Do Real Numbers Really Move? Language, Thought, and Gesture: The Embodied Cognitive Foundations of Mathematics

  • Rafael Núñez


Robotics, artificial intelligence and, in general, any activity involving computer simulation and engineering relies, in a fundamental way, on mathematics. These fields constitute excellent examples of how mathematics can be applied to some area of investigation with enormous success. This, of course, includes embodied oriented approaches in these fields, such as Embodied Artificial Intelligence and Cognitive Robotics. In this chapter, while fully endorsing an embodied oriented approach to cognition, I will address the question of the nature of mathematics itself, that is, mathematics not as an application to some area of investigation, but as a human conceptual system with a precise inferential organization that can be investigated in detail in cognitive science. The main goal of this piece is to show, using techniques in cognitive science such as cognitive semantics and gestures studies, that concepts and human abstraction in general (as it is exemplified in a sublime form by mathematics) is ultimately embodied in nature.


Cognitive Science Mathematical Idea Linguistic Expression Conceptual Metaphor Cartesian Plane 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bates, E. & F. Dick. (2002). Language, Gesture, and the Developing Brain. Developmental Psychobiology, 40(3), 293–310.CrossRefGoogle Scholar
  2. 2.
    Cienki, A. (1998). Metaphoric gestures and some of their relations to verbal metaphoric expressions. In J-P Koenig (ed.) Discourse and Cognition, pp. 189–204. Stanford CA: CSLI Publications.Google Scholar
  3. 3.
    Courant, R. & Robbins, H. (1978). What is Mathematics? New York: Oxford.Google Scholar
  4. 4.
    Fauconnier, G. & M. Turner. (1998). Conceptual Integration Networks. Cognitive Science 22:2, 133–187.CrossRefGoogle Scholar
  5. 5.
    Fauconnier, G. & M. Turner. (2002). The Way We Think: Conceptual Blending and the Mind’s Hidden Complexities. New York: Basic Books.Google Scholar
  6. 6.
    Goldin-Meadow, S. & C. Mylander. (1984). Gestural communication if deaf children: The effects and non-effects of parental input on early language development. Monographs of the Society for Research in Child Development, 49(3), no, 207.Google Scholar
  7. 7.
    Henderson, D. (2001). Experiencing geometry. Upper SaddleRiver, NJ: Prentice Hall.Google Scholar
  8. 8.
    Hersh, R. (1997). What is mathematics, really? New York: Oxford Univ. Press.Google Scholar
  9. 9.
    Hickok, G., Bellugi, U., and Klima, E. (1998). The neural organization of language: Evidence from sign language aphasia. Trends in Cognitive Sciences, 2(4), 129–136.CrossRefGoogle Scholar
  10. 10.
    Iverson, J. & S. Goldin-Meadow. (1998). Why people gesture when they speak. Nature 396, Nov. 19, 1998. p. 228.CrossRefGoogle Scholar
  11. 11.
    Iverson, J. & E. Thelen, E. (1999). In R. Núñez & W. Freeman (Eds.), Reclaiming cognition: The primacy of action, intention, and emotion, pp. 19–40. Thorverton, UK: Imprint Academic.Google Scholar
  12. 12.
    Kendon, A. (1980). Gesticulation and Speech: Two aspects of the process of utterance. In M.R. Key (ed.), The relation between verbal and nonverbal communication, pp. 207–227. The Hague: Mouton.Google Scholar
  13. 13.
    Kendon, A. (2000). Language and gesture: unity or duality? In D. McNeill (Ed.), Language and gesture (pp. 47–63). Cambridge: Cambridge University Press.Google Scholar
  14. 14.
    Lakoff, G. (1993). The contemporary theory of metaphor. In A. Ortony (Ed.), Metaphor and Thought (2nd ed.), pp. 202–251. Cambridge: Cambridge University Press.Google Scholar
  15. 15.
    Lakoff, G. & M. Johnson. (1980). Metaphors we live by. Chicago: University of Chicago Press.Google Scholar
  16. 16.
    Lakoff, G., & R. Núñez (1997). The metaphorical structure of mathematics: Sketching out cognitive foundations for a mind-based mathematics. In L. English (ed.), Mathematical Reasoning: Analogies, Metaphors, and Images. Mahwah, N.J.: Erlbaum.Google Scholar
  17. 17.
    Lakoff, G. and Núñez, R. (2000). Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being. New York: Basic Books.Google Scholar
  18. 18.
    McNeill, D. (1992). Hand and Mind: What Gestures Reveal About Thought. Chicago: Chicago University Press.Google Scholar
  19. 19.
    Mayberry, R. & Jaques, J. (2000) Gesture production during stuttered speech: insights into the nature of gesture-speech integration. In D. McNeill (ed.) Language and Gesture. Cambridge, UK: Cambridge University Press.Google Scholar
  20. 20.
    Narayanan, S. (1997). Embodiment in Language Understanding: Sensory-Motor Representations for Metaphoric Reasoning about Event Descriptions. Ph.D. dissertation, Department of Computer Science, University of California at Berkeley.Google Scholar
  21. 21.
    Núñez, R. (1999). Could the Future Taste Purple? In R. Núñez and W. Freeman, Reclaiming cognition: The primacy of action, intention, and emotion, pp. 41–60. Thorverton, UK: Imprint Academic.Google Scholar
  22. 22.
    Núñez, R. (2000). Mathematical idea analysis: What embodied cognitive science can say about the human nature of mathematics. Opening plenary address in Proceedings of the 24th International Conference for the Psychology of Mathematics Education, 1:3–22. Hiroshima, Japan.Google Scholar
  23. 23.
    Núñez, R. (2003). Fictive and metaphorical motion in technically idealized domains. Proceedings of the 8th International Cognitive Linguistics Conference, Logroño, Spain, July 20-25, p. 215.Google Scholar
  24. 24.
    Núñez, R.(in press). Creating Mathematical Infinities: The Beauty of Transfinite Cardinals. Journal of Pragmatics.Google Scholar
  25. 25.
    Núñez, R., Edwards, L., Matos, J.F. (1999). Embodied Cognition as grounding for situatedness and context in mathematics education. Educational Studies in Mathematics, 39(1-3): 45–65.Google Scholar
  26. 26.
    Núñez, R. & G. Lakoff. (1998). What did Weierstrass really define? The cognitive structure of natural and ɛ-δ continuity. Mathematical Cognition, 4(2): 85–101.Google Scholar
  27. 27.
    Núñez, R. & Lakoff, G. (in press). The Cognitive Foundations of Mathematics: The Role of Conceptual Metaphor. In J. Campbell (ed.) Handbook of Mathematical Cognition. New York: Psychology Press.Google Scholar
  28. 28.
    Núñez, R. & E. Sweetser, (2001). Proceedings of the 7th International Cognitive Linguistics Conference, Santa Barbara, USA, July 22-27, p. 249–250.Google Scholar
  29. 29.
    Sweetser, E. (1990). From Etymology to Pragmatics: Metaphorical and Cultural Aspects of Semantic Structure. New York: Cambridge University Press.Google Scholar
  30. 30.
    Sweetser, E. (1998). Regular metaphoricity in gesture: bodily-based models of speech interaction. In Actes du 16e Congrès International des Linguistes. Elsevier.Google Scholar
  31. 31.
    Talmy, L. (1996). Fictive motion in language and “ception”. In P. Bloom, M. Peterson, L. Nadel, & M. Garrett (eds.), Language and Space. Cambridge: MIT Press.Google Scholar
  32. 32.
    Talmy, L. (1988). Force dynamics in language and cognition. Cognitive Science, 12: 49–100.CrossRefGoogle Scholar
  33. 33.
    Talmy, L. (2003). Toward a Cognitive Semantics. Volume 1: Concept Structuring Systems. Cambridge: MIT Press.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • Rafael Núñez

There are no affiliations available

Personalised recommendations