2000).Google Scholar
  13. 13.
    Ya. M. Pressman, “Evoked potentials in the dog sensorimotor cortex during systematic use of series of electrocutaneous stimuli,” Zh. Vyssh. Nerv. Deyat., 26, No. 3, 481–488 (1976).Google Scholar
  14. 14.
    Ya. M. Pressman and I. N. Tveritskaya, “Responses of the auditory area of the dog cortex to paired sound clicks used repeatedly in standard series,” Zh. Vyssh. Nerv. Deyat., 28, No. 6, 1184–1189 (1978).Google Scholar
  15. 15.
    Zh. I. Reznikova and B. Ya. Ryabko “Transmission of information relating to the quantitative characteristics of objects in ants,” Zh. Vyssh. Nerv. Deyat., 45, No. 3, 500–509 (1995).Google Scholar
  16. 16.
    A. A. Smirnova, Studies of the Ability of Hooded Crows to Generalize Associated with the Processing of Number Information [in Russian], Doctoral Thesis, Moscow State University, Moscow (2000).Google Scholar
  17. 17.
    M. A. Usievich, “Solution of a difficult task by the dog nervous system,” Tr. Fiziol. Lab. im. I. P. Pavlova, 8, 315–320 (1938).Google Scholar
  18. 18.
    V. K. Fedorov, “Studies of higher nervous activity in dogs of the non-retentive type,” Tr. Fiziol. Lab. im. I. P. Pavlova, 15, 241–301 (1949).Google Scholar
  19. 19.
    L. S. Tsvetkova, Impairments to the Recovery of Counting (in Local Brain Lesions). Neurophysiological Studies [in Russian], A. R. Luriya (ed.), Moscow State University, Moscow (1972).Google Scholar
  20. 20.
    V. V. Yakovleva, “Physiological mechanism of the formation of difficult differentiation,” Tr. Fiziol. Lab. im. I. P. Pavlova, 9, 230–269 (1940).Google Scholar
  21. 21.
    D. Ansari, B. Dhital, and S. C. Siong, “Parametric effects of numerical distance on the intraparietal sulcus during passive viewing of rapid numerosity changes,” Brain Res., 1067, No. 1, 181–188 (2006).CrossRefPubMedGoogle Scholar
  22. 22.
    J. D. Balakrishnan and F. G. Ashby, “Subitizing: magical numbers or mere superstition?” Psychol. Res., 54, 80–90 (1992).CrossRefPubMedGoogle Scholar
  23. 23.
    S. T. Boysen and G. G. Berntson, “Numerical competence in a chimpanzee (Pan troglodytes)”, J. Comp. Psychol., 103, No. 1, 23–31 (1989).CrossRefPubMedGoogle Scholar
  24. 24.
    S. T. Boysen, G. G. Berntson, T. A. Shreyer, and M. B. Hannan, Indicating acts during counting by a chimpanzee (Pan troglodytes),” J. Comp. Psychol., 109, No. 1, 47–51 (1995).CrossRefPubMedGoogle Scholar
  25. 25.
    E. M. Brannon and H. S. Terrace, Ordering of the numerosities 1 to 9 by monkey,” Science, 282, 746–749 (1998).CrossRefPubMedGoogle Scholar
  26. 26.
    P. Buckley and C. B. Gillman, “Comparisons of digits and dot patterns,” J. Exp. Psychol., 103, No. 6, 1131–1136 (1974).CrossRefPubMedGoogle Scholar
  27. 27.
    F. Chochon, L. Cohen, P. F. van de Moortele, and S. Dehaene, “Differential contributions of the left and right inferior parietal lobules to number processing,” J. Cogn. Neurosci., 11, No. 6, 617–630 (1999).CrossRefPubMedGoogle Scholar
  28. 28.
    L. Cohen and S. Dehaene, “Calculating without reading: unsuspected residual abilities in pure alexia,” Cogn. Neuropsychol., 17, 563–583 (2000).CrossRefGoogle Scholar
  29. 29.
    L. Cohen, S. Dehaene, F. Chochon, S. Lehericy, and L. Naccache, “Language and calculation within the parietal lobe: a combined cognitive, anatomical and fMRI study,” Neuropsychologia, 38, No. 10, 1426–1440 (2000).CrossRefPubMedGoogle Scholar
  30. 30.
    H. Davis and J. Memmott, “Counting behavior in animals: a critical evaluation,” Psychol. Bull., 92, 547–571 (1982).CrossRefGoogle Scholar
  31. 31.
    S. Dehaene, “The organization of brain activations in number comparison: event-related potentials and the additive-factors methods,” J. Cogn. Neurosci., 8, 47–68 (1996).CrossRefGoogle Scholar
  32. 32.
    S. Dehaene and L. Cohen, “Towards an anatomical and functional model of number processing,” Math. Cogn., 1, 83–120 (1995).Google Scholar
  33. 33.
    S. Dehaene and L. Cohen, “Cerebral pathways for calculation: double dissociation between rote verbal and quantitative knowledge of arithmetic,” Cortex, 33, 219–250 (1997).CrossRefPubMedGoogle Scholar
  34. 34.
    S. Dehaene, G. Dehaene-Lambertz, and L. Cohen, “Abstract representation of numbers in the animal and human brain,” Trends Neurosci., 21, No. 8, 355–361 (1998).CrossRefPubMedGoogle Scholar
  35. 35.
    S. Dehaene, M. Piazza, P. Pinel, and L. Cohen, “Three parietal circuits for number processing,” Cogn. Neuropsychol., 20, 487–506 (2003).CrossRefGoogle Scholar
  36. 36.
    S. Dehaene, E. Spelke, P. Pinel, R. Stanescu, and S. Tsivkin, “Sources of mathematical thinking: behavioral and brain-imaging evidence,” Science, 284, 970–974 (1999).CrossRefPubMedGoogle Scholar
  37. 37.
    N. F. Dronkers, S. Pinker, and A. Damasio, “Language and the aphasias,” in: Principles of Neural Science, E. R. Kandel, J. H. Schwartz, and T. M. Jessell (eds.), McGraw-Hill, New York (2000), 4th Edition, pp. 1169–1185.Google Scholar
  38. 38.
    E. Eger, P. Sterzer, M. O. Russ, A.-L. Giraud, and A. Kleinschmidt, “A supramodal number representation in human intraparietal cortex,” Neuron, 37, 719–725 (2003).CrossRefPubMedGoogle Scholar
  39. 39.
    L. Festinger, “Studies in decision: I. Decision-time, relative frequency of judgment and subjective confidence as related to physical stimulus difference,” J. Exp. Psychol., 32, No. 4, 291–306 (1943).CrossRefGoogle Scholar
  40. 40.
    C. R. Gallistel and R. Gelman, “Preverbal and verbal counting and computation,” Cognition, 44, 43–74 (1992).CrossRefPubMedGoogle Scholar
  41. 41.
    C. R. Gallistel and R. Gelman, “Non-verbal numerical cognition from reals to integers,” Trends Cogn. Sci., 4, No. 2, 59–65 (2000).CrossRefPubMedGoogle Scholar
  42. 42.
    J. Grafman, D. Kampen, J. Rosenberg, A. Salazar, and F. Boller, “Calculation abilities in a patient with a virtual left hemispherectomy,” Behav. Neurol., 2, 183–194 (1989).Google Scholar
  43. 43.
    N. Harskamp and L. van Cipolotti, “Selective impairments for addition, subtraction and multiplication. Implications for the organization of arithmetical facts,” Cortex, 37, 363–388 (2001).CrossRefPubMedGoogle Scholar
  44. 44.
    M. D. Hauser, P. MacNeilage, and M. Ware, “Numerical representation in primates,” Proc. Natl. Acad. Sci. USA, 93, 1514–1517 (1996).CrossRefPubMedGoogle Scholar
  45. 45.
    T. Hyvarinen, “Posterior parietal lobe of primate brain,” Physiol. Rev., 6, 1060–1129 (1982).Google Scholar
  46. 46.
    E. R. Kandel, “From nerve cells to cognition: the internal cellular representation required for perception and action,” in: Principles of Neural Science, E. R. Kandel, J. H. Schwartz, and T. M. Jessell (eds.), McGraw-Hill, New York (2000), 4th Edition, pp. 381–403.Google Scholar
  47. 47.
    O. Koeler, “Thinking without words,” in: Proc. of the 14th Int. Congr. of Zoology, Copenhagen, (1956), pp. 75–88.Google Scholar
  48. 48.
    J. Kong, C. Wang, K. Kwong, M. Vangel, E. Chua, and R. Gollub, “The neural substrate of arithmetic operations and procedure complexity,” Brain Res. Cogn. Brain Res., 22, No. 3, 397–405 (2005).CrossRefPubMedGoogle Scholar
  49. 49.
    Y. Lample,Y. Eshel, R. Gilad, and I. Sarova-Pinhas, “Selective acalculia with sparing of the subtraction process in a patient with left parietotemporal hemorrhage,” Neurology, 44, 1759–1761 (1994).Google Scholar
  50. 50.
    K.-M. Lee, “Cortical areas differentially involved in multiplication and subtraction: a functional magnetic resonance imaging study and correlation with a case of selective acalculia,” Ann. Neurol., 48, No. 4, 657–661 (2000).CrossRefPubMedGoogle Scholar
  51. 51.
    K.-M. Lee and S.-Y. Kang, “Arithmetic operation and working memory: differential suppression in dual task,” Cognition, 83, No. 3, B63–B68 (2002).CrossRefPubMedGoogle Scholar
  52. 52.
    G. Mandler and B. J. Shebo, “Subitizing: an analysis of its component processes,” J. Exp. Psychol., 111, No. 1, 1–22 (1982).Google Scholar
  53. 53.
    T. Matsuzawa, “Use of numbers by a chimpanzee,” Nature, 315, 57–59 (1985).CrossRefPubMedGoogle Scholar
  54. 54.
    W. H. Meck and R. M. Church, “A mode control model of counting and timing process,” J. Exp. Psychol. Anim. Behav. Process, 9, 320–334 (1983).CrossRefPubMedGoogle Scholar
  55. 55.
    J. Mehler and T. G. Bever, “Cognitive capacity of very young children,” Science, 158, 141–142 (1967).CrossRefPubMedGoogle Scholar
  56. 56.
    N. Molko, A. Cachia, D. Riviere, J.-F. Mangin, M. Bruandet, D. Le Bihan, L. Cohen, and S. Dehaene, “Functional and structural alterations of the intraparietal sulcus in a developmental dyscalculia of genetic origin,” Neuron, 40, 847–858 (2003).CrossRefPubMedGoogle Scholar
  57. 57.
    V. B. Mountcastle, J. C. Lynch, A. Georgopoulos, H. Sakata, and C. Acana, “Posterior parietal association cortex of the monkey: command functions for operations within extrapersonal space,” J. Neurophysiol., 38, 871–908 (1975).PubMedGoogle Scholar
  58. 58.
    R. S. Moyer and T. K. Landauer, “Time required for judgments of numerical inequality,” Nature, 215, 1519–1520 (1967).CrossRefPubMedGoogle Scholar
  59. 59.
    L. Naccache and S. Dehaene, “The priming method: imaging unconscious repetition priming reveals an abstract representation of number in the parietal lobes,” Cerebral Cortex, 11, 966–974 (2001).CrossRefPubMedGoogle Scholar
  60. 60.
    A. Nieder, “Of neurons and numbers: how the primate cortex encodes numerical information,” in: The Neurosciences from Basic Research to Therapy. Proc. of the 29th Göttingen Neurobiology, California at the 5th Meeting of the German Neurosciences Society Göttingen (2003), p. 9.Google Scholar
  61. 61.
    A. Nieder and E. K. Miller, “A parietofrontal network for visual numerical information in the monkey,” Proc. Natl. Acad. Sci. USA, 101, No. 19, 7457–7462 (2004).CrossRefPubMedGoogle Scholar
  62. 62.
    S. Van Oeffelen and P. G. Vos, “A probabilistic model for the discrimination of visual number,” Percept. Psychophys., 32, 163–170 (1982).PubMedGoogle Scholar
  63. 63.
    I. M. Pepperberg, “Grey parrot (Psittacus erithacus) numerical abilities: addition and further experiments on a zero-like concept,” J. Comp. Psychol., 120, No. 1, 1–11 (2006).CrossRefPubMedGoogle Scholar
  64. 64.
    I. M. Pepperberg and J. D. Gordon, “Comprehension by a Grey parrot (Psittacus erithacus), including a zero-like conception,” J. Comp. Psychol., 119, No. 2, 197–209 (2005).CrossRefPubMedGoogle Scholar
  65. 65.
    J. Piaget, The Child’s Conception of Number, The Humanities Press, New York (1952).Google Scholar
  66. 66.
    M. Piazza, V. Izard, P. Pinel, D. Le Bithan, and S. Dehaene, Tuning curves for approximate numerosity in the human intraparietal sulcus,” Neuron, 44, 547–555 (2004).CrossRefPubMedGoogle Scholar
  67. 67.
    P. Pinel, H. G. le Clec, P. F. van de Moortele, L. Naccache, D. Le Bihan, and S. Dehaene, “Event-related fMRI analysis of the cerebral circuit for number comparison,” Neuroreport, 10, No. 7, 1473–1479 (1999).CrossRefPubMedGoogle Scholar
  68. 68.
    P. Pinel, S. Dehaene, D. Rivier, and D. le Bihan, “Modulation of parietal activation by semantic distance in number comparison task,” Neuroimage, 14, No. 5, 1013–1026 (2001).CrossRefPubMedGoogle Scholar
  69. 69.
    P. Pinel, M. Piazza, D. Le Bihan, and S. Dehaene, “Distributed and overlapping cerebral representations of number, size and luminance during comparative judgments,” Neuron, 41, 983–993 (2004).CrossRefPubMedGoogle Scholar
  70. 70.
    J. R. Platt and D. M. Johnson, Learn. Motivat., 2, 386–414 (1971).CrossRefGoogle Scholar
  71. 71.
    M. Rilling and C. McDiarmid, Signal detection in fixed-ratio schedules,” Science, 148, 526–527 (1965).CrossRefPubMedGoogle Scholar
  72. 72.
    P. E. Roland and L. Frieberg, “Localization of cortical areas activated by thinking,” J. Neurophysiol., 53, No. 5, 1219–1243 (1985).PubMedGoogle Scholar
  73. 73.
    D. M. Rumbaugh and D. A. Washburn, “Counting by chimpanzees and ordinality judgments by macaques in videoformated task,” in: The Development of Numerical Competence. Animal and Human Models, S. T. Boysen and F. J. Capaldi, (eds.), Laurence Erlbaum Assoc., Hillsdale, N.J. (1993), pp. 87–106.Google Scholar
  74. 74.
    H. Sakata,Y. Takaoka, and A. Kawarasaki, “Somatosensory properties of neurons in superior parietal cortex (area 5) of the rhesus monkey,” Brain Res., 64, 85–102 (1973).CrossRefPubMedGoogle Scholar
  75. 75.
    H. Sawamura, K. Shima, and J. Tanji, “Numerical representation for action in the parietal cortex of the monkey,” Nature, 415, 918–922 (2002).CrossRefPubMedGoogle Scholar
  76. 76.
    M. Shuman and N. Kanwisher, “Numerical magnitude in the human parietal lobe; tests of representational generality and domain specificity,” Neuron, 44, No. 3, 557–569 (2004).CrossRefPubMedGoogle Scholar
  77. 77.
    O. Simon, J.-F. Mangin, L. Cohen, D. Le Bihan, and S. Dehaene, “Topographical layout of hand, eye, calculation, and language-related areas in the human parietal lobe,” Neuron, 33, 475–487 (2002).CrossRefPubMedGoogle Scholar
  78. 78.
    R. Stanescu-Cosson, P. Pinel, P.-F. van de Moortele, D. Le Bihan, L. Cohen, and S. Dehaene, “Cerebral bases of calculation processes: impact of number size on the cerebral circuits for exact and approximate calculation,” Brain, 123, 2240–2255 (2000).CrossRefPubMedGoogle Scholar
  79. 79.
    P. Starkey and R. G. Cooper, “Perception of numbers by human infants,” Science, 210, 1033–1035 (1980).CrossRefPubMedGoogle Scholar
  80. 80.
    P. Starkey, E. S. Spelke, and R. Gelman, “Detection of inter-modal numerical correspondences by human infants,” Science, 222, 179–181 (1983).CrossRefPubMedGoogle Scholar
  81. 81.
    J. Stein, “The effect of cooling parietal lobe areas 5 and 7 upon voluntary movement in awake rhesus monkeys,” J. Physiol. (England), 258, 62–63 (1976).Google Scholar
  82. 82.
    T. Takayama, M. Sugishita, I. Akiguchi, and J. Kimura, “Isolated acalculia due to left parietal lesion,” Arch. Neurol., 51, No. 3, 286–291 (1994).PubMedGoogle Scholar
  83. 83.
    R. F. Thompson, K. S. Mayers, R. T. Robertson, and C. J. Patterson, “Number coding in association cortex of the cat,” Science, 168, 271–273 (1970).CrossRefPubMedGoogle Scholar
  84. 84.
    M. E. Varga, “The number of consecutive clicks in the train as positive or differential conditioned stimulus in dogs,” Acta Neurobiol., 42, 69–74 (1982).Google Scholar
  85. 85.
    M. E. Varga and I. N. Tveritskaya, “‘Counting’ of clicks, as reflected in amplitude of potentials evoked in auditory cortex of the dog,” Acta Neurobiol., 34, 329–338 (1974).Google Scholar
  86. 86.
    J. Whalen et al., “Non-verbal counting in humans: the psychophysics of number representation,” Psychol. Sci., 10, 130–137 (1999).CrossRefGoogle Scholar
  87. 87.
    G. Woodruff and D. Premack, “Primitive mathematical concepts in the chimpanzee: proportionality and numerosity,” Nature, 293, 568–570 (1981).CrossRefPubMedGoogle Scholar
  88. 88.
    K. Wynn, “Addition and subtraction by human infants,” Nature, 358, 749–750 (1992).CrossRefPubMedGoogle Scholar
  89. 89.
    F. Xu and S. S. Spelke, “Large number discrimination in 6-monthold infants,” Cognition, 74, No. 1, B1–B11 (2000).CrossRefGoogle Scholar

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© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  1. 1.Institute of Higher Nervous Activity and NeurophysiologyRussian Academy of SciencesMoscowRussia

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