The Topology of Mathematics in the Mind and Its Interaction with Verbal and Written Language

  • Robert K. LoganEmail author
  • Izabella Pruska-Oldenhoff
Part of the Mathematics in Mind book series (MATHMIN)


When we think of the human mind we most often think of its capacity for verbal language as we are the only living organism capable of speech. We are aware of the fact that the human mind is capable of mathematical thinking and think that mathematics was a later development of the human mind long after humankind had acquired language. In a book soon to be released in the Springer series Mathematics in the Mind edited by Marcel Danesi entitled A Topology of Mind—Spiral Thought Patterns, the Hyperlinking of Text, Ideas and More, we (Logan and Pruska-Oldenhof 2019) argue that human verbal language was as much a product of mathematical thinking as mathematics was a product of verbal thinking. We argue that the origin of verbal language, the origin of the mind, and the origin of mathematic thinking all happened at approximately the same time and that these three elements are basically interlinked. The human mind is a product of the brain and verbal language as was argued in The Extended Mind: The Emergence of Language, the Human Mind and Culture (Logan 2007), but verbal language as we have argued was dependent on the ability of humans to think in terms of sets employing a primitive form of set theory.


Verbal language Mathematics Set theory Spiral Recurrence Figure/ground Hyperlinking Hypertext 


  1. Berners-Lee, T. (1999). Weaving the web. San Francisco: Harper.Google Scholar
  2. Bush, V. (1945). As We May Think. The Atlantic [Boston] July 1945: 101-08.Google Scholar
  3. De Cruz, H. and De Smedt, J. (2013). Mathematical symbols as epistemic actions. Synthese 190 (1): 3-19.CrossRefGoogle Scholar
  4. Eliade, M. (1964). Cosmos and history: The myth of the eternal return. New York: Harper Torchbooks.Google Scholar
  5. Havelock, E. (1963). Preface to Plato. Cambridge, MA: Howard University Press.Google Scholar
  6. Hayles, N. K. (2001). The transformation of narrative and the materiality of hypertext. 1st ed. Vol. 09. Ohio State University Press, 21-39.Google Scholar
  7. Logan, R. K. (2007). The extended mind: The emergence of language, the human mind and culture. Toronto: University of Toronto Press.CrossRefGoogle Scholar
  8. Logan, R. K. and Pruska-Oldenhof, I. (2019). A topology of mind—Spiral thought patterns, the hyperlinking of text, ideas and more. New York: Springer. (In preparation).Google Scholar
  9. Lord, A. B. (1960). The singer of tales. Cambridge, MA: Harvard University Press.Google Scholar
  10. McLuhan, M. (1964). Understanding media: Extensions of man. New York: McGraw Hill.Google Scholar
  11. McLuhan, M. (1975). Communication: McLuhan’s Laws of Media. Technology and Culture 16 (1): 74-78.CrossRefGoogle Scholar
  12. McLuhan, M. (1977). Laws of media. English Journal 67 (8): 92-94.CrossRefGoogle Scholar
  13. McLuhan, M, and McLuhan, E. (1988). Laws of media: The new science. Toronto: University of Toronto Press.Google Scholar
  14. Molinaro, M., McLuhan, C. and Toye, W. (eds.) (1987). Letters of Marshall McLuhan. Toronto: Oxford University Press.Google Scholar
  15. Nelson, T. (1965). Complex information processing: A file structure for the complex, the changing and the indeterminate. Association for Computing Machinery (ACM) ‘65 Proceedings of the 1965 20th National Conference.Google Scholar
  16. Parry, M. (1993). The making of Homeric verse: The collected papers of Milman Parry. Oxford UK: Oxford University Press.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Ryerson UniversityTorontoCanada

Personalised recommendations