Counting on neurons: the neurobiology of numerical competence (original) (raw)

References

  1. Frege, G. The Foundations of Arithmetic. A Logic-Mathematical Enquiry into the Concept of Number. (trans. Austin, J. L.) (Blackwell, Oxford, 1884).
    Google Scholar
  2. Danzig, T. Number, the Language of Science (Free, New York, 1954).
    Google Scholar
  3. Dehaene, S. The Number Sense (Oxford Univ. Press, New York, 1997).
    Google Scholar
  4. Gallistel, C. R. & Gelman, R. Non-verbal numerical cognition: from reals to integers. Trends Cogn. Sci. 4, 59–65 (2000).
    Article CAS PubMed Google Scholar
  5. Henschen, S. E. Über Sprach-, Musik und Rechenmechanismen und ihre Lokalisation im Grobhirn. Z. ges. Neurologie und Psychiatrie 52, 273–298 (1919).
    Google Scholar
  6. Gerstmann, J. Syndrome of finger agnosia, disorientation for right and left agraphia and acalculia. Arch. Neurol. Psychiatry 44, 398–408 (1940).
    Article Google Scholar
  7. Luria, A. R. The Higher Cortical Functions in Man (Basic Books, New York, 1966).
    Google Scholar
  8. Fuson, K. C. & Hall, J. W. in The Development of Mathematical Thinking (ed. Ginsburg, H. P.) 49–107 (Academic, New York, 1983).
    Google Scholar
  9. Wiese, H. Numbers, Language, and the Human Mind (Cambridge Univ. Press, Cambridge, UK, 2003). A book that describes the human number faculty, merging verbal and non-verbal psychological findings into a major linguistic–philosophical concept.
    Book Google Scholar
  10. Wiese, H. Iconic and non-iconic stages in number development: the role of language. Trends Cogn. Sci. 7, 385–390 (2003).
    Article PubMed Google Scholar
  11. Hauser, M. D., Chomsky, N. & Fitch, W. T. The faculty of language: what is it, who has it, and how did it evolve? Science 298, 1569–1579 (2002).
    Article CAS PubMed Google Scholar
  12. Davis, H. & Perusse, R. Numerical competence in animals: definitional issues, current evidence, and a new research agenda. Behav. Brain Sci. 11, 561–615 (1988).
    Article Google Scholar
  13. Brannon, E. M. & Terrace, H. S. Ordering of the numerosities 1 to 9 by monkeys. Science 282, 746–749 (1998). A pioneering behavioural study showing that monkeys are able to understand the ordinal relationship of numerosities.
    Article CAS PubMed Google Scholar
  14. Hauser, M. D., MacNeilage, P. & Ware, M. Numerical representations in primates. Proc. Natl Acad. Sci. USA 93, 1514–1517 (1996).
    Article CAS PubMed PubMed Central Google Scholar
  15. Sulkowski, G. M. & Hauser, M. D. Can rhesus monkeys spontaneously subtract? Cognition 79, 239–262 (2001).
    Article CAS PubMed Google Scholar
  16. Flombaum, J., Junge, J. & Hauser, M. D. Rhesus monkeys (Macaca mulatta) spontaneously compute addition operations over large numbers. Cognition (in the press).
  17. Feigenson, L., Dehaene, S. & Spelke, E. Core systems of number. Trends Cogn. Sci. 8, 307–314 (2004).
    Article PubMed Google Scholar
  18. Wynn, K. Addition and subtraction by human infants. Nature 358, 749–750 (1992).
    Article CAS PubMed Google Scholar
  19. Whalen, J., Gallistel, C. R. & Gelman, R. Nonverbal counting in humans: the psychophysics of number representations. Psychol. Sci. 10, 130–137 (1999).
    Article Google Scholar
  20. Cordes, S., Gelman, R., Gallistel, C. R. & Whalen, J. Variability signatures distinguish verbal from nonverbal counting for both large and small numbers. Psychon. Bull. Rev. 8, 698–707 (2001).
    Article CAS PubMed Google Scholar
  21. Barth, H., Kanwisher, N. & Spelke, E. The construction of large number representations in adults. Cognition 86, 201–221 (2003).
    Article PubMed Google Scholar
  22. Blake, B. Australian Aboriginal Languages: a General Introduction 2nd edn (Univ. Queensland Press, St Lucia, Queensland, 1991).
    Google Scholar
  23. Pica, P., Lemer, C., Izard, V. & Dehaene, S. Exact and approximate arithmetic in an Amazonian indigene group. Science 306, 499–503 (2004). Humans that lack number words for larger numerosities perform approximate numerical computations.
    Article CAS PubMed Google Scholar
  24. Gordon, P. Numerical cognition without words: evidence from Amazonia. Science 306, 496–499 (2004). Cardinality judgments in humans without a verbal number concept are astonishingly poor and reminiscent of the discrimination performances of animals.
    Article CAS PubMed Google Scholar
  25. Hauser, M. D. & Spelke, E. S. in The Cognitive Neurosciences III (ed. Gazzaniga, M.) (MIT Press, Cambridge, Massachusetts, 2004).
    Google Scholar
  26. Meck, W. H. & Church, R. M. A mode control model of counting and timing processes. J. Exp. Psychol. Anim. Behav. Proc. 9, 320–334 (1983).
    Article CAS Google Scholar
  27. Nieder, A. & Miller, E. K. Coding of cognitive magnitude: compressed scaling of numerical information in the primate prefrontal cortex. Neuron 37, 149–157 (2003).
    Article CAS PubMed Google Scholar
  28. Nieder, A. & Miller, E. K. Analog numerical representations in rhesus monkeys: evidence for parallel processing. J. Cogn. Neurosci. 16, 889–901 (2004).
    Article PubMed Google Scholar
  29. Mechner, F. Probability relations within response sequences under ratio reinforcement. J. Exp. Anal. Behav. 1, 109–121 (1958).
    Article CAS PubMed PubMed Central Google Scholar
  30. Van Oeffelen, M. P. & Vos, P. G. A probabilistic model for the discrimination of visual number. Percept. Psychophys. 32, 163–170 (1982).
    Article CAS PubMed Google Scholar
  31. Brannon, E. M. & Terrace, H. S. Representation of the numerosities 1–9 by rhesus macaques (Macaca mulatta). J. Exp. Psychol. Anim. Behav. Process. 26, 31–49 (2000).
    Article CAS PubMed Google Scholar
  32. Kaufman, E. L., Lord, M. W., Reese, T. W. & Volkmann, J. The discrimination of visual number. Am. J. Psychol. 62, 498–525 (1949).
    Article CAS PubMed Google Scholar
  33. Mandler, G. & Shebo, B. J. Subitizing: an analysis of its component processes. J. Exp. Psychol. Gen. 111, 1–22 (1982).
    Article CAS PubMed Google Scholar
  34. Kahneman, D., Treisman, A. & Gibbs, B. The reviewing of object files: object-specific integration of information. Cognit. Psychol. 24, 175–219 (1992).
    Article CAS PubMed Google Scholar
  35. Feigenson, L. & Carey, S. Tracking individuals via object-files: evidence from infants' manual search. Dev. Sci. 6, 568–584 (2003).
    Article Google Scholar
  36. Xu, F. & Spelke, E. S. Large number discrimination in 6-month old infants. Cognition 74, B1–B11 (2000).
    Article CAS PubMed Google Scholar
  37. McCrink, K. & Wynn, K. Large-number addition and subtraction by 9-month-old infants. Psychol. Sci. 15, 776–781 (2004).
    Article PubMed Google Scholar
  38. Hauser, M. D., Carey, S. & Hauser, L. B. Spontaneous number representation in semi-free-ranging rhesus monkeys. Proc. R. Soc. Lond. B 267, 829–833 (2000).
    Article CAS Google Scholar
  39. Uller, C., Hauser, M. D. & Carey, S. Spontaneous representation of number in cotton-top tamarins (Saguinus oedipus). J. Comp. Psychol. 115, 248–257 (2001).
    Article CAS PubMed Google Scholar
  40. Hauser, M. D., Tsao, F., Garcia, P. & Spelke, E. S. Evolutionary foundations of number: spontaneous representation of numerical magnitudes by cotton-top tamarins. Proc. R. Soc. Lond. B 270, 1441–1446 (2003).
    Article Google Scholar
  41. Beran, M. J. & Beran, M. M. Chimpanzees remember the results of one-by-one addition of food items to sets over extended time periods. Psychol. Sci. 15, 94–99 (2004).
    Article PubMed Google Scholar
  42. Balakrishnan, J. D. & Ashby, F. G. Subitizing: magical numbers or mere superstition. Psychol. Res. 54, 80–90 (1992).
    Article CAS PubMed Google Scholar
  43. Pylyshyn, Z. W. Seeing and Visualizing: It's Not What You Think (Bradford Books, MIT Press, Massachusetts, 2003).
    Book Google Scholar
  44. Sathian, K. et al. Neural evidence linking visual object enumeration and attention. J. Cogn. Neurosci. 11, 36–51 (1999).
    Article CAS PubMed Google Scholar
  45. Piazza, M., Mechelli, A., Butterworth, B. & Price, C. J. Are subitizing and counting implemented as separate or functionally overlapping processes? Neuroimage 15, 435–446 (2002).
    Article PubMed Google Scholar
  46. Piazza, M., Giacomini, E., Le Bihan, D. & Dehaene, S. Single-trial classification of parallel pre-attentive and serial attentive processes using functional magnetic resonance imaging. Proc. R. Soc. Lond. B 270, 1237–1245 (2003).
    Article Google Scholar
  47. Nieder, A., Freedman, D. J. & Miller, E. K. Representation of the quantity of visual items in the primate prefrontal cortex. Science 297, 1708–1711 (2002). The authors taught monkeys to judge whether two successively presented visual displays contained the same number of items. Neurons in the prefrontal cortex were maximally activated by a specific number of items, but were unaffected by changes in the exact appearance of the stimuli.
    Article CAS PubMed Google Scholar
  48. Nieder, A. & Miller, E. K. A parieto-frontal network for visual numerical information in the monkey. Proc. Natl Acad. Sci. USA 101, 7457–7462 (2004). A comparison of numerosity-selective neurons recorded in three areas (prefrontal, posterior parietal and anterior temporal) of the same monkeys. Quantity information was first represented in the posterior parietal cortex, but the prefrontal cortex showed the highest proportion of numerosity-selective neurons.
    Article CAS PubMed PubMed Central Google Scholar
  49. Sawamura, H., Shima, K. & Tanji, J. Numerical representation for action in the parietal cortex of the monkey. Nature 415, 918–922 (2002).
    Article CAS PubMed Google Scholar
  50. Romo, R., Brody, C. D., Hernandez, A. & Lemus, L. Neuronal correlates of parametric working memory in the prefrontal cortex. Nature 399, 470–473 (1999).
    Article CAS PubMed Google Scholar
  51. Brody, C. D., Hernandez, A., Zainos, A. & Romo, R. Timing and neural encoding of somatosensory parametric working memory in macaque prefrontal cortex. Cereb. Cortex 13, 1196–1207 (2003).
    Article PubMed Google Scholar
  52. Petrides, M. & Pandya, D. N. in Principles of Frontal Lobe Function (eds Stuss, D. T. & Knight, R. T.) 31–50 (Oxford Univ. Press, Oxford, 2002).
    Book Google Scholar
  53. Miller, E. K. & Cohen, J. D. An integrative theory of prefrontal cortex function. Annu. Rev. Neurosci. 24, 167–202 (2001).
    Article CAS PubMed Google Scholar
  54. Green, D. M. & Swets, J. A. Signal Detection Theory and Psychophysics (Wiley, New York, 1966).
    Google Scholar
  55. Piazza, M., Izard, V., Pinel, P., Le Bihan, D. & Dehaene, S. Tuning curves for approximate numerosity in the human intraparietal sulcus. Neuron 44, 547–555 (2004). Shows that visual numerosities automatically activate the intraparietal sulcus of humans. Using an fMRI adaptation protocol, the authors were able to reconstruct numerosity activation profiles reminiscent to single-neuron numerosity tuning curves.
    Article CAS PubMed Google Scholar
  56. Shuman, M. & Kanwisher, N. Numerical magnitude in the human parietal lobe: tests of representational generality and domain specificity. Neuron 44, 557–569 (2004).
    Article CAS PubMed Google Scholar
  57. Gibbon, J. Scalar expectancy theory and Weber's Law in animal timing. Psychol. Rev. 84, 279–335 (1977).
    Article Google Scholar
  58. Brannon, E. M., Wusthoff, C. J., Gallistel, C. R. & Gibbon, J. Numerical subtraction in the pigeon: evidence for a linear subjective number scale. Psychol. Sci. 12, 238–243 (2001).
    Article CAS PubMed Google Scholar
  59. Dehaene, S. & Mehler, J. Cross-linguistic regularities in the frequency of number words. Cognition 43, 1–29 (1992).
    Article CAS PubMed Google Scholar
  60. Dehaene, S. Subtracting pigeons: logarithmic or linear? Psychol. Sci. 12, 244–246 (2001).
    Article CAS PubMed Google Scholar
  61. Dehaene, S. & Changeux, J. P. Development of elementary numerical abilities: a neuronal model. J. Cogn. Neurosci. 5, 390–407 (1993).
    Article CAS PubMed Google Scholar
  62. Verguts, T. & Fias, W. Representation of number in animals and humans: a neural model. J. Cogn. Neurosci. 16, 1493–1504 (2004).
    Article PubMed Google Scholar
  63. Dehaene, S. The neural basis of the Weber–Fechner law: a logarithmic mental number line. Trends Cogn. Sci. 7, 145–147 (2003).
    Article PubMed Google Scholar
  64. Xia, L., Emmerton, J., Siemann, M. & Delius, J. D. Pigeons (Columba livia) learn to link numerosities with symbols. J. Comp. Psychol. 115, 83–91 (2001).
    Article CAS PubMed Google Scholar
  65. Pepperberg, I. M. Evidence for conceptual quantitative abilities in the African parrot: labeling of cardinal sets. Ethology 75, 37–61 (1987).
    Article Google Scholar
  66. Washburn, D. A. & Rumbaugh, D. M. Ordinal judgements of numerical symbols by macaques (Macaca mulatta). Psychol. Sci. 2, 190–193 (1991).
    Article CAS PubMed Google Scholar
  67. Matsuzawa, T. Use of numbers by a chimpanzee. Nature 315, 57–59 (1985).
    Article CAS PubMed Google Scholar
  68. Boysen, S. T. & Bernston, G. G. Numerical competence in a chimpanzee. J. Comp. Psychol. 103, 23–31 (1989).
    Article CAS PubMed Google Scholar
  69. Eger, E., Sterzer, P., Russ, M. O., Giraud, A. L. & Kleinschmidt, A. A supramodal number representation in human intraparietal cortex. Neuron 37, 719–725 (2003). Functional imaging study showing that both spoken and written numerals can specifically activate the human intraparietal sulcus automatically and task-independently.
    Article CAS PubMed Google Scholar
  70. Naccache, L. & Dehaene, S. The priming method: imaging unconscious repetition priming reveals an abstract representation of number in the parietal lobe. Cereb. Cortex 11, 966–974 (2001).
    Article CAS PubMed Google Scholar
  71. Pinel, P., Piazza M., Le Bihan, D. & Dehaene, S. Distributed and overlapping cerebral representations of number, size, and luminance during comparative judgments. Neuron 41, 983–993 (2004). Using fMRI, the authors report that different types of magnitude (luminance, size and numerical value) activate overlapping parietal regions in humans.
    Article CAS PubMed Google Scholar
  72. Fias, W., Lammertyn, J., Reynvoet, B., Dupont, P. & Orban, G. A. Parietal representation of symbolic and nonsymbolic magnitude. J. Cogn. Neurosci. 15, 47–56 (2003).
    Article PubMed Google Scholar
  73. Kleinschmidt, A. Thinking big; many modules or much cortex? Neuron 41, 842–844 (2004).
    Article CAS PubMed Google Scholar
  74. Nieder, A. The number domain — can we count on parietal cortex? Neuron 44, 407–409 (2004).
    Article CAS PubMed Google Scholar
  75. Dehaene, S., Piazza, M., Pinel, P. & Cohen, L. Three parietal circuits for number processing. Cogn. Neuropsychol. 20, 487–506 (2003).
    Article PubMed Google Scholar
  76. Dehaene, S., Spelke, E., Pinel, P., Stanescu, R. & Tsivkin, S. Sources of mathematical thinking: behavioural and brain imaging evidence. Science 284, 970–974 (1999).
    Article CAS PubMed Google Scholar
  77. Menon, V. et al. Functional optimization of arithmetic processing in perfect performers. Cogn. Brain Res. 9, 343–345 (2000).
    Article CAS Google Scholar
  78. Lee, K. M. 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, 657–661 (2000).
    Article CAS PubMed Google Scholar
  79. Gruber, O., Indefrey, P., Steinmetz, H. & Kleinschmidt, A. Dissociating neural correlates of cognitive components in mental calculation. Cereb. Cortex 11, 350–359 (2001).
    Article CAS PubMed Google Scholar
  80. Simon, O., Mangin, J. F., Cohen, L., Le Bihan, D. & Dehaene, S. 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
  81. Isaacs, E. B., Edmonds, C. J., Lucas, A. & Gadian, D. G. Calculation difficulties in children of very low birthweight: a neural correlate. Brain 124, 1701–1707 (2001).
    Article CAS PubMed Google Scholar
  82. Landerl, K., Bevan, A. & Butterworth, B. Developmental dyscalculia and basic numerical capacities: a study of 8–9-year-old students. Cognition 93, 99–125 (2004).
    Article PubMed Google Scholar
  83. Molko, N. et al. 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
  84. Molko, N. et al. Brain anatomy in Turner syndrome: evidence for impaired social and spatial–numerical networks. Cereb. Cortex 14, 840–850 (2004).
    Article CAS PubMed Google Scholar
  85. Rivera, S. M., Menon, V., White, C. D., Glaser, B. & Reiss, A. L. Functional brain activation during arithmetic processing in females with fragile X syndrome is related to FMR1 protein expression. Hum. Brain Mapp. 16, 206–218 (2002).
    Article PubMed PubMed Central Google Scholar
  86. Eliez, S. et al. Functional brain imaging study of mathematical reasoning abilities in velocardiofacial syndrome (del22q11.2). Genet. Med. 3, 49–55 (2001).
    Article CAS PubMed Google Scholar
  87. Swartz, K. B., Chen, S. & Terrace, H. S. Serial learning by Rhesus monkeys. I. Acquisition and retention of multiple four-item lists. J. Exp. Psychol. Anim. Behav. Process. 17, 396–410 (1991).
    Article CAS PubMed Google Scholar
  88. Straub, R. O., Seidenberg, M. S., Bever, T. G. & Terrace, H. S. Serial learning in the pigeon. J. Exp. Anal. Behav. 32, 137–148 (1979).
    Article CAS PubMed PubMed Central Google Scholar
  89. Terrace, H. S., Son, L. & Brannon, E. Serial expertise by rhesus macaques. Psychol. Sci. 14, 66–73 (2003).
    Article PubMed Google Scholar
  90. Ebbinghaus, H. Memory: a Contribution to Experimental Psychology (Dover, New York, 1964).
    Google Scholar
  91. Ebenholtz, S. M. Serial learning: position learning and sequential associations. J. Exp. Psychol. 66, 353–362 (1963).
    Article CAS PubMed Google Scholar
  92. Chen, S., Swartz, K. B. & Terrace, H. S. Knowledge of the ordinal position of list items in rhesus monkeys. Psychol. Sci. 8, 80–86 (1997). Shows that monkeys understand and use numerical rank information.
    Article Google Scholar
  93. Orlov, T., Yakovlev, V., Hochstein, S. & Zohary, E. Macaque monkeys categorize images by their ordinal number. Nature 404, 77–80 (2000).
    Article CAS PubMed Google Scholar
  94. Orlov, T., Yakovlev, V., Amit, D., Hochstein, S. & Zohary, E. Serial memory strategies in macaque monkeys: behavioral and theoretical aspects. Cereb. Cortex 12, 306–317 (2002).
    Article Google Scholar
  95. Milner B. Interhemispheric differences in the localization of psychological processes in man. Br. Med. Bull. 27, 272–277 (1971).
    Article CAS PubMed Google Scholar
  96. McAndrews, M. P. & Milner, B. The frontal cortex and memory for temporal order. Neuropsychologia 29, 849–859 (1991).
    Article CAS PubMed Google Scholar
  97. Petrides, M. & Milner, B. Deficits on subject-ordered tasks after frontal- and temporal-lobe lesions in man. Neuropsychologia 20, 249–262 (1982).
    Article CAS PubMed Google Scholar
  98. Milner, B., Corsi, P. & Leonard, G. Frontal-lobe contribution to recency judgments. Neuropsychologia 29, 601–618 (1991).
    Article CAS PubMed Google Scholar
  99. Shimamura, A. P., Janowsky, J. S. & Squire, L. R. Memory for the temporal order of events in patients with frontal lobe lesions and amnesic patients. Neuropsychologia 28, 803–813 (1990).
    Article CAS PubMed Google Scholar
  100. Petrides, M. Impairments on nonspatial self-ordered and externally ordered working memory tasks after lesions of the mid-dorsal part of the lateral frontal cortex in the monkey. J. Neurosci. 15, 359–375 (1995).
    Article CAS PubMed PubMed Central Google Scholar
  101. Cabeza, R. et al. Brain regions differentially involved in remembering what and when: a PET study. Neuron 19, 863–870 (1997).
    Article CAS PubMed Google Scholar
  102. Cabeza, R., Anderson, N. D., Houle, S., Mangels, J. A. & Nyberg, L. Age-related differences in neural activity during item and temporal-order memory retrieval: a positron emission tomography study. J. Cogn. Neurosci. 12, 197–206 (2000).
    Article CAS PubMed Google Scholar
  103. Konishi, S. et al. Neural correlates of recency judgment. J. Neurosci. 22, 9549–9555 (2002).
    Article CAS PubMed PubMed Central Google Scholar
  104. Marshuetz, C., Smith, E. E., Jonides, J., DeGutis, J. & Chenevert, T. L. Order information in working memory: fMRI evidence for parietal and prefrontal mechanisms. J. Cogn. Neurosci. 12 Suppl. 2, 130–144 (2000).
    Article PubMed Google Scholar
  105. Bengtsson S. L., Ehrsson, H. H., Forssberg, H. & Ullen, F. Dissociating brain regions controlling the temporal and ordinal structure of learned movement sequences. Eur. J. Neurosci. 19, 2591–2602 (2004).
    Article PubMed Google Scholar
  106. Ninokura, Y., Mushiake, H. & Tanji, J. Representation of the temporal order of visual objects in the primate lateral prefrontal cortex. J. Neurophysiol. 89, 2868–2873 (2003).
    Article PubMed Google Scholar
  107. Ninokura, Y., Mushiake, H. & Tanji, J. Integration of temporal order and object information in the monkey lateral prefrontal cortex. J. Neurophysiol. 91, 555–560 (2004). Single-cell study showing that neurons in the prefrontal cortex of macaques encode the numerical rank of successively-displayed objects.
    Article PubMed Google Scholar
  108. Funahashi, S., Inoue, M. & Kubota, K. Delay-period activity in the primate prefrontal cortex encoding multiple spatial positions and their order of presentation. Behav. Brain Res. 84, 203–223 (1997).
    Article CAS PubMed Google Scholar
  109. Barone, P. & Joseph, J. P. Prefrontal cortex and spatial sequencing in macaque monkey. Exp. Brain Res. 78, 447–464 (1989).
    Article CAS PubMed Google Scholar
  110. Kermadi, I. & Joseph, J. P. Activity in the caudate nucleus of monkey during spatial sequencing. J. Neurophysiol. 74, 911–933 (1995).
    Article CAS PubMed Google Scholar
  111. Procyk, E. & Joseph, J. P. Characterization of serial order encoding in the monkey anterior cingulate sulcus. Eur. J. Neurosci. 14, 1041–1046 (2001).
    Article CAS PubMed PubMed Central Google Scholar
  112. Procyk, E., Tanaka, Y. L. & Joseph, J. P. Anterior cingulate activity during routine and non-routine sequential behaviors in macaques Nature Neurosci. 3, 502–508 (2000).
    Article CAS PubMed Google Scholar
  113. Clower, W. T. & Alexander, G. E. Movement sequence-related activity reflecting numerical order of components in supplementary and presupplementary motor areas. J. Neurophysiol. 80, 1562–1566 (1998).
    Article CAS PubMed Google Scholar
  114. Tanji, J. & Shima, K. Role for supplementary motor area cells in planning several movements ahead. Nature 371, 413–416 (1994).
    Article CAS PubMed Google Scholar
  115. Shima, K. & Tanji, J. Neuronal activity in the supplementary and presupplementary motor areas for temporal organization of multiple movements. J. Neurophysiol. 84, 2148–2160 (2000).
    CAS PubMed Google Scholar
  116. Isoda, M. & Tanji, J. Participation of the primate presupplementary motor area in sequencing multiple saccades. J. Neurophysiol. 92, 653–659 (2004).
    Article PubMed Google Scholar
  117. Isoda, M. & Tanji, J. Contrasting neuronal activity in the supplementary and frontal eye fields during temporal organization of multiple saccades. J. Neurophysiol. 90, 3054–3065 (2003).
    Article PubMed Google Scholar
  118. Carpenter, A. F., Georgopoulos, A. P. & Pellizzer, G. Motor cortical encoding of serial order in a context-recall task. Science 283, 1752–1757 (1999).
    Article CAS PubMed Google Scholar
  119. Gevers, W., Reynvoet, B. & Fias, W. The mental representation of ordinal sequences is spatially organized. Cognition 87, B87–B95 (2003).
    Article PubMed Google Scholar
  120. Cipolotti, L., Butterworth, B. & Denes, G. A specific deficit for numbers in a case of dense acalculia. Brain 114, 2619–2637 (1991).
    Article PubMed Google Scholar
  121. Delazer, M. & Butterworth, B. A dissociation of number meanings. Cogn. Neuropsychol. 14, 613–636 (1997).
    Article Google Scholar
  122. Turconi, E. & Seron, X. Dissociation between order and quantity meanings in a patient with Gerstmann syndrome. Cortex 38, 911–914 (2002).
    Article Google Scholar
  123. Turconi, E., Jemel, B., Rossion, B. & Seron, X. Electrophysiological evidence for differential processing of numerical quantity and order in humans. Brain Res. Cogn. Brain Res. 21, 22–38 (2004).
    Article PubMed Google Scholar
  124. Houde, O. & Tzourio-Mazoyer, N. Neural foundations of logical and mathematical cognition. Nature Rev. Neurosci. 4, 507–514 (2003).
    Article CAS Google Scholar
  125. Hassenstein, B. Otto Koehler — his life and his work. Z. Tierpsychol. 35, 449–464 (1974).
    Article CAS PubMed Google Scholar
  126. Koehler, O. Vom Erlernen unbenannter Anzahlen bei Vögeln. Naturwissenschaften 29, 201–218 (1941).
    Article Google Scholar
  127. Koehler, O. The ability of birds to “count”. Bull. Anim. Behav. 9, 41–45 (1951).
    Google Scholar
  128. Hassmann, M. Vom Erlernen unbenannter Anzahlen beim Eichhörnchen. Z. Tierpsychol. 9, 294–321 (1952).
    Article Google Scholar
  129. 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).
    Article Google Scholar
  130. Wilson, M. L., Hauser, M. D. & Wrangham, R. W. Does participation in intergroup conflict depend on numerical assessment, range location, or rank for wild chimpanzees? Anim. Behav. 61, 1203–1216 (2001).
    Article Google Scholar
  131. Wilson, M. L., Britton, N. F. & Franks, N. R. Chimpanzees and the mathematics of battle. Proc. R. Soc. Lond. B 269, 1107–1112 (2002).
    Article Google Scholar
  132. Hauser, M. D., Carey, S. & Hauser, L. B. Spontaneous number representation in semi-free-ranging rhesus monkeys. Proc. R. Soc. Lond. B 267, 829–833 (2000).
    Article CAS Google Scholar
  133. Lyon, B. E. Egg recognition and counting reduce costs of avian conspecific brood parasitism. Nature 422, 495–499 (2003).
    Article CAS PubMed Google Scholar
  134. Bergman, T. J., Beehner, J. C., Cheney, D. L. & Seyfarth, R. M. Hierarchical classification by rank and kinship in baboons. Science 302, 1234–1236 (2003).
    Article CAS PubMed Google Scholar
  135. Weber, E. H. De Pulsu, Resorptione, Auditu et Tactu: Annotationes Anatomicae et Physiologicae (Koehler, Leipzig, Germany, 1834).
    Google Scholar
  136. Fechner, G. T. Elemente der Psychophysik (Breitkopf & Härtel, Leipzig, Germany, 1860).
    Google Scholar
  137. Randall, D., Burggren, W. & French, K. Eckert Animal Physiology 5th edn (W. H. Freeman & Co., New York, 2002).
    Google Scholar
  138. Dayan, P. & Abbott, L. F. Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems (MIT Press, Cambridge, Massachusetts, 2001).
    Google Scholar
  139. Seron, X., Pesenti, M., Noel, M. P., Deloche, G. & Cornet, J. A. Images of numbers, or 'when 98 is upper left and 6 sky blue'. Cognition 44, 159–196 (1992).
    Article CAS PubMed Google Scholar
  140. Rickmeyer, K. 'Die Zwölf liegt hinter der nächsten Kurve und die Sieben ist pinkrot': Zahlenraumbilder und bunte Zahlen. J. Mathematik-Didaktik 22, 51–71 (2001).
    Article Google Scholar
  141. Galton, F. Visualised numerals. Nature 21, 252–256 (1880).
    Article Google Scholar
  142. Restle, F. Speed of adding and comparing numbers. J. Exp. Psychol. 91, 191–205 (1970).
    Google Scholar
  143. Dehaene, S., Bossini, S. & Giraux, P. The mental representation of parity and number magnitude. J. Exp. Psychol. Gen. 122, 371–396 (1993).
    Article Google Scholar
  144. Fischer, M. H., Castel, A. D., Dodd, M. D. & Pratt, J. Perceiving numbers causes spatial shifts of attention. Nature Neurosci. 6, 555–556 (2003).
    Article CAS PubMed Google Scholar
  145. Moyer, R. S. & Landauer, T. K. Time required for judgments of numerical inequality. Nature 215, 1519–1520 (1967).
    Article CAS PubMed Google Scholar
  146. Zorzi, M., Priftis, K. & Umilta, C. Brain damage: neglect disrupts the mental number line. Nature 417, 138–139 (2002). A lesion study in humans showing that spatial neglect patients misplace the midpoint of a numerical interval when asked to bisect it.
    Article CAS PubMed Google Scholar
  147. Vuilleumier, P., Ortigue, S. & Brugger, P. The number space and neglect. Cortex 40, 399–410 (2004).
    Article PubMed Google Scholar

Download references