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pp 1–24 | Cite as

Numerals and neural reuse

  • Max Jones
S.I.: MathCogEncul

Abstract

Menary (in: Metzinger T, Windt JM (eds) OpenMIND, MIND Group, Frankfurt am Main, 2015) has argued that the development of our capacities for mathematical cognition can be explained in terms of enculturation. Our ancient systems for perceptually estimating numerical quantities are augmented and transformed by interacting with a culturally-enriched environment that provides scaffolds for the acquisition of cognitive practices, leading to the development of a discrete number system for representing number precisely. Numerals and the practices associated with numeral systems play a significant role in this process. However, the details of the relationship between the ancient number system and the discrete number system remain unclear. This lack of clarity is exacerbated by the problem of symbolic estrangement and the fact that unique features of how numeral systems represent require our ancient number system to play a dual role. These issues highlight that Dehaene’s (in: Dehaene S, Duhamel J-R, Hauser MS, Rizolatti G (eds) From monkey brain to human brain, MIT Press, Cambridge, pp 133–157, 2005) neuronal recycling hypothesis may be insufficient to explain the neural mechanisms underlying the process of enculturation. In order to explain mathematical enculturation, and enculturation more generally, it may be necessary to adopt Anderson’s (Behav Brain Sci 33(4):245–266, 2010; After phrenology: neural reuse and the interactive brain, MIT Press, Cambridge, 2014) theory of neural reuse.

Keywords

Mathematical cognition Numerical cognition Enculturation Neuronal recycling Neural reuse Cognitive integration Affordances Philosophy of psychology Philosophy of neuroscience 

Notes

Acknowledgements

This paper is based on a presentation delivered at the symposium on Mathematical Cognition and Enculturation at the European Society for Philosophy and Psychology Conference 2016. Huge thanks to Caterina Dutilh Novaes for organising this brilliant symposium and for her useful insight into this work, as well as Richard Menary, Markus Pantsar, Jean-Charles Pelland, Regina Fabry, Alexander Gillett, Christopher Burr, Zoe Drayson, and Harry Farmer for excellent discussions throughout the event that shaped this work. I’d also like to thank Michael Anderson for fascinating discussions elsewhere on his theory of neural reuse. Many thanks to the anonymous reviewers for their extremely helpful comments.

References

  1. Amalric, M., & Dehaene, S. (2016). Origins of the brain networks for advanced mathematics in expert mathematicians. Proceedings of the National Academy of Sciences, 113(18), 4909–4917.CrossRefGoogle Scholar
  2. Amalric, M., & Dehaene, S. (2018). Cortical circuits for mathematical knowledge: Evidence for a major subdivision within the brain’s semantic networks. Philosophical Transactions of the Royal Society B, 373(1740), 20160515.CrossRefGoogle Scholar
  3. Anderson, M. L. (2010). Neural reuse: A fundamental organizational principle of the brain. Behavioural and Brain Sciences, 33(4), 245–266.CrossRefGoogle Scholar
  4. Anderson, M. L. (2014). After phrenology: Neural reuse and the interactive brain. Cambridge, MA: MIT Press.Google Scholar
  5. Anderson, M. L. (2016). Précis of after phrenology: Neural reuse and the interactive brain. Behavioral and Brain Sciences, 39, 1–45.CrossRefGoogle Scholar
  6. Andres, M., Seron, X., & Olivier, E. (2007). Contribution of hand motor circuits to counting. Journal of Cognitive Neuroscience, 19(4), 563–576.CrossRefGoogle Scholar
  7. Anobile, G., Cicchini, G. M., & Burr, D. C. (2016). Number as a primary perceptual attribute: A review. Perception, 45(1–2), 5–31.CrossRefGoogle Scholar
  8. Ansari, D. (2008). Effects of development and enculturation on number representation in the brain. Nature Reviews Neuroscience, 9(4), 278–291.CrossRefGoogle Scholar
  9. Ansari, D., Garcia, N., Lucas, E., Hamon, K., & Dhital, B. (2005). Neural correlates of symbolic number processing in children and adults. NeuroReport, 16(16), 1769–1773.CrossRefGoogle Scholar
  10. Arsalidou, M., & Taylor, M. J. (2011). Is 2 + 2 = 4? Meta-analyses of brain areas needed for numbers and calculations. Neuroimage, 54(3), 2382–2393.CrossRefGoogle Scholar
  11. Badcock, P. B., Ploeger, A., & Allen, N. B. (2016). After phrenology: Time for a paradigm shift in cognitive science. Behavioral and Brain Sciences, 39, 10–11.CrossRefGoogle Scholar
  12. Beck, J. (2014). Analogue magnitude representations: A philosophical introduction. The British Journal for the Philosophy of Science, 66(4), 829–855.CrossRefGoogle Scholar
  13. Bruineberg, J., Kiverstein, J., & Rietveld, E. (2018). The anticipating brain is not a scientist: the free-energy principle from an ecological-enactive perspective. Synthese, 195(6), 2417–2444.CrossRefGoogle Scholar
  14. Burge, T. (2010). Origins of objectivity. Oxford: Oxford University Press.CrossRefGoogle Scholar
  15. Burr, D. C., Turi, M., & Anobile, G. (2010). Subitizing but not estimation of numerosity requires attentional resources. Journal of Vision, 10((6), 20), 1–10.Google Scholar
  16. Butterworth, B., Reeve, R., Reynolds, F., & Lloyd, D. (2008). Numerical thought with and without words: Evidence from indigenous Australian children. Proceedings of the National Academy of Sciences, 105(35), 13179–13184.CrossRefGoogle Scholar
  17. Cain, C. (2006). Implications of the Marked Artefacts of the Middle Stone Age of Africa. Current Anthropology, 47(4), 675–681.CrossRefGoogle Scholar
  18. Carey, S. (2009). The origin of concepts. Oxford: Oxford University Press.CrossRefGoogle Scholar
  19. Carreiras, M., Monahan, P. J., Lizarazu, M., Duñabeitia, J. A., & Molinaro, N. (2015). Numbers are not like words: Different pathways for literacy and numeracy. Neuroimage, 118, 79–89.CrossRefGoogle Scholar
  20. Chen, F., Hu, Z., Zhao, X., Wang, R., Yang, Z., Wang, X., et al. (2006). Neural correlates of serial abacus mental calculation in children: A functional MRI study. Neuroscience Letters, 403(1–2), 46–51.CrossRefGoogle Scholar
  21. Cisek, P. (2007). Cortical mechanisms of action selection: The affordance competition hypothesis. Philosophical Transactions of the Royal Society of London B: Biological Sciences, 362(1485), 1585–1599.CrossRefGoogle Scholar
  22. Cisek, P., & Kalaska, J. F. (2010). Neural mechanisms for interacting with a world full of action choices. Annual Review of Neuroscience, 33, 269–298.CrossRefGoogle Scholar
  23. Culham, J. C., & Kanwisher, N. G. (2001). Neuroimaging of cognitive functions in human parietal cortex. Current Opinion in Neurobiology, 11(2), 157–163.CrossRefGoogle Scholar
  24. De Cruz, H. (2006). Towards a Darwinian approach to mathematics. Foundations of Science, 11(1–2), 157–196.CrossRefGoogle Scholar
  25. De Cruz, H. (2008). An extended mind perspective on natural number representation. Philosophical Psychology, 21(4), 475–490.CrossRefGoogle Scholar
  26. De Cruz, H. (2012). How do spatial representations enhance cognitive numerical processing? Cognitive Processing, 13(1), 137–140.CrossRefGoogle Scholar
  27. Dehaene, S. (1997). The number sense. Oxford: Oxford University Press.Google Scholar
  28. Dehaene, S. (2005). Evolution of human cortical circuits for reading and arithmetic: The “neuronal recycling” hypothesis. In S. Dehaene, J.-R. Duhamel, M. D. Hauser, & G. Rizolatti (Eds.), From monkey brain to human brain (pp. 133–157). Cambridge, MA: MIT Press.Google Scholar
  29. Dehaene, S. (2009). Reading in the brain: The new science of how we read. New York, NY: Penguin.Google Scholar
  30. Dehaene, S., & Cohen, L. (1995). Towards an anatomical and functional model of number processing. Mathematical Cognition, 1(1), 83–120.Google Scholar
  31. Dehaene, S., & Cohen, L. (2007). Cultural recycling of cortical maps. Neuron, 56(2), 384–398.CrossRefGoogle Scholar
  32. Dehaene, S., Dehaene-Lambertz, G., & Cohen, L. (1998). Abstract representations of numbers in the animal and human brain. Trends in Neurosciences, 21(8), 355–361.CrossRefGoogle Scholar
  33. Dehaene, S., Dupoux, E., & Mehler, J. (1990). Is numerical comparison digital? Analogical and symbolic effects in two-digit number comparison. Journal of Experimental Psychology: Human Perception and Performance, 16(3), 626.Google Scholar
  34. Delazer, M., Domahs, F., Bartha, L., Brenneis, C., Lochy, A., Trieb, T., et al. (2003). Learning complex arithmetic—An fMRI study. Cognitive Brain Research, 18(1), 76–88.CrossRefGoogle Scholar
  35. Feigenson, L., Dehaene, S., & Spelke, E. (2004). Core systems of number. Trends in Cognitive Sciences, 8(7), 307–314.CrossRefGoogle Scholar
  36. Fields, R. D. (2009). The other brain: From dementia to schizophrenia, how new discoveries about the brain are revolutionizing medicine and science. New York, NY: Simon and Schuster.Google Scholar
  37. Fischer, M. H., & Fias, M. H. (2005). Spatial representation of numbers. In J. I. D. Campbell (Ed.), Handbook of mathematical cognition (pp. 43–54). New York, NY: Psychology Press.Google Scholar
  38. Fröhlich, F., & McCormick, D. (2010). Endogenous electric fields may guide neocortical network activity. Neuron, 67, 129–143.CrossRefGoogle Scholar
  39. Gibson, J. J. (1979). The ecological approach to visual perception. Boston, MA: Houghton Mifflin.Google Scholar
  40. Gillebert, C. R., Mantini, D., Thijs, V., Sunaert, S., Dupont, P., & Vandenberghe, R. (2011). Lesion evidence for the critical role of the intraparietal sulcus in spatial attention. Brain, 134(6), 1694–1709.CrossRefGoogle Scholar
  41. Gilmore, C., McCarthy, S., & Spelke, E. (2010). Non-symbolic arithmetic abilities and mathematics achievement in the first year of formal schooling. Cognition, 115(3), 394–406.CrossRefGoogle Scholar
  42. Gordon, P. (2004). Numerical cognition without words: Evidence from Amazonia. Science, 306(5695), 496–499.CrossRefGoogle Scholar
  43. Grefkes, C., & Fink, G. (2005). The functional organization of the intraparietal sulcus in humans and monkeys. Journal of Anatomy, 207(1), 3–17.CrossRefGoogle Scholar
  44. Ischebeck, A., Zamarian, L., Siedentopf, C., Koppelstätter, F., Benke, T., Felber, S., et al. (2006). How specifically do we learn? Imaging the learning of multiplication and subtraction. Neuroimage, 30(4), 1365–1375.CrossRefGoogle Scholar
  45. Jones, M. (2016a). Number concepts for the concept empiricist. Philosophical Psychology, 29(3), 334–348.CrossRefGoogle Scholar
  46. Jones, M. (2016b). Review of After phrenology: Neural reuse and the interactive brain. Philosophical Psychology, 29(7), 1080–1083.CrossRefGoogle Scholar
  47. Jones, M. (2018). Seeing numbers as affordances. In S. Bangu (Ed.), Naturalizing logico-mathematical knowledge: Approaches from philosophy, psychology and cognitive science (pp. 148–163). New York, NY: Routledge.CrossRefGoogle Scholar
  48. Kirsh, D., & Maglio, P. (1994). On distinguishing epistemic from pragmatic action. Cognitive Science, 18(4), 513–549.CrossRefGoogle Scholar
  49. Kitcher, P. (1984). The nature of mathematical knowledge. Oxford: Oxford University Press.Google Scholar
  50. Kramer, S., & McChesney, A. (2003). Writing, notational iconicity, calculus: On writing as a cultural technique. MLN, 118(3), 518–537.CrossRefGoogle Scholar
  51. Laland, K. N., Odling-Smee, J., & Feldman, M. W. (2000). Niche construction, biological evolution, and cultural change. Behavioral and Brain Sciences, 23(1), 131–146.CrossRefGoogle Scholar
  52. Landy, D., & Goldstone, R. L. (2009). How much of symbolic manipulation is just symbol pushing. In Proceedings of the thirty-first annual conference of the cognitive science society, Amsterdam, Netherlands, July 29August 1 (pp. 1072–1077).Google Scholar
  53. Libertus, M., Feigenson, L., & Halberda, J. (2011). Preschool acuity of the approximate number system correlates with school math ability. Developmental Science, 14(6), 1292–1300.CrossRefGoogle Scholar
  54. Longcamp, M., Lagarrigue, A., Nazarian, B., Roth, M., Anton, J. L., Alario, F. X., et al. (2014). Functional specificity in the motor system: Evidence from coupled fMRI and kinematic recordings during letter and digit writing. Human Brain Mapping, 35(12), 6077–6087.CrossRefGoogle Scholar
  55. Lyons, I. M., Ansari, D., & Beilock, S. L. (2012). Symbolic estrangement: Evidence against a strong association between symbols and the quantities they represent. Journal of Experimental Psychology: General, 141(4), 635–641.CrossRefGoogle Scholar
  56. McClelland, T. (2017). AI and affordances for mental action. In J. Bryson , M. De Vos, & J. Padget J (Eds.) Proceedings of AISB Annual Convention 2017 (pp. 372–379). http://aisb2017.cs.bath.ac.uk/conference-edition-proceedings.pdf.
  57. Menary, R. (2006). Attacking the bounds of cognition. Philosophical Psychology, 19(3), 329–344.CrossRefGoogle Scholar
  58. Menary, R. (2007). Cognitive integration: Mind and cognition unbounded. Basingstoke: Palgrave Macmillan.CrossRefGoogle Scholar
  59. Menary, R. (2014). Neuronal recycling, neural plasticity and niche construction. Mind and Language, 29(3), 286–303.CrossRefGoogle Scholar
  60. Menary, R. (2015). Mathematical cognition: A case of enculturation. In T. Metzinger & J. M. Windt (Eds.), OpenMIND. Frankfurt am Main: MIND Group.Google Scholar
  61. Menary, R., & Gillett, A. (2016). Embodying culture: Integrated cognitive systems and cultural evolution. In J. Kiverstein (Ed.), The Routledge handbook of philosophy of the social mind (pp. 72–88). New York, NY: Routledge.Google Scholar
  62. Nieder, A. (2005). Counting on neurons: The neurobiology of numerical competence. Nature Reviews Neuroscience, 6(3), 177–190.CrossRefGoogle Scholar
  63. Nieder, A., & Dehaene, S. (2009). Representation of number in the brain. Annual Review of Neuroscience, 32, 185–208.CrossRefGoogle Scholar
  64. Odling-Smee, F. J., Laland, K. N., & Feldman, M. W. (2003). Niche construction: The neglected process in evolution. Princeton, NJ: Princeton University Press.Google Scholar
  65. Park, J., Hebrank, A., Polk, T. A., & Park, D. C. (2012). Neural dissociation of number from letter recognition and its relationship to parietal numerical processing. Journal of Cognitive Neuroscience, 24(1), 39–50.CrossRefGoogle Scholar
  66. Paz, A. W. (2018). A defense of an Amodal number system. Philosophies, 3(2), 13.CrossRefGoogle Scholar
  67. Penner-Wilger, M., & Anderson, M. L. (2013). The relation between finger gnosis and mathematical ability: Why redeployment of neural circuits best explains the finding. Frontiers in Psychology, 4, 877.CrossRefGoogle Scholar
  68. Pezzulo, G., & Cisek, P. (2016). Navigating the affordance landscape: Feedback control as a process model of behavior and cognition. Trends in Cognitive Sciences, 20(6), 414–424.CrossRefGoogle Scholar
  69. Piazza, M., Pinel, P., Le Bihan, D., & Dehaene, S. (2007). A magnitude code common to numerosities and number symbols in human intraparietal cortex. Neuron, 53(2), 293–305.CrossRefGoogle Scholar
  70. Pica, P., Lemer, C., Izard, V., & Dehaene, S. (2004). Exact and approximate arithmetic in an Amazonian indigene group. Science, 306(5695), 499–503.CrossRefGoogle Scholar
  71. Rietveld, E., & Kiverstein, J. (2014). A rich landscape of affordances. Ecological Psychology, 26(4), 325–352.CrossRefGoogle Scholar
  72. Saxe, G. B. (1982). Culture and the development of numerical cognition: Studies among the Oksapmin of Papua New Guinea. In C. J. Brainerd (Ed.), Children’s logical and mathematical cognition (pp. 157–176). New York, NY: Springer.CrossRefGoogle Scholar
  73. Shum, J., Hermes, D., Foster, B. L., Dastjerdi, M., Rangarajan, V., Winawer, J., et al. (2013). A brain area for visual numerals. Journal of Neuroscience, 33(16), 6709–6715.CrossRefGoogle Scholar
  74. Simon, O., Mangin, J. F., Cohen, L., Le Bihan, D., & Dehaene, S. (2002). Topographical layout of hand, eye, calculation, and language-related areas in the human parietal lobe. Neuron, 33(3), 475–487.CrossRefGoogle Scholar
  75. Spelke, E. S., & Tsivkin, S. (2001). Language and number: A bilingual training study. Cognition, 78(1), 45–88.CrossRefGoogle Scholar
  76. Tang, Y., Zhang, W., Kewel, C., Feng, S., Ji, Y., et al. (2006). Arithmetic processing in the brain shaped by cultures. PNAS, 103(28), 10775–10780.CrossRefGoogle Scholar
  77. Walsh, V. (2003). A theory of magnitude: Common cortical metrics of time, space and quantity. Trends in Cognitive Sciences, 7(11), 483–488.CrossRefGoogle Scholar
  78. Wiese, H. (2003). Iconic and non-iconic stages in number development: The role of language. Trends in Cognitive Sciences, 7(9), 385–390.CrossRefGoogle Scholar
  79. Zhang, J., & Norman, D. (1995). A representational analysis of numeration systems. Cognition, 5(3), 271–295.CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.University of LeedsLeedsUK

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