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

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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.

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References

  1. A. N. Bregadze, “Individual responses of dogs to sequential ‘counting,’” Byull. Éksperim. Biol. Med., 2, 113–114 (1936).

    Google Scholar 

  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. 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).

    CAS  Google Scholar 

  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).

    CAS  Google Scholar 

  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).

    CAS  Google Scholar 

  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).

    CAS  Google Scholar 

  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).

    CAS  Google Scholar 

  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.

  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).

    CAS  Google Scholar 

  10. Z. A. Zorina, A. A. Smirnova, and O. F. Lazareva, “Do crows ‘count’?” Priroda, 2, 72–79 (2001).

    Google Scholar 

  11. N. N. Ladygina-Kots, Development of Mental Functions during the Evolution of Organisms [in Russian], Sovetskaya Nauka, Moscow (1958).

    Google Scholar 

  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. 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. 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. 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. 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).

  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. 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. 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. 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. 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).

    Article  CAS  PubMed  Google Scholar 

  22. J. D. Balakrishnan and F. G. Ashby, “Subitizing: magical numbers or mere superstition?” Psychol. Res., 54, 80–90 (1992).

    Article  CAS  PubMed  Google Scholar 

  23. S. T. Boysen and G. G. Berntson, “Numerical competence in a chimpanzee (Pan troglodytes)”, J. Comp. Psychol., 103, No. 1, 23–31 (1989).

    Article  CAS  PubMed  Google Scholar 

  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).

    Article  CAS  PubMed  Google Scholar 

  25. E. M. Brannon and H. S. Terrace, “Ordering of the numerosities 1 to 9 by monkey,” Science, 282, 746–749 (1998).

    Article  CAS  PubMed  Google Scholar 

  26. P. Buckley and C. B. Gillman, “Comparisons of digits and dot patterns,” J. Exp. Psychol., 103, No. 6, 1131–1136 (1974).

    Article  CAS  PubMed  Google Scholar 

  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).

    Article  CAS  PubMed  Google Scholar 

  28. L. Cohen and S. Dehaene, “Calculating without reading: unsuspected residual abilities in pure alexia,” Cogn. Neuropsychol., 17, 563–583 (2000).

    Article  Google Scholar 

  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).

    Article  CAS  PubMed  Google Scholar 

  30. H. Davis and J. Memmott, “Counting behavior in animals: a critical evaluation,” Psychol. Bull., 92, 547–571 (1982).

    Article  Google Scholar 

  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).

    Article  Google Scholar 

  32. S. Dehaene and L. Cohen, “Towards an anatomical and functional model of number processing,” Math. Cogn., 1, 83–120 (1995).

    Google Scholar 

  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).

    Article  CAS  PubMed  Google Scholar 

  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).

    Article  CAS  PubMed  Google Scholar 

  35. S. Dehaene, M. Piazza, P. Pinel, and L. Cohen, “Three parietal circuits for number processing,” Cogn. Neuropsychol., 20, 487–506 (2003).

    Article  Google Scholar 

  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).

    Article  CAS  PubMed  Google Scholar 

  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. 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).

    Article  CAS  PubMed  Google Scholar 

  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).

    Article  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  41. C. R. Gallistel and R. Gelman, “Non-verbal numerical cognition from reals to integers,” Trends Cogn. Sci., 4, No. 2, 59–65 (2000).

    Article  PubMed  Google Scholar 

  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. 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).

    Article  PubMed  Google Scholar 

  44. M. D. Hauser, P. MacNeilage, and M. Ware, “Numerical representation in primates,” Proc. Natl. Acad. Sci. USA, 93, 1514–1517 (1996).

    Article  CAS  PubMed  Google Scholar 

  45. T. Hyvarinen, “Posterior parietal lobe of primate brain,” Physiol. Rev., 6, 1060–1129 (1982).

    Google Scholar 

  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. O. Koeler, “Thinking without words,” in: Proc. of the 14th Int. Congr. of Zoology, Copenhagen, (1956), pp. 75–88.

  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).

    Article  PubMed  Google Scholar 

  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. 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).

    Article  CAS  PubMed  Google Scholar 

  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).

    Article  PubMed  Google Scholar 

  52. G. Mandler and B. J. Shebo, “Subitizing: an analysis of its component processes,” J. Exp. Psychol., 111, No. 1, 1–22 (1982).

    CAS  Google Scholar 

  53. T. Matsuzawa, “Use of numbers by a chimpanzee,” Nature, 315, 57–59 (1985).

    Article  CAS  PubMed  Google Scholar 

  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).

    Article  CAS  PubMed  Google Scholar 

  55. J. Mehler and T. G. Bever, “Cognitive capacity of very young children,” Science, 158, 141–142 (1967).

    Article  CAS  PubMed  Google Scholar 

  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).

    Article  CAS  PubMed  Google Scholar 

  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).

    CAS  PubMed  Google Scholar 

  58. R. S. Moyer and T. K. Landauer, “Time required for judgments of numerical inequality,” Nature, 215, 1519–1520 (1967).

    Article  CAS  PubMed  Google Scholar 

  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).

    Article  CAS  PubMed  Google Scholar 

  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.

  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).

    Article  CAS  PubMed  Google Scholar 

  62. S. Van Oeffelen and P. G. Vos, “A probabilistic model for the discrimination of visual number,” Percept. Psychophys., 32, 163–170 (1982).

    PubMed  Google Scholar 

  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).

    Article  PubMed  Google Scholar 

  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).

    Article  PubMed  Google Scholar 

  65. J. Piaget, The Child’s Conception of Number, The Humanities Press, New York (1952).

    Google Scholar 

  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).

    Article  CAS  PubMed  Google Scholar 

  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).

    Article  CAS  PubMed  Google Scholar 

  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).

    Article  CAS  PubMed  Google Scholar 

  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).

    Article  CAS  PubMed  Google Scholar 

  70. J. R. Platt and D. M. Johnson, Learn. Motivat., 2, 386–414 (1971).

    Article  Google Scholar 

  71. M. Rilling and C. McDiarmid, “Signal detection in fixed-ratio schedules,” Science, 148, 526–527 (1965).

    Article  CAS  PubMed  Google Scholar 

  72. P. E. Roland and L. Frieberg, “Localization of cortical areas activated by thinking,” J. Neurophysiol., 53, No. 5, 1219–1243 (1985).

    CAS  PubMed  Google Scholar 

  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. 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).

    Article  CAS  PubMed  Google Scholar 

  75. H. Sawamura, K. Shima, and J. Tanji, “Numerical representation for action in the parietal cortex of the monkey,” Nature, 415, 918–922 (2002).

    Article  CAS  PubMed  Google Scholar 

  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).

    Article  CAS  PubMed  Google Scholar 

  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).

    Article  CAS  PubMed  Google Scholar 

  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).

    Article  PubMed  Google Scholar 

  79. P. Starkey and R. G. Cooper, “Perception of numbers by human infants,” Science, 210, 1033–1035 (1980).

    Article  CAS  PubMed  Google Scholar 

  80. P. Starkey, E. S. Spelke, and R. Gelman, “Detection of inter-modal numerical correspondences by human infants,” Science, 222, 179–181 (1983).

    Article  CAS  PubMed  Google Scholar 

  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. T. Takayama, M. Sugishita, I. Akiguchi, and J. Kimura, “Isolated acalculia due to left parietal lesion,” Arch. Neurol., 51, No. 3, 286–291 (1994).

    CAS  PubMed  Google Scholar 

  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).

    Article  CAS  PubMed  Google Scholar 

  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).

    CAS  Google Scholar 

  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).

    CAS  Google Scholar 

  86. J. Whalen et al., “Non-verbal counting in humans: the psychophysics of number representation,” Psychol. Sci., 10, 130–137 (1999).

    Article  Google Scholar 

  87. G. Woodruff and D. Premack, “Primitive mathematical concepts in the chimpanzee: proportionality and numerosity,” Nature, 293, 568–570 (1981).

    Article  CAS  PubMed  Google Scholar 

  88. K. Wynn, “Addition and subtraction by human infants,” Nature, 358, 749–750 (1992).

    Article  CAS  PubMed  Google Scholar 

  89. F. Xu and S. S. Spelke, “Large number discrimination in 6-monthold infants,” Cognition, 74, No. 1, B1–B11 (2000).

    Article  Google Scholar 

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  1. Institute of Higher Nervous Activity and Neurophysiology, Russian Academy of Sciences, Moscow, Russia

    M. E. Varga, O. G. Pavlova & S. V. Nosova

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  1. M. E. Varga
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  2. O. G. Pavlova
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  3. S. V. Nosova
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Correspondence to O. G. Pavlova.

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Translated from Zhurnal Vysshei Nervnoi Deyatel’nosti imeni I. P Pavlova, Vol. 58, No. 6, pp. 663–677, November–December, 2008.

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Varga, M.E., Pavlova, O.G. & Nosova, S.V. The Counting Function and Its Representation in the Parietal Cortex in Humans and Animals. Neurosci Behav Physi 40, 185–196 (2010). https://doi.org/10.1007/s11055-009-9238-z

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